Finite Group Databasebeta

← C2×#20256456 #27097286

Subgroups — C2×#20256456 #27097286

Order 12032.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689858C211yesmaximal, characteristic, complemented
2C2×#15689846C211yesmaximal, characteristic, complemented
3#20256456C2116yesmaximal, direct product factor
4C2×#15689517C211yesmaximal, characteristic, complemented
5C2×#15689512C211yesmaximal, characteristic
6C2×#15689507C211yesmaximal, characteristic, complemented
7C2×#15689346C211yesmaximal, characteristic, complemented
8C2×#15689346C211yesmaximal, characteristic, complemented
9C2×#15689324C211yesmaximal, characteristic, complemented
10C2×#15689339C211yesmaximal, characteristic, complemented
11C2×#15689339C211yesmaximal, characteristic, complemented
12C2×#15689329C211yesmaximal, characteristic, complemented
13C2×#15689236C211yesmaximal, characteristic, complemented
14C2×#15689231C211yesmaximal, characteristic, complemented
15C2×C4×#10625325C211yesmaximal, characteristic, complemented
16C2×C47×#446C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×Dic188C2211yescharacteristic
19C22×#10625325C2211yescharacteristic
20C22×#10625325C2211yescharacteristic
21C22×#10625325C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625325C2211yescharacteristic
24C22×D376C2211yescharacteristic
25C22×D376C2211yescharacteristic
26#15689858—24no—
27#15689858C2218yescomplemented
28#15689846—24no—
29#15689846C2218yescomplemented
30C2×#13094024C2211yescharacteristic
31C2×#13094021C2211yescharacteristic
32C2×#13094019—21no—
33C2×#13094019—21no—
34C2×#13094013—21no—
35C2×#13094012C2211yescharacteristic
36C2×#13094012C2211yescharacteristic
37C2×#13094012C2211yescharacteristic
38C2×#13094012C2211yescharacteristic
39C2×#13094009—21no—
40C2×#13094009—21no—
41C2×#13094000—21no—
42C2×C4×Dic94C2211yescharacteristic
43C2×C4×Dic94C2211yescharacteristic
44C2×C4×Dic94C2211yescharacteristic
45C2×C4×D188C2211yescharacteristic
46C2×C4×D188C2211yescharacteristic
47C2×C4×D188C2211yescharacteristic
48C2×#13093986—21no—
49C2×#13093982—21no—
50#15689517C2218yescomplemented
51#15689512C2218yes—
52#15689507C2218yescomplemented
53#15689346C2218yescomplemented
54#15689346C2218yescomplemented
55#15689339C2218yescomplemented
56#15689339C2218yescomplemented
57#15689329C2218yescomplemented
58#15689324C2218yescomplemented
59#15689236C2218yescomplemented
60#15689231C2218yescomplemented
61C4×#10625325C2218yescomplemented
62C2×#13093956C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093946C2211yescharacteristic
67C2×#13093946C2211yescharacteristic
68C2×#13093946C2211yescharacteristic
69C2×C4×Q8×C47C2211yescharacteristic
70C47×#446C2218yescomplemented
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C4⋊C8×C47C2211yescharacteristic
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×#97×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188—21no—
81C22×D188—21no—
82C22×D188C2311yescharacteristic
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C2×Dic188—24no—
89C2×Dic188—42no—
90C2×Dic188C2314yes—
91C2×Dic188C2314yes—
92C2×#10625325—24no—
93C2×#10625325—42no—
94C2×#10625325—42no—
95C2×#10625325—42no—
96C2×#10625325—42no—
97C2×#10625325C2314yes—
98C2×#10625325C2314yes—
99C2×#10625325C2314yes—
100C2×#10625325C2314yes—
101C2×#10625325C2314yes—
102C2×D376—24no—
