Finite Group Databasebeta

← C2×#20254076 #27086167

Subgroups — C2×#20254076 #27086167

Order 12032.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689747C211yesmaximal, characteristic, complemented
2C2×#15689729C211yesmaximal, characteristic, complemented
3#20254076C2116yesmaximal, direct product factor
4C2×#15689512C211yesmaximal, characteristic, complemented
5C2×#15689480C211yesmaximal, characteristic, complemented
6C2×#15689471C211yesmaximal, characteristic, complemented
7C2×#15689377C211yesmaximal, characteristic, complemented
8C2×#15689370C211yesmaximal, characteristic, complemented
9C2×#15689360C211yesmaximal, characteristic, complemented
10C2×#15689353C211yesmaximal, characteristic, complemented
11C2×#15689234C211yesmaximal, characteristic, complemented
12C2×#15689222C211yesmaximal, characteristic, complemented
13C2×#15689210C211yesmaximal, characteristic, complemented
14C2×#15689205C211yesmaximal, characteristic, complemented
15C2×#15689080C211yesmaximal, characteristic, complemented
16C2×C47×#501C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×#10625325C2211yescharacteristic
19C22×D376C2211yescharacteristic
20C22×D376C2211yescharacteristic
21C22×#10625324C2211yescharacteristic
22C22×C8×D47C2211yescharacteristic
23#15689747—24no—
24#15689747C2218yescomplemented
25#15689729—24no—
26#15689729C2218yescomplemented
27C2×#13094021C2211yescharacteristic
28C2×#13094019—21no—
29C2×#13094013—21no—
30C2×#13094012C2211yescharacteristic
31C2×#13094009—21no—
32C2×#13094009—21no—
33C2×#13094009—21no—
34C2×#13094004C2211yescharacteristic
35C2×#13094000—21no—
36C2×#13093999—21no—
37C2×#13093999—21no—
38C2×#13093999C2211yescharacteristic
39C2×#13093999C2211yescharacteristic
40C2×#13093999C2211yescharacteristic
41C2×#13093989C2211yescharacteristic
42C2×#13093986C2211yescharacteristic
43C2×#13093986C2211yescharacteristic
44C2×#13093986C2211yescharacteristic
45C2×#13093981C2211yescharacteristic
46#15689512C2218yescomplemented
47#15689480C2218yescomplemented
48#15689471C2218yescomplemented
49#15689377C2218yescomplemented
50#15689370C2218yescomplemented
51#15689360C2218yescomplemented
52#15689353C2218yescomplemented
53#15689234C2218yescomplemented
54#15689222C2218yescomplemented
55#15689210C2218yescomplemented
56#15689205C2218yescomplemented
57C2×#13093947C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093944C2211yescharacteristic
62C2×#13093944C2211yescharacteristic
63C2×#13093944C2211yescharacteristic
64C2×#13093944C2211yescharacteristic
65#15689080C2218yescomplemented
66C2×#13093934C2211yescharacteristic
67C2×C4×C47⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic
71C47×#501C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188—21no—
79C22×D188—21no—
80C22×D188—21no—
81C22×D188—21no—
82C22×D188—21no—
83C22×D188C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C4×D47—21no—
87C22×C4×D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47C2311yescharacteristic
90C2×#10625325—24no—
91C2×#10625325—24no—
92C2×#10625325C2314yes—
93C2×#10625325C2314yes—
94C2×D376—24no—
95C2×D376—24no—
96C2×D376C2314yes—
97C2×D376C2314yes—
98C2×#10625324—24no—
