Finite Group Databasebeta

← #29844247

Subgroups — #29844247

Order 15616.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840350C211yesmaximal, characteristic
2#21449006C211yesmaximal, characteristic, complemented
3#21448973C211yesmaximal, characteristic, complemented
4#21448968C211yesmaximal, characteristic, complemented
5#21448958C211yesmaximal, characteristic, complemented
6#21448947C211yesmaximal, characteristic, complemented
7#21448946C211yesmaximal, characteristic, complemented
8#21448870C211yesmaximal, characteristic, complemented
9#21448858C211yesmaximal, characteristic, complemented
10#21448855C211yesmaximal, characteristic, complemented
11#21448814C211yesmaximal, characteristic, complemented
12#21448808C211yesmaximal, characteristic, complemented
13#21448798C211yesmaximal, characteristic, complemented
14#21448769C211yesmaximal, characteristic, complemented
15#21448756C211yesmaximal, characteristic, complemented
16#21448668C211yesmaximal, characteristic, complemented
17#21448633C211yesmaximal, characteristic, complemented
18#21448630C211yesmaximal, characteristic, complemented
19#21448596C211yesmaximal, characteristic, complemented
20#21448575C211yesmaximal, characteristic, complemented
21#21448525C211yesmaximal, characteristic, complemented
22#21448523C211yesmaximal, characteristic, complemented
23#21448507C211yesmaximal, characteristic, complemented
24#21448497C211yesmaximal, characteristic, complemented
25#21448477C211yesmaximal, characteristic, complemented
26#21448474C211yesmaximal, characteristic, complemented
27#21448448C211yesmaximal, characteristic, complemented
28C4×#14519770C211yesmaximal, characteristic, complemented
29#21448360C211yesmaximal, characteristic, complemented
30#21448278C211yesmaximal, characteristic, complemented
31C61×#2342C211yesmaximal, characteristic, complemented
32#16840350C4116yescomplemented
33C2×#14519770C2211yescharacteristic
34C2×#14519770C2211yescharacteristic
35C2×#14519763C2211yescharacteristic
36C2×#14519763C2211yescharacteristic
37C2×#14519759C2211yescharacteristic
38C2×#14519759C2211yescharacteristic
39C2×#14519756C2211yescharacteristic
40C2×#14519751C2211yescharacteristic
41C2×#14519750C2211yescharacteristic
42C2×#14519750C2211yescharacteristic
43C2×#14519746C2211yescharacteristic
44C2×#14519746C2211yescharacteristic
45C2×#14519742C2211yescharacteristic, complemented
46C2×C4×D244C2211yescharacteristic, complemented
47C2×C4×C22⋊D61C2211yescharacteristic
48C2×C4×C22⋊D61C2211yescharacteristic
49C2×C4×C22⋊D61C2211yescharacteristic
50C2×C4×C22⋊D61C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53C2×#14519736C2211yescharacteristic
54C2×#14519735C2211yescharacteristic, complemented
55C2×#14519734C2211yescharacteristic, complemented
56C22×C22⋊Dic61C2211yescharacteristic
57#16839667C2211yescharacteristic, complemented
58#16839666C2211yescharacteristic, complemented
59#16839666C2211yescharacteristic, complemented
60#16839664C2211yescharacteristic, complemented
61#16839662C2211yescharacteristic
62#16839662C2211yescharacteristic
63#16839662C2211yescharacteristic
64#16839662C2211yescharacteristic
65#16839662C2211yescharacteristic
66#16839662C2211yescharacteristic
67#16839662C2211yescharacteristic
68#16839662C2211yescharacteristic
69#16839660C2211yescharacteristic, complemented
70#16839659C2211yescharacteristic, complemented
71#16839659C2211yescharacteristic, complemented
72#16839658C2211yescharacteristic, complemented
73#16839657C2211yescharacteristic, complemented
74#16839657C2211yescharacteristic, complemented
75#16839656C2211yescharacteristic
76#16839656C2211yescharacteristic
77#16839656C2211yescharacteristic
78#16839656C2211yescharacteristic
79#16839656C2211yescharacteristic
80#16839656C2211yescharacteristic
81#16839656C2211yescharacteristic
82#16839656C2211yescharacteristic
83#16839655C2211yescharacteristic
84#16839655C2211yescharacteristic
85#16839655C2211yescharacteristic
86#16839655C2211yescharacteristic
87#16839653C2211yescharacteristic, complemented
88#16839653C2211yescharacteristic, complemented
89#16839652C2211yescharacteristic, complemented
90#16839652C2211yescharacteristic, complemented
91#16839652C2211yescharacteristic, complemented
92#16839652C2211yescharacteristic, complemented
93#16839651C2211yescharacteristic, complemented
