Finite Group Databasebeta

← #29843216

Subgroups — #29843216

Order 15616.

2486 conjugacy classes of subgroups.

The subgroup lattice has 1582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840270C211yesmaximal, characteristic
2#21448984C211yesmaximal, characteristic, complemented
3#21448981C211yesmaximal, characteristic, complemented
4#21448975C211yesmaximal, characteristic, complemented
5#21448972C211yesmaximal, characteristic, complemented
6#21448815C211yesmaximal, characteristic, complemented
7#21448811C211yesmaximal, characteristic, complemented
8#21448807C211yesmaximal, characteristic, complemented
9#21448789C211yesmaximal, characteristic, complemented
10#21448788C211yesmaximal, characteristic, complemented
11#21448758C211yesmaximal, characteristic, complemented
12#21448753C211yesmaximal, characteristic, complemented
13#21448677C211yesmaximal, characteristic, complemented
14#21448673C211yesmaximal, characteristic, complemented
15#21448645C211yesmaximal, characteristic, complemented
16#21448644C211yesmaximal, characteristic, complemented
17#21448582C211yesmaximal, characteristic, complemented
18#21448579C211yesmaximal, characteristic, complemented
19#21448573C211yesmaximal, characteristic, complemented
20#21448570C211yesmaximal, characteristic, complemented
21#21448482C211yesmaximal, characteristic, complemented
22#21448479C211yesmaximal, characteristic, complemented
23#21448476C211yesmaximal, characteristic, complemented
24#21448473C211yesmaximal, characteristic, complemented
25#21448460C211yesmaximal, characteristic, complemented
26#21448458C211yesmaximal, characteristic, complemented
27#21448451C211yesmaximal, characteristic, complemented
28#21448447C211yesmaximal, characteristic, complemented
29#21448198C211yesmaximal, characteristic, complemented
30C2×#16839624C211yesmaximal, characteristic, complemented
31C61×#2359C211yesmaximal, characteristic, complemented
32C22×#11758224C2211yescharacteristic
33C23×C4×D61C2211yescharacteristic
34#16840270C4116yescomplemented
35C2×#14519760C2211yescharacteristic
36C2×#14519755C2211yescharacteristic
37C2×#14519755C2211yescharacteristic
38C2×#14519750C2211yescharacteristic
39C2×#14519750C2211yescharacteristic
40C2×#14519747C2211yescharacteristic
41C2×#14519745C2211yescharacteristic
42C2×D4×Dic61C2211yescharacteristic
43C2×#14519739C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×C4×C22⋊D61C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519737C2211yescharacteristic
49C2×#14519736C2211yescharacteristic
50C2×#14519733C2211yescharacteristic
51C22×#11758198C2211yescharacteristic
52C22×#11758198C2211yescharacteristic
53#16839668C2211yescharacteristic, complemented
54#16839667C2211yescharacteristic, complemented
55#16839666C2211yescharacteristic, complemented
56#16839666C2211yescharacteristic, complemented
57#16839664C2211yescharacteristic
58#16839664C2211yescharacteristic
59#16839663C2211yescharacteristic
60#16839663C2211yescharacteristic
61#16839662C2211yescharacteristic
62#16839662C2211yescharacteristic
63#16839662C2211yescharacteristic
64#16839662C2211yescharacteristic
65#16839661C2211yescharacteristic, complemented
66#16839659C2211yescharacteristic, complemented
67#16839657C2211yescharacteristic, complemented
68#16839655C2211yescharacteristic, complemented
69#16839655C2211yescharacteristic, complemented
70#16839654C2211yescharacteristic
71#16839654C2211yescharacteristic
72#16839654C2211yescharacteristic
73#16839654C2211yescharacteristic
74#16839654C2211yescharacteristic, complemented
75#16839653C2211yescharacteristic
76#16839653C2211yescharacteristic
77#16839653C2211yescharacteristic
78#16839653C2211yescharacteristic
79#16839653C2211yescharacteristic, complemented
80#16839652C2211yescharacteristic
81#16839652C2211yescharacteristic
82#16839652C2211yescharacteristic
83#16839652C2211yescharacteristic
84#16839652C2211yescharacteristic, complemented
85#16839651C2211yescharacteristic
86#16839651C2211yescharacteristic
87#16839651C2211yescharacteristic
88#16839651C2211yescharacteristic
89#16839651C2211yescharacteristic, complemented
90#16839649C2211yescharacteristic, complemented
91#16839649C2211yescharacteristic, complemented
92#16839649C2211yescharacteristic, complemented
93#16839648C2211yescharacteristic, complemented
94#16839648C2211yescharacteristic, complemented
95#16839646C2211yescharacteristic, complemented
96#16839646C2211yescharacteristic, complemented
97#16839646C2211yescharacteristic, complemented
98#16839644C2211yescharacteristic, complemented
99#16839644C2211yescharacteristic, complemented
100#16839644C2211yescharacteristic, complemented
101#16839643C2211yescharacteristic, complemented
102#16839643C2211yescharacteristic, complemented
103#16839643C2211yescharacteristic, complemented
104#16839642C2211yescharacteristic
105#16839641C2211yescharacteristic
106#16839641C2211yescharacteristic
107#16839641C2211yescharacteristic
108#16839641C2211yescharacteristic, complemented
109#16839640C2211yescharacteristic
110#16839640C2211yescharacteristic
111#16839640C2211yescharacteristic
112#16839640C2211yescharacteristic
113#16839639C2211yescharacteristic
114#16839639C2211yescharacteristic
115#16839639C2211yescharacteristic
