Finite Group Databasebeta

← C2×#20253411 #27084298

Subgroups — C2×#20253411 #27084298

Order 12032.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689658C211yesmaximal, characteristic, complemented
2C2×C4×#10625352C211yesmaximal, characteristic, complemented
3#20253411C2116yesmaximal, direct product factor
4C2×#15689467C211yesmaximal, characteristic, complemented
5C2×#15689450C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689346C211yesmaximal, characteristic, complemented
8C2×#15689338C211yesmaximal, characteristic, complemented
9C2×#15689286C211yesmaximal, characteristic, complemented
10C2×#15689269C211yesmaximal, characteristic
11C2×#15689217C211yesmaximal, characteristic, complemented
12C2×#15689214C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689203C211yesmaximal, characteristic, complemented
15C2×#15689175C211yesmaximal, characteristic, complemented
16C2×C47×#478C211yesmaximal, characteristic, complemented
17C22×#10625352C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625335C2211yescharacteristic
21C22×#10625334C2211yescharacteristic
22#15689658—24no—
23#15689658C2218yescomplemented
24C2×#13094019—21no—
25C2×#13094012C2211yescharacteristic
26C2×#13094009—21no—
27C2×#13094004C2211yescharacteristic
28C2×#13093999C2211yescharacteristic
29C4×#10625352—24no—
30C4×#10625352C2218yescomplemented
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989C2211yescharacteristic
33C2×#13093989C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic
35C2×#13093986—21no—
36C2×#13093986C2211yescharacteristic
37C2×C4×C22⋊D47—21no—
38C2×(C22⋊D47)⋊C4—21no—
39C2×#13093982—21no—
40C2×#13093982C2211yescharacteristic
41C2×#13093980—21no—
42C22×C4×Dic47—21no—
43C2×C42×D47C2211yescharacteristic
44#15689467C2218yescomplemented
45#15689450C2218yescomplemented
46#15689427C2218yescomplemented
47#15689346C2218yescomplemented
48#15689338C2218yescomplemented
49#15689286C2218yescomplemented
50#15689269C2218yes—
51#15689217C2218yescomplemented
52#15689214C2218yescomplemented
53#15689210C2218yescomplemented
54#15689203C2218yescomplemented
55#15689175C2218yescomplemented
56C2×#13093957C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093947C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093947C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×C4×D4×C47C2211yescharacteristic
71C47×#478C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×#102×C47C2211yescharacteristic
77C2×#10625352—24no—
78C2×#10625352—22no—
79C2×#10625352—24no—
80C2×#10625352C2314yes—
81C22×Dic94C2311yescharacteristic
82C22×Dic94C2311yescharacteristic
83C22×D188—21no—
84C22×D188C2311yescharacteristic
85C22×C22⋊D47—21no—
86C23×Dic47—21no—
87C23×Dic47—21no—
88C22×C4×D47—21no—
89C22×C4×D47D411yescharacteristic
90C22×C4×D47D411yescharacteristic
91C22×C4×D47C2311yescharacteristic
92C2×Dic188—24no—
93C2×Dic188C2314yes—
94C2×#10625325—24no—
95C2×#10625325C2314yes—
96C2×#10625335—24no—
97C2×#10625335C2314yes—
98C2×#10625334—24no—
99C2×#10625334C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102#13094019—28no—
103#13094012—22no—
104#13094012C2314yes—
105#13094009—28no—
106#13094004—22no—
107#13094004C2314yes—
108#13093999—22no—
