Finite Group Databasebeta

← #25106921

Subgroups — #25106921

Order 11008.

894 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143039C211yesmaximal, characteristic
2#19143038C211yesmaximal, characteristic
3C2×#14582864C211yesmaximal, characteristic
4#19134802C211yesmaximal, characteristic, complemented
5#19134801C211yesmaximal, characteristic, complemented
6#19134801C211yesmaximal, characteristic, complemented
7#19134800C211yesmaximal, characteristic, complemented
8#19134799C211yesmaximal, characteristic, complemented
9#19134798C211yesmaximal, characteristic, complemented
10#19134798C211yesmaximal, characteristic, complemented
11#19134636C211yesmaximal, characteristic, complemented
12#19134634C211yesmaximal, characteristic, complemented
13#19134632C211yesmaximal, characteristic, complemented
14#19134630C211yesmaximal, characteristic, complemented
15C43×#1855C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22C2×#13063261C2211yescharacteristic
23C2×#13063261C2211yescharacteristic
24C2×#13063260C2211yescharacteristic
25C2×#13063260C2211yescharacteristic
26C2×#13063260C2211yescharacteristic
27C2×#13063260C2211yescharacteristic
28#14582867—21no—
29#14582867—21no—
30#14582865—21no—
31#14582865—21no—
32#14582864—21no—
33#14582864—21no—
34#14582864—21no—
35#14582864—21no—
36#14582864C412yes—
37#14582864C412yes—
38#14582864C412yes—
39#14582864C412yes—
40#14582863C2211yescharacteristic
41#14582862C2211yescharacteristic
42#14582862C2211yescharacteristic
43#14582862C2211yescharacteristic
44#14582862C2211yescharacteristic
45#14582862C2211yescharacteristic
46#14582862C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50#14582664C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×#108×C43C2211yescharacteristic
58C2×#108×C43C2211yescharacteristic
59C43×#407C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#341C2211yescharacteristic
62C43×#341C2211yescharacteristic
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C411yescharacteristic
68C2×#10621898C2×C411yescharacteristic
69C2×#10621898C2×C411yescharacteristic
70C2×#10621898C2×C411yescharacteristic
71C2×#10621898D411yescharacteristic
72C2×#10621898D411yescharacteristic
73C2×#10621898D411yescharacteristic
74C2×#10621898D411yescharacteristic
75C22×Dic86Q811yescharacteristic
76C22×D172Q811yescharacteristic
77C22×C22⋊D43Q811yescharacteristic
78C22×C22⋊D43Q811yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—21no—
82C2×#10621877—41no—
83C2×#10621877—41no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621872—21no—
89C2×#10621872—21no—
90C2×#10621872—41no—
91C2×#10621872—41no—
92C2×#10621872C2×C412yes—
93C2×#10621872C2×C412yes—
94M16×D43—41no—
95M16×D43—41no—
96M16×D43—41no—
97M16×D43—41no—
98C22×C43⋊C8—21no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—21no—
102C2×C8×D43—21no—
103C2×C8×D43—41no—
104C2×C8×D43—41no—
105C2×C8×D43C2×C412yes—
106C2×C8×D43C2×C412yes—
107#13063261—41no—
108#13063261—41no—
109#13063260—41no—
110#13063260—41no—
111#13063260—41no—
112#13063260—41no—
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2×C412yes—
116C22⋊(C43⋊C8)C2×C412yes—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8C2×C412yes—
130(C2×D43)⋊C8C2×C412yes—
131(C2×D43)⋊C8C2×C412yes—
132(C2×D43)⋊C8C2×C412yes—
133C23×C4×C43C2311yescharacteristic
134C2×M16×C43—21no—
135C2×M16×C43—41no—
136C2×M16×C43—41no—
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43—21no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#108×C43—41no—
145#108×C43—41no—
146C22⋊C8×C43—21no—
147C22⋊C8×C43—21no—
148C22⋊C8×C43C2×C412yes—
149C22⋊C8×C43C2×C412yes—
150C24×C43C2×Q811yescharacteristic
151C23×D43C2×Q811yescharacteristic
152C23×D43C2×Q811yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43C22×C411yescharacteristic
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×Q811yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—41no—
