Finite Group Databasebeta

← #25101870

Subgroups — #25101870

Order 11008.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582855C211yesmaximal, characteristic, complemented
2#19137204C211yesmaximal, characteristic, complemented
3#19135569C211yesmaximal, characteristic, complemented
4#19135557C211yesmaximal, characteristic, complemented
5#19135412C211yesmaximal, characteristic, complemented
6#19135407C211yesmaximal, characteristic, complemented
7#19135034C211yesmaximal, characteristic
8#19135029C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic
10#19135019C211yesmaximal, characteristic, complemented
11#19134425C211yesmaximal, characteristic, complemented
12#19134420C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C2×C43×#542C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×#13063249C2211yescharacteristic
19C2×#13063249C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26#14582855—24no—
27C2×#13063236C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582792—21no—
32#14582792—21no—
33#14582785—21no—
34#14582785—21no—
35#14582769C2211yescharacteristic
36#14582765C2211yescharacteristic
37#14582759C2211yescharacteristic
38#14582759C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49C43×#542—24no—
50C43×#542C418yescomplemented
51C2×C4⋊Q8×C43C2211yescharacteristic
52C2×#126×C43—21no—
53C2×#124×C43—21no—
54C2×#124×C43C2211yescharacteristic
55C2×#123×C43—21no—
56C2×C22⋊Q8×C43—21no—
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C2×#10621877—22no—
63C2×#10621877—22no—
64C2×#10621877—22no—
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—22no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43—21no—
82#13063249—22no—
83#13063249—22no—
84#13063249—22no—
85#13063249—22no—
86#13063246—22no—
87#13063246—22no—
88#13063246—22no—
89#13063246—22no—
90#13063236—22no—
91#13063236—22no—
92C4×C43⋊C8—22no—
93C4×C43⋊C8—22no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C22×Q8×C43—21no—
101C22×Q8×C43C2311yescharacteristic
102C22×D4×C43—21no—
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106C4⋊Q8×C43—22no—
107C4⋊Q8×C43C2×C414yes—
108#126×C43—28no—
109#124×C43—28no—
110#124×C43—22no—
111#124×C43C2×C414yes—
112#123×C43—28no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—28no—
115C22⋊Q8×C43C2×C414yes—
116#121×C43—22no—
117#121×C43C2×C414yes—
118C4×Q8×C43—22no—
119C4×Q8×C43C2×C414yes—
120C4×D4×C43—22no—
121C4×D4×C43C2×C414yes—
122#117×C43C2×C414yes—
123#117×C43D414yes—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43D411yescharacteristic
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43D411yescharacteristic
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C42×C43—21no—
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C2×Q8×C43—24no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—81no—
150C2×Q8×C43—81no—
151C2×Q8×C43C22×C412yes—
152C2×D4×C43—21no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C22×C412yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—24no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—81no—
170C22×C4×C43—81no—
171C22×C4×C43C22×C412yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C4⋊C4×C43—24no—
184C4⋊C4×C43—24no—
185C4⋊C4×C43—24no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43C22⋊C414yes—
189C4⋊C4×C43C22⋊C414yes—
190C4⋊C4×C43C22×C412yes—
191C4⋊C4×C43C22×C412yes—
192C22⋊C4×C43—24no—
193C22⋊C4×C43—24no—
194C22⋊C4×C43—24no—
195C22⋊C4×C43—24no—
196C22⋊C4×C43—24no—
197C22⋊C4×C43C22⋊C414yes—
198C22⋊C4×C43C22⋊C414yes—
199C42×C43—24no—
200C42×C43C22×C412yes—
201C42×C43C22×C412yes—
202C42×C43C2×D412yes—
203C42×C43C2×D412yes—
204C22⋊Dic43—81no—
205C22⋊Dic43—81no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—81no—
215C4⋊Dic43—81no—
216C4×Dic43—81no—
217C4×Dic43—81no—
218#10621877—28no—
