Finite Group Databasebeta

← #25106859

Subgroups — #25106859

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D43C211yesmaximal, characteristic
2#19136977C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4#19134797C211yesmaximal, characteristic, complemented
5#19134796C211yesmaximal, characteristic, complemented
6#19134795C211yesmaximal, characteristic, complemented
7#19134794C211yesmaximal, characteristic, complemented
8#19134793C211yesmaximal, characteristic, complemented
9#19134792C211yesmaximal, characteristic, complemented
10#19134791C211yesmaximal, characteristic, complemented
11#19134623C211yesmaximal, characteristic, complemented
12#19134621C211yesmaximal, characteristic, complemented
13#19134619C211yesmaximal, characteristic, complemented
14#19134617C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063259C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063257C2211yescharacteristic, complemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C22⋊C8×D43C418yescomplemented
32#14582761—21no—
33#14582760—21no—
34#14582759C2211yescharacteristic
35#14582756C2211yescharacteristic
36#14582756C2211yescharacteristic
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582754—21no—
42#14582754—21no—
43C22⋊C4×Dic43—21no—
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4—21no—
46#14582746—21no—
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic, complemented
55C2×#106×C43C2211yescharacteristic, complemented
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic, complemented
59C43×#340C2211yescharacteristic, complemented
60C24×D43D411yescharacteristic
61C23×Dic43D411yescharacteristic
62C22×C4×D43—41no—
63C22×C4×D43—41no—
64C22×C4×D43—41no—
65C22×C4×D43—41no—
66C22×C4×D43C2×C414yes—
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43Q814yes—
70C22×C4×D43C2311yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—41no—
75C2×C8×D43—41no—
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78C2×C8×D43C2×C414yes—
79C2×C8×D43C2×C414yes—
80#13063284—41no—
81#13063284—41no—
82#13063283—41no—
83#13063283—41no—
84#13063283—41no—
85#13063283—41no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063259—41no—
104#13063258—41no—
105#13063258—41no—
106#13063257—41no—
107#13063256—41no—
108#13063256—41no—
109C22⋊(C43⋊C8)C2×C414yes—
110(C2×D43)⋊C8C2×C414yes—
111(C2×D43)⋊C8C2×C414yes—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C23×C4×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122#117×C43—41no—
123#117×C43—41no—
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43—21no—
131#107×C43—41no—
132#106×C43—41no—
133C22⋊C8×C43C2×C414yes—
134#95×C43—21no—
135C24×C43C2×D411yescharacteristic
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—41no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43—41no—
142C23×D43C4⋊C414yes—
143C23×D43C2×D411yescharacteristic
144C23×D43C2×D411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C22×C412yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×Q812yes—
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43C4⋊C414yes—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—41no—
175C2×C4×D43—41no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—44no—
179C2×C4×D43—44no—
180C2×C4×D43—44no—
181C2×C4×D43—44no—
182C2×C4×D43C4⋊C414yes—
183C2×C4×D43C4⋊C414yes—
184C2×C4×D43C22×C412yes—
185C2×C4×D43C22×C412yes—
186C2×C4×D43C2×Q812yes—
187C2×C4×D43C2×Q812yes—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43C22×C412yes—
193C2×C8×C43C22×C412yes—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C22⋊C4×C43—42no—
203C22⋊C4×C43—42no—
204C42×C43—42no—
205C22⋊Dic43—42no—
206C22⋊Dic43—42no—
207(C2×D43)⋊C4—42no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4×Dic43—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8C22×C412yes—
231C2×C43⋊C8C22×C412yes—
232C8×D43—44no—
233C8×D43—44no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43C2×C4⋊C412yes—
241C23×C43C22×D411yescharacteristic
