Finite Group Databasebeta

← #25065508

Subgroups — #25065508

Order 11008.

988 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic
2#19143725C211yesmaximal, characteristic, complemented
3#19143717C211yesmaximal, characteristic, complemented
4#19133331C211yesmaximal, characteristic, complemented
5#19133315C211yesmaximal, characteristic, complemented
6#19133314C211yesmaximal, characteristic, complemented
7#19133300C211yesmaximal, characteristic, complemented
8#19133299C211yesmaximal, characteristic, complemented
9#19133271C211yesmaximal, characteristic, complemented
10#19133261C211yesmaximal, characteristic, complemented
11#19133261C211yesmaximal, characteristic, complemented
12#19133258C211yesmaximal, characteristic, complemented
13#19133245C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1547C211yesmaximal, characteristic, complemented
16#14583632—21no—
17#14583631—21no—
18#14583568—21no—
19#14583567—21no—
20#14583546—21no—
21#14583544—21no—
22#14583542—21no—
23#14583537—21no—
24#14583502C412yes—
25#14583500C412yes—
26#14583465C412yes—
27#14583454C2211yescharacteristic
28#14583450C2211yescharacteristic
29#14583449C2211yescharacteristic
30#14583447C2211yescharacteristic
31#127×D43C2211yescharacteristic
32#14583371C412yes—
33C4×#10621898C2211yescharacteristic
34#14583028—21no—
35#14583023—21no—
36#14582976—21no—
37#14582975—21no—
38#14582975—21no—
39#14582970—21no—
40#14582969—21no—
41C8×C22⋊D43—21no—
42#14582956C2211yescharacteristic, complemented
43#14582955C2211yescharacteristic, complemented
44#14582952C2211yescharacteristic, complemented
45#14582951C2211yescharacteristic
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic, complemented
48#14582921C2211yescharacteristic
49#14582921C2211yescharacteristic
50#14582921C2211yescharacteristic, complemented
51C4⋊C8×D43C2211yescharacteristic, complemented
52#14582646C2211yescharacteristic, complemented
53#14582646C2211yescharacteristic, complemented
54#14582645C2211yescharacteristic, complemented
55#14582645C2211yescharacteristic, complemented
56#14582644C2211yescharacteristic, complemented
57#14582644C2211yescharacteristic, complemented
58#14582643C2211yescharacteristic
59#14582643C2211yescharacteristic
60#14582642C2211yescharacteristic
61#14582642C2211yescharacteristic
62#14582642C2211yescharacteristic
63#14582642C2211yescharacteristic
64C43×#532C2211yescharacteristic
65C43×#423C2211yescharacteristic, complemented
66C2×C4⋊C8×C43C2211yescharacteristic, complemented
67C43×#332C2211yescharacteristic, complemented
68C43×#332C2211yescharacteristic, complemented
69C43×#331C2211yescharacteristic
70C43×#331C2211yescharacteristic
71C2×#10621902—21no—
72C2×#10621898—21no—
73C2×#10621898C2×C411yescharacteristic
74C2×#10621900—21no—
75C2×D4×D43—21no—
76C2×D4×D43—21no—
77C2×D4×D43C2×C412yes—
78C2×#10621872—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C2×C8×D43—21no—
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063321—22no—
85#13063321—21no—
86#13063321—21no—
87#13063321C2×C412yes—
88#13063316C2×C412yes—
89#13063314—21no—
90#13063313—21no—
91#13063312—21no—
92#13063311—22no—
93#13063309—22no—
94#13063308—22no—
95#13063307—22no—
96#13063307—22no—
97#13063305—21no—
98#13063301—21no—
99#13063300—21no—
100#13063300C2×C412yes—
101#13063299—21no—
102#13063299—22no—
103#13063299C2×C412yes—
104#13063298—22no—
105#13063297—22no—
106#13063296—21no—
107#13063296—22no—
108#13063296C2×C412yes—
109#13063295—22no—
110#13063293—22no—
111Q8×Dic43—21no—
