Finite Group Databasebeta

← C2×#20255301 #27092713

Subgroups — C2×#20255301 #27092713

Order 12032.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689841C211yesmaximal, characteristic, complemented
2C2×#15689772C211yesmaximal, characteristic
3#20255301C2116yesmaximal, direct product factor
4C2×#15689472C211yesmaximal, characteristic, complemented
5C2×#15689464C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689401C211yesmaximal, characteristic, complemented
8C2×#15689364C211yesmaximal, characteristic, complemented
9C2×#15689363C211yesmaximal, characteristic, complemented
10C2×#15689332C211yesmaximal, characteristic, complemented
11C2×#15689286C211yesmaximal, characteristic, complemented
12C2×#15689285C211yesmaximal, characteristic, complemented
13C2×#15689214C211yesmaximal, characteristic, complemented
14C2×C8×C22⋊D47C211yesmaximal, characteristic, complemented
15C2×#15689116C211yesmaximal, characteristic, complemented
16C2×C47×#416C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×C8×D47C2211yescharacteristic
22#15689841—24no—
23#15689841C2218yescomplemented
24#15689772—24no—
25#15689772C2218yes—
26C2×#13094023C2211yescharacteristic
27C2×#13094022C2211yescharacteristic
28C2×#13094018—21no—
29C2×#13094017—21no—
30C2×#13094010—21no—
31C2×#13094007—21no—
32C2×#13094005—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094003C2211yescharacteristic
35C2×#13094003C2211yescharacteristic
36C2×#13094000C2211yescharacteristic
37C2×#13093996—21no—
38C2×C4×Dic94—21no—
39C2×#13093989C2211yescharacteristic
40C2×D4×Dic47C2211yescharacteristic
41C2×C4×C22⋊D47C2211yescharacteristic
42C2×#13093982C2211yescharacteristic
43C22×Dic47⋊C4—21no—
44#15689472C2218yescomplemented
45#15689464C2218yescomplemented
46#15689463C2218yescomplemented
47#15689401C2218yescomplemented
48#15689364C2218yescomplemented
49#15689363C2218yescomplemented
50#15689332C2218yescomplemented
51#15689286C2218yescomplemented
52#15689285C2218yescomplemented
53#15689214C2218yescomplemented
54C8×C22⋊D47C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59#15689116C2218yescomplemented
60C2×#13093949C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×#41×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×#117×C47C2211yescharacteristic
72C47×#416C2218yescomplemented
73C2×#103×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—42no—
80C2×#10625352C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×C22⋊D47—21no—
85C22×C22⋊D47D411yescharacteristic
86C23×Dic47—21no—
87C23×Dic47—21no—
88C22×C4×D47C2311yescharacteristic
89C2×Dic188—42no—
90C2×Dic188C2314yes—
91C2×#10625337—42no—
92C2×#10625337C2314yes—
93C2×#10625335—24no—
94C2×#10625335C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C2×C8×D47—42no—
98C2×C8×D47C2314yes—
99#13094023—22no—
100#13094023C2314yes—
101#13094022—22no—
102#13094022C2314yes—
103#13094018—28no—
104#13094017—28no—
105#13094010—28no—
106#13094007—28no—
107#13094005—28no—
108#13094004—22no—
109#13094004C2314yes—
110#13094003—22no—
111#13094003—22no—
112#13094003C2314yes—
113#13094003C2314yes—
114#13094000—22no—
115#13094000C2314yes—
116#13093996—28no—
117C4×Dic94—28no—
118#13093989—22no—
119#13093989C2314yes—
120D4×Dic47—22no—
121D4×Dic47C2314yes—
122C4×C22⋊D47D414yes—
123C4×C22⋊D47C2314yes—
124#13093982—22no—
125#13093982C2314yes—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47C2311yescharacteristic
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—28no—
137C2×Dic47⋊C4D411yescharacteristic
138C2×C22⋊Dic47—21no—
139C2×C22⋊Dic47—21no—
140C2×C22⋊Dic47—21no—
141C2×C22⋊Dic47D411yescharacteristic
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4D411yescharacteristic
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47C2311yescharacteristic
