Finite Group Databasebeta

← #25065069

Subgroups — #25065069

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148464C211yesmaximal, characteristic
2#19143703C211yesmaximal, characteristic, complemented
3#19143262C211yesmaximal, characteristic, complemented
4#19133299C211yesmaximal, characteristic, complemented
5#19133291C211yesmaximal, characteristic, complemented
6#19133287C211yesmaximal, characteristic, complemented
7#19133284C211yesmaximal, characteristic, complemented
8#19133261C211yesmaximal, characteristic, complemented
9#19133255C211yesmaximal, characteristic, complemented
10#19133254C211yesmaximal, characteristic, complemented
11#19133251C211yesmaximal, characteristic, complemented
12#19133244C211yesmaximal, characteristic, complemented
13#19133243C211yesmaximal, characteristic, complemented
14#331×D43C211yesmaximal, characteristic, complemented
15C43×#1553C211yesmaximal, characteristic, complemented
16#14583632C412yes—
17#14583631—21no—
18#14583568—21no—
19#14583567C412yes—
20#14583546C412yes—
21#14583544C412yes—
22#14583542—21no—
23#14583537—21no—
24#14583502—21no—
25#14583500—21no—
26#14583465—21no—
27#14583454C2211yescharacteristic
28#14583450C2211yescharacteristic
29#14583449C2211yescharacteristic
30#14583447C2211yescharacteristic
31#127×D43C2211yescharacteristic
32#14583371—21no—
33C4×#10621898C2211yescharacteristic
34C8×Dic86—21no—
35C8×D172—21no—
36(C22⋊D43)⋊C8—21no—
37(C22⋊D43)⋊C8—21no—
38#14582961—21no—
39#14582957—21no—
40#14582955C2211yescharacteristic, complemented
41#14582952C2211yescharacteristic, complemented
42#14582951C2211yescharacteristic
43#14582951C2211yescharacteristic, complemented
44#14582951C2211yescharacteristic, complemented
45#14582921C2211yescharacteristic
46C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49C4⋊C8×D43C2211yescharacteristic, complemented
50#14582864—21no—
51#14582856—21no—
52#14582647C2211yescharacteristic, complemented
53#14582647C2211yescharacteristic, complemented
54#14582647C2211yescharacteristic, complemented
55#14582647C2211yescharacteristic, complemented
56#14582645C2211yescharacteristic, complemented
57#14582645C2211yescharacteristic, complemented
58#14582643C2211yescharacteristic
59#14582643C2211yescharacteristic
60#14582642C2211yescharacteristic
61#14582642C2211yescharacteristic
62#14582642C2211yescharacteristic
63#14582642C2211yescharacteristic
64C43×#532C2211yescharacteristic
65C43×#432C2211yescharacteristic, complemented
66C43×#431C2211yescharacteristic, complemented
67C43×#332C2211yescharacteristic, complemented
68C43×#332C2211yescharacteristic, complemented
69C43×#331C2211yescharacteristic
70C43×#331C2211yescharacteristic
71C2×#10621902—21no—
72C2×#10621898C2×C412yes—
73C2×#10621898D411yescharacteristic
74C2×#10621900C2×C412yes—
75C2×D4×D43—21no—
76C2×D4×D43—21no—
77C2×D4×D43C2×C412yes—
78C2×#10621872—21no—
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83#13063325C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063321—22no—
86#13063321—21no—
87#13063321—21no—
88#13063321C2×C412yes—
89#13063316—21no—
90#13063314—21no—
91#13063313C2×C412yes—
92#13063312C2×C412yes—
93#13063311—22no—
94#13063309—22no—
95#13063308—22no—
96#13063307—22no—
97#13063307—22no—
98#13063305C2×C412yes—
99#13063301—21no—
100#13063300—21no—
101#13063300C2×C412yes—
102#13063299—21no—
103#13063299—21no—
104#13063299—22no—
105#13063298—22no—
106#13063297—22no—
107#13063296—21no—
108#13063296—21no—
109#13063296—22no—
110#13063295—22no—
111#13063293—22no—
112Q8×Dic43—21no—
113C4×Dic86C2×C411yescharacteristic
114C4×Dic86D411yescharacteristic
115#13063290C2×C412yes—
116C4×D172—21no—
117C4×D172—21no—
118C4×D172C2×C411yescharacteristic
119C4×D172D411yescharacteristic
120D4×Dic43—21no—
121D4×Dic43—21no—
122#13063287—21no—
123#13063287C2×C412yes—
124C4×C22⋊D43—22no—
125C4×C22⋊D43C2×C411yescharacteristic
126C4×C22⋊D43C2×C411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128C4×C22⋊D43D411yescharacteristic
129(C22⋊D43)⋊C4—22no—
130#13063284D411yescharacteristic