99C2×#10625324C2314yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2311yescharacteristic
102C2×C8×D47—24no—
103C2×C8×D47C2314yes—
104#13094021—22no—
105#13094021C2314yes—
106#13094019—28no—
107#13094013—28no—
108#13094012—22no—
109#13094012C2314yes—
110#13094009—28no—
111#13094009—28no—
112#13094009—28no—
113#13094004—22no—
114#13094004C2314yes—
115#13094000—28no—
116#13093999—22no—
117#13093999—22no—
118#13093999—22no—
119#13093999—28no—
120#13093999—28no—
121#13093999C2314yes—
122#13093999C2314yes—
123#13093999C2314yes—
124#13093989—22no—
125#13093989C2314yes—
126#13093986—22no—
127#13093986—22no—
128#13093986—22no—
129#13093986C2314yes—
130#13093986C2314yes—
131#13093986C2314yes—
132#13093981D414yes—
133#13093981C2314yes—
134C2×C4⋊Dic47—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4D411yescharacteristic
137C2×Dic47⋊C4D411yescharacteristic
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
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)⋊C4D411yescharacteristic
148C2×(C2×D47)⋊C4D411yescharacteristic
149C2×C4×Dic47—21no—
150C2×C4×Dic47C2311yescharacteristic
151#13093947C2314yes—
152#13093947C2314yes—
153#13093944C2314yes—
154#13093944C2314yes—
155#13093944C2314yes—
156#13093944C2314yes—
157#13093944C2314yes—
158#13093944C2314yes—
159#13093934C2314yes—
160C4×C47⋊C8C2314yes—
161C8×Dic47C2314yes—
162C22×Q8×C47—21no—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4⋊Q8×C47—22no—
166C4⋊Q8×C47C2314yes—
167#125×C47—22no—
168#125×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C4⋊C4×C47C2311yescharacteristic
176C2×C42×C47C2311yescharacteristic
177#107×C47C2314yes—
178#107×C47C2314yes—
179#106×C47C2314yes—
180#106×C47C2314yes—
181#97×C47C2314yes—
182C23×D47—21no—
183C23×D47—21no—
184C23×D47—21no—
185C23×D47C2×D411yescharacteristic
186C2×Q8×C47—24no—
187C2×Q8×C47—82no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×Dic47—21no—
196C22×Dic47C2×D411yescharacteristic
197C22×Dic47C2×D411yescharacteristic
198C22×Dic47C2×D411yescharacteristic
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—21no—
206C2×D188—21no—
207C2×D188—21no—
208C2×D188—24no—
209C2×D188—24no—
210C2×D188—24no—
211C2×D188—24no—
212C2×D188—24no—
213C2×D188—82no—
214C2×D188—82no—
215C2×D188—82no—
216C2×D188—82no—
217C2×D188—82no—
218C2×D188C2412yes—
219C2×D188C2412yes—
220C2×D188C2412yes—
221C2×C4×D47—22no—
222C2×C4×D47—22no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—82no—
227C2×C4×D47—82no—
228C2×C4×D47—82no—
229C2×C4×D47C2×D412yes—
230C2×C4×D47C2412yes—
231C2×Dic94—22no—
232C2×Dic94—22no—
233C2×Dic94—21no—
234C2×Dic94C2412yes—
235C2×C8×C47#4114yes—
236C2×C8×C47#4114yes—
237C2×C8×C47C2412yes—
238C2×C8×C47C2412yes—
239C4⋊C4×C47—24no—
240C4⋊C4×C47—24no—
241C4⋊C4×C47—24no—
242C4⋊C4×C47—21no—
243C4⋊C4×C47—21no—
244C4⋊C4×C47—21no—
245C4⋊C4×C47—21no—
246C4⋊C4×C47C2412yes—
247C4⋊C4×C47C2412yes—
248C4⋊C4×C47C2412yes—
249C4⋊C4×C47C2412yes—
250C42×C47C2×D412yes—
251C42×C47C2412yes—
252(C2×D47)⋊C4—24no—
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)⋊C4C2×D414yes—
262(C2×D47)⋊C4C2×D414yes—
263C4⋊Dic47—24no—
264Dic47⋊C4—24no—
265Dic47⋊C4C2×D414yes—
266Dic47⋊C4C2×D414yes—
267C4×Dic47—24no—
268C4×Dic47C2×D412yes—
