Finite Group Databasebeta

← #25140048

Subgroups — #25140048

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583220C211yesmaximal, characteristic, complemented
2C2×#14582895C211yesmaximal, characteristic, complemented
3#19137544C211yesmaximal, characteristic, complemented
4#19136133C211yesmaximal, characteristic, complemented
5#19135998C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135774C211yesmaximal, characteristic, complemented
8#19135226C211yesmaximal, characteristic, complemented
9#19135212C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134888C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134622C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C43×#2407C211yesmaximal, characteristic
16C23×C43⋊C8C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19#14583220—24no—
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24#14582895—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36#14582802—21no—
37#14582792—21no—
38#14582792—21no—
39#14582769C2211yescharacteristic
40#14582759C2211yescharacteristic
41#14582759C2211yescharacteristic
42C4⋊C4×Dic43—21no—
43C4×C4⋊Dic43C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C22×#41×C43C2211yescharacteristic
51C2×C22⋊Q8×C43C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#394—21no—
55C43×#392—21no—
56C43×#391C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#386—21no—
59C43×#385—21no—
60C43×#380C2211yescharacteristic
61C22×C43⋊C8—22no—
62C22×C43⋊C8—22no—
63C22×C43⋊C8—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063284—22no—
69#13063284—22no—
70#13063284—41no—
71#13063284—41no—
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×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063258—41no—
87#13063258—41no—
88#13063256—22no—
89#13063249—22no—
90#13063249—22no—
91#13063249—22no—
92#13063249—41no—
93#13063246—22no—
94#13063246—22no—
95#13063246—41no—
96#13063246D414yescomplemented
97C22⋊(C43⋊C8)—22no—
98C22⋊(C43⋊C8)—22no—
99C22⋊(C43⋊C8)—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C2×#41×C43—22no—
104C2×#41×C43—22no—
105C2×#41×C43—22no—
106C2×#41×C43—22no—
107C2×#41×C43—41no—
108C2×#41×C43—41no—
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43—21no—
112C22×D4×C43D411yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C23×C4×C43—21no—
115C23×C4×C43C2311yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C22⋊Q8×C43—22no—
118C22⋊Q8×C43—41no—
119#121×C43—22no—
120#121×C43—41no—
121C4×D4×C43—22no—
122C4×D4×C43—22no—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43D411yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141#41×C43—28no—
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43#4112yes—
151C2×D4×C43—22no—
152C2×D4×C43—21no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43C2×D412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
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—42no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43#4112yes—
187C22×C4×C43#4112yes—
188C22×C4×C43C2411yescharacteristic
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C4⋊C4×C43—22no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—42no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—22no—
201C22⋊C4×C43—42no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—81no—
205C22⋊C4×C43—81no—
206C42×C43—21no—
207C42×C43—21no—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—42no—
220C4⋊Dic43—81no—
221C4⋊Dic43C2×D412yes—
222C4×Dic43—42no—
223C4×Dic43—42no—
224C4×Dic43—42no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—44no—
237C2×C43⋊C8C2×D412yes—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—22no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43#12312yes—
259C23×C43C22×D411yescharacteristic
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—44no—
267D4×C43—48no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—84no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—48no—
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×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43#12312yes—
300C2×C4×C43#13512yes—
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43C2×#4111yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43H(5,𝔽2)11yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×Dic43—22no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24874—431nomaximal, Sylow
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—42no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—41no—
338C22×C43—42no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43C2×#12311yescharacteristic
346C22×C43D4211yescharacteristic
347C22×C43#54611yescharacteristic
348C22×C43C2×#13511yescharacteristic
349C22×C43#57511yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57811yescharacteristic
352C4×C43—22no—
353C4×C43—22no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—42no—
357C4×C43—81no—
358C4×C43—81no—
359C4×C43#52511yescharacteristic
360C4×C43#53811yescharacteristic
361C4×C43#54611yescharacteristic
362C4×C43#55111yescharacteristic
363Dic43—42no—
364Dic43—81no—
365Dic43—81no—
366Dic43—81no—
367C2×#482—431no—
368C2×#416—431no—
369#2407D4311yescharacteristic
370#2354—431no—
371#2095—431no—
372#2071—431no—
373#2036—431no—
374#2033—431no—
375#1927—431no—
376#1925—431no—
377#1873—431no—
378#1869—431no—
379#1854—431no—
380#1808—431no—
381#1788—431no—
382C2×C43—42no—
383C2×C43—81no—
384C2×C43—82no—
385C2×C43#241811yescharacteristic