131#13063283—21no—
132#13063282D411yescharacteristic
133#13063282D411yescharacteristic
134C2×(C2×D43)⋊C4—22no—
135C22⋊C4×D43—22no—
136C42×D43C2311yescharacteristic
137C42×D43C2311yescharacteristic
138C4⋊(C43⋊C8)—21no—
139C4⋊(C43⋊C8)C2311yescharacteristic
140C4⋊(C43⋊C8)C2311yescharacteristic
141C4⋊(C43⋊C8)C2311yescharacteristic
142C4⋊(C43⋊C8)C2311yescharacteristic
143Dic43⋊C8—21no—
144Dic43⋊C8—21no—
145Dic43⋊C8—21no—
146Dic43⋊C8—21no—
147C22⋊(C43⋊C8)—21no—
148(C2×D43)⋊C8—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151(C2×D43)⋊C8—21no—
152#13063235—21no—
153C4×C43⋊C8—21no—
154C8×Dic43—21no—
155C8×Dic43—21no—
156C8×Dic43—21no—
157C2×#41×C43—21no—
158C4⋊Q8×C43C2311yescharacteristic
159#127×C43C2311yescharacteristic
160#124×C43—21no—
161#121×C43—21no—
162#121×C43C2×C412yes—
163C4×D4×C43—21no—
164C4×D4×C43C2×C412yes—
165C2×C42×C43C2311yescharacteristic
166C4⋊C8×C43C2311yescharacteristic
167C4⋊C8×C43C2311yescharacteristic
168C4⋊C8×C43C2311yescharacteristic
169C4⋊C8×C43C2311yescharacteristic
170C22⋊C8×C43—21no—
171C22⋊C8×C43—21no—
172#97×C43—21no—
173C4×C8×C43—21no—
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—82no—
197D4×D43—42no—
198D4×D43—42no—
199D4×D43—81no—
200D4×D43—81no—
201D4×D43—82no—
202#10621898—22no—
203#10621898—22no—
204#10621898—82no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—22no—
208C2×D172C22⋊C411yescharacteristic
209C2×D172C22×C412yes—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43C22×C411yescharacteristic
213C2×C4×D43C22×C411yescharacteristic
214C2×C4×D43C2×D411yescharacteristic
215C2×C4×D43C2×D411yescharacteristic
216C2×C4×D43C2×D411yescharacteristic
217C2×C4×D43C2×D411yescharacteristic
218C2×Dic86C22⋊C411yescharacteristic
219C2×Dic86C22×C412yes—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43C22×C412yes—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C42×C43C22×C411yescharacteristic
229C42×C43C2×D411yescharacteristic
230C42×C43C2×D411yescharacteristic
231C42×C43C2411yescharacteristic
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43C22⋊C411yescharacteristic
235C22⋊Dic43C22⋊C411yescharacteristic
236(C2×D43)⋊C4—22no—
237(C2×D43)⋊C4—22no—
238(C2×D43)⋊C4—22no—
239(C2×D43)⋊C4—22no—
240(C2×D43)⋊C4—22no—
241(C2×D43)⋊C4C22⋊C411yescharacteristic
242(C2×D43)⋊C4C22⋊C411yescharacteristic
243(C2×D43)⋊C4C22⋊C411yescharacteristic
244(C2×D43)⋊C4C22⋊C411yescharacteristic
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—22no—
248C4⋊Dic43C22⋊C411yescharacteristic
249C4⋊Dic43C22⋊C411yescharacteristic
250Dic43⋊C4—22no—
251Dic43⋊C4C22⋊C411yescharacteristic
252Dic43⋊C4C22⋊C411yescharacteristic
253Dic43⋊C4C22⋊C411yescharacteristic
254Dic43⋊C4C22⋊C411yescharacteristic
255C4×Dic43—22no—
256C4×Dic43C22×C411yescharacteristic
257C4×Dic43C22×C411yescharacteristic
258C4×Dic43C2×D411yescharacteristic
259C4×Dic43C2×D411yescharacteristic
260C4×Dic43C2×D411yescharacteristic
261C4×Dic43C2×D411yescharacteristic
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—81no—
267#10621872—42no—
268C8×D43—42no—
269C8×D43—81no—
270C8×D43—81no—
271C23×C43—22no—
272C23×C43C2×C22⋊C411yescharacteristic
273C22×D43—22no—
274C22×D43—44no—
275C22×D43—82no—
276C22×D43—82no—
277C22×D43C2×C22⋊C411yescharacteristic
278C22×D43C2×C22⋊C411yescharacteristic
279Q8×C43—41no—
280Q8×C43—41no—
281D4×C43—42no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—82no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—41no—
293C2×C4×C43—82no—
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C2×C22⋊C411yescharacteristic
296C2×C4×C43C2×C22⋊C411yescharacteristic
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C22⋊D43—22no—
301C22⋊D43—22no—
302C22⋊D43—44no—
303C22⋊D43—82no—
304C22⋊D43—82no—
305C22⋊D43—82no—
306C22⋊D43—82no—
307C2×Dic43—22no—
308C2×Dic43—82no—
309C2×Dic43C2×C22⋊C411yescharacteristic
310C2×Dic43C2×C22⋊C411yescharacteristic
311C2×Dic43C2×C22⋊C411yescharacteristic
312C2×Dic43C2×C22⋊C411yescharacteristic
313C2×Dic43C2×C22⋊C411yescharacteristic