112C4×Dic86D411yescharacteristic
113C4×Dic86D411yescharacteristic
114#13063290—21no—
115C4×D172—21no—
116C4×D172C2×C412yes—
117C4×D172D411yescharacteristic
118C4×D172D411yescharacteristic
119D4×Dic43—21no—
120D4×Dic43C2×C412yes—
121#13063287—21no—
122#13063287C2×C412yes—
123C4×C22⋊D43—22no—
124C4×C22⋊D43D411yescharacteristic
125C4×C22⋊D43D411yescharacteristic
126C4×C22⋊D43D411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128(C22⋊D43)⋊C4—22no—
129#13063284C2×C411yescharacteristic
130#13063283C2×C412yes—
131#13063282C2×C411yescharacteristic
132#13063282C2×C411yescharacteristic
133C2×(C2×D43)⋊C4—22no—
134C22⋊C4×D43—22no—
135C42×D43C2311yescharacteristic
136C42×D43C2311yescharacteristic
137C4⋊(C43⋊C8)C2311yescharacteristic
138C4⋊(C43⋊C8)C2311yescharacteristic
139C4⋊(C43⋊C8)C2311yescharacteristic
140C4⋊(C43⋊C8)C2311yescharacteristic
141Dic43⋊C8—21no—
142Dic43⋊C8—21no—
143Dic43⋊C8—21no—
144Dic43⋊C8—21no—
145C22⋊(C43⋊C8)—21no—
146C22⋊(C43⋊C8)—21no—
147(C2×D43)⋊C8—21no—
148(C2×D43)⋊C8—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151#13063236—21no—
152#13063235—21no—
153C4×C43⋊C8—21no—
154C8×Dic43—21no—
155C8×Dic43—21no—
156C8×Dic43—21no—
157C2×#41×C43—21no—
158C2×M16×C43—21no—
159C22×C8×C43—21no—
160C4⋊Q8×C43C2311yescharacteristic
161#127×C43C2311yescharacteristic
162#124×C43—21no—
163#121×C43—21no—
164#121×C43C2×C412yes—
165C4×D4×C43—21no—
166C4×D4×C43C2×C412yes—
167C2×C42×C43C2311yescharacteristic
168C4⋊C8×C43—21no—
169C4⋊C8×C43—21no—
170C4⋊C8×C43C2311yescharacteristic
171C4⋊C8×C43C2311yescharacteristic
172C4⋊C8×C43C2311yescharacteristic
173C4⋊C8×C43C2311yescharacteristic
174C23×D43—22no—
175#41×C43—81no—
176#41×C43—81no—
177C2×Q8×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—22no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—22no—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43C22⋊C411yescharacteristic
192C2×C22⋊D43C22⋊C411yescharacteristic
193C22×Dic43—22no—
194#10621902—81no—
195#10621902—81no—
196#10621900—81no—
197#10621900—81no—
198D4×D43—44no—
199D4×D43—81no—
200D4×D43—81no—
201D4×D43—81no—
202D4×D43—81no—
203#10621898—42no—
204#10621898—81no—
205#10621898—81no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—22no—
209C2×D172C22⋊C411yescharacteristic
210C2×D172C22×C412yes—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43C22×C411yescharacteristic
214C2×C4×D43C22×C411yescharacteristic
215C2×C4×D43C2×D411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×Dic86—21no—
220C2×Dic86C22⋊C411yescharacteristic
221M16×C43—81no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—21no—
225C2×C8×C43—21no—
226C2×C8×C43—81no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43C22×C412yes—
229C22⋊C4×C43—22no—
230C22⋊C4×C43—22no—
231C42×C43C22×C411yescharacteristic
232C42×C43C2×D411yescharacteristic
233C42×C43C2×D411yescharacteristic
234C42×C43C2411yescharacteristic
235C22⋊Dic43—22no—
236C22⋊Dic43—22no—
237C22⋊Dic43C22⋊C411yescharacteristic
238C22⋊Dic43C22⋊C411yescharacteristic
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4—22no—
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—22no—
244(C2×D43)⋊C4C22⋊C411yescharacteristic
245(C2×D43)⋊C4C22⋊C411yescharacteristic
246(C2×D43)⋊C4C22⋊C411yescharacteristic
247(C2×D43)⋊C4C22⋊C411yescharacteristic
248C4⋊Dic43—21no—
249C4⋊Dic43—22no—
250C4⋊Dic43C22⋊C411yescharacteristic
251C4⋊Dic43C22⋊C411yescharacteristic
252C4⋊Dic43C22×C412yes—
253Dic43⋊C4—22no—
254Dic43⋊C4C22⋊C411yescharacteristic
255Dic43⋊C4C22⋊C411yescharacteristic
