Finite Group Databasebeta

← #29839572

Subgroups — #29839572

Order 15616.

3374 conjugacy classes of subgroups.

The subgroup lattice has 1694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840268C211yesmaximal, characteristic
2C2×C4×#11758224C211yesmaximal, characteristic, complemented
3C22×#14519733C211yesmaximal, characteristic, complemented
4#21448860C211yesmaximal, characteristic, complemented
5#21448854C211yesmaximal, characteristic, complemented
6#21448849C211yesmaximal, characteristic, complemented
7#21448843C211yesmaximal, characteristic, complemented
8#21448836C211yesmaximal, characteristic, complemented
9#21448830C211yesmaximal, characteristic, complemented
10#21448825C211yesmaximal, characteristic, complemented
11#21448819C211yesmaximal, characteristic, complemented
12#21448817C211yesmaximal, characteristic, complemented
13#21448813C211yesmaximal, characteristic, complemented
14#21448809C211yesmaximal, characteristic, complemented
15#21448805C211yesmaximal, characteristic, complemented
16#21448803C211yesmaximal, characteristic, complemented
17#21448798C211yesmaximal, characteristic, complemented
18#21448798C211yesmaximal, characteristic, complemented
19#21448304C211yesmaximal, characteristic, complemented
20#21448298C211yesmaximal, characteristic, complemented
21#21448281C211yesmaximal, characteristic, complemented
22#21448279C211yesmaximal, characteristic, complemented
23#21448261C211yesmaximal, characteristic, complemented
24#21448259C211yesmaximal, characteristic, complemented
25#21448259C211yesmaximal, characteristic, complemented
26#21448255C211yesmaximal, characteristic, complemented
27C4×D4×Dic61C211yesmaximal, characteristic, complemented
28C4×#14519737C211yesmaximal, characteristic, complemented
29C4×#14519733C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
31C61×#2358C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C24×Dic61C2211yescharacteristic
34#16840268C4116yescomplemented
35C2×#14519761C2211yescharacteristic
36C2×#14519758C2211yescharacteristic
37C2×#14519754C2211yescharacteristic
38C2×#14519754C2211yescharacteristic
39C2×#14519749C2211yescharacteristic
40C2×#14519749C2211yescharacteristic
41C2×#14519746C2211yescharacteristic
42C4×#11758224—28no—
43C2×C4×Dic122C2211yescharacteristic, complemented
44C2×#14519742C2211yescharacteristic, complemented
45C2×D4×Dic61C2211yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×D4×Dic61C2211yescharacteristic
49C2×C4×C22⋊D61C2211yescharacteristic
50C2×C4×C22⋊D61C2211yescharacteristic
51C2×C4×C22⋊D61C2211yescharacteristic, complemented
52C2×#14519737C2211yescharacteristic
53C2×#14519737C2211yescharacteristic
54C2×#14519737C2211yescharacteristic
55C2×#14519737C2211yescharacteristic
56C2×#14519737C2211yescharacteristic, complemented
57C2×#14519735C2211yescharacteristic, complemented
58C2×#14519733—28no—
59C2×#14519733C2211yescharacteristic
60C2×#14519733C2211yescharacteristic
61C2×#14519733C2211yescharacteristic
62C2×#14519733C2211yescharacteristic
63C2×#14519733C2211yescharacteristic
64C2×#14519733C2211yescharacteristic
65C2×#14519733C2211yescharacteristic
66C2×#14519733C2211yescharacteristic
67C2×#14519733C2211yescharacteristic
68C2×#14519733C2211yescharacteristic, complemented
69C22×#11758196C2211yescharacteristic
70C22×#11758196C2211yescharacteristic
71C22×C22⋊Dic61C2211yescharacteristic
72C22×C22⋊Dic61C2211yescharacteristic
73C22×C4×Dic61C2211yescharacteristic
74C22×C4×Dic61C2211yescharacteristic
75C22×C4×Dic61C2211yescharacteristic
76C22×C4×Dic61C2211yescharacteristic
77C22×C4×Dic61C2211yescharacteristic, complemented
78C2×C42×D61C2211yescharacteristic, complemented
79#16839666C2211yescharacteristic, complemented
80#16839666C2211yescharacteristic, complemented
81#16839665C2211yescharacteristic
82#16839662C2211yescharacteristic
83#16839662C2211yescharacteristic
84#16839662C2211yescharacteristic, complemented
85#16839662C2211yescharacteristic, complemented
86#16839660C2211yescharacteristic, complemented
87#16839659C2211yescharacteristic, complemented
88#16839659C2211yescharacteristic, complemented
89#16839659C2211yescharacteristic, complemented
90#16839658C2211yescharacteristic, complemented
91#16839657C2211yescharacteristic, complemented
92#16839657C2211yescharacteristic, complemented
93#16839657C2211yescharacteristic, complemented
94#16839656C2211yescharacteristic
95#16839656C2211yescharacteristic
96#16839656C2211yescharacteristic, complemented
97#16839656C2211yescharacteristic, complemented
98#16839655C2211yescharacteristic
99#16839655C2211yescharacteristic
100#16839654C2211yescharacteristic, complemented
101#16839653C2211yescharacteristic, complemented
102#16839652C2211yescharacteristic, complemented
103#16839651C2211yescharacteristic, complemented
104#16839650C2211yescharacteristic
105#16839650C2211yescharacteristic
106#16839650C2211yescharacteristic, complemented
107#16839650C2211yescharacteristic, complemented
108#16839649C2211yescharacteristic, complemented
109#16839647C2211yescharacteristic, complemented
110#16839647C2211yescharacteristic, complemented
111#16839646C2211yescharacteristic, complemented
112#16839645C2211yescharacteristic, complemented
113#16839645C2211yescharacteristic, complemented
114#16839644C2211yescharacteristic, complemented
115#16839643C2211yescharacteristic, complemented
116#16839642C2211yescharacteristic
117#16839642C2211yescharacteristic
118#16839642C2211yescharacteristic
119#16839641C2211yescharacteristic
120#16839641C2211yescharacteristic
121#16839639C2211yescharacteristic
