Finite Group Databasebeta

← #29715694

Subgroups — #29715694

Order 15616.

1478 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519797C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839989C211yesmaximal, characteristic, complemented
4C2×D4×#92418C211yesmaximal, characteristic, complemented
5#21449164C211yesmaximal, characteristic, complemented
6#21447141C211yesmaximal, characteristic, complemented
7#21447129C211yesmaximal, characteristic, complemented
8#21446827C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446676C211yesmaximal, characteristic, complemented
11#21446672C211yesmaximal, characteristic, complemented
12#21445842C211yesmaximal, characteristic, complemented
13#21445759C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2407C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519797—24no—
18C2×#14519797—24no—
19C2×#14519797—24no—
20C22×#11758202C2211yescharacteristic
21C22×#11758200C2211yescharacteristic
22C22×#11758201C2211yescharacteristic
23C22×#11758199C2211yescharacteristic
24C23×#92418C2211yescharacteristic
25C23×#92418C2211yescharacteristic
26C2×#14519756C2211yescharacteristic
27C2×#14519751C2211yescharacteristic
28#16839993—24no—
29#16839989—24no—
30D4×#92418—24no—
31C2×#14519708C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C4×#92418C2211yescharacteristic
45#16839677—21no—
46#16839670—21no—
47#16839668C2211yescharacteristic
48#16839664C2211yescharacteristic
49#16839638—21no—
50#16839633—21no—
51#16839622C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C61×#394—21no—
59C61×#392—21no—
60C61×#391C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C61×#386—21no—
63C61×#385—21no—
64C61×#380C2211yescharacteristic
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C4×D61—21no—
76#14519797—232no—
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202—22no—
80C2×#11758200—22no—
81C2×#11758200—22no—
82C2×#11758200D414yescomplemented
83C2×#11758201—22no—
84C2×#11758201—22no—
85C2×#11758201D414yescomplemented
86C2×#11758199—22no—
87C2×#11758199—22no—
88C2×#11758199—22no—
89C22×#92418—22no—
90C22×#92418—22no—
91C22×#92418—22no—
92C22×#92418—22no—
93C22×#92418—22no—
94C22×#92418D414yescomplemented
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99#14519756—22no—
100#14519756—41no—
101#14519751—22no—
102#14519751—41no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×C22⋊Dic61—21no—
107C2×C22⋊Dic61—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111#14519708—22no—
112#14519708—22no—
113C4⋊#92418—22no—
114#14519701—22no—
115#14519701—41no—
116#14519700—22no—
117#14519700—41no—
118#14519698—22no—
119#14519698—41no—
120#14519697—22no—
121#14519697—41no—
122C22⋊#92418—22no—
123C22⋊#92418—22no—
124C4×#92418—22no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128C2×#41×C61—22no—
129C2×#41×C61—22no—
130C2×#41×C61—22no—
131C2×#41×C61—22no—
132C2×#41×C61—41no—
133C2×#41×C61—41no—
134C22×Q8×C61C2311yescharacteristic
135C22×D4×C61—21no—
136C22×D4×C61—21no—
137C22×D4×C61D411yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—41no—
144#121×C61—22no—
145#121×C61—41no—
146C4×D4×C61—22no—
147C4×D4×C61—22no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61D411yescharacteristic
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61D411yescharacteristic
158C2×C22⋊C4×C61D411yescharacteristic
159C2×C42×C61C2311yescharacteristic
160#95×C61—21no—
161#95×C61—21no—
162#95×C61—21no—
163C24×C61—21no—
164C24×C61C2×D411yescharacteristic
165C24×C61C2×D411yescharacteristic
166C23×D61—21no—
167#41×C61—28no—
168#41×C61—44no—
