Finite Group Databasebeta

← #29695443

Subgroups — #29695443

Order 15616.

1530 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840425C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic
3C22×#14519700C211yesmaximal, characteristic, complemented
4C2×#103×D61C211yesmaximal, characteristic, complemented
5C4⋊C4×C22⋊D61C211yesmaximal, characteristic
6#21446740C211yesmaximal, characteristic, complemented
7#21446619C211yesmaximal, characteristic, complemented
8#21446243C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic, complemented
10#21446125C211yesmaximal, characteristic, complemented
11#21445823C211yesmaximal, characteristic, complemented
12#21445755C211yesmaximal, characteristic, complemented
13#21445752C211yesmaximal, characteristic, complemented
14#21445638C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C23×Dic122C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840425—24no—
21#16840425C418yescomplemented
22C2×#14519776—21no—
23C2×#14519775C2211yescharacteristic
24C2×#14519757C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519754—21no—
27C2×#14519742C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737—21no—
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839825—24no—
33C2×#14519706C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519702C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700—24no—
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519700C2211yescharacteristic
45#103×D61—24no—
46C2×#14519689C2211yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48#16839657—21no—
49#16839635—21no—
50#16839633—21no—
51#16839631C2211yescharacteristic
52#16839622C2211yescharacteristic
53#16839619C2211yescharacteristic
54C4⋊C4×Dic61C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—22no—
65C22×Dic122—22no—
66C22×Dic122—21no—
67C22×Dic122—22no—
68C22×Dic122—21no—
69C22×Dic122—41no—
70C22×Dic122—41no—
71C22×Dic122C2×C414yescomplemented
72C22×Dic122C2311yescharacteristic
73C22×Dic122C2311yescharacteristic
74C2×Q8×D61—22no—
75C2×Q8×D61—22no—
76C2×Q8×D61—22no—
77C2×Q8×D61—41no—
78C2×Q8×D61—41no—
79C2×Q8×D61C2×C414yescomplemented
80C22×C22⋊D61D411yescharacteristic
81C23×Dic61—21no—
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C22×#92418—22no—
86C22×#92418—22no—
87C22×#92418—41no—
88C22×#92418C2311yescharacteristic
89C22×#92418C2311yescharacteristic
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—41no—
93#14519776—28no—
94#14519775—22no—
95#14519775C2×C414yescomplemented
96#14519757—22no—
97#14519757C2×C414yescomplemented
98#14519755—28no—
99#14519754—28no—
100#14519742—22no—
101#14519742C2×C414yescomplemented
102C4×C22⋊D61—44no—
103C4×C22⋊D61C2×C414yes—
104C4×C22⋊D61D414yes—
105#14519737—28no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196—21no—
112C2×#11758196—21no—
113C2×#11758196—21no—
114C2×#11758196—21no—
115C2×#11758196D411yescharacteristic
116C4⋊C4×D61—22no—
117C4⋊C4×D61—41no—
118C2×C22⋊Dic61—21no—
119C2×C22⋊Dic61D411yescharacteristic
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×C4×Dic61—21no—
124C2×C4×Dic61—21no—
125C2×C4×Dic61C2311yescharacteristic
126#14519706—22no—
127#14519702—22no—
128#14519702—22no—
129#14519702—41no—
130#14519702—41no—
131#14519701—22no—
132#14519701—41no—
133#14519700—22no—
134#14519700—22no—
135#14519700—22no—
136#14519700D414yescomplemented
137#14519689—22no—
138C8×Dic61—22no—
139#14519684—21no—
140#14519684—21no—
141#14519684—21no—
142C22×Q8×C61C2311yescharacteristic
143C23×C4×C61—21no—
144C23×C4×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22⋊Q8×C61—22no—
148C22⋊Q8×C61C2×C414yescomplemented
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—22no—
151C2×C4⋊C4×C61—21no—
152C2×C4⋊C4×C61—41no—
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157#103×C61—22no—
158#103×C61—41no—
159C22⋊C8×C61—22no—
160C24×C61C2×D411yescharacteristic
161C23×D61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C22×C412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—42no—
177C22×C4×C61—42no—
178C22×C4×C61—81no—
179C22×C4×C61C22×C412yes—