122#16839639C2211yescharacteristic
123#16839638C2211yescharacteristic
124#16839638C2211yescharacteristic
125#16839637C2211yescharacteristic
126#16839637C2211yescharacteristic
127#16839636C2211yescharacteristic, complemented
128#16839635C2211yescharacteristic
129#16839635C2211yescharacteristic
130#16839635C2211yescharacteristic, complemented
131#16839634C2211yescharacteristic
132#16839634C2211yescharacteristic
133#16839634C2211yescharacteristic, complemented
134#16839633C2211yescharacteristic, complemented
135C4⋊C4×Dic61C2211yescharacteristic, complemented
136C4⋊C4×Dic61C2211yescharacteristic, complemented
137C4⋊C4×Dic61C2211yescharacteristic, complemented
138C4×#11758196C2211yescharacteristic, complemented
139C4×#11758196C2211yescharacteristic, complemented
140C4×#11758196C2211yescharacteristic, complemented
141C4×C4⋊Dic61C2211yescharacteristic, complemented
142#16839613C2211yescharacteristic, complemented
143#16839613C2211yescharacteristic, complemented
144#16839613C2211yescharacteristic, complemented
145#16839613C2211yescharacteristic, complemented
146#16839613C2211yescharacteristic, complemented
147C22⋊C4×Dic61C2211yescharacteristic
148C22⋊C4×Dic61C2211yescharacteristic
149C22⋊C4×Dic61C2211yescharacteristic
150C22⋊C4×Dic61C2211yescharacteristic
151C22⋊C4×Dic61C2211yescharacteristic
152C22⋊C4×Dic61C2211yescharacteristic
153C22⋊C4×Dic61C2211yescharacteristic
154C22⋊C4×Dic61C2211yescharacteristic
155C22⋊C4×Dic61C2211yescharacteristic
156C22⋊C4×Dic61C2211yescharacteristic
157C22⋊C4×Dic61C2211yescharacteristic
158C22⋊C4×Dic61C2211yescharacteristic
159C22⋊C4×Dic61C2211yescharacteristic, complemented
160C22⋊C4×Dic61C2211yescharacteristic, complemented
161C22⋊C4×Dic61C2211yescharacteristic, complemented
162C4×#11758198C2211yescharacteristic, complemented
163C4×C22⋊Dic61C2211yescharacteristic
164C4×C22⋊Dic61C2211yescharacteristic
165C4×C22⋊Dic61C2211yescharacteristic, complemented
166#16839609C2211yescharacteristic, complemented
167#16839609C2211yescharacteristic, complemented
168#16839609C2211yescharacteristic, complemented
169#16839607C2211yescharacteristic, complemented
170#16839607C2211yescharacteristic, complemented
171C2×#14519684C2211yescharacteristic
172C2×#14519684C2211yescharacteristic
173C42×Dic61C2211yescharacteristic, complemented
174C42×Dic61C2211yescharacteristic, complemented
175C2×#120×C61C2211yescharacteristic
176C2×C4×D4×C61C2211yescharacteristic
177C2×C4×D4×C61C2211yescharacteristic
178C22×C22⋊C4×C61C2211yescharacteristic
179C22×C22⋊C4×C61C2211yescharacteristic
180C61×#390C2211yescharacteristic
181C61×#388C2211yescharacteristic
182C61×#388C2211yescharacteristic
183C61×#386C2211yescharacteristic
184C61×#386C2211yescharacteristic
185C61×#386C2211yescharacteristic
186C61×#385C2211yescharacteristic
187C61×#385C2211yescharacteristic
188C4×C22⋊C4×C61C2211yescharacteristic
189C4×C22⋊C4×C61C2211yescharacteristic
190C2×#11758224—24no—
191C2×#11758224—24no—
192C2×#11758224C2×C418yescomplemented
193C22×Dic122C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C23×Dic61—24no—
199C23×Dic61—24no—
200C23×Dic61C2×C418yescomplemented
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C23×Dic61C2311yescharacteristic
205C23×Dic61C2311yescharacteristic
206C23×Dic61C2311yescharacteristic
207C23×Dic61C2311yescharacteristic
208C23×Dic61C2311yescharacteristic
209C23×Dic61C2311yescharacteristic
210C23×Dic61C2311yescharacteristic
211C23×Dic61C2311yescharacteristic
212C23×Dic61C2311yescharacteristic
213C22×C4×D61C2311yescharacteristic
214C22×C4×D61C2311yescharacteristic
215C22×C4×D61C2311yescharacteristic
216#14519761C2×C418yescomplemented
217#14519758C2×C418yescomplemented
218#14519754C2×C418yescomplemented
219#14519754C2×C418yescomplemented
220#14519749C2×C418yescomplemented
221#14519749C2×C418yescomplemented
222#14519746C2×C418yescomplemented
223C4×Dic122—24no—
224#14519742—24no—
225D4×Dic61—24no—
226D4×Dic61—24no—
227D4×Dic61C2×C418yescomplemented
228D4×Dic61C2×C418yescomplemented
229C4×C22⋊D61—24no—
230C4×C22⋊D61—24no—
231C4×C22⋊D61—24no—
232#14519737—24no—
233#14519737—24no—
234#14519737—24no—
235#14519737C2×C418yescomplemented
236#14519737C2×C418yescomplemented
237#14519735—24no—
238#14519733—24no—
239#14519733—24no—
240#14519733—24no—
241#14519733—24no—
242#14519733—24no—
243#14519733—24no—
244#14519733—24no—
245#14519733—24no—
246#14519733C2×C418yescomplemented
247#14519733D418yescomplemented
248C2×C4⋊Dic61C2311yescharacteristic
249C2×C4⋊Dic61C2311yescharacteristic
250C2×C4⋊Dic61C2311yescharacteristic
251C2×C4⋊Dic61C2311yescharacteristic
252C2×C4⋊Dic61C2311yescharacteristic
253C2×#11758196—24no—
254C2×#11758196—24no—
255C2×#11758196C2311yescharacteristic
256C2×#11758196C2311yescharacteristic
257C2×#11758196C2311yescharacteristic
258C2×#11758196C2311yescharacteristic
259C2×#11758196C2311yescharacteristic
260C2×#11758196C2311yescharacteristic
261C2×#11758196C2311yescharacteristic
262C2×#11758196C2311yescharacteristic
263C2×#11758196C2311yescharacteristic
264C2×#11758196C2311yescharacteristic
265C2×#11758196C2311yescharacteristic
266C2×#11758196C2311yescharacteristic
267C2×#11758196C2311yescharacteristic
268C2×#11758196C2311yescharacteristic
269C2×#11758196C2311yescharacteristic
270C2×#11758196C2311yescharacteristic
271C2×#11758196C2311yescharacteristic
272C2×#11758196C2311yescharacteristic
273C2×C22⋊Dic61—24no—
274C2×C22⋊Dic61—24no—
275C2×C22⋊Dic61C2311yescharacteristic
276C2×C22⋊Dic61C2311yescharacteristic
277C2×C22⋊Dic61C2311yescharacteristic
278C2×C22⋊Dic61C2311yescharacteristic
