Finite Group Databasebeta

← #30616066

Subgroups — #30616066

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462278C211yesmaximal, characteristic, complemented
2C4×D4×#6923C211yesmaximal, characteristic
3#21461899C211yesmaximal, characteristic, complemented
4#21461898C211yesmaximal, characteristic, complemented
5#21461883C211yesmaximal, characteristic, complemented
6#21461880C211yesmaximal, characteristic, complemented
7#21461812C211yesmaximal, characteristic
8#21461812C211yesmaximal, characteristic
9#21461784C211yesmaximal, characteristic
10#21461782C211yesmaximal, characteristic
11#21461633C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461589C211yesmaximal, characteristic
14#21461535C211yesmaximal, characteristic, complemented
15#440×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C22×C4×#6923—21no—
19C2×#14519846C2211yescharacteristic
20C2×#14519845C2211yescharacteristic
21C2×#14519840C2211yescharacteristic
22C2×#14519840C2211yescharacteristic
23C2×#14519839C2211yescharacteristic
24C2×#14519839C2211yescharacteristic
25#16840721C2211yescharacteristic
26(C2×#6923)⋊Q8C2211yescharacteristic
27(C2×#6923)⋊Q8C2211yescharacteristic
28#16840713C2211yescharacteristic
29#16840713C2211yescharacteristic
30#16840711—21no—
31#16840711—21no—
32C4⋊C4×#6923C2211yescharacteristic
33C4⋊C4×#6923C2211yescharacteristic
34C4×C4⋊#6923—21no—
35C4×C4⋊#6923C2211yescharacteristic
36C4×C4⋊#6923C2211yescharacteristic
37C22⋊C4×#6923—21no—
38C22⋊C4×#6923—21no—
39C4×C22⋊#6923—21no—
40#16840698—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
67C23×#6923—21no—
68C23×#6923—21no—
69C2×D61⋊C8C2311yescharacteristic
70C2×D61⋊C8C2311yescharacteristic
71D4×#6923—22no—
72D4×#6923—22no—
73D4×#6923—22no—
74D4×#6923—22no—
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×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86C2×C4×#6923—21no—
87C2×C4×#6923—44no—
88C2×C4×#6923D411yescharacteristic
89C2×C4×#6923D411yescharacteristic
90C2×C4×#6923D411yescharacteristic
91C2×C4×#6923D411yescharacteristic
92C2×C4×#6923C2311yescharacteristic
93C2×C4×#6923C2311yescharacteristic
94#14519846—22no—
95#14519845—22no—
96#14519840—22no—
97#14519840—22no—
98#14519839—22no—
99#14519839—22no—
100#14519832—21no—
101#14519832—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)⋊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, complemented
123C4×Dic122—21no—
124C4×Dic122C2×C411yescharacteristic, complemented
125#14519742—21no—
126#14519742C2×C411yescharacteristic, complemented
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, complemented
139#14519710C2×C411yescharacteristic, complemented
140#14519710C2×C411yescharacteristic, complemented
141#14519702C2×C411yescharacteristic, complemented
142#14519701C2×C411yescharacteristic, complemented
143#14519700C2×C411yescharacteristic, complemented
144#14519699C2×C411yescharacteristic
145#14519698C2×C411yescharacteristic
146#14519697C2×C411yescharacteristic
147#14519688C2×C411yescharacteristic, complemented
148#14519687C2×C411yescharacteristic, complemented
149#14519687C2×C411yescharacteristic, complemented
150C2×SD16×C61C2×C411yescharacteristic
151C4×Q8×C61C2×C411yescharacteristic, complemented
152C4×D4×C61C2×C411yescharacteristic
153#107×C61C2×C411yescharacteristic, complemented
154#103×C61C2×C411yescharacteristic, complemented
155#102×C61C2×C411yescharacteristic
156#97×C61C2×C411yescharacteristic, complemented
157C23×D61—21no—
158C22×#6923—24no—
