Finite Group Databasebeta

← #25106872

Subgroups — #25106872

Order 11008.

1194 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D43C211yesmaximal, characteristic
2#19136974C211yesmaximal, characteristic
3#380×D43C211yesmaximal, characteristic
4#19134796C211yesmaximal, characteristic, complemented
5#19134794C211yesmaximal, characteristic, complemented
6#19134792C211yesmaximal, characteristic, complemented
7#19134789C211yesmaximal, characteristic, complemented
8#19134786C211yesmaximal, characteristic, complemented
9#19134784C211yesmaximal, characteristic, complemented
10#19134781C211yesmaximal, 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×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23C2×#13063259C2211yescharacteristic, complemented
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28C2×#13063256C2211yescharacteristic, complemented
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C22⋊C8×D43C418yescomplemented
33#14582760—21no—
34#14582759C2211yescharacteristic
35#14582758—21no—
36#14582757—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582754—21no—
44C4×(C2×D43)⋊C4—21no—
45C4×(C2×D43)⋊C4—21no—
46#95×D43—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—21no—
63C22×C4×D43—21no—
64C22×C4×D43—41no—
65C22×C4×D43—41no—
66C22×C4×D43—41no—
67C22×C4×D43—41no—
68C22×C4×D43C2×C414yes—
69C22×C4×D43D411yescharacteristic
70C22×C4×D43D411yescharacteristic
71C22×C4×D43Q814yes—
72C22×C4×D43C2311yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—41no—
77C2×C8×D43—41no—
78C2×C8×D43—41no—
79C2×C8×D43—41no—
80C2×C8×D43C2×C414yescomplemented
81C2×C8×D43C2×C414yescomplemented
82#13063284—41no—
83#13063284—41no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C4⋊C4×D43—41no—
91C4⋊C4×D43—41no—
92C4⋊C4×D43—41no—
93C4⋊C4×D43—41no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C22⋊C4×D43—44no—
103C2×C4×Dic43—21no—
104#13063259—41no—
105#13063258—41no—
106#13063258—41no—
107#13063257—41no—
108#13063256—41no—
109#13063256—41no—
110C22⋊(C43⋊C8)C2×C414yescomplemented
111(C2×D43)⋊C8C2×C414yes—
112(C2×D43)⋊C8C2×C414yes—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C23×C4×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123#117×C43—41no—
124#117×C43—41no—
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C42×C43—21no—
132#107×C43—41no—
133#106×C43—41no—
134C22⋊C8×C43C2×C414yescomplemented
135#95×C43—21no—
136C24×C43C2×D411yescharacteristic
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—22no—
140C23×D43—22no—
141C23×D43—41no—
142C23×D43—41no—
143C23×D43C4⋊C414yes—
144C23×D43C2×D411yescharacteristic
145C23×D43C2×D411yescharacteristic
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×C43—21no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×Q812yes—
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43C4⋊C414yes—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
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—21no—
175C2×C4×D43—41no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C2×C4×D43—44no—
184C2×C4×D43—44no—
185C2×C4×D43—44no—
186C2×C4×D43—44no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43C4⋊C414yes—
190C2×C4×D43C4⋊C414yes—
191C2×C4×D43C22×C412yes—
192C2×C4×D43C22×C412yes—
193C2×C4×D43C2×Q812yes—
194C2×C4×D43C2×Q812yes—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43C22×C412yes—
200C2×C8×C43C22×C412yes—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C42×C43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230C4×Dic43—42no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C22×C412yes—
236C2×C43⋊C8C22×C412yes—
237C8×D43—44no—
238C8×D43—44no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C2×C4⋊C412yes—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—28no—
256C22×D43—28no—
257C22×D43—44no—
258C22×D43—44no—
259C22×D43—44no—
260C22×D43—44no—
261C22×D43—44no—
262C22×D43C2×C4⋊C412yes—
263C22×D43C2×C4⋊C412yes—
264C22×D43#13512yes—
265C22×D43#13512yes—
