Finite Group Databasebeta

← C2×#20255660 #27093151

Subgroups — C2×#20255660 #27093151

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×#15689807C211yesmaximal, characteristic, complemented
2C2×#15689784C211yesmaximal, characteristic
3#20255660C2116yesmaximal, direct product factor
4C2×#15689479C211yesmaximal, characteristic, complemented
5C2×#15689457C211yesmaximal, characteristic, complemented
6C2×#15689448C211yesmaximal, characteristic, complemented
7C2×#15689428C211yesmaximal, characteristic, complemented
8C2×#15689378C211yesmaximal, characteristic, complemented
9C2×#15689371C211yesmaximal, characteristic, complemented
10C2×#15689347C211yesmaximal, characteristic, complemented
11C2×#15689284C211yesmaximal, characteristic, complemented
12C2×Q16×Dic47C211yesmaximal, characteristic, complemented
13C2×#15689198C211yesmaximal, characteristic, complemented
14C2×#15689123C211yesmaximal, characteristic, complemented
15C2×#15689132C211yesmaximal, characteristic, complemented
16C2×C47×#451C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625329C2211yescharacteristic
20C22×#10625324C2211yescharacteristic
21#15689807—24no—
22#15689807C2218yescomplemented
23#15689784—24no—
24#15689784C2218yes—
25C2×#13094017—21no—
26C2×#13094015C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094013—21no—
29C2×#13094013C2211yescharacteristic
30C2×#13094006—21no—
31C2×#13094000—21no—
32C2×#13094000C2211yescharacteristic
33C2×#13094000C2211yescharacteristic
34C2×#13093998—21no—
35C2×#13093998C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×Q8×Dic47C2211yescharacteristic
38C2×C4×C22⋊D47—21no—
39C2×C4×C22⋊D47C2211yescharacteristic
40C2×#13093983C2211yescharacteristic
41C2×#13093982—21no—
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689479C2218yescomplemented
44#15689457C2218yescomplemented
45#15689448C2218yescomplemented
46#15689428C2218yescomplemented
47#15689378C2218yescomplemented
48#15689371C2218yescomplemented
49#15689347C2218yescomplemented
50#15689284C2218yescomplemented
51Q16×Dic47C2218yescomplemented
52#15689198C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57#15689132C2218yescomplemented
58#15689123C2218yescomplemented
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C23×Q8×C47C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C22×Q16×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#451C2218yescomplemented
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C2×#10625354—22no—
78C2×#10625354—24no—
79C2×#10625354—42no—
80C2×#10625354C2314yes—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×C22⋊D47—21no—
84C22×C22⋊D47D411yescharacteristic
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47C2311yescharacteristic
88C2×#10625336—42no—
89C2×#10625336C2314yes—
90C2×#10625329—42no—
91C2×#10625329C2314yes—
92C2×#10625324—42no—
93C2×#10625324C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96#13094017—28no—
97#13094015—22no—
98#13094015C2314yes—
99#13094014—28no—
100#13094013—28no—
101#13094013—22no—
102#13094013C2314yes—
103#13094006—28no—
104#13094000—22no—
105#13094000—22no—
106#13094000—28no—
107#13094000C2314yes—
108#13094000C2314yes—
109#13093998—22no—
110#13093998—28no—
111#13093998C2314yes—
112Q8×Dic47—22no—
113Q8×Dic47—22no—
114Q8×Dic47C2314yes—
115Q8×Dic47C2314yes—
116C4×C22⋊D47—28no—
117C4×C22⋊D47D414yes—
118C4×C22⋊D47C2314yes—
119#13093983—22no—
120#13093983C2314yes—
121#13093982—28no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4D411yescharacteristic
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47C2311yescharacteristic
147#13093958C2314yes—
148#13093957C2314yes—
149#13093956C2314yes—
150Dic47⋊C8C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154#13093948C2314yes—
155#13093948C2314yes—
156#13093946C2314yes—
157#13093946C2314yes—
158#13093944C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C22×Q8×C47—22no—
162C22×Q8×C47—21no—
163C22×Q8×C47—24no—
164C22×Q8×C47—42no—
165C22×Q8×C47C2311yescharacteristic
166C22×Q8×C47C2311yescharacteristic
167C22×Q8×C47C2314yes—
168C22×Q8×C47C2311yescharacteristic
169C23×C4×C47—21no—
170C23×C4×C47C2311yescharacteristic
171C2×Q16×C47—24no—
172C2×Q16×C47—42no—
173C2×Q16×C47C2314yes—
174C2×Q16×C47C2314yes—
175C22×C8×C47C2311yescharacteristic
176C22×C8×C47C2311yescharacteristic
177C22⋊Q8×C47—22no—
178C22⋊Q8×C47C2314yes—
179C2×C4⋊C4×C47—21no—
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C22⋊C4×C47—21no—
182#103×C47C2314yes—
183#103×C47C2314yes—