103C2×D376—42no—
104C2×D376C2314yes—
105C2×D376C2314yes—
106#13094024—22no—
107#13094024C2314yes—
108#13094021—22no—
109#13094021C2314yes—
110#13094019—28no—
111#13094019—28no—
112#13094013—28no—
113#13094012—22no—
114#13094012—22no—
115#13094012—22no—
116#13094012—22no—
117#13094012C2314yes—
118#13094012C2314yes—
119#13094012C2314yes—
120#13094012C2314yes—
121#13094009—28no—
122#13094009—28no—
123#13094000—28no—
124C4×Dic94—22no—
125C4×Dic94—22no—
126C4×Dic94—22no—
127C4×Dic94C2314yes—
128C4×Dic94C2314yes—
129C4×Dic94C2314yes—
130C4×D188—22no—
131C4×D188—22no—
132C4×D188—22no—
133C4×D188C2314yes—
134C4×D188C2314yes—
135C4×D188C2314yes—
136#13093986—28no—
137#13093982—28no—
138C2×C4⋊Dic47—21no—
139C2×C4⋊Dic47—21no—
140C2×C4⋊Dic47C2311yescharacteristic
141C2×C4⋊Dic47C2311yescharacteristic
142C2×Dic47⋊C4—21no—
143C2×Dic47⋊C4—21no—
144C2×Dic47⋊C4—21no—
145C2×(C2×D47)⋊C4—21no—
146C2×(C2×D47)⋊C4—21no—
147C2×(C2×D47)⋊C4—21no—
148C2×(C2×D47)⋊C4—21no—
149C2×(C2×D47)⋊C4—21no—
150C2×(C2×D47)⋊C4—21no—
151C2×(C2×D47)⋊C4—21no—
152C2×(C2×D47)⋊C4—21no—
153C2×(C2×D47)⋊C4—21no—
154C2×(C2×D47)⋊C4—21no—
155C2×(C2×D47)⋊C4—21no—
156C2×C4×Dic47—21no—
157C2×C4×Dic47—21no—
158C2×C4×Dic47—21no—
159#13093956C2314yes—
160#13093949C2314yes—
161#13093949C2314yes—
162#13093949C2314yes—
163#13093946C2314yes—
164#13093946C2314yes—
165#13093946C2314yes—
166C22×Q8×C47D411yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170C22×C8×C47C2311yescharacteristic
171C4×Q8×C47D414yes—
172C4×Q8×C47C2314yes—
173C2×C4⋊C4×C47D411yescharacteristic
174C2×C4⋊C4×C47D411yescharacteristic
175C2×C4⋊C4×C47D411yescharacteristic
176C2×C42×C47C2311yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yes—
180C4⋊C8×C47C2314yes—
181C4⋊C8×C47C2314yes—
182#97×C47C2314yes—
183#97×C47C2314yes—
184C4×C8×C47C2314yes—
185C23×D47—21no—
186C23×D47—21no—
187C23×D47—21no—
188C2×Q8×C47—42no—
189C2×Q8×C47C2×D414yes—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—22no—
206C2×D188—22no—
207C2×D188—22no—
208C2×D188—24no—
209C2×D188—21no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—24no—
213C2×D188—44no—
214C2×D188—82no—
215C2×D188C2412yes—
216C2×D188C2412yes—
217C2×D188C2412yes—
218C2×C4×D47—24no—
219C2×C4×D47—24no—
220C2×C4×D47—24no—
221C2×C4×D47—44no—
222C2×C4×D47—82no—
223C2×C4×D47—82no—
224C2×Dic94—22no—
225C2×Dic94—22no—
226C2×Dic94—22no—
227C2×Dic94—22no—
228C2×Dic94—22no—
229C2×Dic94—22no—
230C2×Dic94—21no—
231C2×Dic94—21no—
232C2×Dic94—21no—
233C2×Dic94C2412yes—
234C2×Dic94C2412yes—
235C2×Dic94C2412yes—
236C2×C8×C47—22no—
237C2×C8×C47—22no—
238C2×C8×C47—22no—
239C2×C8×C47#4114yes—
240C2×C8×C47C2412yes—
241C2×C8×C47C2412yes—
242C2×C8×C47C2412yes—
243C2×C8×C47C2412yes—
244C4⋊C4×C47C2×D414yes—
245C4⋊C4×C47C2×D414yes—
246C4⋊C4×C47C2×D414yes—
247C42×C47C2×D412yes—
248C42×C47C2×D412yes—
249C42×C47C2×D412yes—
250C42×C47C2412yes—
251C42×C47C2412yes—
252C42×C47C2412yes—
253(C2×D47)⋊C4—24no—
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—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263(C2×D47)⋊C4—24no—
264C4⋊Dic47—24no—
265C4⋊Dic47—24no—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47C2412yes—
269C4⋊Dic47C2412yes—
270Dic47⋊C4—24no—
271Dic47⋊C4—24no—
272Dic47⋊C4—24no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47—24no—
276Dic188—28no—
277Dic188—44no—
278D376—28no—
