Finite Group Databasebeta

← #34023175

Subgroups — #34023175

Order 18688.

844 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626418C211yesmaximal, characteristic
2#22626368C211yesmaximal, characteristic
3#22626011C211yesmaximal, characteristic, complemented
4#22626011C211yesmaximal, characteristic, complemented
5#22625994C211yesmaximal, characteristic, complemented
6#22625992C211yesmaximal, characteristic, complemented
7#22625916C211yesmaximal, characteristic
8#22625880C211yesmaximal, characteristic
9#22625836C211yesmaximal, characteristic
10#22625747C211yesmaximal, characteristic, complemented
11#107×#64408C211yesmaximal, characteristic, complemented
12#22625704C211yesmaximal, characteristic, complemented
13#103×#64408C211yesmaximal, characteristic, complemented
14#22625662C211yesmaximal, characteristic
15#485×D73C211yesmaximal, characteristic
16C2×Q8×#64408C2211yescharacteristic
17C2×#14556670C2211yescharacteristic
18C22×C4⋊#64408C2211yescharacteristic
19C2×#14556660C2211yescharacteristic
20C2×#14556660C2211yescharacteristic
21C2×#14556654C2211yescharacteristic
22C2×#14556654C2211yescharacteristic
23#17989555C2211yescharacteristic
24C2×#14556645C2211yescharacteristic
25C2×C8×#64408C2211yescharacteristic
26(C2×#64408)⋊Q8C2211yescharacteristic
27#17989538—21no—
28#17989538C2211yescharacteristic
29#17989537—21no—
30#17989537—21no—
31#17989536—21no—
32#17989529C2211yescharacteristic
33C4⋊C4×#64408C2211yescharacteristic
34C4⋊C4×#64408C2211yescharacteristic
35C4⋊C4×#64408C2211yescharacteristic
36C4⋊C4×#64408C2211yescharacteristic
37C4⋊C4×#64408C2211yescharacteristic
38C4×C4⋊#64408—21no—
39C4×C4⋊#64408—21no—
40C22⋊C4×#64408—21no—
41C22⋊C4×#64408—21no—
42#17989461C2211yescharacteristic
43#17989461C2211yescharacteristic
44#17989460C2211yescharacteristic
45#17989460C2211yescharacteristic
46#17989460C2211yescharacteristic
47#17989460C2211yescharacteristic
48#17989460C2211yescharacteristic
49#17989460C2211yescharacteristic
50#17989452C2211yescharacteristic
51#17989452C2211yescharacteristic
52C22⋊Q8×D73C2211yescharacteristic
53#117×D73C2211yescharacteristic
54#17988931C411yescharacteristic, complemented
55#17988930C411yescharacteristic, complemented
56#17988929C411yescharacteristic, complemented
57#17988928C411yescharacteristic, complemented
58#17988927C411yescharacteristic, complemented
59#17988926C411yescharacteristic, complemented
60#17988925C411yescharacteristic, complemented
61#107×D73C2211yescharacteristic
62#106×D73C2211yescharacteristic
63#103×D73C2211yescharacteristic
64#103×D73C2211yescharacteristic
65C22⋊C8×D73C2211yescharacteristic
66#485×C73C411yescharacteristic, complemented
67C23×#64408—21no—
68C2×#11924036C2311yescharacteristic
69C2×#11924036C2311yescharacteristic
70Q8×#64408—22no—
71Q8×#64408—22no—
72#14556670—22no—
73#14556670—22no—
74C2×C4⋊#64408—22no—
75C2×C4⋊#64408—22no—
76C2×C4⋊#64408—21no—
77C2×C4⋊#64408—21no—
78C2×C4⋊#64408—21no—
79C2×C4⋊#64408D411yescharacteristic
80C2×C4⋊#64408D411yescharacteristic
81C2×C4⋊#64408C2311yescharacteristic
82C2×C4⋊#64408C2311yescharacteristic