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—28no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43—44no—
258C22×D43—44no—
259C22×D43C2×C4⋊C412yes—
260C22×D43C2×C4⋊C412yes—
261C22×D43#13512yes—
262C22×D43#13512yes—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
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—41no—
281C2×C4×C43C2×C4⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×Q811yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—44no—
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—
304C2×Dic43—41no—
305C2×Dic43C2×C4⋊C412yes—
306C2×Dic43C2×C4⋊C412yes—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—44no—
316C4×D43—44no—
317C8×C43—22no—
318C8×C43—22no—
319C43⋊C8—22no—
320C43⋊C8—22no—
321#21939—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43C22×C4⋊C411yescharacteristic
330C22×C43#53411yescharacteristic
331C22×C43#53411yescharacteristic
332C22×C43C2×#13511yescharacteristic
333C22×C43C2×#13511yescharacteristic
334C22×C43#57511yescharacteristic
335C22×C43#57511yescharacteristic
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—22no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—416no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43#42714yes—
351C4×C43—22no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43—81no—
355C4×C43—81no—
356C4×C43#51811yescharacteristic
357C4×C43#51811yescharacteristic
358C4×C43#54311yescharacteristic
359C4×C43#54311yescharacteristic
360Dic43—22no—
361Dic43—22no—
362Dic43—81no—
363Dic43—81no—
364Dic43—81no—
365Dic43—81no—
366C22×C22⋊C8—431no—
367#2280—431no—
368#2280—431no—
369#1854—431no—
370#1854—431no—
371#1854—431no—
372#1854—431no—
373#1854—431no—
374#1854—431no—
375#1854—431no—
376#1854D4311yescharacteristic, complemented
377#1808—431no—
378#1808—431no—
379#1807—431no—
380#1807—431no—
381C2×C43—42no—
382C2×C43#231511yescharacteristic
383C2×C43C2×#42711yescharacteristic
384C2×C43#291111yescharacteristic
385C2×C43#319111yescharacteristic
386C2×C43#319111yescharacteristic
387C2×C43#319111yescharacteristic
388C2×C43#319111yescharacteristic
389D43—24no—
390D43—42no—
391C24×C4—431no—
392C23×C8—431no—
393C23×C8—431no—
394C2×#117—431no—
395C2×#117—431no—
396C2×#117—431no—
397C2×#117C2×D4311yescharacteristic
398C2×#107—431no—
399C2×#107—431no—
400C2×#107—431no—
401C2×#107C2×D4311yescharacteristic, complemented
402C2×#106—431no—
403C2×#106—431no—
404C2×#106—431no—
405C2×#106C2×D4311yescharacteristic, complemented
406C2×C22⋊C8—431no—
407C2×C22⋊C8—431no—
408C2×C22⋊C8—431no—
409C2×C22⋊C8—438no—
410C2×C22⋊C8C2×D4311yescharacteristic
411#381—861no—
412#381—861no—
413#380—431no—
414#380—431no—
415#380—431no—
416#380—431no—
417#380—431no—
418#380—431no—
419#380—431no—
420#380C2×D4311yescharacteristic
421#379—861no—
422#379—861no—
423C4×C22⋊C4—861no—
424C4×C22⋊C4—861no—
425C4×C22⋊C4—861no—
426C4×C22⋊C4—861no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340C2×D4311yescharacteristic, complemented
434#340C2×D4311yescharacteristic, complemented
435C43#2193911yescharacteristic, complemented, Sylow
436C25—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—434no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—434no—
444C23×C4—1721no—
445C23×C4—1721no—
446C23×C4—1721no—
447C23×C4—1721no—
448C23×C4C22×D4311yescharacteristic
449C22×C8—431no—
450C22×C8—431no—
451C22×C8—434no—
452C22×C8—434no—
453C22×C8—1721no—
454C22×C8—1721no—
455C22×C8—1721no—
456C22×C8—1721no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#117—41no—
460#117—41no—
461#117—1721no—
462#117—1721no—
463#117—1721no—
464#117—1721no—
465#117—1721no—
466#117—1721no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—21no—
488C2×C42—861no—
489C2×C42—861no—
490C2×C42—861no—
491#107—41no—
492#107—1721no—
493#107—1721no—
494#107—1721no—
495#106—41no—
496#106—1721no—
497#106—1721no—
498#106—1721no—
499C22⋊C8—434no—
500C22⋊C8—434no—
501C22⋊C8—434no—
502C22⋊C8C4×D4314yes—
503#95—21no—
504#95—861no—
505#95—861no—
506#95—861no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511C24—431no—