256Dic43⋊C4C22⋊C411yescharacteristic
257Dic43⋊C4C22⋊C411yescharacteristic
258C4×Dic43—22no—
259C4×Dic43C22×C411yescharacteristic
260C4×Dic43C22×C411yescharacteristic
261C4×Dic43C2×D411yescharacteristic
262C4×Dic43C2×D411yescharacteristic
263C4×Dic43C2×D411yescharacteristic
264C4×Dic43C2×D411yescharacteristic
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269#10621872—81no—
270#10621872—81no—
271#10621872—81no—
272C8×D43—81no—
273C23×C43—22no—
274C23×C43C2×C22⋊C411yescharacteristic
275C22×D43—22no—
276C22×D43—44no—
277C22×D43—82no—
278C22×D43—82no—
279C22×D43C2×C22⋊C411yescharacteristic
280C22×D43C2×C22⋊C411yescharacteristic
281Q8×C43—41no—
282Q8×C43—41no—
283D4×C43—42no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—82no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—22no—
294C2×C4×C43—41no—
295C2×C4×C43—82no—
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C22⋊D43—22no—
303C22⋊D43—41no—
304C22⋊D43—44no—
305C22⋊D43—82no—
306C22⋊D43—82no—
307C22⋊D43—82no—
308C22⋊D43—82no—
309C2×Dic43—22no—
310C2×Dic43—82no—
311C2×Dic43C2×C22⋊C411yescharacteristic
312C2×Dic43C2×C22⋊C411yescharacteristic
313C2×Dic43C2×C22⋊C411yescharacteristic
314C2×Dic43C2×C22⋊C411yescharacteristic
315C2×Dic43C2×C22⋊C411yescharacteristic
316C2×Dic43C2×C22⋊C411yescharacteristic
317D172—41no—
318D172—42no—
319D172—41no—
320D172—41no—
321D172—41no—
322D172—41no—
323D172—82no—
324C4×D43—21no—
325C4×D43—21no—
326C4×D43—21no—
327C4×D43—21no—
328C4×D43—21no—
329C4×D43—21no—
330C4×D43—21no—
331C4×D43—21no—
332C4×D43—22no—
333C4×D43—41no—
334C4×D43—82no—
335C4×D43—82no—
336Dic86—22no—
337Dic86—41no—
338Dic86—41no—
339C8×C43—41no—
340C8×C43—41no—
341C8×C43—41no—
342C8×C43—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347#17776—431nomaximal, Sylow
348C22×C43—21no—
349C22×C43—21no—
350C22×C43—21no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43C22×C22⋊C411yescharacteristic
355C2×D43—21no—
356C2×D43—21no—
357C2×D43—21no—
358C2×D43—21no—
359C2×D43—21no—
360C2×D43—21no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—164no—
365C4×C43—21no—
366C4×C43—21no—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—42no—
370C4×C43#57611yescharacteristic
371C4×C43#57611yescharacteristic
372C4×C43#57711yescharacteristic
373C4×C43#57711yescharacteristic
374Dic43—21no—
375Dic43—21no—
376Dic43—21no—
377Dic43—21no—
378Dic43—21no—
379Dic43—42no—
380Dic43#41312yes—
381#3508—431no—
382#2991—431no—
383#2990—431no—
384#1561—431no—
385#1557—431no—
386#1557—431no—
387#1553—431no—
388#1553—431no—
389#1547—431no—
390#1547D4311yescharacteristic, complemented
391#1545—431no—
392#1545—431no—
393#1544—431no—
394#1540—431no—
395#1540—431no—
396C2×C43—41no—
397C2×C43—82no—
398C2×C43C2×#41311yescharacteristic
399C2×C43#289711yescharacteristic
400C2×C43#289711yescharacteristic
401D43—41no—
402D43—41no—
403D43—82no—
404#559—861no—
405#559—861no—
406#550—861no—
407#550—861no—
408#546—861no—
409#546—861no—
410#546—861no—
411#546—861no—
412#540—432no—
413#540—432no—
414#535—432no—
415#533—431no—
416#532—431no—
417#532—431no—
418#532—431no—
419#532C2×D4311yescharacteristic
420C2×#127—431no—
421#518—432no—
422C4×#41—431no—
423#446—861no—
424C8×Q8—861no—
425#436—861no—
426#436—861no—
427#436—861no—
428#435—861no—
429#435—861no—
430C8×D4—861no—
431#432—431no—
432#432—431no—
433#431—431no—
434#431—431no—
435#431—431no—
436#431—431no—
437#423—431no—
438#423—431no—
439#423—431no—
440#423C2×D4311yescharacteristic, complemented
441C2×C4⋊C8—431no—