83C2×C4⋊#64408C2311yescharacteristic
84C2×C4⋊#64408C2311yescharacteristic
85C2×C22⋊#64408—21no—
86C2×C22⋊#64408D411yescharacteristic
87C2×C22⋊#64408D411yescharacteristic
88C2×C4×#64408—21no—
89C2×C4×#64408—21no—
90C2×C4×#64408—21no—
91C2×C4×#64408—21no—
92C2×C4×#64408—21no—
93C2×C4×#64408—21no—
94C2×C4×#64408C2311yescharacteristic
95C2×C4×#64408C2311yescharacteristic
96#14556660—22no—
97#14556660—22no—
98#14556654—22no—
99#14556654—22no—
100#14556648—21no—
101C22⋊#10596833—21no—
102#14556645—22no—
103C8×#64408—22no—
104(C2×#64408)⋊C4—21no—
105(C2×#64408)⋊C4—21no—
106(C2×#64408)⋊C4—21no—
107(C2×#64408)⋊C4—21no—
108(C2×#64408)⋊C4—21no—
109(C2×#64408)⋊C4—21no—
110(C2×#64408)⋊C4—21no—
111(C2×#64408)⋊C4—21no—
112(C2×#64408)⋊C4—21no—
113C2×Q8×D73C2311yescharacteristic
114C22×C4×D73C2311yescharacteristic
115C2×C8×D73C2311yescharacteristic
116C2×C8×D73C2311yescharacteristic
117#14556571C2×C411yescharacteristic
118#14556570C2×C411yescharacteristic
119#14556569—21no—
120#14556568—21no—
121#14556567C2×C411yescharacteristic
122#14556550C2×C411yescharacteristic
123#14556549C2×C411yescharacteristic
124#14556549C2×C411yescharacteristic
125#14556548—21no—
126#14556547—21no—
127C4⋊C4×D73—21no—
128C4⋊C4×D73C2311yescharacteristic
129C4⋊C4×D73C2311yescharacteristic
130C4⋊C4×D73C2311yescharacteristic
131C22⋊C4×D73—21no—
132C22⋊C4×D73—21no—
133C42×D73—21no—
134#14556525C2×C411yescharacteristic, complemented
135#14556524C2×C411yescharacteristic, complemented
136#14556524C2×C411yescharacteristic, complemented
137#14556523C2×C411yescharacteristic, complemented
138#14556522C2×C411yescharacteristic, complemented
139#14556522C2×C411yescharacteristic, complemented
140#14556516C2×C411yescharacteristic, complemented
141#14556516C2×C411yescharacteristic, complemented
142#14556515C2×C411yescharacteristic, complemented
143#14556515C2×C411yescharacteristic, complemented
144#14556514C2×C411yescharacteristic, complemented
145#14556514C2×C411yescharacteristic, complemented
146C22⋊#10596831C2×C411yescharacteristic
147#14556503C2×C411yescharacteristic
148#14556503C2×C411yescharacteristic
149C22⋊Q8×C73C2×C411yescharacteristic
150#117×C73C2×C411yescharacteristic
151#107×C73C2×C411yescharacteristic, complemented
152#106×C73C2×C411yescharacteristic, complemented
153#103×C73C2×C411yescharacteristic, complemented
154#103×C73C2×C411yescharacteristic, complemented
155C22⋊C8×C73C2×C411yescharacteristic
156C22×#64408—21no—
157C22×#64408—21no—
158C22×#64408—24no—
159C22×#64408—21no—
160C22×#64408—21no—
161C22×#64408—81no—
162C22×#64408—81no—
163C22×#64408C2×D411yescharacteristic
164C22×#64408C2×D411yescharacteristic
165C22×#64408C2×D411yescharacteristic
166C22×#64408C2×D411yescharacteristic
167#11924036—21no—
168#11924036—21no—
169#11924036—21no—
170#11924036—21no—
171C2×#10596833—21no—
172C2×#10596833—21no—
173C4⋊#64408—24no—
174C4⋊#64408—22no—
175C4⋊#64408—22no—
176C4⋊#64408—21no—
177C4⋊#64408—21no—
178C4⋊#64408—21no—
179C4⋊#64408—21no—
180C4⋊#64408—21no—
181C4⋊#64408—21no—
182C4⋊#64408—42no—
183C4⋊#64408—81no—
184C4⋊#64408#4112yes—