279D376—44no—
280#10625325—28no—
281#10625325—44no—
282#10625325—44no—
283#10625325—44no—
284#10625325—44no—
285C23×C47C22×D411yescharacteristic
286C22×D47—22no—
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298Q8×C47—44no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D412yes—
307C2×C4×C47C22×D412yes—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D412yes—
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47H(5,𝔽2)12yes—
314C2×C4×C47C2511yescharacteristic
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—42no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325D188—22no—
326D188—22no—
327D188—22no—
328D188—22no—
329D188—22no—
330D188—22no—
331D188—48no—
332D188—42no—
333D188—42no—
334D188—42no—
335D188—84no—
336C4×D47—48no—
337C4×D47—84no—
338C4×D47—84no—
339Dic94—22no—
340Dic94—22no—
341Dic94—22no—
342Dic94—22no—
343Dic94—22no—
344Dic94—22no—
345Dic94—42no—
346Dic94—42no—
347Dic94—42no—
348C8×C47—22no—
349C8×C47—22no—
350C8×C47—22no—
351C8×C47C2×#4114yes—
352C2×#3401—471nomaximal, Sylow
353C22×C47#55012yes—
354C22×C47#57512yes—
355C22×C47#57712yes—
356C22×C47C23×D411yescharacteristic
357C2×D47—42no—
358C2×D47—42no—
359C2×D47—42no—
360C2×D47—42no—
361C2×D47—42no—
362C2×D47—42no—
363C2×D47—42no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—84no—
367C2×D47—84no—
368C2×D47—84no—
369C4×C47—22no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—22no—
374C4×C47—22no—
375C4×C47#55012yes—
376C4×C47C22×#4111yescharacteristic
377C4×C47C2×H(5,𝔽2)11yescharacteristic
378Dic47—42no—
379Dic47—42no—
380Dic47—42no—
381Dic47—42no—
382Dic47—42no—
383C2×#559—471no—
384C2×#556—471no—
385#3401—4716no—
386C2×#497—471no—
387C2×#496—471no—
388C2×#495—471no—
389C2×#464—471no—
390C2×#464—471no—
391C2×#460—471no—
392C2×#463—471no—
393C2×#463—471no—
394C2×#461—471no—
395C2×#446D4711yescharacteristic, complemented
396C2×#442—471no—
397C2×#441—471no—
398C2×C4×SD16—471no—
399C2×C47#340114yescomplemented
400C2×C47C2×#55011yescharacteristic
401C2×C47C2×#57511yescharacteristic
402C2×C47C2×#57711yescharacteristic
403D47—82no—
404D47—82no—
405D47—82no—
406C22×Q16—471no—
407C22×Q16—471no—
408C22×SD16—471no—
409C22×SD16—471no—
410C22×SD16—471no—
411C22×SD16—471no—
412C22×SD16—471no—
413C22×D8—471no—
414C22×D8—471no—
415#559—478no—
416#559—944no—
417#556—478no—
418#556—944no—
419C2×C4⋊Q8—471no—
420C2×#127—471no—
421C2×#126—941no—
422C2×#126—941no—
423C2×#124—471no—
424C2×#124—471no—
425C2×#124—471no—
426C2×#124—471no—
427C2×#124—941no—
428C2×#123—941no—
429C2×#123—941no—
430C2×C22⋊Q8—941no—
431C2×C4×Q8—471no—
432C2×C4×Q8—471no—
433C2×C4×Q8—471no—
434C2×C4×Q8C2×D4711yescharacteristic
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×C4×D4—471no—
438C2×C4×D4—941no—
439C2×#117—941no—
440#497—478no—
441#496—478no—
442#495—478no—
443#464—478no—
444#464—478no—
445#463—478no—
446#463—478no—
447#461—478no—
448#460—478no—
449#446C2×D4718yescomplemented
450#442—478no—
451#441—478no—
452C4×SD16—478no—
453C2×#106—471no—
454C2×C4⋊C8C2×D4711yescharacteristic
455C2×C4⋊C8C2×D4711yescharacteristic
456C2×C4⋊C8C2×D4711yescharacteristic
457C2×#103—471no—
458C2×#103—471no—
459C2×#103—471no—
460C2×#102—471no—
461C2×#102—471no—
462C2×#102—471no—
463C2×#97C2×D4711yescharacteristic
464C2×#97C2×D4711yescharacteristic
465C2×C4×C8C2×D4711yescharacteristic