184C22⋊C8×C47C2314yes—
185C24×C47C2×D411yescharacteristic
186C23×D47—21no—
187C23×D47C2×D411yescharacteristic
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47—24no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—28no—
194C2×Q8×C47—22no—
195C2×Q8×C47—22no—
196C2×Q8×C47—22no—
197C2×Q8×C47—22no—
198C2×Q8×C47—44no—
199C2×Q8×C47—44no—
200C2×Q8×C47—48no—
201C2×Q8×C47#4114yes—
202C2×Q8×C47C2412yes—
203C2×Q8×C47C2412yes—
204C2×Q8×C47C2412yes—
205C22×C4×C47—21no—
206C22×C4×C47—22no—
207C22×C4×C47—22no—
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—24no—
212C22×C4×C47—44no—
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D412yes—
215C22×C4×C47C2412yes—
216C22×C4×C47C2411yescharacteristic
217C2×C22⋊D47—24no—
218C2×C22⋊D47—42no—
219C2×C22⋊D47—44no—
220C2×C22⋊D47C2×D414yes—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47C2×D411yescharacteristic
225C22×Dic47C2×D411yescharacteristic
226C22×Dic47C2×D411yescharacteristic
227#10625354—28no—
228#10625354—44no—
229#10625354—48no—
230C2×D188—22no—
231C2×D188—22no—
232C2×D188—24no—
233C2×D188—21no—
234C2×D188—44no—
235C2×D188C2412yes—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—24no—
239C2×C4×D47—24no—
240C2×C4×D47—44no—
241C2×C4×D47—44no—
242C2×C4×D47C2×D412yes—
243C2×C4×D47C2412yes—
244Q16×C47—28no—
245Q16×C47—44no—
246C2×C8×C47—22no—
247C2×C8×C47—22no—
248C2×C8×C47C2412yes—
249C2×C8×C47C2412yes—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47C2412yes—
253C22⋊C4×C47—24no—
254C22⋊Dic47—24no—
255C22⋊Dic47C2×D414yes—
256#10625336—44no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4C2×D414yes—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47—21no—
266C4⋊Dic47—24no—
267C4⋊Dic47—24no—
268C4⋊Dic47—24no—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276Dic47⋊C4C2×D414yes—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47C2×D412yes—
281C4×Dic47C2412yes—
282#10625329—44no—
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—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47C22×D412yes—
301Q8×C47—24no—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—22no—
307Q8×C47—48no—
308Q8×C47—42no—
309Q8×C47—42no—
310Q8×C47C2×#4114yes—
311C2×C4×C47—24no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—24no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—48no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47C22×D412yes—
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4112yes—
327C2×C4×C47H(5,𝔽2)12yes—
328C2×C4×C47C2511yescharacteristic
329C22⋊D47—44no—
330C22⋊D47—48no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342C2×Dic47C22×D412yes—
343D188—22no—
344D188—22no—
345D188—48no—
346D188—42no—
347C4×D47—24no—
348C4×D47—22no—
349C4×D47—22no—
350C4×D47—48no—
351C4×D47—48no—
352C8×C47—22no—
353C8×C47—22no—
354C47⋊C8—22no—
355C47⋊C8—22no—
356C2×#3327—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—22no—
367C2×D47—22no—
368C2×D47—44no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—84no—
373C4×C47—24no—
374C4×C47—22no—
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×#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×#451D4711yescharacteristic, complemented
399C2×C4×Q16—471no—
400C2×#436—471no—
401C2×#417—471no—
402C2×#419—471no—
403C2×C47—42no—
404C2×C47#332714yescomplemented
405C2×C47C2×#54611yescharacteristic
406C2×C47C2×#57511yescharacteristic
407C2×C47C2×#57811yescharacteristic
408D47—42no—
409D47—82no—
410C22×#41—471no—
411C23×Q8C2×D4711yescharacteristic
412C22×Q16C2×D4711yescharacteristic
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—941no—
430C2×C22⋊Q8C2×D4711yescharacteristic
431C2×#121—471no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×Q8—471no—
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#451C2×D4718yescomplemented
449C4×Q16—478no—
450#436—478no—
451C2×#107—471no—
452C2×#107—471no—
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⋊C8C2×D4711yescharacteristic
469C2×C4×C8—471no—
470C47C2×#332711yescharacteristic, complemented, Sylow
471C2×#41—474no—
472C2×#41—942no—
473C2×#41—944no—
474C2×#41—1882no—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8C22×D4711yescharacteristic
480C22×Q8C22×D4711yescharacteristic
481C22×Q8C22×D4714yes—
482C22×Q8C22×D4711yescharacteristic
483C22×D4—471no—
484C22×D4—471no—
485C22×D4—941no—
486C22×D4—941no—
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4C22×D4711yescharacteristic
492C2×Q16—24no—
493C2×Q16—42no—
494C2×Q16C22×D4714yes—
