Finite Group Databasebeta

← #34023294

Subgroups — #34023294

Order 18688.

876 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626426C211yesmaximal, characteristic, complemented
2#22626370C211yesmaximal, characteristic
3#22626110C211yesmaximal, characteristic, complemented
4#22626044C211yesmaximal, characteristic, complemented
5#22625994C211yesmaximal, characteristic, complemented
6#22625993C211yesmaximal, characteristic, complemented
7#22625896C211yesmaximal, characteristic
8#22625894C211yesmaximal, characteristic
9#22625801C211yesmaximal, characteristic
10#22625747C211yesmaximal, characteristic, complemented
11#106×#64408C211yesmaximal, characteristic, complemented
12#22625720C211yesmaximal, characteristic, complemented
13#22625702C211yesmaximal, characteristic
14#102×#64408C211yesmaximal, characteristic
15#476×D73C211yesmaximal, characteristic
16C2×D4×#64408C2211yescharacteristic
17C2×D4×#64408C2211yescharacteristic
18C2×#14556660C2211yescharacteristic
19C2×#14556659C2211yescharacteristic
20#17989588C2211yescharacteristic
21C2×#14556653C2211yescharacteristic
22C2×#14556653C2211yescharacteristic
23C2×#14556645C2211yescharacteristic
24C2×C8×#64408C2211yescharacteristic
25(C2×#64408)⋊Q8—21no—
26(C2×#64408)⋊Q8—21no—
27#17989538C2211yescharacteristic
28#17989538C2211yescharacteristic
29#17989536—21no—
30#17989536—21no—
31#17989531C2211yescharacteristic
32C4⋊C4×#64408C2211yescharacteristic
33C4⋊C4×#64408C2211yescharacteristic
34C4⋊C4×#64408C2211yescharacteristic
35C4⋊C4×#64408C2211yescharacteristic
36C4×C4⋊#64408C2211yescharacteristic
37C22⋊C4×#64408—21no—
38C22⋊C4×#64408—21no—
39C4×C22⋊#64408—21no—
40#17989523C2211yescharacteristic
41C2×(C2×#64408)⋊C4—21no—
42#17989461C2211yescharacteristic
43#17989461C2211yescharacteristic
44#17989460C2211yescharacteristic
45#17989460C2211yescharacteristic
46#17989460C2211yescharacteristic
47#17989460C2211yescharacteristic
48#17989460C2211yescharacteristic
49#17989460C2211yescharacteristic
50#17989452C2211yescharacteristic
51#17989452C2211yescharacteristic
52C4⋊Q8×D73C2211yescharacteristic
53C4×D4×D73C2211yescharacteristic
54#17988878C411yescharacteristic, complemented
55#17988877C411yescharacteristic, complemented
56#17988876C411yescharacteristic, complemented
57#17988876C411yescharacteristic, complemented
58#17988875C411yescharacteristic, complemented
59#17988875C411yescharacteristic, complemented
60#17988874C411yescharacteristic, complemented
61#106×D73C2211yescharacteristic
62#106×D73C2211yescharacteristic
63C4⋊C8×D73C2211yescharacteristic
64#102×D73C2211yescharacteristic
65#102×D73C2211yescharacteristic
66#476×C73C411yescharacteristic, complemented
67C23×#64408—21no—
68C23×#64408—21no—
69C2×#11924036C2311yescharacteristic
70C2×#11924036C2311yescharacteristic
71D4×#64408—22no—
72D4×#64408—22no—
73D4×#64408—22no—
74D4×#64408Q814yescomplemented
75C2×C4⋊#64408—21no—
76C2×C4⋊#64408—21no—
77C2×C4⋊#64408C2311yescharacteristic
78C2×C4⋊#64408C2311yescharacteristic
79C2×C4⋊#64408C2311yescharacteristic
80C2×C4⋊#64408C2311yescharacteristic
