Finite Group Databasebeta

← C2×#20255661 #27093152

Subgroups — C2×#20255661 #27093152

Order 12032.

2114 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×#15689814C211yesmaximal, characteristic, complemented
2C2×#15689785C211yesmaximal, characteristic
3#20255661C2116yesmaximal, direct product factor
4C2×#15689478C211yesmaximal, characteristic, complemented
5C2×#15689460C211yesmaximal, characteristic, complemented
6C2×#15689450C211yesmaximal, characteristic, complemented
7C2×#15689430C211yesmaximal, characteristic, complemented
8C2×#15689380C211yesmaximal, characteristic, complemented
9C2×#15689372C211yesmaximal, characteristic, complemented
10C2×#15689345C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×#15689277C211yesmaximal, characteristic, complemented
13C2×#15689202C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689130C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C22×#10625337C2211yescharacteristic
20C22×#10625336C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×#10625324C2211yescharacteristic
23#15689814—24no—
24#15689814C2218yescomplemented
25#15689785—24no—
26#15689785C2218yes—
27C2×#13094018—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094014—21no—
30C2×#13094012—21no—
31C2×#13094012C2211yescharacteristic
32C2×#13094009—21no—
33C2×#13094004—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094000C2211yescharacteristic
36C2×#13094000C2211yescharacteristic
37C2×#13093999—21no—
38C2×#13093999C2211yescharacteristic
39C2×C4×D188—21no—
40C2×C4×D188C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×#13093981—21no—
43C2×C4⋊C4×D47C2211yescharacteristic
44#15689478C2218yescomplemented
45#15689460C2218yescomplemented
46#15689450C2218yescomplemented
47#15689430C2218yescomplemented
48#15689380C2218yescomplemented
49#15689372C2218yescomplemented
50#15689345C2218yescomplemented
51#15689284C2218yescomplemented
52#15689277C2218yescomplemented
53#15689202C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57#15689130C2218yescomplemented
58#15689123C2218yescomplemented
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C4×Q16×C47C2218yescomplemented
73C2×#107×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C22×Dic94—21no—
82C22×Dic94C2311yescharacteristic
83C2×Q8×D47—22no—
84C2×Q8×D47—24no—
85C2×Q8×D47—42no—
86C2×Q8×D47C2314yes—
87C22×D188—21no—
88C22×D188—21no—
89C22×D188D411yescharacteristic
90C22×D188C2311yescharacteristic
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47C2311yescharacteristic
95C22×C4×D47C2311yescharacteristic
96C2×#10625337—42no—
97C2×#10625337C2314yes—
98C2×#10625336—42no—
99C2×#10625336C2314yes—
100C2×#10625324—42no—
101C2×#10625324—42no—
102C2×#10625324C2314yes—
103C2×#10625324C2314yes—
104C22×C47⋊C8C2311yescharacteristic
105C22×C47⋊C8C2311yescharacteristic
106#13094018—28no—
107#13094016—22no—
108#13094016C2314yes—
109#13094014—28no—
110#13094012—22no—
111#13094012—28no—
112#13094012C2314yes—
113#13094009—28no—
114#13094004—22no—
115#13094004—28no—
116#13094004C2314yes—
117#13094000—22no—
118#13094000—22no—
119#13094000C2314yes—
120#13094000C2314yes—
121#13093999—28no—
122#13093999—22no—
123#13093999C2314yes—
124C4×D188—28no—
125C4×D188D414yes—
126C4×D188C2314yes—
127#13093982—22no—
128#13093982C2314yes—
129#13093981—28no—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47D411yescharacteristic
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C2×Dic47⋊C4—21no—
138C2×Dic47⋊C4—21no—
139C4⋊C4×D47—22no—
140C4⋊C4×D47C2314yes—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×(C2×D47)⋊C4—21no—
144C2×(C2×D47)⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×(C2×D47)⋊C4D411yescharacteristic