185C4⋊#64408#4112yes—
186C22⋊#64408—22no—
187C22⋊#64408—22no—
188C22⋊#64408—81no—
189C4×#64408—21no—
190C4×#64408—21no—
191C4×#64408—42no—
192C4×#64408—81no—
193C4×#64408—81no—
194C4×#64408—81no—
195C4×#64408—81no—
196C4×#64408—81no—
197C4×#64408#4112yes—
198C4×#64408#4112yes—
199C23×D73C2×D411yescharacteristic
200C2×Dic146—21no—
201C2×Dic146C22×C411yescharacteristic
202Q8×D73—21no—
203Q8×D73—21no—
204Q8×D73—21no—
205Q8×D73—21no—
206C22×Dic73#4111yescharacteristic
207C2×C4×D73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—21no—
213C2×C4×D73—21no—
214C2×C4×D73—21no—
215C2×C4×D73C22×C411yescharacteristic
216C2×C4×D73C2×D411yescharacteristic
217C2×C4×D73#4111yescharacteristic
218C2×C4×D73C2411yescharacteristic
219C2×#10596831C22×C411yescharacteristic
220C2×#10596831C22×C411yescharacteristic
221C8×D73—21no—
222C8×D73—21no—
223C8×D73—21no—
224C8×D73—21no—
225C4⋊Dic73—21no—
226C4⋊Dic73C22×C411yescharacteristic
227C4⋊Dic73C22×C411yescharacteristic
228C4⋊Dic73C22×C411yescharacteristic
229#11924007—21no—
230#11924007—21no—
231#11924007—21no—
232#11924007—21no—
233#11924007—21no—
234C22⋊Dic73—21no—
235C22⋊Dic73—21no—
236#11924005—21no—
237#11924005—21no—
238#11924005—21no—
239#11924005—21no—
240C4×Dic73—21no—
241C4×Dic73—21no—
242C4×Dic73—21no—
243C2×Q8×C73C22×C411yescharacteristic
244C22×C4×C73C22×C411yescharacteristic
245C2×C8×C73C22×C411yescharacteristic
246C2×C8×C73C22×C411yescharacteristic
247C4⋊C4×C73—21no—
248C4⋊C4×C73C22×C411yescharacteristic
249C4⋊C4×C73C22×C411yescharacteristic
250C4⋊C4×C73C22×C411yescharacteristic
251C22⋊C4×C73—21no—
252C22⋊C4×C73—21no—
253C42×C73—21no—
254C23×C73C4×D411yescharacteristic
255C22×D73—21no—
256C22×D73—21no—
257C22×D73—21no—
258C22×D73—21no—
259C22×D73—21no—
260C22×D73—21no—
261C22×D73C4×D411yescharacteristic
262C22×D73C22×D411yescharacteristic
263C2×#64408—21no—
264C2×#64408—21no—
265C2×#64408—21no—
266C2×#64408—21no—
267C2×#64408—21no—
268C2×#64408—21no—
269C2×#64408—22no—
270C2×#64408—22no—
271C2×#64408—21no—
272C2×#64408—21no—
273C2×#64408—21no—
274C2×#64408—21no—
275C2×#64408—41no—
276C2×#64408—41no—
277C2×#64408—41no—
278C2×#64408—41no—
279C2×#64408—41no—
280C2×#64408—41no—
281C2×#64408—41no—
282C2×#64408—41no—
283C2×#64408—41no—
284C2×#64408—41no—
285C2×#64408—84no—
286C2×#64408#12312yes—
287C2×#64408#12312yes—
288Q8×C73—21no—
289Q8×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73C4×D411yescharacteristic
297C2×C4×C73C23×C411yescharacteristic
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—21no—
301C2×Dic73—21no—
302C2×Dic73—21no—
303C2×Dic73—21no—
304C2×Dic73C4×D411yescharacteristic
305C2×Dic73C2×#4111yescharacteristic
306C4×D73—21no—
307C4×D73—21no—
308C4×D73—21no—
309C4×D73—21no—
310C4×D73—21no—
311C4×D73—21no—
312C4×D73—41no—
313C4×D73—41no—
314C4×D73—41no—
315C4×D73—41no—
316C4×D73—41no—
317C4×D73—41no—
318C4×D73—41no—
319C4×D73—41no—
320C4×D73C2×#4111yescharacteristic
321C4×D73C2×#4111yescharacteristic
322C4×D73C2×#4111yescharacteristic
323C4×D73C2×#4111yescharacteristic
324Dic146—21no—
325Dic146—21no—
326Dic146—41no—
327Dic146—41no—
