Finite Group Databasebeta

← #25097634

Subgroups — #25097634

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583378C211yesmaximal, characteristic
2C2×#106×D43C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic
4C2×#14582892C211yesmaximal, characteristic
5#19137217C211yesmaximal, characteristic, complemented
6#19134866C211yesmaximal, characteristic, complemented
7#19134864C211yesmaximal, characteristic, complemented
8#19134862C211yesmaximal, characteristic, complemented
9#19134860C211yesmaximal, characteristic, complemented
10#19134858C211yesmaximal, characteristic, complemented
11#19134856C211yesmaximal, characteristic, complemented
12#19134854C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1864C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583378—24no—
20#14583378—24no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×C4×C22⋊D43—21no—
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063283C2211yescharacteristic
27C2×#13063282C2211yescharacteristic
28C2×#13063281—21no—
29C22×Dic43⋊C4—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32C2×#13063257C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063256C2211yescharacteristic
35#106×D43—24no—
36#14582897—24no—
37#14582892C418yescomplemented
38C2×#13063250C2211yescharacteristic
39C2×#13063250C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582795C2211yescharacteristic
47#14582773—21no—
48#14582770—21no—
49#14582768—21no—
50#14582763—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582654C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×#106×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C43×#389C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#336C2211yescharacteristic
64C2×#10621900—22no—
65C2×#10621900—22no—
66C2×#10621900—22no—
67C2×#10621900C2×C414yes—
68C2×#10621900D414yes—
69C2×#10621900Q814yes—
70C22×Dic86C2311yescharacteristic
71C22×C22⋊D43—21no—
72C23×Dic43—21no—
73C23×Dic43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43C2×C414yescomplemented
85C4×Dic86—22no—
86C4×Dic86—22no—
87#13063290—22no—
88#13063290—22no—
89D4×Dic43—22no—
90D4×Dic43—22no—
91C4×C22⋊D43—28no—
92(C22⋊D43)⋊C4—28no—
93#13063283—22no—
94#13063283C2×C414yescomplemented
95#13063282—22no—
96#13063282—22no—
97#13063281—28no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—28no—
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⋊C4D411yescharacteristic
110C2×Dic43⋊C4D411yescharacteristic
111C4⋊C4×D43—22no—
112C4⋊C4×D43—22no—
113C4⋊C4×D43—22no—
114C4⋊C4×D43D414yes—
115C2×C22⋊Dic43—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×(C2×D43)⋊C4D411yescharacteristic
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123#13063257—22no—
124#13063256—22no—
125#13063256—22no—
126#13063250—22no—
127#13063250C2×C414yescomplemented
128#13063248—22no—
129#13063248C2×C414yescomplemented
130#13063246—22no—
131#13063246C2×C414yescomplemented
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×D4×C43C2311yescharacteristic
136C23×C4×C43—21no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C4×D4×C43—22no—
140C4×D4×C43—22no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#106×C43—22no—
148#102×C43—22no—
149#102×C43C2×C414yescomplemented
150#95×C43—21no—
151C24×C43—21no—
152C23×D43C2×D411yescharacteristic
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C412yes—
157C2×D4×C43C2×D412yes—
158C2×D4×C43C2×Q812yes—
159C22×C4×C43—24no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—81no—
164C22×C4×C43—81no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2411yescharacteristic
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C22×Dic43—24no—
172C22×Dic43—24no—
173C22×Dic43—24no—
174C22×Dic43—24no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184#10621900—28no—
185#10621900—28no—
186#10621900—28no—
187#10621900C4⋊C4116yescomplemented
188C2×C4×D43—24no—
189C2×C4×D43—42no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C4×D43—81no—
193C2×C4×D43—81no—
194C2×C4×D43C22×C412yes—
195C2×C4×D43C2×D412yes—
196C2×C4×D43C2×D412yes—
197C2×C4×D43C2×Q812yes—
198C2×C4×D43#4112yes—
199C2×C4×D43#4112yes—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86C22×C412yes—
204C2×Dic86C2×D412yes—
205C2×Dic86C2×Q812yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43C22×C412yes—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—81no—
217C4⋊C4×C43C22×C412yes—
218C4⋊C4×C43C2×D412yes—
219C22⋊C4×C43—24no—
220C42×C43—21no—
221C42×C43—21no—