150C2×C4×Dic47—21no—
151#13093957C2314yes—
152#13093955C2314yes—
153C4⋊(C47⋊C8)C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093947C2314yes—
159#13093946C2314yes—
160#13093946C2314yes—
161#13093944C2314yes—
162(C2×D47)⋊C8C2314yes—
163(C2×D47)⋊C8C2314yes—
164C22×Q8×C47C2311yescharacteristic
165C22×Q8×C47C2311yescharacteristic
166C2×Q16×C47—24no—
167C2×Q16×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C4×Q8×C47—22no—
171C4×Q8×C47—22no—
172C4×Q8×C47C2314yes—
173C4×Q8×C47C2314yes—
174C2×C4⋊C4×C47—21no—
175C2×C4⋊C4×C47—21no—
176C2×C4⋊C4×C47C2311yescharacteristic
177C2×C4⋊C4×C47C2311yescharacteristic
178C2×C42×C47—21no—
179C2×C42×C47—21no—
180C2×C42×C47C2311yescharacteristic
181#107×C47C2314yes—
182#103×C47C2314yes—
183#103×C47C2314yes—
184C4×C8×C47C2314yes—
185C23×D47—21no—
186C23×D47C2×D411yescharacteristic
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#4114yes—
194C2×Q8×C47C2412yes—
195C2×Q8×C47C2412yes—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208#10625354—28no—
209#10625354—44no—
210#10625354—48no—
211Q8×D47—28no—
212Q8×D47—44no—
213Q8×D47—48no—
214C2×D188—22no—
215C2×D188—22no—
216C2×D188—24no—
217C2×D188—24no—
218C2×D188—21no—
219C2×D188—42no—
220C2×D188—44no—
221C2×D188—44no—
222C2×D188C2×D414yes—
223C2×D188C2412yes—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47C2×D412yes—
235C2×C4×D47C2×D412yes—
236C2×C4×D47C2412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—22no—
239C2×Dic94—22no—
240C2×Dic94—21no—
241C2×Dic94—24no—
242C2×Dic94—44no—
243C2×Dic94C2412yes—
244Q16×C47—28no—
245C2×C8×C47—22no—
246C2×C8×C47—22no—
247C2×C8×C47C2412yes—
248C2×C8×C47C2412yes—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—21no—
253C4⋊C4×C47C2412yes—
254C4⋊C4×C47C2412yes—
255C42×C47—24no—
256C42×C47—24no—
257C42×C47C2×D412yes—
258C42×C47C2412yes—
259#10625337—44no—
260#10625336—44no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267(C2×D47)⋊C4—24no—
268(C2×D47)⋊C4C2×D414yes—
269(C2×D47)⋊C4C2×D414yes—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—24no—
273C4⋊Dic47C2×D414yes—
274C4⋊Dic47C2412yes—
275C4⋊Dic47C2412yes—
276Dic47⋊C4—24no—
277Dic47⋊C4—24no—
278Dic47⋊C4—24no—
279Dic47⋊C4—24no—
280Dic47⋊C4—24no—
281C4×Dic47—24no—
282C2×C47⋊C8—22no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8C2412yes—
285C2×C47⋊C8C2412yes—
286#10625324—44no—
287#10625324—44no—
288C23×C47C22×D411yescharacteristic
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47C22×D412yes—
300C22×D47C22×D412yes—
301Q8×C47—24no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—42no—
306Q8×C47C2×#4114yes—
307C2×C4×C47—24no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4112yes—
321C2×C4×C47H(5,𝔽2)12yes—
322C2×C4×C47C2511yescharacteristic
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47C22×D412yes—
332C2×Dic47C22×D412yes—
333D188—22no—
334D188—22no—
335D188—44no—
336D188—48no—
337D188—48no—
338D188—42no—
339C4×D47—24no—
340C4×D47—24no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—22no—
345C4×D47—48no—
346C4×D47—48no—
347C4×D47—48no—
348Dic94—22no—
349Dic94—22no—
350Dic94—48no—
351Dic94—42no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3327—471nomaximal, Sylow
357C22×C47#54612yes—
358C22×C47#57512yes—
359C22×C47#57812yes—
360C22×C47C23×D411yescharacteristic
361C2×D47—22no—
362C2×D47—22no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—22no—
366C2×D47—22no—
367C2×D47—44no—
368C2×D47—44no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—84no—
373C4×C47—24no—
374C4×C47—22no—
375C4×C47—22no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47#54612yes—