116#16839639C2211yescharacteristic, complemented
117#16839638C2211yescharacteristic, complemented
118#16839638C2211yescharacteristic, complemented
119#16839637C2211yescharacteristic
120#16839637C2211yescharacteristic, complemented
121#16839636C2211yescharacteristic, complemented
122#16839635C2211yescharacteristic
123#16839634C2211yescharacteristic
124#16839633C2211yescharacteristic, complemented
125#16839629C2211yescharacteristic, complemented
126#16839629C2211yescharacteristic, complemented
127#16839627C2211yescharacteristic, complemented
128#16839626C2211yescharacteristic, complemented
129#16839624C2211yescharacteristic
130#16839624C2211yescharacteristic
131#16839624C2211yescharacteristic
132#16839624C2211yescharacteristic
133#16839624C2211yescharacteristic
134#16839624C2211yescharacteristic
135#16839624C2211yescharacteristic
136#16839624C2211yescharacteristic
137#16839624C2211yescharacteristic, complemented
138#16839623C2211yescharacteristic
139#16839623C2211yescharacteristic
140#16839623C2211yescharacteristic, complemented
141#16839620C2211yescharacteristic, complemented
142#16839619C2211yescharacteristic
143#16839619C2211yescharacteristic
144#16839619C2211yescharacteristic
145#16839619C2211yescharacteristic
146#16839619C2211yescharacteristic, complemented
147#16839617C2211yescharacteristic
148#16839617C2211yescharacteristic
149C4⋊C4×Dic61C2211yescharacteristic, complemented
150C4⋊C4×Dic61C2211yescharacteristic, complemented
151C4×#11758196C2211yescharacteristic, complemented
152C4×#11758196C2211yescharacteristic, complemented
153#16839613C2211yescharacteristic, complemented
154C22⋊C4×Dic61C2211yescharacteristic
155C22⋊C4×Dic61C2211yescharacteristic
156C22⋊C4×Dic61C2211yescharacteristic, complemented
157C22⋊C4×Dic61C2211yescharacteristic, complemented
158C4×#11758198C2211yescharacteristic
159C4×#11758198C2211yescharacteristic
160C4×#11758198C2211yescharacteristic
161C4×#11758198C2211yescharacteristic
162C4×#11758198C2211yescharacteristic, complemented
163C4×#11758198C2211yescharacteristic, complemented
164C4×C22⋊Dic61C2211yescharacteristic
165#16839609C2211yescharacteristic, complemented
166#16839608C2211yescharacteristic, complemented
167#16839607C2211yescharacteristic, complemented
168C2×#14519684C2211yescharacteristic
169C2×#14519684C2211yescharacteristic
170C2×#14519684C2211yescharacteristic
171C2×#14519684C2211yescharacteristic, complemented
172#95×D61C2211yescharacteristic, complemented
173C2×#123×C61C2211yescharacteristic
174C2×C4×D4×C61C2211yescharacteristic
175C2×#117×C61C2211yescharacteristic
176C61×#389C2211yescharacteristic, complemented
177C61×#388C2211yescharacteristic, complemented
178C61×#388C2211yescharacteristic, complemented
179C61×#387C2211yescharacteristic, complemented
180C61×#387C2211yescharacteristic, complemented
181C61×#386C2211yescharacteristic
182C61×#385C2211yescharacteristic
183C61×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C61C2211yescharacteristic, complemented
185C4×C22⋊C4×C61C2211yescharacteristic
186C4×C22⋊C4×C61C2211yescharacteristic, complemented
187C2×#95×C61C2211yescharacteristic
188C24×D61C2311yescharacteristic
189C2×#11758224—42no—
190C2×#11758224—42no—
191C2×#11758224C2×C418yes—
192C22×Dic122C2311yescharacteristic
193C22×D244C2311yescharacteristic
194C22×D244C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C22×C22⋊D61C2311yescharacteristic
197C22×C22⋊D61C2311yescharacteristic
198C22×C22⋊D61C2311yescharacteristic
199C23×Dic61C2311yescharacteristic
200C23×Dic61C2311yescharacteristic
201C23×Dic61C2311yescharacteristic
202C23×Dic61C2311yescharacteristic
203C23×Dic61C2311yescharacteristic
204C22×C4×D61—42no—
205C22×C4×D61—42no—
206C22×C4×D61C2×C418yescomplemented
207C22×C4×D61C2311yescharacteristic
208C22×C4×D61C2311yescharacteristic
209C22×C4×D61C2311yescharacteristic
210C22×C4×D61C2311yescharacteristic
211C22×C4×D61C2311yescharacteristic
212C22×C4×D61C2311yescharacteristic
213C22×C4×D61C2311yescharacteristic
214#14519760C2×C418yescomplemented
215#14519755C2×C418yescomplemented
216#14519755C2×C418yescomplemented
217#14519750C2×C418yescomplemented
218#14519750C2×C418yescomplemented
219#14519747C2×C418yescomplemented
220#14519745C2×C418yescomplemented
221D4×Dic61—42no—
222#14519739C2×C418yescomplemented
223#14519739C2×C418yescomplemented
224C4×C22⋊D61—42no—
225#14519737—42no—
226#14519737C2×C418yescomplemented
227#14519737C2×C418yescomplemented
228#14519736—42no—
229#14519733C2×C418yescomplemented
230C2×C4⋊Dic61C2311yescharacteristic
231C2×C4⋊Dic61C2311yescharacteristic
232C2×C4⋊Dic61C2311yescharacteristic
233C2×C4⋊Dic61C2311yescharacteristic
234C2×C4⋊Dic61C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×C22⋊Dic61C2311yescharacteristic
246C2×C22⋊Dic61C2311yescharacteristic
247C2×C22⋊Dic61C2311yescharacteristic
248C2×C22⋊Dic61C2311yescharacteristic
249C2×C22⋊Dic61C2311yescharacteristic
250C2×C22⋊Dic61C2311yescharacteristic
251C2×#11758198—42no—
252C2×#11758198—42no—
253C2×#11758198C2311yescharacteristic
254C2×#11758198C2311yescharacteristic
255C2×#11758198C2311yescharacteristic
256C2×#11758198C2311yescharacteristic
257C2×#11758198C2311yescharacteristic
258C2×#11758198C2311yescharacteristic
259C2×#11758198C2311yescharacteristic