164C2×C22⋊D43—41no—
165C2×C22⋊D43—41no—
166C2×C22⋊D43—41no—
167C2×C22⋊D43C4⋊C411yescharacteristic
168C2×C22⋊D43C4⋊C411yescharacteristic
169C2×C22⋊D43C4⋊C411yescharacteristic
170C2×C22⋊D43C4⋊C411yescharacteristic
171C2×C22⋊D43C4⋊C411yescharacteristic
172C2×C22⋊D43C4⋊C411yescharacteristic
173C2×C22⋊D43C4⋊C411yescharacteristic
174C2×C22⋊D43C4⋊C411yescharacteristic
175C22×Dic43C2×Q811yescharacteristic
176C22×Dic43C2×Q811yescharacteristic
177#10621898—41no—
178#10621898—41no—
179#10621898—41no—
180#10621898—41no—
181#10621898—41no—
182#10621898—41no—
183#10621898—41no—
184#10621898—41no—
185#10621898—41no—
186#10621898—41no—
187#10621898—41no—
188#10621898—41no—
189#10621898—41no—
190#10621898—41no—
191#10621898—41no—
192#10621898—41no—
193C2×D172—41no—
194C2×D172—41no—
195C2×D172C4⋊C411yescharacteristic
196C2×D172C4⋊C411yescharacteristic
197C2×D172C4⋊C411yescharacteristic
198C2×D172C4⋊C411yescharacteristic
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43C22×C411yescharacteristic
208C2×C4×D43C22×C411yescharacteristic
209C2×C4×D43C22×C411yescharacteristic
210C2×C4×D43C22×C411yescharacteristic
211C2×C4×D43C2×D411yescharacteristic
212C2×C4×D43C2×D411yescharacteristic
213C2×C4×D43C2×D411yescharacteristic
214C2×C4×D43C2×D411yescharacteristic
215C2×Dic86—41no—
216C2×Dic86—41no—
217C2×Dic86C4⋊C411yescharacteristic
218C2×Dic86C4⋊C411yescharacteristic
219C2×Dic86C4⋊C411yescharacteristic
220C2×Dic86C4⋊C411yescharacteristic
221M16×C43—21no—
222M16×C43—21no—
223M16×C43—21no—
224M16×C43—21no—
225M16×C43—21no—
226M16×C43—21no—
227M16×C43—21no—
228M16×C43—21no—
229M16×C43—42no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—42no—
239C2×C8×C43C22×C412yes—
240C2×C8×C43C22×C412yes—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877—21no—
246#10621877—21no—
247#10621877—21no—
248#10621877—21no—
249#10621877—42no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—42no—
259C2×C43⋊C8C22×C412yes—
260C2×C43⋊C8C22×C412yes—
261#10621872—42no—
262#10621872—42no—
263#10621872—42no—
264#10621872—42no—
265C8×D43—42no—
266C8×D43—42no—
267C8×D43—42no—
268C8×D43—42no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C2×C4⋊C411yescharacteristic
274C23×C43C2×C4⋊C411yescharacteristic
275C23×C43C22×Q811yescharacteristic
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43C2×C4⋊C411yescharacteristic
285C22×D43C2×C4⋊C411yescharacteristic
286C22×D43C2×C4⋊C411yescharacteristic
287C22×D43C2×C4⋊C411yescharacteristic
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43C2×C4⋊C411yescharacteristic
299C2×C4×C43C2×C4⋊C411yescharacteristic
300C2×C4×C43C23×C411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C22⋊D43—41no—
307C22⋊D43—41no—
308C22⋊D43—41no—
309C22⋊D43—41no—
310C22⋊D43—41no—
311C22⋊D43—41no—
312C22⋊D43—41no—
313C22⋊D43—41no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43C2×C4⋊C411yescharacteristic
319C2×Dic43C2×C4⋊C411yescharacteristic
320C2×Dic43C2×C4⋊C411yescharacteristic
321C2×Dic43C2×C4⋊C411yescharacteristic
322D172—41no—
323D172—41no—
324D172—41no—
325D172—41no—
326C4×D43—21no—
327C4×D43—21no—
328C4×D43—21no—
329C4×D43—21no—
330C4×D43—21no—
331C4×D43—21no—
332C4×D43—21no—
333C4×D43—21no—
334C4×D43—21no—
335C4×D43—21no—
336C4×D43—21no—
337C4×D43—21no—
338C4×D43—21no—
339C4×D43—21no—
340C4×D43—21no—
341C4×D43—21no—
342Dic86—41no—
343Dic86—41no—
344Dic86—41no—
345Dic86—41no—
346C8×C43—22no—
347C8×C43—22no—
348C8×C43—41no—
349C8×C43—41no—
350C8×C43—41no—
351C8×C43—41no—
352C43⋊C8—22no—
353C43⋊C8—22no—
354C43⋊C8—41no—
355C43⋊C8—41no—
356C43⋊C8—41no—
357C43⋊C8—41no—
358#21950—431nomaximal, Sylow
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43C22×C4⋊C411yescharacteristic
370C22×C43#54311yescharacteristic
371C22×C43#54311yescharacteristic
372C2×D43—21no—
373C2×D43—21no—
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—21no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—81no—
