Finite Group Databasebeta

← #29717265

Subgroups — #29717265

Order 15616.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840013C211yesmaximal, characteristic, complemented
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839907C211yesmaximal, characteristic, complemented
4C2×#16839729C211yesmaximal, characteristic, complemented
5#21451543C211yesmaximal, characteristic, complemented
6#21447012C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446820C211yesmaximal, characteristic, complemented
9#21446815C211yesmaximal, characteristic, complemented
10#21446253C211yesmaximal, characteristic, complemented
11#21446248C211yesmaximal, characteristic, complemented
12#21446136C211yesmaximal, characteristic, complemented
13#21446012C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#537C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519751C2211yescharacteristic
23#16840013—24no—
24#16839993—24no—
25#16839907—24no—
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36#16839729—24no—
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839673—21no—
42#16839670—21no—
43#16839670—21no—
44#16839670—21no—
45#16839622C2211yescharacteristic
46#16839622C2211yescharacteristic
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C61×#537—24no—
55C61×#537—24no—
56C2×C22⋊Q8×C61—21no—
57C2×C22⋊Q8×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61—21no—
60C2×#121×C61—21no—
61C2×#121×C61—21no—
62C2×#121×C61C2211yescharacteristic
63C2×#121×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×D244C2311yescharacteristic
66C22×C22⋊D61—21no—
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C2×#11758201—22no—
70C2×#11758201—22no—
71C2×#11758201—41no—
72C2×#11758199—22no—
73C2×#11758199—22no—
74C2×#11758199—41no—
75C2×#11758194—22no—
76C2×#11758194—22no—
77C2×#11758194—41no—
78C22×#92418—22no—
79C22×#92418—22no—
80C22×#92418—41no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85#14519751—22no—
86#14519751—22no—
87#14519751—22no—
88#14519751—22no—
89#14519751—41no—
90#14519751—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100#14519708—22no—
101#14519708—22no—
102#14519701—22no—
103#14519701—22no—
104#14519701—41no—
105#14519698—22no—
106#14519698—22no—
107#14519698—41no—
108#14519697—22no—
109#14519697—22no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—22no—
113C22⋊#92418D414yescomplemented
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—22no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61—41no—
129C22×Q8×C61D411yescharacteristic
130C22×Q8×C61C2311yescharacteristic
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61D411yescharacteristic
136C22×D4×C61D411yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C23×C4×C61—21no—
139C23×C4×C61—21no—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C22⋊Q8×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61D414yescomplemented
148#121×C61—28no—
149#121×C61—28no—
150#121×C61—28no—
151#121×C61—22no—
152#121×C61—22no—
153#121×C61—22no—
154#121×C61D414yescomplemented
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61—21no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61—22no—
159C2×C4⋊C4×C61—22no—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61—21no—
164C2×C22⋊C4×C61—21no—
165C2×C22⋊C4×C61—21no—
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170C23×D61—21no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178#41×C61—44no—
179C2×Q8×C61—22no—
180C2×Q8×C61—22no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—41no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—22no—
190C2×D4×C61—22no—
191C2×D4×C61—22no—
192C2×D4×C61—22no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—41no—
203C2×D4×C61—41no—
204C2×D4×C61—41no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—81no—
208C2×D4×C61—81no—
209C2×D4×C61—81no—
210C2×D4×C61—81no—
211C2×D4×C61C2×D412yes—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—24no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—42no—
232C22×C4×C61—42no—
233C22×C4×C61—81no—
234C22×C4×C61—81no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61#4112yes—
242C22×C4×C61C2411yescharacteristic
243C2×C22⋊D61—42no—
244C2×C22⋊D61—42no—
245C2×C22⋊D61—42no—
246C2×C22⋊D61—81no—
247C2×C22⋊D61—81no—
248C2×C22⋊D61—81no—
249C2×C22⋊D61—81no—
250C2×C22⋊D61—81no—
251C2×C22⋊D61—81no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—24no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C2×D412yes—
267C4⋊C4×C61C2×D412yes—
268C22⋊C4×C61—24no—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—24no—
271C22⋊C4×C61—24no—
272C22⋊Dic61—81no—
273C22⋊Dic61—81no—
