Finite Group Databasebeta

← #25150247

Subgroups — #25150247

Order 11008.

1094 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583509C211yesmaximal, characteristic, complemented
2C2×#14583290C211yesmaximal, characteristic, complemented
3C2×#14583252C211yesmaximal, characteristic, complemented
4#19140356C211yesmaximal, characteristic
5#19135605C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135598C211yesmaximal, characteristic
8#19135562C211yesmaximal, characteristic, complemented
9#19135395C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic, complemented
12#19134937C211yesmaximal, characteristic, complemented
13#19134934C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19#14583509—24no—
20#14583509—24no—
21C2×#13063323C2211yescharacteristic
22C2×#13063318—21no—
23C2×#13063318—21no—
24C2×#13063316—21no—
25C2×#13063316C2211yescharacteristic
26C2×#13063315—21no—
27C2×#13063312C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063304C2211yescharacteristic
30C2×Q8×Dic43C2211yescharacteristic
31C2×#13063290C2211yescharacteristic
32C2×#13063284C2211yescharacteristic
33#14583290—24no—
34#14583252—24no—
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582822—21no—
45#14582822—21no—
46#14582813—21no—
47#14582813—21no—
48#14582804C2211yescharacteristic
49#14582802C2211yescharacteristic
50#14582768C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C2×Dic172—22no—
66C2×Dic172—22no—
67C2×Dic172—41no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—41no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—41no—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063323—22no—
77#13063323D414yescomplemented
78#13063318—28no—
79#13063318—28no—
80#13063316—28no—
81#13063316—22no—
82#13063316D414yescomplemented
83#13063315—28no—
84#13063312—22no—
85#13063312—22no—
86#13063304—22no—
87#13063304—22no—
88#13063304—41no—
89#13063304—41no—
90Q8×Dic43—22no—
91Q8×Dic43—22no—
92#13063290—22no—
93#13063290—22no—
94#13063284—22no—
95#13063284—22no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43D411yescharacteristic
99C2×C4⋊Dic43D411yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43D411yescharacteristic
117C2×C22⋊Dic43D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43C2311yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122#13063250—22no—
123#13063250—41no—
124#13063249—41no—
125#13063248—22no—
126#13063248—41no—
127#13063246—22no—
128C22⋊(C43⋊C8)—22no—
129#13063235—22no—
130C8×Dic43—22no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C22×Q8×C43C2311yescharacteristic
134C22×D4×C43—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C2×SD16×C43—22no—
138C2×SD16×C43—22no—
139C2×SD16×C43—41no—
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—22no—
144#121×C43—41no—
145#121×C43—41no—
146C2×C4⋊C4×C43—21no—
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43—21no—
151#103×C43—41no—
152#102×C43—22no—
153C22⋊C8×C43—22no—
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C2×D412yes—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—42no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2411yescharacteristic
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86C2×D412yes—
202SD16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43#4112yes—
209C4⋊C4×C43—24no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43C2×D412yes—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—42no—
216C22⋊Dic43—24no—
217C22⋊Dic43—22no—
218C22⋊Dic43—22no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224#10621885—44no—
225#10621883—44no—
226C4⋊Dic43—24no—
227C4⋊Dic43—21no—
228C4⋊Dic43—24no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C2×D412yes—
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—42no—
240Dic43⋊C4—81no—
241Dic43⋊C4—81no—
242C4×Dic43—24no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43C2×D412yes—
247C4×Dic43C2×D412yes—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8#4112yes—
254Dic172—44no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43C22×D411yescharacteristic
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—84no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43#12012yes—
324C2×Dic43#12012yes—
325Dic86—22no—
326Dic86—22no—
327Dic86—41no—
328Dic86—41no—
329Dic86—41no—
330Dic86—41no—
331Dic86—41no—
332Dic86—41no—
333C8×C43—22no—
334C8×C43—41no—
335C43⋊C8—22no—
336C43⋊C8—41no—
337#25612—431nomaximal, Sylow
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43C2×#12011yescharacteristic
353C22×C43#53211yescharacteristic
354C22×C43#53511yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57811yescharacteristic
358C22×C43#57811yescharacteristic
359C4×C43—41no—
360C4×C43—42no—
361C4×C43—42no—
362C4×C43—81no—
363C4×C43#54611yescharacteristic
364C4×C43#54611yescharacteristic
365C4×C43#55011yescharacteristic
366C4×C43#55011yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—41no—
371Dic43—41no—
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375C2×#541—431no—
376C2×#497—431no—
377C2×#488—431no—
378#2620—431no—
379#2001—431no—
380#2001—431no—
381#2000—431no—
382#2000D4311yescharacteristic
383#1992—431no—
384#1956—431no—
385#1880—431no—
386#1880—431no—
387#1878—431no—
388#1878—431no—
389#1750—431no—
390C2×C43—81no—
391C2×C43—161no—
392C2×C43#243111yescharacteristic
393C2×C43#301311yescharacteristic
394C2×C43#301311yescharacteristic
395C2×C43#317811yescharacteristic