328#10596833—41no—
329#10596833—41no—
330C8×C73—21no—
331C8×C73—21no—
332#10596831—21no—
333#10596831—21no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—21no—
337C22×C73C2×C4×D411yescharacteristic
338C2×D73—21no—
339C2×D73—21no—
340C2×D73—21no—
341C2×D73—41no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73C2×#12311yescharacteristic
346C2×D73#52511yescharacteristic
347C2×D73#57611yescharacteristic
348C2×D73#57711yescharacteristic
349C2×D73#57811yescharacteristic
350C2×D73#57811yescharacteristic
351#64408—22no—
352#64408—22no—
353#64408—41no—
354#64408—41no—
355#64408—42no—
356#64408—42no—
357#64408—81no—
358#64408—81no—
359C4×C73—21no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73C4×#4111yescharacteristic
365C4×C73C4×#4111yescharacteristic
366Dic73—21no—
367Dic73—41no—
368Dic73—41no—
369Dic73—41no—
370Dic73—41no—
371Dic73#52911yescharacteristic
372Dic73#52911yescharacteristic
373#21589—731nomaximal, Sylow
374C2×C73—41no—
375C2×C73C4×#12311yescharacteristic
376C2×C73#294711yescharacteristic
377C2×C73#295111yescharacteristic
378D73—41no—
379D73#309711yescharacteristic
380D73#309811yescharacteristic
381D73#311811yescharacteristic
382D73#312711yescharacteristic
383C2×#485—731no—
384#2323—731no—
385#2274—731no—
386#1928—731no—
387#1928—731no—
388#1920—731no—
389#1918—731no—
390#1872—731no—
391#1852—731no—
392#1825—731no—
393#1776—731no—
394C4×#107—731no—
395#1763—731no—
396C4×#103—731no—
397#1750—731no—
398C73#2158911yescharacteristic, complemented, Sylow
399C2×C22⋊Q8—731no—
400C2×C4×Q8—731no—
401C2×#117—731no—
402C2×#117—731no—
403C22×C4⋊C4—731no—
404#485—731no—
405#485—731no—
406#485—731no—
407#485—731no—
408#485—731no—
409#485—731no—
410#485—731no—
411#485#6440811yescharacteristic, complemented
412C2×#107—731no—
413C2×#107—731no—
414C2×#107—731no—
415C2×#106—731no—
416C2×#103—731no—
417C2×#103—731no—
418C2×#103—731no—
419C2×#103—731no—
420C2×C22⋊C8—731no—
421C2×C22⋊C8—731no—
422C2×#97—731no—
423C2×C4×C8—731no—
424#391—731no—
425#389—731no—
426#389—1461no—
427#388—1461no—
428#388—1461no—
429#387—1461no—
430#380—731no—
431C4×C4⋊C4—731no—
432C4×C4⋊C4—731no—
433C4×C4⋊C4—731no—
434C4×C4⋊C4—731no—
435C4×C4⋊C4—731no—
436C4×C4⋊C4—1461no—
437C4×C4⋊C4—1461no—
438C4×C22⋊C4—1461no—
439C4×C22⋊C4—1461no—
440#340—731no—
441#340—731no—
442#340—731no—
443#340—731no—
444#340—731no—
445#340—731no—
446#340—731no—
447#340—731no—
448#336—731no—
449#336—731no—
450C22×Q8—731no—
451C23×C4—731no—
452C23×C4—1461no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456C22×C8—731no—
457C22⋊Q8—731no—
458C22⋊Q8—731no—
459C22⋊Q8—731no—
460C22⋊Q8—1461no—
461C22⋊Q8—1461no—
462C22⋊Q8C2×#6440811yescharacteristic
463C4×Q8—1462no—
464C4×Q8—1462no—
465#117—731no—
466#117—731no—
467#117—731no—
468#117—1461no—
469#117—1462no—
470#117—1462no—
471#117—1461no—
472#117C2×#6440811yescharacteristic
473C2×C4⋊C4—731no—
474C2×C4⋊C4—731no—
475C2×C4⋊C4—731no—
476C2×C4⋊C4—731no—
477C2×C4⋊C4—731no—
478C2×C4⋊C4—731no—
479C2×C4⋊C4—731no—
480C2×C4⋊C4—731no—
481C2×C4⋊C4—731no—
482C2×C4⋊C4—1461no—
483C2×C4⋊C4—1461no—