387C2×D43—81no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43#51811yescharacteristic
391C4×C43#51811yescharacteristic
392C4×C43#53411yescharacteristic
393C4×C43#53411yescharacteristic
394Dic43—21no—
395Dic43—21no—
396Dic43—21no—
397Dic43—21no—
398#2879—431no—
399#2879—431no—
400C2×#408—431no—
401#1855—431no—
402#1855—431no—
403#1855—431no—
404#1855—431no—
405#1855—431no—
406#1855—431no—
407#1855—431no—
408#1855D4311yescharacteristic, complemented
409#1811—431no—
410#1811—431no—
411#1810—431no—
412#1810—431no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—41no—
416C2×C43—41no—
417C2×C43#231511yescharacteristic
418C2×C43#291611yescharacteristic
419C2×C43#291611yescharacteristic
420D43—41no—
421D43—41no—
422D43—41no—
423D43—41no—
424C22×#41—431no—
425C22×M16—431no—
426C22×M16—431no—
427C22×M16—431no—
428C22×M16—431no—
429C22×M16C2×D4311yescharacteristic
430C23×C8—431no—
431C2×#108—431no—
432C2×#108—431no—
433C2×#108—431no—
434C2×#108—431no—
435C2×#108—431no—
436C2×#108—431no—
437C2×#108C2×D4311yescharacteristic
438C2×#108C2×D4311yescharacteristic
439#408—432no—
440#408—432no—
441#408—432no—
442#408—432no—
443#408—861no—
444#408—861no—
445#408—861no—
446#408—861no—
447#408—861no—
448#408—861no—
449#408—861no—
450#408—861no—
451#407—431no—
452#407—431no—
453#407—431no—
454#407—431no—
455#407—431no—
456#407—431no—
457#407—431no—
458#407C2×D4311yescharacteristic
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×C22⋊C8—431no—
462C2×C22⋊C8C2×D4311yescharacteristic
463#341—431no—
464#341—431no—
465#341—431no—
466#341—431no—
467#341—431no—
468#341—431no—
469#341C2×D4311yescharacteristic
470#341C2×D4311yescharacteristic
471C43#2195011yescharacteristic, complemented, Sylow
472C2×#41—431no—
473C2×#41—431no—
474C2×#41—431no—
475C2×#41—431no—
476C2×#41—431no—
477C2×#41—431no—
478C2×#41—431no—
479C2×#41—431no—
480C2×#41—1721no—
481C2×#41—1721no—
482C2×#41—1721no—
483C2×#41—1721no—
484C22×Q8—431no—
485C22×D4—431no—
486C22×D4—431no—
487C22×D4—431no—
488C23×C4—431no—
489C23×C4—431no—
490C23×C4C22×D4311yescharacteristic
491C2×M16—21no—
492C2×M16—41no—
493C2×M16—41no—
494C2×M16—432no—
495C2×M16—432no—
496C2×M16—431no—
497C2×M16—431no—
498C2×M16—431no—
499C2×M16—431no—
500C2×M16—861no—
501C2×M16—861no—
502C2×M16—861no—
503C2×M16—1721no—
504C2×M16—1721no—
505C2×M16—1721no—
506C2×M16—1721no—
507C2×M16—1721no—
508C2×M16—1721no—
509C2×M16—1721no—
510C2×M16—1721no—
511C2×M16C22×D4311yescharacteristic
512C2×M16C22×D4311yescharacteristic
513C2×M16C22×D4311yescharacteristic
514C2×M16C22×D4311yescharacteristic
515C22×C8—21no—
516C22×C8—431no—
517C22×C8—431no—
518C22×C8—432no—
519C22×C8—432no—
520C22×C8—861no—
521C22×C8—861no—
522C22×C8—861no—
523C22×C8—1721no—
524C22×C8—1721no—
525C22×C8C22×D4311yescharacteristic
526C22×C8C22×D4311yescharacteristic
527#108—41no—
528#108—41no—
529#108—1721no—
530#108—1721no—
531#108—1721no—
532#108—1721no—
533#108—1721no—
534#108—1721no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—432no—
538C22⋊C8—432no—
539C22⋊C8—432no—
540C22⋊C8—432no—
541C22⋊C8—432no—
542C22⋊C8—432no—
543C22⋊C8—861no—
544C22⋊C8—861no—
545C22⋊C8—861no—
546C22⋊C8—861no—
547C22⋊C8—861no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550C22⋊C8—861no—
551C22⋊C8—861no—
552C22⋊C8—861no—
553C22⋊C8—861no—
554C22⋊C8—861no—
555C22⋊C8—861no—
556C22⋊C8—861no—
557C22⋊C8C4×D4312yes—
558C22⋊C8C4×D4312yes—
559C24—431no—
560C24—431no—
561C24Q8×D4311yescharacteristic
562#41—1721no—
563#41—1721no—
564#41—1721no—
565#41—1721no—
566#41—1721no—
567#41—1721no—
568#41—1721no—
569#41—1721no—
570#41—1721no—
571#41—1721no—
572#41—1721no—
573#41—1721no—
574#41—1721no—
575#41—1721no—
576#41—1721no—
577#41—1721no—
578C2×Q8—431no—
579C2×Q8—431no—
580C2×Q8—431no—
581C2×Q8—431no—
582C2×Q8—1721no—
583C2×Q8—1721no—
584C2×D4—431no—
585C2×D4—431no—
586C2×D4—431no—
587C2×D4—431no—