466C47C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—471no—
468C22×Q8—471no—
469C22×Q8—471no—
470C22×Q8D18811yescharacteristic
471C22×D4—471no—
472C22×D4—471no—
473C22×D4—471no—
474C22×D4—941no—
475C22×D4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C23×C4—941no—
479C2×Q16—474no—
480C2×Q16—474no—
481C2×Q16—944no—
482C2×Q16—1882no—
483C2×SD16—474no—
484C2×SD16—474no—
485C2×SD16—474no—
486C2×SD16—474no—
487C2×SD16—474no—
488C2×SD16—944no—
489C2×SD16—1882no—
490C2×SD16—1882no—
491C2×SD16—1882no—
492C2×SD16—1882no—
493C2×D8—474no—
494C2×D8—474no—
495C2×D8—944no—
496C2×D8—1882no—
497C22×C8C22×D4711yescharacteristic
498C22×C8C22×D4711yescharacteristic
499C22×C8C22×D4711yescharacteristic
500C22×C8C22×D4711yescharacteristic
501C4⋊Q8—474no—
502C4⋊Q8—942no—
503#127—474no—
504#127—942no—
505#126—948no—
506#126—948no—
507#124—474no—
508#124—474no—
509#124—474no—
510#124—474no—
511#124—948no—
512#124—942no—
513#124—942no—
514#124—942no—
515#124—942no—
516#123—948no—
517#123—948no—
518C22⋊Q8—948no—
519C4×Q8—474no—
520C4×Q8—474no—
521C4×Q8—474no—
522C4×Q8—942no—
523C4×Q8—942no—
524C4×Q8—942no—
525C4×Q8D18814yes—
526C4×Q8C22×D4714yes—
527C4×D4—474no—
528C4×D4—474no—
529C4×D4—474no—
530C4×D4—948no—
531C4×D4—942no—
532C4×D4—942no—
533C4×D4—942no—
534#117—948no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4D18811yescharacteristic
543C2×C4⋊C4D18811yescharacteristic
544C2×C4⋊C4D18811yescharacteristic
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—941no—
549C2×C22⋊C4—941no—
550C2×C22⋊C4—941no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C42—941no—
557C2×C42—941no—
558C2×C42—941no—
559C2×C42C22×D4711yescharacteristic
560C2×C42C22×D4711yescharacteristic
561C2×C42C22×D4711yescharacteristic
562#106—474no—
563C4⋊C8C22×D4714yes—
564C4⋊C8C22×D4714yes—
565C4⋊C8C22×D4714yes—
566#103—474no—
567#103—474no—
568#103—474no—
569#102—474no—
570#102—474no—
571#102—474no—
572#97C22×D4714yes—
573#97C22×D4714yes—
574C4×C8C22×D4714yes—
575C24—941no—
576C24—941no—
577C24—941no—
578C2×Q8—42no—
579C2×Q8—472no—
580C2×Q8—472no—
581C2×Q8—472no—
582C2×Q8—941no—
583C2×Q8—941no—
584C2×Q8—941no—
585C2×Q8—942no—
586C2×Q8—942no—
587C2×Q8—942no—
588C2×Q8—942no—
589C2×Q8—942no—
590C2×Q8—942no—
591C2×Q8C2×D18814yes—
592C2×D4—472no—
593C2×D4—472no—
594C2×D4—472no—
595C2×D4—944no—
596C2×D4—941no—
597C2×D4—944no—
598C2×D4—941no—
599C2×D4—941no—
600C2×D4—942no—
601C2×D4—942no—
602C2×D4—942no—
603C2×D4—942no—
604C2×D4—942no—
605C2×D4—942no—
606C2×D4—3762no—
607C2×D4—1884no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—944no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—3762no—
617C22×C4—3762no—
618C22×C4—1884no—
619C22×C4C2×D18811yescharacteristic
620C22×C4C2×D18811yescharacteristic
621C22×C4C2×D18811yescharacteristic
622C22×C4C2×D18811yescharacteristic
623C22×C4C2×D18811yescharacteristic
624C22×C4C2×D18811yescharacteristic
625C22×C4C23×D4711yescharacteristic
626Q16—948no—
627Q16—1884no—
628SD16—948no—
629SD16—1884no—
630SD16—1884no—
631SD16—1884no—
632SD16—1884no—
633D8—948no—
634D8—1884no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8#1062535414yes—
639C2×C8C23×D4712yes—
640C2×C8C23×D4712yes—
641C2×C8C23×D4712yes—
642C2×C8C23×D4712yes—
643C4⋊C4—472no—
644C4⋊C4—472no—
645C4⋊C4—944no—
646C4⋊C4—944no—
647C4⋊C4—944no—
648C4⋊C4—941no—
