Finite Group Databasebeta

← #29716348

Subgroups — #29716348

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455612C211yesmaximal, characteristic, complemented
2C4×#14519802C211yesmaximal, characteristic
3#21451020C211yesmaximal, characteristic, complemented
4#21447166C211yesmaximal, characteristic, complemented
5#21447161C211yesmaximal, characteristic, complemented
6#21446972C211yesmaximal, characteristic, complemented
7#21446972C211yesmaximal, characteristic, complemented
8#21446813C211yesmaximal, characteristic, complemented
9#21446764C211yesmaximal, characteristic, complemented
10#21446195C211yesmaximal, characteristic
11#21446195C211yesmaximal, characteristic
12#21446052C211yesmaximal, characteristic, complemented
13#21446045C211yesmaximal, characteristic, complemented
14#21445839C211yesmaximal, characteristic, complemented
15C61×#3504C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840059—21no—
19#16840059—21no—
20#16840049—21no—
21#16840039—21no—
22#16839872—21no—
23#16839860—21no—
24C4×#11758201—21no—
25C4×#11758199—21no—
26#16839805C2211yescharacteristic
27#16839805C2211yescharacteristic
28#16839805C2211yescharacteristic
29#16839786C2211yescharacteristic
30C2×#14519704C2211yescharacteristic
31C2×#14519704C2211yescharacteristic
32#16839766C2211yescharacteristic
33#16839766C2211yescharacteristic
34#16839766C2211yescharacteristic
35#16839763C2211yescharacteristic
36C4×#11758194C2211yescharacteristic
37#16839684—22no—
38#16839663C2211yescharacteristic
39#16839663C2211yescharacteristic
40#16839633—22no—
41#16839631C2211yescharacteristic
42#16839627C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839531C2211yescharacteristic
45#16839531C2211yescharacteristic
46#16839531C2211yescharacteristic
47#16839531C2211yescharacteristic
48#16839521C2211yescharacteristic
49#16839521C2211yescharacteristic
50#16839521C2211yescharacteristic
51#16839521C2211yescharacteristic
52#16839521C2211yescharacteristic
53#16839521C2211yescharacteristic
54C61×#557—21no—
55C61×#557—21no—
56C61×#554—21no—
57C61×#554—21no—
58C61×#554—22no—
59C61×#554—22no—
60C61×#544—21no—
61C61×#544—21no—
62C61×#544C2211yescharacteristic
63C61×#544C2211yescharacteristic
64C61×#533—21no—
65C61×#533C2211yescharacteristic
66C2×#125×C61—21no—
67C2×#125×C61C2211yescharacteristic
68C61×#520C2211yescharacteristic
69C61×#520C2211yescharacteristic
70C4×#41×C61C2211yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C4×D61—21no—
73#14519802—22no—
74#14519802Q814yescomplemented
75C2×#11758201—21no—
76C2×#11758199—21no—
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C4×D244—21no—
82C4×D244—21no—
83C4×D244—21no—
84C4×D244—21no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×#11758196—22no—
88C2×#11758198—21no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519710—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708—21no—
99C4⋊#92418—21no—
100C4⋊#92418—21no—
101#14519704—22no—
102#14519704—22no—
103#14519701—21no—
104#14519698—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—21no—
111#14519688—21no—
112C4×#92418—21no—
113#14519684—22no—
114#14519684—21no—
115C2×#41×C61C2311yescharacteristic
116C4⋊Q8×C61—22no—
117C4⋊Q8×C61—22no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61—21no—
122C4⋊Q8×C61D411yescharacteristic
123C4⋊Q8×C61D411yescharacteristic
124#125×C61—22no—
125#125×C61—22no—
126#125×C61—22no—
127#125×C61—22no—
128#125×C61—21no—
129#125×C61—21no—
130#125×C61—21no—
131#125×C61—21no—
132#125×C61—21no—
133#125×C61—21no—
134#125×C61—21no—
135#125×C61—21no—
136#125×C61D411yescharacteristic
137#125×C61D411yescharacteristic
138C22⋊Q8×C61—22no—
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—22no—
144C22⋊Q8×C61—21no—
145C22⋊Q8×C61—21no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61—22no—