279C2×C22⋊Dic61C2311yescharacteristic
280C2×C22⋊Dic61C2311yescharacteristic
281C2×C22⋊Dic61C2311yescharacteristic
282C2×C22⋊Dic61C2311yescharacteristic
283C2×C22⋊Dic61C2311yescharacteristic
284C2×C22⋊Dic61C2311yescharacteristic
285C2×C22⋊Dic61C2311yescharacteristic
286C2×C22⋊Dic61C2311yescharacteristic
287C2×C22⋊Dic61C2311yescharacteristic
288C2×C22⋊Dic61C2311yescharacteristic
289C2×C22⋊Dic61C2311yescharacteristic
290C2×C22⋊Dic61C2311yescharacteristic
291C2×#11758198C2311yescharacteristic
292C2×#11758198C2311yescharacteristic
293C2×#11758198C2311yescharacteristic
294C2×#11758198C2311yescharacteristic
295C2×#11758198C2311yescharacteristic
296C2×#11758198C2311yescharacteristic
297C2×#11758198C2311yescharacteristic
298C2×#11758198C2311yescharacteristic
299C2×C4×Dic61—24no—
300C2×C4×Dic61—24no—
301C2×C4×Dic61—24no—
302C2×C4×Dic61—24no—
303C2×C4×Dic61—24no—
304C2×C4×Dic61C2311yescharacteristic
305C2×C4×Dic61C2311yescharacteristic
306C2×C4×Dic61C2311yescharacteristic
307C2×C4×Dic61C2311yescharacteristic
308C2×C4×Dic61C2311yescharacteristic
309C2×C4×Dic61C2311yescharacteristic
310C2×C4×Dic61C2311yescharacteristic
311C2×C4×Dic61C2311yescharacteristic
312C2×C4×Dic61C2311yescharacteristic
313C2×C4×Dic61C2311yescharacteristic
314C2×C4×Dic61C2311yescharacteristic
315C2×C4×Dic61C2311yescharacteristic
316C2×C4×Dic61C2311yescharacteristic
317C2×C4×Dic61C2311yescharacteristic
318C2×C4×Dic61C2311yescharacteristic
319C2×C4×Dic61C2311yescharacteristic
320C2×C4×Dic61C2311yescharacteristic
321C2×C4×Dic61C2311yescharacteristic
322C2×C4×Dic61C2311yescharacteristic
323C2×C4×Dic61C2311yescharacteristic
324C2×C4×Dic61C2311yescharacteristic
325C2×C4×Dic61C2311yescharacteristic
326C2×C4×Dic61C2311yescharacteristic
327C2×C4×Dic61C2311yescharacteristic
328C2×C4×Dic61C2311yescharacteristic
329C2×C4×Dic61C2311yescharacteristic
330C2×C4×Dic61C2311yescharacteristic
331C42×D61—24no—
332#14519684C2311yescharacteristic
333#14519684C2311yescharacteristic
334#14519684C2311yescharacteristic
335#14519684C2311yescharacteristic
336#14519684C2311yescharacteristic
337#14519684C2311yescharacteristic
338#14519684C2311yescharacteristic
339#14519684C2311yescharacteristic
340#14519684C2311yescharacteristic
341#14519684C2311yescharacteristic
342#14519684C2311yescharacteristic
343#14519684C2311yescharacteristic
344#14519684C2311yescharacteristic
345#14519684C2311yescharacteristic
346#14519684C2311yescharacteristic
347#14519684C2311yescharacteristic
348#14519684C2311yescharacteristic
349#14519684C2311yescharacteristic
350#14519684C2311yescharacteristic
351#14519684C2311yescharacteristic
352#14519684C2311yescharacteristic
353#14519684C2311yescharacteristic
354#14519684C2311yescharacteristic
355#14519684C2311yescharacteristic
356#14519684C2311yescharacteristic
357#14519684C2311yescharacteristic
358C25×C61C2311yescharacteristic
359C22×D4×C61C2311yescharacteristic
360C22×D4×C61C2311yescharacteristic
361C22×D4×C61C2311yescharacteristic
362C23×C4×C61C2311yescharacteristic
363C23×C4×C61C2311yescharacteristic
364C23×C4×C61C2311yescharacteristic
365C23×C4×C61C2311yescharacteristic
366C23×C4×C61C2311yescharacteristic
367#120×C61C2×C418yescomplemented
368C4×D4×C61—24no—
369C4×D4×C61—24no—
370C2×C4⋊C4×C61C2311yescharacteristic
371C2×C4⋊C4×C61C2311yescharacteristic
372C2×C4⋊C4×C61C2311yescharacteristic
373C2×C22⋊C4×C61—24no—
374C2×C22⋊C4×C61—24no—
375C2×C22⋊C4×C61C2311yescharacteristic
376C2×C22⋊C4×C61C2311yescharacteristic
377C2×C22⋊C4×C61C2311yescharacteristic
378C2×C22⋊C4×C61C2311yescharacteristic
379C2×C22⋊C4×C61C2311yescharacteristic
380C2×C22⋊C4×C61C2311yescharacteristic
381C2×C22⋊C4×C61C2311yescharacteristic
382C2×C22⋊C4×C61C2311yescharacteristic
383C2×C22⋊C4×C61C2311yescharacteristic
384C2×C22⋊C4×C61C2311yescharacteristic
385C2×C22⋊C4×C61C2311yescharacteristic
386C2×C22⋊C4×C61C2311yescharacteristic
387C2×C22⋊C4×C61C2311yescharacteristic
388C2×C22⋊C4×C61C2311yescharacteristic
389C2×C42×C61C2311yescharacteristic
390C2×C42×C61C2311yescharacteristic
391C2×C42×C61C2311yescharacteristic
392#95×C61C2311yescharacteristic
393#95×C61C2311yescharacteristic
394#95×C61C2311yescharacteristic
395#95×C61C2311yescharacteristic
396#95×C61C2311yescharacteristic
397#95×C61C2311yescharacteristic
398C24×C61—22no—
399C24×C61—22no—
400C24×C61—22no—
401C24×C61—22no—
402C24×C61—41no—
403C24×C61—41no—
404C24×C61C22×C414yes—
405C24×C61C2411yescharacteristic
406C24×C61C2411yescharacteristic
407C24×C61C2411yescharacteristic
408C24×C61C2411yescharacteristic
409C23×D61C2411yescharacteristic
410C2×D4×C61—22no—
411C2×D4×C61—22no—
412C2×D4×C61—22no—
413C2×D4×C61—22no—
414C2×D4×C61—41no—
415C2×D4×C61—41no—
416C2×D4×C61C22×C414yes—
417C2×D4×C61C22×C414yes—
418C2×D4×C61C22×C414yes—
419C22×C4×C61—22no—
420C22×C4×C61—22no—
421C22×C4×C61—22no—
422C22×C4×C61—22no—
423C22×C4×C61—22no—
424C22×C4×C61—22no—
425C22×C4×C61—22no—
426C22×C4×C61—22no—
427C22×C4×C61—22no—
428C22×C4×C61—22no—
429C22×C4×C61—41no—
430C22×C4×C61—41no—
431C22×C4×C61—41no—
432C22×C4×C61—41no—
433C22×C4×C61—41no—
434C22×C4×C61C2411yescharacteristic
435C22×C4×C61C2411yescharacteristic
436C22×C4×C61C2411yescharacteristic
437C22×C4×C61C2411yescharacteristic
438C22×C4×C61C2411yescharacteristic
439C22×C4×C61C2411yescharacteristic
440C22×C4×C61C2411yescharacteristic
441C22×C4×C61C2411yescharacteristic
442C22×C4×C61C2411yescharacteristic
443C22×C4×C61C2411yescharacteristic
444C22×C4×C61C2411yescharacteristic
445C2×C22⋊D61—22no—
446C2×C22⋊D61—22no—
447C2×C22⋊D61—22no—
448C2×C22⋊D61—22no—
449C2×C22⋊D61—22no—
450C2×C22⋊D61—22no—
451C2×C22⋊D61—41no—
