Finite Group Databasebeta

← #30616073

Subgroups — #30616073

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462302C211yesmaximal, characteristic
2#21462259C211yesmaximal, characteristic, complemented
3#21461897C211yesmaximal, characteristic
4#21461896C211yesmaximal, characteristic
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461815C211yesmaximal, characteristic
8#21461815C211yesmaximal, characteristic
9#21461785C211yesmaximal, characteristic, complemented
10#21461783C211yesmaximal, characteristic, complemented
11#21461633C211yesmaximal, characteristic, complemented
12C4×#14519840C211yesmaximal, characteristic, complemented
13C4×#14519839C211yesmaximal, characteristic
14#21461539C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519846C2211yescharacteristic
19C2×#14519845C2211yescharacteristic
20C2×#14519840C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519839C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C4×D61⋊C8C2211yescharacteristic
25#16840714C2211yescharacteristic
26#16840714C2211yescharacteristic
27#16840713C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840712—21no—
30#16840712—21no—
31#16840705—21no—
32#16840704—21no—
33C4⋊C4×#6923—21no—
34C4⋊C4×#6923—21no—
35C4⋊C4×#6923C2211yescharacteristic
36C4⋊C4×#6923C2211yescharacteristic
37C4×C4⋊#6923—21no—
38C4×C4⋊#6923C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840698—21no—
41#16840698C2211yescharacteristic
42#16840636C2211yescharacteristic
43#16840636C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48(C2×#6923)⋊C8C2211yescharacteristic
49(C2×#6923)⋊C8C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52C2×SD16×D61C2211yescharacteristic
53C4×Q8×D61C2211yescharacteristic
54C4×D4×D61C2211yescharacteristic
55#16839865C411yescharacteristic, complemented
56#16839864C411yescharacteristic, complemented
57#16839863C411yescharacteristic, complemented
58#16839862C411yescharacteristic, complemented
59#16839861C411yescharacteristic, complemented
60#16839860C411yescharacteristic, complemented
61#16839859C411yescharacteristic, complemented
62#107×D61C2211yescharacteristic
63#103×D61C2211yescharacteristic
64#102×D61C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#440C411yescharacteristic, complemented
67C2×D61⋊C8C2311yescharacteristic
68C2×D61⋊C8C2311yescharacteristic
69Q8×#6923—22no—
70Q8×#6923—22no—
71Q8×#6923—22no—
72Q8×#6923—22no—
73C2×C4⋊#6923—21no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923C2311yescharacteristic
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923C2311yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93#14519846—22no—
94#14519845—22no—
95#14519840—22no—
96#14519840—22no—
97#14519839—22no—
98#14519839—22no—
99C4×#92420—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4D411yescharacteristic
108(C2×#6923)⋊C4D411yescharacteristic
109(C2×#6923)⋊C4D411yescharacteristic
110(C2×#6923)⋊C4D411yescharacteristic
111C2×Q8×D61C2311yescharacteristic
112C2×D4×D61C2311yescharacteristic
113C22×C4×D61—21no—
114C2×#11758190C2×C411yescharacteristic
115C2×#11758200C2×C411yescharacteristic
116C2×#11758201C2×C411yescharacteristic
117SD16×D61—22no—
118SD16×D61—22no—
119C2×C8×D61C2311yescharacteristic
120C2×C8×D61C2311yescharacteristic
121Q8×Dic61C2×C411yescharacteristic
122C4×Dic122—21no—
123C4×Dic122C2×C411yescharacteristic
124#14519742—21no—
125#14519742C2×C411yescharacteristic
126C4×D244C2×C411yescharacteristic
127D4×Dic61C2×C411yescharacteristic
128#14519739C2×C411yescharacteristic
129C4×C22⋊D61—21no—
130#14519737—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61C2311yescharacteristic
133C4⋊C4×D61C2311yescharacteristic
134C22⋊C4×D61—21no—
135C42×D61—21no—
136C42×D61C2311yescharacteristic