588C2×D4—431no—
589C2×D4—431no—
590C2×D4—431no—
591C2×D4—431no—
592C2×D4—431no—
593C2×D4—431no—
594C2×D4—431no—
595C2×D4—431no—
596C2×D4—1721no—
597C2×D4—1721no—
598C2×D4—1721no—
599C2×D4—1721no—
600C2×D4—1721no—
601C2×D4—1721no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—431no—
607C22×C4—431no—
608C22×C4—431no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4C2×C4×D4311yescharacteristic
625C22×C4C2×C4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4Q8×D4311yescharacteristic
629C22×C4C23×D4311yescharacteristic
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—42no—
639M16—861no—
640M16—861no—
641M16—861no—
642M16—861no—
643M16—861no—
644M16—861no—
645M16—861no—
646M16—861no—
647M16—1722no—
648M16—1722no—
649M16—1722no—
650M16—1722no—
651M16—1722no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—1722no—
672C2×C8—1722no—
673C2×C8—1722no—
674C2×C8—1722no—
675C2×C8—1722no—
676C2×C8C2×C4×D4312yes—
677C2×C8C2×C4×D4312yes—
678C23—21no—
679C23—21no—
680C23—41no—
681C23—41no—
682C23—431no—
683C23—431no—
684C23—431no—
685C23—431no—
686C23—861no—
687C23—861no—
688C23—861no—
689C23—861no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23C4⋊C4×D4311yescharacteristic
695C23C4⋊C4×D4311yescharacteristic
696C23C2×Q8×D4311yescharacteristic
697Q8—1721no—
698Q8—1721no—
699Q8—1721no—
700Q8—1721no—
701D4—1721no—
702D4—1721no—
703D4—1721no—
704D4—1721no—
705D4—1721no—
706D4—1721no—
707D4—1721no—
708D4—1721no—
709D4—1721no—
710D4—1721no—
711D4—1721no—
712D4—1721no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—431no—
724C2×C4—431no—
725C2×C4—431no—
726C2×C4—431no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—861no—
738C2×C4—861no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—861no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—861no—
747C2×C4C4⋊C4×D4311yescharacteristic
748C2×C4C4⋊C4×D4311yescharacteristic
749C2×C4C22×C4×D4311yescharacteristic
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4#1306337011yescharacteristic
752C2×C4#1306337011yescharacteristic
753C2×C4#1306337111yescharacteristic
754C2×C4#1306337111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—862no—
762C8—862no—
763C8—1721no—
764C8—1721no—
765C8—1721no—
766C8—1721no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—81no—
776C22—81no—
777C22—861no—
778C22—861no—
779C22—861no—
780C22—861no—
781C22—861no—
782C22—861no—
783C22—861no—
784C22—861no—
785C22—861no—
786C22—861no—
787C22—861no—
788C22—861no—
789C22—3441no—
790C22—3441no—
791C22—1722no—
792C22—1722no—
793C22C2×C4⋊C4×D4311yescharacteristic
794C22#1458352411yescharacteristic
795C22#1458352411yescharacteristic
796C4—21no—
797C4—21no—
798C4—861no—
799C4—861no—
800C4—861no—
801C4—861no—
802C4#1458337111yescharacteristic
803C4#1458337111yescharacteristic
804C4#1458345911yescharacteristic
805C4#1458346011yescharacteristic
806C2—21no—
807C2—21no—
808C2—41no—
809C2—41no—
810C2—1721no—
811C2—1721no—
812C2—1721no—
813C2—1721no—
814C2#1913720611yescharacteristic
815C2#1914320311yescharacteristic
816C2#1914320511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1855C2
socleC22×C43C22×C4⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1855D43
hypocenterC43#21950
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
4. #19134802C2semidirect
5. #19134801C2semidirect
6. #19134801C2semidirect
7. #19134800C2semidirect
8. #19134799C2semidirect
9. #19134798C2semidirect
10. #19134798C2semidirect
11. #19134636C2semidirect
12. #19134634C2semidirect
13. #19134632C2semidirect
14. #19134630C2semidirect
15. C43×#1855C2semidirect
408. #1855D43semidirect
471. C43#21950semidirect

Maximal subgroups

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

subgroupindex
#191430392
#191430382
C2×#145828642
#191348022
#191348012
#191348002
#191347992
#191347982
#191346362
#191346342
#191346322
#191346302
C43×#18552
#2195043