81C2×C22⋊#64408—21no—
82C2×C22⋊#64408—21no—
83C2×C4×#64408—21no—
84C2×C4×#64408—21no—
85C2×C4×#64408—21no—
86C2×C4×#64408—21no—
87C2×C4×#64408—21no—
88C2×C4×#64408C2311yescharacteristic
89C2×C4×#64408C2311yescharacteristic
90#14556660—22no—
91#14556659—22no—
92#14556658—21no—
93C4⋊#10596833—21no—
94#14556653—22no—
95#14556653—22no—
96#14556645—22no—
97C8×#64408—22no—
98(C2×#64408)⋊C4—21no—
99(C2×#64408)⋊C4—21no—
100(C2×#64408)⋊C4—21no—
101(C2×#64408)⋊C4—21no—
102(C2×#64408)⋊C4—21no—
103(C2×#64408)⋊C4—21no—
104(C2×#64408)⋊C4—21no—
105(C2×#64408)⋊C4—21no—
106(C2×#64408)⋊C4—21no—
107(C2×#64408)⋊C4D411yescharacteristic
108(C2×#64408)⋊C4D411yescharacteristic
109(C2×#64408)⋊C4D411yescharacteristic
110(C2×#64408)⋊C4D411yescharacteristic
111C2×Q8×D73—21no—
112C2×D4×D73C2311yescharacteristic
113C22×C4×D73—21no—
114C2×C8×D73C2311yescharacteristic
115C2×C8×D73C2311yescharacteristic
116#14556591C2×C411yescharacteristic, complemented
117#14556590—21no—
118#14556590C2×C411yescharacteristic, complemented
119#14556590C2×C411yescharacteristic, complemented
120#14556589—21no—
121C4×D292C2×C411yescharacteristic
122D4×Dic73C2×C411yescharacteristic
123#14556553C2×C411yescharacteristic
124C4×C22⋊D73—21no—
125#14556551—21no—
126C4⋊C4×D73—21no—
127C4⋊C4×D73C2311yescharacteristic
128C4⋊C4×D73C2311yescharacteristic
129C4⋊C4×D73C2311yescharacteristic
130C22⋊C4×D73—21no—
131C42×D73C2311yescharacteristic
132#14556523C2×C411yescharacteristic, complemented
133#14556523C2×C411yescharacteristic, complemented
134#14556522C2×C411yescharacteristic, complemented
135#14556522C2×C411yescharacteristic, complemented
136#14556522C2×C411yescharacteristic, complemented
137#14556522C2×C411yescharacteristic, complemented
138C4⋊#10596831C2×C411yescharacteristic, complemented
139#14556520C2×C411yescharacteristic, complemented
140#14556520C2×C411yescharacteristic, complemented
141#14556513C2×C411yescharacteristic
142#14556513C2×C411yescharacteristic
143#14556512C2×C411yescharacteristic
144#14556512C2×C411yescharacteristic
145#14556511C2×C411yescharacteristic
146#14556511C2×C411yescharacteristic
147C4⋊Q8×C73C2×C411yescharacteristic, complemented
148C4×D4×C73C2×C411yescharacteristic
149#106×C73C2×C411yescharacteristic, complemented
150#106×C73C2×C411yescharacteristic, complemented
151C4⋊C8×C73C2×C411yescharacteristic, complemented
152#102×C73C2×C411yescharacteristic
153#102×C73C2×C411yescharacteristic
154C22×#64408—21no—
155C22×#64408—21no—
156C22×#64408—24no—
157C22×#64408—24no—
158C22×#64408—21no—
159C22×#64408—21no—
160C22×#64408—81no—
161C22×#64408—81no—
162C22×#64408—81no—
163C22×#64408—81no—
164C22×#64408C2×D411yescharacteristic
165C22×#64408C2×D411yescharacteristic
166C22×#64408C2×D411yescharacteristic
167C22×#64408C2×D411yescharacteristic
168#11924036—21no—
169#11924036—21no—
170#11924036—21no—
171#11924036—21no—
172C2×#10596833—21no—
173C2×#10596833—21no—
174C4⋊#64408—21no—
175C4⋊#64408—21no—
176C4⋊#64408—21no—
177C4⋊#64408—21no—
178C4⋊#64408—21no—
179C4⋊#64408—21no—
180C4⋊#64408—81no—
181C4⋊#64408—81no—
182C4⋊#64408C2×Q812yes—