266C22×D43AGL(1,ℤ/8)12yes—
267C22×D43#13712yes—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
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—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C2×C4⋊C412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×Q811yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—44no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43C2×C4⋊C412yes—
311C2×Dic43C2×C4⋊C412yes—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—44no—
321C4×D43—44no—
322C4×D43—84no—
323C4×D43—84no—
324C8×C43—22no—
325C8×C43—22no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328#21941—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C22×C4⋊C411yescharacteristic
337C22×C43#53411yescharacteristic
338C22×C43#53411yescharacteristic
339C22×C43C2×#13511yescharacteristic
340C22×C43C2×#13511yescharacteristic
341C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C43C2×#13711yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—416no—
356C2×D43#42714yes—
357C2×D43#42814yes—
358C4×C43—22no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43#51811yescharacteristic
364C4×C43#51811yescharacteristic
365C4×C43#54311yescharacteristic
366C4×C43#54311yescharacteristic
367Dic43—22no—
368Dic43—22no—
369Dic43—81no—
370Dic43—81no—
371Dic43—81no—
372Dic43—81no—
373C22×C22⋊C8—431no—
374#2280—431no—
375C2×#380—431no—
376#1854—431no—
377#1854—431no—
378#1854—431no—
379#1854D4311yescharacteristic, complemented
380#1853—431no—
381#1853—431no—
382#1852—431no—
383#1852—431no—
384#1808—431no—
385#1808—431no—
386#1807—431no—
387#1807—431no—
388C2×C43—42no—
389C2×C43#231511yescharacteristic
390C2×C43C2×#42711yescharacteristic
391C2×C43C2×#42811yescharacteristic
392C2×C43#318811yescharacteristic
393C2×C43#318811yescharacteristic
394C2×C43#319011yescharacteristic
395C2×C43#319011yescharacteristic
396D43—24no—
397D43—24no—
398C24×C4—431no—
399C23×C8—431no—
400C23×C8—431no—
401C2×#117—431no—
402C2×#117C2×D4311yescharacteristic
403C22×C4⋊C4—431no—
404C22×C4⋊C4—431no—
405C22×C22⋊C4—861no—
406C2×#107—431no—
407C2×#107—431no—
408C2×#107—431no—
409C2×#107C2×D4311yescharacteristic, complemented
410C2×#106—431no—
411C2×#106—431no—
412C2×#106—431no—
413C2×#106C2×D4311yescharacteristic, complemented
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8—438no—
418C2×C22⋊C8C2×D4311yescharacteristic
419#381—861no—
420#380—431no—
421#380—431no—
422#380—431no—
423#380—431no—
424#380—431no—
425#380—431no—
426#380—431no—
427#380—861no—
428#380—861no—
429#380C2×D4311yescharacteristic
430#379—861no—
431C4×C22⋊C4—861no—
432C4×C22⋊C4—861no—
433C2×#95—861no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340C2×D4311yescharacteristic, complemented
441#340C2×D4311yescharacteristic, complemented
442C43#2194111yescharacteristic, complemented, Sylow
443C25—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—434no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—434no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4—1721no—
454C23×C4—1721no—
455C23×C4—1721no—
456C23×C4—1721no—
457C23×C4C22×D4311yescharacteristic
458C22×C8—431no—
459C22×C8—431no—
460C22×C8—434no—
461C22×C8—434no—
462C22×C8—1721no—
463C22×C8—1721no—
464C22×C8—1721no—
465C22×C8—1721no—
466C22×C8C22×D4311yescharacteristic
467C22×C8C22×D4311yescharacteristic
468#117—41no—
469#117—41no—
470#117—1721no—
471#117—1721no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—1721no—
479C2×C4⋊C4—1721no—
480C2×C4⋊C4—1721no—
481C2×C4⋊C4—1721no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—1724no—
497C2×C42—21no—
498C2×C42—861no—
499#107—41no—
500#107—1721no—
501#107—1721no—
502#107—1721no—
503#106—41no—
504#106—1721no—
505#106—1721no—
506#106—1721no—
507C22⋊C8—434no—
508C22⋊C8—434no—
509C22⋊C8—434no—
510C22⋊C8C4×D4314yescomplemented
511#95—21no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519C24—431no—
520C24—431no—
521C24—434no—
522C24—862no—
523C24—862no—
524C24—862no—
525C24—862no—