109#13093999C2314yes—
110C4×Dic94—22no—
111C4×Dic94C2314yes—
112#13093989—22no—
113#13093989—22no—
114#13093989C2314yes—
115#13093989C2314yes—
116D4×Dic47—22no—
117D4×Dic47C2314yes—
118#13093986—28no—
119#13093986—22no—
120#13093986C2314yes—
121C4×C22⋊D47—28no—
122(C22⋊D47)⋊C4—28no—
123#13093982—22no—
124#13093982—28no—
125#13093982C2314yes—
126#13093980—28no—
127C2×C4⋊Dic47—21no—
128C2×C4⋊Dic47C2311yescharacteristic
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×C22⋊Dic47—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—28no—
144C2×C4×Dic47D411yescharacteristic
145C2×C4×Dic47D411yescharacteristic
146C2×C4×Dic47C2311yescharacteristic
147C42×D47D414yes—
148C42×D47C2314yes—
149#13093957C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152#13093949C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093946C2314yes—
157#13093944C2314yes—
158(C2×D47)⋊C8C2314yes—
159(C2×D47)⋊C8C2314yes—
160C8×Dic47C2314yes—
161C8×Dic47C2314yes—
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166#125×C47—22no—
167#125×C47C2314yes—
168C4×D4×C47—22no—
169C4×D4×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#106×C47C2314yes—
179C4⋊C8×C47C2314yes—
180#102×C47C2314yes—
181#102×C47C2314yes—
182C24×C47—21no—
183C23×D47—21no—
184C23×D47C2×D411yescharacteristic
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47#4114yes—
188C2×D4×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—44no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—28no—
198C2×C22⋊D47—24no—
199C22×Dic47—28no—
200C22×Dic47—21no—
201C22×Dic47—24no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—44no—
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209#10625352—216no—
210#10625352—28no—
211#10625352—28no—
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—24no—
215C2×D188—21no—
216C2×D188—44no—
217C2×D188C2412yes—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—24no—
221C2×C4×D47—24no—
222C2×C4×D47—42no—
223C2×C4×D47—44no—
224C2×C4×D47C2×D412yes—
225C2×C4×D47C2×D414yes—
226C2×C4×D47C2×D414yes—
227C2×C4×D47C2412yes—
228C2×Dic94—21no—
229C2×Dic94—22no—
230C2×Dic94—22no—
231C2×Dic94—22no—
232C2×Dic94—21no—
233C2×Dic94#4114yes—
234C2×Dic94C2412yes—
235C2×Dic94C2412yes—
236C2×C8×C47—22no—
237C2×C8×C47—22no—
238C2×C8×C47C2412yes—
239C2×C8×C47C2412yes—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47C2412yes—
246C4⋊C4×C47C2412yes—
247C4⋊C4×C47C2412yes—
248C22⋊C4×C47—24no—
249C42×C47C2×D412yes—
250C42×C47C2412yes—
251C22⋊Dic47—24no—
252#10625335—28no—
253#10625334—28no—
254(C2×D47)⋊C4—24no—
255(C2×D47)⋊C4—24no—
256(C2×D47)⋊C4—24no—
257(C2×D47)⋊C4—24no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260C4⋊Dic47—21no—
261C4⋊Dic47—24no—
262C4⋊Dic47C2412yes—
263Dic47⋊C4—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4—24no—
266C4×Dic47—24no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47C2×D412yes—
271C4×Dic47C2×D414yes—
272C4×Dic47C2×D414yes—
273C4×Dic47C2412yes—
274C2×C47⋊C8—22no—
275C2×C47⋊C8—22no—
276C2×C47⋊C8C2412yes—
277C2×C47⋊C8C2412yes—
278Dic188—28no—
279#10625325—28no—
280C23×C47—24no—
281C23×C47—22no—
282C23×C47—42no—
283C23×C47—42no—
284C23×C47C22×D411yescharacteristic
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47C22×D412yes—
