Finite Group Databasebeta

← #29695475

Subgroups — #29695475

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840431C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3C2×#16839758C211yesmaximal, characteristic, complemented
4C2×#16839757C211yesmaximal, characteristic, complemented
5#21448763C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446245C211yesmaximal, characteristic, complemented
9#21446244C211yesmaximal, characteristic, complemented
10#21446139C211yesmaximal, characteristic, complemented
11#21446138C211yesmaximal, characteristic, complemented
12#21445822C211yesmaximal, characteristic, complemented
13#21445758C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840431—24no—
20#16840431C418yescomplemented
21C2×#14519773—21no—
22C2×#14519773C2211yescharacteristic
23C2×#14519751—21no—
24C2×#14519751C2211yescharacteristic
25C2×#14519748—21no—
26C2×#14519748C2211yescharacteristic
27C2×Q8×Dic61C2211yescharacteristic
28C2×C4×C22⋊D61—21no—
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519736C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32#16839825—24no—
33C2×#14519706C2211yescharacteristic
34#16839758—24no—
35#16839757—24no—
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46#16839662—21no—
47#16839656—21no—
48#16839651—21no—
49#16839631C2211yescharacteristic
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52#16839613—21no—
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×#102×C61C2211yescharacteristic
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C2×#11758226—22no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—41no—
68C2×#11758226—41no—
69C2×#11758226C2×C414yes—
70C22×D244—21no—
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C22×C4×D61—21no—
78C22×C4×D61C2311yescharacteristic
79C22×#92418—22no—
80C22×#92418—22no—
81C22×#92418—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—22no—
86C2×C8×D61—41no—
87#14519773—28no—
88#14519773—22no—
89#14519773C2×C414yes—
90#14519751—22no—
91#14519751—28no—
92#14519751C2×C414yes—
93#14519748—22no—
94#14519748—28no—
95#14519748C2×C414yes—
96Q8×Dic61—22no—
97Q8×Dic61C2×C414yes—
98C4×C22⋊D61—28no—
99C4×C22⋊D61C2×C414yes—
100C4×C22⋊D61D414yes—
101#14519736—22no—
102#14519736—41no—
103#14519735—22no—
104#14519735—41no—
105C2×C4⋊Dic61—21no—
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C2×#11758196—21no—
111C2×#11758196D411yescharacteristic
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61D411yescharacteristic
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—21no—
123C2×C4×Dic61C2311yescharacteristic
124#14519706—22no—
125#14519701—22no—
126#14519701D414yescomplemented
127#14519699—22no—
128#14519699—41no—
129#14519698—22no—
130#14519698—22no—
131#14519697—22no—
132#14519697—41no—
133#14519689—22no—
134C8×Dic61—22no—
135#14519684—21no—
136#14519684—21no—
137C2×#41×C61—22no—
138C2×#41×C61—22no—
139C2×#41×C61—22no—
140C2×#41×C61—41no—
141C2×#41×C61—41no—
142C2×#41×C61C2×C414yes—
143C22×Q8×C61C2311yescharacteristic
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61—21no—
147C23×C4×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153#103×C61—22no—
154#103×C61—22no—
155#102×C61—41no—
156#102×C61—41no—
157C22⋊C8×C61—22no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
161C23×D61—21no—
162C23×D61C2×D411yescharacteristic
163#41×C61—28no—
164#41×C61—44no—
165#41×C61—44no—
166#41×C61—44no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61C22×C412yes—
171C2×Q8×C61C2×D412yes—
172C2×Q8×C61#4112yes—
173C2×D4×C61—24no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—24no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61C22×C412yes—