159C22×#6923—24no—
160C22×#6923—21no—
161C22×#6923—21no—
162C22×#6923—21no—
163C22×#6923—21no—
164C22×#6923—42no—
165C22×#6923—42no—
166C22×#6923—42no—
167C22×#6923—42no—
168C22×#6923C2×D411yescharacteristic
169C22×#6923C2×D411yescharacteristic
170C22×#6923C2×D411yescharacteristic
171C22×#6923C2×D411yescharacteristic
172C2×Q8×C61C22×C411yescharacteristic
173C2×D4×C61C22×C411yescharacteristic
174C22×C4×C61—21no—
175C2×C22⋊D61—21no—
176C22×Dic61—21no—
177Q8×D61—21no—
178Q8×D61—21no—
179Q8×D61—21no—
180Q8×D61—21no—
181D4×D61—21no—
182D4×D61—21no—
183D4×D61#4112yes—
184D4×D61#4112yes—
185C2×D244C22×C411yescharacteristic
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61C2×D411yescharacteristic
194C2×C4×D61C2×D411yescharacteristic
195C2×C4×D61C2411yescharacteristic
196C2×Dic122—21no—
197C2×Dic122C22×C411yescharacteristic
198C22⋊#6923—24no—
199C22⋊#6923—24no—
200C2×#92420—21no—
201C2×#92420—21no—
202C4⋊#6923—21no—
203C4⋊#6923—21no—
204C4⋊#6923—21no—
205C4⋊#6923—21no—
206C4⋊#6923—21no—
207C4⋊#6923—21no—
208C4⋊#6923—42no—
209C4⋊#6923—42no—
210C4⋊#6923#4112yes—
211C4⋊#6923#4112yes—
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—22no—
265C22×D61—22no—
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—48no—
284C2×#6923—48no—
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×#6923—41no—
294C2×#6923—41no—
295C2×#6923AGL(1,ℤ/8)12yes—
296C2×#6923#13712yes—
297Q8×C61—21no—
298Q8×C61—21no—
299D4×C61—21no—
300D4×C61#11712yes—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—42no—
305C2×C4×C61C4×D411yescharacteristic
306C2×C4×C61C4×D411yescharacteristic
307C2×C4×C61C23×C411yescharacteristic
308C22⋊D61—22no—
309C22⋊D61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—42no—
314C2×Dic61C4×D411yescharacteristic
315C2×Dic61C4×D411yescharacteristic
316C2×Dic61C2×#4111yescharacteristic
317D244—21no—
318D244#11712yes—
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×D61—41no—
330C4×D61—41no—
331C4×D61C2×#4111yescharacteristic
332C4×D61C2×#4111yescharacteristic
333C4×D61C2×#4111yescharacteristic
334C4×D61C2×#4111yescharacteristic
335Dic122—21no—
336Dic122—21no—
337Dic122—41no—
338Dic122—41no—
339#92420—41no—
340#92420—41no—
341C8×C61—21no—
342C8×C61—21no—
343#92418—21no—
344#92418—21no—
345#21121—611nomaximal, Sylow
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61C2×C4×D411yescharacteristic
350C2×D61—22no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61#52511yescharacteristic
358C2×D61#52511yescharacteristic
359C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
360C2×D61C2×#13711yescharacteristic
361C2×D61#57511yescharacteristic
362C2×D61#57511yescharacteristic
363#6923—22no—
364#6923—22no—
365#6923—42no—
366#6923—41no—
367#6923—42no—
368#6923—41no—
369#6923—81no—
370#6923—81no—
371C4×C61—21no—
372C4×C61—21no—
373C4×C61—41no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61C2×#11711yescharacteristic
377C4×C61C4×#4111yescharacteristic
378Dic61—21no—
379Dic61—21no—
380Dic61—41no—
381Dic61—41no—
382Dic61—41no—
383Dic61#52911yescharacteristic
384Dic61#52911yescharacteristic
385C2×#440—611no—
386#2295—611no—
387C42×D4—611no—
388#1928—611no—
389#1927—611no—
390#1921—611no—
391#1918—611no—
392#1877—611no—
393#1877—611no—
394#1864—611no—
395#1862—611no—
396#1776—611no—
397#1763—611no—
398#1762—611no—
399#1745—611no—
400C2×C61—42no—
401C2×C61#229011yescharacteristic
402C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C61C4×#13711yescharacteristic
404D61—42no—