314C2×Dic43C2×C22⋊C411yescharacteristic
315D172—22no—
316D172—42no—
317D172—41no—
318D172—41no—
319D172—41no—
320D172—41no—
321D172—82no—
322C4×D43—21no—
323C4×D43—21no—
324C4×D43—21no—
325C4×D43—21no—
326C4×D43—21no—
327C4×D43—21no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—82no—
331C4×D43—82no—
332C4×D43#13512yes—
333C4×D43#13512yes—
334Dic86—22no—
335Dic86—42no—
336C8×C43—41no—
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340C43⋊C8—41no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#17724—431nomaximal, Sylow
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43C22×C22⋊C411yescharacteristic
352C2×D43—21no—
353C2×D43—21no—
354C2×D43—21no—
355C2×D43—21no—
356C2×D43—21no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—164no—
361C2×D43#41612yes—
362C4×C43—21no—
363C4×C43—21no—
364C4×C43—21no—
365C4×C43—21no—
366C4×C43—42no—
367C4×C43C2×#13511yescharacteristic
368C4×C43C2×#13511yescharacteristic
369C4×C43#57611yescharacteristic
370C4×C43#57711yescharacteristic
371Dic43—21no—
372Dic43—21no—
373Dic43—21no—
374Dic43—21no—
375Dic43—21no—
376Dic43—42no—
377Dic43#41612yes—
378#3508—431no—
379#2988—431no—
380#2925—431no—
381#1553—431no—
382#1553D4311yescharacteristic, complemented
383#1551—431no—
384#1551—431no—
385#1550—431no—
386#1545—431no—
387#1543—431no—
388#1543—431no—
389#1542—431no—
390#1540—431no—
391#1540—431no—
392C2×#331—431no—
393C2×C43—41no—
394C2×C43—82no—
395C2×C43#288811yescharacteristic
396C2×C43C2×#41611yescharacteristic
397C2×C43#289711yescharacteristic
398D43—22no—
399D43—41no—
400D43—82no—
401#559—432no—
402#559—861no—
403#550—432no—
404#550—861no—
405#546—432no—
406#546—432no—
407#546—861no—
408#546—861no—
409#540—861no—
410#540—861no—
411#535—861no—
412#533—431no—
413#532—431no—
414#532—431no—
415#532—431no—
416#532C2×D4311yescharacteristic
417C2×#127—431no—
418#518—861no—
419C4×#41—431no—
420C8×Q8—861no—
421C8×D4—861no—
422C8×D4—861no—
423C8×D4—861no—
424#433—861no—
425#433—861no—
426#432—431no—
427#432C2×D4311yescharacteristic, complemented
428#431—431no—
429#431—431no—
430#431—431no—
431#431—431no—
432#431C2×D4311yescharacteristic, complemented
433#423—431no—
434C2×C4⋊C8—431no—
435C2×C4⋊C8—431no—
436C2×C4⋊C8—431no—
437C2×C4⋊C8—431no—
438#408—861no—
439#405—861no—
440#333—431no—
441#333—431no—
442#333—431no—
443#333—431no—
444#332—431no—
445#332—431no—
446#332C2×D4311yescharacteristic, complemented
447#332C2×D4311yescharacteristic, complemented
448#331—431no—
449#331—431no—
450#331—431no—
451#331—431no—
452#331—431no—
453#331—431no—
454#331C2×D4311yescharacteristic
455#331C2×D4311yescharacteristic
456C43#1772411yescharacteristic, complemented, Sylow
457C2×#41—21no—
458C2×#41—431no—
459C2×#41—432no—
460C2×#41—432no—
461C2×#41—861no—
462C22×D4—432no—
463C22×D4—861no—
464C22×D4—861no—
465C2×M16—861no—
466C22×C8—861no—
467C22×C8—861no—
468C22×C8—861no—
469C22×C8—861no—
470C4⋊Q8—431no—
471C4⋊Q8C22×D4311yescharacteristic
472#127—432no—
473#127—431no—
474#127—861no—
475#127—861no—
476#127—862no—
477#127C22×D4311yescharacteristic
478#125—861no—
479#124—21no—
480#124—432no—
481#124—432no—
482#124—861no—
483#124—862no—
484#123—862no—
485#123—862no—
486#123—862no—
487#123—862no—
488C22⋊Q8—432no—
489C22⋊Q8—861no—
490#121—21no—
491#121—432no—
492#121—862no—
493#121—862no—
494#121—862no—
495#121—862no—
496#121—861no—
497#121—861no—
498#121—861no—
499#121—861no—
500#121—861no—
501#121C4×D4312yes—
502#120—862no—
503#120—862no—
504C4×Q8—431no—
505C4×Q8—431no—
506C4×Q8—432no—
507C4×Q8—861no—
508C4×D4—21no—
509C4×D4—431no—
510C4×D4—431no—
511C4×D4—431no—
512C4×D4—431no—
513C4×D4—432no—
514C4×D4—431no—
515C4×D4—431no—
516C4×D4—861no—
517C4×D4—861no—
518C4×D4—861no—
519C4×D4—862no—
520C4×D4—862no—
521C4×D4—861no—
522C4×D4—861no—
523C4×D4C4×D4312yes—
524#117—431no—
525#117—431no—
526#117—431no—
527#117—861no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C42—431no—
531C2×C42—431no—
532C2×C42C22×D4311yescharacteristic
533C4⋊C8—431no—
534C4⋊C8—431no—
535C4⋊C8—431no—
536C4⋊C8—431no—