193C22×C4×C61C2×D411yescharacteristic
194C22×C4×C61C2×D412yes—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—24no—
199C2×C22⋊D61—24no—
200C2×C22⋊D61—22no—
201C2×C22⋊D61—22no—
202C2×C22⋊D61—42no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—81no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61C22⋊C414yes—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61C2×D411yescharacteristic
215C22×Dic61C2×D411yescharacteristic
216C22×Dic61C2×D411yescharacteristic
217#11758226—28no—
218#11758226—44no—
219#11758226—44no—
220#11758226—44no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—24no—
226C2×D244—21no—
227C2×D244—42no—
228C2×D244—42no—
229C2×D244C22×C412yes—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—24no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×C4×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C22⋊C4×C61—81no—
250C22⋊Dic61—24no—
251C22⋊Dic61—42no—
252C22⋊Dic61C22⋊C414yes—
253#11758198—24no—
254#11758198—42no—
255#11758198—81no—
256#11758198C22⋊C414yes—
257C4⋊Dic61—21no—
258C4⋊Dic61—21no—
259C4⋊Dic61—24no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61C22×C412yes—
263C4⋊Dic61C2×D412yes—
264#11758196—42no—
265#11758196—81no—
266#11758196C22⋊C414yes—
267C4×Dic61—24no—
268C4×Dic61—42no—
269C4×Dic61—42no—
270C4×Dic61—42no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—44no—
279C2×#92418C2×D412yes—
280C8×D61—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61C2×C22⋊C412yes—
310Q8×C61—22no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61C4×D414yes—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—48no—
317D4×C61—41no—
318D4×C61—41no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—48no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61C2×C22⋊C412yes—
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C22⋊D61—28no—
343C22⋊D61—48no—
344C22⋊D61—84no—
345C22⋊D61—84no—
346C22⋊D61—84no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C412yes—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363C2×Dic61#13512yes—
364C2×Dic61#13512yes—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—41no—
369D244—41no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—48no—
375C8×C61—41no—
376C8×C61—41no—
377#92418—22no—
378#92418—41no—
379#22418—611nomaximal, Sylow
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61C22×C22⋊C411yescharacteristic
395C22×C61D4211yescharacteristic
396C22×C61#54611yescharacteristic
397C22×C61C2×#13511yescharacteristic
398C22×C61C2×#13511yescharacteristic
399C22×C61#57611yescharacteristic
400C22×C61#57711yescharacteristic
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C2×D61—81no—
415C4×C61—24no—
416C4×C61—22no—
417C4×C61—81no—
418C4×C61—81no—
419C4×C61C2×C4×D411yescharacteristic
420C4×C61#51811yescharacteristic
421C4×C61D4211yescharacteristic
422C4×C61#54611yescharacteristic
423Dic61—22no—
424Dic61—22no—
425Dic61—42no—
426Dic61—42no—
427Dic61—81no—
428Dic61#41614yescomplemented
429C2×#550—611no—
430C2×C8×D4—611no—
431C2×#416—611no—
432C2×#416—611no—
433#2354—611no—
434#1982—611no—
435#1957—611no—
436#1893—611no—
437#1893—611no—
438#1875—611no—
439#1875—611no—
440#1803—611no—
441#1788—611no—
442#1788D6111yescharacteristic, complemented
443C4×#103—611no—
444C2×C61—42no—
445C2×C61—82no—
446C2×C61D4×C22⋊C411yescharacteristic
447C2×C61C2×#41611yescharacteristic
448C2×C61#289711yescharacteristic
449C2×C61#328411yescharacteristic
450C2×C61#328711yescharacteristic
451C2×C61#330411yescharacteristic
452C2×C61#330511yescharacteristic