405D61#311011yescharacteristic
406D61#311111yescharacteristic
407D61#311411yescharacteristic
408D61#311611yescharacteristic
409C22×SD16—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C22×C42—1221no—
415#440—611no—
416#440—611no—
417#440—611no—
418#440—611no—
419#440—611no—
420#440—611no—
421#440—611no—
422#440#692311yescharacteristic, complemented
423C2×#107—611no—
424C2×#107—611no—
425C2×#106—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×#97—611no—
433C2×#97—611no—
434#391—611no—
435#391—611no—
436#389—611no—
437#389—611no—
438#387—1221no—
439#387—1221no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442C4×C4⋊C4—611no—
443C4×C4⋊C4—611no—
444C4×C4⋊C4—1221no—
445C4×C22⋊C4—1221no—
446C4×C22⋊C4—1221no—
447C4×C22⋊C4—1221no—
448#376—1221no—
449C43—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#340—611no—
455#340—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460C61#2112111yescharacteristic, complemented, Sylow
461C22×Q8—611no—
462C22×D4—611no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4—1221no—
466C2×SD16—611no—
467C2×SD16—611no—
468C2×SD16—611no—
469C2×SD16—1222no—
470C2×SD16—1222no—
471C2×SD16C2×#692311yescharacteristic
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C4×Q8—611no—
477C4×Q8—611no—
478C4×Q8—611no—
479C4×Q8—1221no—
480C4×Q8—1221no—
481C4×Q8C2×#692311yescharacteristic, complemented
482C4×D4—611no—
483C4×D4—611no—
484C4×D4—611no—
485C4×D4—1221no—
486C4×D4—1221no—
487C4×D4—1222no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4C2×#692311yescharacteristic
492C2×C4⋊C4—611no—
493C2×C4⋊C4—611no—
494C2×C4⋊C4—611no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—611no—
509C2×C42—611no—
510C2×C42—611no—
511C2×C42—1221no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42—2444no—
517#107—611no—
518#107—611no—
519#107—611no—
520#107—1222no—
521#107C2×#692311yescharacteristic, complemented
522#106—1222no—
523#103—611no—
524#103—611no—
525#103—611no—
526#103—1222no—
527#103—1222no—
528#103C2×#692311yescharacteristic, complemented
529#102—611no—
530#102—611no—
531#102—611no—
532#102—1222no—
533#102—1222no—
534#102C2×#692311yescharacteristic
535#97—611no—
536#97—611no—
537#97—611no—
538#97—1221no—
539#97—1221no—
540#97C2×#692311yescharacteristic, complemented
541#95—1221no—
542#95—1221no—
543#95—1221no—
544#95—1221no—
545#95—1221no—
546#95—1221no—
547#95—1221no—
548#95—1221no—
549#95—1221no—
550#95—1221no—
551C24—1221no—
552C2×Q8—611no—
553C2×Q8—1221no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8C22×#692311yescharacteristic
559C2×D4—612no—
560C2×D4—612no—
561C2×D4—611no—
562C2×D4—1221no—
563C2×D4—1221no—
564C2×D4—1221no—
565C2×D4C22×#692311yescharacteristic
566C22×C4—21no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1224no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4—2442no—
592SD16—22no—
593SD16—1222no—
594SD16—1222no—
595SD16—1222no—
596C2×C8—611no—
597C2×C8—611no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8C22×#692311yescharacteristic
609C2×C8C22×#692311yescharacteristic
610C4⋊C4—21no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—611no—
614C4⋊C4—611no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—1221no—
624C4⋊C4—1221no—
625C4⋊C4—1221no—
626C4⋊C4—2442no—
627C4⋊C4—2442no—
628C4⋊C4C22×#692311yescharacteristic
629C4⋊C4C22×#692311yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—1221no—
632C22⋊C4—1221no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1221no—
636C42—21no—