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D412yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61C22⋊C414yes—
184C2×C22⋊D61SD1614yes—
185C2×C22⋊D61Q1614yes—
186C22×Dic61—21no—
187C22×Dic61—24no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196Q8×D61—28no—
197Q8×D61—44no—
198Q8×D61—44no—
199Q8×D61—44no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—24no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×C4×D61—42no—
209C2×C4×D61—81no—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C2×D412yes—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—21no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—28no—
220C2×Dic122—24no—
221C2×Dic122—21no—
222C2×Dic122—24no—
223C2×Dic122—44no—
224C2×Dic122—44no—
225C2×Dic122—44no—
226C2×Dic122—42no—
227C2×Dic122—42no—
228C2×Dic122—42no—
229C2×Dic122—42no—
230C2×Dic122C22×C412yes—
231C2×Dic122C22×C412yes—
232C2×Dic122C2×D412yes—
233C2×Dic122#4112yes—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C4⋊C4×C61—24no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—42no—
246C4⋊C4×C61C22×C412yes—
247C4⋊C4×C61C2×D412yes—
248C22⋊C4×C61—24no—
249C22⋊Dic61—42no—
250C22⋊Dic61C22⋊C414yes—
251#11758198—24no—
252#11758198—42no—
253#11758198C22⋊C414yes—
254C4⋊Dic61—24no—
255C4⋊Dic61—21no—
256C4⋊Dic61—21no—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259#11758196—24no—
260#11758196—24no—
261#11758196—24no—
262#11758196—42no—
263#11758196—42no—
264#11758196—81no—
265#11758196C22⋊C414yes—
266C4×Dic61—24no—
267C4×Dic61—42no—
268C4×Dic61C22×C412yes—
269C4×Dic61C2×D412yes—
270C2×#92418—21no—
271C2×#92418—21no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—44no—
276C2×#92418C2×D412yes—
277C8×D61—44no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61C2×C22⋊C412yes—
283C23×C61C2×SD1612yes—
284C23×C61C2×Q1612yes—
285C23×C61C22×D411yescharacteristic
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61C2×C22⋊C412yes—
291C22×D61C2×SD1612yes—
292C22×D61C2×Q1612yes—
293Q8×C61—22no—
294Q8×C61—22no—
295Q8×C61—41no—
296Q8×C61—41no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—41no—
310C2×C4×C61—41no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—84no—
316C2×C4×C61C2×C22⋊C412yes—
317C2×C4×C61C23×C411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61H(5,𝔽2)11yescharacteristic
322C2×C4×C61H(5,𝔽2)11yescharacteristic
323C22⋊D61#103116yescomplemented
324C2×Dic61—22no—
325C2×Dic61—21no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—21no—
329C2×Dic61—21no—
330C2×Dic61—21no—
331C2×Dic61—22no—
332C2×Dic61—48no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61C2×C22⋊C412yes—
342C2×Dic61C2×C22⋊C412yes—
343C2×Dic61C2×C22⋊C412yes—
344C2×Dic61C2×SD1612yes—
345C2×Dic61C2×Q1612yes—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—48no—
351C4×D61—84no—
352Dic122—22no—
353Dic122—22no—
354Dic122—22no—
355Dic122—22no—
356Dic122—22no—
357Dic122—48no—
358Dic122—48no—
359Dic122—41no—
360Dic122—41no—
361Dic122C4×D414yescomplemented
362C8×C61—41no—
363C8×C61—41no—
364#92418—22no—
365#92418—41no—
366D4×#103—611nomaximal, Sylow
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61C2×#10314yescomplemented
374C22×C61C22×C22⋊C411yescharacteristic
375C22×C61D4211yescharacteristic
376C22×C61#54611yescharacteristic
377C22×C61C22×SD1611yescharacteristic
378C22×C61C22×Q1611yescharacteristic
379C22×C61#57711yescharacteristic
380C22×C61#57811yescharacteristic
381C2×D61—22no—
382C2×D61—22no—
383C2×D61—22no—
384C2×D61—22no—
385C2×D61—22no—
386C2×D61—22no—
387C2×D61C2×#10314yescomplemented
388C4×C61—22no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—42no—
392C4×C61—81no—
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#51811yescharacteristic
395C4×C61D4211yescharacteristic
396C4×C61#54611yescharacteristic
397Dic61—24no—
398Dic61—22no—
399Dic61—22no—
400Dic61—42no—
401Dic61—81no—
402Dic61—81no—
403Dic61C2×#10314yescomplemented
404C2×D4×Q8—611no—
405C2×C8×D4—611no—
406C22×#103—611no—
407C22×#103—611no—
408D4×C4⋊C4—611no—
409#1981—611no—
410#1956—611no—
411#1892—611no—