169#41×C61—44no—
170#41×C61—44no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61C2×D412yes—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—81no—
191C2×D4×C61C2×D412yes—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—42no—
206C22×C4×C61—42no—
207C22×C4×C61—42no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61#4112yes—
214C22×C4×C61C2411yescharacteristic
215C2×C22⋊D61—42no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C2×C22⋊D61—42no—
219C2×C22⋊D61—42no—
220C2×C22⋊D61—81no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224#11758222—28no—
225#11758222—44no—
226#11758222—44no—
227#11758222—44no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244C2×D412yes—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—42no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122C2×D412yes—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—42no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—81no—
255C22⋊C4×C61—81no—
256C42×C61—21no—
257C42×C61—21no—
258C22⋊Dic61—42no—
259C22⋊Dic61—81no—
260#11758202—28no—
261#11758201—28no—
262#11758200—28no—
263#11758199—28no—
264#11758198—42no—
265#11758198—42no—
266#11758198—81no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271#11758196—42no—
272C2×#92418—21no—
273C2×#92418—21no—
274C2×#92418—28no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—44no—
282C2×#92418C2×D412yes—
283C2×#92418C2×D412yes—
284C2×#92418C2×D412yes—
285C2×#92418C2×D412yes—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61#12112yes—
306C23×C61#13512yescomplemented
307C23×C61C22×D411yescharacteristic
308C22×D61—22no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315Q8×C61—22no—
316Q8×C61—22no—
317Q8×C61—41no—
318Q8×C61—41no—
319D4×C61—28no—
320D4×C61—22no—
321D4×C61—22no—
322D4×C61—48no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—84no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—48no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61#12112yes—
355C2×C4×C61#13512yescomplemented
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C22⋊D61—48no—
363C22⋊D61—84no—
364C2×Dic61—22no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373D244—22no—
374D244—22no—
375D244—41no—
376D244—41no—
377C4×D61—48no—
378Dic122—22no—
379Dic122—22no—
380Dic122—41no—
381Dic122—41no—
382#92418—22no—
383#92418—41no—
384#92418—41no—
385#92418#12014yes—
386#24265—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61C2×#12111yescharacteristic
409C22×C61D4211yescharacteristic
410C22×C61D4211yescharacteristic
411C22×C61C2×#13511yescharacteristic
412C22×C61C2×#13511yescharacteristic
413C22×C61#57711yescharacteristic
414C22×C61#57711yescharacteristic
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C2×D61—81no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—41no—
425C4×C61—42no—
426C4×C61—41no—
427C4×C61—81no—
428C4×C61—81no—
429C4×C61C2×#12011yescharacteristic
430C4×C61#53511yescharacteristic
431C4×C61#54611yescharacteristic
432C4×C61#54611yescharacteristic
433Dic61—42no—
434Dic61—81no—
435Dic61—81no—
436C22×#135—611no—
437C2×#465—611no—
438C2×#465—611no—
439C2×C8×D4—611no—
440#2407—611no—
441#2407D6111yescharacteristic, complemented
442#2056—611no—
443#2054—611no—
444#2001—611no—
445#1999—611no—
446#1968—611no—
447#1968—611no—
448#1807—611no—
449#1788—611no—
450#1788—611no—
451C2×C61—42no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61#240811yescharacteristic
455C2×C61#305011yescharacteristic
456C2×C61#306011yescharacteristic
457C2×C61#328211yescharacteristic
458C2×C61#328211yescharacteristic