396C2×C43#317811yescharacteristic
397C2×C43#322211yescharacteristic
398C2×C43#322311yescharacteristic
399C22×Q16—431no—
400C22×Q16—431no—
401C22×SD16—431no—
402C22×SD16C2×D4311yescharacteristic
403#541—864no—
404#541—864no—
405C2×C4⋊Q8—431no—
406C2×#126—861no—
407C2×#126—861no—
408C2×#125—431no—
409C2×#125—861no—
410C2×#125—861no—
411C2×#124—431no—
412C2×C22⋊Q8—431no—
413C2×C22⋊Q8—431no—
414C2×C22⋊Q8C2×D4311yescharacteristic
415C2×#121C2×D4311yescharacteristic
416C2×C4×Q8—431no—
417C2×C4×Q8—431no—
418C2×#117—431no—
419#497—864no—
420#488—864no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103C2×D4311yescharacteristic
427C2×#102—431no—
428C2×#102C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8C2×D4311yescharacteristic
431C2×#97—431no—
432C2×C4×C8—431no—
433#396—861no—
434#396—861no—
435#394—861no—
436#394—861no—
437#391—431no—
438#390—431no—
439#384—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340C2×D4311yescharacteristic
444#336—431no—
445#336—431no—
446C43#2561211yescharacteristic, complemented, Sylow
447C22×Q8—431no—
448C22×Q8—431no—
449C22×Q8C22×D4311yescharacteristic
450C22×D4—21no—
451C22×D4C22×D4311yescharacteristic
452C23×C4C22×D4311yescharacteristic
453C2×Q16—862no—
454C2×Q16—862no—
455C2×Q16—862no—
456C2×Q16—862no—
457C2×Q16—1721no—
458C2×Q16—1721no—
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—41no—
462C2×SD16—862no—
463C2×SD16—862no—
464C2×SD16—1721no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4⋊Q8—434no—
470C4⋊Q8—862no—
471#126—868no—
472#126—868no—
473#125—434no—
474#125—862no—
475#125—868no—
476#125—868no—
477#124—862no—
478#124—862no—
479C22⋊Q8—22no—
480C22⋊Q8—22no—
481C22⋊Q8—862no—
482C22⋊Q8—862no—
483C22⋊Q8—1721no—
484C22⋊Q8—1721no—
485#121—41no—
486#121—41no—
487C4×Q8—862no—
488C4×Q8—862no—
489C4×Q8—862no—
490C4×Q8—862no—
491#117—862no—
492#117—862no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—431no—
513C2×C22⋊C4—431no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C42—431no—
521C2×C42—431no—
522C2×C42—861no—
523C2×C42—861no—
524#103—41no—
525#103—862no—
526#103—862no—
527#103—1721no—
528#103—1721no—
529#103—1721no—
530#102—22no—
531#102—862no—
532C22⋊C8—22no—
533C22⋊C8—862no—
534#97—862no—
535C4×C8—862no—
536#95—861no—
537#95—861no—
538C24—21no—
539C24D4×D4311yescharacteristic
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—432no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8D4×D4312yes—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—81no—
566C2×D4—81no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586Q16—1724no—
587Q16—1724no—
588SD16—44no—
589SD16—1724no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—432no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8#1062190012yes—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—432no—
607C4⋊C4—862no—
608C4⋊C4—862no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—3441no—
620C4⋊C4—3441no—
621C4⋊C4—1722no—
622C4⋊C4D4×D4312yes—
623C22⋊C4—24no—
624C22⋊C4—42no—
625C22⋊C4—862no—
626C22⋊C4—862no—
627C22⋊C4—864no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C22⋊C4—1722no—
633C42—432no—
634C42—432no—
635C42—864no—
636C42—864no—
637C42—861no—
638C42—861no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23C2×D4×D4311yescharacteristic
654Q8—22no—
655Q8—22no—
656Q8—41no—
657Q8—41no—
658Q8—862no—
659Q8—862no—
660Q8—1721no—
661Q8—1721no—
662Q8—1721no—
663Q8—1721no—
664Q8—1721no—
665Q8—1721no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—432no—
688C2×C4—432no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4C2×D4×D4311yescharacteristic
713C2×C4#41×D4311yescharacteristic
714C2×C4C2×#1062190011yescharacteristic
715C2×C4#1306337011yescharacteristic
716C2×C4#1306337011yescharacteristic
717C8—22no—
718C8—41no—
719C8—862no—
720C8—1721no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22#120×D4311yescharacteristic
736C22#1458344411yescharacteristic
737C22#1458346411yescharacteristic
738C22#1458370511yescharacteristic
739C22#1458370911yescharacteristic
740C22#1458371311yescharacteristic
741C22#1458371511yescharacteristic
742C4—41no—
743C4—42no—
744C4—42no—
745C4—81no—
746C4—862no—
747C4—862no—
748C4—3441no—
749C4—3441no—
750C4—1722no—
751C4—1721no—
752C4—1722no—
753C4—1721no—
754C4#1458353611yescharacteristic
755C4#1458353811yescharacteristic
756C4#1458356711yescharacteristic
757C4#1458356911yescharacteristic
758C2—81no—
759C2—161no—
760C2#1913820911yescharacteristic
761C2#1914390511yescharacteristic
762C2#1914390811yescharacteristic
763C2#1914525611yescharacteristic
764C2#1914525811yescharacteristic
765C2#1914566311yescharacteristic
766C2#1914567611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
hypercenter#2000D43
hypocenterC43#25612
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#14583509C2semidirect
2. C2×#14583290C2semidirect
3. C2×#14583252C2semidirect
5. #19135605C2semidirect
6. #19135603C2semidirect
8. #19135562C2semidirect
9. #19135395C2semidirect
10. #19134952C2semidirect
11. #19134947C2semidirect
12. #19134937C2semidirect
13. #19134934C2semidirect
14. #19134363C2semidirect
77. #13063323D4semidirect
82. #13063316D4semidirect
446. C43#25612semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145832902
C2×#145832522
#191403562
#191356052
#191356032
#191355982
#191355622
#191353952
#191349522
#191349472
#191349372
#191349342
#191343632
C43×#20002
#2561243