484C2×C4⋊C4—1461no—
485C2×C4⋊C4—1462no—
486C2×C4⋊C4—1462no—
487C2×C4⋊C4—1461no—
488C2×C22⋊C4—731no—
489C2×C22⋊C4—731no—
490C2×C22⋊C4—1461no—
491C2×C22⋊C4—1461no—
492C2×C22⋊C4—1461no—
493C2×C42—731no—
494C2×C42—731no—
495C2×C42—1461no—
496C2×C42—1461no—
497C2×C42—1461no—
498C2×C42—1461no—
499C2×C42—1461no—
500C2×C42—1461no—
501C2×C42—1461no—
502#107—731no—
503#107—731no—
504#107—731no—
505#107—1462no—
506#107—1462no—
507#107C2×#6440811yescharacteristic, complemented
508#106—731no—
509#106—731no—
510#106—731no—
511#106C2×#6440811yescharacteristic, complemented
512#103—731no—
513#103—731no—
514#103—731no—
515#103—731no—
516#103—731no—
517#103—731no—
518#103—1462no—
519#103—1462no—
520#103C2×#6440811yescharacteristic, complemented
521#103C2×#6440811yescharacteristic, complemented
522C22⋊C8—731no—
523C22⋊C8—731no—
524C22⋊C8—731no—
525C22⋊C8—1461no—
526C22⋊C8—1461no—
527C22⋊C8C2×#6440811yescharacteristic
528#97—1462no—
529C4×C8—1462no—
530#95—1461no—
531#95—1461no—
532#95—1461no—
533#95—1461no—
534#95—1461no—
535#95—1461no—
536#95—1461no—
537#95—1461no—
538#95—1461no—
539C24—731no—
540C2×Q8—731no—
541C2×Q8—1461no—
542C2×Q8—1461no—
543C2×Q8—1461no—
544C2×Q8—1461no—
545C2×Q8—1461no—
546C2×Q8C22×#6440811yescharacteristic
547C22×C4—5841no—
548C22×C4—5841no—
549C22×C4—731no—
550C22×C4—731no—
551C22×C4—731no—
552C22×C4—731no—
553C22×C4—731no—
554C22×C4—731no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—1461no—
559C22×C4—1461no—
560C22×C4—1461no—
561C22×C4—1461no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1461no—
567C22×C4—1461no—
568C22×C4—1461no—
569C22×C4—1461no—
570C22×C4—1464no—
571C22×C4C22×#6440811yescharacteristic
572C2×C8—731no—
573C2×C8—731no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8C22×#6440811yescharacteristic
585C2×C8C22×#6440811yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—2922no—
588C4⋊C4—5841no—
589C4⋊C4—732no—
590C4⋊C4—732no—
591C4⋊C4—731no—
592C4⋊C4—731no—
593C4⋊C4—731no—
594C4⋊C4—1461no—
595C4⋊C4—1461no—
596C4⋊C4—1461no—
597C4⋊C4—1461no—
598C4⋊C4—1461no—
599C4⋊C4—1461no—
600C4⋊C4—1461no—
601C4⋊C4—1461no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4—1461no—
605C4⋊C4—1462no—
606C4⋊C4—1462no—
607C4⋊C4—1464no—
608C4⋊C4—1461no—
609C4⋊C4C22×#6440811yescharacteristic
610C4⋊C4C22×#6440811yescharacteristic
611C4⋊C4C22×#6440811yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—5841no—
615C22⋊C4—1461no—
616C22⋊C4—1461no—
617C22⋊C4—1461no—
618C22⋊C4—1461no—
619C22⋊C4—1462no—
620C22⋊C4—1462no—
621C22⋊C4—1461no—
622C22⋊C4—1461no—
623C42—21no—
624C42—2922no—
625C42—5841no—
626C42—5841no—
627C42—5841no—
628C42—5841no—
629C42—5841no—
630C42—732no—
631C42—732no—
632C42—1461no—
633C42—1461no—
634C42—1461no—
635C42—1461no—
636C42—1461no—
637C23—731no—
638C23—731no—
639C23—1461no—
640C23—1461no—
641C23—1461no—
642C23—1461no—
643C23—1461no—
644C23—1461no—
645C23D4×#6440811yescharacteristic
646Q8—21no—
647Q8—21no—
648Q8—2921no—
649Q8—2921no—
650Q8—1461no—
651Q8—1461no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—2921no—
659C2×C4—2921no—
660C2×C4—2921no—