293D4×C47—24no—
294D4×C47—22no—
295D4×C47C2×#4114yes—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—48no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D411yescharacteristic
308C2×C4×C47C2×#4112yes—
309C2×C4×C47C2×#4112yes—
310C2×C4×C47C2511yescharacteristic
311C22⋊D47—216no—
312C2×Dic47—216no—
313C2×Dic47—24no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—42no—
320C2×Dic47—42no—
321C2×Dic47—48no—
322C2×Dic47#13514yes—
323C2×Dic47C22×D412yes—
324C2×Dic47C22×D412yes—
325C2×Dic47C22×D412yes—
326D188—22no—
327D188—22no—
328D188—48no—
329D188—42no—
330C4×D47—24no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—28no—
334C4×D47—44no—
335C4×D47—48no—
336Dic94—24no—
337Dic94—22no—
338Dic94—22no—
339Dic94—22no—
340Dic94—42no—
341Dic94C2×#4114yes—
342C8×C47—22no—
343C8×C47—22no—
344C47⋊C8—22no—
345C47⋊C8—22no—
346C2×#3102—471nomaximal, Sylow
347C22×C47—24no—
348C22×C47—48no—
349C22×C47—42no—
350C22×C47—42no—
351C22×C47#52512yes—
352C22×C47C2×#13512yes—
353C22×C47#57512yes—
354C22×C47C23×D411yescharacteristic
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—22no—
358C2×D47—44no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—84no—
363C4×C47—22no—
364C4×C47—22no—
365C4×C47—42no—
366C4×C47—42no—
367C4×C47—42no—
368C4×C47#52512yes—
369C4×C47C22×#4111yescharacteristic
370C4×C47C22×#4111yescharacteristic
371Dic47—24no—
372Dic47—22no—
373Dic47—22no—
374Dic47—42no—
375Dic47—42no—
376Dic47C2×#13514yes—
377C2×#529—471no—
378C2×C4×#41—471no—
379#3102—4716no—
380C2×#485—471no—
381C2×#482—471no—
382C2×#479—471no—
383C2×#478D4711yescharacteristic, complemented
384C2×#464—471no—
385C2×#463—471no—
386C2×#452—471no—
387C2×#449—471no—
388C2×C4×Q16—471no—
389C2×C4×SD16—471no—
390C2×C4×SD16—471no—
391C2×C4×D8—471no—
392C2×#431—471no—
393C2×C47—44no—
394C2×C47#310214yescomplemented
395C2×C47C2×#52511yescharacteristic
396C2×C47C22×#13511yescharacteristic
397C2×C47C2×#57511yescharacteristic
398D47—42no—
399D47—82no—
400C22×#41—471no—
401C22×Q16—471no—
402C22×SD16—471no—
403C22×SD16—471no—
404C22×D8—471no—
405#529—478no—
406#529—944no—
407C2×#126—941no—
408C2×#125C2×D4711yescharacteristic
409C2×#124—471no—
410C2×#123—941no—
411C2×C22⋊Q8—471no—
412C2×#121—471no—
413C4×#41—478no—
414C4×#41—944no—
415C2×C4×Q8—471no—
416C2×C4×Q8—471no—
417C2×C4×Q8—471no—
418C2×C4×D4—471no—
419C2×C4×D4—471no—
420C2×C4×D4—941no—
421C2×C4×D4—941no—
422C2×C4×D4—941no—
423C2×C4×D4C2×D4711yescharacteristic
424C2×#117—471no—
425C2×#117—941no—
426C2×#117—941no—
427C22×C42—471no—
428C22×C42—941no—
429#485—478no—
430#482—478no—
431#479—478no—
432#478C2×D4718yescomplemented
433#464—478no—
434#463—478no—
435#452—478no—
436#449—478no—
437C4×Q16—478no—
438C4×SD16—478no—
439C4×SD16—478no—
440C4×D8—478no—
441#431—478no—
442C2×#107—471no—
443C2×#107C2×D4711yescharacteristic
444C2×#106—471no—
445C2×#106C2×D4711yescharacteristic
446C2×C4⋊C8—471no—
447C2×C4⋊C8C2×D4711yescharacteristic
448C2×#103—471no—
449C2×#103—471no—
450C2×#103—471no—
451C2×#103—471no—
452C2×#102—471no—
453C2×#102—471no—
454C2×#102C2×D4711yescharacteristic
455C2×#102C2×D4711yescharacteristic
456C2×C22⋊C8—471no—
457C2×C22⋊C8—471no—
458C2×C4×C8—471no—