148C4×Q8×C61—22no—
149C4×Q8×C61—22no—
150C4×Q8×C61—21no—
151C4×Q8×C61—21no—
152C4×Q8×C61—21no—
153C4×Q8×C61—21no—
154C4×Q8×C61D411yescharacteristic
155C4×Q8×C61D411yescharacteristic
156C4×D4×C61—21no—
157C4×D4×C61—21no—
158C4×D4×C61—21no—
159C4×D4×C61—21no—
160C4×D4×C61—22no—
161C4×D4×C61—22no—
162C4×D4×C61D411yescharacteristic
163C4×D4×C61D411yescharacteristic
164#117×C61—21no—
165#117×C61—21no—
166#117×C61—21no—
167#117×C61C2311yescharacteristic
168#117×C61C2311yescharacteristic
169#117×C61C2311yescharacteristic
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—22no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61D412yes—
175C2×C4⋊C4×C61D412yes—
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C4⋊C4×C61C2311yescharacteristic
178C2×C42×C61—21no—
179C2×C42×C61C2311yescharacteristic
180C23×D61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61C2×Q812yes—
184#41×C61#4112yes—
185C2×Q8×C61—22no—
186C2×Q8×C61—22no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61C2×D411yescharacteristic
190C2×D4×C61—21no—
191C2×D4×C61C2×D411yescharacteristic
192C22×C4×C61—21no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C2×D412yes—
198C22×C4×C61C2×D412yes—
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2411yescharacteristic
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244C2×Q812yes—
211C2×C4×D61—41no—
212C2×C4×D61—41no—
213C2×C4×D61—82no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61C2×D411yescharacteristic
239C4⋊C4×C61C2×D411yescharacteristic
240C4⋊C4×C61C2×D411yescharacteristic
241C4⋊C4×C61C2×D411yescharacteristic
242C4⋊C4×C61C2×D411yescharacteristic
243C4⋊C4×C61C2×D411yescharacteristic
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C42×C61—22no—
252C42×C61—22no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61C2×D411yescharacteristic
259C42×C61C2×D411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262#11758201—24no—
263#11758199—24no—
264#11758198—44no—
265#11758198—41no—
266#11758198—41no—
267#11758198—82no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—42no—
271#11758196—82no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—21no—
279#11758194—21no—
280#11758194—21no—
281#11758194—21no—
282#11758194—21no—
283#11758194C2×Q812yes—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C23×C61—21no—
289C23×C61C22×D411yescharacteristic
290C22×D61—22no—
291C22×D61—42no—
292C22×D61—42no—
293C22×D61—41no—
294C22×D61—41no—
295Q8×C61—21no—
296Q8×C61—81no—
297Q8×C61—81no—
298Q8×C61—82no—
299Q8×C61—82no—
300Q8×C61C22⋊Q812yes—
301D4×C61—22no—
302D4×C61—22no—
303D4×C61—21no—
304D4×C61C22⋊Q812yes—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—42no—
320C2×C4×C61—81no—
321C2×C4×C61—81no—
322C2×C4×C61—82no—
323C2×C4×C61—82no—
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
327C2×C4×C61#12011yescharacteristic
328C2×C4×C61C22×D411yescharacteristic
329C2×C4×C61C22×D411yescharacteristic
330C2×C4×C61C22×Q811yescharacteristic
331C2×C4×C61C2×#4111yescharacteristic
332C2×C4×C612−1+411yescharacteristic
333C2×C4×C612−1+411yescharacteristic
334C2×Dic61—22no—
335C2×Dic61—41no—
336C2×Dic61—41no—
337C2×Dic61—42no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340C2×Dic61—41no—
341C2×Dic61—41no—
342D244—22no—
343D244—22no—
344D244—41no—
345D244—41no—
346C4×D61—82no—
347C4×D61—82no—
348#92418—22no—
349#92418—41no—
350#92418—41no—
351#92418—41no—
352#24324—611nomaximal, Sylow
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61C2×#12011yescharacteristic
359C22×C61#54811yescharacteristic
360C22×C61D4×Q811yescharacteristic
361C2×D61—44no—
362C2×D61—42no—
363C2×D61—82no—
364C2×D61—81no—
365C2×D61—81no—
366C4×C61—22no—
367C4×C61—21no—