274C22⋊Dic61—81no—
275#11758201—44no—
276#11758199—44no—
277#11758198—42no—
278#11758198—42no—
279#11758198—42no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286#11758194—44no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—44no—
298C2×#92418C2×D412yes—
299C2×#92418C2×D412yes—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61#12012yes—
327C23×C61#12112yes—
328C23×C61C22×D411yescharacteristic
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—44no—
339Q8×C61—41no—
340Q8×C61—41no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—44no—
344D4×C61—44no—
345D4×C61—44no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—84no—
350D4×C61—84no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—21no—
354C2×C4×C61—21no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—48no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—84no—
381C2×C4×C61#12012yes—
382C2×C4×C61#12112yes—
383C2×C4×C61C22×D411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C2×C4×C61C2×#4111yescharacteristic
387C2×C4×C61H(5,𝔽2)11yescharacteristic
388C2×C4×C61H(5,𝔽2)11yescharacteristic
389C22⋊D61—84no—
390C22⋊D61—84no—
391C22⋊D61—84no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401D244—41no—
402D244—41no—
403D244—41no—
404D244—41no—
405#92418—22no—
406#92418—22no—
407#92418—41no—
408#92418—41no—
409#24397—611nomaximal, Sylow
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—41no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61C2×#12011yescharacteristic
439C22×C61C2×#12111yescharacteristic
440C22×C61#53411yescharacteristic
441C22×C61#57611yescharacteristic
442C22×C61#57711yescharacteristic
443C22×C61#57711yescharacteristic
444C22×C61#57711yescharacteristic
445C2×D61—81no—
446C2×D61—81no—
447C2×D61—81no—
448C2×D61—81no—
449C2×D61—81no—
450C2×D61—81no—
451C2×D61—81no—
452C4×C61—22no—
453C4×C61—22no—
454C4×C61—41no—
455C4×C61—42no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61D4211yescharacteristic
459C4×C61D4211yescharacteristic
460C4×C61#54611yescharacteristic
461C4×C61#54611yescharacteristic
462Dic61—81no—
463Dic61—81no—
464Dic61—81no—
465C2×#537D6111yescharacteristic, complemented
466C2×#469—611no—
467C2×#465—611no—
468C2×#449—611no—
469C2×#408—611no—
470#2615—611no—
471#2035—611no—
472#2034—611no—
473#2000—611no—
474#1999—611no—
475#1894—611no—
476#1893—611no—
477#1874—611no—
478#1853—611no—
479#1788—611no—
480C2×C61—42no—
481C2×C61—42no—
482C2×C61—81no—
483C2×C61—82no—
484C2×C61#241011yescharacteristic
485C2×C61#301011yescharacteristic
486C2×C61#301211yescharacteristic
487C2×C61#306011yescharacteristic
488C2×C61#306211yescharacteristic
489C2×C61#319811yescharacteristic
490C2×C61#320411yescharacteristic
491D61—161no—
492C22×#41C2×D6111yescharacteristic
493C22×#41C2×D6111yescharacteristic
494C22×SD16—611no—
495C22×D8—611no—
496C22×M16—611no—
497C23×C8—611no—
498#537—24no—
499#537—24no—
500C2×C22⋊Q8—21no—
501C2×C22⋊Q8C2×D6111yescharacteristic
502C2×C22⋊Q8C2×D6111yescharacteristic
503C2×#121—21no—
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—611no—
507C2×#121—611no—
508C2×#121—611no—
509C2×#121C2×D6111yescharacteristic
510C2×#121C2×D6111yescharacteristic
511C22×C4⋊C4C2×D6111yescharacteristic
512#469—1224no—
513#465—1224no—
514#449—1224no—
515C2×#106—611no—
516C2×#106—611no—
517C2×#103—611no—
518C2×#103—611no—
519C2×#103—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525#408—1224no—
526C2×C22⋊C8—611no—
527C2×C22⋊C8—611no—
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530#393—1221no—
531#392—1221no—
532#392—1221no—
533#392—1221no—
534#380—611no—
535#380—611no—
536#380—611no—
537#340—611no—
538#340—611no—
539#340—611no—
540#340—611no—
541C61#2439711yescharacteristic, complemented, Sylow
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C22⋊D6111yescharacteristic
555C22×Q8C22×D6111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—611no—
560C22×D4—1221no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4C22⋊D6111yescharacteristic
564C22×D4C22⋊D6111yescharacteristic
565C22×D4C22⋊D6111yescharacteristic
566C22×D4C22×D6111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C22×D6111yescharacteristic
570C23×C4C22×D6111yescharacteristic
571C23×C4C22×D6111yescharacteristic
572C2×SD16—1222no—
573C2×SD16—1222no—
574C2×SD16—2441no—
575C2×D8—1222no—
576C2×D8—1222no—
577C2×D8—2441no—
578C2×M16—1222no—
579C2×M16—1222no—
580C2×M16—2441no—
581C22×C8—611no—
582C22×C8—611no—
583C22×C8—611no—
584C22×C8—611no—
585C22×C8—1222no—
586C22×C8—1222no—
587C22×C8—2441no—
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8C22⋊D6114yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—1222no—