459C2×C4×C8—471no—
460C47C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—474no—
462C2×#41—942no—
463C2×#41—944no—
464C2×#41—944no—
465C22×Q8—471no—
466C22×Q8—471no—
467C22×D4—471no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4C22×D4711yescharacteristic
471C23×C4—21no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C2×Q16—474no—
479C2×Q16—944no—
480C2×SD16—474no—
481C2×SD16—474no—
482C2×SD16—944no—
483C2×SD16—944no—
484C2×D8—474no—
485C2×D8—944no—
486C22×C8—471no—
487C22×C8—471no—
488C22×C8C22×D4711yescharacteristic
489C22×C8C22×D4711yescharacteristic
490#126—948no—
491#125—22no—
492#125C22×D4714yes—
493#124—474no—
494#124—942no—
495#123—948no—
496C22⋊Q8—474no—
497C22⋊Q8—942no—
498#121—474no—
499#121—942no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—474no—
503C4×Q8—942no—
504C4×Q8—942no—
505C4×Q8—942no—
506C4×D4—22no—
507C4×D4—474no—
508C4×D4—474no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—948no—
512C4×D4—948no—
513C4×D4—948no—
514C4×D4C22×D4714yes—
515#117—474no—
516#117—948no—
517#117—948no—
518#117—942no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—471no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C4⋊C4—941no—
525C2×C4⋊C4—941no—
526C2×C4⋊C4C22×D4711yescharacteristic
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C42—471no—
538C2×C42—471no—
539C2×C42—471no—
540C2×C42—474no—
541C2×C42—474no—
542C2×C42—948no—
543C2×C42—941no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42C22×D4711yescharacteristic
548#107—474no—
549#107C22×D4714yes—
550#106—474no—
551#106C22×D4714yes—
552C4⋊C8—474no—
553C4⋊C8C22×D4714yes—
554#103—474no—
555#103—474no—
556#103—474no—
557#103—474no—
558#102—474no—
559#102—474no—
560#102C22×D4714yes—
561#102C22×D4714yes—
562C22⋊C8—474no—
563C22⋊C8—474no—
564C4×C8—474no—
565C4×C8—474no—
566C24—21no—
567C24—471no—
568C24—941no—
569#41—948no—
570#41—9416no—
571#41—948no—
572C2×Q8—474no—
573C2×Q8—472no—
574C2×Q8—472no—
575C2×Q8—941no—
576C2×Q8—941no—
577C2×Q8—942no—
578C2×Q8—942no—
579C2×Q8—942no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—472no—
583C2×D4—944no—
584C2×D4—944no—
585C2×D4—948no—
586C2×D4—941no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—1884no—
590C2×D4#1062535414yes—
591C2×D4C23×D4712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—44no—
597C22×C4—471no—
598C22×C4—471no—
599C22×C4—471no—
600C22×C4—472no—
601C22×C4—474no—
602C22×C4—472no—
603C22×C4—474no—
604C22×C4—944no—
605C22×C4—944no—
606C22×C4—944no—
607C22×C4—944no—
608C22×C4—948no—
609C22×C4—941no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—1882no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620Q16—948no—
621SD16—948no—
622SD16—948no—
623D8—948no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—472no—
627C2×C8—472no—
628C2×C8—942no—
629C2×C8—942no—
630C2×C8C23×D4712yes—
631C2×C8C23×D4712yes—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—472no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—941no—
643C4⋊C4C23×D4712yes—
644C4⋊C4C23×D4712yes—
645C4⋊C4C23×D4712yes—
646C22⋊C4—24no—
647C22⋊C4—944no—
648C22⋊C4—944no—
649C22⋊C4—944no—
650C22⋊C4—944no—
651C22⋊C4—944no—
652C22⋊C4—944no—
653C22⋊C4—944no—
654C42—474no—
655C42—474no—
