Finite Group Databasebeta

← #30621691

Subgroups — #30621691

Order 15616.

1306 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840796C211yesmaximal, characteristic, complemented
2C2×#16840791C211yesmaximal, characteristic, complemented
3C2×#16840733C211yesmaximal, characteristic, complemented
4C22×#14519834C211yesmaximal, characteristic, complemented
5#21461941C211yesmaximal, characteristic, complemented
6#21461894C211yesmaximal, characteristic, complemented
7#21461891C211yesmaximal, characteristic, complemented
8#21461799C211yesmaximal, characteristic, complemented
9#21461799C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461765C211yesmaximal, characteristic, complemented
12#21461762C211yesmaximal, characteristic, complemented
13#21461560C211yesmaximal, characteristic, complemented
14C22⋊C4×#92420C211yesmaximal, characteristic, complemented
15#21448320C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758213C2211yescharacteristic, complemented
19C23×#92420C2211yescharacteristic
20C23×#92420C2211yescharacteristic
21#16840796—24no—
22#16840791—24no—
23C2×C4⋊#92420C2211yescharacteristic, complemented
24C2×C4⋊#92420C2211yescharacteristic, complemented
25C2×C4⋊#92420C2211yescharacteristic, complemented
26#16840733—24no—
27C2×#14519834—24no—
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic, complemented
35C2×#14519834C2211yescharacteristic, complemented
36C2×#14519834C2211yescharacteristic, complemented
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×#14519832C2211yescharacteristic, complemented
40C2×C4×#92420C2211yescharacteristic, complemented
41C2×C4×#92420C2211yescharacteristic, complemented
42#16840628C2211yescharacteristic, complemented
43#16840628C2211yescharacteristic, complemented
44#16840628C2211yescharacteristic, complemented
45#16840628C2211yescharacteristic, complemented
46#16840628C2211yescharacteristic, complemented
47#16840628C2211yescharacteristic, complemented
48C23×C4×D61C2211yescharacteristic
49C2×#14519747C411yescharacteristic
50C2×#14519739C2211yescharacteristic
51C2×#14519739C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53#16839641C411yescharacteristic
54#16839640C411yescharacteristic
55#16839640C411yescharacteristic
56#16839633C411yescharacteristic
57#16839633C411yescharacteristic
58#16839617C411yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60#16839609C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#385C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—22no—
68C2×#11758213—22no—
69C2×#11758213—41no—
70C2×#11758213—41no—
71C2×#11758213—41no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—22no—
75C22×#92420—22no—
76C22×#92420—41no—
77C22×#92420—41no—
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85C22×#92420C2311yescharacteristic
86C4⋊#92420—22no—
87C4⋊#92420—22no—
88C4⋊#92420—41no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—22no—
93#14519834—22no—
94#14519834—22no—
95#14519834—22no—
96#14519834—41no—
97#14519834D414yescomplemented
98C22⋊#92420—22no—
99C22⋊#92420D414yescomplemented
100#14519832—22no—
101C4×#92420—22no—
102C4×#92420—41no—
103C24×D61C2×C411yescharacteristic
104C22×D244C2×C411yescharacteristic
105C22×D244C2×C411yescharacteristic
106C22×C22⋊D61C2×C411yescharacteristic
107C23×Dic61C2311yescharacteristic
108C22×C4×D61—22no—
109C22×C4×D61—22no—
110C22×C4×D61—22no—
111C22×C4×D61—22no—
112C22×C4×D61—41no—
113C22×C4×D61—41no—
114C22×C4×D61C2×C411yescharacteristic
115C22×C4×D61C2×C411yescharacteristic
116C22×C4×D61C2311yescharacteristic
117C22×C4×D61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119#14519747—24no—
120#14519739—22no—
121#14519739—22no—
122#14519739—41no—
123#14519739—41no—
124#14519737—22no—
125#14519737—22no—
126C2×#11758196C2×C411yescharacteristic