94#16839651C2211yescharacteristic, complemented
95#16839650C2211yescharacteristic
96#16839650C2211yescharacteristic
97#16839650C2211yescharacteristic
98#16839650C2211yescharacteristic
99#16839650C2211yescharacteristic
100#16839650C2211yescharacteristic
101#16839650C2211yescharacteristic
102#16839650C2211yescharacteristic
103#16839649C2211yescharacteristic, complemented
104#16839649C2211yescharacteristic, complemented
105#16839649C2211yescharacteristic, complemented
106#16839649C2211yescharacteristic, complemented
107#16839647C2211yescharacteristic, complemented
108#16839647C2211yescharacteristic, complemented
109#16839647C2211yescharacteristic, complemented
110#16839647C2211yescharacteristic, complemented
111#16839646C2211yescharacteristic, complemented
112#16839646C2211yescharacteristic, complemented
113#16839644C2211yescharacteristic, complemented
114#16839644C2211yescharacteristic, complemented
115#16839641C2211yescharacteristic
116#16839641C2211yescharacteristic
117#16839640C2211yescharacteristic, complemented
118#16839640C2211yescharacteristic, complemented
119#16839639C2211yescharacteristic
120#16839639C2211yescharacteristic
121#16839638C2211yescharacteristic
122#16839638C2211yescharacteristic
123#16839638C2211yescharacteristic
124#16839638C2211yescharacteristic
125#16839638C2211yescharacteristic
126#16839638C2211yescharacteristic
127#16839638C2211yescharacteristic
128#16839638C2211yescharacteristic
129#16839637C2211yescharacteristic
130#16839637C2211yescharacteristic
131#16839636C2211yescharacteristic, complemented
132#16839636C2211yescharacteristic, complemented
133#16839635C2211yescharacteristic
134#16839635C2211yescharacteristic
135#16839634C2211yescharacteristic
136#16839634C2211yescharacteristic
137#16839633C2211yescharacteristic, complemented
138#16839633C2211yescharacteristic, complemented
139#16839631C2211yescharacteristic, complemented
140#16839629C2211yescharacteristic, complemented
141#16839629C2211yescharacteristic, complemented
142#16839626C2211yescharacteristic, complemented
143#16839625C2211yescharacteristic
144#16839622C2211yescharacteristic
145#16839621C2211yescharacteristic, complemented
146#16839619C2211yescharacteristic, complemented
147#16839618C2211yescharacteristic
148C4⋊C4×Dic61C2211yescharacteristic, complemented
149C4⋊C4×Dic61C2211yescharacteristic, complemented
150C4×#11758196C2211yescharacteristic, complemented
151C4×#11758196C2211yescharacteristic, complemented
152C4×#11758196C2211yescharacteristic, complemented
153C4×#11758196C2211yescharacteristic, complemented
154C4×#11758196C2211yescharacteristic, complemented
155C4×C4⋊Dic61C2211yescharacteristic, complemented
156C22⋊C4×Dic61C2211yescharacteristic
157C22⋊C4×Dic61C2211yescharacteristic
158C22⋊C4×Dic61C2211yescharacteristic
159C22⋊C4×Dic61C2211yescharacteristic
160C4×#11758198C2211yescharacteristic, complemented
161C4×C22⋊Dic61C2211yescharacteristic
162C4×C22⋊Dic61C2211yescharacteristic
163C4×C22⋊Dic61C2211yescharacteristic
164#16839609C2211yescharacteristic, complemented
165#16839609C2211yescharacteristic, complemented
166#16839609C2211yescharacteristic, complemented
167#16839609C2211yescharacteristic, complemented
168#16839609C2211yescharacteristic, complemented
169#16839607C2211yescharacteristic, complemented
170#95×D61C2211yescharacteristic, complemented
171#95×D61C2211yescharacteristic, complemented
172C42×Dic61C2211yescharacteristic, complemented
173C2×#117×C61C2211yescharacteristic
174C22×C22⋊C4×C61C2211yescharacteristic
175C22×C22⋊C4×C61C2211yescharacteristic
176C61×#388C2211yescharacteristic
177C61×#388C2211yescharacteristic
178C61×#388C2211yescharacteristic
179C61×#388C2211yescharacteristic
180C61×#385C2211yescharacteristic
181C61×#385C2211yescharacteristic
182C61×#381C2211yescharacteristic
183C61×#380C2211yescharacteristic
184C61×#379C2211yescharacteristic
185C4×C22⋊C4×C61C2211yescharacteristic
186C4×C22⋊C4×C61C2211yescharacteristic
187C4×C22⋊C4×C61C2211yescharacteristic
188C22×Dic122C2311yescharacteristic
189C22×D244C2311yescharacteristic
190C22×C22⋊D61C2311yescharacteristic
191C22×C22⋊D61C2311yescharacteristic
192C22×C22⋊D61C2311yescharacteristic
193C22×C22⋊D61C2311yescharacteristic
194C22×C22⋊D61C2311yescharacteristic
195C22×C22⋊D61C2311yescharacteristic