459C2×C61#328411yescharacteristic
460C2×C61#328411yescharacteristic
461D61—82no—
462C22×#41—611no—
463C22×#41C2×D6111yescharacteristic
464C2×#135—1224no—
465C2×#135—1224no—
466C2×#135—1224no—
467C22×Q16—611no—
468C22×SD16—611no—
469C22×SD16—611no—
470C22×D8—611no—
471C23×C8—611no—
472C23×C8—611no—
473C2×C22⋊Q8—611no—
474C2×C22⋊Q8C2×D6111yescharacteristic
475C2×#121—611no—
476C2×#121C2×D6111yescharacteristic
477C2×C4×D4C2×D6111yescharacteristic
478#465—1224no—
479#465—1224no—
480C8×D4—1224no—
481C2×#106—611no—
482C2×#106—611no—
483C2×C4⋊C8—611no—
484C2×#103—611no—
485C2×#103—611no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×C22⋊C8—611no—
493C2×C22⋊C8—611no—
494C2×C4×C8—611no—
495#394—21no—
496#394—1221no—
497#392—21no—
498#392—1221no—
499#391—611no—
500#391C2×D6111yescharacteristic
501#390—611no—
502#390C2×D6111yescharacteristic
503#386—21no—
504#386—1221no—
505#385—21no—
506#385—1221no—
507#380—611no—
508#380C2×D6111yescharacteristic
509#340—611no—
510#340—611no—
511C61#2426511yescharacteristic, complemented, Sylow
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—41no—
517C2×#41—41no—
518C2×#41—1222no—
519C2×#41—1222no—
520C2×#41—1222no—
521C2×#41—1222no—
522C2×#41—2441no—
523C2×#41—2441no—
524C22×Q8—611no—
525C22×Q8C22×D6111yescharacteristic
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—611no—
529C22×D4—1221no—
530C22×D4—1221no—
531C22×D4C22⋊D6111yescharacteristic
532C22×D4C22×D6111yescharacteristic
533C23×C4—21no—
534C23×C4—1221no—
535C23×C4C22×D6111yescharacteristic
536C23×C4C22×D6111yescharacteristic
537#135—12232no—
538C2×Q16—1222no—
539C2×Q16—1222no—
540C2×Q16—1222no—
541C2×SD16—614no—
542C2×SD16—614no—
543C2×SD16—1222no—
544C2×SD16—1222no—
545C2×SD16—1222no—
546C2×SD16—1222no—
547C2×D8—1222no—
548C2×D8—1222no—
549C2×D8—1222no—
550C22×C8—611no—
551C22×C8—614no—
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—611no—
555C22×C8—1222no—
556C22×C8—1222no—
557C22×C8—1222no—
558C22×C8—1222no—
559C22×C8—1222no—
560C22⋊Q8—22no—
561C22⋊Q8—41no—
562C22⋊Q8—1222no—
563C22⋊Q8—2441no—
564#121—22no—
565#121—41no—
566#121—1222no—
567#121—2441no—
568C4×D4—22no—
569C4×D4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4C22⋊D6111yescharacteristic
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C4⋊C4C22×D6111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4C22⋊D6111yescharacteristic
588C2×C22⋊C4C22⋊D6111yescharacteristic
589C2×C42C22×D6111yescharacteristic
590#106—1222no—
591#106—1222no—
592C4⋊C8—1222no—
593#103—1222no—
594#103—1222no—
595#103—2441no—
596#103—2441no—
597#102—1222no—
598#102—1222no—
599#102—2441no—
600#102—2441no—
601C22⋊C8—1222no—
602C22⋊C8—1222no—
603C4×C8—1222no—
604#95—21no—
605#95—21no—
606#95—21no—
607#95—1221no—
608#95—1221no—
609#95—1221no—
610C24—21no—
611C24—1221no—
612C24C2×C22⋊D6111yescharacteristic
613C24C2×C22⋊D6111yescharacteristic
614#41—28no—
615#41—44no—
616#41—44no—
617#41—44no—
618#41—1228no—
619#41—2444no—
620#41—2444no—
621#41—2444no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—612no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—1221no—
633C2×Q8D4×D6112yes—
634C2×D4—22no—
635C2×D4—22no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—612no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—4881no—
655C2×D4—2442no—
656C2×D4—2442no—
657C2×D4—2442no—
658C2×D4—2442no—
659C2×D4—2442no—
660C2×D4D4×D6112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4D4×D6112yes—
684C22×C4#1175822412yes—
685C22×C4C2×C22⋊D6111yescharacteristic
686C22×C4C2×C22⋊D6111yescharacteristic