127C2×C22⋊Dic61C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×#11758198C2×C411yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C2×C4×Dic61C2311yescharacteristic
139C2×C4×Dic61C2311yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144C23×C4×C61C2×C411yescharacteristic
145C2×C4⋊C4×C61C2×C411yescharacteristic
146C2×C4⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61C2×C411yescharacteristic
149#95×C61C2×C411yescharacteristic
150#95×C61C2×C411yescharacteristic
151C24×C61C22×C411yescharacteristic
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—41no—
158C23×D61—41no—
159C23×D61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C23×D61C22×C411yescharacteristic
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—41no—
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—22no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C2×D412yes—
183C22×Dic61#4112yes—
184C22×Dic61C2411yescharacteristic
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—41no—
190C2×D244—41no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—22no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214C2×C4×D61—44no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61C2×D412yes—
218C2×C4×D61#4112yes—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—21no—
231C2×#92420—21no—
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—44no—
240C2×#92420—44no—
241C2×#92420C2×D412yes—
242C2×#92420C2×D412yes—
243C2×#92420C2×D412yes—
244C2×#92420C2×D412yes—
245#11758213—44no—
246#11758213—44no—
247#11758213—44no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—41no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61M1614yescomplemented
252C22⋊Dic61—22no—
253#11758198—22no—
254#11758198—22no—
255#11758198—22no—
256#11758198—22no—
257#11758198—22no—
258#11758198—22no—
259#11758198—41no—
260#11758198—41no—
261#11758198—41no—
262#11758196—22no—
263C4×Dic61—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61C4×D412yes—
274C23×C61C2×M1612yes—
275C23×C61#13112yes—
276C23×C61C23×C411yescharacteristic
277C22×D61—28no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61—21no—
287C22×D61—21no—
288C22×D61—21no—
289C22×D61—21no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—21no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61—44no—
303C22×D61C4×D412yes—
304C22×D61#13112yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—44no—
321C2×C4×C61C4×D412yes—
322C2×C4×C61C2×M1612yes—
323C2×C4×C61C2×M1612yes—
324C22⋊D61—44no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61C4×D412yes—
341C2×Dic61C22×D411yescharacteristic
342C2×Dic61C22×D411yescharacteristic
343C2×Dic61C2×#4111yescharacteristic
344C2×Dic61C2×#4111yescharacteristic
345C2×Dic61H(5,𝔽2)11yescharacteristic
346C2×Dic61H(5,𝔽2)11yescharacteristic
347D244—44no—
348D244—44no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—44no—
354C4×D61—44no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363#92420—22no—
364#92420—22no—
365#92420—22no—
366#92420—22no—
367#92420—41no—
368#92420—41no—
369#92420—41no—
370#92420—41no—
371#22848—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61#43614yescomplemented
379C22×C61C2×C4×D411yescharacteristic
380C22×C61C2×C4×D411yescharacteristic
381C22×C61#51811yescharacteristic
382C22×C61C22×M1611yescharacteristic
383C22×C61C2×#13111yescharacteristic
384C22×C61C2×#13111yescharacteristic
385C22×C61#56811yescharacteristic
386C2×D61—22no—
387C2×D61—22no—
388C2×D61—22no—
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—416no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—22no—
409C4×C61—22no—
410C4×C61—22no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—41no—
414Dic61—22no—
415Dic61—41no—
416Dic61—41no—
417Dic61—41no—
418Dic61D4211yescharacteristic
419Dic61#54611yescharacteristic
420Dic61#54611yescharacteristic