149#13093958C2314yes—
150#13093957C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093947C2314yes—
158#13093945C2314yes—
159C22⋊(C47⋊C8)C2314yes—
160(C2×D47)⋊C8C2314yes—
161C8×Dic47C2314yes—
162C2×#41×C47—22no—
163C2×#41×C47—24no—
164C2×#41×C47—42no—
165C2×#41×C47C2314yes—
166C22×Q8×C47C2311yescharacteristic
167C22×D4×C47—21no—
168C22×D4×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C22×C8×C47—42no—
172C22×C8×C47C2311yescharacteristic
173C22×C8×C47C2311yescharacteristic
174C22×C8×C47C2314yes—
175#117×C47—22no—
176#117×C47C2314yes—
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C22⋊C4×C47—21no—
180C2×C42×C47—21no—
181#103×C47C2314yes—
182#103×C47C2314yes—
183#102×C47C2314yes—
184#102×C47C2314yes—
185C24×C47—21no—
186C24×C47C2×D411yescharacteristic
187C23×D47C2×D411yescharacteristic
188#41×C47—28no—
189#41×C47—44no—
190#41×C47—48no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C2412yes—
195C2×D4×C47—24no—
196C2×D4×C47—21no—
197C2×D4×C47—22no—
198C2×D4×C47—44no—
199C2×D4×C47#4114yes—
200C2×D4×C47C2412yes—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—24no—
207C22×C4×C47—44no—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2411yescharacteristic
212C2×C22⋊D47—24no—
213C2×C22⋊D47—24no—
214C2×C22⋊D47—44no—
215C2×C22⋊D47C2×D414yes—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—24no—
221C22×Dic47—24no—
222C22×Dic47—44no—
223C22×Dic47—44no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227#10625352—28no—
228#10625352—44no—
229#10625352—48no—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2412yes—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94—22no—
237C2×Dic94—22no—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—24no—
241C2×Dic94—44no—
242C2×Dic94C2412yes—
243C2×Dic94C2412yes—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47—44no—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C4⋊C4×C47—21no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47C2412yes—
252C4⋊C4×C47C2412yes—
253C22⋊C4×C47—24no—
254C42×C47—24no—
255C22⋊Dic47—24no—
256C22⋊Dic47—24no—
257C22⋊Dic47—24no—
258C22⋊Dic47C2×D414yes—
259#10625337—44no—
260#10625335—28no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4C2×D414yes—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—24no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4C2×D414yes—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47C2×D412yes—
281C4×Dic47C2412yes—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286Dic188—44no—
287C8×D47—44no—
288C23×C47—24no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—42no—
294C23×C47—42no—
295C23×C47C22×D412yes—
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—42no—
304D4×C47—24no—
305D4×C47—22no—
306D4×C47—48no—
307D4×C47C2×#4114yes—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—48no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47C22×D412yes—
320C2×C4×C47C22×D411yescharacteristic
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47C2511yescharacteristic
324C22⋊D47—28no—
325C22⋊D47—48no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—48no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—48no—
338C2×Dic47#13514yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—22no—
345Dic94—22no—
346Dic94—22no—
347Dic94—22no—
348Dic94—22no—
349Dic94—42no—
350Dic94—42no—
351Dic94—48no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3302—471nomaximal, Sylow
357C22×C47—24no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—44no—
362C22×C47—48no—
363C22×C47—42no—
364C22×C47—42no—
365C22×C47#54612yes—
366C22×C47C2×#13512yes—
367C22×C47#57812yes—
368C22×C47C23×D411yescharacteristic
369C2×D47—22no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47#54612yes—
