Finite Group Databasebeta

← #30616069

Subgroups — #30616069

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462276C211yesmaximal, characteristic
2C4×Q8×#6923C211yesmaximal, 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
12#21461591C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic
14#21461535C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×Q8×#6923C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×#14519856—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25#16840721C2211yescharacteristic
26#16840714C2211yescharacteristic
27#16840714C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840712—21no—
31#16840712—21no—
32C4⋊C4×#6923—21no—
33C4⋊C4×#6923—21no—
34C4⋊C4×#6923C2211yescharacteristic
35C4⋊C4×#6923C2211yescharacteristic
36C4×C4⋊#6923—21no—
37C4×C4⋊#6923C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C4×C22⋊#6923—21no—
40C42×#6923—21no—
41C42×#6923C2211yescharacteristic
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—
73#14519856—44no—
74C2×C4⋊#6923—21no—
75C2×C4⋊#6923—21no—
76C2×C4⋊#6923—21no—
77C2×C4⋊#6923—21no—
78C2×C4⋊#6923C2311yescharacteristic
79C2×C4⋊#6923C2311yescharacteristic
80C2×C4⋊#6923C2311yescharacteristic
81C2×C4⋊#6923C2311yescharacteristic
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C22⋊#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—21no—
88C2×C4×#6923—21no—
89C2×C4×#6923—21no—
90C2×C4×#6923—21no—
91C2×C4×#6923—21no—
92C2×C4×#6923D411yescharacteristic
93C2×C4×#6923D411yescharacteristic
94C2×C4×#6923D411yescharacteristic
95C2×C4×#6923D411yescharacteristic
96C2×C4×#6923C2311yescharacteristic
97C2×C4×#6923C2311yescharacteristic
98#14519846—22no—
99#14519845—22no—
100#14519840—22no—
101#14519840—22no—
102#14519839—22no—
103#14519839—22no—
104#14519832—21no—
105#14519832—21no—
106(C2×#6923)⋊C4—21no—
107(C2×#6923)⋊C4—21no—
108(C2×#6923)⋊C4—21no—
109(C2×#6923)⋊C4—21no—
110(C2×#6923)⋊C4—21no—
111(C2×#6923)⋊C4—21no—
112C2×Q8×D61C2311yescharacteristic
113C2×D4×D61C2311yescharacteristic
114C22×C4×D61—21no—
115C2×#11758190C2×C411yescharacteristic
116C2×#11758200C2×C411yescharacteristic
117C2×#11758201C2×C411yescharacteristic
118SD16×D61—22no—
119SD16×D61—22no—
120C2×C8×D61C2311yescharacteristic
121C2×C8×D61C2311yescharacteristic
122Q8×Dic61C2×C411yescharacteristic
123C4×Dic122—21no—
124C4×Dic122C2×C411yescharacteristic
125#14519742—21no—
126#14519742C2×C411yescharacteristic
127C4×D244C2×C411yescharacteristic
128D4×Dic61C2×C411yescharacteristic
129#14519739C2×C411yescharacteristic
130C4×C22⋊D61—21no—
131#14519737—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61C2311yescharacteristic
134C4⋊C4×D61C2311yescharacteristic
135C22⋊C4×D61—21no—
136C42×D61—21no—
137C42×D61C2311yescharacteristic
138#14519711C2×C411yescharacteristic
139#14519710C2×C411yescharacteristic
140#14519710C2×C411yescharacteristic
141#14519702C2×C411yescharacteristic
142#14519701C2×C411yescharacteristic
143#14519700C2×C411yescharacteristic
144#14519699C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519688C2×C411yescharacteristic
148#14519687C2×C411yescharacteristic
149#14519687C2×C411yescharacteristic
150C2×SD16×C61C2×C411yescharacteristic
151C4×Q8×C61C2×C411yescharacteristic
152C4×D4×C61C2×C411yescharacteristic
153#107×C61C2×C411yescharacteristic
154#103×C61C2×C411yescharacteristic
155#102×C61C2×C411yescharacteristic
156#97×C61C2×C411yescharacteristic
157C23×D61—21no—
158C22×#6923—21no—
159C22×#6923—21no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923C2×D411yescharacteristic
163C22×#6923C2×D411yescharacteristic
164C22×#6923C2×D411yescharacteristic
165C22×#6923C2×D411yescharacteristic