368C4×C61—21no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—42no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—42no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—41no—
379C4×C61C2×C22⋊Q811yescharacteristic
380C4×C61#53611yescharacteristic
381C4×C61#54811yescharacteristic
382C4×C61D4×Q811yescharacteristic
383Dic61—42no—
384Dic61—81no—
385Dic61—81no—
386#3504D6111yescharacteristic, complemented
387#3077—611no—
388C4×AGL(1,ℤ/8)—611no—
389#2566—611no—
390#2061—611no—
391#2060—611no—
392#2027—611no—
393#2027—611no—
394#1998—611no—
395#1986—611no—
396#1883—611no—
397#1883—611no—
398#1860—611no—
399#1859—611no—
400#1806—611no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—42no—
404C2×C61#240911yescharacteristic
405C2×C61#301811yescharacteristic
406C2×C61#302111yescharacteristic
407D61—82no—
408C2×AGL(1,ℤ/8)—611no—
409#557—21no—
410#557—21no—
411#554—21no—
412#554—21no—
413#554—22no—
414#554—22no—
415#544—21no—
416#544—21no—
417#544C2×D6111yescharacteristic
418#544C2×D6111yescharacteristic
419#533—21no—
420#533C2×D6111yescharacteristic
421C2×#125—21no—
422C2×#125C2×D6111yescharacteristic
423#520C2×D6111yescharacteristic
424#520C2×D6111yescharacteristic
425C4×#41C2×D6111yescharacteristic
426C2×C4×D4—611no—
427#478—1221no—
428#478—1221no—
429#476—1221no—
430#474—1221no—
431#442—1221no—
432#440—1221no—
433C4×SD16—1221no—
434C4×D8—1221no—
435#428—611no—
436#428—611no—
437#428—611no—
438#423—611no—
439C2×#104—611no—
440C2×#104—611no—
441#418—611no—
442#418—611no—
443#418—611no—
444#417—611no—
445C4×M16—611no—
446#396—1222no—
447#390—611no—
448#390—611no—
449#385—1222no—
450#384—611no—
451#382—611no—
452C4×C4⋊C4—611no—
453#343—611no—
454#343—611no—
455#343—611no—
456#343—611no—
457#339—611no—
458#339—611no—
459#339—611no—
460#339—611no—
461#339—611no—
462#339—611no—
463C61#2432411yescharacteristic, complemented, Sylow
464C2×#41C22×D6111yescharacteristic
465C22×D4—611no—
466C23×C4—1221no—
467AGL(1,ℤ/8)—614no—
468AGL(1,ℤ/8)—1222no—
469C2×SD16—1221no—
470C2×D8—1221no—
471C2×M16—611no—
472C2×M16—611no—
473C2×M16—611no—
474C2×M16—611no—
475C4⋊Q8—22no—
476C4⋊Q8—22no—
477C4⋊Q8—21no—
478C4⋊Q8—21no—
479C4⋊Q8—21no—
480C4⋊Q8—21no—
481C4⋊Q8C22⋊D6111yescharacteristic
482C4⋊Q8C22⋊D6111yescharacteristic
483#125—22no—
484#125—22no—
485#125—22no—
486#125—22no—
487#125—21no—
488#125—21no—
489#125—21no—
490#125—21no—
491#125—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125C22⋊D6111yescharacteristic
496#125C22⋊D6111yescharacteristic
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—22no—
502C22⋊Q8—22no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C4×Q8—22no—
508C4×Q8—22no—
509C4×Q8—21no—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C22⋊D6111yescharacteristic
514C4×Q8C22⋊D6111yescharacteristic
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—22no—
520C4×D4—22no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4C22⋊D6111yescharacteristic
526C4×D4C22⋊D6111yescharacteristic
527#117—21no—
528#117—21no—
529#117—21no—
530#117C22×D6111yescharacteristic
531#117C22×D6111yescharacteristic
532#117C22×D6111yescharacteristic
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—1222no—
539C2×C4⋊C4—1221no—
540C2×C4⋊C4C22⋊D6112yes—
541C2×C4⋊C4C22⋊D6112yes—
542C2×C4⋊C4C22×D6111yescharacteristic
543C2×C4⋊C4C22×D6111yescharacteristic
544C2×C22⋊C4—1222no—
545C2×C22⋊C4—1221no—
546C2×C22⋊C4—1222no—
547C2×C42—21no—
548C2×C42—611no—
549C2×C42—611no—
550C2×C42C22×D6111yescharacteristic
551#107—1221no—
552#107—1221no—
553#107—1221no—
554#106—1221no—
555#106—1221no—
556#106—1221no—
557C4⋊C8—1221no—
558C4⋊C8—1221no—
559#104—1222no—
560#104—1222no—
561#103—1221no—
562#102—1221no—
563#102—1221no—
564#102—1221no—
565#102—1221no—
566#102—1221no—
567#102—1221no—
568#102—1221no—
569#97—1221no—
570C4×C8—1221no—
571#95—1221no—
572#95—1222no—
573C24—1221no—
574#41—21no—