196C23×Dic61C2311yescharacteristic
197C23×Dic61C2311yescharacteristic
198C22×C4×D61C2311yescharacteristic
199C22×C4×D61C2311yescharacteristic
200C22×C4×D61C2311yescharacteristic
201C22×C4×D61C2311yescharacteristic
202C22×C4×D61C2311yescharacteristic
203C22×C4×D61C2311yescharacteristic
204#14519770C2×C418yescomplemented
205#14519770C2×C418yescomplemented
206#14519763C2×C418yescomplemented
207#14519763C2×C418yescomplemented
208#14519759C2×C418yescomplemented
209#14519759C2×C418yescomplemented
210#14519756C2×C418yescomplemented
211#14519751C2×C418yescomplemented
212#14519750C2×C418yescomplemented
213#14519750C2×C418yescomplemented
214#14519746C2×C418yescomplemented
215#14519746C2×C418yescomplemented
216#14519742—42no—
217C4×D244—42no—
218C4×C22⋊D61—42no—
219C4×C22⋊D61—42no—
220C4×C22⋊D61C2×C418yescomplemented
221C4×C22⋊D61C2×C418yescomplemented
222#14519737—42no—
223#14519737—42no—
224#14519736—42no—
225#14519735—42no—
226#14519734—42no—
227C2×C4⋊Dic61C2311yescharacteristic
228C2×C4⋊Dic61C2311yescharacteristic
229C2×C4⋊Dic61C2311yescharacteristic
230C2×C4⋊Dic61C2311yescharacteristic
231C2×C4⋊Dic61C2311yescharacteristic
232C2×C4⋊Dic61C2311yescharacteristic
233C2×#11758196C2311yescharacteristic
234C2×#11758196C2311yescharacteristic
235C2×#11758196C2311yescharacteristic
236C2×#11758196C2311yescharacteristic
237C2×#11758196C2311yescharacteristic
238C2×#11758196C2311yescharacteristic
239C2×#11758196C2311yescharacteristic
240C2×#11758196C2311yescharacteristic
241C2×#11758196C2311yescharacteristic
242C2×#11758196C2311yescharacteristic
243C2×#11758196C2311yescharacteristic
244C2×#11758196C2311yescharacteristic
245C2×#11758196C2311yescharacteristic
246C2×#11758196C2311yescharacteristic
247C2×#11758196C2311yescharacteristic
248C2×#11758196C2311yescharacteristic
249C2×C22⋊Dic61—42no—
250C2×C22⋊Dic61C2311yescharacteristic
251C2×C22⋊Dic61C2311yescharacteristic
252C2×C22⋊Dic61C2311yescharacteristic
253C2×C22⋊Dic61C2311yescharacteristic
254C2×C22⋊Dic61C2311yescharacteristic
255C2×C22⋊Dic61C2311yescharacteristic
256C2×C22⋊Dic61C2311yescharacteristic
257C2×C22⋊Dic61C2311yescharacteristic
258C2×C22⋊Dic61C2311yescharacteristic
259C2×C22⋊Dic61C2311yescharacteristic
260C2×C22⋊Dic61C2311yescharacteristic
261C2×C22⋊Dic61C2311yescharacteristic
262C2×C22⋊Dic61C2311yescharacteristic
263C2×C22⋊Dic61C2311yescharacteristic
264C2×C22⋊Dic61C2311yescharacteristic
265C2×C22⋊Dic61C2311yescharacteristic
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×#11758198C2311yescharacteristic
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
294C2×C4×Dic61C2311yescharacteristic
295C2×C4×Dic61C2311yescharacteristic
296C2×C4×Dic61C2311yescharacteristic
297C2×C4×Dic61C2311yescharacteristic
298C2×C4×Dic61C2311yescharacteristic
299C2×C4×Dic61C2311yescharacteristic
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
332C25×C61C2311yescharacteristic
333C23×C4×C61C2311yescharacteristic
334C23×C4×C61C2311yescharacteristic
335C23×C4×C61C2311yescharacteristic
336C23×C4×C61C2311yescharacteristic
337#117×C61—42no—
338C2×C4⋊C4×C61C2311yescharacteristic
339C2×C4⋊C4×C61C2311yescharacteristic
340C2×C4⋊C4×C61C2311yescharacteristic
341C2×C4⋊C4×C61C2311yescharacteristic
342C2×C22⋊C4×C61—42no—
343C2×C22⋊C4×C61C2×C418yescomplemented
344C2×C22⋊C4×C61C2311yescharacteristic
345C2×C22⋊C4×C61C2311yescharacteristic
346C2×C22⋊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×C22⋊C4×C61C2311yescharacteristic
356C2×C22⋊C4×C61C2311yescharacteristic
357C2×C22⋊C4×C61C2311yescharacteristic
358C2×C42×C61C2311yescharacteristic
359C2×C42×C61C2311yescharacteristic
360C2×C42×C61C2311yescharacteristic
361C2×C42×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×C61—41no—
371C24×C61—41no—
372C24×C61—41no—
373C24×C61—41no—
374C24×C61—41no—
375C24×C61—41no—
376C24×C61C22×C414yes—
377C24×C61C2411yescharacteristic
378C24×C61C2411yescharacteristic
379C24×C61C2411yescharacteristic
380C23×D61C2411yescharacteristic
381C23×D61C2411yescharacteristic
382C22×C4×C61—22no—
383C22×C4×C61—41no—
384C22×C4×C61—41no—
385C22×C4×C61—41no—
386C22×C4×C61—41no—
387C22×C4×C61—41no—
388C22×C4×C61—41no—
389C22×C4×C61—41no—
390C22×C4×C61—41no—
391C22×C4×C61—41no—
392C22×C4×C61C22×C414yes—
393C22×C4×C61C22×C414yes—
394C22×C4×C61C2411yescharacteristic
395C22×C4×C61C2411yescharacteristic