442C2×C4⋊C8C2×D4311yescharacteristic, complemented
443#332—431no—
444#332—431no—
445#332—431no—
446#332—431no—
447#332—431no—
448#332—431no—
449#332C2×D4311yescharacteristic, complemented
450#332C2×D4311yescharacteristic, complemented
451#331—431no—
452#331—431no—
453#331—431no—
454#331—431no—
455#331—431no—
456#331—431no—
457#331C2×D4311yescharacteristic
458#331C2×D4311yescharacteristic
459C43#1777611yescharacteristic, complemented, Sylow
460C2×#41—21no—
461C2×#41—431no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C22×D4—432no—
466C22×D4—861no—
467C22×D4—861no—
468C2×M16—21no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C22×C8—21no—
473C22×C8—861no—
474C4⋊Q8—431no—
475C4⋊Q8C22×D4311yescharacteristic
476#127—432no—
477#127—431no—
478#127—861no—
479#127—861no—
480#127—862no—
481#127C22×D4311yescharacteristic
482#125—432no—
483#124—21no—
484#124—861no—
485#124—861no—
486#124—862no—
487#124—861no—
488#123—862no—
489#123—862no—
490#123—862no—
491#123—862no—
492C22⋊Q8—861no—
493C22⋊Q8—861no—
494#121—21no—
495#121—432no—
496#121—432no—
497#121—432no—
498#121—862no—
499#121—862no—
500#121—862no—
501#121—862no—
502#121—861no—
503#121—861no—
504#121—861no—
505#121C4×D4312yes—
506#120—862no—
507#120—862no—
508C4×Q8—431no—
509C4×Q8—431no—
510C4×Q8—861no—
511C4×Q8—861no—
512C4×D4—21no—
513C4×D4—431no—
514C4×D4—431no—
515C4×D4—431no—
516C4×D4—431no—
517C4×D4—432no—
518C4×D4—432no—
519C4×D4—432no—
520C4×D4—431no—
521C4×D4—431no—
522C4×D4—861no—
523C4×D4—861no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—861no—
527C4×D4C4×D4312yes—
528#117—431no—
529#117—431no—
530#117—431no—
531#117—432no—
532C2×C22⋊C4—862no—
533C2×C22⋊C4—862no—
534C2×C42—431no—
535C2×C42—431no—
536C2×C42C22×D4311yescharacteristic
537C4⋊C8—21no—
538C4⋊C8—21no—
539C4⋊C8—431no—
540C4⋊C8—431no—
541C4⋊C8—431no—
542C4⋊C8—431no—
543C4⋊C8—861no—
544C4⋊C8—861no—
545C4⋊C8—861no—
546C4⋊C8—861no—
547C4⋊C8C22×D4311yescharacteristic
548C4⋊C8C22×D4311yescharacteristic
549C4⋊C8C22×D4311yescharacteristic
550C4⋊C8C22×D4311yescharacteristic
551C22⋊C8—861no—
552C22⋊C8—861no—
553C22⋊C8—861no—
554C22⋊C8—861no—
555C22⋊C8—861no—
556C22⋊C8—861no—
557#97—861no—
558#97—861no—
559C4×C8—861no—
560C4×C8—861no—
561C4×C8—861no—
562C4×C8—861no—
563C24—862no—
564#41—81no—
565#41—81no—
566#41—3441no—
567#41—3441no—
568#41—3441no—
569#41—3441no—
570#41—3441no—
571#41—3441no—
572#41—1722no—
573C2×Q8—21no—
574C2×Q8—431no—
575C2×Q8—861no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—431no—
580C2×D4—431no—
581C2×D4—431no—
582C2×D4—432no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—862no—
586C2×D4—862no—
587C2×D4—862no—
588C2×D4—862no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—3441no—
592C2×D4—3441no—
593C2×D4—3441no—
594C2×D4—3441no—
595C2×D4—1724no—
596C2×D4C2×C4×D4312yes—
597C22×C4—22no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—431no—
603C22×C4—431no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4C2×C4×D4311yescharacteristic
608C22×C4D4×D4311yescharacteristic
609C22×C4D4×D4311yescharacteristic
610M16—81no—
611M16—3441no—
612M16—3441no—
613M16—3441no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—81no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—3441no—
624C4⋊C4—21no—
625C4⋊C4—431no—
626C4⋊C4—431no—
627C4⋊C4—431no—
628C4⋊C4—431no—
629C4⋊C4—431no—
630C4⋊C4—431no—
631C4⋊C4—432no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—861no—
635C4⋊C4C2×C4×D4312yes—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—431no—