219C2×C43⋊C8—28no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8#4112yes—
229C2×C43⋊C8#4112yes—
230C2×C43⋊C8#4112yes—
231C2×C43⋊C8#4112yes—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—22no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43C2×C22⋊C412yes—
246C23×C43C22×D411yescharacteristic
247Q8×C43—22no—
248Q8×C43—22no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43—84no—
252D4×C43—22no—
253D4×C43—22no—
254D4×C43—41no—
255D4×C43—41no—
256D4×C43—84no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—84no—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C2×C22⋊C412yes—
283C2×C4×C43C2×C22⋊C412yes—
284C2×C4×C43C2×C22⋊C412yes—
285C2×C4×C43C2×C22⋊C412yes—
286C2×C4×C43C23×C411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C43⋊C8—22no—
305C43⋊C8—22no—
306C43⋊C8—22no—
307C43⋊C8—22no—
308#21412—431nomaximal, Sylow
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—42no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—81no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43C22×C22⋊C411yescharacteristic
324C22×C43#53211yescharacteristic
325C22×C43#53211yescharacteristic
326C22×C43#57611yescharacteristic
327C22×C43#57711yescharacteristic
328C22×C43#57711yescharacteristic
329C22×C43#57811yescharacteristic
330C4×C43—22no—
331C4×C43—22no—
332C4×C43—22no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—42no—
336C4×C43—42no—
337C4×C43—42no—
338C4×C43C4×#4111yescharacteristic
339C4×C43C4×#4111yescharacteristic
340C4×C43#52511yescharacteristic
341C4×C43#52511yescharacteristic
342Dic43—81no—
343Dic43—81no—
344Dic43—81no—
345Dic43—81no—
346C2×#542D4311yescharacteristic
347C2×#405—431no—
348#2314—431no—
349#1993—431no—
350#1990—431no—
351#1959—431no—
352#1958—431no—
353#1895—431no—
354#1894—431no—
355#1893—431no—
356#1892—431no—
357#1763—431no—
358#1762—431no—
359C4×#103—431no—
360C4×#102—431no—
361C2×C43—42no—
362C2×C43—82no—
363C2×C43#229711yescharacteristic
364C2×C43#289711yescharacteristic
365C2×C43#289811yescharacteristic
366C2×C43#317311yescharacteristic
367C2×C43#317511yescharacteristic
368C2×C43#317811yescharacteristic
369C2×C43#317911yescharacteristic
370C22×M16—431no—
371C23×C8—431no—
372#542—24no—
373#542Dic4318yescomplemented
374C2×C4⋊Q8C2×D4311yescharacteristic
375C2×#126—21no—
376C2×#124—21no—
377C2×#124C2×D4311yescharacteristic
378C2×#123—21no—
379C2×C22⋊Q8—21no—
380C2×C22⋊Q8C2×D4311yescharacteristic
381C2×#121C2×D4311yescharacteristic
382C2×C4×Q8C2×D4311yescharacteristic
383C2×C4×D4C2×D4311yescharacteristic
384C2×#117C2×D4311yescharacteristic
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#102—431no—
390C2×#102—431no—
391C2×#102—431no—
392C2×#102—431no—
393#405—864no—
394C2×#97—431no—
395C2×#97—431no—
396C2×C4×C8—431no—
397C2×C4×C8—431no—
398#388—861no—
399#388—861no—
400#387—861no—
401#387—861no—
402#384—431no—
403#382—431no—
404#380—431no—
405#380—431no—
406C4×C4⋊C4—431no—
407C4×C4⋊C4—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416C43#2141211yescharacteristic, complemented, Sylow
417C22×Q8—21no—
418C22×Q8C22×D4311yescharacteristic
419C22×D4—21no—
420C22×D4C22×D4311yescharacteristic
421C23×C4—21no—
422C23×C4C22×D4311yescharacteristic
423C2×M16—862no—
424C2×M16—862no—
425C2×M16—862no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—431no—
429C22×C8—431no—
430C22×C8—862no—
431C22×C8—862no—
432C22×C8—862no—
433C4⋊Q8—22no—
434C4⋊Q8C2×Dic4314yes—
435#126—28no—
436#124—28no—
437#124—22no—
438#124C2×Dic4314yes—
439#123—28no—
440C22⋊Q8—22no—
441C22⋊Q8—28no—
442C22⋊Q8C2×Dic4314yes—
443#121—22no—
444#121C2×Dic4314yes—
445C4×Q8—22no—
446C4×Q8C2×Dic4314yes—
447C4×D4—22no—
448C4×D4C2×Dic4314yes—
449#117C2×Dic4314yes—
450#117C22⋊D4314yes—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22⋊D4311yescharacteristic