396C22×C4×C61C2411yescharacteristic
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
406C2×C22⋊D61—41no—
407C2×C22⋊D61—41no—
408C2×C22⋊D61—41no—
409C2×C22⋊D61—41no—
410C2×C22⋊D61—41no—
411C2×C22⋊D61—41no—
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—
422C2×C22⋊D61C22×C414yes—
423C2×C22⋊D61C22×C414yes—
424C22×Dic61—22no—
425C22×Dic61—41no—
426C22×Dic61—41no—
427C22×Dic61—41no—
428C22×Dic61—41no—
429C22×Dic61—41no—
430C22×Dic61C2411yescharacteristic
431C22×Dic61C2411yescharacteristic
432C22×Dic61C2411yescharacteristic
433C22×Dic61C2411yescharacteristic
434C22×Dic61C2411yescharacteristic
435C22×Dic61C2411yescharacteristic
436C22×Dic61C2411yescharacteristic
437C22×Dic61C2411yescharacteristic
438C22×Dic61C2411yescharacteristic
439C22×Dic61C2411yescharacteristic
440C22×Dic61C2411yescharacteristic
441C22×Dic61C2411yescharacteristic
442C22×Dic61C2411yescharacteristic
443C22×Dic61C2411yescharacteristic
444C2×D244—41no—
445C2×D244—41no—
446C2×D244C22×C414yes—
447C2×C4×D61—22no—
448C2×C4×D61—41no—
449C2×C4×D61—41no—
450C2×C4×D61—41no—
451C2×C4×D61—41no—
452C2×C4×D61—41no—
453C2×C4×D61—41no—
454C2×C4×D61—41no—
455C2×C4×D61—41no—
456C2×C4×D61—41no—
457C2×C4×D61—41no—
458C2×C4×D61—41no—
459C2×C4×D61—41no—
460C2×C4×D61—41no—
461C2×C4×D61—41no—
462C2×C4×D61—41no—
463C2×C4×D61C22×C414yes—
464C2×C4×D61C22×C414yes—
465C2×Dic122—41no—
466C2×Dic122—41no—
467C2×Dic122C22×C414yes—
468C4⋊C4×C61—22no—
469C4⋊C4×C61—41no—
470C4⋊C4×C61—41no—
471C4⋊C4×C61—41no—
472C22⋊C4×C61—22no—
473C22⋊C4×C61—22no—
474C22⋊C4×C61—41no—
475C22⋊C4×C61—41no—
476C22⋊C4×C61—41no—
477C22⋊C4×C61—41no—
478C22⋊C4×C61—41no—
479C22⋊C4×C61—41no—
480C22⋊C4×C61—41no—
481C22⋊C4×C61—41no—
482C22⋊C4×C61C22×C414yes—
483C22⋊C4×C61C22×C414yes—
484C22⋊C4×C61C22×C414yes—
485C22⋊C4×C61C22×C414yes—
486C42×C61—22no—
487C42×C61—41no—
488C42×C61—41no—
489C42×C61—41no—
490C22⋊Dic61—22no—
491C22⋊Dic61—22no—
492C22⋊Dic61—41no—
493C22⋊Dic61—41no—
494C22⋊Dic61—41no—
495C22⋊Dic61—41no—
496C22⋊Dic61—41no—
497C22⋊Dic61—41no—
498C22⋊Dic61—41no—
499C22⋊Dic61—41no—
500C22⋊Dic61C22×C414yes—
501C22⋊Dic61C22×C414yes—
502C22⋊Dic61C22×C414yes—
503C22⋊Dic61C22×C414yes—
504C22⋊Dic61C22×C414yes—
505C22⋊Dic61C22×C414yes—
506#11758198—22no—
507#11758198—22no—
508#11758198—22no—
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#11758198C22×C414yes—
519#11758198C22×C414yes—
520#11758198C22×C414yes—
521#11758198C22×C414yes—
522C4⋊Dic61—22no—
523C4⋊Dic61—41no—
524C4⋊Dic61—41no—
525C4⋊Dic61—41no—
526C4⋊Dic61C22×C414yes—
527C4⋊Dic61C22×C414yes—
528#11758196—22no—
529#11758196—41no—
530#11758196—41no—
531#11758196—41no—
532#11758196—41no—
533#11758196—41no—
534#11758196—41no—
535#11758196—41no—
536#11758196—41no—
537#11758196—41no—
538#11758196—41no—
539#11758196—41no—
540#11758196C22×C414yes—
541#11758196C22×C414yes—
542#11758196C22×C414yes—
543#11758196C22×C414yes—
544C4×Dic61—22no—
545C4×Dic61—22no—
546C4×Dic61—22no—
547C4×Dic61—22no—
548C4×Dic61—41no—
549C4×Dic61—41no—
550C4×Dic61—41no—
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×Dic61C22×C414yes—
561C4×Dic61C22×C414yes—
562C23×C61—21no—
563C23×C61—21no—
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×C61—21no—
575C23×C61—21no—
576C23×C61—21no—
577C23×C61—21no—
578C23×C61—21no—
579C23×C61—21no—
580C23×C61—44no—
581C23×C61—44no—
582C23×C61—44no—
583C23×C61—82no—
584C23×C61—82no—
585C23×C61—82no—
586C23×C61—82no—
587C23×C61C23×C412yes—
588C23×C61C23×C412yes—
589C23×C61C23×C412yes—
590C23×C61C2511yescharacteristic
591C22×D61—21no—
592C22×D61—21no—
593C22×D61—21no—
594C22×D61—21no—
595C22×D61—21no—
596C22×D61—21no—
597C22×D61—21no—
598C22×D61—21no—
599C22×D61—21no—
600C22×D61—21no—
601C22×D61—21no—
602C22×D61—21no—
603C22×D61C23×C412yes—
604C22×D61C23×C412yes—
605C2×C4×C61—21no—
606C2×C4×C61—21no—
607C2×C4×C61—21no—
608C2×C4×C61—21no—
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—44no—
637C2×C4×C61—44no—
638C2×C4×C61—82no—
639C2×C4×C61—82no—
640C2×C4×C61C23×C412yes—
641C2×C4×C61C23×C412yes—
642C2×C4×C61C23×C412yes—
643C2×C4×C61C23×C412yes—
644C2×C4×C61H(5,𝔽2)12yes—
645C22⋊D61—44no—
646C22⋊D61—44no—
647C22⋊D61—44no—
648C22⋊D61—44no—
649C22⋊D61—44no—
650C22⋊D61—44no—
651C2×Dic61—21no—
652C2×Dic61—21no—
653C2×Dic61—21no—
654C2×Dic61—21no—
655C2×Dic61—21no—
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—82no—