537C4⋊C8—861no—
538C4⋊C8—861no—
539C4⋊C8—861no—
540C4⋊C8—861no—
541C4⋊C8—861no—
542C4⋊C8C22×D4311yescharacteristic
543C4⋊C8C22×D4311yescharacteristic
544C4⋊C8C22×D4311yescharacteristic
545C4⋊C8C22×D4311yescharacteristic
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—861no—
549C22⋊C8—861no—
550C22⋊C8—861no—
551C22⋊C8—861no—
552C22⋊C8—861no—
553#97—21no—
554#97—861no—
555C4×C8—21no—
556C4×C8—861no—
557C4×C8—861no—
558C4×C8—861no—
559C4×C8—861no—
560C24—862no—
561#41—81no—
562#41—81no—
563#41—862no—
564#41—862no—
565#41—3442no—
566#41—3441no—
567#41—3441no—
568#41—3442no—
569C2×Q8—21no—
570C2×Q8—431no—
571C2×Q8—432no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—431no—
576C2×D4—431no—
577C2×D4—431no—
578C2×D4—432no—
579C2×D4—862no—
580C2×D4—862no—
581C2×D4—862no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—862no—
585C2×D4—861no—
586C2×D4—861no—
587C2×D4—3441no—
588C2×D4—3441no—
589C2×D4—3442no—
590C2×D4—1722no—
591C2×D4—1722no—
592C2×D4C2×C4×D4312yes—
593C22×C4—22no—
594C22×C4—431no—
595C22×C4—431no—
596C22×C4—431no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4C2×C4×D4311yescharacteristic
604C22×C4D4×D4311yescharacteristic
605C22×C4D4×D4311yescharacteristic
606M16—1722no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—3441no—
616C2×C8—3441no—
617C2×C8—3441no—
618C2×C8—1722no—
619C4⋊C4—21no—
620C4⋊C4—431no—
621C4⋊C4—431no—
622C4⋊C4—431no—
623C4⋊C4—431no—
624C4⋊C4—431no—
625C4⋊C4—431no—
626C4⋊C4—862no—
627C4⋊C4—862no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4C2×C4×D4312yes—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—431no—
634C22⋊C4—431no—
635C22⋊C4—431no—
636C22⋊C4—431no—
637C22⋊C4—431no—
638C22⋊C4—431no—
639C22⋊C4—862no—
640C22⋊C4—862no—
641C22⋊C4—862no—
642C22⋊C4—862no—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C42—431no—
647C42—431no—
648C42—431no—
649C42—431no—
650C42—431no—
651C42—431no—
652C42—862no—
653C42C2×C4×D4311yescharacteristic
654C42D4×D4311yescharacteristic
655C42D4×D4311yescharacteristic
656C42C23×D4311yescharacteristic
657C23—22no—
658C23—431no—
659C23—431no—
660C23—862no—
661C23—3442no—
662C23—3442no—
663C23—1724no—
664C23C22⋊C4×D4311yescharacteristic
665Q8—41no—
666Q8—41no—
667Q8—862no—
668Q8—1722no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—862no—
676D4—862no—
677D4—862no—
678D4—3442no—
679D4—3442no—
680D4—3442no—
681D4—3442no—
682D4—3442no—
683D4—1722no—
684D4—1724no—
685D4—1721no—
686D4—1721no—
687D4—1721no—
688D4—1721no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—431no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—431no—
700C2×C4—431no—
701C2×C4—431no—
702C2×C4—431no—
703C2×C4—431no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—862no—
711C2×C4—3442no—
712C2×C4—3442no—
713C2×C4—3442no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4C22⋊C4×D4311yescharacteristic
717C2×C4C22⋊C4×D4311yescharacteristic
718C2×C4C22⋊C4×D4311yescharacteristic
719C2×C4C22×C4×D4311yescharacteristic
720C2×C4C2×D4×D4311yescharacteristic
721C2×C4C2×D4×D4311yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—1721no—
727C8—1721no—
728C8—1721no—
729C8—1721no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—432no—
737C22—861no—
738C22—861no—
739C22—861no—
740C22—861no—
741C22—861no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22—6884no—
746C22C2×C22⋊C4×D4311yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—42no—
752C4—432no—
753C4—861no—
754C4—861no—
755C4—861no—
756C4—861no—
757C4—861no—
758C4—1722no—
759C4#135×D4311yescharacteristic
760C4#135×D4311yescharacteristic
761C4#1458370311yescharacteristic
762C4#1458370911yescharacteristic
763C2—41no—
764C2—82no—
765C2—862no—
766C2—3442no—
767C2—1721no—
768C2#1914307211yescharacteristic
769C2#416×D4311yescharacteristic
770C2#1914312011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1553C2
socleC22×C43C22×C22⋊C4
prime radical#19148464C2
cosocleC42×C43C24
hypercenter#1553D43
hypocenterC43#17724
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1553

