Finite Group Databasebeta

← C2×#20255490 #27092938

Subgroups — C2×#20255490 #27092938

Order 12032.

2126 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×#15689807C211yesmaximal, characteristic, complemented
2C2×#15689775C211yesmaximal, characteristic
3#20255490C2116yesmaximal, direct product factor
4C2×#15689490C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689461C211yesmaximal, characteristic, complemented
7C2×#15689426C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689331C211yesmaximal, characteristic, complemented
10C2×#15689284C211yesmaximal, characteristic, complemented
11C2×#15689283C211yesmaximal, characteristic, complemented
12C2×#15689226C211yesmaximal, characteristic, complemented
13C2×#15689194C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689120C211yesmaximal, characteristic, complemented
16C2×C47×#467C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625350C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22#15689807—24no—
23#15689807C2218yescomplemented
24#15689775—24no—
25#15689775C2218yes—
26C2×#13094022C2211yescharacteristic
27C2×#13094017—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094009—21no—
31C2×#13094006—21no—
32C2×#13094006—21no—
33C2×#13094004C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×#13093997—21no—
36C2×Q8×Dic47C2211yescharacteristic
37C2×#13093986C2211yescharacteristic
38C2×C4×C22⋊D47C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093982—21no—
41C2×C4⋊C4×D47—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689490C2218yescomplemented
44#15689461C2218yescomplemented
45#15689460C2218yescomplemented
46#15689426C2218yescomplemented
47#15689380C2218yescomplemented
48#15689331C2218yescomplemented
49#15689284C2218yescomplemented
50#15689283C2218yescomplemented
51#15689226C2218yescomplemented
52#15689194C2218yescomplemented
53C2×#13093957C2211yescharacteristic
54C2×#13093955C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56#15689123C2218yescomplemented
57#15689120C2218yescomplemented
58C2×#13093949C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#467C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C2×#10625350—22no—
82C2×#10625350—24no—
83C2×#10625350—42no—
84C2×#10625350C2314yes—
85C22×Dic94C2311yescharacteristic
86C22×D188—21no—
87C22×D188C2311yescharacteristic
88C22×C22⋊D47—21no—
89C22×C22⋊D47D411yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C2×#10625337—42no—
96C2×#10625337C2314yes—
97C2×#10625336—24no—
98C2×#10625336C2314yes—
99C2×#10625324—42no—
100C2×#10625324C2314yes—
101C22×C47⋊C8C2311yescharacteristic
102C22×C47⋊C8C2311yescharacteristic
103#13094022—22no—
104#13094022C2314yes—
105#13094017—28no—
106#13094015—22no—
107#13094015C2314yes—
108#13094014—28no—
109#13094009—28no—
110#13094006—28no—
111#13094006—28no—
112#13094004—22no—
113#13094004C2314yes—
114#13094000—22no—
115#13094000C2314yes—
116#13093997—28no—
117Q8×Dic47—22no—
118Q8×Dic47C2314yes—
119#13093986—22no—
120#13093986C2314yes—
121C4×C22⋊D47D414yes—
122C4×C22⋊D47C2314yes—
123#13093983—22no—
124#13093983C2314yes—
125#13093982—28no—
126C2×C4⋊Dic47—21no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47—21no—
129C2×C4⋊Dic47C2311yescharacteristic
130C2×C4⋊Dic47C2311yescharacteristic
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4—21no—
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C4⋊C4×D47—22no—
138C4⋊C4×D47—28no—
139C4⋊C4×D47C2314yes—
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#13093957C2314yes—
150#13093955C2314yes—
151Dic47⋊C8C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157#13093946C2314yes—
158#13093946C2314yes—
159#13093944C2314yes—
160C22⋊(C47⋊C8)C2314yes—
161(C2×D47)⋊C8C2314yes—