412#1892—611no—
413#1872—611no—
414#1872D6111yescharacteristic, complemented
415#1803—611no—
416#1787—611no—
417#1787—611no—
418C4×#103—611no—
419C2×C61—24no—
420C2×C61D4×C22⋊C411yescharacteristic
421C2×C61C22×#10311yescharacteristic
422C2×C61#289811yescharacteristic
423C2×C61D4×SD1611yescharacteristic
424C2×C61D4×Q1611yescharacteristic
425C2×C61#329811yescharacteristic
426C2×C61#329911yescharacteristic
427D61—24no—
428C23×Q8—611no—
429C23×Q8—611no—
430C23×C8—611no—
431C23×C8—611no—
432D4×Q8—618no—
433D4×Q8—1224no—
434C2×C4⋊Q8—611no—
435C2×C4⋊Q8—1221no—
436C2×C22⋊Q8—611no—
437C2×C22⋊Q8—1221no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8C2×D6111yescharacteristic
440C2×C4×Q8—611no—
441C2×C4×D4—611no—
442C2×C4×D4—1221no—
443C2×C4×D4—1221no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4C2×D6111yescharacteristic
446C8×D4—1224no—
447C2×C4⋊C8—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#103—611no—
451C2×#103—611no—
452C2×#103—611no—
453C2×#103—611no—
454C2×#103—611no—
455C2×#103—611no—
456C2×#103—611no—
457C2×#103—611no—
458C2×#103—1224no—
459C2×#103—1224no—
460C2×#103C2×D6111yescharacteristic
461C2×#103C2×D6111yescharacteristic
462C2×C22⋊C8—611no—
463C2×C22⋊C8C2×D6111yescharacteristic
464C2×C4×C8—611no—
465#389—1221no—
466#385—1221no—
467#385—1221no—
468#384—611no—
469#380—611no—
470#380—611no—
471C4×C4⋊C4—611no—
472#340—611no—
473#340—611no—
474#340C2×D6111yescharacteristic
475#340C2×D6111yescharacteristic
476C61D4×#10311yescharacteristic, complemented, Sylow
477C22×Q8—614no—
478C22×Q8—614no—
479C22×Q8—611no—
480C22×Q8—611no—
481C22×Q8—1221no—
482C22×Q8—1222no—
483C22×Q8—1222no—
484C22×Q8—1222no—
485C22×Q8—1221no—
486C22×Q8—1222no—
487C22×Q8—1222no—
488C22×Q8—1222no—
489C22×Q8—2441no—
490C22×Q8—2441no—
491C22×Q8—2441no—
492C22×Q8—2441no—
493C22×Q8C22×D6111yescharacteristic
494C22×D4—611no—
495C23×C4—21no—
496C23×C4—611no—
497C23×C4—1221no—
498C23×C4—1221no—
499C23×C4—1221no—
500C23×C4C22×D6111yescharacteristic
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—1222no—
504C22×C8—1222no—
505C22×C8—1222no—
506C22×C8—1222no—
507C22×C8—2441no—
508C22×C8—2441no—
509C22×C8C22×D6111yescharacteristic
510C22×C8C22×D6111yescharacteristic
511C4⋊Q8—614no—
512C4⋊Q8—1222no—
513C4⋊Q8—1228no—
514C22⋊Q8—22no—
515C22⋊Q8—614no—
516C22⋊Q8—1228no—
517C22⋊Q8—1228no—
518C22⋊Q8—1222no—
519C22⋊Q8C4×D6114yescomplemented
520C4×Q8—614no—
521C4×Q8—1222no—
522C4×D4—614no—
523C4×D4—614no—
524C4×D4—1228no—
525C4×D4—2444no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—611no—
531C2×C4⋊C4—611no—
532C2×C4⋊C4—611no—
533C2×C4⋊C4—1221no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C4⋊C4—1221no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4—1221no—
541C2×C4⋊C4—2441no—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C4⋊C4C22×D6111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C42—611no—
552C2×C42—1221no—
553C2×C42—1221no—
554C4⋊C8—1222no—
555#103—22no—
556#103—41no—
557#103—614no—
558#103—1222no—
559#103—1222no—
560#103—1222no—
561#103—1222no—
562#103—1222no—
563#103—1222no—
564#103—2441no—
565#103—2441no—
566#103—2441no—
567C22⋊C8—22no—
568C22⋊C8—1222no—
569C4×C8—1222no—
570#95—1221no—
571#95—1221no—
572#95—1221no—
573C24—611no—
574C24D4×D6111yescharacteristic
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—612no—
581C2×Q8—612no—
582C2×Q8—612no—
583C2×Q8—612no—
584C2×Q8—1224no—
585C2×Q8—1228no—
586C2×Q8—1221no—
587C2×Q8—1221no—
588C2×Q8—1221no—
589C2×Q8—1221no—
590C2×Q8—1224no—
591C2×Q8—1228no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×Q8—2442no—
597C2×Q8—2442no—
598C2×Q8—2444no—
599C2×Q8—2444no—
600C2×Q8—2444no—
601C2×Q8—2442no—
602C2×Q8—2442no—
603C2×Q8—2444no—
604C2×Q8—2444no—
605C2×Q8—2444no—
606C2×Q8C2×C4×D6112yes—
607C2×D4—614no—
608C2×D4—614no—
609C2×D4—614no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—1224no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1224no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—4881no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2442no—