687C22×C4C2×C22⋊D6111yescharacteristic
688C22×C4C2×C22⋊D6111yescharacteristic
689C22×C4C23×D6111yescharacteristic
690Q16—1228no—
691SD16—1228no—
692SD16—1228no—
693D8—1228no—
694C2×C8—612no—
695C2×C8—612no—
696C2×C8—612no—
697C2×C8—612no—
698C2×C8—1228no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—2444no—
708C4⋊C4—22no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—42no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—2442no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—81no—
725C22⋊C4—81no—
726C22⋊C4—4881no—
727C22⋊C4—4881no—
728C22⋊C4—2442no—
729C22⋊C4—2442no—
730C22⋊C4—2442no—
731C42—21no—
732C42—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—1222no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23#1451974912yes—
760C23#1451979712yescomplemented
761C23C22×C22⋊D6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766Q8—1222no—
767Q8—1222no—
768Q8—2441no—
769Q8—2441no—
770D4—28no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4—1222no—
778D4—1222no—
779D4—4884no—
780D4—2448no—
781D4—2441no—
782D4—2441no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—1222no—
812C2×C4—2448no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4#1451974912yes—
822C2×C4#1451979712yescomplemented
823C2×C4C2×D4×D6111yescharacteristic
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×#1175822411yescharacteristic
827C2×C4#1451982211yescharacteristic
828C2×C4#1451982211yescharacteristic
829C8—614no—
830C8—1222no—
831C8—2441no—
832C8—2441no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—4881no—
855C22—4881no—
856C22—4881no—
857C22—4881no—
858C22—2442no—
859C22—2442no—
860C22—2442no—
861C22C2×#1451974911yescharacteristic
862C22D4×C22⋊D6111yescharacteristic
863C22D4×C22⋊D6111yescharacteristic
864C22C2×#1451979711yescharacteristic
865C22C2×#1451979711yescharacteristic
866C22#1684057011yescharacteristic
867C22#1684057311yescharacteristic
868C4—22no—
869C4—22no—
870C4—41no—
871C4—41no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—4881no—
876C4—4881no—
877C4—2442no—
878C4#120×D6111yescharacteristic
879C4#1684032711yescharacteristic
880C4#1684039911yescharacteristic
881C4#1684039911yescharacteristic
882C2—42no—
883C2—42no—
884C2—82no—
885C2—4882no—
886C2#2144917211yescharacteristic
887C2#2145539711yescharacteristic
888C2#2145547811yescharacteristic
889C2#2145752211yescharacteristic
890C2#2145752711yescharacteristic
891C2#2145754511yescharacteristic
892C2#2145754911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2407C2
socleC23×C61C22×D4
hypercenter#2407D61
hypocenterC61#24265
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C22×#14519797C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839989C2semidirect
4. C2×D4×#92418C2semidirect
5. #21449164C2semidirect
6. #21447141C2semidirect
7. #21447129C2semidirect
8. #21446827C2semidirect
9. #21446815C2semidirect
10. #21446676C2semidirect
11. #21446672C2semidirect
12. #21445842C2semidirect
13. #21445759C2semidirect
14. #21445757C2semidirect
15. C61×#2407C2semidirect
82. C2×#11758200D4semidirect
85. C2×#11758201D4semidirect
94. C22×#92418D4semidirect
306. C23×C61#135semidirect
355. C2×C4×C61#135semidirect
441. #2407D61semidirect
511. C61#24265semidirect
760. C23#14519797semidirect
822. C2×C4#14519797semidirect

Maximal subgroups

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

subgroupindex
C22×#145197972
C2×#168399932
C2×#168399892
C2×D4×#924182
#214491642
#214471412
#214471292
#214468272
#214468152
#214466762
#214466722
#214458422
#214457592
#214457572
C61×#24072
#2426561