380C4×C47C22×#4111yescharacteristic
381C4×C47C2×H(5,𝔽2)11yescharacteristic
382Dic47—22no—
383Dic47—22no—
384Dic47—42no—
385Dic47—42no—
386Dic47—42no—
387C2×#552—471no—
388C2×#548—471no—
389#3327—4716no—
390C2×#488—471no—
391C2×#484—471no—
392C2×#482—471no—
393C2×#479—471no—
394C2×#470—471no—
395C2×#468—471no—
396C2×#464—471no—
397C2×#452—471no—
398C2×#451—471no—
399C2×C4×Q16D4711yescharacteristic, complemented
400C2×#436—471no—
401C2×#417—471no—
402C2×#419—471no—
403C2×C47#332714yescomplemented
404C2×C47C2×#54611yescharacteristic
405C2×C47C2×#57511yescharacteristic
406C2×C47C2×#57811yescharacteristic
407D47—42no—
408D47—42no—
409D47—82no—
410C22×#41—471no—
411C23×Q8—471no—
412C22×Q16—471no—
413C22×Q16C2×D4711yescharacteristic
414C22×SD16—471no—
415C22×M16—471no—
416C22×M16—471no—
417#552—478no—
418#552—944no—
419#548—478no—
420#548—944no—
421C2×#126—941no—
422C2×#125—471no—
423C2×#125—941no—
424C2×#124—471no—
425C2×#124—941no—
426C2×#123—941no—
427C2×C22⋊Q8—471no—
428C2×C22⋊Q8—471no—
429C2×C22⋊Q8—471no—
430C2×C22⋊Q8—941no—
431C2×#121—471no—
432C2×#121—941no—
433C2×C4×Q8C2×D4711yescharacteristic
434C2×C4×Q8C2×D4711yescharacteristic
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×#117—471no—
438C2×#117—941no—
439C22×C4⋊C4—471no—
440#488—478no—
441#484—478no—
442#482—478no—
443#479—478no—
444#470—478no—
445#468—478no—
446#464—478no—
447#452—478no—
448#451—478no—
449C4×Q16C2×D4718yescomplemented
450#436—478no—
451C2×#107—471no—
452C2×#107C2×D4711yescharacteristic
453C2×#106—471no—
454C2×C4⋊C8—471no—
455#419—478no—
456#417—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×C4×C8C2×D4711yescharacteristic
470C47C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—474no—
472C2×#41—942no—
473C2×#41—944no—
474C2×#41—1882no—
475C22×Q8—474no—
476C22×Q8—471no—
477C22×Q8—941no—
478C22×Q8—942no—
479C22×Q8—944no—
480C22×Q8—1882no—
481C22×Q8C22×D4711yescharacteristic
482C22×Q8C22×D4711yescharacteristic
483C22×D4—471no—
484C22×D4—471no—
485C22×D4—941no—
486C22×D4—941no—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C2×Q16—24no—
493C2×Q16—474no—
494C2×Q16—1882no—
495C2×Q16C22×D4714yes—
496C2×SD16—474no—
497C2×SD16—1882no—
498C2×M16—474no—
499C2×M16—474no—
500C2×M16—1882no—
501C2×M16—1882no—
502C22×C8—471no—
503C22×C8—471no—
504C22×C8C22×D4711yescharacteristic
505C22×C8C22×D4711yescharacteristic
506#126—948no—
507#125—474no—
508#125—948no—
509#125—942no—
510#124—474no—
511#124—948no—
512#124—942no—
513#123—948no—
514C22⋊Q8—474no—
515C22⋊Q8—474no—
516C22⋊Q8—474no—
517C22⋊Q8—948no—
518C22⋊Q8—942no—
519C22⋊Q8—942no—
520C22⋊Q8—942no—
521#121—474no—
522#121—942no—
523#121—948no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8C22×D4714yes—
527C4×Q8C22×D4714yes—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—948no—
531#117—474no—
532#117—948no—
533#117—942no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—474no—
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⋊C4C22×D4711yescharacteristic
548C2×C4⋊C4C22×D4711yescharacteristic
549C2×C22⋊C4—471no—
550C2×C22⋊C4—471no—
551C2×C22⋊C4—941no—
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—21no—
560C2×C42—941no—
561C2×C42C22×D4711yescharacteristic
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—
578C4×C8C22×D4714yes—
579C24—471no—
580C24—471no—
581C24—941no—
582#41—948no—
583#41—1884no—
584#41—1888no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—472no—
591C2×Q8—944no—
592C2×Q8—941no—
593C2×Q8—948no—
594C2×Q8—942no—
595C2×Q8—942no—
596C2×Q8—1884no—
597C2×Q8—1884no—
598C2×Q8—1888no—
599C2×Q8#1062535014yes—
600C2×Q8C23×D4712yes—
601C2×Q8C23×D4712yes—
602C2×D4—474no—