162#13093934C2314yes—
163C22×Q8×C47C2311yescharacteristic
164C22×Q8×C47C2311yescharacteristic
165C23×C4×C47C2311yescharacteristic
166C2×Q16×C47—42no—
167C2×Q16×C47C2314yes—
168C22×C8×C47—42no—
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2314yes—
172C22⋊Q8×C47—22no—
173C22⋊Q8×C47—22no—
174C22⋊Q8×C47C2314yes—
175C22⋊Q8×C47C2314yes—
176C2×C4⋊C4×C47—21no—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47C2311yescharacteristic
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C22⋊C4×C47—21no—
181C2×C22⋊C4×C47—21no—
182#107×C47C2314yes—
183#103×C47C2314yes—
184#103×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C2412yes—
195C2×Q8×C47C2412yes—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2412yes—
205C22×C4×C47C2411yescharacteristic
206C2×C22⋊D47—24no—
207C2×C22⋊D47—42no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47C2×D414yes—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47C2×D411yescharacteristic
214C22×Dic47C2×D411yescharacteristic
215C22×Dic47C2×D411yescharacteristic
216#10625354—28no—
217#10625354—44no—
218#10625354—48no—
219#10625350—28no—
220#10625350—44no—
221#10625350—48no—
222C2×D188—21no—
223C2×D188—22no—
224C2×D188—24no—
225C2×D188—44no—
226C2×D188#4114yes—
227C2×D188C2412yes—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—24no—
231C2×C4×D47—24no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—44no—
235C2×C4×D47—44no—
236C2×C4×D47—44no—
237C2×C4×D47—44no—
238C2×C4×D47C2×D412yes—
239C2×C4×D47C2412yes—
240C2×Dic94—22no—
241C2×Dic94—22no—
242C2×Dic94—21no—
243C2×Dic94C2412yes—
244Q16×C47—44no—
245C2×C8×C47—22no—
246C2×C8×C47—22no—
247C2×C8×C47—44no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—24no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47—21no—
254C4⋊C4×C47C2412yes—
255C4⋊C4×C47C2412yes—
256C22⋊C4×C47—24no—
257C22⋊C4×C47—24no—
258C22⋊Dic47—24no—
259C22⋊Dic47C2×D414yes—
260#10625337—44no—
261#10625336—28no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4C2×D414yes—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—24no—
269C4⋊Dic47—24no—
270C4⋊Dic47—24no—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4C2×D414yes—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D412yes—
282C4×Dic47C2412yes—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—22no—
285C2×C47⋊C8C2412yes—
286C2×C47⋊C8C2412yes—
287#10625324—44no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47C22×D412yes—
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—24no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306Q8×C47—42no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—42no—
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—44no—
325C22⋊D47—48no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47C22×D412yes—
336C2×Dic47C22×D412yes—
337C2×Dic47C22×D412yes—
338D188—24no—
339D188—22no—
340D188—48no—
341D188C2×#4114yes—
342C4×D47—24no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—48no—
346C4×D47—48no—
347C4×D47—48no—
348C4×D47—48no—
349Dic94—22no—
350Dic94—22no—
351Dic94—42no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3315—471nomaximal, Sylow
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—44no—
361C22×C47#54612yes—
362C22×C47#57512yes—
363C22×C47#57812yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—22no—
366C2×D47—24no—
367C2×D47—22no—
368C2×D47—22no—
369C2×D47—44no—
370C2×D47—48no—
371C2×D47—42no—
372C2×D47—42no—
373C4×C47—22no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47#54612yes—
379C4×C47C22×#4111yescharacteristic
380C4×C47C2×H(5,𝔽2)11yescharacteristic
381Dic47—22no—
382Dic47—22no—
383Dic47—22no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#547—471no—