452C2×C22⋊D61—41no—
453C2×C22⋊D61C22×C414yes—
454C2×C22⋊D61C22×C414yes—
455C2×C22⋊D61C22×C414yes—
456C2×C22⋊D61C22×C414yes—
457C22×Dic61—22no—
458C22×Dic61—22no—
459C22×Dic61—232no—
460C22×Dic61—22no—
461C22×Dic61—22no—
462C22×Dic61—22no—
463C22×Dic61—22no—
464C22×Dic61—22no—
465C22×Dic61—22no—
466C22×Dic61—22no—
467C22×Dic61—22no—
468C22×Dic61—22no—
469C22×Dic61—22no—
470C22×Dic61—22no—
471C22×Dic61—22no—
472C22×Dic61—22no—
473C22×Dic61—22no—
474C22×Dic61—22no—
475C22×Dic61—22no—
476C22×Dic61—22no—
477C22×Dic61—22no—
478C22×Dic61—22no—
479C22×Dic61—22no—
480C22×Dic61—41no—
481C22×Dic61—41no—
482C22×Dic61—41no—
483C22×Dic61—41no—
484C22×Dic61—41no—
485C22×Dic61C22×C414yes—
486C22×Dic61C22×C414yes—
487C22×Dic61C22×C414yes—
488C22×Dic61C22×C414yes—
489C22×Dic61C22×C414yes—
490C22×Dic61C22×C414yes—
491C22×Dic61C22×C414yes—
492C22×Dic61C2×D414yes—
493C22×Dic61#4114yes—
494C22×Dic61C2411yescharacteristic
495C22×Dic61C2411yescharacteristic
496C22×Dic61C2411yescharacteristic
497C22×Dic61C2411yescharacteristic
498C22×Dic61C2411yescharacteristic
499C22×Dic61C2411yescharacteristic
500C22×Dic61C2411yescharacteristic
501C22×Dic61C2411yescharacteristic
502C22×Dic61C2411yescharacteristic
503C22×Dic61C2411yescharacteristic
504C22×Dic61C2411yescharacteristic
505C22×Dic61C2411yescharacteristic
506C22×Dic61C2411yescharacteristic
507C22×Dic61C2411yescharacteristic
508C22×Dic61C2411yescharacteristic
509#11758224—232no—
510C2×C4×D61—22no—
511C2×C4×D61—22no—
512C2×C4×D61—22no—
513C2×C4×D61—22no—
514C2×C4×D61—22no—
515C2×C4×D61—22no—
516C2×C4×D61—41no—
517C2×C4×D61—41no—
518C2×C4×D61C22×C414yes—
519C2×Dic122—22no—
520C2×Dic122—22no—
521C2×Dic122C22×C414yes—
522C4⋊C4×C61—22no—
523C4⋊C4×C61—22no—
524C4⋊C4×C61—41no—
525C22⋊C4×C61—22no—
526C22⋊C4×C61—22no—
527C22⋊C4×C61—22no—
528C22⋊C4×C61—22no—
529C22⋊C4×C61—22no—
530C22⋊C4×C61—22no—
531C22⋊C4×C61—22no—
532C22⋊C4×C61—22no—
533C22⋊C4×C61—41no—
534C22⋊C4×C61C22×C414yes—
535C22⋊C4×C61C22×C414yes—
536C22⋊C4×C61C22×C414yes—
537C22⋊C4×C61C2×D414yes—
538C22⋊C4×C61#4114yescomplemented
539C42×C61—22no—
540C42×C61—22no—
541C42×C61—41no—
542C22⋊Dic61—22no—
543C22⋊Dic61—22no—
544C22⋊Dic61—22no—
545C22⋊Dic61—22no—
546C22⋊Dic61—22no—
547C22⋊Dic61—22no—
548C22⋊Dic61—22no—
549C22⋊Dic61—22no—
550C22⋊Dic61—41no—
551C22⋊Dic61C22×C414yes—
552C22⋊Dic61C22×C414yes—
553C22⋊Dic61C22×C414yes—
554C22⋊Dic61C22×C414yes—
555C22⋊Dic61C22×C414yes—
556C22⋊Dic61C2×D414yes—
557C22⋊Dic61#4114yescomplemented
558#11758198—22no—
559#11758198—22no—
560#11758198—22no—
561#11758198—22no—
562#11758198—41no—
563#11758198—41no—
564#11758198C22×C414yes—
565#11758198C22×C414yes—
566C4⋊Dic61—22no—
567C4⋊Dic61—22no—
568C4⋊Dic61—41no—
569C4⋊Dic61C22×C414yes—
570C4⋊Dic61C22×C414yes—
571#11758196—22no—
572#11758196—22no—
573#11758196—22no—
574#11758196—22no—
575#11758196—22no—
576#11758196—22no—
577#11758196—22no—
578#11758196—22no—
579#11758196—22no—
580#11758196—22no—
581#11758196—41no—
582#11758196—41no—
583#11758196C22×C414yes—
584#11758196C22×C414yes—
585#11758196C22×C414yes—
586#11758196C22×C414yes—
587#11758196C2×D414yes—
588#11758196C2×D414yes—
589C4×Dic61—22no—
590C4×Dic61—22no—
591C4×Dic61—22no—
592C4×Dic61—22no—
593C4×Dic61—22no—
594C4×Dic61—22no—
595C4×Dic61—22no—
596C4×Dic61—22no—
597C4×Dic61—22no—
598C4×Dic61—22no—
599C4×Dic61—22no—
600C4×Dic61—22no—
601C4×Dic61—22no—
602C4×Dic61—22no—
603C4×Dic61—22no—
604C4×Dic61—22no—
605C4×Dic61—22no—
606C4×Dic61—22no—
607C4×Dic61—22no—
608C4×Dic61—22no—
609C4×Dic61—41no—
610C4×Dic61—41no—
611C4×Dic61—41no—
612C4×Dic61C22×C414yes—
613C4×Dic61C22×C414yes—
614C4×Dic61C2×D414yes—
615C4×Dic61C2×D414yes—
616C23×C61—21no—
617C23×C61—21no—
618C23×C61—21no—
619C23×C61—21no—
620C23×C61—21no—
621C23×C61—21no—
622C23×C61—21no—
623C23×C61—21no—
624C23×C61—28no—
625C23×C61—28no—
626C23×C61—21no—
627C23×C61—21no—
628C23×C61—21no—
629C23×C61—21no—
630C23×C61—21no—
631C23×C61—21no—
632C23×C61—21no—
633C23×C61—21no—
634C23×C61—21no—
635C23×C61—21no—
636C23×C61—21no—
637C23×C61—21no—
638C23×C61—44no—
639C23×C61—44no—
640C23×C61—44no—
641C23×C61—44no—
642C23×C61—44no—
643C23×C61C23×C412yes—
644C23×C61C23×C412yes—
645C23×C61C23×C412yes—
646C23×C61C23×C412yes—
647C23×C61C22×D412yes—
648C23×C61C2×#4112yes—
649C23×C61C2×#4112yes—
650C23×C61C2×#4112yes—
651C23×C61C2511yescharacteristic
652C22×D61—21no—
653C22×D61—21no—
654C22×D61—21no—
655C22×D61—21no—
656C22×D61—21no—
657C22×D61—21no—
658C22×D61C23×C412yes—
659D4×C61—28no—
660D4×C61—28no—
661D4×C61—44no—
662C2×C4×C61—21no—
663C2×C4×C61—21no—
664C2×C4×C61—21no—
665C2×C4×C61—21no—
666C2×C4×C61—21no—
667C2×C4×C61—21no—
668C2×C4×C61—21no—
669C2×C4×C61—21no—
670C2×C4×C61—21no—
671C2×C4×C61—21no—
672C2×C4×C61—21no—
673C2×C4×C61—21no—
674C2×C4×C61—21no—
675C2×C4×C61—21no—
676C2×C4×C61—21no—
677C2×C4×C61—21no—
678C2×C4×C61—21no—
679C2×C4×C61—21no—
680C2×C4×C61—21no—
681C2×C4×C61—21no—
682C2×C4×C61—21no—
683C2×C4×C61—21no—
684C2×C4×C61—21no—
685C2×C4×C61—21no—
686C2×C4×C61—21no—
687C2×C4×C61—21no—
688C2×C4×C61—44no—
689C2×C4×C61—44no—
690C2×C4×C61—44no—
691C2×C4×C61—44no—
692C2×C4×C61—44no—
693C2×C4×C61C23×C412yes—
694C2×C4×C61C23×C412yes—
695C2×C4×C61C23×C412yes—
696C2×C4×C61C22×D412yes—
697C2×C4×C61C22×D412yes—
698C2×C4×C61C2×#4112yes—
699C2×C4×C61C2×#4112yes—
700C22⋊D61—28no—
701C22⋊D61—28no—
702C22⋊D61—28no—
703C22⋊D61—44no—
704C2×Dic61—28no—
705C2×Dic61—21no—
706C2×Dic61—21no—
707C2×Dic61—21no—
708C2×Dic61—21no—
709C2×Dic61—21no—
710C2×Dic61—21no—
711C2×Dic61—21no—
712C2×Dic61—21no—
713C2×Dic61—21no—
714C2×Dic61—21no—
715C2×Dic61—21no—