421Dic61#55111yescharacteristic
422C2×#436—611no—
423C2×#435—611no—
424C2×#407—611no—
425C22×C22⋊C8—611no—
426C4×#120—611no—
427#1954—611no—
428#1924—611no—
429#1923—611no—
430#1870—611no—
431#1870—611no—
432#1869—611no—
433#1851—611no—
434#1850—611no—
435#1753—611no—
436C8×C22⋊C4—611no—
437C2×C61—24no—
438C2×C61#235811yescharacteristic
439C2×C61C2×#43611yescharacteristic
440C2×C61#292911yescharacteristic
441C2×C61#293311yescharacteristic
442C2×C61D4×M1611yescharacteristic
443C2×C61#297411yescharacteristic
444C2×C61#297611yescharacteristic
445D61—42no—
446D61—42no—
447D61—81no—
448C24×C4—611no—
449C22×M16—611no—
450C22×M16—611no—
451C22×M16—611no—
452C23×C8—611no—
453C23×C8—611no—
454C2×#120—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458#436—1224no—
459#435—1224no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×C4⋊C8—611no—
463#407—1224no—
464C2×C22⋊C8—611no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475C2×C22⋊C8—1224no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C2×C4×C8—611no—
479#386—611no—
480#386—611no—
481#386—611no—
482#385—611no—
483#385—611no—
484#385#692311yescharacteristic
485#379—611no—
486C4×C22⋊C4—611no—
487C4×C22⋊C4—611no—
488C4×C22⋊C4—611no—
489#336—611no—
490#336—611no—
491#336—611no—
492#336—611no—
493#336—611no—
494#336—611no—
495C61#2284811yescharacteristic, complemented, Sylow
496C25—611no—
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—1222no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—2441no—
511C23×C4—2441no—
512C23×C4C2×#692311yescharacteristic
513C2×M16—1222no—
514C2×M16—1222no—
515C2×M16—1222no—
516C2×M16—1222no—
517C2×M16—1222no—
518C2×M16—1222no—
519C2×M16—2441no—
520C2×M16—2441no—
521C2×M16—2441no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—1222no—
532C22×C8—1222no—
533C22×C8—1222no—
534C22×C8—2441no—
535C22×C8—2441no—
536#120—1224no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—2441no—
542C4×D4—2441no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4C2×#692311yescharacteristic
545C2×C4⋊C4C2×#692311yescharacteristic
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4—611no—
554C2×C22⋊C4—611no—
555C2×C22⋊C4—611no—
556C2×C22⋊C4C2×#692311yescharacteristic
557C2×C22⋊C4C2×#692311yescharacteristic
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C4⋊C8—1222no—
562C4⋊C8—1222no—
563C4⋊C8—2441no—
564C22⋊C8—614no—
565C22⋊C8—614no—
566C22⋊C8—1222no—
567C22⋊C8—1222no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—2441no—
575#97—1222no—
576C4×C8—1222no—
577C4×C8—2441no—
578#95—611no—
579#95—611no—
580#95—611no—
581#95—611no—
582#95C2×#692311yescharacteristic
583#95C2×#692311yescharacteristic
584C24—611no—
585C24—611no—
586C24—611no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24—1222no—
591C24—1222no—
592C24—2441no—
593C24—2441no—
594C24C22×#692311yescharacteristic
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—2441no—
603C2×D4—2441no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—611no—
608C22×C4—612no—
609C22×C4—612no—
610C22×C4—611no—
611C22×C4—612no—
612C22×C4—612no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1222no—
640C22×C4—2441no—
641C22×C4—2441no—
642C22×C4—2444no—
643C22×C4—2444no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4C22×#692311yescharacteristic
647C22×C4C22×#692311yescharacteristic
648C22×C4C22×#692311yescharacteristic
649C22×C4C22×#692311yescharacteristic
650C22×C4C22×#692311yescharacteristic
651C22×C4C22×#692311yescharacteristic
652M16—2444no—
653M16—2444no—
654M16—2444no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—612no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—2444no—
680C2×C8—2444no—
681C4⋊C4—22no—
682C4⋊C4—41no—
683C4⋊C4—1222no—
684C22⋊C4—22no—
685C22⋊C4—1222no—
686C22⋊C4—1222no—
687C22⋊C4—1222no—
688C22⋊C4—1222no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—2441no—