166C2×Q8×C61C22×C411yescharacteristic
167C2×D4×C61C22×C411yescharacteristic
168C22×C4×C61—21no—
169C2×C22⋊D61—21no—
170C22×Dic61—21no—
171Q8×D61—21no—
172Q8×D61—21no—
173Q8×D61#4112yes—
174Q8×D61#4112yes—
175D4×D61—21no—
176D4×D61—21no—
177D4×D61—21no—
178D4×D61—21no—
179C2×D244C22×C411yescharacteristic
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—42no—
186C2×C4×D61—42no—
187C2×C4×D61C2×D411yescharacteristic
188C2×C4×D61C2×D411yescharacteristic
189C2×C4×D61C2411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122C22×C411yescharacteristic
192C22⋊#6923—42no—
193C22⋊#6923—42no—
194C22⋊#6923—42no—
195C22⋊#6923—42no—
196C2×#92420—21no—
197C2×#92420—21no—
198C4⋊#6923—24no—
199C4⋊#6923—24no—
200C4⋊#6923—21no—
201C4⋊#6923—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—42no—
207C4⋊#6923—42no—
208C4⋊#6923#4112yes—
209C4⋊#6923#4112yes—
210C4×#6923—24no—
211C4×#6923—24no—
212C4×#6923—22no—
213C4×#6923—22no—
214C4×#6923—21no—
215C4×#6923—21no—
216C4×#6923—21no—
217C4×#6923—21no—
218C4×#6923—41no—
219C4×#6923—41no—
220C4×#6923—42no—
221C4×#6923—42no—
222C4×#6923—42no—
223C4×#6923—42no—
224D61⋊C8—21no—
225D61⋊C8—21no—
226D61⋊C8—21no—
227D61⋊C8—21no—
228SD16×C61—22no—
229C2×C8×C61C22×C411yescharacteristic
230C2×C8×C61C22×C411yescharacteristic
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C22⋊C4×C61—21no—
235C42×C61—21no—
236C42×C61C22×C411yescharacteristic
237C22⋊Dic61—21no—
238#11758201—22no—
239#11758200—22no—
240#11758198—21no—
241#11758198—21no—
242C4⋊Dic61—21no—
243C4⋊Dic61C22×C411yescharacteristic
244C4⋊Dic61C22×C411yescharacteristic
245#11758196—21no—
246#11758196—21no—
247#11758196—21no—
248#11758196—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61C22×C411yescharacteristic
253C4×Dic61#4111yescharacteristic
254C4×Dic61#4111yescharacteristic
255C2×#92418C22×C411yescharacteristic
256C2×#92418C22×C411yescharacteristic
257#11758190—22no—
258C8×D61—21no—
259C8×D61—21no—
260C8×D61—21no—
261C8×D61—21no—
262C23×C61—21no—
263C22×D61—21no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268C22×D61—41no—
269C22×D61—41no—
270C22×D61C22×D411yescharacteristic
271C2×#6923—21no—
272C2×#6923—21no—
273C2×#6923—21no—
274C2×#6923—21no—
275C2×#6923—21no—
276C2×#6923—21no—
277C2×#6923—22no—
278C2×#6923—22no—
279C2×#6923—21no—
280C2×#6923—21no—
281C2×#6923—21no—
282C2×#6923—21no—
283C2×#6923—41no—
284C2×#6923—41no—
285C2×#6923—41no—
286C2×#6923—41no—
287C2×#6923—41no—
288C2×#6923—41no—
289C2×#6923—41no—
290C2×#6923—41no—
291C2×#6923—41no—
292C2×#6923—41no—
293C2×#6923AGL(1,ℤ/8)12yes—
294C2×#6923#13712yes—
295Q8×C61—21no—
296Q8×C61#11712yescomplemented
297D4×C61—21no—
298D4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—42no—
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61C4×D411yescharacteristic
305C2×C4×C61C23×C411yescharacteristic
306C22⋊D61—41no—
307C22⋊D61—41no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—42no—
312C2×Dic61C4×D411yescharacteristic
313C2×Dic61C4×D411yescharacteristic
314C2×Dic61C2×#4111yescharacteristic
315D244—21no—
316D244—21no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—21no—
320C4×D61—21no—
321C4×D61—21no—
322C4×D61—21no—
323C4×D61—42no—
324C4×D61—42no—
325C4×D61—41no—
326C4×D61—41no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61C2×#4111yescharacteristic
330C4×D61C2×#4111yescharacteristic
331C4×D61C2×#4111yescharacteristic
332C4×D61C2×#4111yescharacteristic
333Dic122—21no—
334Dic122—22no—
335Dic122—22no—
336Dic122#11712yescomplemented
337#92420—41no—
338#92420—41no—
339C8×C61—21no—
340C8×C61—21no—
341#92418—21no—
342#92418—21no—
343#21124—611nomaximal, Sylow