637C42—611no—
638C42—611no—
639C42—611no—
640C42—1221no—
641C42—1221no—
642C42—1222no—
643C42—1221no—
644C42—1221no—
645C42—1221no—
646C42—1221no—
647C42—1222no—
648C42—1221no—
649C42—2442no—
650C42—2441no—
651C42—2441no—
652C42—2442no—
653C42—2442no—
654C42—2442no—
655C42C22×#692311yescharacteristic
656C23—21no—
657C23—611no—
658C23—1222no—
659C23—1222no—
660C23—1221no—
661C23—2441no—
662C23—2441no—
663C23—2441no—
664C23—2441no—
665Q8—21no—
666Q8—21no—
667Q8—1221no—
668Q8—1221no—
669Q8—2441no—
670Q8—2441no—
671D4—21no—
672D4—612no—
673D4—1222no—
674D4—1222no—
675D4—1221no—
676D4#1451985612yes—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—42no—
681C2×C4—611no—
682C2×C4—611no—
683C2×C4—611no—
684C2×C4—611no—
685C2×C4—611no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—611no—
689C2×C4—611no—
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—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1222no—
705C2×C4—1222no—
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—2441no—
716C2×C4—2441no—
717C2×C4—2442no—
718C2×C4—2448no—
719C2×C4—2448no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4D4×#692311yescharacteristic
731C2×C4D4×#692311yescharacteristic
732C2×C4C23×#692311yescharacteristic
733C8—21no—
734C8—21no—
735C8—1221no—
736C8—1221no—
737C8—2441no—
738C8—2441no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—611no—
743C22—611no—
744C22—611no—
745C22—611no—
746C22—611no—
747C22—611no—
748C22—1222no—
749C22—2442no—
750C22—2442no—
751C22—2442no—
752C22—2442no—
753C22—2441no—
754C22—2441no—
755C22C2×D4×#692311yescharacteristic
756C4—21no—
757C4—21no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—611no—
762C4—611no—
763C4—1222no—
764C4—1222no—
765C4—1221no—
766C4—1221no—
767C4—4881no—
768C4—4881no—
769C4—2441no—
770C4—2441no—
771C4—2442no—
772C4—2442no—
773C4—2441no—
774C4—2441no—
775C4—2441no—
776C4C2×#1451985611yescharacteristic
777C4#41×#692311yescharacteristic
778C2—42no—
779C2—611no—
780C2—611no—
781C2—611no—
782C2—611no—
783C2—2442no—
784C2#2146227311yescharacteristic
785C2AGL(1,ℤ/8)×#692311yescharacteristic
786C2#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#21121
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
1. #21462278C2semidirect
3. #21461899C2semidirect
4. #21461898C2semidirect
5. #21461883C2semidirect
6. #21461880C2semidirect
11. #21461633C2semidirect
12. #21461591C2semidirect
14. #21461535C2semidirect
55. #16839865C4semidirect
56. #16839864C4semidirect
57. #16839863C4semidirect
58. #16839862C4semidirect
59. #16839861C4semidirect
60. #16839860C4semidirect
61. #16839859C4semidirect
66. C61×#440C4semidirect
122. Q8×Dic61C2×C4semidirect
124. C4×Dic122C2×C4semidirect
126. #14519742C2×C4semidirect
138. #14519711C2×C4semidirect
139. #14519710C2×C4semidirect
140. #14519710C2×C4semidirect
141. #14519702C2×C4semidirect
142. #14519701C2×C4semidirect
143. #14519700C2×C4semidirect
147. #14519688C2×C4semidirect
148. #14519687C2×C4semidirect
149. #14519687C2×C4semidirect
151. C4×Q8×C61C2×C4semidirect
153. #107×C61C2×C4semidirect
154. #103×C61C2×C4semidirect
156. #97×C61C2×C4semidirect
422. #440#6923semidirect
460. C61#21121semidirect
481. C4×Q8C2×#6923semidirect
521. #107C2×#6923semidirect
528. #103C2×#6923semidirect
540. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622782
C4×D4×#69232
#214618992
#214618982
#214618832
#214618802
#214618122
#214617842
#214617822
#214616332
#214615912
#214615892
#214615352
#440×D612
#2112161