639C22⋊C4—431no—
640C22⋊C4—431no—
641C22⋊C4—431no—
642C22⋊C4—431no—
643C22⋊C4—431no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C42—431no—
652C42—431no—
653C42—431no—
654C42—431no—
655C42—431no—
656C42—431no—
657C42—862no—
658C42C2×C4×D4311yescharacteristic
659C42D4×D4311yescharacteristic
660C42D4×D4311yescharacteristic
661C42C23×D4311yescharacteristic
662C23—22no—
663C23—431no—
664C23—431no—
665C23—862no—
666C23—3442no—
667C23—3442no—
668C23—1724no—
669C23C22⋊C4×D4311yescharacteristic
670Q8—41no—
671Q8—41no—
672Q8—862no—
673Q8—1721no—
674Q8—1721no—
675D4—42no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—862no—
682D4—3442no—
683D4—3442no—
684D4—3442no—
685D4—3442no—
686D4—3442no—
687D4—1721no—
688D4—1722no—
689D4—1724no—
690D4—1721no—
691D4—1721no—
692D4—1721no—
693D4—1721no—
694D4—1721no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—431no—
703C2×C4—431no—
704C2×C4—431no—
705C2×C4—431no—
706C2×C4—431no—
707C2×C4—431no—
708C2×C4—862no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—862no—
718C2×C4—3442no—
719C2×C4—3442no—
720C2×C4—3442no—
721C2×C4—1721no—
722C2×C4C22⋊C4×D4311yescharacteristic
723C2×C4C22⋊C4×D4311yescharacteristic
724C2×C4C22⋊C4×D4311yescharacteristic
725C2×C4C22×C4×D4311yescharacteristic
726C2×C4C2×D4×D4311yescharacteristic
727C2×C4C2×D4×D4311yescharacteristic
728C8—41no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—1721no—
733C8—1721no—
734C8—1721no—
735C8—1721no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—861no—
743C22—861no—
744C22—861no—
745C22—861no—
746C22—861no—
747C22—861no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—6884no—
752C22C2×C22⋊C4×D4311yescharacteristic
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—42no—
758C4—432no—
759C4—861no—
760C4—861no—
761C4—861no—
762C4—861no—
763C4—861no—
764C4—1722no—
765C4#1458370011yescharacteristic
766C4#1458370311yescharacteristic
767C4#1458370511yescharacteristic
768C4#1458370811yescharacteristic
769C2—41no—
770C2—82no—
771C2—3442no—
772C2—1721no—
773C2—1721no—
774C2#413×D4311yescharacteristic
775C2#1914311611yescharacteristic
776C2#1914311911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C22×C22⋊C4
prime radical#19148464C2
cosocleC42×C43C24
hypercenter#1547D43
hypocenterC43#17776
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #19143725C2semidirect
3. #19143717C2semidirect
4. #19133331C2semidirect
5. #19133315C2semidirect
6. #19133314C2semidirect
7. #19133300C2semidirect
8. #19133299C2semidirect
9. #19133271C2semidirect
10. #19133261C2semidirect
11. #19133261C2semidirect
12. #19133258C2semidirect
13. #19133245C2semidirect
14. #19133241C2semidirect
15. C43×#1547C2semidirect
42. #14582956C22semidirect
43. #14582955C22semidirect
44. #14582952C22semidirect
47. #14582951C22semidirect
50. #14582921C22semidirect
51. C4⋊C8×D43C22semidirect
52. #14582646C22semidirect
53. #14582646C22semidirect
54. #14582645C22semidirect
55. #14582645C22semidirect
56. #14582644C22semidirect
57. #14582644C22semidirect
65. C43×#423C22semidirect
66. C2×C4⋊C8×C43C22semidirect
67. C43×#332C22semidirect
68. C43×#332C22semidirect
390. #1547D43semidirect
440. #423C2×D43semidirect
442. C2×C4⋊C8C2×D43semidirect
449. #332C2×D43semidirect
450. #332C2×D43semidirect
459. C43#17776semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191437252
#191437172
#191333312
#191333152
#191333142
#191333002
#191332992
#191332712
#191332612
#191332582
#191332452
#191332412
C43×#15472
#1777643