649C4⋊C4—941no—
650C4⋊C4—944no—
651C4⋊C4—944no—
652C4⋊C4C2×D18814yes—
653C4⋊C4C2×D18814yes—
654C4⋊C4C2×D18814yes—
655C22⋊C4—944no—
656C22⋊C4—944no—
657C22⋊C4—944no—
658C22⋊C4—944no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—944no—
663C22⋊C4—944no—
664C22⋊C4—944no—
665C22⋊C4—944no—
666C42—944no—
667C42—944no—
668C42—944no—
669C42C2×D18812yes—
670C42C2×D18812yes—
671C42C2×D18812yes—
672C42C23×D4712yes—
673C42C23×D4712yes—
674C42C23×D4712yes—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23C22×D18811yescharacteristic
688Q8—44no—
689Q8—942no—
690Q8—942no—
691Q8—942no—
692Q8—942no—
693Q8—942no—
694Q8—942no—
695Q8—1882no—
696Q8—1882no—
697Q8—1882no—
698D4—942no—
699D4—942no—
700D4—942no—
701D4—942no—
702D4—942no—
703D4—942no—
704D4—3764no—
705D4—1888no—
706D4—1882no—
707D4—1882no—
708D4—1882no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—3764no—
721C2×C4—3764no—
722C2×C4—1888no—
723C2×C4—1882no—
724C2×C4—1882no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4C22×D18812yes—
729C2×C4C22×D18812yes—
730C2×C4C22×D18812yes—
731C2×C4C22×D18812yes—
732C2×C4C22×D18812yes—
733C2×C4C22×D18812yes—
734C2×C4C22×D18811yescharacteristic
735C2×C4C2×#1062535412yes—
736C2×C4#1309407012yes—
737C2×C4C24×D4711yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8C2×#1062535414yes—
742C22—3764no—
743C22—3764no—
744C22—3764no—
745C22—1882no—
746C22—1882no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22#1568979512yes—
755C22#1568992312yes—
756C22#1568993512yes—
757C22C23×D18811yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—1882no—
765C4—1882no—
766C4—1882no—
767C4—1882no—
768C4—1882no—
769C4#1568979512yes—
770C4C22×#1062535411yescharacteristic
771C4C2×#1309407011yescharacteristic
772C2—3762no—
773C2—3762no—
774C2—3762no—
775C2#2025645614yesdirect product factor
776C2C2×#1568979511yescharacteristic
777C2C2×#1568992311yescharacteristic
778C2C2×#1568993511yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#446C2
socleC23×C47C22×D4
prime radicalC2×#15689512C2
hypercenterC2×#446D47
hypocenterC47C2×#3401
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#15689858C2semidirect
2. C2×#15689846C2semidirect
3. #20256456C2direct (N × H)
4. C2×#15689517C2semidirect
6. C2×#15689507C2semidirect
7. C2×#15689346C2semidirect
8. C2×#15689346C2semidirect
9. C2×#15689324C2semidirect
10. C2×#15689339C2semidirect
11. C2×#15689339C2semidirect
12. C2×#15689329C2semidirect
13. C2×#15689236C2semidirect
14. C2×#15689231C2semidirect
15. C2×C4×#10625325C2semidirect
16. C2×C47×#446C2semidirect
27. #15689858C22semidirect
29. #15689846C22semidirect
50. #15689517C22semidirect
52. #15689507C22semidirect
53. #15689346C22semidirect
54. #15689346C22semidirect
55. #15689339C22semidirect
56. #15689339C22semidirect
57. #15689329C22semidirect
58. #15689324C22semidirect
59. #15689236C22semidirect
60. #15689231C22semidirect
61. C4×#10625325C22semidirect
70. C47×#446C22semidirect
395. C2×#446D47semidirect
399. C2×C47#3401semidirect
449. #446C2×D47semidirect
466. C47C2×#3401semidirect
775. C2#20256456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898582
C2×#156898462
#202564562
C2×#156895172
C2×#156895122
C2×#156895072
C2×#156893462
C2×#156893242
C2×#156893392
C2×#156893292
C2×#156892362
C2×#156892312
C2×C4×#106253252
C2×C47×#4462
C2×#340147