137#14519711C2×C411yescharacteristic
138#14519710C2×C411yescharacteristic
139#14519710C2×C411yescharacteristic
140#14519702C2×C411yescharacteristic
141#14519701C2×C411yescharacteristic
142#14519700C2×C411yescharacteristic
143#14519699C2×C411yescharacteristic
144#14519698C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519688C2×C411yescharacteristic
147#14519687C2×C411yescharacteristic
148#14519687C2×C411yescharacteristic
149C2×SD16×C61C2×C411yescharacteristic
150C4×Q8×C61C2×C411yescharacteristic
151C4×D4×C61C2×C411yescharacteristic
152#107×C61C2×C411yescharacteristic
153#103×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic
156C23×D61—21no—
157C22×#6923—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923C2×D411yescharacteristic
162C22×#6923C2×D411yescharacteristic
163C22×#6923C2×D411yescharacteristic
164C22×#6923C2×D411yescharacteristic
165C2×Q8×C61C22×C411yescharacteristic
166C2×D4×C61C22×C411yescharacteristic
167C22×C4×C61—21no—
168C2×C22⋊D61—21no—
169C22×Dic61—21no—
170Q8×D61—21no—
171Q8×D61—21no—
172Q8×D61#4112yes—
173Q8×D61#4112yes—
174D4×D61—21no—
175D4×D61—21no—
176D4×D61—21no—
177D4×D61—21no—
178C2×D244C22×C411yescharacteristic
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—81no—
185C2×C4×D61—81no—
186C2×C4×D61C2×D411yescharacteristic
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2411yescharacteristic
189C2×Dic122—21no—
190C2×Dic122C22×C411yescharacteristic
191C22⋊#6923—81no—
192C22⋊#6923—81no—
193C22⋊#6923—81no—
194C22⋊#6923—81no—
195C2×#92420—21no—
196C2×#92420—21no—
197C4⋊#6923—24no—
198C4⋊#6923—24no—
199C4⋊#6923—21no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—81no—
206C4⋊#6923—81no—
207C4⋊#6923#4112yes—
208C4⋊#6923#4112yes—
209C4×#6923—24no—
210C4×#6923—24no—
211C4×#6923—21no—
212C4×#6923—21no—
213C4×#6923—21no—
214C4×#6923—21no—
215C4×#6923—81no—
216C4×#6923—81no—
217C4×#6923—81no—
218C4×#6923—81no—
219D61⋊C8—21no—
220D61⋊C8—21no—
221D61⋊C8—21no—
222D61⋊C8—21no—
223SD16×C61—22no—
224C2×C8×C61C22×C411yescharacteristic
225C2×C8×C61C22×C411yescharacteristic
226C4⋊C4×C61—21no—
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C411yescharacteristic
229C22⋊C4×C61—21no—
230C42×C61—21no—
231C42×C61C22×C411yescharacteristic
232C22⋊Dic61—21no—
233#11758201—22no—
234#11758200—22no—
235#11758198—21no—
236#11758198—21no—
237C4⋊Dic61—21no—
238C4⋊Dic61C22×C411yescharacteristic
239C4⋊Dic61C22×C411yescharacteristic
240#11758196—21no—
241#11758196—21no—
242#11758196—21no—
243#11758196—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61C22×C411yescharacteristic
248C4×Dic61#4111yescharacteristic
249C4×Dic61#4111yescharacteristic
250C2×#92418C22×C411yescharacteristic
251C2×#92418C22×C411yescharacteristic
252#11758190—22no—
253C8×D61—21no—
254C8×D61—21no—
255C8×D61—21no—
256C8×D61—21no—
257C23×C61—21no—
258C22×D61—21no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61C22×D411yescharacteristic
266C2×#6923—21no—
267C2×#6923—21no—
268C2×#6923—21no—
269C2×#6923—21no—
270C2×#6923—22no—
271C2×#6923—22no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—21no—
278C2×#6923—21no—
279C2×#6923—21no—
280C2×#6923—41no—
281C2×#6923—41no—
282C2×#6923—41no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290Q8×C61—21no—
291Q8×C61#11712yes—
292D4×C61—21no—
293D4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—81no—
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C23×C411yescharacteristic
301C22⋊D61—41no—
302C22⋊D61—41no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—81no—
307C2×Dic61C4×D411yescharacteristic
308C2×Dic61C4×D411yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310D244—21no—
311D244—21no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—21no—
315C4×D61—21no—