716C2×Dic61—21no—
717C2×Dic61—21no—
718C2×Dic61—21no—
719C2×Dic61—21no—
720C2×Dic61—21no—
721C2×Dic61—21no—
722C2×Dic61—21no—
723C2×Dic61—28no—
724C2×Dic61—28no—
725C2×Dic61—28no—
726C2×Dic61—28no—
727C2×Dic61—28no—
728C2×Dic61—21no—
729C2×Dic61—21no—
730C2×Dic61—21no—
731C2×Dic61—21no—
732C2×Dic61—21no—
733C2×Dic61—21no—
734C2×Dic61—21no—
735C2×Dic61—21no—
736C2×Dic61—21no—
737C2×Dic61—21no—
738C2×Dic61—21no—
739C2×Dic61—21no—
740C2×Dic61—44no—
741C2×Dic61—44no—
742C2×Dic61—44no—
743C2×Dic61—44no—
744C2×Dic61—44no—
745C2×Dic61C4×D4116yescomplemented
746C2×Dic61C23×C412yes—
747C2×Dic61C23×C412yes—
748C2×Dic61C23×C412yes—
749C2×Dic61C23×C412yes—
750C2×Dic61C23×C412yes—
751C2×Dic61C23×C412yes—
752C2×Dic61C23×C412yes—
753C2×Dic61C22×D412yes—
754C2×Dic61C22×D412yes—
755C2×Dic61C22×D412yes—
756C2×Dic61C22×D412yes—
757C2×Dic61C2×#4112yes—
758C2×Dic61C2×#4112yes—
759C2×Dic61C2×#4112yes—
760C2×Dic61C2×#4112yes—
761C4×D61—28no—
762C4×D61—44no—
763C4×D61—44no—
764Dic122—28no—
765#34136—611nomaximal, Sylow
766C22×C61—22no—
767C22×C61—22no—
768C22×C61—22no—
769C22×C61—22no—
770C22×C61—22no—
771C22×C61—22no—
772C22×C61—22no—
773C22×C61—22no—
774C22×C61—22no—
775C22×C61—22no—
776C22×C61—22no—
777C22×C61—22no—
778C22×C61—22no—
779C22×C61—22no—
780C22×C61—22no—
781C22×C61—22no—
782C22×C61—22no—
783C22×C61—22no—
784C22×C61—416no—
785C22×C61—41no—
786C22×C61—41no—
787C22×C61—41no—
788C22×C61—41no—
789C22×C61—41no—
790C22×C61—41no—
791C22×C61—41no—
792C22×C61—41no—
793C22×C61C2×C4×D414yes—
794C22×C61C4×#4114yescomplemented
795C22×C61C24×C411yescharacteristic
796C22×C61C23×D411yescharacteristic
797C22×C61C22×#4111yescharacteristic
798C22×C61C22×#4111yescharacteristic
799C22×C61C22×#4111yescharacteristic
800C22×C61#58511yescharacteristic
801C22×C61#58511yescharacteristic
802C2×D61—22no—
803C2×D61—22no—
804C2×D61—22no—
805C2×D61—41no—
806C2×D61—41no—
807C2×D61—41no—
808C2×D61—41no—
809C4×C61—22no—
810C4×C61—22no—
811C4×C61—22no—
812C4×C61—22no—
813C4×C61—22no—
814C4×C61—22no—
815C4×C61—22no—
816C4×C61—41no—
817C4×C61—41no—
818C4×C61—41no—
819C4×C61—41no—
820Dic61—22no—
821Dic61—22no—
822Dic61—22no—
823Dic61—22no—
824Dic61—22no—
825Dic61—22no—
826Dic61—22no—
827Dic61—22no—
828Dic61—22no—
829Dic61—41no—
830Dic61—41no—
831Dic61—41no—
832Dic61—41no—
833Dic61C2×C4×D414yes—
834Dic61C2×C4×D414yes—
835C2×#525—611no—
836C2×C4×#41—611no—
837C22×#117—611no—
838#2363—611no—
839#2363—611no—
840#2362—611no—
841#2362—611no—
842#2361—611no—
843#2361—611no—
844#2360—611no—
845#2360—611no—
846#2359—611no—
847#2359—611no—
848#2359—611no—
849#2359—611no—
850#2358—611no—
851#2358—611no—
852#2358—611no—
853#2358D6111yescharacteristic, complemented
854#2297—611no—
855#2296—611no—
856#2293—611no—
857#2293—611no—
858#2290—611no—
859#2290—611no—
860#2290—611no—
861#2290—611no—
862C42×D4—611no—
863C42×D4—611no—
864C4×#117—611no—
865C2×C4×C22⋊C4—611no—
866C2×C61—24no—
867C2×C61—24no—
868C2×C61—42no—
869C2×C61—42no—
870C2×C61C22×C4×D411yescharacteristic
871C2×C61C2×C4×#4111yescharacteristic
872C2×C61#342811yescharacteristic
873C2×C61D4×#4111yescharacteristic
874C2×C61D4×#4111yescharacteristic
875C2×C61#347511yescharacteristic
876C2×C61#347511yescharacteristic
877D61—42no—
878C22×#41—611no—
879C24×C4—611no—
880#525—6116no—
881C2×#123—611no—
882C2×#123—611no—
883C2×C22⋊Q8—611no—
884C2×C22⋊Q8—611no—
885C2×#121—611no—
886C2×#121—611no—
887C2×#120—611no—
888C2×#120C2×D6111yescharacteristic
889C4×#41—1228no—
890C2×C4×Q8—611no—
891C2×C4×Q8—611no—
892C2×C4×D4—611no—
893C2×C4×D4—611no—
894C2×C4×D4—611no—
895C2×C4×D4—611no—
896C2×C4×D4—611no—
897C2×C4×D4—611no—
898C2×C4×D4—611no—
899C2×C4×D4—611no—
900C2×C4×D4—611no—
901C2×C4×D4—611no—
902C2×C4×D4—611no—
903C2×C4×D4—611no—
904C2×C4×D4C2×D6111yescharacteristic
905C2×C4×D4C2×D6111yescharacteristic
906C2×#117—611no—
907C2×#117—611no—
908C2×#117—611no—
909C2×#117—611no—
910C2×#117—611no—
911C2×#117—611no—
912C2×#117—611no—
913C2×#117—611no—
914C2×#117—611no—
915C2×#117—611no—
916C2×#117—611no—
917C2×#117—1228no—
918C22×C4⋊C4—611no—
919C22×C4⋊C4—611no—
920C22×C22⋊C4—611no—
921C22×C22⋊C4—611no—
922C22×C22⋊C4C2×D6111yescharacteristic
923C22×C22⋊C4C2×D6111yescharacteristic
924C22×C42—611no—
925C22×C42—611no—
926C22×C42—611no—
927C22×C42—611no—
928C22×C42—611no—
929C22×C42—611no—
930#391—611no—
931#391—611no—
932#390—611no—
933#390—611no—
934#390—611no—
935#390—611no—
936#390—611no—
937#390C2×D6111yescharacteristic
938#389—611no—
939#389—611no—
940#389—611no—
941#389—611no—
942#389—611no—
943#389—611no—
944#389—611no—
945#389—611no—
946#388—611no—
947#388—611no—
948#388—611no—
949#388—611no—
950#388—611no—
951#388—611no—
952#388—611no—
953#388—611no—
954#388—611no—
955#388—611no—
956#388—611no—
957#388—611no—
958#388—611no—
959#388—611no—
960#388C2×D6111yescharacteristic
961#388C2×D6111yescharacteristic
962#387—611no—
963#387—611no—
964#387—611no—
965#387—611no—
966#387—611no—
967#387—611no—
968#387—611no—
969#387—611no—
970#386—611no—
971#386—611no—
972#386—611no—
973#386—611no—
974#386—611no—
975#386—611no—
976#386—611no—
977#386—611no—
978#386—611no—
979#386C2×D6111yescharacteristic
980#386C2×D6111yescharacteristic
981#386C2×D6111yescharacteristic
982#385—611no—
983#385—611no—
984#385—611no—
985#385—611no—
986#385—611no—
987#385—611no—
988#385—611no—
989#385—611no—
990#385—611no—
991#385—611no—
992#385C2×D6111yescharacteristic
993#385C2×D6111yescharacteristic
994C4×C4⋊C4—611no—
995C4×C4⋊C4—611no—
996C4×C4⋊C4—611no—
997C4×C4⋊C4—611no—
998C4×C4⋊C4—611no—
999C4×C4⋊C4—611no—
1000C4×C4⋊C4—611no—
1001C4×C4⋊C4—611no—