687C2×Dic61—82no—
688C2×Dic61C23×C412yes—
689C2×Dic61C23×C412yes—
690C2×Dic61C23×C412yes—
691C2×Dic61C23×C412yes—
692C2×Dic61C23×C412yes—
693C2×Dic61C23×C412yes—
694C2×Dic61H(5,𝔽2)12yes—
695D244—44no—
696C4×D61—44no—
697C4×D61—44no—
698C4×D61—82no—
699C4×D61—82no—
700C4×D61—82no—
701C4×D61—82no—
702Dic122—44no—
703#34446—611nomaximal, Sylow
704C22×C61—22no—
705C22×C61—22no—
706C22×C61—22no—
707C22×C61—22no—
708C22×C61—22no—
709C22×C61—22no—
710C22×C61—22no—
711C22×C61—22no—
712C22×C61—22no—
713C22×C61—41no—
714C22×C61—41no—
715C22×C61—41no—
716C22×C61—41no—
717C22×C61—41no—
718C22×C61—41no—
719C22×C61—41no—
720C22×C61—41no—
721C22×C61—41no—
722C22×C61—41no—
723C22×C61—41no—
724C22×C61—41no—
725C22×C61—88no—
726C22×C61C24×C411yescharacteristic
727C22×C61C2×H(5,𝔽2)11yescharacteristic
728C22×C61C2×H(5,𝔽2)11yescharacteristic
729C22×C61#58511yescharacteristic
730C22×C61#58511yescharacteristic
731C22×C61#58511yescharacteristic
732C22×C61#58511yescharacteristic
733C2×D61—22no—
734C2×D61—22no—
735C2×D61—22no—
736C2×D61—22no—
737C2×D61—22no—
738C2×D61—22no—
739C2×D61—41no—
740C2×D61—41no—
741C2×D61—41no—
742C2×D61—41no—
743C2×D61—41no—
744C2×D61—41no—
745C2×D61—41no—
746C2×D61—41no—
747C4×C61—22no—
748C4×C61—22no—
749C4×C61—22no—
750C4×C61—22no—
751C4×C61—22no—
752C4×C61—41no—
753C4×C61—41no—
754C4×C61—41no—
755C4×C61—41no—
756C4×C61—41no—
757C4×C61—41no—
758C4×C61—41no—
759Dic61—22no—
760Dic61—22no—
761Dic61—22no—
762Dic61—22no—
763Dic61—22no—
764Dic61—22no—
765Dic61—22no—
766Dic61—41no—
767Dic61—41no—
768Dic61—41no—
769Dic61—41no—
770Dic61—41no—
771Dic61—41no—
772Dic61—41no—
773C2×#538—611no—
774#2383—611no—
775#2377—611no—
776#2376—611no—
777#2375—611no—
778#2374—611no—
779#2373—611no—
780#2364—611no—
781#2363—611no—
782#2363—611no—
783#2359—611no—
784#2359—611no—
785#2358—611no—
786#2354—611no—
787#2353—611no—
788#2342—611no—
789#2342D6111yescharacteristic, complemented
790#2337—611no—
791#2337—611no—
792#2334—611no—
793#2332—611no—
794#2326—611no—
795#2325—611no—
796#2324—611no—
797#2323—611no—
798#2321—611no—
799#2321—611no—
800#2318—611no—
801C4×#126—611no—
802C4×#124—611no—
803#2293—611no—
804C2×C61—42no—
805C2×C61—42no—
806C2×C61—42no—
807C2×C61#342811yescharacteristic
808C2×C61C4×H(5,𝔽2)11yescharacteristic
809C2×C61C4×H(5,𝔽2)11yescharacteristic
810C2×C61#354511yescharacteristic
811C2×C61#354611yescharacteristic
812C2×C61#356011yescharacteristic
813C2×C61#356611yescharacteristic
814D61—42no—
815D61—42no—
816#538—6116no—
817C2×#126—611no—
818C2×#126—611no—
819C2×#124—611no—
820C2×#124—611no—
821C2×#123—611no—
822C2×#123—611no—
823C2×C22⋊Q8—611no—
824C2×#121—611no—
825C2×#121—611no—
826C2×#121—611no—
827C2×#120—611no—
828C2×#120—611no—
829C2×C4×Q8—611no—
830C2×C4×D4—611no—
831C2×C4×D4—611no—
832C2×C4×D4—611no—
833C2×C4×D4—611no—
834C2×C4×D4—611no—
835C2×C4×D4—611no—
836C2×C4×D4—611no—
837C2×#117—611no—
838C2×#117—611no—
839C2×#117—611no—
840C2×#117C2×D6111yescharacteristic
841C22×C22⋊C4—611no—
842C22×C22⋊C4C2×D6111yescharacteristic
843C22×C22⋊C4C2×D6111yescharacteristic
844#391—611no—
845#391—611no—
846#391—611no—
847#390—611no—
848#390—611no—
849#390—611no—
850#390—611no—
851#390—611no—
852#390—611no—
853#390—611no—
854#390—611no—
855#390—611no—
856#389—611no—
857#389—611no—
858#389—611no—
859#389—611no—
860#389—611no—
861#389—611no—
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#388—611no—
885#388—611no—
886#388—611no—
887#388—611no—
888#388—611no—
889#388—611no—
890#388C2×D6111yescharacteristic
891#388C2×D6111yescharacteristic
892#388C2×D6111yescharacteristic
893#388C2×D6111yescharacteristic
894#387—611no—
895#387—611no—
896#387—611no—
897#387—611no—
898#387—611no—
899#387—611no—
900#387—611no—
901#387—611no—
902#387—611no—
903#387—611no—
904#387—611no—
905#387—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#386—611no—
918#386—611no—
919#386—611no—
920#385—611no—
921#385—611no—
922#385—611no—
923#385—611no—
924#385—611no—
925#385—611no—
926#385—611no—
927#385—611no—
928#385—611no—
929#385—611no—
930#385C2×D6111yescharacteristic
931#385C2×D6111yescharacteristic
932#384—611no—
933#383—611no—
934#383—611no—
935#382—611no—
936#381—611no—
937#381C2×D6111yescharacteristic
938#380—611no—
939#380—611no—
940#380—611no—
941#380C2×D6111yescharacteristic