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61C2×C4×D411yescharacteristic
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—81no—
352C2×D61—81no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61#52511yescharacteristic
356C2×D61#52511yescharacteristic
357C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
358C2×D61C2×#13711yescharacteristic
359C2×D61#57511yescharacteristic
360C2×D61#57511yescharacteristic
361#6923—22no—
362#6923—22no—
363#6923—41no—
364#6923—42no—
365#6923—41no—
366#6923—42no—
367#6923—81no—
368#6923—81no—
369C4×C61—21no—
370C4×C61—21no—
371C4×C61—22no—
372C4×C61—41no—
373C4×C61—41no—
374C4×C61C2×#11711yescharacteristic
375C4×C61C4×#4111yescharacteristic
376Dic61—21no—
377Dic61—21no—
378Dic61—22no—
379Dic61—41no—
380Dic61—41no—
381Dic61#52911yescharacteristic
382Dic61#52911yescharacteristic
383C2×#440—611no—
384#2293—611no—
385C42×Q8—611no—
386#1926—611no—
387#1925—611no—
388#1921—611no—
389#1918—611no—
390#1880—611no—
391#1880—611no—
392#1865—611no—
393#1863—611no—
394#1776—611no—
395#1763—611no—
396#1762—611no—
397#1745—611no—
398C2×C61—81no—
399C2×C61#229011yescharacteristic
400C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
401C2×C61C4×#13711yescharacteristic
402D61—81no—
403D61#311111yescharacteristic
404D61#311211yescharacteristic
405D61#311511yescharacteristic
406D61#311711yescharacteristic
407C22×SD16—611no—
408C2×C4×Q8—611no—
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×#117—1221no—
413#440—611no—
414#440—611no—
415#440—611no—
416#440—611no—
417#440—611no—
418#440—611no—
419#440—611no—
420#440#692311yescharacteristic, complemented
421C2×#107—611no—
422C2×#107—611no—
423C2×#106—611no—
424C2×#103—611no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#97—611no—
431C2×#97—611no—
432#390—611no—
433#390—611no—
434#389—611no—
435#389—611no—
436#388—1221no—
437#388—1221no—
438C4×C4⋊C4—611no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442C4×C4⋊C4—1221no—
443C4×C4⋊C4—1221no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446C43—611no—
447C43—1221no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458C61#2112411yescharacteristic, complemented, Sylow
459C22×Q8—611no—
460C22×D4—611no—
461C23×C4—1221no—
462C2×SD16—611no—
463C2×SD16—611no—
464C2×SD16—611no—
465C2×SD16—1222no—
466C2×SD16—1222no—
467C2×SD16C2×#692311yescharacteristic
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—611no—
472C4×Q8—611no—
473C4×Q8—611no—
474C4×Q8—611no—
475C4×Q8—1221no—
476C4×Q8—1221no—
477C4×Q8—1222no—
478C4×Q8—1222no—
479C4×Q8—1222no—
480C4×Q8—1222no—
481C4×Q8C2×#692311yescharacteristic
482C4×D4—611no—
483C4×D4—611no—
484C4×D4—611no—
485C4×D4—1221no—
486C4×D4—1221no—
487C4×D4C2×#692311yescharacteristic
488#117—2444no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—611no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519#107—611no—
520#107—611no—
521#107—611no—
522#107—1222no—
523#107C2×#692311yescharacteristic
524#106—1222no—
525#103—611no—
526#103—611no—
527#103—611no—
528#103—1222no—
529#103—1222no—
530#103C2×#692311yescharacteristic
531#102—611no—
532#102—611no—
533#102—611no—
534#102—1222no—
535#102—1222no—
536#102C2×#692311yescharacteristic
537#97—611no—
538#97—611no—
539#97—611no—
540#97—1221no—
541#97—1221no—
542#97C2×#692311yescharacteristic
543#95—1221no—
544#95—1221no—
545#95—1221no—
546#95—1221no—
547#95—1221no—
548#95—1221no—
549C24—1221no—
550C2×Q8—612no—
551C2×Q8—612no—
552C2×Q8—611no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8C22×#692311yescharacteristic
557C2×D4—611no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4C22×#692311yescharacteristic
564C22×C4—21no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—2442no—