600#121—1222no—
601#121—1222no—
602#121—1222no—
603#121—2441no—
604#121—2441no—
605#121C22⋊D6114yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4C22×D6111yescharacteristic
615C2×C4⋊C4C22×D6111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626#106—1222no—
627#106—1222no—
628#103—1222no—
629#103—1222no—
630#103—2441no—
631#102—1222no—
632#102—1222no—
633#102—1222no—
634#102—1222no—
635#102—2441no—
636C22⋊C8—614no—
637C22⋊C8—1222no—
638C22⋊C8—1222no—
639C22⋊C8—1222no—
640#95—1221no—
641#95—1221no—
642#95—1221no—
643C24—21no—
644C24—1221no—
645C24C2×C22⋊D6111yescharacteristic
646C24C2×C22⋊D6111yescharacteristic
647C24C2×C22⋊D6111yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×C22⋊D6112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—41no—
680C2×D4—41no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—81no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—4881no—
695C2×D4—4881no—
696C2×D4—4881no—
697C2×D4—4881no—
698C2×D4—4881no—
699C2×D4—4881no—
700C2×D4—2442no—
701C2×D4—2442no—
702C2×D4—2442no—
703C2×D4C2×C22⋊D6112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—81no—
726C22×C4—81no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4D4×D6112yes—
731C22×C4#1175822412yes—
732C22×C4C2×C22⋊D6111yescharacteristic
733C22×C4C2×C22⋊D6112yes—
734C22×C4C2×C22⋊D6112yes—
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C23×D6111yescharacteristic
738SD16—2444no—
739D8—2444no—
740M16—2444no—
741C2×C8—612no—
742C2×C8—612no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—1221no—
752C2×C8—1221no—
753C2×C8—2444no—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—24no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4C2×C22⋊D6112yes—
766C4⋊C4C2×C22⋊D6112yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—4881no—
772C22⋊C4—4881no—
773C22⋊C4—4881no—
774C22⋊C4—2442no—
775C22⋊C4—2442no—
776C22⋊C4—2442no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—2441no—
804C23—2441no—
805C23—2441no—
806C23—2441no—
807C23—2441no—
808C23—2441no—
809C23—2441no—
810C23#1451974612yes—
811C23#1451974912yes—
812C23C22×C22⋊D6111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—84no—
827D4—84no—
828D4—4884no—
829D4—4884no—
830D4—4884no—
831D4—2441no—
832D4—2441no—
833D4—2441no—
834D4—2441no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—84no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4#1451974612yes—
875C2×C4#1451974912yes—
876C2×C4C2×D4×D6111yescharacteristic
877C2×C4C22×C22⋊D6111yescharacteristic
878C2×C4C22×C22⋊D6111yescharacteristic
879C2×C4C2×#1175822411yescharacteristic
880C2×C4#1451982211yescharacteristic
881C2×C4#1451982211yescharacteristic
882C8—1222no—
883C8—1222no—
884C8—2441no—
885C8—2441no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—4881no—
915C22—4881no—
916C22—4881no—
917C22—4881no—
918C22—4881no—
919C22—4881no—
920C22—4881no—
921C22C2×#1451974611yescharacteristic
922C22C2×#1451974911yescharacteristic
923C22#1684032111yescharacteristic
924C22#1684056511yescharacteristic
925C22#1684057011yescharacteristic
926C22#1684057011yescharacteristic
927C22#1684057311yescharacteristic
928C4—22no—
929C4—22no—
930C4—42no—
931C4—42no—
932C4—41no—
933C4—42no—
934C4—4881no—
935C4—4881no—
936C4—4881no—
937C4D4×C22⋊D6111yescharacteristic
938C4D4×C22⋊D6111yescharacteristic
939C4#1684040611yescharacteristic
940C4#1684040611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—9761no—
946C2#2144919311yescharacteristic
947C2#2145510511yescharacteristic
948C2#2145512311yescharacteristic
949C2#2145547811yescharacteristic
950C2#2145550111yescharacteristic
951C2#2145666511yescharacteristic
952C2#2145672511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#537C2
socleC23×C61C22×D4
hypercenterC2×#537D61
hypocenterC61#24397
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16840013C2semidirect
2. C2×#16839993C2semidirect
3. C2×#16839907C2semidirect
4. C2×#16839729C2semidirect
5. #21451543C2semidirect
6. #21447012C2semidirect
7. #21447005C2semidirect
8. #21446820C2semidirect
9. #21446815C2semidirect
10. #21446253C2semidirect
11. #21446248C2semidirect
12. #21446136C2semidirect
13. #21446012C2semidirect
14. #21445759C2semidirect
15. C2×C61×#537C2semidirect
113. C22⋊#92418D4semidirect
147. C22⋊Q8×C61D4semidirect
154. #121×C61D4semidirect
465. C2×#537D61semidirect
541. C61#24397semidirect
592. C22⋊Q8C22⋊D61semidirect
605. #121C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400132
C2×#168399932
C2×#168399072
C2×#168397292
#214515432
#214470122
#214470052
#214468202
#214468152
#214462532
#214462482
#214461362
#214460122
#214457592
C2×C61×#5372
#2439761