512C24—431no—
513C24—434no—
514C24—862no—
515C24—862no—
516C24—1721no—
517C24—1721no—
518C24—1721no—
519C24—1721no—
520C24D4×D4311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—434no—
532C22×C4—432no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—434no—
537C22×C4—434no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—1724no—
551C22×C4—1724no—
552C22×C4—1724no—
553C22×C4—1724no—
554C22×C4—1721no—
555C22×C4—1721no—
556C22×C4—1721no—
557C22×C4—1721no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4C2×C4×D4312yes—
561C22×C4D4×D4311yescharacteristic
562C22×C4Q8×D4312yes—
563C22×C4C23×D4311yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—432no—
569C2×C8—432no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—1724no—
575C2×C8—1724no—
576C2×C8C2×C4×D4312yes—
577C2×C8C2×C4×D4312yes—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C22⋊C4—1722no—
604C22⋊C4—1722no—
605C22⋊C4—1722no—
606C42—42no—
607C42—1722no—
608C42—1722no—
609C42—1722no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—432no—
617C23—432no—
618C23—432no—
619C23—432no—
620C23—868no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—1724no—
632C23—1724no—
633C23—1724no—
634C23—1724no—
635C23—1724no—
636C23—1724no—
637C23C4⋊C4×D4312yes—
638C23C2×D4×D4311yescharacteristic
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—1724no—
672C2×C4—1724no—
673C2×C4—1724no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
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×C4C4⋊C4×D4312yes—
687C2×C4C22×C4×D4311yescharacteristic
688C2×C4C2×Q8×D4311yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337011yescharacteristic
691C2×C4#1306337111yescharacteristic
692C2×C4#1306337111yescharacteristic
693C8—22no—
694C8—22no—
695C8—862no—
696C8—862no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—434no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—862no—
709C22—862no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—862no—
714C22—17216no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22C2×C4⋊C4×D4311yescharacteristic
720C22#1458345911yescharacteristic
721C22#1458346011yescharacteristic
722C22#135×D4311yescharacteristic
723C22#135×D4311yescharacteristic
724C22#1458369511yescharacteristic
725C22#1458369811yescharacteristic
726C4—22no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4—81no—
731C4—862no—
732C4—862no—
733C4—3441no—
734C4—3441no—
735C4—3441no—
736C4—3441no—
737C4#1458337111yescharacteristic
738C4#1458337111yescharacteristic
739C4#1458352411yescharacteristic
740C4#1458352411yescharacteristic
741C2—42no—
742C2—864no—
743C2—1722no—
744C2#1913720611yescharacteristic
745C2#427×D4311yescharacteristic
746C2#1914318211yescharacteristic
747C2#1914538511yescharacteristic
748C2#1914538611yescharacteristic
749C2#1914538711yescharacteristic
750C2#1914539011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#21939
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #19134797C2semidirect
5. #19134796C2semidirect
6. #19134795C2semidirect
7. #19134794C2semidirect
8. #19134793C2semidirect
9. #19134792C2semidirect
10. #19134791C2semidirect
11. #19134623C2semidirect
12. #19134621C2semidirect
13. #19134619C2semidirect
14. #19134617C2semidirect
15. C43×#1854C2semidirect
22. C2×#13063259C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063258C22semidirect
25. C2×#13063257C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063256C22semidirect
31. C22⋊C8×D43C4semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
54. C2×#107×C43C22semidirect
55. C2×#106×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#340C22semidirect
376. #1854D43semidirect
401. C2×#107C2×D43semidirect
405. C2×#106C2×D43semidirect
433. #340C2×D43semidirect
434. #340C2×D43semidirect
435. C43#21939semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D432
#191369772
#191369742
#191347972
#191347962
#191347952
#191347942
#191347932
#191347922
#191347912
#191346232
#191346212
#191346192
#191346172
C43×#18542
#2193943