461C2×C4⋊C4C22⋊D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C4⋊C4C22×D4311yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4C22⋊D4311yescharacteristic
472C2×C22⋊C4C22⋊D4311yescharacteristic
473C2×C42—21no—
474C2×C42—861no—
475C2×C42—861no—
476C2×C42C22×D4311yescharacteristic
477C2×C42C22×D4311yescharacteristic
478#103—862no—
479#103—862no—
480#103—862no—
481#103—862no—
482#102—862no—
483#102—862no—
484#102—862no—
485#102—862no—
486#97—862no—
487#97—862no—
488C4×C8—862no—
489C4×C8—862no—
490#95—861no—
491#95—861no—
492#95—861no—
493#95—861no—
494#95—861no—
495#95—861no—
496C24—21no—
497C24C2×C22⋊D4311yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—81no—
505C2×Q8—81no—
506C2×Q8C22×Dic4312yes—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—81no—
514C2×D4—81no—
515C2×D4C22×Dic4312yes—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4C22×Dic4312yes—
531C22×C4C2×C22⋊D4311yescharacteristic
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C2×C22⋊D4312yes—
537C22×C4C23×D4311yescharacteristic
538M16—868no—
539C2×C8—432no—
540C2×C8—432no—
541C2×C8—432no—
542C2×C8—432no—
543C2×C8—868no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—3441no—
566C4⋊C4—3441no—
567C4⋊C4C22⋊Dic4314yes—
568C4⋊C4C22⋊Dic4314yes—
569C4⋊C4C22×Dic4312yes—
570C4⋊C4C22×Dic4312yes—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—3441no—
577C22⋊C4—3441no—
578C22⋊C4C22⋊Dic4314yes—
579C22⋊C4C22⋊Dic4314yes—
580C42—24no—
581C42—3441no—
582C42—3441no—
583C42C22×Dic4312yes—
584C42C22×Dic4312yes—
585C42C2×C22⋊D4312yes—
586C42C2×C22⋊D4312yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×C22⋊Dic4312yes—
601C23C22×C22⋊D4311yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—84no—
607D4—22no—
608D4—22no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4C2×C22⋊Dic4312yes—
649C2×C4C2×C22⋊Dic4312yes—
650C2×C4C2×C22⋊Dic4312yes—
651C2×C4C2×C22⋊Dic4312yes—
652C2×C4C2×C22⋊Dic4312yes—
653C2×C4C23×Dic4311yescharacteristic
654C2×C4C22×C22⋊D4311yescharacteristic
655C2×C4#41×D4311yescharacteristic
656C2×C4#41×D4311yescharacteristic
657C2×C4#41×D4311yescharacteristic
658C2×C4#41×D4311yescharacteristic
659C8—862no—
660C8—862no—
661C8—862no—
662C8—862no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C22×C22⋊Dic4311yescharacteristic
678C22#1458344511yescharacteristic
679C22#1458344511yescharacteristic
680C22#1458370211yescharacteristic
681C22#1458370711yescharacteristic
682C22#1458371011yescharacteristic
683C22#1458371411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—3441no—
693C4—3441no—
694C4—3441no—
695C4—3441no—
696C4#41×Dic4311yescharacteristic
697C4#41×Dic4311yescharacteristic
698C4#1458340611yescharacteristic
699C4#1458340611yescharacteristic
700C2—42no—
701C2—82no—
702C2#1913708611yescharacteristic
703C2#1914312111yescharacteristic
704C2#1914312811yescharacteristic
705C2#1914520611yescharacteristic
706C2#1914522811yescharacteristic
707C2#1914525711yescharacteristic
708C2#1914527211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#542C2
socleC23×C43C22×D4
prime radicalC2×#121×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#542D43
hypocenterC43#21412
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#14582855C2semidirect
2. #19137204C2semidirect
3. #19135569C2semidirect
4. #19135557C2semidirect
5. #19135412C2semidirect
6. #19135407C2semidirect
8. #19135029C2semidirect
10. #19135019C2semidirect
11. #19134425C2semidirect
12. #19134420C2semidirect
13. C4×#13063249C2semidirect
14. C4×#13063246C2semidirect
50. C43×#542C4semidirect
373. #542Dic43semidirect
416. C43#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#145828552
#191372042
#191355692
#191355572
#191354122
#191354072
#191350342
#191350292
#191350242
#191350192
#191344252
#191344202
C4×#130632492
C4×#130632462
C2×C43×#5422
#2141243