260C2×#11758198C2311yescharacteristic
261C2×#11758198C2311yescharacteristic
262C2×#11758198C2311yescharacteristic
263C2×#11758198C2311yescharacteristic
264C2×#11758198C2311yescharacteristic
265C2×#11758198C2311yescharacteristic
266C2×#11758198C2311yescharacteristic
267C2×#11758198C2311yescharacteristic
268C2×#11758198C2311yescharacteristic
269C2×#11758198C2311yescharacteristic
270C2×#11758198C2311yescharacteristic
271C2×#11758198C2311yescharacteristic
272C2×#11758198C2311yescharacteristic
273C2×#11758198C2311yescharacteristic
274C2×#11758198C2311yescharacteristic
275C2×#11758198C2311yescharacteristic
276C2×#11758198C2311yescharacteristic
277C2×#11758198C2311yescharacteristic
278C2×#11758198C2311yescharacteristic
279C2×#11758198C2311yescharacteristic
280C2×#11758198C2311yescharacteristic
281C2×C4×Dic61C2311yescharacteristic
282C2×C4×Dic61C2311yescharacteristic
283C2×C4×Dic61C2311yescharacteristic
284C2×C4×Dic61C2311yescharacteristic
285C2×C4×Dic61C2311yescharacteristic
286C2×C4×Dic61C2311yescharacteristic
287C2×C4×Dic61C2311yescharacteristic
288C2×C4×Dic61C2311yescharacteristic
289C2×C4×Dic61C2311yescharacteristic
290C2×C4×Dic61C2311yescharacteristic
291C2×C4×Dic61C2311yescharacteristic
292C2×C4×Dic61C2311yescharacteristic
293C2×C4×Dic61C2311yescharacteristic
294#14519684C2311yescharacteristic
295#14519684C2311yescharacteristic
296#14519684C2311yescharacteristic
297#14519684C2311yescharacteristic
298#14519684C2311yescharacteristic
299#14519684C2311yescharacteristic
300#14519684C2311yescharacteristic
301#14519684C2311yescharacteristic
302#14519684C2311yescharacteristic
303#14519684C2311yescharacteristic
304#14519684C2311yescharacteristic
305#14519684C2311yescharacteristic
306#14519684C2311yescharacteristic
307#14519684C2311yescharacteristic
308#14519684C2311yescharacteristic
309#14519684C2311yescharacteristic
310#14519684C2311yescharacteristic
311#14519684C2311yescharacteristic
312#14519684C2311yescharacteristic
313#14519684C2311yescharacteristic
314#14519684C2311yescharacteristic
315#14519684C2311yescharacteristic
316#14519684C2311yescharacteristic
317#14519684C2311yescharacteristic
318#14519684C2311yescharacteristic
319#14519684C2311yescharacteristic
320#14519684C2311yescharacteristic
321#14519684C2311yescharacteristic
322#14519684C2311yescharacteristic
323#14519684C2311yescharacteristic
324#14519684C2311yescharacteristic
325#14519684C2311yescharacteristic
326#14519684C2311yescharacteristic
327#14519684C2311yescharacteristic
328#14519684C2311yescharacteristic
329#14519684C2311yescharacteristic
330#14519684C2311yescharacteristic
331#14519684C2311yescharacteristic
332C22×D4×C61C2311yescharacteristic
333C23×C4×C61C2311yescharacteristic
334C23×C4×C61C2311yescharacteristic
335C23×C4×C61C2311yescharacteristic
336C23×C4×C61C2311yescharacteristic
337#123×C61C2×C418yescomplemented
338C4×D4×C61—42no—
339#117×C61—42no—
340C2×C4⋊C4×C61C2311yescharacteristic
341C2×C4⋊C4×C61C2311yescharacteristic
342C2×C4⋊C4×C61C2311yescharacteristic
343C2×C4⋊C4×C61C2311yescharacteristic
344C2×C4⋊C4×C61C2311yescharacteristic
345C2×C4⋊C4×C61C2311yescharacteristic
346C2×C4⋊C4×C61C2311yescharacteristic
347C2×C22⋊C4×C61C2311yescharacteristic
348C2×C22⋊C4×C61C2311yescharacteristic
349C2×C22⋊C4×C61C2311yescharacteristic
350C2×C22⋊C4×C61C2311yescharacteristic
351C2×C22⋊C4×C61C2311yescharacteristic
352C2×C22⋊C4×C61C2311yescharacteristic
353C2×C22⋊C4×C61C2311yescharacteristic
354C2×C22⋊C4×C61C2311yescharacteristic
355C2×C42×C61C2311yescharacteristic
356C2×C42×C61C2311yescharacteristic
357C2×C42×C61C2311yescharacteristic
358C2×C42×C61C2311yescharacteristic
359C2×C42×C61C2311yescharacteristic
360#95×C61C2311yescharacteristic
361#95×C61C2311yescharacteristic
362#95×C61C2311yescharacteristic
363#95×C61C2311yescharacteristic
364#95×C61C2311yescharacteristic
365#95×C61C2311yescharacteristic
366#95×C61C2311yescharacteristic
367#95×C61C2311yescharacteristic
368#95×C61C2311yescharacteristic
369#95×C61C2311yescharacteristic
370C24×C61C2411yescharacteristic
371C24×C61C2411yescharacteristic
372C23×D61—22no—
373C23×D61—22no—
374C23×D61—41no—
375C23×D61—41no—
376C23×D61—41no—
377C23×D61—41no—
378C23×D61C22×C414yes—
379C23×D61C2411yescharacteristic
380C23×D61C2411yescharacteristic
381C23×D61C2411yescharacteristic
382C2×D4×C61—22no—
383C2×D4×C61—22no—
384C2×D4×C61C22×C414yes—
385C22×C4×C61—22no—
386C22×C4×C61—22no—
387C22×C4×C61—22no—
388C22×C4×C61—22no—
389C22×C4×C61—41no—
390C22×C4×C61—41no—
391C22×C4×C61—41no—
392C22×C4×C61—41no—
393C22×C4×C61—41no—
394C22×C4×C61—41no—
395C22×C4×C61—41no—
396C22×C4×C61C22×C414yes—
397C22×C4×C61C2411yescharacteristic
398C22×C4×C61C2411yescharacteristic
399C22×C4×C61C2411yescharacteristic
400C22×C4×C61C2411yescharacteristic
401C22×C4×C61C2411yescharacteristic
402C22×C4×C61C2411yescharacteristic
403C22×C4×C61C2411yescharacteristic
404C22×C4×C61C2411yescharacteristic
405C22×C4×C61C2411yescharacteristic
406C22×C4×C61C2411yescharacteristic
407C22×C4×C61C2411yescharacteristic
408C22×C4×C61C2411yescharacteristic
409C22×C4×C61C2411yescharacteristic
410C2×C22⋊D61—22no—
411C2×C22⋊D61—22no—
412C2×C22⋊D61—41no—
413C2×C22⋊D61—41no—
414C2×C22⋊D61—41no—
415C2×C22⋊D61—41no—
416C2×C22⋊D61—41no—
417C2×C22⋊D61—41no—