603C2×D4—472no—
604C2×D4—944no—
605C2×D4—944no—
606C2×D4—941no—
607C2×D4—942no—
608C2×D4—942no—
609C2×D4—1882no—
610C2×D4—1884no—
611C2×D4—1884no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—471no—
617C22×C4—471no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4—1884no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638Q16—28no—
639Q16—1884no—
640SD16—1884no—
641M16—1884no—
642M16—1884no—
643C2×C8—22no—
644C2×C8—22no—
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—941no—
665C4⋊C4—941no—
666C4⋊C4C23×D4712yes—
667C4⋊C4C23×D4712yes—
668C22⋊C4—474no—
669C22⋊C4—474no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C22⋊C4—944no—
676C22⋊C4—944no—
677C42—24no—
678C42—24no—
679C42—944no—
680C42D4×D4712yes—
681C42C23×D4712yes—
682C23—472no—
683C23—472no—
684C23—942no—
685C23—942no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—1882no—
692C23—1882no—
693C23—1882no—
694C23C2×D4×D4711yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—942no—
701Q8—942no—
702Q8—1888no—
703Q8—1882no—
704Q8C2×#1062535014yes—
705D4—942no—
706D4—942no—
707D4—1884no—
708D4—1888no—
709D4—1888no—
710D4—1882no—
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—472no—
722C2×C4—472no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—942no—
728C2×C4—942no—
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—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4C2×D4×D4712yes—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4C2×#1062535012yes—
744C2×C4#1309407012yes—
745C2×C4C24×D4711yescharacteristic
746C8—22no—
747C8—22no—
748C8—942no—
749C8—942no—
750C22—942no—
751C22—942no—
752C22—942no—
753C22—942no—
754C22—942no—
755C22—942no—
756C22—3764no—
757C22—1882no—
758C22—1882no—
759C22—1882no—
760C22—1884no—
761C22—1884no—
762C22#1568976912yes—
763C22#1568992012yes—
764C22#1568993612yes—
765C22C22×D4×D4711yescharacteristic
766C4—24no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—942no—
773C4—942no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976912yes—
778C4C22×#1062535011yescharacteristic
779C4C2×#1309407011yescharacteristic
780C2—3762no—
781C2—1882no—
782C2—1882no—
783C2#2025566114yesdirect product factor
784C2C2×#1568976911yescharacteristic
785C2C2×#1568992011yescharacteristic
786C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689785C2
hypercenterC2×C4×Q16D47
hypocenterC47C2×#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#15689814C2semidirect
3. #20255661C2direct (N × H)
4. C2×#15689478C2semidirect
5. C2×#15689460C2semidirect
6. C2×#15689450C2semidirect
7. C2×#15689430C2semidirect
8. C2×#15689380C2semidirect
9. C2×#15689372C2semidirect
10. C2×#15689345C2semidirect
11. C2×#15689284C2semidirect
12. C2×#15689277C2semidirect
13. C2×#15689202C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689130C2semidirect
16. C2×C4×Q16×C47C2semidirect
24. #15689814C22semidirect
44. #15689478C22semidirect
45. #15689460C22semidirect
46. #15689450C22semidirect
47. #15689430C22semidirect
48. #15689380C22semidirect
49. #15689372C22semidirect
50. #15689345C22semidirect
51. #15689284C22semidirect
52. #15689277C22semidirect
53. #15689202C22semidirect
57. #15689130C22semidirect
58. #15689123C22semidirect
72. C4×Q16×C47C22semidirect
399. C2×C4×Q16D47semidirect
403. C2×C47#3327semidirect
449. C4×Q16C2×D47semidirect
470. C47C2×#3327semidirect
783. C2#20255661direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898142
C2×#156897852
#202556612
C2×#156894782
C2×#156894602
C2×#156894502
C2×#156894302
C2×#156893802
C2×#156893722
C2×#156893452
C2×#156892842
C2×#156892772
C2×#156892022
C2×#156891232
C2×#156891302
C2×C4×Q16×C472
C2×#332747