1002C4×C4⋊C4—611no—
1003C4×C4⋊C4—611no—
1004C4×C4⋊C4—611no—
1005C4×C4⋊C4—611no—
1006C4×C22⋊C4—611no—
1007C4×C22⋊C4—611no—
1008C4×C22⋊C4—611no—
1009C4×C22⋊C4—611no—
1010C4×C22⋊C4—611no—
1011C4×C22⋊C4—611no—
1012C4×C22⋊C4—611no—
1013C4×C22⋊C4—611no—
1014C4×C22⋊C4—611no—
1015C4×C22⋊C4—611no—
1016C4×C22⋊C4—611no—
1017C4×C22⋊C4—611no—
1018C4×C22⋊C4—611no—
1019C4×C22⋊C4—611no—
1020C4×C22⋊C4—611no—
1021C4×C22⋊C4—611no—
1022C4×C22⋊C4—611no—
1023C4×C22⋊C4—611no—
1024C4×C22⋊C4—611no—
1025C4×C22⋊C4—611no—
1026C4×C22⋊C4—611no—
1027C4×C22⋊C4—611no—
1028C4×C22⋊C4C2×D6111yescharacteristic
1029C4×C22⋊C4C2×D6111yescharacteristic
1030#376—611no—
1031#376—611no—
1032C2×#95—611no—
1033C2×#95—611no—
1034C43—611no—
1035C43—611no—
1036C61#3413611yescharacteristic, complemented, Sylow
1037C25C22×D6111yescharacteristic
1038C2×#41—618no—
1039C2×#41—1224no—
1040C2×#41—1224no—
1041C22×Q8—611no—
1042C22×D4—611no—
1043C22×D4—611no—
1044C22×D4—611no—
1045C22×D4—611no—
1046C22×D4C22×D6111yescharacteristic
1047C22×D4C22×D6111yescharacteristic
1048C22×D4C22×D6111yescharacteristic
1049C23×C4—611no—
1050C23×C4—618no—
1051C23×C4—611no—
1052C23×C4—611no—
1053C23×C4—611no—
1054C23×C4—611no—
1055C23×C4—611no—
1056C23×C4—611no—
1057C23×C4—611no—
1058C23×C4—611no—
1059C23×C4—611no—
1060C23×C4—611no—
1061C23×C4—611no—
1062C23×C4—611no—
1063C23×C4—611no—
1064C23×C4—611no—
1065C23×C4—1224no—
1066C23×C4—1224no—
1067C23×C4C22×D6111yescharacteristic
1068C23×C4C22×D6111yescharacteristic
1069C23×C4C22×D6111yescharacteristic
1070C23×C4C22×D6111yescharacteristic
1071C23×C4C22×D6111yescharacteristic
1072#123—618no—
1073#123—618no—
1074C22⋊Q8—618no—
1075C22⋊Q8—618no—
1076#121—618no—
1077#121—618no—
1078#120—618no—
1079#120C4×D6118yescomplemented
1080C4×Q8—1224no—
1081C4×Q8—1224no—
1082C4×D4—24no—
1083C4×D4—24no—
1084C4×D4—618no—
1085C4×D4—618no—
1086C4×D4—618no—
1087C4×D4—618no—
1088C4×D4—1224no—
1089C4×D4—1224no—
1090C4×D4—1224no—
1091C4×D4—1224no—
1092C4×D4—1224no—
1093C4×D4—1224no—
1094C4×D4—1224no—
1095C4×D4—1224no—
1096#117—618no—
1097#117—618no—
1098#117—1224no—
1099#117—1224no—
1100#117—1224no—
1101#117—1224no—
1102#117—1224no—
1103#117—1224no—
1104#117—1224no—
1105#117—1224no—
1106#117—1224no—
1107C2×C4⋊C4—611no—
1108C2×C4⋊C4—611no—
1109C2×C4⋊C4—611no—
1110C2×C4⋊C4—611no—
1111C2×C4⋊C4—611no—
1112C2×C4⋊C4—611no—
1113C2×C4⋊C4—611no—
1114C2×C4⋊C4—611no—
1115C2×C4⋊C4—611no—
1116C2×C4⋊C4—611no—
1117C2×C4⋊C4—611no—
1118C2×C4⋊C4—611no—
1119C2×C4⋊C4—611no—
1120C2×C4⋊C4—611no—
1121C2×C4⋊C4—611no—
1122C2×C4⋊C4—611no—
1123C2×C4⋊C4—611no—
1124C2×C4⋊C4—611no—
1125C2×C4⋊C4—611no—
1126C2×C4⋊C4—611no—
1127C2×C4⋊C4—611no—
1128C2×C4⋊C4—611no—
1129C2×C4⋊C4—611no—
1130C2×C4⋊C4—1224no—
1131C2×C4⋊C4—1224no—
1132C2×C4⋊C4C22×D6111yescharacteristic
1133C2×C4⋊C4C22×D6111yescharacteristic
1134C2×C4⋊C4C22×D6111yescharacteristic
1135C2×C22⋊C4—24no—
1136C2×C22⋊C4—24no—
1137C2×C22⋊C4—611no—
1138C2×C22⋊C4—611no—
1139C2×C22⋊C4—611no—
1140C2×C22⋊C4—611no—
1141C2×C22⋊C4—611no—
1142C2×C22⋊C4—611no—
1143C2×C22⋊C4—611no—
1144C2×C22⋊C4—611no—
1145C2×C22⋊C4—611no—
1146C2×C22⋊C4—611no—
1147C2×C22⋊C4—611no—
1148C2×C22⋊C4—611no—
1149C2×C22⋊C4—611no—
1150C2×C22⋊C4—611no—
1151C2×C22⋊C4—611no—
1152C2×C22⋊C4—611no—
1153C2×C22⋊C4—611no—
1154C2×C22⋊C4—611no—
1155C2×C22⋊C4—611no—
1156C2×C22⋊C4—611no—
1157C2×C22⋊C4—611no—
1158C2×C22⋊C4—611no—
1159C2×C22⋊C4—611no—
1160C2×C22⋊C4—611no—
1161C2×C22⋊C4—1224no—
1162C2×C22⋊C4—1224no—
1163C2×C22⋊C4C22×D6111yescharacteristic
1164C2×C22⋊C4C22×D6111yescharacteristic
1165C2×C22⋊C4C22×D6111yescharacteristic
1166C2×C22⋊C4C22×D6111yescharacteristic
1167C2×C22⋊C4C22×D6111yescharacteristic
1168C2×C22⋊C4C22×D6111yescharacteristic
1169C2×C22⋊C4C22×D6111yescharacteristic
1170C2×C22⋊C4C22×D6111yescharacteristic
1171C2×C22⋊C4C22×D6111yescharacteristic
1172C2×C22⋊C4C22×D6111yescharacteristic
1173C2×C22⋊C4C22×D6111yescharacteristic
1174C2×C22⋊C4C22×D6111yescharacteristic
1175C2×C22⋊C4C22×D6111yescharacteristic
1176C2×C22⋊C4C22×D6111yescharacteristic
1177C2×C42—611no—
1178C2×C42—611no—
1179C2×C42—611no—
1180C2×C42—611no—
1181C2×C42—611no—
1182C2×C42—611no—
1183C2×C42—611no—
1184C2×C42—611no—
1185C2×C42—611no—
1186C2×C42—611no—
1187C2×C42—611no—
1188C2×C42—611no—
1189C2×C42—611no—
1190C2×C42—611no—
1191C2×C42—611no—
1192C2×C42—611no—
1193C2×C42—611no—
1194C2×C42—611no—
1195C2×C42—611no—
1196C2×C42—611no—
1197C2×C42—611no—
1198C2×C42—611no—
1199C2×C42—611no—
1200C2×C42—611no—
1201C2×C42—611no—
1202C2×C42—611no—
1203C2×C42—611no—
1204C2×C42—1224no—
1205C2×C42—1224no—
1206C2×C42—1224no—
1207C2×C42—1224no—
1208C2×C42—1224no—
1209C2×C42—1224no—
1210C2×C42C22×D6111yescharacteristic
1211C2×C42C22×D6111yescharacteristic
1212C2×C42C22×D6111yescharacteristic
1213#95—611no—
1214#95—611no—
1215#95—611no—
1216#95—611no—
1217#95—611no—
1218#95—611no—
1219#95—611no—
1220#95—611no—
1221#95—611no—
1222#95—611no—
1223#95—611no—
1224#95—611no—
1225#95—611no—
1226#95—611no—
1227#95—611no—
1228#95—611no—
1229#95—611no—
1230#95—611no—
1231#95—611no—
1232#95—611no—
1233#95—611no—
1234#95—611no—
1235#95—611no—
1236#95—611no—
1237#95—611no—
1238#95—611no—
1239#95C22×D6111yescharacteristic
1240#95C22×D6111yescharacteristic
1241#95C22×D6111yescharacteristic
1242#95C22×D6111yescharacteristic
1243#95C22×D6111yescharacteristic
1244#95C22×D6111yescharacteristic
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—41no—
1250C24—41no—
1251C24—611no—
1252C24C2×C4×D6114yes—
1253C24C23×D6111yescharacteristic
1254C24C23×D6111yescharacteristic
1255C24C23×D6111yescharacteristic
1256C24C23×D6111yescharacteristic