418C2×C22⋊D61C22×C414yes—
419C2×C22⋊D61C22×C414yes—
420C2×C22⋊D61C22×C414yes—
421C2×C22⋊D61C22×C414yes—
422C22×Dic61—22no—
423C22×Dic61—22no—
424C22×Dic61—22no—
425C22×Dic61—22no—
426C22×Dic61—41no—
427C22×Dic61—41no—
428C22×Dic61—41no—
429C22×Dic61—41no—
430C22×Dic61—41no—
431C22×Dic61—41no—
432C22×Dic61—41no—
433C22×Dic61—41no—
434C22×Dic61—41no—
435C22×Dic61C22×C414yes—
436C22×Dic61C22×C414yes—
437C22×Dic61C2411yescharacteristic
438C22×Dic61C2411yescharacteristic
439C22×Dic61C2411yescharacteristic
440C22×Dic61C2411yescharacteristic
441C22×Dic61C2411yescharacteristic
442C22×Dic61C2411yescharacteristic
443C22×Dic61C2411yescharacteristic
444C22×Dic61C2411yescharacteristic
445C22×Dic61C2411yescharacteristic
446C22×Dic61C2411yescharacteristic
447C22×Dic61C2411yescharacteristic
448C22×Dic61C2411yescharacteristic
449C22×Dic61C2411yescharacteristic
450#11758224—416no—
451C2×D244—41no—
452C2×D244—41no—
453C2×D244—41no—
454C2×D244—41no—
455C2×D244C22×C414yes—
456C2×D244C22×C414yes—
457C2×C4×D61—416no—
458C2×C4×D61—41no—
459C2×C4×D61—41no—
460C2×C4×D61—41no—
461C2×C4×D61—41no—
462C2×C4×D61—41no—
463C2×C4×D61—41no—
464C2×C4×D61—41no—
465C2×C4×D61—41no—
466C2×C4×D61—41no—
467C2×C4×D61—41no—
468C2×C4×D61—41no—
469C2×C4×D61—41no—
470C2×C4×D61—41no—
471C2×C4×D61—41no—
472C2×C4×D61—41no—
473C2×C4×D61—41no—
474C2×C4×D61C22×C414yes—
475C2×C4×D61C22×C414yes—
476C2×C4×D61C22×C414yes—
477C2×C4×D61C22×C414yes—
478C2×C4×D61C22×C414yes—
479C2×Dic122—41no—
480C2×Dic122—41no—
481C2×Dic122C22×C414yes—
482C4⋊C4×C61—41no—
483C4⋊C4×C61—41no—
484C4⋊C4×C61—41no—
485C4⋊C4×C61—41no—
486C4⋊C4×C61—41no—
487C4⋊C4×C61C22×C414yes—
488C4⋊C4×C61C22×C414yes—
489C22⋊C4×C61—22no—
490C22⋊C4×C61—22no—
491C22⋊C4×C61—41no—
492C22⋊C4×C61—41no—
493C22⋊C4×C61—41no—
494C22⋊C4×C61C22×C414yes—
495C22⋊C4×C61C22×C414yes—
496C22⋊C4×C61C22×C414yes—
497C42×C61—41no—
498C42×C61—41no—
499C42×C61—41no—
500C42×C61—41no—
501C42×C61—41no—
502C22⋊Dic61—22no—
503C22⋊Dic61—22no—
504C22⋊Dic61—41no—
505C22⋊Dic61—41no—
506C22⋊Dic61—41no—
507C22⋊Dic61C22×C414yes—
508#11758198—41no—
509#11758198—41no—
510#11758198—41no—
511#11758198—41no—
512#11758198—41no—
513#11758198—41no—
514#11758198—41no—
515#11758198—41no—
516#11758198—41no—
517#11758198—41no—
518#11758198—41no—
519#11758198—41no—
520#11758198—41no—
521#11758198—41no—
522#11758198—41no—
523#11758198—41no—
524#11758198—41no—
525#11758198—41no—
526#11758198—41no—
527#11758198—41no—
528#11758198—41no—
529#11758198—41no—
530#11758198C22×C414yes—
531#11758198C22×C414yes—
532#11758198C22×C414yes—
533#11758198C22×C414yes—
534#11758198C22×C414yes—
535#11758198C22×C414yes—
536C4⋊Dic61—41no—
537C4⋊Dic61—41no—
538C4⋊Dic61—41no—
539C4⋊Dic61—41no—
540C4⋊Dic61—41no—
541#11758196—41no—
542#11758196—41no—
543#11758196—41no—
544#11758196—41no—
545#11758196—41no—
546#11758196—41no—
547#11758196C22×C414yes—
548#11758196C22×C414yes—
549#11758196C22×C414yes—
550#11758196C22×C414yes—
551C4×Dic61—41no—
552C4×Dic61—41no—
553C4×Dic61—41no—
554C4×Dic61—41no—
555C4×Dic61—41no—
556C4×Dic61—41no—
557C4×Dic61—41no—
558C4×Dic61—41no—
559C4×Dic61—41no—
560C4×Dic61—41no—
561C4×Dic61—41no—
562C4×Dic61C22×C414yes—
563C4×Dic61C22×C414yes—
564C23×C61—21no—
565C23×C61—21no—
566C23×C61—21no—
567C23×C61—21no—
568C23×C61—21no—
569C23×C61—21no—
570C23×C61—21no—
571C23×C61—21no—
572C23×C61—21no—
573C23×C61—21no—
574C23×C61C23×C412yes—
575C23×C61C23×C412yes—
576C23×C61H(5,𝔽2)12yes—
577C23×C61H(5,𝔽2)12yes—
578C23×C61C2511yescharacteristic
579C22×D61—28no—
580C22×D61—21no—
581C22×D61—21no—
582C22×D61—21no—
583C22×D61—21no—
584C22×D61—21no—
585C22×D61—21no—
586C22×D61—21no—
587C22×D61—21no—
588C22×D61—21no—
589C22×D61—21no—
590C22×D61—21no—
591C22×D61—21no—
592C22×D61—21no—
593C22×D61—21no—
594C22×D61—21no—
595C22×D61—21no—
596C22×D61—21no—
597C22×D61—21no—
598C22×D61—44no—
599C22×D61—44no—
600C22×D61—44no—
601C22×D61—44no—
602C22×D61—44no—
603C22×D61—44no—
604C22×D61C23×C412yes—
605C22×D61C23×C412yes—
606C22×D61C23×C412yes—
607D4×C61—28no—
608C2×C4×C61—28no—
609C2×C4×C61—21no—
610C2×C4×C61—21no—
611C2×C4×C61—21no—
612C2×C4×C61—21no—
613C2×C4×C61—21no—
614C2×C4×C61—21no—
615C2×C4×C61—21no—
616C2×C4×C61—21no—
617C2×C4×C61—21no—
618C2×C4×C61—21no—
619C2×C4×C61—21no—
620C2×C4×C61—21no—
621C2×C4×C61—21no—
622C2×C4×C61—21no—
623C2×C4×C61—21no—
624C2×C4×C61—21no—
625C2×C4×C61—21no—
626C2×C4×C61—21no—
627C2×C4×C61—21no—
628C2×C4×C61—21no—
629C2×C4×C61—21no—
630C2×C4×C61—21no—
631C2×C4×C61—21no—
632C2×C4×C61—21no—
633C2×C4×C61—21no—
634C2×C4×C61—21no—
635C2×C4×C61—21no—
636C2×C4×C61—21no—
637C2×C4×C61—21no—
638C2×C4×C61—21no—
639C2×C4×C61—21no—
640C2×C4×C61—21no—
641C2×C4×C61—21no—
642C2×C4×C61—21no—
643C2×C4×C61—82no—
644C2×C4×C61—82no—
645C2×C4×C61—82no—
646C2×C4×C61C23×C412yes—
647C2×C4×C61C23×C412yes—
648C2×C4×C61C23×C412yes—
649C2×C4×C61C23×C412yes—
650C2×C4×C61C23×C412yes—
651C22⋊D61—28no—
652C22⋊D61—44no—
653C22⋊D61—44no—
654C22⋊D61—44no—
655C2×Dic61—28no—
656C2×Dic61—21no—
657C2×Dic61—21no—
658C2×Dic61—21no—
659C2×Dic61—21no—
660C2×Dic61—21no—
661C2×Dic61—21no—
662C2×Dic61—21no—
663C2×Dic61—21no—
664C2×Dic61—21no—
665C2×Dic61—21no—
666C2×Dic61—21no—
667C2×Dic61—21no—
668C2×Dic61—21no—
669C2×Dic61—21no—
670C2×Dic61—21no—