693C22⋊C4—2441no—
694C22⋊C4—2441no—
695C22⋊C4#1175821314yescomplemented
696C42—1221no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42—1221no—
701C42—1221no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—612no—
707C23—612no—
708C23—1228no—
709C23—1221no—
710C23—1221no—
711C23—1221no—
712C23—1221no—
713C23—1221no—
714C23—1221no—
715C23—1221no—
716C23—1221no—
717C23—1221no—
718C23—1221no—
719C23—1221no—
720C23—1221no—
721C23—1221no—
722C23—1221no—
723C23—1221no—
724C23—1221no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—2444no—
729C23—2444no—
730C23—2444no—
731C23—2444no—
732C23—2444no—
733C23—2444no—
734C23D4×#692312yes—
735C23C2×#1175821312yes—
736C23#1451986512yes—
737C23C23×#692311yescharacteristic
738D4—2444no—
739D4—2444no—
740D4—2444no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—44no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—611no—
760C2×C4—611no—
761C2×C4—611no—
762C2×C4—611no—
763C2×C4—612no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—2444no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2444no—
793C2×C4D4×#692312yes—
794C2×C4C2×#1175821312yes—
795C2×C4C2×#1175821312yes—
796C8—1222no—
797C8—1222no—
798C8—1222no—
799C8—1222no—
800C8—2441no—
801C8—2441no—
802C8—2441no—
803C8—2441no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—1222no—
811C22—1222no—
812C22—1222no—
813C22—1222no—
814C22—1222no—
815C22—1222no—
816C22—24416no—
817C22—2441no—
818C22—2441no—
819C22—2441no—
820C22—2441no—
821C22—2441no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22#1684079614yescomplemented
833C22C2×D4×#692311yescharacteristic
834C22C2×D4×#692311yescharacteristic
835C22#1684082911yescharacteristic
836C22C22×#1175821311yescharacteristic
837C22D61⋊#13111yescharacteristic
838C22C2×#1451986511yescharacteristic
839C22#1684084111yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—611no—
847C4—611no—
848C4—611no—
849C4—611no—
850C4—1222no—
851C4—2441no—
852C4—2441no—
853C4—2441no—
854C2—24no—
855C2—4881no—
856C2—2442no—
857C2—2442no—
858C2#2146234111yescharacteristic
859C2C2×#1684079611yescharacteristic
860C2#2146253511yescharacteristic
861C2#2146255311yescharacteristic
862C2D4×#1175821311yescharacteristic
863C2#2146267911yescharacteristic
864C2#2146268911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#385C4
prime radicalC2×#14519747C4
cosocleC22×Dic61C24
hypercenter#385#6923
hypocenterC61#22848
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#16840796C2semidirect
2. C2×#16840791C2semidirect
3. C2×#16840733C2semidirect
4. C22×#14519834C2semidirect
5. #21461941C2semidirect
6. #21461894C2semidirect
7. #21461891C2semidirect
8. #21461799C2semidirect
9. #21461799C2semidirect
10. #21461794C2semidirect
11. #21461765C2semidirect
12. #21461762C2semidirect
13. #21461560C2semidirect
14. C22⋊C4×#92420C2semidirect
18. C22×#11758213C22semidirect
23. C2×C4⋊#92420C22semidirect
24. C2×C4⋊#92420C22semidirect
25. C2×C4⋊#92420C22semidirect
34. C2×#14519834C22semidirect
35. C2×#14519834C22semidirect
36. C2×#14519834C22semidirect
39. C2×#14519832C22semidirect
40. C2×C4×#92420C22semidirect
41. C2×C4×#92420C22semidirect
42. #16840628C22semidirect
43. #16840628C22semidirect
44. #16840628C22semidirect
45. #16840628C22semidirect
46. #16840628C22semidirect
47. #16840628C22semidirect
97. #14519834D4semidirect
99. C22⋊#92420D4semidirect
251. C22⋊C4×C61M16semidirect
378. C22×C61#436semidirect
495. C61#22848semidirect
695. C22⋊C4#11758213semidirect
832. C22#16840796semidirect

Maximal subgroups

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

subgroupindex
C2×#168407962
C2×#168407912
C2×#168407332
C22×#145198342
#214619412
#214618942
#214618912
#214617992
#214617942
#214617652
#214617622
#214615602
C22⋊C4×#924202
#214483202
#2284861