661C2×C4—2921no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—2921no—
675C2×C4—2921no—
676C2×C4—5844no—
677C2×C4—731no—
678C2×C4—731no—
679C2×C4—731no—
680C2×C4—731no—
681C2×C4—731no—
682C2×C4—732no—
683C2×C4—732no—
684C2×C4—731no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1461no—
691C2×C4—1461no—
692C2×C4—1461no—
693C2×C4—1462no—
694C2×C4—1462no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1461no—
699C2×C4—1461no—
700C2×C4—1461no—
701C2×C4—1461no—
702C2×C4—1461no—
703C2×C4—1461no—
704C2×C4—1461no—
705C2×C4—1461no—
706C2×C4—1461no—
707C2×C4—1461no—
708C2×C4—1461no—
709C2×C4D4×#6440811yescharacteristic
710C2×C4C23×#6440811yescharacteristic
711C8—21no—
712C8—21no—
713C8—2921no—
714C8—2921no—
715C8—1461no—
716C8—1461no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—2921no—
721C22—2921no—
722C22—2921no—
723C22—2921no—
724C22—731no—
725C22—731no—
726C22—731no—
727C22—731no—
728C22—731no—
729C22—731no—
730C22—1461no—
731C22—1461no—
732C22—1461no—
733C22C2×D4×#6440811yescharacteristic
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—2922no—
740C4—2922no—
741C4—2921no—
742C4—2921no—
743C4—2921no—
744C4—2921no—
745C4—2921no—
746C4—2921no—
747C4—5841no—
748C4—5841no—
749C4—731no—
750C4—731no—
751C4—1462no—
752C4—1462no—
753C4—1461no—
754C4#41×#6440811yescharacteristic
755C4#41×#6440811yescharacteristic
756C2—41no—
757C2—2921no—
758C2—731no—
759C2—731no—
760C2—731no—
761C2—731no—
762C2#123×#6440811yescharacteristic
763C2#2262668911yescharacteristic
764C2#2262669311yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#485×C73C4
socleC22×C73C2×C4×D4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenter#485#64408
hypocenterC73#21589
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #22626011C2semidirect
4. #22626011C2semidirect
5. #22625994C2semidirect
6. #22625992C2semidirect
10. #22625747C2semidirect
11. #107×#64408C2semidirect
12. #22625704C2semidirect
13. #103×#64408C2semidirect
54. #17988931C4semidirect
55. #17988930C4semidirect
56. #17988929C4semidirect
57. #17988928C4semidirect
58. #17988927C4semidirect
59. #17988926C4semidirect
60. #17988925C4semidirect
66. #485×C73C4semidirect
134. #14556525C2×C4semidirect
135. #14556524C2×C4semidirect
136. #14556524C2×C4semidirect
137. #14556523C2×C4semidirect
138. #14556522C2×C4semidirect
139. #14556522C2×C4semidirect
140. #14556516C2×C4semidirect
141. #14556516C2×C4semidirect
142. #14556515C2×C4semidirect
143. #14556515C2×C4semidirect
144. #14556514C2×C4semidirect
145. #14556514C2×C4semidirect
151. #107×C73C2×C4semidirect
152. #106×C73C2×C4semidirect
153. #103×C73C2×C4semidirect
154. #103×C73C2×C4semidirect
398. C73#21589semidirect
411. #485#64408semidirect
507. #107C2×#64408semidirect
511. #106C2×#64408semidirect
520. #103C2×#64408semidirect
521. #103C2×#64408semidirect

Maximal subgroups

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

subgroupindex
#226264182
#226263682
#226260112
#226259942
#226259922
#226259162
#226258802
#226258362
#226257472
#107×#644082
#226257042
#103×#644082
#226256622
#485×D732
#2158973