183C4⋊#64408#4112yes—
184C22⋊#64408—24no—
185C22⋊#64408—24no—
186C4×#64408—21no—
187C4×#64408—21no—
188C4×#64408—81no—
189C4×#64408—81no—
190C4×#64408—81no—
191C4×#64408—81no—
192C4×#64408—81no—
193C4×#64408C2×Q812yes—
194C4×#64408#4112yes—
195C23×D73—21no—
196C2×Dic146—21no—
197C2×Dic146—21no—
198C2×Dic146—21no—
199Q8×D73—81no—
200Q8×D73—81no—
201C2×D292C22×C411yescharacteristic
202C2×C22⋊D73—21no—
203D4×D73—21no—
204D4×D73—21no—
205D4×D73C2×Q812yes—
206D4×D73#4112yes—
207C22×Dic73—21no—
208C2×C4×D73—21no—
209C2×C4×D73—21no—
210C2×C4×D73—21no—
211C2×C4×D73—21no—
212C2×C4×D73—21no—
213C2×C4×D73—81no—
214C2×C4×D73—81no—
215C2×C4×D73C2×D411yescharacteristic
216C2×C4×D73C2×D411yescharacteristic
217C2×C4×D73C2411yescharacteristic
218C2×#10596831C22×C411yescharacteristic
219C2×#10596831C22×C411yescharacteristic
220C8×D73—21no—
221C8×D73—21no—
222C8×D73—21no—
223C8×D73—21no—
224C4⋊Dic73—21no—
225C4⋊Dic73C22×C411yescharacteristic
226C4⋊Dic73C22×C411yescharacteristic
227C4⋊Dic73C22×C411yescharacteristic
228#11924007—21no—
229#11924007—21no—
230#11924007—21no—
231#11924007—21no—
232#11924007—21no—
233C22⋊Dic73—21no—
234#11924005—21no—
235#11924005—21no—
236C4×Dic73C22×C411yescharacteristic
237C4×Dic73#4111yescharacteristic
238C4×Dic73#4111yescharacteristic
239C2×Q8×C73—21no—
240C2×D4×C73C22×C411yescharacteristic
241C22×C4×C73—21no—
242C2×C8×C73C22×C411yescharacteristic
243C2×C8×C73C22×C411yescharacteristic
244C4⋊C4×C73—21no—
245C4⋊C4×C73C22×C411yescharacteristic
246C4⋊C4×C73C22×C411yescharacteristic
247C4⋊C4×C73C22×C411yescharacteristic
248C22⋊C4×C73—21no—
249C42×C73C22×C411yescharacteristic
250C23×C73—21no—
251C22×D73—21no—
252C22×D73—22no—
253C22×D73—22no—
254C22×D73—41no—
255C22×D73—41no—
256C22×D73—41no—
257C22×D73—41no—
258C22×D73C22×D411yescharacteristic
259C2×#64408—21no—
260C2×#64408—21no—
261C2×#64408—21no—
262C2×#64408—21no—
263C2×#64408—22no—
264C2×#64408—21no—
265C2×#64408—21no—
266C2×#64408—22no—
267C2×#64408—21no—
268C2×#64408—21no—
269C2×#64408—21no—
270C2×#64408—21no—
271C2×#64408—41no—
272C2×#64408—41no—
273C2×#64408—41no—
274C2×#64408—41no—
275C2×#64408—41no—
276C2×#64408—41no—
277C2×#64408—41no—
278C2×#64408—41no—
279C2×#64408—41no—
280C2×#64408—41no—
281C2×#64408—84no—
282C2×#64408—84no—
283C2×#64408C22⋊Q812yes—
284C2×#64408C22⋊Q812yes—
285Q8×C73—81no—
286D4×C73—21no—
287D4×C73C4×Q812yes—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—81no—
292C2×C4×C73C4×D411yescharacteristic
293C2×C4×C73C4×D411yescharacteristic
294C2×C4×C73C23×C411yescharacteristic
295C22⋊D73—22no—
296C22⋊D73—22no—
297C2×Dic73—21no—
298C2×Dic73—21no—
299C2×Dic73—21no—
300C2×Dic73—81no—
301C2×Dic73C4×D411yescharacteristic
302C2×Dic73C4×D411yescharacteristic
303C2×Dic73C2×#4111yescharacteristic
304D292—21no—
305D292C4×Q812yes—
306C4×D73—21no—
307C4×D73—21no—
308C4×D73—21no—
309C4×D73—21no—
310C4×D73—41no—
311C4×D73—41no—
312C4×D73—41no—
313C4×D73—41no—
314C4×D73—41no—
315C4×D73—41no—
316C4×D73—81no—
317C4×D73—81no—
318C4×D73C22×Q811yescharacteristic
319C4×D73C2×#4111yescharacteristic