316C4×D61—21no—
317C4×D61—21no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—81no—
323C4×D61—81no—
324C4×D61C2×#4111yescharacteristic
325C4×D61C2×#4111yescharacteristic
326C4×D61C2×#4111yescharacteristic
327C4×D61C2×#4111yescharacteristic
328Dic122—21no—
329Dic122—22no—
330Dic122—22no—
331Dic122#11712yes—
332#92420—41no—
333#92420—41no—
334C8×C61—21no—
335C8×C61—21no—
336#92418—21no—
337#92418—21no—
338#21128—611nomaximal, Sylow
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61C2×C4×D411yescharacteristic
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—81no—
347C2×D61—81no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61#52511yescharacteristic
351C2×D61#52511yescharacteristic
352C2×D61#57611yescharacteristic
353C2×D61#57711yescharacteristic
354C2×D61#57711yescharacteristic
355C2×D61#57811yescharacteristic
356#6923—41no—
357#6923—42no—
358#6923—41no—
359#6923—41no—
360#6923—42no—
361#6923—41no—
362#6923—81no—
363#6923—81no—
364C4×C61—21no—
365C4×C61—21no—
366C4×C61—22no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61C2×#11711yescharacteristic
370C4×C61C4×#4111yescharacteristic
371Dic61—21no—
372Dic61—21no—
373Dic61—22no—
374Dic61—41no—
375Dic61—41no—
376Dic61#52911yescharacteristic
377Dic61#52911yescharacteristic
378C2×#440—611no—
379#2319—611no—
380#2276—611no—
381#1926—611no—
382#1925—611no—
383#1921—611no—
384#1918—611no—
385#1880—611no—
386#1880—611no—
387#1865—611no—
388#1863—611no—
389#1776—611no—
390C4×#103—611no—
391C4×#102—611no—
392#1746—611no—
393C2×C61—81no—
394C2×C61#229011yescharacteristic
395C2×C61#294611yescharacteristic
396C2×C61#294711yescharacteristic
397D61—81no—
398D61#311911yescharacteristic
399D61#312111yescharacteristic
400D61#312411yescharacteristic
401D61#312611yescharacteristic
402C22×SD16—611no—
403C2×C4×Q8—611no—
404C2×C4×Q8—611no—
405C2×C4×Q8—611no—
406C2×C4×D4—611no—
407#440—611no—
408#440—611no—
409#440—611no—
410#440—611no—
411#440—611no—
412#440—611no—
413#440—611no—
414#440#692311yescharacteristic, complemented
415C2×#107—611no—
416C2×#107—611no—
417C2×#106—611no—
418C2×#103—611no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#97—611no—
425C2×C4×C8—611no—
426#390—611no—
427#390—611no—
428#389—611no—
429#389—611no—
430#388—1221no—
431#388—1221no—
432#381—1221no—
433#380—1221no—
434C4×C4⋊C4—611no—
435C4×C4⋊C4—611no—
436C4×C4⋊C4—611no—
437C4×C4⋊C4—611no—
438C4×C4⋊C4—1221no—
439C4×C4⋊C4—1221no—
440C4×C4⋊C4—1221no—
441#376—611no—
442#376—1221no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#336—611no—
450#336—611no—
451#336—611no—
452#336—611no—
453C61#2112811yescharacteristic, complemented, Sylow
454C22×Q8—611no—
455C22×D4—611no—
456C23×C4—1221no—
457C2×SD16—611no—
458C2×SD16—611no—
459C2×SD16—611no—
460C2×SD16—1222no—
461C2×SD16—1222no—
462C2×SD16C2×#692311yescharacteristic
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C4×Q8—611no—
468C4×Q8—611no—
469C4×Q8—611no—
470C4×Q8—1221no—
471C4×Q8—1221no—
472C4×Q8—1222no—
473C4×Q8—1222no—
474C4×Q8—1222no—
475C4×Q8—1222no—
476C4×Q8C2×#692311yescharacteristic
477C4×D4—611no—
478C4×D4—611no—
479C4×D4—611no—
480C4×D4—1221no—
481C4×D4—1221no—
482C4×D4C2×#692311yescharacteristic
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42—1221no—
509#107—611no—
510#107—611no—
511#107—611no—
512#107—1222no—
513#107C2×#692311yescharacteristic
514#106—1222no—
515#103—611no—
516#103—611no—
517#103—611no—
518#103—1222no—
519#103—1222no—
520#103C2×#692311yescharacteristic
521#102—611no—
522#102—611no—
523#102—611no—
524#102—1222no—
525#102—1222no—
526#102C2×#692311yescharacteristic
527#97—611no—
528#97—611no—
529#97—611no—
530#97C2×#692311yescharacteristic
531C4×C8—1221no—
532C4×C8—1221no—
533#95—611no—