378C4×C47C22×#4111yescharacteristic
379C4×C47C2×H(5,𝔽2)11yescharacteristic
380Dic47—22no—
381Dic47—22no—
382Dic47—42no—
383Dic47—42no—
384Dic47—42no—
385Dic47—42no—
386Dic47C2×#13514yes—
387C2×#556—471no—
388C2×#547—471no—
389#3302—4716no—
390C2×#487—471no—
391C2×#485—471no—
392C2×#485—471no—
393C2×#474—471no—
394C2×#467—471no—
395C2×#467—471no—
396C2×#462—471no—
397C2×#452—471no—
398C2×#452—471no—
399C2×C4×SD16—471no—
400C2×C8×D4—471no—
401C2×#416—471no—
402C2×#416D4711yescharacteristic, complemented
403C2×C47—42no—
404C2×C47—44no—
405C2×C47#330214yescomplemented
406C2×C47C2×#54611yescharacteristic
407C2×C47C22×#13511yescharacteristic
408C2×C47C2×#57811yescharacteristic
409D47—42no—
410C22×#41—471no—
411C22×#41C2×D4711yescharacteristic
412C22×Q16—471no—
413C22×Q16—471no—
414C22×SD16—471no—
415C23×C8—471no—
416C23×C8C2×D4711yescharacteristic
417#556—478no—
418#556—944no—
419#547—478no—
420#547—944no—
421C2×C4⋊Q8—471no—
422C2×C4⋊Q8—471no—
423C2×#126—941no—
424C2×#126—941no—
425C2×#124—941no—
426C2×#123—941no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—471no—
431C2×C22⋊Q8—471no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×Q8—941no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×#117—471no—
438C2×#117C2×D4711yescharacteristic
439C22×C4⋊C4—941no—
440#487—478no—
441#485—478no—
442#485—478no—
443#474—478no—
444#467—478no—
445#467—478no—
446#462—478no—
447#452—478no—
448#452—478no—
449C4×SD16—478no—
450C8×D4—478no—
451C2×#107—471no—
452C2×#107—471no—
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#416—478no—
456#416C2×D4718yescomplemented
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#103—471no—
461C2×#103—471no—
462C2×#103C2×D4711yescharacteristic
463C2×#103C2×D4711yescharacteristic
464C2×#102—471no—
465C2×#102C2×D4711yescharacteristic
466C2×#102C2×D4711yescharacteristic
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×C4×C8—471no—
470C47C2×#330211yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41—474no—
475C2×#41—942no—
476C2×#41—944no—
477C2×#41—1882no—
478C2×#41C22×D4714yes—
479C22×Q8—471no—
480C22×Q8—471no—
481C22×Q8—941no—
482C22×Q8C22×D4711yescharacteristic
483C22×D4—21no—
484C22×D4—471no—
485C22×D4—941no—
486C22×D4C22×D4711yescharacteristic
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—474no—
493C2×Q16—474no—
494C2×Q16—1882no—
495C2×Q16—1882no—
496C2×SD16—474no—
497C2×SD16—944no—
498C22×C8—42no—
499C22×C8—471no—
500C22×C8—471no—
501C22×C8—474no—
502C22×C8—1882no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4714yes—
506C4⋊Q8—474no—
507C4⋊Q8—474no—
508C4⋊Q8—942no—
509C4⋊Q8—942no—
510#126—948no—
511#126—948no—
512#124—948no—
513#123—948no—
514#123—948no—
515C22⋊Q8—474no—
516C22⋊Q8—474no—
517C22⋊Q8—474no—
518C22⋊Q8—474no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521C22⋊Q8—942no—
522C22⋊Q8—942no—
523#121—948no—
524C4×Q8—474no—
525C4×Q8—948no—
526C4×Q8—942no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—942no—
531#117—22no—
532#117—474no—
533#117—942no—
534#117C22×D4714yes—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—948no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4—941no—
544C2×C4⋊C4—941no—
545C2×C4⋊C4—941no—
546C2×C4⋊C4—941no—
547C2×C4⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4—471no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—21no—
559C2×C42—471no—
560C2×C42—941no—
561C2×C42—941no—
562#107—474no—
563#107—474no—
564#106—474no—
565C4⋊C8—474no—
566#103—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102C22×D4714yes—
575#102C22×D4714yes—
576C22⋊C8—474no—
577C22⋊C8—474no—
578C4×C8—474no—
579C24—21no—
580C24—471no—
581C24D4×D4711yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585#41—948no—