386C2×C43#309111yescharacteristic
387C2×C43#309811yescharacteristic
388C2×C43#326811yescharacteristic
389C2×C43#328311yescharacteristic
390C2×C43#330511yescharacteristic
391C2×C43#331311yescharacteristic
392C22×#41C2×D4311yescharacteristic
393C23×C8—431no—
394C2×C22⋊Q8C2×D4311yescharacteristic
395C2×#121C2×D4311yescharacteristic
396C2×C4×D4C2×D4311yescharacteristic
397C2×#117—431no—
398C2×#117—431no—
399#482—864no—
400C2×#107—431no—
401C2×#107—431no—
402C2×#107—431no—
403C2×#106—431no—
404#416—864no—
405C2×#103—431no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416#394—21no—
417#392—21no—
418#391C2×D4311yescharacteristic
419#390—861no—
420#390C2×D4311yescharacteristic
421#388—861no—
422#388—861no—
423#386—21no—
424#385—21no—
425#384—431no—
426#380—431no—
427#380—431no—
428#380C2×D4311yescharacteristic
429C4×C4⋊C4—431no—
430C4×C4⋊C4—861no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#336—431no—
436#336—431no—
437C43#2487411yescharacteristic, complemented, Sylow
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—41no—
443C2×#41—41no—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22⋊D4311yescharacteristic
448C22×D4C22×D4311yescharacteristic
449C23×C4—21no—
450C23×C4C22×D4311yescharacteristic
451C23×C4C22×D4311yescharacteristic
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8—431no—
456C22×C8—862no—
457C22×C8—862no—
458C22×C8—1721no—
459C22⋊Q8—22no—
460C22⋊Q8—41no—
461#121—22no—
462#121—41no—
463C4×D4—22no—
464C4×D4—22no—
465#117—862no—
466#117—862no—
467#117—1721no—
468#117—1721no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4C22⋊D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4C22⋊D4311yescharacteristic
489C2×C22⋊C4C22⋊D4311yescharacteristic
490C2×C42—861no—
491C2×C42—861no—
492C2×C42—861no—
493C2×C42C22×D4311yescharacteristic
494#107—862no—
495#107—1721no—
496#107—1721no—
497#106—862no—
498#103—862no—
499#103—862no—
500#103—862no—
501#103—1721no—
502#102—434no—
503#102—862no—
504#102—862no—
505#102—1721no—
506C22⋊C8—862no—
507C22⋊C8—862no—
508C22⋊C8—1721no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—861no—
513#95—861no—
514#95—861no—
515C24—21no—
516C24C2×C22⋊D4311yescharacteristic
517C24C2×C22⋊D4311yescharacteristic
518#41—28no—
519#41—44no—
520#41—44no—
521#41—44no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8#1062190012yes—
528C2×D4—22no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—81no—
542C2×D4D4×D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4#1062190012yes—
564C22×C4#1062190012yes—
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C22×C4C2×C22⋊D4311yescharacteristic
568C22×C4C2×C22⋊D4311yescharacteristic
569C22×C4C23×D4311yescharacteristic
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—1724no—
583C4⋊C4—22no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—432no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—3441no—
598C4⋊C4—1722no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C42—21no—
611C42—21no—
612C42—1722no—
613C42—1722no—
614C42—1722no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23#1306330612yes—
636C23C22×C22⋊D4311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641D4—22no—
642D4—22no—
643D4—44no—
644D4—48no—
645D4—41no—
646D4—41no—
647D4—84no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—48no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—862no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4#1306330612yes—
689C2×C4#1306334512yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4C2×#1062190011yescharacteristic
692C2×C4C2×#1062190011yescharacteristic
693C2×C4C2×#1062190011yescharacteristic
694C2×C4#1306337011yescharacteristic
695C2×C4#1306337011yescharacteristic
696C8—862no—
697C8—1721no—
698C8—1721no—
699C8—1721no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22C2×#1306330611yescharacteristic
722C22D4×C22⋊D4311yescharacteristic
723C22#1458354311yescharacteristic
724C22C2×#1306334511yescharacteristic
725C22#1458369711yescharacteristic
726C22#1458370211yescharacteristic
727C22#1458371411yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—42no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4—3441no—
736C4—3441no—
737C4—3441no—
738C4—1722no—
739C4#1458340511yescharacteristic
740C4#1458348411yescharacteristic
741C4#1458353611yescharacteristic
742C4#1458358011yescharacteristic
743C2—42no—
744C2—81no—
745C2—82no—
746C2#1913805311yescharacteristic
747C2#1914450411yescharacteristic
748C2#1914456911yescharacteristic
749C2#1914613111yescharacteristic
750C2#1914631311yescharacteristic
751C2#1914654511yescharacteristic
752C2#1914666111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2407C2
socleC23×C43C22×D4
hypercenter#2407D43
hypocenterC43#24874
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#14583220C2semidirect
2. C2×#14582895C2semidirect
3. #19137544C2semidirect
4. #19136133C2semidirect
5. #19135998C2semidirect
6. #19135795C2semidirect
7. #19135774C2semidirect
8. #19135226C2semidirect
9. #19135212C2semidirect
10. #19134908C2semidirect
11. #19134888C2semidirect
12. #19134792C2semidirect
13. #19134622C2semidirect
14. #19134535C2semidirect
96. #13063246D4semidirect
437. C43#24874semidirect

Maximal subgroups

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

subgroupindex
C2×#145832202
C2×#145828952
#191375442
#191361332
#191359982
#191357952
#191357742
#191352262
#191352122
#191349082
#191348882
#191347922
#191346222
#191345352
C43×#24072
#2487443