656C42—472no—
657C42—472no—
658C42—944no—
659C42—944no—
660C42—944no—
661C42—944no—
662C42D4×D4712yes—
663C42C23×D4712yes—
664C23—24no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—472no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—1882no—
674C23—1882no—
675C23—1882no—
676C23C2×D4×D4711yescharacteristic
677Q8—474no—
678Q8—944no—
679Q8—942no—
680Q8—942no—
681Q8—942no—
682Q8—1882no—
683D4—24no—
684D4—22no—
685D4—9416no—
686D4—942no—
687D4—942no—
688D4—1888no—
689D4—1882no—
690D4C2×#1062535414yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—474no—
701C2×C4—472no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—948no—
705C2×C4—9416no—
706C2×C4—942no—
707C2×C4—944no—
708C2×C4—942no—
709C2×C4—942no—
710C2×C4—944no—
711C2×C4—942no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—1884no—
716C2×C4—1888no—
717C2×C4—1888no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4C2×D4×D4712yes—
721C2×C4C2×D4×D4712yes—
722C2×C4C2×D4×D4711yescharacteristic
723C2×C4#41×D4712yes—
724C2×C4C2×#1062535412yes—
725C2×C4C24×D4711yescharacteristic
726C8—22no—
727C8—22no—
728C8—942no—
729C8—942no—
730C22—24no—
731C22—42no—
732C22—42no—
733C22—48no—
734C22—942no—
735C22—942no—
736C22—942no—
737C22—3764no—
738C22—1882no—
739C22—1882no—
740C22—1882no—
741C22—1884no—
742C22#1568963612yes—
743C22#135×D4712yes—
744C22#1568991912yes—
745C22C22×D4×D4711yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—474no—
752C4—942no—
753C4—942no—
754C4—944no—
755C4—1882no—
756C4—1882no—
757C4#1568963612yes—
758C4C2×#41×D4711yescharacteristic
759C4C22×#1062535411yescharacteristic
760C2—44no—
761C2—3762no—
762C2—1882no—
763C2#2025341114yesdirect product factor
764C2C2×#1568963611yescharacteristic
765C2C2×#135×D4711yescharacteristic
766C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#478C2
socleC23×C47C22×D4
prime radicalC2×#15689269C2
hypercenterC2×#478D47
hypocenterC47C2×#3102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#15689658C2semidirect
2. C2×C4×#10625352C2semidirect
3. #20253411C2direct (N × H)
4. C2×#15689467C2semidirect
5. C2×#15689450C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689346C2semidirect
8. C2×#15689338C2semidirect
9. C2×#15689286C2semidirect
11. C2×#15689217C2semidirect
12. C2×#15689214C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689203C2semidirect
15. C2×#15689175C2semidirect
16. C2×C47×#478C2semidirect
23. #15689658C22semidirect
30. C4×#10625352C22semidirect
44. #15689467C22semidirect
45. #15689450C22semidirect
46. #15689427C22semidirect
47. #15689346C22semidirect
48. #15689338C22semidirect
49. #15689286C22semidirect
51. #15689217C22semidirect
52. #15689214C22semidirect
53. #15689210C22semidirect
54. #15689203C22semidirect
55. #15689175C22semidirect
71. C47×#478C22semidirect
383. C2×#478D47semidirect
394. C2×C47#3102semidirect
432. #478C2×D47semidirect
460. C47C2×#3102semidirect
763. C2#20253411direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896582
C2×C4×#106253522
#202534112
C2×#156894672
C2×#156894502
C2×#156894272
C2×#156893462
C2×#156893382
C2×#156892862
C2×#156892692
C2×#156892172
C2×#156892142
C2×#156892102
C2×#156892032
C2×#156891752
C2×C47×#4782
C2×#310247