269C4×Dic47C2412yes—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8C2412yes—
273C2×C47⋊C8C2412yes—
274D376—28no—
275D376—28no—
276#10625325—28no—
277#10625325—28no—
278#10625324—28no—
279C8×D47—28no—
280C23×C47C22×D411yescharacteristic
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47C22×D412yes—
297Q8×C47—84no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47C22×D412yes—
309C2×C4×C47C22×D412yes—
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C2×#4112yes—
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2511yescharacteristic
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—42no—
319C2×Dic47C22×D412yes—
320C2×Dic47C22×D412yes—
321C2×Dic47C22×D412yes—
322D188—22no—
323D188—22no—
324D188—22no—
325D188—22no—
326D188—22no—
327D188—22no—
328D188—42no—
329D188—42no—
330D188—42no—
331D188—84no—
332D188—84no—
333D188—84no—
334D188—84no—
335D188—84no—
336C4×D47—24no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—84no—
340C4×D47—84no—
341C4×D47—84no—
342Dic94—22no—
343Dic94—22no—
344Dic94—42no—
345C8×C47C2×#4114yes—
346C8×C47C2×#4114yes—
347C47⋊C8—22no—
348C47⋊C8—22no—
349C2×#3179—471nomaximal, Sylow
350C22×C47#53212yes—
351C22×C47#57612yes—
352C22×C47#57712yes—
353C22×C47C23×D411yescharacteristic
354C2×D47—22no—
355C2×D47—22no—
356C2×D47—22no—
357C2×D47—44no—
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—42no—
367C2×D47—84no—
368C2×D47—84no—
369C2×D47—84no—
370C4×C47—22no—
371C4×C47—22no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47—42no—
376C4×C47#53212yes—
377C4×C47C22×#4111yescharacteristic
378C4×C47C22×#4111yescharacteristic
379Dic47—22no—
380Dic47—22no—
381Dic47—22no—
382Dic47—42no—
383C2×#542—471no—
384C2×#540—471no—
385#3179—4716no—
386C2×#501D4711yescharacteristic, complemented
387C2×#496—471no—
388C2×#488—471no—
389C2×#486—471no—
390C2×#469—471no—
391C2×#468—471no—
392C2×#466—471no—
393C2×#465—471no—
394C2×#442—471no—
395C2×#440—471no—
396C2×C4×SD16—471no—
397C2×C4×D8—471no—
398C2×#405—471no—
399C2×C47#317914yescomplemented
400C2×C47C2×#53211yescharacteristic
401C2×C47C2×#57611yescharacteristic
402C2×C47C2×#57711yescharacteristic
403D47—42no—
404D47—82no—
405D47—82no—
406D47—82no—
407C22×SD16—471no—
408C22×SD16—471no—
409C22×D8—471no—
410C22×D8—471no—
411C22×M16—471no—
412C23×C8—471no—
413#542—478no—
414#542—944no—
415#540—478no—
416#540—944no—
417C2×C4⋊Q8C2×D4711yescharacteristic
418C2×#127—471no—
419C2×#126—941no—
420C2×#125C2×D4711yescharacteristic
421C2×#124—471no—
422C2×#124—941no—
423C2×#123—941no—
424C2×#123—941no—
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429C2×#121—471no—
430C2×#121—471no—
431C2×#121—941no—
432C2×#121—941no—
433C2×C4×Q8—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—471no—
437C2×#117—471no—
438#501C2×D4718yescomplemented
439#496—478no—
440#488—478no—
441#486—478no—
442#469—478no—
443#468—478no—
444#466—478no—
445#465—478no—
446#442—478no—
447#440—478no—
448C4×SD16—478no—
449C4×D8—478no—
450C2×#107C2×D4711yescharacteristic
451C2×#107C2×D4711yescharacteristic
452C2×#106C2×D4711yescharacteristic
453C2×#106C2×D4711yescharacteristic
454C2×#103—471no—
455C2×#103—471no—
456C2×#102—471no—
457C2×#102—471no—
458C2×#102—471no—