526C24—1721no—
527C24—1721no—
528C24D4×D4311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—431no—
538C22×C4—431no—
539C22×C4—434no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—432no—
544C22×C4—434no—
545C22×C4—434no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—1724no—
559C22×C4—1724no—
560C22×C4—1724no—
561C22×C4—1724no—
562C22×C4—1721no—
563C22×C4—1721no—
564C22×C4—1721no—
565C22×C4—1721no—
566C22×C4—1722no—
567C22×C4—1722no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1721no—
573C22×C4—1721no—
574C22×C4C2×C4×D4312yes—
575C22×C4D4×D4311yescharacteristic
576C22×C4Q8×D4312yes—
577C22×C4C23×D4311yescharacteristic
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—432no—
583C2×C8—432no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C2×C8—1724no—
589C2×C8—1724no—
590C2×C8C2×C4×D4312yes—
591C2×C8C2×C4×D4312yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—1722no—
609C4⋊C4—1722no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—1722no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C22⋊C4—1722no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C42—42no—
621C42—1722no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—432no—
629C23—432no—
630C23—432no—
631C23—432no—
632C23—432no—
633C23—432no—
634C23—868no—
635C23—868no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—1724no—
645C23—1724no—
646C23—1724no—
647C23—1724no—
648C23—1724no—
649C23C4⋊C4×D4312yes—
650C23C2×D4×D4311yescharacteristic
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—3444no—
684C2×C4—3444no—
685C2×C4—1724no—
686C2×C4—1724no—
687C2×C4—1724no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4C4⋊C4×D4312yes—
701C2×C4C22×C4×D4311yescharacteristic
702C2×C4C2×Q8×D4311yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337111yescharacteristic
706C2×C4#1306337111yescharacteristic
707C8—22no—
708C8—22no—
709C8—862no—
710C8—862no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—434no—
719C22—434no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—17216no—
733C22C2×C4⋊C4×D4311yescharacteristic
734C22#1458345911yescharacteristic
735C22#1458346011yescharacteristic
736C22#135×D4311yescharacteristic
737C22#135×D4311yescharacteristic
738C22AGL(1,ℤ/8)×D4311yescharacteristic
739C22#137×D4311yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4—862no—
746C4—862no—
747C4—3441no—
748C4—3441no—
749C4—3441no—
750C4—3441no—
751C4#1458337111yescharacteristic
752C4#1458337111yescharacteristic
753C4#1458352411yescharacteristic
754C4#1458352411yescharacteristic
755C2—42no—
756C2—864no—
757C2—864no—
758C2#1913720611yescharacteristic
759C2#427×D4311yescharacteristic
760C2#428×D4311yescharacteristic
761C2#1914535811yescharacteristic
762C2#1914536411yescharacteristic
763C2#1914537411yescharacteristic
764C2#1914538011yescharacteristic
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#21941
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. #19134796C2semidirect
5. #19134794C2semidirect
6. #19134792C2semidirect
7. #19134789C2semidirect
8. #19134786C2semidirect
9. #19134784C2semidirect
10. #19134781C2semidirect
11. #19134623C2semidirect
12. #19134621C2semidirect
13. #19134619C2semidirect
14. #19134617C2semidirect
15. C43×#1854C2semidirect
23. C2×#13063259C22semidirect
24. C2×#13063258C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×#13063256C22semidirect
28. C2×#13063256C22semidirect
32. 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
80. C2×C8×D43C2×C4semidirect
81. C2×C8×D43C2×C4semidirect
110. C22⋊(C43⋊C8)C2×C4semidirect
134. C22⋊C8×C43C2×C4semidirect
379. #1854D43semidirect
409. C2×#107C2×D43semidirect
413. C2×#106C2×D43semidirect
440. #340C2×D43semidirect
441. #340C2×D43semidirect
442. C43#21941semidirect
510. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D432
#191369742
#380×D432
#191347962
#191347942
#191347922
#191347892
#191347862
#191347842
#191347812
#191346232
#191346212
#191346192
#191346172
C43×#18542
#2194143