389#3315—4716no—
390C2×#491—471no—
391C2×#484—471no—
392C2×#485—471no—
393C2×#478—471no—
394C2×#470—471no—
395C2×#467D4711yescharacteristic, complemented
396C2×#462—471no—
397C2×#452—471no—
398C2×#452—471no—
399C2×#440—471no—
400C2×#435—471no—
401C2×#417—471no—
402C2×#416—471no—
403C2×C47—42no—
404C2×C47#331514yescomplemented
405C2×C47C2×#54611yescharacteristic
406C2×C47C2×#57511yescharacteristic
407C2×C47C2×#57811yescharacteristic
408D47—42no—
409D47—44no—
410C22×#41—471no—
411C22×#41—471no—
412C22×Q16—471no—
413C22×Q16C2×D4711yescharacteristic
414C22×SD16—471no—
415C22×M16—471no—
416C23×C8C2×D4711yescharacteristic
417#552—478no—
418#552—944no—
419#547—478no—
420#547—944no—
421C2×C4⋊Q8—471no—
422C2×#126—941no—
423C2×#125—471no—
424C2×#125—941no—
425C2×#123—941no—
426C2×#123—941no—
427C2×#123—941no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8C2×D4711yescharacteristic
431C2×C22⋊Q8C2×D4711yescharacteristic
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×#117—471no—
437C2×#117—941no—
438C22×C4⋊C4—471no—
439C22×C4⋊C4—941no—
440#491—478no—
441#485—478no—
442#484—478no—
443#478—478no—
444#470—478no—
445#467C2×D4718yescomplemented
446#462—478no—
447#452—478no—
448#452—478no—
449#440—478no—
450#435—478no—
451C2×#107—471no—
452C2×#107C2×D4711yescharacteristic
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#417—478no—
456#416—478no—
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×#102—471no—
466C2×#102—471no—
467C2×C22⋊C8—471no—
468C2×C22⋊C8—471no—
469C2×#97—471no—
470C47C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—474no—
472C2×#41—474no—
473C2×#41—944no—
474C2×#41—942no—
475C2×#41—942no—
476C2×#41—944no—
477C2×#41—1882no—
478C2×#41—1882no—
479C22×Q8—471no—
480C22×Q8C22×D4711yescharacteristic
481C22×Q8C22×D4711yescharacteristic
482C22×D4—471no—
483C22×D4—471no—
484C22×D4—941no—
485C22×D4—941no—
486C23×C4—471no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—42no—
493C2×Q16—474no—
494C2×Q16—1882no—
495C2×Q16C22×D4714yes—
496C2×SD16—474no—
497C2×SD16—944no—
498C2×M16—474no—
499C2×M16—1882no—
500C22×C8—42no—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4714yes—
506C4⋊Q8—474no—
507C4⋊Q8—942no—
508#126—948no—
509#125—474no—
510#125—942no—
511#125—948no—
512#123—948no—
513#123—948no—
514#123—948no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—474no—
518C22⋊Q8—474no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521C22⋊Q8C22×D4714yes—
522C22⋊Q8C22×D4714yes—
523#121—948no—
524C4×Q8—474no—
525C4×Q8—942no—
526C4×D4—474no—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—942no—
530#117—474no—
531#117—948no—
532#117—942no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—474no—
539C2×C4⋊C4—948no—
540C2×C4⋊C4—942no—
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⋊C4—941no—
548C2×C4⋊C4—941no—
549C2×C4⋊C4C22×D4711yescharacteristic
550C2×C4⋊C4C22×D4711yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—471no—
554C2×C22⋊C4—471no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C22⋊C4—941no—
559C2×C42—471no—
560C2×C42—941no—
561C2×C42—941no—
562#107—474no—
563#107C22×D4714yes—
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#102—474no—
575#102—474no—
576C22⋊C8—474no—
577C22⋊C8—474no—
578#97—474no—
579C24—471no—
580C24—941no—
581C24D4×D4711yescharacteristic
582#41—948no—
583#41—948no—
584#41—1884no—
585#41—1888no—
586#41—1884no—
587#41—1888no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—472no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8—942no—
598C2×Q8C23×D4712yes—
599C2×Q8C23×D4712yes—
600C2×D4—474no—
601C2×D4—474no—
602C2×D4—472no—
603C2×D4—944no—
604C2×D4—944no—
605C2×D4—941no—
606C2×D4—942no—
607C2×D4—1884no—
608C2×D4—1882no—