534#95—611no—
535#95—611no—
536#95—611no—
537#95—1221no—
538#95—1221no—
539#95—1221no—
540#95—1221no—
541#95—1221no—
542#95—1221no—
543C24—1221no—
544C2×Q8—612no—
545C2×Q8—612no—
546C2×Q8—611no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8C22×#692311yescharacteristic
551C2×D4—611no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4C22×#692311yescharacteristic
558C22×C4—21no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—611no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—4881no—
577C22×C4—4881no—
578SD16—22no—
579SD16—1222no—
580SD16—1222no—
581SD16—1222no—
582C2×C8—611no—
583C2×C8—611no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8C22×#692311yescharacteristic
595C2×C8C22×#692311yescharacteristic
596C4⋊C4—21no—
597C4⋊C4—612no—
598C4⋊C4—612no—
599C4⋊C4—611no—
600C4⋊C4—611no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—1221no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1224no—
612C4⋊C4—1224no—
613C4⋊C4—1221no—
614C4⋊C4—4881no—
615C4⋊C4—4881no—
616C4⋊C4C22×#692311yescharacteristic
617C4⋊C4C22×#692311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—1221no—
620C22⋊C4—1221no—
621C22⋊C4—1221no—
622C22⋊C4—4881no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C22⋊C4—4881no—
626C42—21no—
627C42—611no—
628C42—611no—
629C42—611no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—1221no—
634C42—1221no—
635C42—1221no—
636C42—1224no—
637C42—1224no—
638C42—1221no—
639C42—4881no—
640C42—4881no—
641C42—4881no—
642C42—4881no—
643C42C22×#692311yescharacteristic
644C23—21no—
645C23—611no—
646C23—1221no—
647C23—2441no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653Q8—21no—
654Q8—612no—
655Q8—1222no—
656Q8—1222no—
657Q8—1221no—
658Q8#1451985612yes—
659D4—21no—
660D4—21no—
661D4—1221no—
662D4—1221no—
663D4—2441no—
664D4—2441no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—81no—
669C2×C4—611no—
670C2×C4—611no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—4881no—
700C2×C4—4881no—
701C2×C4—4881no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4D4×#692311yescharacteristic
717C2×C4D4×#692311yescharacteristic
718C2×C4C23×#692311yescharacteristic
719C8—21no—
720C8—21no—
721C8—1221no—
722C8—1221no—
723C8—2441no—
724C8—2441no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—611no—
729C22—611no—
730C22—611no—
731C22—611no—
732C22—611no—
733C22—611no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22C2×D4×#692311yescharacteristic
742C4—22no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—41no—
747C4—611no—
748C4—611no—
749C4—1222no—
750C4—1221no—
751C4—1221no—
752C4—4881no—
753C4—4881no—
754C4—2441no—
755C4—2441no—
756C4—2441no—
757C4—2441no—
758C4—2442no—
759C4—2442no—
760C4—2441no—
761C4—2441no—
762C4C2×#1451985611yescharacteristic
763C4#41×#692311yescharacteristic
764C2—81no—
765C2—611no—
766C2—611no—
767C2—611no—
768C2—611no—
769C2—4881no—
770C2#2146227311yescharacteristic
771C2#2146257611yescharacteristic
772C2#2146257711yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#440C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenter#440#6923
hypocenterC61#21128
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #21462259C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
9. #21461785C2semidirect
10. #21461783C2semidirect
11. #21461633C2semidirect
12. C4×#14519840C2semidirect
14. #21461539C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
414. #440#6923semidirect
453. C61#21128semidirect

Maximal subgroups

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

subgroupindex
#214623022
#214622592
#214618972
#214618962
#214618832
#214618802
#214618152
#214617852
#214617832
#214616332
C4×#145198402
C4×#145198392
#214615392
#440×D612
#2112861