459C2×#102—471no—
460C2×#102—471no—
461C2×#102—471no—
462#405—478no—
463C2×#97—471no—
464C2×#97C2×D4711yescharacteristic
465C2×C4×C8—471no—
466C2×C4×C8—471no—
467C47C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8—471no—
470C22×D4—471no—
471C22×D4—471no—
472C22×D4—471no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C22×D4—941no—
478C23×C4—471no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4—941no—
482C2×SD16—474no—
483C2×SD16—474no—
484C2×SD16—944no—
485C2×SD16—944no—
486C2×D8—474no—
487C2×D8—474no—
488C2×D8—944no—
489C2×D8—944no—
490C2×M16—474no—
491C2×M16—944no—
492C22×C8—471no—
493C22×C8—471no—
494C22×C8—474no—
495C22×C8—944no—
496C22×C8C22×D4711yescharacteristic
497C22×C8C22×D4711yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D4714yes—
500#127—474no—
501#127—942no—
502#126—948no—
503#125—22no—
504#125C22×D4714yes—
505#124—474no—
506#124—948no—
507#124—942no—
508#123—948no—
509#123—948no—
510#123—948no—
511C22⋊Q8—474no—
512C22⋊Q8—942no—
513C22⋊Q8—948no—
514#121—474no—
515#121—474no—
516#121—474no—
517#121—948no—
518#121—948no—
519#121—942no—
520#121—942no—
521#121—942no—
522C4×Q8—474no—
523C4×Q8—942no—
524C4×D4—474no—
525C4×D4—474no—
526C4×D4—474no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530#117—474no—
531#117—474no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—941no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4C22×D4711yescharacteristic
540C2×C4⋊C4C22×D4711yescharacteristic
541C2×C4⋊C4C22×D4711yescharacteristic
542C2×C4⋊C4C22×D4711yescharacteristic
543C2×C22⋊C4—471no—
544C2×C22⋊C4—471no—
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×C42—471no—
555C2×C42—941no—
556C2×C42C22×D4711yescharacteristic
557#107C22×D4714yes—
558#107C22×D4714yes—
559#106C22×D4714yes—
560#106C22×D4714yes—
561#103—474no—
562#103—474no—
563#102—474no—
564#102—474no—
565#102—474no—
566#102—474no—
567#102—474no—
568#102—474no—
569#97—474no—
570#97C22×D4714yes—
571C4×C8—474no—
572C4×C8—474no—
573C24—471no—
574C24—941no—
575C24—941no—
576C24—941no—
577C2×Q8—24no—
578C2×Q8—82no—
579C2×Q8—472no—
580C2×Q8—941no—
581C2×Q8—942no—
582C2×Q8—942no—
583C2×D4—472no—
584C2×D4—472no—
585C2×D4—472no—
586C2×D4—944no—
587C2×D4—944no—
588C2×D4—944no—
589C2×D4—944no—
590C2×D4—944no—
591C2×D4—941no—
592C2×D4—941no—
593C2×D4—941no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—3762no—
601C2×D4—3762no—
602C2×D4—3762no—
603C2×D4—3762no—
604C2×D4—3762no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—471no—
610C22×C4—471no—
611C22×C4—471no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—941no—
620C22×C4—3762no—
621C22×C4—3762no—
622C22×C4—3762no—
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4C23×D4711yescharacteristic
626SD16—948no—
627SD16—948no—
628D8—948no—
629D8—948no—
630M16—948no—
631C2×C8—472no—
632C2×C8—472no—
633C2×C8—942no—
634C2×C8—942no—
635C2×C8—948no—
636C2×C8#1062535414yes—
637C2×C8#1062535414yes—
638C2×C8C23×D4712yes—
639C2×C8C23×D4712yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—474no—
648C4⋊C4—474no—
649C4⋊C4—944no—
650C4⋊C4—944no—
651C4⋊C4C23×D4712yes—
652C4⋊C4C23×D4712yes—
653C4⋊C4C23×D4712yes—
654C4⋊C4C23×D4712yes—
655C22⋊C4—474no—