641C22×C4—2442no—
642C22×C4—2442no—
643C22×C4C2×C4×D6112yes—
644C22×C4D4×D6112yes—
645C22×C4D4×D6111yescharacteristic
646C22×C4C23×D6111yescharacteristic
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—612no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—1221no—
657C2×C8—1221no—
658C2×C8—1221no—
659C2×C8—2444no—
660C2×C8—2444no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—614no—
668C4⋊C4—1224no—
669C4⋊C4—1224no—
670C4⋊C4—1224no—
671C4⋊C4—1224no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—4881no—
677C4⋊C4—2442no—
678C4⋊C4—2442no—
679C4⋊C4C2×C4×D6112yes—
680C4⋊C4D4×D6112yes—
681C22⋊C4—24no—
682C22⋊C4—614no—
683C22⋊C4—614no—
684C22⋊C4—1224no—
685C22⋊C4—2442no—
686C22⋊C4—2442no—
687C42—612no—
688C42—612no—
689C42—1224no—
690C42—2442no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—612no—
696C23—612no—
697C23—612no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1221no—
702C23C22⋊C4×D6112yes—
703C23SD16×D6112yes—
704C23Q16×D6112yes—
705C23C2×D4×D6111yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—41no—
709Q8—41no—
710Q8—614no—
711Q8—1222no—
712Q8—1222no—
713Q8—1222no—
714Q8—1222no—
715Q8—1222no—
716Q8—2448no—
717Q8—2448no—
718Q8—2441no—
719Q8—2441no—
720D4—6116no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—84no—
740C2×C4—612no—
741C2×C4—612no—
742C2×C4—612no—
743C2×C4—612no—
744C2×C4—612no—
745C2×C4—1222no—
746C2×C4—1221no—
747C2×C4—1221no—
748C2×C4—1221no—
749C2×C4—1222no—
750C2×C4—1221no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—4884no—
758C2×C4—2448no—
759C2×C4—2448no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4C22⋊C4×D6112yes—
769C2×C4C22×C4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C2×D4×D6111yescharacteristic
772C2×C4#41×D6111yescharacteristic
773C2×C4#1451982211yescharacteristic
774C2×C4#1451982311yescharacteristic
775C8—41no—
776C8—41no—
777C8—1222no—
778C8—2441no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—614no—
786C22—1222no—
787C22—1222no—
788C22—1222no—
789C22—1222no—
790C22—1222no—
791C22—1222no—
792C22#103×D6114yescomplemented
793C22C2×C22⋊C4×D6111yescharacteristic
794C22#1684039411yescharacteristic
795C22#1684040411yescharacteristic
796C22C2×SD16×D6111yescharacteristic
797C22C2×Q16×D6111yescharacteristic
798C22#1684057211yescharacteristic
799C22#1684057811yescharacteristic
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—614no—
806C4—1222no—
807C4—1222no—
808C4—1224no—
809C4—4881no—
810C4—4881no—
811C4—2442no—
812C4C4×D4×D6111yescharacteristic
813C4#1684023411yescharacteristic
814C4#1684039611yescharacteristic
815C4#1684040111yescharacteristic
816C2—24no—
817C2—1224no—
818C2#2144863711yescharacteristic
819C2C2×#103×D6111yescharacteristic
820C2#2145435011yescharacteristic
821C2#2145751311yescharacteristic
822C2#2145756411yescharacteristic
823C2#2145768211yescharacteristic
824C2#2145769311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
cosocleC22×C4×C61C24
hypercenter#1872D61
hypocenterC61D4×#103
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C22×#14519700C2semidirect
4. C2×#103×D61C2semidirect
6. #21446740C2semidirect
7. #21446619C2semidirect
8. #21446243C2semidirect
9. #21446241C2semidirect
10. #21446125C2semidirect
11. #21445823C2semidirect
12. #21445755C2semidirect
13. #21445752C2semidirect
14. #21445638C2semidirect
15. C61×#1872C2semidirect
21. #16840425C4semidirect
71. C22×Dic122C2×C4semidirect
79. C2×Q8×D61C2×C4semidirect
95. #14519775C2×C4semidirect
97. #14519757C2×C4semidirect
101. #14519742C2×C4semidirect
136. #14519700D4semidirect
148. C22⋊Q8×C61C2×C4semidirect
323. C22⋊D61#103semidirect
361. Dic122C4×D4semidirect
373. C22×C61C2×#103semidirect
387. C2×D61C2×#103semidirect
403. Dic61C2×#103semidirect
414. #1872D61semidirect
476. C61D4×#103semidirect
519. C22⋊Q8C4×D61semidirect
792. C22#103×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404252
C2×#168398252
C22×#145197002
C2×#103×D612
C4⋊C4×C22⋊D612
#214467402
#214466192
#214462432
#214462412
#214461252
#214458232
#214457552
#214457522
#214456382
C61×#18722
D4×#10361