609C2×D4—1884no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—471no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—944no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—944no—
630C22×C4—1884no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4D4×D4712yes—
635C22×C4D4×D4711yescharacteristic
636C22×C4C23×D4712yes—
637C22×C4C23×D4711yescharacteristic
638Q16—44no—
639Q16—1884no—
640SD16—948no—
641M16—1884no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—44no—
645C2×C8—472no—
646C2×C8—472no—
647C2×C8—942no—
648C2×C8—942no—
649C2×C8C23×D4712yes—
650C2×C8C23×D4712yes—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—474no—
656C4⋊C4—472no—
657C4⋊C4—472no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—944no—
664C4⋊C4—944no—
665C4⋊C4—944no—
666C4⋊C4—941no—
667C4⋊C4—941no—
668C4⋊C4C23×D4712yes—
669C4⋊C4C23×D4712yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—474no—
673C22⋊C4—474no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C22⋊C4—944no—
678C42—472no—
679C42—472no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—472no—
686C23—942no—
687C23—944no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—1882no—
692C23—1882no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—942no—
702Q8—942no—
703Q8—1882no—
704D4—474no—
705D4—944no—
706D4—942no—
707D4—1888no—
708D4—1884no—
709D4—1888no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—472no—
723C2×C4—472no—
724C2×C4—472no—
725C2×C4—942no—
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—1888no—
735C2×C4—1888no—
736C2×C4—1888no—
737C2×C4—1888no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4#41×D4712yes—
744C2×C4#1309406912yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—942no—
755C22—944no—
756C22—942no—
757C22—942no—
758C22—1884no—
759C22—1888no—
760C22—1882no—
761C22—1882no—
762C22#1568976212yes—
763C22#1568992012yes—
764C22#1568993612yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—942no—
772C4—942no—
773C4—942no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976212yes—
778C4C2×#41×D4711yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—1882no—
782C2—1884no—
783C2#2025549014yesdirect product factor
784C2C2×#1568976211yescharacteristic
785C2C2×#1568992011yescharacteristic
786C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#467C2
socleC23×C47C22×D4
prime radicalC2×#15689775C2
hypercenterC2×#467D47
hypocenterC47C2×#3315
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#15689807C2semidirect
3. #20255490C2direct (N × H)
4. C2×#15689490C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689461C2semidirect
7. C2×#15689426C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689331C2semidirect
10. C2×#15689284C2semidirect
11. C2×#15689283C2semidirect
12. C2×#15689226C2semidirect
13. C2×#15689194C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689120C2semidirect
16. C2×C47×#467C2semidirect
23. #15689807C22semidirect
43. #15689490C22semidirect
44. #15689461C22semidirect
45. #15689460C22semidirect
46. #15689426C22semidirect
47. #15689380C22semidirect
48. #15689331C22semidirect
49. #15689284C22semidirect
50. #15689283C22semidirect
51. #15689226C22semidirect
52. #15689194C22semidirect
56. #15689123C22semidirect
57. #15689120C22semidirect
73. C47×#467C22semidirect
395. C2×#467D47semidirect
404. C2×C47#3315semidirect
445. #467C2×D47semidirect
470. C47C2×#3315semidirect
783. C2#20255490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898072
C2×#156897752
#202554902
C2×#156894902
C2×#156894602
C2×#156894612
C2×#156894262
C2×#156893802
C2×#156893312
C2×#156892842
C2×#156892832
C2×#156892262
C2×#156891942
C2×#156891232
C2×#156891202
C2×C47×#4672
C2×#331547