671C2×Dic61—21no—
672C2×Dic61—21no—
673C2×Dic61—21no—
674C2×Dic61—21no—
675C2×Dic61—21no—
676C2×Dic61—21no—
677C2×Dic61—21no—
678C2×Dic61—21no—
679C2×Dic61—21no—
680C2×Dic61—21no—
681C2×Dic61—21no—
682C2×Dic61—21no—
683C2×Dic61—21no—
684C2×Dic61—21no—
685C2×Dic61—21no—
686C2×Dic61—21no—
687C2×Dic61—21no—
688C2×Dic61—21no—
689C2×Dic61—21no—
690C2×Dic61—44no—
691C2×Dic61—82no—
692C2×Dic61—82no—
693C2×Dic61—82no—
694C2×Dic61C23×C412yes—
695C2×Dic61C23×C412yes—
696C2×Dic61C23×C412yes—
697C2×Dic61C23×C412yes—
698C2×Dic61C23×C412yes—
699D244—44no—
700D244—44no—
701C4×D61—44no—
702C4×D61—44no—
703C4×D61—44no—
704C4×D61—44no—
705C4×D61—44no—
706C4×D61—82no—
707C4×D61—82no—
708Dic122—44no—
709#34396—611nomaximal, Sylow
710C22×C61—22no—
711C22×C61—22no—
712C22×C61—22no—
713C22×C61—22no—
714C22×C61—22no—
715C22×C61—22no—
716C22×C61—22no—
717C22×C61—22no—
718C22×C61—22no—
719C22×C61—41no—
720C22×C61—41no—
721C22×C61—41no—
722C22×C61—41no—
723C22×C61#51814yes—
724C22×C61C24×C411yescharacteristic
725C22×C61C2×H(5,𝔽2)11yescharacteristic
726C22×C61C2×H(5,𝔽2)11yescharacteristic
727C22×C61#58511yescharacteristic
728C22×C61#58511yescharacteristic
729C22×C61#58511yescharacteristic
730C22×C61#58511yescharacteristic
731C2×D61—22no—
732C2×D61—22no—
733C2×D61—22no—
734C2×D61—22no—
735C2×D61—22no—
736C2×D61—22no—
737C2×D61—22no—
738C2×D61—22no—
739C2×D61—22no—
740C2×D61—416no—
741C2×D61—41no—
742C2×D61—41no—
743C2×D61—41no—
744C2×D61—41no—
745C2×D61—41no—
746C2×D61—41no—
747C2×D61—41no—
748C2×D61—41no—
749C2×D61—41no—
750C2×D61—41no—
751C2×D61—41no—
752C2×D61—41no—
753C4×C61—22no—
754C4×C61—22no—
755C4×C61—22no—
756C4×C61—22no—
757C4×C61—22no—
758C4×C61—41no—
759C4×C61—41no—
760C4×C61—41no—
761C4×C61—41no—
762C4×C61—41no—
763C4×C61—41no—
764C4×C61—41no—
765C4×C61—41no—
766Dic61—22no—
767Dic61—22no—
768Dic61—22no—
769Dic61—22no—
770Dic61—22no—
771Dic61—41no—
772Dic61—41no—
773Dic61—41no—
774Dic61—41no—
775Dic61—41no—
776Dic61—41no—
777Dic61—41no—
778Dic61—41no—
779C2×#525—611no—
780#2378—611no—
781#2378—611no—
782#2377—611no—
783#2377—611no—
784#2359—611no—
785#2359—611no—
786#2359—611no—
787#2359D6111yescharacteristic, complemented
788#2357—611no—
789#2357—611no—
790#2353—611no—
791#2353—611no—
792#2343—611no—
793#2343—611no—
794#2339—611no—
795#2339—611no—
796#2333—611no—
797#2333—611no—
798#2332—611no—
799#2332—611no—
800#2321—611no—
801#2321—611no—
802#2321—611no—
803#2321—611no—
804#2319—611no—
805#2319—611no—
806#2318—611no—
807#2318—611no—
808#2280—611no—
809C2×#381—611no—
810C2×C61—24no—
811C2×C61—42no—
812C2×C61C2×#51811yescharacteristic
813C2×C61#342811yescharacteristic
814C2×C61#342811yescharacteristic
815C2×C61#353311yescharacteristic
816C2×C61#353311yescharacteristic
817C2×C61#353311yescharacteristic
818C2×C61#353311yescharacteristic
819D61—42no—
820D61—42no—
821D61—42no—
822C22×#41—611no—
823C24×C4—611no—
824#525—6116no—
825C2×#123—611no—
826C2×#123C2×D6111yescharacteristic
827C2×C22⋊Q8—611no—
828C2×C22⋊Q8—611no—
829C2×#121—611no—
830C2×#121—611no—
831C2×#120—611no—
832C2×#120—611no—
833C2×C4×D4—611no—
834C2×C4×D4—611no—
835C2×C4×D4—611no—
836C2×C4×D4—611no—
837C2×C4×D4—611no—
838C2×C4×D4—611no—
839C2×C4×D4—611no—
840C2×C4×D4C2×D6111yescharacteristic
841C2×#117—611no—
842C2×#117—611no—
843C2×#117C2×D6111yescharacteristic
844C22×C22⋊C4—611no—
845C22×C22⋊C4—611no—
846#391—611no—
847#391—611no—
848#391—611no—
849#391—611no—
850#390—611no—
851#390—611no—
852#390—611no—
853#390—611no—
854#390—611no—
855#390—611no—
856#390—611no—
857#390—611no—
858#389—611no—
859#389—611no—
860#389—611no—
861#389C2×D6111yescharacteristic, complemented
862#388—611no—
863#388—611no—
864#388—611no—
865#388—611no—
866#388—611no—
867#388—611no—
868#388—611no—
869#388—611no—
870#388—611no—
871#388—611no—
872#388—611no—
873#388—611no—
874#388—611no—
875#388—611no—
876#388—611no—
877#388—611no—
878#388—611no—
879#388—611no—
880#388—611no—
881#388—611no—
882#388—611no—
883#388—611no—
884#388C2×D6111yescharacteristic, complemented
885#388C2×D6111yescharacteristic, complemented
886#387—611no—
887#387—611no—
888#387—611no—
889#387—611no—
890#387—611no—
891#387—611no—
892#387—611no—
893#387—611no—
894#387—611no—
895#387—611no—
896#387—611no—
897#387—611no—
898#387—611no—
899#387—611no—
900#387C2×D6111yescharacteristic, complemented
901#387C2×D6111yescharacteristic, complemented
902#386—611no—
903#386—611no—
904#386—611no—
905#386—611no—
906#386—611no—
907#386—611no—
908#386—611no—
909#386—611no—
910#386—611no—
911#386—611no—
912#386—611no—
913#386—611no—
914#386—611no—
915#386—611no—
916#386—611no—
917#386C2×D6111yescharacteristic
918#385—611no—
919#385—611no—
920#385—611no—
921#385—611no—
922#385—611no—
923#385—611no—
924#385C2×D6111yescharacteristic
925#385C2×D6111yescharacteristic, complemented
926#383—611no—
927#383—611no—
928#382—611no—
929#382—611no—
930#381—611no—
931#381—611no—
932#381—611no—
933#381—611no—
934#381—611no—
935#381—611no—
936#381—611no—
937#381—611no—
938#381—611no—
939#381—611no—
940#381—611no—
941#381—611no—
942#380—611no—
943#380—611no—
944#380—611no—
945#380—611no—
946#380—611no—
947#380—611no—
948#379—611no—
949#379—611no—
950C4×C4⋊C4—611no—
951C4×C4⋊C4—611no—
952C4×C4⋊C4—611no—
953C4×C4⋊C4—611no—