583C22×C4—2442no—
584SD16—22no—
585SD16—1222no—
586SD16—1222no—
587SD16—1222no—
588C2×C8—611no—
589C2×C8—611no—
590C2×C8—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8C22×#692311yescharacteristic
601C2×C8C22×#692311yescharacteristic
602C4⋊C4—21no—
603C4⋊C4—612no—
604C4⋊C4—612no—
605C4⋊C4—611no—
606C4⋊C4—611no—
607C4⋊C4—1221no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1224no—
618C4⋊C4—1224no—
619C4⋊C4—1221no—
620C4⋊C4—2442no—
621C4⋊C4—2442no—
622C4⋊C4C22×#692311yescharacteristic
623C4⋊C4C22×#692311yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—1221no—
626C22⋊C4—1221no—
627C22⋊C4—1221no—
628C22⋊C4—2442no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C22⋊C4—2442no—
632C42—21no—
633C42—611no—
634C42—611no—
635C42—611no—
636C42—1221no—
637C42—1221no—
638C42—1222no—
639C42—1221no—
640C42—1221no—
641C42—1221no—
642C42—1221no—
643C42—1222no—
644C42—1224no—
645C42—1224no—
646C42—1221no—
647C42—2442no—
648C42—2441no—
649C42—2441no—
650C42—2442no—
651C42—2442no—
652C42—2442no—
653C42C22×#692311yescharacteristic
654C23—21no—
655C23—611no—
656C23—1221no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23—2441no—
661C23—2441no—
662C23—2441no—
663Q8—21no—
664Q8—612no—
665Q8—1222no—
666Q8—1222no—
667Q8—1221no—
668Q8#1451985612yescomplemented
669D4—21no—
670D4—21no—
671D4—1221no—
672D4—1221no—
673D4—2441no—
674D4—2441no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—42no—
679C2×C4—611no—
680C2×C4—611no—
681C2×C4—611no—
682C2×C4—611no—
683C2×C4—611no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—611no—
687C2×C4—611no—
688C2×C4—1221no—
689C2×C4—1222no—
690C2×C4—1222no—
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—1221no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—2442no—
710C2×C4—2442no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2442no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4D4×#692311yescharacteristic
727C2×C4D4×#692311yescharacteristic
728C2×C4C23×#692311yescharacteristic
729C8—21no—
730C8—21no—
731C8—1221no—
732C8—1221no—
733C8—2441no—
734C8—2441no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—611no—
739C22—611no—
740C22—611no—
741C22—611no—
742C22—611no—
743C22—611no—
744C22—4881no—
745C22—4881no—
746C22—4881no—
747C22—4881no—
748C22—2441no—
749C22—2441no—
750C22—2441no—
751C22C2×D4×#692311yescharacteristic
752C4—22no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—611no—
758C4—611no—
759C4—1222no—
760C4—1222no—
761C4—1222no—
762C4—1221no—
763C4—1221no—
764C4—4881no—
765C4—4881no—
766C4—2441no—
767C4—2441no—
768C4—2442no—
769C4—2442no—
770C4—2441no—
771C4—2441no—
772C4C2×#1451985611yescharacteristic
773C4#41×#692311yescharacteristic
774C2—81no—
775C2—611no—
776C2—611no—
777C2—611no—
778C2—611no—
779C2—4881no—
780C2#2146227311yescharacteristic
781C2AGL(1,ℤ/8)×#692311yescharacteristic
782C2#137×#692311yescharacteristic
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#21124
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. C4×Q8×#6923C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
9. #21461785C2semidirect
10. #21461783C2semidirect
11. #21461633C2semidirect
12. #21461591C2semidirect
14. #21461535C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
296. Q8×C61#117semidirect
336. Dic122#117semidirect
420. #440#6923semidirect
458. C61#21124semidirect
668. Q8#14519856semidirect

Maximal subgroups

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

subgroupindex
#214622762
C4×Q8×#69232
#214618972
#214618962
#214618832
#214618802
#214618152
#214617852
#214617832
#214616332
#214615912
#214615892
#214615352
#440×D612
#2112461