453D61—42no—
454D61—82no—
455C22×#41—611no—
456C22×#41C2×D6111yescharacteristic
457C23×C8—611no—
458C23×C8—611no—
459#550—618no—
460#550—1224no—
461C2×#127—611no—
462C2×#127—1221no—
463C2×#121—611no—
464C2×#121—611no—
465C2×#121—1221no—
466C2×#121—1221no—
467C2×C4×Q8—611no—
468C2×C4×D4—611no—
469C2×C4×D4—1221no—
470C2×#117—611no—
471C2×#117—611no—
472C8×D4—1224no—
473C2×C4⋊C8—611no—
474#416—1224no—
475#416—1224no—
476C2×#103—611no—
477C2×#103—611no—
478C2×#103C2×D6111yescharacteristic
479C2×#103C2×D6111yescharacteristic
480C2×#102—611no—
481C2×#102—611no—
482C2×#102—611no—
483C2×#102—611no—
484C2×#102—611no—
485C2×#102—611no—
486C2×#102C2×D6111yescharacteristic
487C2×#102C2×D6111yescharacteristic
488C2×C22⋊C8—611no—
489C2×C22⋊C8C2×D6111yescharacteristic
490C2×C4×C8—611no—
491#390—1221no—
492#388—1221no—
493#388—1221no—
494#384—611no—
495#380—611no—
496#380C2×D6111yescharacteristic
497C4×C4⋊C4—611no—
498C4×C4⋊C4—1221no—
499#340—611no—
500#340—611no—
501#340—611no—
502#340—611no—
503C61#2241811yescharacteristic, complemented, Sylow
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—614no—
510C2×#41—1222no—
511C2×#41—1222no—
512C2×#41—1222no—
513C2×#41—2441no—
514C2×#41—2441no—
515C2×#41C4×D6114yes—
516C22×Q8C22×D6111yescharacteristic
517C22×D4—21no—
518C22×D4—611no—
519C22×D4—611no—
520C22×D4—1221no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4—1221no—
525C22×D4C22×D6111yescharacteristic
526C23×C4—21no—
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4C22×D6111yescharacteristic
530C22×C8—611no—
531C22×C8—611no—
532C22×C8—1222no—
533C22×C8—1222no—
534C22×C8—1222no—
535C22×C8—1222no—
536C22×C8—2441no—
537C22×C8—2441no—
538C22×C8C22×D6111yescharacteristic
539C22×C8C22×D6111yescharacteristic
540#127—614no—
541#127—1222no—
542#127—1228no—
543#121—614no—
544#121—614no—
545#121—1228no—
546#121—1228no—
547#121—1222no—
548#121—1222no—
549C4×Q8—614no—
550C4×Q8—1222no—
551C4×D4—614no—
552C4×D4—614no—
553C4×D4—1228no—
554#117—1222no—
555#117—1222no—
556#117—2441no—
557#117—2441no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4C22×D6111yescharacteristic
566C2×C4⋊C4C22×D6111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—611no—
569C2×C22⋊C4—611no—
570C2×C22⋊C4—1221no—
571C2×C22⋊C4—1221no—
572C2×C22⋊C4—1221no—
573C2×C22⋊C4—1221no—
574C2×C22⋊C4—1221no—
575C2×C42—611no—
576C2×C42—1221no—
577C2×C42—1221no—
578C2×C42—1221no—
579C2×C42—1221no—
580C4⋊C8—1222no—
581#103—22no—
582#103—22no—
583#103—614no—
584#103—1222no—
585#102—41no—
586#102—41no—
587#102—1222no—
588#102—1222no—
589#102—1222no—
590#102—1222no—
591#102—2441no—
592#102—2441no—
593C22⋊C8—22no—
594C22⋊C8—1222no—
595C4×C8—1222no—
596#95—21no—
597#95—1221no—
598#95—1221no—
599C24—21no—
600C24—611no—
601C24—1221no—
602C24D4×D6111yescharacteristic
603#41—28no—
604#41—44no—
605#41—44no—
606#41—44no—
607#41—1228no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×C4×D6112yes—
615C2×Q8D4×D6112yes—
616C2×Q8#1175822412yes—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—614no—
626C2×D4—612no—
627C2×D4—1224no—
628C2×D4—1222no—
629C2×D4—1222no—
630C2×D4—1224no—
631C2×D4—1224no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—4881no—
640C2×D4—4881no—
641C2×D4—4881no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2442no—
649C2×D4C2×C4×D6112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—612no—
664C22×C4—612no—
665C22×C4—1224no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—2442no—
674C22×C4—2442no—
675C22×C4C2×C4×D6112yes—
676C22×C4D4×D6112yes—
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—612no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—2444no—