586#41—1884no—
587#41—1888no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—472no—
592C2×Q8—472no—
593C2×Q8—944no—
594C2×Q8—941no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8—942no—
599C2×Q8—942no—
600C2×Q8—1884no—
601C2×Q8C23×D4712yes—
602C2×D4—24no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—44no—
606C2×D4—474no—
607C2×D4—944no—
608C2×D4—944no—
609C2×D4—1884no—
610C2×D4#1062535014yes—
611C2×D4C23×D4712yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—44no—
619C22×C4—471no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—472no—
623C22×C4—472no—
624C22×C4—944no—
625C22×C4—944no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—1884no—
639Q16—1884no—
640SD16—948no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—44no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—1884no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—474no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—941no—
665C4⋊C4—941no—
666C4⋊C4C23×D4712yes—
667C4⋊C4C23×D4712yes—
668C22⋊C4—24no—
669C22⋊C4—474no—
670C22⋊C4—474no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C42—24no—
678C42—472no—
679C42—472no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—472no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—942no—
699Q8—942no—
700Q8—942no—
701Q8—942no—
702Q8—1888no—
703Q8—1882no—
704Q8—1882no—
705D4—24no—
706D4—22no—
707D4—48no—
708D4—948no—
709D4—1888no—
710D4C2×#1062535014yes—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—474no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—944no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—1888no—
736C2×C4—1888no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4C2×#1062535012yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—42no—
755C22—44no—
756C22—48no—
757C22—42no—
758C22—942no—
759C22—942no—
760C22—942no—
761C22—1884no—
762C22#1568976312yes—
763C22#135×D4712yes—
764C22#1568993712yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—474no—
771C4—942no—
772C4—942no—
773C4—1882no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976312yes—
778C4C22×#1062535011yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—44no—
782C2—1882no—
783C2#2025530114yesdirect product factor
784C2C2×#1568976311yescharacteristic
785C2C2×#135×D4711yescharacteristic
786C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#416C2
socleC23×C47C22×D4
prime radicalC2×#15689772C2
hypercenterC2×#416D47
hypocenterC47C2×#3302
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#15689841C2semidirect
3. #20255301C2direct (N × H)
4. C2×#15689472C2semidirect
5. C2×#15689464C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689401C2semidirect
8. C2×#15689364C2semidirect
9. C2×#15689363C2semidirect
10. C2×#15689332C2semidirect
11. C2×#15689286C2semidirect
12. C2×#15689285C2semidirect
13. C2×#15689214C2semidirect
14. C2×C8×C22⋊D47C2semidirect
15. C2×#15689116C2semidirect
16. C2×C47×#416C2semidirect
23. #15689841C22semidirect
44. #15689472C22semidirect
45. #15689464C22semidirect
46. #15689463C22semidirect
47. #15689401C22semidirect
48. #15689364C22semidirect
49. #15689363C22semidirect
50. #15689332C22semidirect
51. #15689286C22semidirect
52. #15689285C22semidirect
53. #15689214C22semidirect
54. C8×C22⋊D47C22semidirect
59. #15689116C22semidirect
72. C47×#416C22semidirect
402. C2×#416D47semidirect
405. C2×C47#3302semidirect
456. #416C2×D47semidirect
470. C47C2×#3302semidirect
783. C2#20255301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898412
C2×#156897722
#202553012
C2×#156894722
C2×#156894642
C2×#156894632
C2×#156894012
C2×#156893642
C2×#156893632
C2×#156893322
C2×#156892862
C2×#156892852
C2×#156892142
C2×C8×C22⋊D472
C2×#156891162
C2×C47×#4162
C2×#330247