1257#41—12232no—
1258C2×Q8—614no—
1259C2×Q8—1222no—
1260C2×Q8—1222no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—22no—
1264C2×D4—22no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—614no—
1268C2×D4—614no—
1269C2×D4—614no—
1270C2×D4—614no—
1271C2×D4—1222no—
1272C2×D4—1222no—
1273C2×D4—1222no—
1274C2×D4—1222no—
1275C2×D4—1222no—
1276C2×D4—1222no—
1277C2×D4—2441no—
1278C2×D4—2441no—
1279C2×D4C2×C4×D6114yes—
1280C2×D4C2×C4×D6114yes—
1281C2×D4C2×C4×D6114yes—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—614no—
1298C22×C4—614no—
1299C22×C4—614no—
1300C22×C4—611no—
1301C22×C4—611no—
1302C22×C4—614no—
1303C22×C4—614no—
1304C22×C4—614no—
1305C22×C4—614no—
1306C22×C4—614no—
1307C22×C4—614no—
1308C22×C4—611no—
1309C22×C4—611no—
1310C22×C4—611no—
1311C22×C4—611no—
1312C22×C4—611no—
1313C22×C4—611no—
1314C22×C4—611no—
1315C22×C4—611no—
1316C22×C4—611no—
1317C22×C4—614no—
1318C22×C4—611no—
1319C22×C4—611no—
1320C22×C4—611no—
1321C22×C4—611no—
1322C22×C4—1222no—
1323C22×C4—1222no—
1324C22×C4—1222no—
1325C22×C4—1222no—
1326C22×C4—1222no—
1327C22×C4—1222no—
1328C22×C4—1222no—
1329C22×C4—1222no—
1330C22×C4—1222no—
1331C22×C4—12232no—
1332C22×C4—1222no—
1333C22×C4—1222no—
1334C22×C4—1222no—
1335C22×C4—1222no—
1336C22×C4—1222no—
1337C22×C4—1222no—
1338C22×C4—1222no—
1339C22×C4—1222no—
1340C22×C4—1222no—
1341C22×C4—1222no—
1342C22×C4—1222no—
1343C22×C4—1222no—
1344C22×C4—1222no—
1345C22×C4—1222no—
1346C22×C4—1222no—
1347C22×C4—1222no—
1348C22×C4—1222no—
1349C22×C4—1222no—
1350C22×C4—1222no—
1351C22×C4—2441no—
1352C22×C4—2441no—
1353C22×C4—2441no—
1354C22×C4—2441no—
1355C22×C4—2441no—
1356C22×C4—2441no—
1357C22×C4—2441no—
1358C22×C4C23×D6111yescharacteristic
1359C22×C4C23×D6111yescharacteristic
1360C22×C4C23×D6111yescharacteristic
1361C22×C4C23×D6111yescharacteristic
1362C22×C4C23×D6111yescharacteristic
1363C22×C4C23×D6111yescharacteristic
1364C22×C4C23×D6111yescharacteristic
1365C22×C4C23×D6111yescharacteristic
1366C22×C4C23×D6111yescharacteristic
1367C22×C4C23×D6111yescharacteristic
1368C22×C4C23×D6111yescharacteristic
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—41no—
1372C4⋊C4—614no—
1373C4⋊C4—614no—
1374C4⋊C4—614no—
1375C4⋊C4—614no—
1376C4⋊C4—614no—
1377C4⋊C4—614no—
1378C4⋊C4—614no—
1379C4⋊C4—614no—
1380C4⋊C4—1222no—
1381C4⋊C4—1222no—
1382C4⋊C4—1222no—
1383C4⋊C4—1222no—
1384C4⋊C4—1222no—
1385C4⋊C4—1222no—
1386C4⋊C4—1222no—
1387C4⋊C4—1222no—
1388C4⋊C4—1222no—
1389C4⋊C4—1222no—
1390C4⋊C4—1222no—
1391C4⋊C4—1222no—
1392C4⋊C4—2441no—
1393C4⋊C4—2441no—
1394C4⋊C4—2441no—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—22no—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—41no—
1404C22⋊C4—614no—
1405C22⋊C4—614no—
1406C22⋊C4—614no—
1407C22⋊C4—614no—
1408C22⋊C4—614no—
1409C22⋊C4—614no—
1410C22⋊C4—614no—
1411C22⋊C4—614no—
1412C22⋊C4—614no—
1413C22⋊C4—1222no—
1414C22⋊C4—1222no—
1415C22⋊C4—1222no—
1416C22⋊C4—1222no—
1417C22⋊C4—1222no—
1418C22⋊C4—1222no—
1419C22⋊C4—1222no—
1420C22⋊C4—1222no—
1421C22⋊C4—1222no—
1422C22⋊C4—1222no—
1423C22⋊C4—1222no—
1424C22⋊C4—1222no—
1425C22⋊C4—2441no—
1426C22⋊C4—2441no—
1427C22⋊C4—2441no—
1428C22⋊C4C2×C4×D6114yes—
1429C22⋊C4C2×C4×D6114yes—
1430C22⋊C4C2×C4×D6114yes—
1431C22⋊C4D4×D6114yes—
1432C22⋊C4#1175822414yescomplemented
1433C42—22no—
1434C42—22no—
1435C42—41no—
1436C42—614no—
1437C42—614no—
1438C42—614no—
1439C42—614no—
1440C42—1222no—
1441C42—1222no—
1442C42—1222no—
1443C42—1222no—
1444C42—1222no—
1445C42—1222no—
1446C42—1222no—
1447C42—1222no—
1448C42—1222no—
1449C42—1222no—
1450C42—1222no—
1451C42—1222no—
1452C42—1222no—
1453C42—1222no—
1454C42—1222no—
1455C42—1222no—
1456C42—1222no—
1457C42—1222no—
1458C42—1222no—
1459C42—1222no—
1460C42—2441no—
1461C42—2441no—
1462C42—2441no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—28no—
1472C23—28no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—44no—
1486C23—44no—
1487C23—44no—
1488C23—44no—
1489C23—44no—
1490C23—612no—
1491C23—1221no—
1492C23—1221no—
1493C23—1221no—
1494C23—1221no—
1495C23—1221no—
1496C23—1221no—
1497C23C22×C4×D6112yes—
1498C23C22×C4×D6112yes—
1499C23C22×C4×D6112yes—
1500C23C22×C4×D6112yes—
1501C23C2×D4×D6112yes—
1502C23#41×D6112yes—
1503C23#41×D6112yes—
1504C23C2×#1175822412yes—
1505C23C24×D6111yescharacteristic
1506Q8—1228no—
1507D4—28no—
1508D4—28no—
1509D4—44no—
1510D4—1228no—
1511D4—1228no—
1512D4—1228no—
1513D4—2444no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—44no—
1541C2×C4—44no—
1542C2×C4—44no—
1543C2×C4—44no—
1544C2×C4—44no—
1545C2×C4—6116no—
1546C2×C4—612no—
1547C2×C4—612no—
1548C2×C4—612no—
1549C2×C4—612no—
1550C2×C4—612no—
1551C2×C4—612no—
1552C2×C4—612no—
1553C2×C4—612no—
1554C2×C4—612no—
1555C2×C4—612no—
1556C2×C4—612no—
1557C2×C4—612no—
1558C2×C4—612no—
1559C2×C4—612no—
1560C2×C4—612no—
1561C2×C4—1228no—
1562C2×C4—1228no—
1563C2×C4—1228no—
1564C2×C4—1228no—
1565C2×C4—1228no—
1566C2×C4—1228no—
1567C2×C4—1228no—
1568C2×C4—1221no—
1569C2×C4—1221no—
1570C2×C4—1221no—
1571C2×C4—1221no—
1572C2×C4—1221no—
1573C2×C4—1221no—
1574C2×C4—1221no—
1575C2×C4—1221no—
1576C2×C4—1221no—
1577C2×C4—1221no—
1578C2×C4—1221no—
1579C2×C4—1221no—
1580C2×C4—1221no—
1581C2×C4—1221no—
1582C2×C4—1221no—
1583C2×C4—1221no—
1584C2×C4—1221no—
1585C2×C4—1221no—
1586C2×C4—1221no—
1587C2×C4—1221no—
1588C2×C4—1221no—
1589C2×C4—1221no—
1590C2×C4—1221no—
1591C2×C4—1221no—
1592C2×C4—1221no—
1593C2×C4—1221no—
1594C2×C4—1221no—
1595C2×C4—1221no—
1596C2×C4—1221no—
1597C2×C4—1221no—
1598C2×C4—2444no—
1599C2×C4—2444no—
1600C2×C4—2444no—
1601C2×C4—2444no—
1602C2×C4—2444no—