575#41—21no—
576#41Q8×D6112yes—
577#41#1175822612yes—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8C2×C22⋊D6111yescharacteristic
583C2×D4—21no—
584C2×D4—612no—
585C2×D4—1221no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4C2×C22⋊D6111yescharacteristic
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—4882no—
600C22×C4—2441no—
601C22×C4—2441no—
602C22×C4C2×C22⋊D6112yes—
603C22×C4C2×C22⋊D6112yes—
604C22×C4C2×C22⋊D6111yescharacteristic
605C22×C4C2×C22⋊D6111yescharacteristic
606C22×C4C23×D6111yescharacteristic
607SD16—1224no—
608D8—1224no—
609M16—612no—
610M16—1221no—
611M16—1221no—
612M16—1221no—
613M16—1221no—
614M16—1221no—
615M16—1221no—
616M16—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—1221no—
646C4⋊C4—1221no—
647C4⋊C4—4882no—
648C4⋊C4—2442no—
649C4⋊C4C2×C22⋊D6111yescharacteristic
650C4⋊C4C2×C22⋊D6111yescharacteristic
651C4⋊C4C2×C22⋊D6111yescharacteristic
652C4⋊C4C2×C22⋊D6111yescharacteristic
653C4⋊C4C2×C22⋊D6111yescharacteristic
654C4⋊C4C2×C22⋊D6111yescharacteristic
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—4882no—
663C22⋊C4—2444no—
664C22⋊C4—2441no—
665C22⋊C4—2441no—
666C42—22no—
667C42—22no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—1221no—
674C42—1221no—
675C42—1221no—
676C42—1221no—
677C42C2×C22⋊D6111yescharacteristic
678C42C2×C22⋊D6111yescharacteristic
679C42C2×C22⋊D6111yescharacteristic
680C42C2×C22⋊D6111yescharacteristic
681C23—21no—
682C23—1222no—
683C23—2442no—
684C23—2442no—
685C23—2441no—
686C23—2441no—
687C23C22×C22⋊D6111yescharacteristic
688Q8—21no—
689Q8—81no—
690Q8—81no—
691Q8—82no—
692Q8—82no—
693Q8#1451975312yes—
694D4—22no—
695D4—22no—
696D4—21no—
697D4—1222no—
698D4—1222no—
699D4—2441no—
700D4—2441no—
701D4#1451975312yes—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—1222no—
722C2×C4—4882no—
723C2×C4—4882no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4#1451974611yescharacteristic
732C2×C4#1451974611yescharacteristic
733C2×C4#1451974611yescharacteristic
734C2×C4#1451974611yescharacteristic
735C2×C4C22×C22⋊D6111yescharacteristic
736C2×C4C22×C22⋊D6111yescharacteristic
737C2×C4C2×Q8×D6111yescharacteristic
738C2×C4C2×#1175822611yescharacteristic
739C2×C4#1451982511yescharacteristic
740C2×C4#1451982511yescharacteristic
741C8—1222no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C22—21no—
746C22—21no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—4882no—
751C22—4881no—
752C22—4881no—
753C22—2444no—
754C22—2442no—
755C22C2×#1451974611yescharacteristic
756C22#1684042311yescharacteristic
757C22Q8×C22⋊D6111yescharacteristic
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—4881no—
772C4—4881no—
773C4—2442no—
774C4C2×#1451975311yescharacteristic
775C4#1684033611yescharacteristic
776C4#1684042311yescharacteristic
777C4Q8×C22⋊D6111yescharacteristic
778C2—21no—
779C2—21no—
780C2—42no—
781C2—4882no—
782C2#2144917811yescharacteristic
783C2#2145516811yescharacteristic
784C2#2145519111yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3504C2
socleC22×C61C2×#120
prime radicalC2×#14519802C22
hypercenter#3504D61
hypocenterC61#24324
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #21455612C2semidirect
3. #21451020C2semidirect
4. #21447166C2semidirect
5. #21447161C2semidirect
6. #21446972C2semidirect
7. #21446972C2semidirect
8. #21446813C2semidirect
9. #21446764C2semidirect
12. #21446052C2semidirect
13. #21446045C2semidirect
14. #21445839C2semidirect
15. C61×#3504C2semidirect
74. #14519802Q8semidirect
386. #3504D61semidirect
463. C61#24324semidirect

Maximal subgroups

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

subgroupindex
#214556122
C4×#145198022
#214510202
#214471662
#214471612
#214469722
#214468132
#214467642
#214461952
#214460522
#214460452
#214458392
C61×#35042
#2432461