954C4×C4⋊C4—611no—
955C4×C4⋊C4C2×D6111yescharacteristic, complemented
956C4×C22⋊C4—611no—
957C4×C22⋊C4—611no—
958C4×C22⋊C4—611no—
959C4×C22⋊C4—611no—
960C4×C22⋊C4—611no—
961C4×C22⋊C4—611no—
962C4×C22⋊C4—611no—
963C4×C22⋊C4—611no—
964C4×C22⋊C4—611no—
965C4×C22⋊C4—611no—
966C4×C22⋊C4—611no—
967C4×C22⋊C4—611no—
968C4×C22⋊C4C2×D6111yescharacteristic
969C4×C22⋊C4C2×D6111yescharacteristic, complemented
970#376—611no—
971#376—611no—
972C2×#95—611no—
973C2×#95—611no—
974C2×#95—611no—
975C2×#95—611no—
976C2×#95—611no—
977C2×#95C2×D6111yescharacteristic
978C61#3439611yescharacteristic, complemented, Sylow
979C25—611no—
980C2×#41—618no—
981C2×#41—2442no—
982C2×#41—2442no—
983C22×Q8—611no—
984C22×D4—611no—
985C22×D4—611no—
986C22×D4—611no—
987C22×D4—611no—
988C22×D4—611no—
989C22×D4—611no—
990C22×D4C22×D6111yescharacteristic
991C23×C4—611no—
992C23×C4—611no—
993C23×C4—618no—
994C23×C4—611no—
995C23×C4—611no—
996C23×C4—611no—
997C23×C4—611no—
998C23×C4—611no—
999C23×C4—611no—
1000C23×C4—611no—
1001C23×C4—611no—
1002C23×C4—611no—
1003C23×C4—611no—
1004C23×C4—2442no—
1005C23×C4—2442no—
1006C23×C4C22×D6111yescharacteristic
1007C23×C4C22×D6111yescharacteristic
1008C23×C4C22×D6111yescharacteristic
1009C23×C4C22×D6111yescharacteristic
1010#123—618no—
1011#123C4×D6118yescomplemented
1012C22⋊Q8—618no—
1013C22⋊Q8—618no—
1014#121—618no—
1015#121—618no—
1016#120—618no—
1017#120—618no—
1018C4×D4—42no—
1019C4×D4—618no—
1020C4×D4—618no—
1021C4×D4—618no—
1022C4×D4—618no—
1023C4×D4—2442no—
1024C4×D4—2442no—
1025C4×D4—2442no—
1026#117—42no—
1027#117—618no—
1028#117—2442no—
1029C2×C4⋊C4—611no—
1030C2×C4⋊C4—611no—
1031C2×C4⋊C4—611no—
1032C2×C4⋊C4—611no—
1033C2×C4⋊C4—611no—
1034C2×C4⋊C4—611no—
1035C2×C4⋊C4—611no—
1036C2×C4⋊C4—611no—
1037C2×C4⋊C4—611no—
1038C2×C4⋊C4—611no—
1039C2×C4⋊C4—611no—
1040C2×C4⋊C4—611no—
1041C2×C4⋊C4—611no—
1042C2×C4⋊C4—611no—
1043C2×C4⋊C4—611no—
1044C2×C4⋊C4C22×D6111yescharacteristic
1045C2×C4⋊C4C22×D6111yescharacteristic
1046C2×C4⋊C4C22×D6111yescharacteristic
1047C2×C4⋊C4C22×D6111yescharacteristic
1048C2×C4⋊C4C22×D6111yescharacteristic
1049C2×C4⋊C4C22×D6111yescharacteristic
1050C2×C4⋊C4C22×D6111yescharacteristic
1051C2×C22⋊C4—611no—
1052C2×C22⋊C4—611no—
1053C2×C22⋊C4—611no—
1054C2×C22⋊C4—611no—
1055C2×C22⋊C4—611no—
1056C2×C22⋊C4—611no—
1057C2×C22⋊C4—611no—
1058C2×C22⋊C4—611no—
1059C2×C22⋊C4—611no—
1060C2×C22⋊C4—611no—
1061C2×C22⋊C4—611no—
1062C2×C22⋊C4—611no—
1063C2×C22⋊C4—611no—
1064C2×C22⋊C4—611no—
1065C2×C22⋊C4—611no—
1066C2×C22⋊C4—611no—
1067C2×C22⋊C4—611no—
1068C2×C22⋊C4—611no—
1069C2×C22⋊C4—611no—
1070C2×C22⋊C4—611no—
1071C2×C22⋊C4—611no—
1072C2×C22⋊C4—611no—
1073C2×C22⋊C4—611no—
1074C2×C22⋊C4—611no—
1075C2×C22⋊C4—611no—
1076C2×C22⋊C4—611no—
1077C2×C22⋊C4—611no—
1078C2×C22⋊C4—611no—
1079C2×C22⋊C4—611no—
1080C2×C22⋊C4—611no—
1081C2×C22⋊C4—611no—
1082C2×C22⋊C4—611no—
1083C2×C22⋊C4—611no—
1084C2×C22⋊C4—611no—
1085C2×C22⋊C4—2442no—
1086C2×C22⋊C4—2442no—
1087C2×C22⋊C4C22×D6111yescharacteristic
1088C2×C22⋊C4C22×D6111yescharacteristic
1089C2×C22⋊C4C22×D6111yescharacteristic
1090C2×C22⋊C4C22×D6111yescharacteristic
1091C2×C22⋊C4C22×D6111yescharacteristic
1092C2×C22⋊C4C22×D6111yescharacteristic
1093C2×C22⋊C4C22×D6111yescharacteristic
1094C2×C22⋊C4C22×D6111yescharacteristic
1095C2×C42—611no—
1096C2×C42—611no—
1097C2×C42—611no—
1098C2×C42—611no—
1099C2×C42—611no—
1100C2×C42—611no—
1101C2×C42—611no—
1102C2×C42—611no—
1103C2×C42—611no—
1104C2×C42—611no—
1105C2×C42—611no—
1106C2×C42—611no—
1107C2×C42—611no—
1108C2×C42C22×D6111yescharacteristic
1109C2×C42C22×D6111yescharacteristic
1110C2×C42C22×D6111yescharacteristic
1111C2×C42C22×D6111yescharacteristic
1112C2×C42C22×D6111yescharacteristic
1113#95—611no—
1114#95—611no—
1115#95—611no—
1116#95—611no—
1117#95—611no—
1118#95—611no—
1119#95—611no—
1120#95—611no—
1121#95—611no—
1122#95—611no—
1123#95—611no—
1124#95—611no—
1125#95—611no—
1126#95—611no—
1127#95—611no—
1128#95—611no—
1129#95—611no—
1130#95—611no—
1131#95—611no—
1132#95—611no—
1133#95—611no—
1134#95—611no—
1135#95—611no—
1136#95—611no—
1137#95—611no—
1138#95—611no—
1139#95—611no—
1140#95—611no—
1141#95—611no—
1142#95—611no—
1143#95—611no—
1144#95—611no—
1145#95—611no—
1146#95—611no—
1147#95—611no—
1148#95—611no—
1149#95—611no—
1150#95—611no—
1151#95C22×D6111yescharacteristic
1152#95C22×D6111yescharacteristic
1153#95C22×D6111yescharacteristic
1154#95C22×D6111yescharacteristic
1155#95C22×D6111yescharacteristic
1156#95C22×D6111yescharacteristic
1157#95C22×D6111yescharacteristic
1158#95C22×D6111yescharacteristic
1159#95C22×D6111yescharacteristic
1160#95C22×D6111yescharacteristic
1161C24—611no—
1162C24—611no—
1163C24—611no—
1164C24—614no—
1165C24—1222no—
1166C24—1222no—
1167C24—2441no—
1168C24—2441no—
1169C24—2441no—
1170C24—2441no—
1171C24C23×D6111yescharacteristic
1172C24C23×D6111yescharacteristic
1173#41—24416no—
1174C2×Q8—614no—
1175C2×Q8—2441no—
1176C2×Q8—2441no—
1177C2×D4—22no—
1178C2×D4—22no—
1179C2×D4—614no—
1180C2×D4—614no—
1181C2×D4—614no—
1182C2×D4—614no—
1183C2×D4—614no—
1184C2×D4—614no—
1185C2×D4—1222no—
1186C2×D4—1222no—
1187C2×D4—2441no—
1188C2×D4—2441no—
1189C2×D4—2441no—
1190C2×D4—2441no—
1191C2×D4—2441no—
1192C2×D4—2441no—
1193C2×D4—2441no—
1194C2×D4—2441no—
1195C2×D4—2441no—