Complements

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

NH ≅ G/Ntype
2. #19143703C2semidirect
3. #19143262C2semidirect
4. #19133299C2semidirect
5. #19133291C2semidirect
6. #19133287C2semidirect
7. #19133284C2semidirect
8. #19133261C2semidirect
9. #19133255C2semidirect
10. #19133254C2semidirect
11. #19133251C2semidirect
12. #19133244C2semidirect
13. #19133243C2semidirect
14. #331×D43C2semidirect
15. C43×#1553C2semidirect
40. #14582955C22semidirect
41. #14582952C22semidirect
43. #14582951C22semidirect
44. #14582951C22semidirect
46. C2×C4⋊(C43⋊C8)C22semidirect
49. C4⋊C8×D43C22semidirect
52. #14582647C22semidirect
53. #14582647C22semidirect
54. #14582647C22semidirect
55. #14582647C22semidirect
56. #14582645C22semidirect
57. #14582645C22semidirect
65. C43×#432C22semidirect
66. C43×#431C22semidirect
67. C43×#332C22semidirect
68. C43×#332C22semidirect
382. #1553D43semidirect
427. #432C2×D43semidirect
432. #431C2×D43semidirect
446. #332C2×D43semidirect
447. #332C2×D43semidirect
456. C43#17724semidirect

Maximal subgroups

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

subgroupindex
#191484642
#191437032
#191432622
#191332992
#191332912
#191332872
#191332842
#191332612
#191332552
#191332542
#191332512
#191332442
#191332432
#331×D432
C43×#15532
#1772443