320C4×D73C2×#4111yescharacteristic
321C4×D73C2×#4111yescharacteristic
322Dic146—81no—
323Dic146—81no—
324Dic146—81no—
325#10596833—41no—
326#10596833—41no—
327C8×C73—21no—
328C8×C73—21no—
329#10596831—21no—
330#10596831—21no—
331C22×C73—22no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73C2×C4×D411yescharacteristic
335C2×D73—22no—
336C2×D73—41no—
337C2×D73—41no—
338C2×D73—42no—
339C2×D73—42no—
340C2×D73—42no—
341C2×D73—42no—
342C2×D73C2×C22⋊Q811yescharacteristic
343C2×D73#52511yescharacteristic
344C2×D73#57611yescharacteristic
345C2×D73#57711yescharacteristic
346C2×D73#57711yescharacteristic
347C2×D73#57711yescharacteristic
348#64408—22no—
349#64408—22no—
350#64408—42no—
351#64408—41no—
352#64408—42no—
353#64408—41no—
354#64408—81no—
355#64408—81no—
356C4×C73—21no—
357C4×C73—21no—
358C4×C73—41no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73C2×C4×Q811yescharacteristic
362C4×C73C4×#4111yescharacteristic
363Dic73—21no—
364Dic73—21no—
365Dic73—41no—
366Dic73—41no—
367Dic73—41no—
368Dic73#52911yescharacteristic
369Dic73#53311yescharacteristic
370#21623—731nomaximal, Sylow
371C2×C73—42no—
372C2×C73C4×C22⋊Q811yescharacteristic
373C2×C73#294611yescharacteristic
374C2×C73#294911yescharacteristic
375D73—42no—
376D73#308111yescharacteristic
377D73#308411yescharacteristic
378D73#311811yescharacteristic
379D73#312511yescharacteristic
380C2×#476—731no—
381#2331—731no—
382#2275—731no—
383#1988—731no—
384#1949—731no—
385#1920—731no—
386#1919—731no—
387#1864—731no—
388#1862—731no—
389#1804—731no—
390#1776—731no—
391C4×#106—731no—
392#1768—731no—
393#1762—731no—
394C4×#102—731no—
395C73#2162311yescharacteristic, complemented, Sylow
396C2×C4⋊Q8—731no—
397C2×C4×D4—731no—
398C2×C4×D4—731no—
399C2×C4×D4—731no—
400#476—731no—
401#476—731no—
402#476—731no—
403#476—731no—
404#476—731no—
405#476—731no—
406#476—731no—
407#476#6440811yescharacteristic, complemented
408C2×#107—731no—
409C2×#106—731no—
410C2×#106—731no—
411C2×#106—731no—
412C2×C4⋊C8—731no—
413C2×C4⋊C8—731no—
414C2×#102—731no—
415C2×#102—731no—
416C2×#102—731no—
417C2×#102—731no—
418C2×#97—731no—
419C2×C4×C8—731no—
420#391—1461no—
421#391—1461no—
422#389—731no—
423#389—731no—
424#387—1461no—
425#387—1461no—
426#382—731no—
427C4×C4⋊C4—731no—
428C4×C4⋊C4—731no—
429C4×C4⋊C4—731no—
430C4×C4⋊C4—731no—
431C4×C4⋊C4—731no—
432C4×C22⋊C4—1461no—
433C4×C22⋊C4—1461no—
434C4×C22⋊C4—1461no—
435#376—731no—
436C2×#95—1461no—
437#340—731no—
438#340—731no—
439#340—731no—
440#340—731no—
441#340—731no—
442#340—731no—
443#340—731no—
444#340—731no—
445#336—731no—
446#336—731no—
447C22×Q8—1461no—
448C22×D4—731no—
449C23×C4—1461no—
450C23×C4—1461no—
451C23×C4—1461no—
452C22×C8—731no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456C4⋊Q8—731no—
457C4⋊Q8—731no—
458C4⋊Q8—731no—
459C4⋊Q8—1461no—
460C4⋊Q8—1461no—
461C4⋊Q8C2×#6440811yescharacteristic, complemented
462C4×D4—734no—
463C4×D4—731no—
464C4×D4—731no—
465C4×D4—731no—
466C4×D4—1461no—
467C4×D4—1461no—
468C4×D4—1462no—
469C4×D4—1462no—
470C4×D4—1462no—
471C4×D4C2×#6440811yescharacteristic
472C2×C4⋊C4—731no—