942#379—611no—
943#379C2×D6111yescharacteristic
944C4×C4⋊C4—611no—
945C4×C4⋊C4—611no—
946C4×C4⋊C4—611no—
947C4×C4⋊C4—611no—
948C4×C4⋊C4—611no—
949C4×C4⋊C4—611no—
950C4×C4⋊C4—611no—
951C4×C4⋊C4—611no—
952C4×C22⋊C4—611no—
953C4×C22⋊C4—611no—
954C4×C22⋊C4—611no—
955C4×C22⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
966C4×C22⋊C4C2×D6111yescharacteristic
967C4×C22⋊C4C2×D6111yescharacteristic
968#376—611no—
969C2×#95—611no—
970C2×#95—611no—
971C43—611no—
972C61#3444611yescharacteristic, complemented, Sylow
973C25C22×D6111yescharacteristic
974C22×Q8—611no—
975C22×D4—611no—
976C22×D4—611no—
977C22×D4—611no—
978C22×D4—611no—
979C22×D4—611no—
980C22×D4—611no—
981C22×D4—611no—
982C23×C4—611no—
983C23×C4—611no—
984C23×C4—611no—
985C23×C4—611no—
986C23×C4—611no—
987C23×C4—611no—
988C23×C4—611no—
989C23×C4—611no—
990C23×C4C22×D6111yescharacteristic
991C23×C4C22×D6111yescharacteristic
992C23×C4C22×D6111yescharacteristic
993C23×C4C22×D6111yescharacteristic
994#126—618no—
995#126—618no—
996#124—618no—
997#124—618no—
998#123—618no—
999#123—618no—
1000C22⋊Q8—618no—
1001#121—618no—
1002#121—618no—
1003#121—618no—
1004#120—618no—
1005#120—618no—
1006C4×Q8—2442no—
1007C4×D4—618no—
1008C4×D4—618no—
1009C4×D4—2442no—
1010C4×D4—2442no—
1011C4×D4—2442no—
1012C4×D4—2442no—
1013C4×D4—2442no—
1014#117—42no—
1015#117—2442no—
1016#117—2442no—
1017#117—2442no—
1018C2×C4⋊C4—611no—
1019C2×C4⋊C4—611no—
1020C2×C4⋊C4—611no—
1021C2×C4⋊C4—611no—
1022C2×C4⋊C4—611no—
1023C2×C4⋊C4—611no—
1024C2×C4⋊C4—611no—
1025C2×C4⋊C4—611no—
1026C2×C4⋊C4—611no—
1027C2×C4⋊C4—611no—
1028C2×C4⋊C4—611no—
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⋊C4C22×D6111yescharacteristic
1041C2×C4⋊C4C22×D6111yescharacteristic
1042C2×C4⋊C4C22×D6111yescharacteristic
1043C2×C4⋊C4C22×D6111yescharacteristic
1044C2×C22⋊C4—42no—
1045C2×C22⋊C4—611no—
1046C2×C22⋊C4—611no—
1047C2×C22⋊C4—611no—
1048C2×C22⋊C4—611no—
1049C2×C22⋊C4—611no—
1050C2×C22⋊C4—611no—
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—2442no—
1078C2×C22⋊C4C4×D6118yescomplemented
1079C2×C22⋊C4C22×D6111yescharacteristic
1080C2×C22⋊C4C22×D6111yescharacteristic
1081C2×C22⋊C4C22×D6111yescharacteristic
1082C2×C22⋊C4C22×D6111yescharacteristic
1083C2×C22⋊C4C22×D6111yescharacteristic
1084C2×C22⋊C4C22×D6111yescharacteristic
1085C2×C22⋊C4C22×D6111yescharacteristic
1086C2×C22⋊C4C22×D6111yescharacteristic
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×C42—611no—
1094C2×C42—611no—
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×C42—611no—
1109C2×C42—611no—
1110C2×C42—611no—
1111C2×C42C22×D6111yescharacteristic
1112C2×C42C22×D6111yescharacteristic
1113C2×C42C22×D6111yescharacteristic
1114C2×C42C22×D6111yescharacteristic
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#95C22×D6111yescharacteristic
1148#95C22×D6111yescharacteristic
1149#95C22×D6111yescharacteristic
1150#95C22×D6111yescharacteristic
1151#95C22×D6111yescharacteristic
1152#95C22×D6111yescharacteristic
1153#95C22×D6111yescharacteristic
1154#95C22×D6111yescharacteristic
1155C24—41no—
1156C24—41no—
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24—611no—
1162C24—611no—
1163C24C2×C4×D6114yes—
1164C24C23×D6111yescharacteristic
1165C24C23×D6111yescharacteristic
1166C24C23×D6111yescharacteristic
1167C2×Q8—614no—
1168C2×Q8—2441no—
1169C2×Q8—2441no—
1170C2×D4—614no—
1171C2×D4—614no—
1172C2×D4—614no—
1173C2×D4—614no—
1174C2×D4—614no—
1175C2×D4—614no—
1176C2×D4—614no—
1177C2×D4—2441no—
1178C2×D4—2441no—
1179C2×D4—2441no—
1180C2×D4—2441no—
1181C2×D4—2441no—
1182C2×D4—2441no—
1183C2×D4—2441no—
1184C2×D4—2441no—
1185C2×D4—2441no—
1186C2×D4—2441no—
1187C2×D4—2441no—
1188C2×D4—2441no—
1189C2×D4—2441no—
1190C2×D4—2441no—
1191C22×C4—22no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—41no—
1200C22×C4—41no—
1201C22×C4—611no—
1202C22×C4—611no—
1203C22×C4—611no—
1204C22×C4—611no—
1205C22×C4—611no—
1206C22×C4—611no—
1207C22×C4—611no—
1208C22×C4—614no—
1209C22×C4—614no—
1210C22×C4—611no—
1211C22×C4—611no—
1212C22×C4—611no—
1213C22×C4—611no—
1214C22×C4—611no—
1215C22×C4—611no—
1216C22×C4—611no—
1217C22×C4—1222no—
1218C22×C4—1222no—
1219C22×C4—2441no—
1220C22×C4—2441no—
1221C22×C4—2441no—
1222C22×C4—2441no—
1223C22×C4—2441no—
1224C22×C4—2441no—
1225C22×C4—2441no—
1226C22×C4—2441no—
1227C22×C4—2441no—