222C22⋊Dic43—24no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—81no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C2×D412yes—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—42no—
239Dic43⋊C4—81no—
240Dic43⋊C4—81no—
241C4×Dic43—24no—
242C4×Dic43—24no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—24no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8C22×C412yes—
252#10621872—44no—
253C8×D43—28no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43C22×D411yescharacteristic
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43C4×D412yes—
267C22×D43#12012yes—
268C22×D43C22⋊Q812yes—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43C2×C4⋊C414yes—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—84no—
289C2×C4×C43C23×C411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×Q811yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C22⋊D43—216no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—216no—
300C2×Dic43—22no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—84no—
316C2×Dic43C4×D412yes—
317C2×Dic43#12012yes—
318C2×Dic43C22⋊Q812yes—
319C4×D43—84no—
320C4×D43—84no—
321C4×D43C2×C4⋊C414yes—
322C4×D43C4×D414yes—
323C4×D43C22⋊Q814yes—
324C4×D43#12314yes—
325Dic86—22no—
326Dic86—22no—
327Dic86—22no—
328Dic86C2×C4⋊C414yes—
329C8×C43—22no—
330C8×C43—41no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333#20882—431nomaximal, Sylow
334C22×C43—24no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43C2×C4×D411yescharacteristic
342C22×C43C2×#12011yescharacteristic
343C22×C43C2×C22⋊Q811yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57711yescharacteristic
346C22×C43#57711yescharacteristic
347C22×C43#57711yescharacteristic
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43#38514yes—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—81no—
360C4×C43C22×C4⋊C411yescharacteristic
361C4×C43C2×C4×D411yescharacteristic
362C4×C43C2×C22⋊Q811yescharacteristic
363C4×C43C2×#12311yescharacteristic
364Dic43—24no—
365Dic43—42no—
366Dic43—42no—
367Dic43—41no—
368Dic43—41no—
369Dic43—81no—
370Dic43#38514yes—
371C2×#520—431no—
372C22×#106—431no—
373C2×#417—431no—
374C2×#416—431no—
375#2317—431no—
376#1865—431no—
377#1865—431no—
378#1865—431no—
379#1865—431no—
380#1864—431no—
381#1864—431no—
382#1864—431no—
383#1864D4311yescharacteristic, complemented
384#1736—431no—
385#1729—431no—
386C2×C43—44no—
387C2×C43C2×#38511yescharacteristic
388C2×C43#295211yescharacteristic
389C2×C43#295211yescharacteristic
390C2×C43#300911yescharacteristic
391C2×C43#301011yescharacteristic
392C2×C43#308411yescharacteristic
393C2×C43#308411yescharacteristic
394D43—24no—
395C22×#41—431no—
396C22×M16—431no—
397C23×C8—431no—
398#520—864no—
399#520—864no—
400C2×C4×Q8—431no—
401C2×C4×Q8—431no—
402C2×C4×D4—431no—
403C2×C4×D4—861no—
404C2×C4×D4—861no—
405C2×C4×D4C2×D4311yescharacteristic
406C2×#117—431no—
407C2×#117—431no—
408C2×#117—861no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—861no—
412C2×#106—431no—
413C2×#106—431no—
414C2×#106—431no—
415C2×#106—864no—
416C2×#106C2×D4311yescharacteristic
417#417—864no—
418#416—438no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102C2×D4311yescharacteristic
426C2×#102C2×D4311yescharacteristic
427#389—431no—
428#389—431no—
429#389—431no—
430#389C2×D4311yescharacteristic
431#385—861no—
432#385—861no—
433#384—861no—
434#382—861no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340C2×D4311yescharacteristic
439#336—431no—
440#336—431no—
441#336—431no—
442#336C2×D4311yescharacteristic
443C43#2088211yescharacteristic, complemented, Sylow
444C2×#41—434no—
445C2×#41—434no—
446C2×#41—434no—
447C2×#41—862no—
448C2×#41—862no—
449C2×#41—862no—
450C22×Q8—431no—
451C22×D4—861no—
452C22×D4C22×D4311yescharacteristic
453C23×C4—21no—
454C23×C4—431no—
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4—861no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—434no—
464C22×C8—431no—
465C22×C8—862no—
466C22×C8—862no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4×Q8—862no—
470C4×Q8—862no—
471C4×Q8—862no—
472C4×Q8—862no—
473C4×D4—22no—
474C4×D4—22no—
475C4×D4—868no—
476C4×D4—862no—
477C4×D4—868no—
478C4×D4—862no—
479#117—434no—
480#117—862no—
481#117—862no—
482#117—868no—
483#117—862no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—434no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—862no—
492C2×C4⋊C4—862no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—868no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—431no—