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—1461no—
480C2×C4⋊C4—1461no—
481C2×C4⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C22⋊C4—1461no—
485C2×C42—731no—
486C2×C42—731no—
487C2×C42—731no—
488C2×C42—1461no—
489C2×C42—1461no—
490C2×C42—1461no—
491C2×C42—1461no—
492C2×C42—1461no—
493#107—1462no—
494#106—731no—
495#106—731no—
496#106—731no—
497#106—731no—
498#106—731no—
499#106—731no—
500#106—1462no—
501#106C2×#6440811yescharacteristic, complemented
502#106C2×#6440811yescharacteristic, complemented
503C4⋊C8—731no—
504C4⋊C8—731no—
505C4⋊C8—731no—
506C4⋊C8—1461no—
507C4⋊C8—1461no—
508C4⋊C8C2×#6440811yescharacteristic, complemented
509#102—731no—
510#102—731no—
511#102—731no—
512#102—731no—
513#102—731no—
514#102—731no—
515#102—1462no—
516#102—1462no—
517#102C2×#6440811yescharacteristic
518#102C2×#6440811yescharacteristic
519#97—1462no—
520C4×C8—1462no—
521#95—731no—
522#95—731no—
523#95—731no—
524#95—731no—
525#95—1461no—
526#95—1461no—
527#95—1461no—
528#95—1461no—
529#95—1461no—
530#95—1461no—
531#95—1461no—
532#95—1461no—
533#95—1461no—
534C24—1461no—
535C2×Q8—21no—
536C2×Q8—5841no—
537C2×Q8—5841no—
538C2×Q8—1461no—
539C2×Q8—1461no—
540C2×Q8—1461no—
541C2×D4—732no—
542C2×D4—732no—
543C2×D4—731no—
544C2×D4—1461no—
545C2×D4—1461no—
546C2×D4—1461no—
547C2×D4C22×#6440811yescharacteristic
548C22×C4—21no—
549C22×C4—5841no—
550C22×C4—5841no—
551C22×C4—5841no—
552C22×C4—5841no—
553C22×C4—5841no—
554C22×C4—5841no—
555C22×C4—731no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—731no—
559C22×C4—731no—
560C22×C4—731no—
561C22×C4—731no—
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—1461no—
571C22×C4—1464no—
572C22×C4—1464no—
573C22×C4—1461no—
574C2×C8—731no—
575C2×C8—731no—
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×C8—1461no—
585C2×C8—1461no—
586C2×C8C22×#6440811yescharacteristic
587C2×C8C22×#6440811yescharacteristic
588C4⋊C4—21no—
589C4⋊C4—5841no—
590C4⋊C4—5841no—
591C4⋊C4—732no—
592C4⋊C4—732no—
593C4⋊C4—731no—
594C4⋊C4—731no—
595C4⋊C4—731no—
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—1461no—
606C4⋊C4—1461no—
607C4⋊C4—1461no—
608C4⋊C4C22×#6440811yescharacteristic
609C4⋊C4C22×#6440811yescharacteristic
610C4⋊C4C22×#6440811yescharacteristic
611C22⋊C4—21no—
612C22⋊C4—1461no—
613C22⋊C4—1461no—
614C22⋊C4—1464no—
615C22⋊C4—1464no—
616C22⋊C4—1461no—
617C42—5841no—
618C42—5841no—
619C42—5841no—
620C42—5841no—
621C42—5841no—
622C42—732no—
623C42—732no—
624C42—731no—
625C42—731no—
626C42—731no—
627C42—1461no—
628C42—1461no—
629C42C22×#6440811yescharacteristic
630C23—21no—
631C23—2921no—
632C23—2921no—
633C23—2921no—
634C23—2921no—
635C23—731no—
636C23—1462no—
637C23—1462no—
638C23—1461no—
639Q8—81no—
640Q8—5841no—
641Q8—5841no—
642Q8—5841no—
643D4—21no—
644D4—732no—
645D4—1462no—
646D4—1462no—
647D4—1461no—
648D4Q8×#6440812yes—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—81no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
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—5841no—
670C2×C4—5841no—
671C2×C4—5844no—
672C2×C4—5841no—