656C22⋊C4—474no—
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—472no—
667C42—472no—
668C42—944no—
669C42D4×D4712yes—
670C42C23×D4712yes—
671C23—472no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—942no—
677C23—942no—
678C23—1882no—
679C23—1882no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23C2×D4×D4711yescharacteristic
688Q8—84no—
689Q8—942no—
690Q8—942no—
691Q8—1882no—
692D4—942no—
693D4—942no—
694D4—942no—
695D4—942no—
696D4—942no—
697D4—942no—
698D4—3764no—
699D4—3764no—
700D4—3764no—
701D4—3764no—
702D4—3764no—
703D4—1882no—
704D4—1882no—
705D4—1882no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—472no—
717C2×C4—472no—
718C2×C4—472no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—944no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—3764no—
727C2×C4—3764no—
728C2×C4—3764no—
729C2×C4—1882no—
730C2×C4C2×D4×D4712yes—
731C2×C4C2×D4×D4712yes—
732C2×C4C2×D4×D4711yescharacteristic
733C2×C4C2×#1062535412yes—
734C2×C4C2×#1062535412yes—
735C2×C4C24×D4711yescharacteristic
736C8—942no—
737C8—942no—
738C8C2×#1062535414yes—
739C8C2×#1062535414yes—
740C22—942no—
741C22—942no—
742C22—942no—
743C22—3764no—
744C22—3764no—
745C22—3764no—
746C22—1882no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22—1882no—
755C22—1884no—
756C22#1568967412yes—
757C22#1568992712yes—
758C22#1568993212yes—
759C22C22×D4×D4711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—942no—
767C4—942no—
768C4—942no—
769C4—1882no—
770C4#1568967412yes—
771C4C22×#1062535411yescharacteristic
772C4C22×#1062535411yescharacteristic
773C2—3762no—
774C2—3762no—
775C2—3762no—
776C2—1882no—
777C2#2025407614yesdirect product factor
778C2C2×#1568967411yescharacteristic
779C2C2×#1568992711yescharacteristic
780C2C2×#1568993211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
hypercenterC2×#501D47
hypocenterC47C2×#3179
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#15689747C2semidirect
2. C2×#15689729C2semidirect
3. #20254076C2direct (N × H)
4. C2×#15689512C2semidirect
5. C2×#15689480C2semidirect
6. C2×#15689471C2semidirect
7. C2×#15689377C2semidirect
8. C2×#15689370C2semidirect
9. C2×#15689360C2semidirect
10. C2×#15689353C2semidirect
11. C2×#15689234C2semidirect
12. C2×#15689222C2semidirect
13. C2×#15689210C2semidirect
14. C2×#15689205C2semidirect
15. C2×#15689080C2semidirect
16. C2×C47×#501C2semidirect
24. #15689747C22semidirect
26. #15689729C22semidirect
46. #15689512C22semidirect
47. #15689480C22semidirect
48. #15689471C22semidirect
49. #15689377C22semidirect
50. #15689370C22semidirect
51. #15689360C22semidirect
52. #15689353C22semidirect
53. #15689234C22semidirect
54. #15689222C22semidirect
55. #15689210C22semidirect
56. #15689205C22semidirect
65. #15689080C22semidirect
71. C47×#501C22semidirect
386. C2×#501D47semidirect
399. C2×C47#3179semidirect
438. #501C2×D47semidirect
467. C47C2×#3179semidirect
777. C2#20254076direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897472
C2×#156897292
#202540762
C2×#156895122
C2×#156894802
C2×#156894712
C2×#156893772
C2×#156893702
C2×#156893602
C2×#156893532
C2×#156892342
C2×#156892222
C2×#156892102
C2×#156892052
C2×#156890802
C2×C47×#5012
C2×#317947