1603C2×C4—2444no—
1604C2×C4—2444no—
1605C2×C4C22×C4×D6112yes—
1606C2×C4C22×C4×D6112yes—
1607C2×C4C22×C4×D6112yes—
1608C2×C4C2×D4×D6112yes—
1609C2×C4C2×D4×D6112yes—
1610C2×C4C2×#1175822412yes—
1611C2×C4C2×#1175822412yes—
1612C22—22no—
1613C22—22no—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—416no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—1222no—
1640C22—1222no—
1641C22—1222no—
1642C22—2441no—
1643C22—2441no—
1644C22—2441no—
1645C22—2441no—
1646C22C4×D4×D6114yes—
1647C22C4×#1175822414yescomplemented
1648C22C23×C4×D6111yescharacteristic
1649C22C22×D4×D6111yescharacteristic
1650C22C2×#41×D6111yescharacteristic
1651C22C2×#41×D6111yescharacteristic
1652C22C22×#1175822411yescharacteristic
1653C22#1684059711yescharacteristic
1654C22#1684059711yescharacteristic
1655C4—22no—
1656C4—22no—
1657C4—22no—
1658C4—22no—
1659C4—22no—
1660C4—22no—
1661C4—22no—
1662C4—41no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—614no—
1667C4—614no—
1668C4—1222no—
1669C4—1222no—
1670C4—1222no—
1671C4—1222no—
1672C4—1222no—
1673C4—1222no—
1674C4—1222no—
1675C4—1222no—
1676C4—1222no—
1677C4—2441no—
1678C4—2441no—
1679C4—2441no—
1680C4—2441no—
1681C2—24no—
1682C2—24no—
1683C2—42no—
1684C2—42no—
1685C2—2442no—
1686C2C2×C4×D4×D6111yescharacteristic
1687C2C2×C4×#1175822411yescharacteristic
1688C2#2145901711yescharacteristic
1689C2D4×#1175822411yescharacteristic
1690C2#2145930311yescharacteristic
1691C2#2145937011yescharacteristic
1692C2#2145937411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2358C2
socle, cosocleC23×C61C25
prime radicalC2×#16840268C2
hypercenter#2358D61
hypocenterC61#34136
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2358

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4×#11758224C2semidirect
3. C22×#14519733C2semidirect
4. #21448860C2semidirect
5. #21448854C2semidirect
6. #21448849C2semidirect
7. #21448843C2semidirect
8. #21448836C2semidirect
9. #21448830C2semidirect
10. #21448825C2semidirect
11. #21448819C2semidirect
12. #21448817C2semidirect
13. #21448813C2semidirect
14. #21448809C2semidirect
15. #21448805C2semidirect
16. #21448803C2semidirect
17. #21448798C2semidirect
18. #21448798C2semidirect
19. #21448304C2semidirect
20. #21448298C2semidirect
21. #21448281C2semidirect
22. #21448279C2semidirect
23. #21448261C2semidirect
24. #21448259C2semidirect
25. #21448259C2semidirect
26. #21448255C2semidirect
27. C4×D4×Dic61C2semidirect
28. C4×#14519737C2semidirect
29. C4×#14519733C2semidirect
30. C2×C22⋊C4×Dic61C2semidirect
31. C61×#2358C2semidirect
34. #16840268C4semidirect
43. C2×C4×Dic122C22semidirect
44. C2×#14519742C22semidirect
51. C2×C4×C22⋊D61C22semidirect
56. C2×#14519737C22semidirect
57. C2×#14519735C22semidirect
68. C2×#14519733C22semidirect
77. C22×C4×Dic61C22semidirect
78. C2×C42×D61C22semidirect
79. #16839666C22semidirect
80. #16839666C22semidirect
84. #16839662C22semidirect
85. #16839662C22semidirect
86. #16839660C22semidirect
87. #16839659C22semidirect
88. #16839659C22semidirect
89. #16839659C22semidirect
90. #16839658C22semidirect
91. #16839657C22semidirect
92. #16839657C22semidirect
93. #16839657C22semidirect
96. #16839656C22semidirect
97. #16839656C22semidirect
100. #16839654C22semidirect
101. #16839653C22semidirect
102. #16839652C22semidirect
103. #16839651C22semidirect
106. #16839650C22semidirect
107. #16839650C22semidirect
108. #16839649C22semidirect
109. #16839647C22semidirect
110. #16839647C22semidirect
111. #16839646C22semidirect
112. #16839645C22semidirect
113. #16839645C22semidirect
114. #16839644C22semidirect
115. #16839643C22semidirect
127. #16839636C22semidirect
130. #16839635C22semidirect
133. #16839634C22semidirect
134. #16839633C22semidirect
135. C4⋊C4×Dic61C22semidirect
136. C4⋊C4×Dic61C22semidirect
137. C4⋊C4×Dic61C22semidirect
138. C4×#11758196C22semidirect
139. C4×#11758196C22semidirect
140. C4×#11758196C22semidirect
141. C4×C4⋊Dic61C22semidirect
142. #16839613C22semidirect
143. #16839613C22semidirect
144. #16839613C22semidirect
145. #16839613C22semidirect
146. #16839613C22semidirect
159. C22⋊C4×Dic61C22semidirect
160. C22⋊C4×Dic61C22semidirect
161. C22⋊C4×Dic61C22semidirect
162. C4×#11758198C22semidirect
165. C4×C22⋊Dic61C22semidirect
166. #16839609C22semidirect
167. #16839609C22semidirect
168. #16839609C22semidirect
169. #16839607C22semidirect
170. #16839607C22semidirect
173. C42×Dic61C22semidirect
174. C42×Dic61C22semidirect
192. C2×#11758224C2×C4semidirect
200. C23×Dic61C2×C4semidirect
216. #14519761C2×C4semidirect
217. #14519758C2×C4semidirect
218. #14519754C2×C4semidirect
219. #14519754C2×C4semidirect
220. #14519749C2×C4semidirect
221. #14519749C2×C4semidirect
222. #14519746C2×C4semidirect
227. D4×Dic61C2×C4semidirect
228. D4×Dic61C2×C4semidirect
235. #14519737C2×C4semidirect
236. #14519737C2×C4semidirect
246. #14519733C2×C4semidirect
247. #14519733D4semidirect
367. #120×C61C2×C4semidirect
538. C22⋊C4×C61#41semidirect
557. C22⋊Dic61#41semidirect
745. C2×Dic61C4×D4semidirect
794. C22×C61C4×#41semidirect
853. #2358D61semidirect
1036. C61#34136semidirect
1079. #120C4×D61semidirect
1432. C22⋊C4#11758224semidirect
1647. C22C4×#11758224semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168402682
C2×C4×#117582242
C22×#145197332
#214488602
#214488542
#214488492
#214488432
#214488362
#214488302
#214488252
#214488192
#214488172
#214488132
#214488092
#214488052
#214488032
#214487982
#214483042
#214482982
#214482812
#214482792
#214482612
#214482592
#214482552
C4×D4×Dic612
C4×#145197372
C4×#145197332
C2×C22⋊C4×Dic612
C61×#23582
#3413661