673C2×C4—5844no—
674C2×C4—731no—
675C2×C4—731no—
676C2×C4—731no—
677C2×C4—731no—
678C2×C4—731no—
679C2×C4—732no—
680C2×C4—732no—
681C2×C4—731no—
682C2×C4—731no—
683C2×C4—1461no—
684C2×C4—1461no—
685C2×C4—1461no—
686C2×C4—1461no—
687C2×C4—1461no—
688C2×C4—1461no—
689C2×C4—1461no—
690C2×C4—1462no—
691C2×C4—1462no—
692C2×C4—1461no—
693C2×C4—1461no—
694C2×C4—1461no—
695C2×C4—1461no—
696C2×C4—1461no—
697C2×C4—1461no—
698C2×C4—1461no—
699C2×C4—1461no—
700C2×C4—1461no—
701C2×C4—1461no—
702C2×C4D4×#6440811yescharacteristic
703C2×C4D4×#6440811yescharacteristic
704C2×C4C23×#6440811yescharacteristic
705C8—21no—
706C8—21no—
707C8—2921no—
708C8—2921no—
709C8—1461no—
710C8—1461no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—2922no—
715C22—2922no—
716C22—2922no—
717C22—2922no—
718C22—2921no—
719C22—2921no—
720C22—731no—
721C22—731no—
722C22—731no—
723C22—731no—
724C22—731no—
725C22—731no—
726C22—1462no—
727C22C2×D4×#6440811yescharacteristic
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—2922no—
734C4—2922no—
735C4—2921no—
736C4—2921no—
737C4—2921no—
738C4—2921no—
739C4—2921no—
740C4—5841no—
741C4—5841no—
742C4—731no—
743C4—731no—
744C4—1462no—
745C4—1462no—
746C4—1461no—
747C4—1461no—
748C4C2×Q8×#6440811yescharacteristic
749C4#41×#6440811yescharacteristic
750C2—42no—
751C2—2922no—
752C2—731no—
753C2—731no—
754C2—731no—
755C2—731no—
756C2C22⋊Q8×#6440811yescharacteristic
757C2#2262668811yescharacteristic
758C2#2262669111yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#476×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×D4×D73C23
cosocleC2×C4×D73C24
hypercenter#476#64408
hypocenterC73#21623
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #22626426C2semidirect
3. #22626110C2semidirect
4. #22626044C2semidirect
5. #22625994C2semidirect
6. #22625993C2semidirect
10. #22625747C2semidirect
11. #106×#64408C2semidirect
12. #22625720C2semidirect
54. #17988878C4semidirect
55. #17988877C4semidirect
56. #17988876C4semidirect
57. #17988876C4semidirect
58. #17988875C4semidirect
59. #17988875C4semidirect
60. #17988874C4semidirect
66. #476×C73C4semidirect
74. D4×#64408Q8semidirect
116. #14556591C2×C4semidirect
118. #14556590C2×C4semidirect
119. #14556590C2×C4semidirect
132. #14556523C2×C4semidirect
133. #14556523C2×C4semidirect
134. #14556522C2×C4semidirect
135. #14556522C2×C4semidirect
136. #14556522C2×C4semidirect
137. #14556522C2×C4semidirect
138. C4⋊#10596831C2×C4semidirect
139. #14556520C2×C4semidirect
140. #14556520C2×C4semidirect
147. C4⋊Q8×C73C2×C4semidirect
149. #106×C73C2×C4semidirect
150. #106×C73C2×C4semidirect
151. C4⋊C8×C73C2×C4semidirect
395. C73#21623semidirect
407. #476#64408semidirect
461. C4⋊Q8C2×#64408semidirect
501. #106C2×#64408semidirect
502. #106C2×#64408semidirect
508. C4⋊C8C2×#64408semidirect

Maximal subgroups

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

subgroupindex
#226264262
#226263702
#226261102
#226260442
#226259942
#226259932
#226258962
#226258942
#226258012
#226257472
#106×#644082
#226257202
#226257022
#102×#644082
#476×D732
#2162373