1196C2×D4—2441no—
1197C2×D4C2×C4×D6114yes—
1198C22×C4—22no—
1199C22×C4—22no—
1200C22×C4—22no—
1201C22×C4—22no—
1202C22×C4—41no—
1203C22×C4—41no—
1204C22×C4—41no—
1205C22×C4—41no—
1206C22×C4—41no—
1207C22×C4—41no—
1208C22×C4—41no—
1209C22×C4—614no—
1210C22×C4—611no—
1211C22×C4—611no—
1212C22×C4—611no—
1213C22×C4—611no—
1214C22×C4—611no—
1215C22×C4—614no—
1216C22×C4—614no—
1217C22×C4—614no—
1218C22×C4—614no—
1219C22×C4—614no—
1220C22×C4—614no—
1221C22×C4—611no—
1222C22×C4—611no—
1223C22×C4—611no—
1224C22×C4—611no—
1225C22×C4—611no—
1226C22×C4—611no—
1227C22×C4—611no—
1228C22×C4—611no—
1229C22×C4—1222no—
1230C22×C4—1222no—
1231C22×C4—1222no—
1232C22×C4—1222no—
1233C22×C4—2441no—
1234C22×C4—2441no—
1235C22×C4—2441no—
1236C22×C4—2441no—
1237C22×C4—2441no—
1238C22×C4—2441no—
1239C22×C4—24416no—
1240C22×C4—2441no—
1241C22×C4—2441no—
1242C22×C4—2441no—
1243C22×C4—2441no—
1244C22×C4—2441no—
1245C22×C4—2441no—
1246C22×C4—2441no—
1247C22×C4—2441no—
1248C22×C4—2441no—
1249C22×C4—2441no—
1250C22×C4—2441no—
1251C22×C4—2441no—
1252C22×C4—2441no—
1253C22×C4—2441no—
1254C22×C4—2441no—
1255C22×C4—2441no—
1256C22×C4—2441no—
1257C22×C4—2441no—
1258C22×C4—2441no—
1259C22×C4C2×C4×D6114yes—
1260C22×C4C23×D6111yescharacteristic
1261C22×C4C23×D6111yescharacteristic
1262C22×C4C23×D6111yescharacteristic
1263C22×C4C23×D6111yescharacteristic
1264C22×C4C23×D6111yescharacteristic
1265C22×C4C23×D6111yescharacteristic
1266C22×C4C23×D6111yescharacteristic
1267C22×C4C23×D6111yescharacteristic
1268C22×C4C23×D6111yescharacteristic
1269C22×C4C23×D6111yescharacteristic
1270C22×C4C23×D6111yescharacteristic
1271C22×C4C23×D6111yescharacteristic
1272C22×C4C23×D6111yescharacteristic
1273C4⋊C4—41no—
1274C4⋊C4—41no—
1275C4⋊C4—41no—
1276C4⋊C4—41no—
1277C4⋊C4—41no—
1278C4⋊C4—614no—
1279C4⋊C4—614no—
1280C4⋊C4—614no—
1281C4⋊C4—614no—
1282C4⋊C4—2441no—
1283C4⋊C4—2441no—
1284C4⋊C4—2441no—
1285C4⋊C4—2441no—
1286C4⋊C4—2441no—
1287C4⋊C4—2441no—
1288C4⋊C4—2441no—
1289C4⋊C4—2441no—
1290C4⋊C4—2441no—
1291C4⋊C4—2441no—
1292C4⋊C4—2441no—
1293C4⋊C4C2×C4×D6114yes—
1294C4⋊C4C2×C4×D6114yes—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—614no—
1301C22⋊C4—614no—
1302C22⋊C4—614no—
1303C22⋊C4—614no—
1304C22⋊C4—614no—
1305C22⋊C4—614no—
1306C22⋊C4—614no—
1307C22⋊C4—1222no—
1308C22⋊C4—1222no—
1309C22⋊C4—2441no—
1310C22⋊C4—2441no—
1311C22⋊C4—2441no—
1312C22⋊C4—2441no—
1313C22⋊C4—2441no—
1314C22⋊C4—2441no—
1315C22⋊C4—2441no—
1316C22⋊C4—2441no—
1317C22⋊C4—2441no—
1318C22⋊C4—2441no—
1319C22⋊C4—2441no—
1320C22⋊C4—2441no—
1321C22⋊C4—2441no—
1322C22⋊C4—2441no—
1323C22⋊C4—2441no—
1324C22⋊C4—2441no—
1325C22⋊C4—2441no—
1326C22⋊C4—2441no—
1327C22⋊C4—2441no—
1328C22⋊C4—2441no—
1329C22⋊C4—2441no—
1330C22⋊C4—2441no—
1331C22⋊C4—2441no—
1332C22⋊C4—2441no—
1333C22⋊C4—2441no—
1334C22⋊C4C2×C4×D6114yes—
1335C22⋊C4C2×C4×D6114yes—
1336C22⋊C4C2×C4×D6114yes—
1337C42—41no—
1338C42—41no—
1339C42—41no—
1340C42—41no—
1341C42—41no—
1342C42—614no—
1343C42—614no—
1344C42—2441no—
1345C42—2441no—
1346C42—2441no—
1347C42—2441no—
1348C42—2441no—
1349C42—2441no—
1350C42—2441no—
1351C42—2441no—
1352C42—2441no—
1353C42—2441no—
1354C42—2441no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—612no—
1366C23—612no—
1367C23—612no—
1368C23—1228no—
1369C23—1221no—
1370C23—1221no—
1371C23—1221no—
1372C23—1221no—
1373C23—1221no—
1374C23—1221no—
1375C23—1221no—
1376C23—1221no—
1377C23—1221no—
1378C23—1221no—
1379C23—1221no—
1380C23—1221no—
1381C23—1221no—
1382C23—1221no—
1383C23—1221no—
1384C23—1221no—
1385C23—1221no—
1386C23—1221no—
1387C23—2444no—
1388C23—2444no—
1389C23—2444no—
1390C23—2444no—
1391C23—2444no—
1392C23—2444no—
1393C23C22×C4×D6112yes—
1394C23C22×C4×D6112yes—
1395C23#1451982212yes—
1396C23#1451982312yes—
1397C23C24×D6111yescharacteristic
1398Q8—2444no—
1399D4—28no—
1400D4—1228no—
1401D4—2444no—
1402D4—2444no—
1403D4—2444no—
1404D4—2444no—
1405D4—2444no—
1406C2×C4—28no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—82no—
1442C2×C4—82no—
1443C2×C4—82no—
1444C2×C4—612no—
1445C2×C4—612no—
1446C2×C4—612no—
1447C2×C4—612no—
1448C2×C4—612no—
1449C2×C4—1228no—
1450C2×C4—1221no—
1451C2×C4—1221no—
1452C2×C4—1221no—
1453C2×C4—1221no—
1454C2×C4—1221no—
1455C2×C4—1221no—
1456C2×C4—1221no—
1457C2×C4—1221no—
1458C2×C4—1221no—
1459C2×C4—1221no—
1460C2×C4—1221no—
1461C2×C4—1221no—
1462C2×C4—1221no—
1463C2×C4—1221no—
1464C2×C4—1221no—
1465C2×C4—1221no—
1466C2×C4—1221no—
1467C2×C4—1221no—
1468C2×C4—1221no—
1469C2×C4—1221no—
1470C2×C4—1221no—
1471C2×C4—1221no—
1472C2×C4—1221no—
1473C2×C4—1221no—
1474C2×C4—1221no—
1475C2×C4—1221no—
1476C2×C4—1221no—
1477C2×C4—1221no—
1478C2×C4—1221no—
1479C2×C4—1221no—
1480C2×C4—1221no—
1481C2×C4—1221no—
1482C2×C4—1221no—
1483C2×C4—1221no—
1484C2×C4—4882no—
1485C2×C4—4882no—
1486C2×C4—4882no—
1487C2×C4—4882no—
1488C2×C4—4882no—
1489C2×C4—2444no—
1490C2×C4—2444no—
1491C2×C4—2444no—
1492C2×C4—2444no—
1493C2×C4—2444no—
1494C2×C4—2444no—
1495C2×C4C22×C4×D6112yes—
1496C2×C4C22×C4×D6112yes—
1497C2×C4C22×C4×D6112yes—
1498C2×C4C22×C4×D6112yes—
1499C2×C4C22×C4×D6112yes—
1500C22—22no—
1501C22—22no—
1502C22—22no—
1503C22—22no—
1504C22—22no—
1505C22—22no—
1506C22—22no—
1507C22—22no—
1508C22—22no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—1222no—
1514C22—1222no—