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—942no—
509#125—948no—
510#124—474no—
511#124—942no—
512#124—948no—
513#123—948no—
514C22⋊Q8—22no—
515C22⋊Q8—474no—
516C22⋊Q8—474no—
517C22⋊Q8—948no—
518C22⋊Q8—942no—
519C22⋊Q8—942no—
520C22⋊Q8C22×D4714yes—
521#121—474no—
522#121—948no—
523#121—942no—
524C4×Q8—474no—
525C4×Q8—474no—
526C4×Q8—942no—
527C4×Q8—942no—
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—471no—
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⋊C4—941no—
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—471no—
559C2×C42—941no—
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#102—474no—
575#102—474no—
576C22⋊C8—474no—
577C22⋊C8C22×D4714yes—
578C4×C8—474no—
579C24—471no—
580C24—941no—
581C24D4×D4711yescharacteristic
582#41—948no—
583#41—1884no—
584#41—1888no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—28no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—44no—
596C2×Q8—44no—
597C2×Q8—48no—
598C2×Q8#1062535214yes—
599C2×Q8C23×D4712yes—
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—1884no—
610C2×D4—1882no—
611C2×D4—1884no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—44no—
620C22×C4—471no—
621C22×C4—471no—
622C22×C4—471no—
623C22×C4—472no—
624C22×C4—472no—
625C22×C4—944no—
626C22×C4—944no—
627C22×C4—942no—
628C22×C4—942no—
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—28no—
639Q16—44no—
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—21no—
653C4⋊C4—474no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—472no—
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⋊C4—941no—
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—472no—
678C42—472no—
679C42—944no—
680C42—944no—
681C42—944no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—472no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—1882no—
691C23—1882no—
692C23—1882no—
693C23C2×D4×D4712yes—
694C23C2×D4×D4711yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—48no—
702Q8—42no—
703Q8—42no—
704Q8C2×#1062535214yes—
705D4—942no—
706D4—942no—
707D4—1888no—
708D4—1884no—
709D4—1888no—
710D4—1882no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—472no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—944no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—1888no—
737C2×C4—1888no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1882no—
741C2×C4C2×D4×D4712yes—
742C2×C4C2×D4×D4711yescharacteristic
743C2×C4C2×#1062535212yes—
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—942no—
756C22—942no—
757C22—3764no—
758C22—1882no—
759C22—1882no—
760C22—1882no—
761C22—1884no—
762C22#1568976012yes—
763C22#1568992212yes—
764C22#1568993612yes—
765C22C22×D4×D4711yescharacteristic
766C4—22no—
767C4—24no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—942no—
772C4—942no—
773C4—942no—
774C4—1882no—
775C4—1882no—
776C4—1882no—
777C4#1568976012yes—
778C4C22×#1062535211yescharacteristic
779C4C2×#1309406911yescharacteristic
780C2—42no—
781C2—3762no—
782C2—1882no—
783C2#2025566014yesdirect product factor
784C2C2×#1568976011yescharacteristic
785C2C2×#1568992211yescharacteristic
786C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC2×#15689784C2
hypercenterC2×#451D47
hypocenterC47C2×#3327
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#15689807C2semidirect
3. #20255660C2direct (N × H)
4. C2×#15689479C2semidirect
5. C2×#15689457C2semidirect
6. C2×#15689448C2semidirect
7. C2×#15689428C2semidirect
8. C2×#15689378C2semidirect
9. C2×#15689371C2semidirect
10. C2×#15689347C2semidirect
11. C2×#15689284C2semidirect
12. C2×Q16×Dic47C2semidirect
13. C2×#15689198C2semidirect
14. C2×#15689123C2semidirect
15. C2×#15689132C2semidirect
16. C2×C47×#451C2semidirect
22. #15689807C22semidirect
43. #15689479C22semidirect
44. #15689457C22semidirect
45. #15689448C22semidirect
46. #15689428C22semidirect
47. #15689378C22semidirect
48. #15689371C22semidirect
49. #15689347C22semidirect
50. #15689284C22semidirect
51. Q16×Dic47C22semidirect
52. #15689198C22semidirect
57. #15689132C22semidirect
58. #15689123C22semidirect
73. C47×#451C22semidirect
398. C2×#451D47semidirect
404. C2×C47#3327semidirect
448. #451C2×D47semidirect
470. C47C2×#3327semidirect
783. C2#20255660direct (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×#156897842
#202556602
C2×#156894792
C2×#156894572
C2×#156894482
C2×#156894282
C2×#156893782
C2×#156893712
C2×#156893472
C2×#156892842
C2×Q16×Dic472
C2×#156891982
C2×#156891232
C2×#156891322
C2×C47×#4512
C2×#332747