692C2×C8—2444no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—614no—
698C4⋊C4—612no—
699C4⋊C4—612no—
700C4⋊C4—1224no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—4881no—
706C4⋊C4—2442no—
707C22⋊C4—81no—
708C22⋊C4—614no—
709C22⋊C4—614no—
710C22⋊C4—1224no—
711C22⋊C4—1224no—
712C22⋊C4—4881no—
713C22⋊C4—2442no—
714C22⋊C4—2442no—
715C42—612no—
716C42—612no—
717C42—1224no—
718C42—2442no—
719C42—2442no—
720C42—2442no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—612no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1222no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23—2441no—
747C23—2441no—
748C23C22⋊C4×D6112yes—
749C23C2×D4×D6111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8#1451973714yes—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—41no—
758D4—41no—
759D4—1228no—
760D4—1222no—
761D4—1222no—
762D4—4884no—
763D4—4884no—
764D4—4884no—
765D4—2448no—
766D4—2448no—
767D4—2441no—
768D4—2441no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—612no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—612no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1221no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—2448no—
801C2×C4—2441no—
802C2×C4—2441no—
803C2×C4—2441no—
804C2×C4—2441no—
805C2×C4—2441no—
806C2×C4—2441no—
807C2×C4—2441no—
808C2×C4C22⋊C4×D6112yes—
809C2×C4C22×C4×D6111yescharacteristic
810C2×C4C2×D4×D6111yescharacteristic
811C2×C4C2×D4×D6111yescharacteristic
812C2×C4C2×#1175822411yescharacteristic
813C2×C4#1451982211yescharacteristic
814C2×C4#1451982211yescharacteristic
815C8—41no—
816C8—41no—
817C8—1222no—
818C8—2441no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—4881no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2441no—
844C22—2441no—
845C22—2441no—
846C22—2441no—
847C22C2×C22⋊C4×D6111yescharacteristic
848C22#1684039411yescharacteristic
849C22#1684039911yescharacteristic
850C22#135×D6111yescharacteristic
851C22#135×D6111yescharacteristic
852C22#1684056611yescharacteristic
853C22#1684057111yescharacteristic
854C4—22no—
855C4—24no—
856C4—81no—
857C4—81no—
858C4—614no—
859C4—1222no—
860C4—1222no—
861C4—4881no—
862C4—2442no—
863C4—2442no—
864C4C2×#1451973711yescharacteristic
865C4#1684023511yescharacteristic
866C4#1684039411yescharacteristic
867C4#1684039911yescharacteristic
868C2—42no—
869C2—82no—
870C2—4882no—
871C2—2442no—
872C2#2144863511yescharacteristic
873C2#416×D6111yescharacteristic
874C2#2145434311yescharacteristic
875C2#2145754211yescharacteristic
876C2#2145757211yescharacteristic
877C2#2145775111yescharacteristic
878C2#2145776211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1788C2
socleC23×C61C22×D4
prime radicalC2×#16840431C2
cosocleC22×C4×C61C24
hypercenter#1788D61
hypocenterC61#22418
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. C2×#16839758C2semidirect
4. C2×#16839757C2semidirect
5. #21448763C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446245C2semidirect
9. #21446244C2semidirect
10. #21446139C2semidirect
11. #21446138C2semidirect
12. #21445822C2semidirect
13. #21445758C2semidirect
14. #103×Dic61C2semidirect
15. C61×#1788C2semidirect
20. #16840431C4semidirect
126. #14519701D4semidirect
428. Dic61#416semidirect
442. #1788D61semidirect
503. C61#22418semidirect

Maximal subgroups

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

subgroupindex
C2×#168404312
C2×#168398252
C2×#168397582
C2×#168397572
#214487632
#214467442
#214466232
#214462452
#214462442
#214461392
#214461382
#214458222
#214457582
#103×Dic612
C61×#17882
#2241861