1228C22×C4—2441no—
1229C22×C4—2441no—
1230C22×C4—2441no—
1231C22×C4—2441no—
1232C22×C4—2441no—
1233C22×C4—2441no—
1234C22×C4—2441no—
1235C22×C4—2441no—
1236C22×C4—2441no—
1237C22×C4—2441no—
1238C22×C4—2441no—
1239C22×C4C2×C4×D6114yes—
1240C22×C4C2×C4×D6114yes—
1241C22×C4C23×D6111yescharacteristic
1242C22×C4C23×D6111yescharacteristic
1243C22×C4C23×D6111yescharacteristic
1244C22×C4C23×D6111yescharacteristic
1245C22×C4C23×D6111yescharacteristic
1246C22×C4C23×D6111yescharacteristic
1247C22×C4C23×D6111yescharacteristic
1248C22×C4C23×D6111yescharacteristic
1249C22×C4C23×D6111yescharacteristic
1250C22×C4C23×D6111yescharacteristic
1251C22×C4C23×D6111yescharacteristic
1252C22×C4C23×D6111yescharacteristic
1253C4⋊C4—22no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—614no—
1258C4⋊C4—614no—
1259C4⋊C4—614no—
1260C4⋊C4—614no—
1261C4⋊C4—614no—
1262C4⋊C4—614no—
1263C4⋊C4—1222no—
1264C4⋊C4—1222no—
1265C4⋊C4—2441no—
1266C4⋊C4—2441no—
1267C4⋊C4—2441no—
1268C4⋊C4—2441no—
1269C4⋊C4—2441no—
1270C4⋊C4—2441no—
1271C4⋊C4—2441no—
1272C4⋊C4—2441no—
1273C4⋊C4—2441no—
1274C4⋊C4—2441no—
1275C4⋊C4—2441no—
1276C4⋊C4—2441no—
1277C4⋊C4—2441no—
1278C4⋊C4—2441no—
1279C22⋊C4—22no—
1280C22⋊C4—22no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—614no—
1290C22⋊C4—614no—
1291C22⋊C4—614no—
1292C22⋊C4—614no—
1293C22⋊C4—614no—
1294C22⋊C4—614no—
1295C22⋊C4—614no—
1296C22⋊C4—614no—
1297C22⋊C4—614no—
1298C22⋊C4—614no—
1299C22⋊C4—1222no—
1300C22⋊C4—1222no—
1301C22⋊C4—1222no—
1302C22⋊C4—1222no—
1303C22⋊C4—1222no—
1304C22⋊C4—2441no—
1305C22⋊C4—2441no—
1306C22⋊C4—2441no—
1307C22⋊C4—2441no—
1308C22⋊C4—2441no—
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⋊C4C2×C4×D6114yes—
1322C22⋊C4C2×C4×D6114yes—
1323C22⋊C4C2×C4×D6114yes—
1324C22⋊C4C2×C4×D6114yes—
1325C42—22no—
1326C42—41no—
1327C42—41no—
1328C42—41no—
1329C42—614no—
1330C42—614no—
1331C42—1222no—
1332C42—1222no—
1333C42—1222no—
1334C42—1222no—
1335C42—2441no—
1336C42—2441no—
1337C42—2441no—
1338C42—2441no—
1339C42—2441no—
1340C42—2441no—
1341C42—2441no—
1342C42—2441no—
1343C42—2441no—
1344C42—2441no—
1345C42—2441no—
1346C42—2441no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—44no—
1366C23—44no—
1367C23—44no—
1368C23—82no—
1369C23—82no—
1370C23—82no—
1371C23—82no—
1372C23—612no—
1373C23—612no—
1374C23—1221no—
1375C23—1221no—
1376C23—1221no—
1377C23—1221no—
1378C23—1221no—
1379C23—1221no—
1380C23—1221no—
1381C23—1221no—
1382C23—1221no—
1383C23—1221no—
1384C23—1221no—
1385C23—1221no—
1386C23C22×C4×D6112yes—
1387C23C22×C4×D6112yes—
1388C23C22×C4×D6112yes—
1389C23C24×D6111yescharacteristic
1390Q8—2444no—
1391D4—2444no—
1392D4—2444no—
1393D4—2444no—
1394D4—2444no—
1395D4—2444no—
1396D4—2444no—
1397D4—2444no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
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—44no—
1430C2×C4—44no—
1431C2×C4—82no—
1432C2×C4—82no—
1433C2×C4—612no—
1434C2×C4—612no—
1435C2×C4—612no—
1436C2×C4—612no—
1437C2×C4—612no—
1438C2×C4—612no—
1439C2×C4—612no—
1440C2×C4—1221no—
1441C2×C4—1221no—
1442C2×C4—1221no—
1443C2×C4—1221no—
1444C2×C4—1221no—
1445C2×C4—1221no—
1446C2×C4—1221no—
1447C2×C4—1221no—
1448C2×C4—1221no—
1449C2×C4—1221no—
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—4882no—
1476C2×C4—4882no—
1477C2×C4—4882no—
1478C2×C4—4882no—
1479C2×C4—4882no—
1480C2×C4—4882no—
1481C2×C4—2444no—
1482C2×C4—2444no—
1483C2×C4C22×C4×D6112yes—
1484C2×C4C22×C4×D6112yes—
1485C2×C4C22×C4×D6112yes—
1486C2×C4C22×C4×D6112yes—
1487C2×C4#1451982212yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—41no—
1498C22—41no—
1499C22—41no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—88no—
1510C22—1222no—
1511C22—1222no—
1512C22—1222no—
1513C22—1222no—
1514C22—1222no—
1515C22—1222no—
1516C22—2441no—
1517C22—2441no—
1518C22—2441no—
1519C22—2441no—
1520C22—2441no—
1521C22—2441no—
1522C22—2441no—
1523C22—2441no—
1524C22C23×C4×D6111yescharacteristic
1525C22H(5,𝔽2)×D6111yescharacteristic
1526C22C2×#1451982211yescharacteristic
1527C22#1684059711yescharacteristic
1528C22#1684059811yescharacteristic
1529C22#1684059811yescharacteristic
1530C22#1684059811yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—22no—
1536C4—41no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—41no—
1543C4—1222no—
1544C4—1222no—
1545C4—1222no—
1546C4—1222no—
1547C4—1222no—