507C2×C22⋊C4—431no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C42—431no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515#106—22no—
516#106—862no—
517#106—862no—
518#106—862no—
519#103—434no—
520#103—434no—
521#103—862no—
522#103—862no—
523#102—22no—
524#102—434no—
525#102—862no—
526#102C4×D4314yescomplemented
527#95—21no—
528#95—861no—
529#95—861no—
530#95—861no—
531C24—21no—
532C24—431no—
533#41—4316no—
534#41—868no—
535#41—868no—
536#41—868no—
537C2×Q8—432no—
538C2×Q8—432no—
539C2×Q8—432no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—864no—
547C2×D4—864no—
548C2×D4—864no—
549C2×D4C2×C4×D4312yes—
550C2×D4D4×D4312yes—
551C2×D4Q8×D4312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—431no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—864no—
571C22×C4—861no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—3441no—
577C22×C4—3441no—
578C22×C4—3441no—
579C22×C4—3441no—
580C22×C4—3441no—
581C22×C4—3441no—
582C22×C4—1722no—
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586M16—1724no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—432no—
593C2×C8—868no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8C2×C4×D4312yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—81no—
605C4⋊C4—432no—
606C4⋊C4—432no—
607C4⋊C4—862no—
608C4⋊C4—864no—
609C4⋊C4—862no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—3441no—
617C4⋊C4—3441no—
618C4⋊C4—3441no—
619C4⋊C4—1722no—
620C4⋊C4C2×C4×D4312yes—
621C4⋊C4D4×D4312yes—
622C22⋊C4—24no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C42—21no—
628C42—21no—
629C42—864no—
630C42—864no—
631C42—864no—
632C42—861no—
633C42—861no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—432no—
642C23—432no—
643C23—432no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23C2×D4×D4311yescharacteristic
649Q8—434no—
650Q8—862no—
651Q8—862no—
652Q8—862no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—8616no—
657D4C4⋊C4×D4314yes—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—434no—
678C2×C4—434no—
679C2×C4—434no—
680C2×C4—434no—
681C2×C4—8616no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—861no—
687C2×C4—862no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—3444no—
694C2×C4—3444no—
695C2×C4—3444no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4C22×C4×D4311yescharacteristic
704C2×C4C2×D4×D4311yescharacteristic
705C2×C4C2×D4×D4311yescharacteristic
706C2×C4C2×Q8×D4311yescharacteristic
707C2×C4#41×D4311yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C8—22no—
710C8—41no—
711C8—862no—
712C8—1721no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—434no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22—862no—
726C22—862no—
727C22C4×D4×D4311yescharacteristic
728C22#120×D4311yescharacteristic
729C22C22⋊Q8×D4311yescharacteristic
730C22#1458370511yescharacteristic
731C22#1458370611yescharacteristic
732C22#1458370911yescharacteristic
733C22#1458370911yescharacteristic
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—81no—
739C4—434no—
740C4—864no—
741C4—3441no—
742C4—1722no—
743C4—1721no—
744C4—1722no—
745C4—1721no—
746C4C2×C4⋊C4×D4311yescharacteristic
747C4C4×D4×D4311yescharacteristic
748C4C22⋊Q8×D4311yescharacteristic
749C4#123×D4311yescharacteristic
750C2—44no—
751C2—864no—
752C2#385×D4311yescharacteristic
753C2#1914347311yescharacteristic
754C2#1914347711yescharacteristic
755C2#1914386711yescharacteristic
756C2#1914387811yescharacteristic
757C2#1914445211yescharacteristic
758C2#1914445811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1864C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC22×C4×C43C24
hypercenter#1864D43
hypocenterC43#20882
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#106×D43C2semidirect
5. #19137217C2semidirect
6. #19134866C2semidirect
7. #19134864C2semidirect
8. #19134862C2semidirect
9. #19134860C2semidirect
10. #19134858C2semidirect
11. #19134856C2semidirect
12. #19134854C2semidirect
13. #19134313C2semidirect
14. #19134290C2semidirect
15. C43×#1864C2semidirect
37. #14582892C4semidirect
84. C2×C8×D43C2×C4semidirect
94. #13063283C2×C4semidirect
127. #13063250C2×C4semidirect
129. #13063248C2×C4semidirect
131. #13063246C2×C4semidirect
149. #102×C43C2×C4semidirect
187. #10621900C4⋊C4semidirect
383. #1864D43semidirect
443. C43#20882semidirect
526. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
C2×#106×D432
C2×#145828972
C2×#145828922
#191372172
#191348662
#191348642
#191348622
#191348602
#191348582
#191348562
#191348542
#191343132
#191342902
C43×#18642
#2088243