1515C22—1222no—
1516C22—1222no—
1517C22—1222no—
1518C22—1222no—
1519C22—1222no—
1520C22—1222no—
1521C22—1222no—
1522C22—24416no—
1523C22—2441no—
1524C22—2441no—
1525C22—2441no—
1526C22—2441no—
1527C22—2441no—
1528C22—2441no—
1529C22—2441no—
1530C22—2441no—
1531C22—2441no—
1532C22—2441no—
1533C22—2441no—
1534C22—2441no—
1535C22#1684023414yes—
1536C22C23×C4×D6111yescharacteristic
1537C22C2×#1451982211yescharacteristic
1538C22C2×#1451982311yescharacteristic
1539C22#1684059711yescharacteristic
1540C22#1684059811yescharacteristic
1541C22#1684059811yescharacteristic
1542C22#1684059911yescharacteristic
1543C4—22no—
1544C4—22no—
1545C4—22no—
1546C4—22no—
1547C4—22no—
1548C4—41no—
1549C4—41no—
1550C4—41no—
1551C4—41no—
1552C4—41no—
1553C4—41no—
1554C4—41no—
1555C4—41no—
1556C4—1222no—
1557C4—1222no—
1558C4—1222no—
1559C4—1222no—
1560C4—1222no—
1561C4—2441no—
1562C4—2441no—
1563C4—2441no—
1564C4—2441no—
1565C4—2441no—
1566C4—2441no—
1567C4—2441no—
1568C4—2441no—
1569C2—24no—
1570C2—42no—
1571C2—2442no—
1572C2—2442no—
1573C2—2442no—
1574C2C2×#1684023411yescharacteristic
1575C2#2145901811yescharacteristic
1576C2#2145901911yescharacteristic
1577C2#2145997811yescharacteristic
1578C2#2145998511yescharacteristic
1579C2#2145998911yescharacteristic
1580C2#2145999111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2359C2
socle, cosocleC23×C61C25
prime radicalC2×#16840270C2
hypercenter#2359D61
hypocenterC61#34396
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
2. #21448984C2semidirect
3. #21448981C2semidirect
4. #21448975C2semidirect
5. #21448972C2semidirect
6. #21448815C2semidirect
7. #21448811C2semidirect
8. #21448807C2semidirect
9. #21448789C2semidirect
10. #21448788C2semidirect
11. #21448758C2semidirect
12. #21448753C2semidirect
13. #21448677C2semidirect
14. #21448673C2semidirect
15. #21448645C2semidirect
16. #21448644C2semidirect
17. #21448582C2semidirect
18. #21448579C2semidirect
19. #21448573C2semidirect
20. #21448570C2semidirect
21. #21448482C2semidirect
22. #21448479C2semidirect
23. #21448476C2semidirect
24. #21448473C2semidirect
25. #21448460C2semidirect
26. #21448458C2semidirect
27. #21448451C2semidirect
28. #21448447C2semidirect
29. #21448198C2semidirect
30. C2×#16839624C2semidirect
31. C61×#2359C2semidirect
34. #16840270C4semidirect
53. #16839668C22semidirect
54. #16839667C22semidirect
55. #16839666C22semidirect
56. #16839666C22semidirect
65. #16839661C22semidirect
66. #16839659C22semidirect
67. #16839657C22semidirect
68. #16839655C22semidirect
69. #16839655C22semidirect
74. #16839654C22semidirect
79. #16839653C22semidirect
84. #16839652C22semidirect
89. #16839651C22semidirect
90. #16839649C22semidirect
91. #16839649C22semidirect
92. #16839649C22semidirect
93. #16839648C22semidirect
94. #16839648C22semidirect
95. #16839646C22semidirect
96. #16839646C22semidirect
97. #16839646C22semidirect
98. #16839644C22semidirect
99. #16839644C22semidirect
100. #16839644C22semidirect
101. #16839643C22semidirect
102. #16839643C22semidirect
103. #16839643C22semidirect
108. #16839641C22semidirect
116. #16839639C22semidirect
117. #16839638C22semidirect
118. #16839638C22semidirect
120. #16839637C22semidirect
121. #16839636C22semidirect
124. #16839633C22semidirect
125. #16839629C22semidirect
126. #16839629C22semidirect
127. #16839627C22semidirect
128. #16839626C22semidirect
137. #16839624C22semidirect
140. #16839623C22semidirect
141. #16839620C22semidirect
146. #16839619C22semidirect
149. C4⋊C4×Dic61C22semidirect
150. C4⋊C4×Dic61C22semidirect
151. C4×#11758196C22semidirect
152. C4×#11758196C22semidirect
153. #16839613C22semidirect
156. C22⋊C4×Dic61C22semidirect
157. C22⋊C4×Dic61C22semidirect
162. C4×#11758198C22semidirect
163. C4×#11758198C22semidirect
165. #16839609C22semidirect
166. #16839608C22semidirect
167. #16839607C22semidirect
171. C2×#14519684C22semidirect
172. #95×D61C22semidirect
176. C61×#389C22semidirect
177. C61×#388C22semidirect
178. C61×#388C22semidirect
179. C61×#387C22semidirect
180. C61×#387C22semidirect
183. C61×#385C22semidirect
184. C4×C4⋊C4×C61C22semidirect
186. C4×C22⋊C4×C61C22semidirect
206. C22×C4×D61C2×C4semidirect
214. #14519760C2×C4semidirect
215. #14519755C2×C4semidirect
216. #14519755C2×C4semidirect
217. #14519750C2×C4semidirect
218. #14519750C2×C4semidirect
219. #14519747C2×C4semidirect
220. #14519745C2×C4semidirect
222. #14519739C2×C4semidirect
223. #14519739C2×C4semidirect
226. #14519737C2×C4semidirect
227. #14519737C2×C4semidirect
229. #14519733C2×C4semidirect
337. #123×C61C2×C4semidirect
787. #2359D61semidirect
861. #389C2×D61semidirect
884. #388C2×D61semidirect
885. #388C2×D61semidirect
900. #387C2×D61semidirect
901. #387C2×D61semidirect
925. #385C2×D61semidirect
955. C4×C4⋊C4C2×D61semidirect
969. C4×C22⋊C4C2×D61semidirect
978. C61#34396semidirect
1011. #123C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402702
#214489842
#214489812
#214489752
#214489722
#214488152
#214488112
#214488072
#214487892
#214487882
#214487582
#214487532
#214486772
#214486732
#214486452
#214486442
#214485822
#214485792
#214485732
#214485702
#214484822
#214484792
#214484762
#214484732
#214484602
#214484582
#214484512
#214484472
#214481982
C2×#168396242
C61×#23592
#3439661