1548C4—1222no—
1549C4—1222no—
1550C4—2441no—
1551C4—2441no—
1552C4—2441no—
1553C4—2441no—
1554C4—2441no—
1555C4—2441no—
1556C4—2441no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—2442no—
1561C2—2442no—
1562C2#2145902011yescharacteristic
1563C2#2145902311yescharacteristic
1564C2C4×#1451982211yescharacteristic
1565C2#2146017211yescharacteristic
1566C2#2146018611yescharacteristic
1567C2#2146035911yescharacteristic
1568C2#2146047711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingC61×#2342C2
socle, cosocleC23×C61C25
prime radicalC2×#16840350C2
hypercenter#2342D61
hypocenterC61#34446
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #2342

Complements

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

NH ≅ G/Ntype
2. #21449006C2semidirect
3. #21448973C2semidirect
4. #21448968C2semidirect
5. #21448958C2semidirect
6. #21448947C2semidirect
7. #21448946C2semidirect
8. #21448870C2semidirect
9. #21448858C2semidirect
10. #21448855C2semidirect
11. #21448814C2semidirect
12. #21448808C2semidirect
13. #21448798C2semidirect
14. #21448769C2semidirect
15. #21448756C2semidirect
16. #21448668C2semidirect
17. #21448633C2semidirect
18. #21448630C2semidirect
19. #21448596C2semidirect
20. #21448575C2semidirect
21. #21448525C2semidirect
22. #21448523C2semidirect
23. #21448507C2semidirect
24. #21448497C2semidirect
25. #21448477C2semidirect
26. #21448474C2semidirect
27. #21448448C2semidirect
28. C4×#14519770C2semidirect
29. #21448360C2semidirect
30. #21448278C2semidirect
31. C61×#2342C2semidirect
32. #16840350C4semidirect
45. C2×#14519742C22semidirect
46. C2×C4×D244C22semidirect
54. C2×#14519735C22semidirect
55. C2×#14519734C22semidirect
57. #16839667C22semidirect
58. #16839666C22semidirect
59. #16839666C22semidirect
60. #16839664C22semidirect
69. #16839660C22semidirect
70. #16839659C22semidirect
71. #16839659C22semidirect
72. #16839658C22semidirect
73. #16839657C22semidirect
74. #16839657C22semidirect
87. #16839653C22semidirect
88. #16839653C22semidirect
89. #16839652C22semidirect
90. #16839652C22semidirect
91. #16839652C22semidirect
92. #16839652C22semidirect
93. #16839651C22semidirect
94. #16839651C22semidirect
103. #16839649C22semidirect
104. #16839649C22semidirect
105. #16839649C22semidirect
106. #16839649C22semidirect
107. #16839647C22semidirect
108. #16839647C22semidirect
109. #16839647C22semidirect
110. #16839647C22semidirect
111. #16839646C22semidirect
112. #16839646C22semidirect
113. #16839644C22semidirect
114. #16839644C22semidirect
117. #16839640C22semidirect
118. #16839640C22semidirect
131. #16839636C22semidirect
132. #16839636C22semidirect
137. #16839633C22semidirect
138. #16839633C22semidirect
139. #16839631C22semidirect
140. #16839629C22semidirect
141. #16839629C22semidirect
142. #16839626C22semidirect
145. #16839621C22semidirect
146. #16839619C22semidirect
148. C4⋊C4×Dic61C22semidirect
149. C4⋊C4×Dic61C22semidirect
150. C4×#11758196C22semidirect
151. C4×#11758196C22semidirect
152. C4×#11758196C22semidirect
153. C4×#11758196C22semidirect
154. C4×#11758196C22semidirect
155. C4×C4⋊Dic61C22semidirect
160. C4×#11758198C22semidirect
164. #16839609C22semidirect
165. #16839609C22semidirect
166. #16839609C22semidirect
167. #16839609C22semidirect
168. #16839609C22semidirect
169. #16839607C22semidirect
170. #95×D61C22semidirect
171. #95×D61C22semidirect
172. C42×Dic61C22semidirect
204. #14519770C2×C4semidirect
205. #14519770C2×C4semidirect
206. #14519763C2×C4semidirect
207. #14519763C2×C4semidirect
208. #14519759C2×C4semidirect
209. #14519759C2×C4semidirect
210. #14519756C2×C4semidirect
211. #14519751C2×C4semidirect
212. #14519750C2×C4semidirect
213. #14519750C2×C4semidirect
214. #14519746C2×C4semidirect
215. #14519746C2×C4semidirect
220. C4×C22⋊D61C2×C4semidirect
221. C4×C22⋊D61C2×C4semidirect
343. C2×C22⋊C4×C61C2×C4semidirect
789. #2342D61semidirect
972. C61#34446semidirect
1078. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403502
#214490062
#214489732
#214489682
#214489582
#214489472
#214489462
#214488702
#214488582
#214488552
#214488142
#214488082
#214487982
#214487692
#214487562
#214486682
#214486332
#214486302
#214485962
#214485752
#214485252
#214485232
#214485072
#214484972
#214484772
#214484742
#214484482
C4×#145197702
#214483602
#214482782
C61×#23422
#3444661