Finite Group Databasebeta

← C2×#20254635 #27088461

Subgroups — C2×#20254635 #27088461

Order 12032.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689751C211yesmaximal, characteristic, complemented
2#20254635C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689522C211yesmaximal, characteristic, complemented
5C2×#15689487C211yesmaximal, characteristic, complemented
6C2×#15689469C211yesmaximal, characteristic, complemented
7C2×#15689439C211yesmaximal, characteristic, complemented
8C2×#15689444C211yesmaximal, characteristic, complemented
9C2×#15689444C211yesmaximal, characteristic, complemented
10C2×#15689434C211yesmaximal, characteristic, complemented
11C2×#15689423C211yesmaximal, characteristic, complemented
12C2×#15689423C211yesmaximal, characteristic, complemented
13C2×#15689413C211yesmaximal, characteristic, complemented
14C2×#15689403C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#540C211yesmaximal, characteristic
17#15689751—24no—
18#15689751C2218yescomplemented
19C2×#13094024C2211yescharacteristic
20C2×#13094024C2211yescharacteristic
21C2×#13094023—21no—
22C2×#13094016C2211yescharacteristic
23C2×#13094016C2211yescharacteristic
24C2×#13094015—21no—
25C2×#13094001—21no—
26C2×#13094001—21no—
27C2×#13093983C2211yescharacteristic
28C22×C4⋊Dic47C2211yescharacteristic
29#15689533C2218yescomplemented
30#15689522C2218yescomplemented
31#15689487C2218yescomplemented
32#15689469C2218yescomplemented
33#15689444C2218yescomplemented
34#15689444C2218yescomplemented
35#15689439C2218yescomplemented
36#15689434C2218yescomplemented
37#15689423C2218yescomplemented
38#15689423C2218yescomplemented
39#15689413C2218yescomplemented
40#15689403C2218yescomplemented
41#15689184C2218yescomplemented
42C2×#13093957C2211yescharacteristic
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093945C2211yescharacteristic
53C2×#13093945C2211yescharacteristic
54C2×#13093945C2211yescharacteristic
55C2×#13093945C2211yescharacteristic
56C2×#13093945C2211yescharacteristic
57C2×#13093945C2211yescharacteristic
58C2×#13093945C2211yescharacteristic
59C2×#13093945C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#540—24no—
65C47×#540C2218yes—
66C2×#127×C47C2211yescharacteristic
67C2×#125×C47C2211yescharacteristic
68C2×#123×C47—21no—
69C2×#123×C47—21no—
70C2×#121×C47—21no—
71C2×#121×C47—21no—
72C2×#121×C47C2211yescharacteristic
73C2×#121×C47C2211yescharacteristic
74C2×C4×D4×C47C2211yescharacteristic
75C2×C4×D4×C47C2211yescharacteristic
76C2×#117×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C23×Dic47—21no—
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84#13094024—22no—
85#13094024—22no—
86#13094024C2314yes—
87#13094024C2314yes—
88#13094023—28no—
89#13094016—22no—
90#13094016—22no—
91#13094016C2314yes—
92#13094016C2314yes—
93#13094015—28no—
94#13094001—28no—
95#13094001—28no—
96#13093983—22no—
97#13093983C2314yes—
98C2×C4⋊Dic47—22no—
99C2×C4⋊Dic47—21no—
100C2×C4⋊Dic47—21no—
101C2×C4⋊Dic47—21no—
102C2×C4⋊Dic47C2314yes—
103C2×C4⋊Dic47C2311yescharacteristic
104C2×C4⋊Dic47C2311yescharacteristic
105C2×C4⋊Dic47C2311yescharacteristic
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4—21no—
108C2×Dic47⋊C4—21no—
109C2×Dic47⋊C4—21no—
110C2×Dic47⋊C4—21no—
111C2×C22⋊Dic47—21no—
112C2×C4×Dic47—21no—
113#13093957C2314yes—
114#13093957C2314yes—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093955C2314yes—
118#13093955C2314yes—
119#13093955C2314yes—
120#13093955C2314yes—
121C4⋊(C47⋊C8)C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123#13093945C2314yes—
124#13093945C2314yes—
125#13093945C2314yes—
126#13093945C2314yes—
127#13093945C2314yes—
128#13093945C2314yes—
129#13093945C2314yes—
130#13093945C2314yes—
131C22⋊(C47⋊C8)C2314yes—
132C22⋊(C47⋊C8)C2314yes—
133#13093935C2314yes—
134C4×C47⋊C8C2314yes—
135C22×D4×C47—21no—
136C22×D4×C47—21no—
137C22×D4×C47—21no—
138C22×D4×C47—21no—
139C22×D4×C47C2311yescharacteristic
140C22×D4×C47C2311yescharacteristic
141C23×C4×C47—21no—
142C23×C4×C47—21no—
143C23×C4×C47C2311yescharacteristic
144#127×C47—22no—
145#127×C47C2314yes—
146#125×C47—22no—
147#125×C47C2314yes—
148#123×C47—28no—
149#123×C47—28no—
150#121×C47—22no—
151#121×C47—22no—
152#121×C47—28no—
153#121×C47—28no—
154#121×C47C2314yes—
155#121×C47C2314yes—
156C4×D4×C47—22no—
157C4×D4×C47—22no—
158C4×D4×C47C2314yes—
159C4×D4×C47C2314yes—
160#117×C47D414yes—
161#117×C47C2314yes—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47D411yescharacteristic
165C2×C4⋊C4×C47D411yescharacteristic
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C4⋊C4×C47C2311yescharacteristic
168C2×C22⋊C4×C47—21no—
169C2×C22⋊C4×C47—21no—
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C24×C47—21no—
177C24×C47—21no—
178C24×C47C2×D411yescharacteristic
179C2×D4×C47—24no—
180C2×D4×C47—24no—
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—24no—
184C2×D4×C47—24no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—82no—
190C2×D4×C47—82no—
191C2×D4×C47—82no—
192C2×D4×C47—82no—
193C2×D4×C47C2412yes—
194C2×D4×C47C2412yes—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—24no—
200C22×C4×C47—24no—
201C22×C4×C47—82no—
202C22×C4×C47—82no—
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D412yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2411yescharacteristic
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—24no—
216C22×Dic47—82no—
217C2×Dic94—24no—
218C2×Dic94—24no—
219C2×Dic94—82no—
220C2×Dic94—82no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47C2×D414yes—
226C4⋊C4×C47C2×D414yes—
227C4⋊C4×C47C2412yes—
228C4⋊C4×C47C2412yes—
229C22⋊C4×C47—24no—
230C22⋊C4×C47—24no—
231C22⋊C4×C47—24no—
232C22⋊C4×C47—24no—
233C22⋊C4×C47C2×D414yes—
234C22⋊C4×C47C2×D414yes—
235C42×C47C2×D412yes—
236C42×C47C2×D412yes—
237C42×C47C2412yes—
238C42×C47C2412yes—
239C22⋊Dic47—24no—
240C4⋊Dic47—24no—
241C4⋊Dic47—21no—
242C4⋊Dic47—21no—
243C4⋊Dic47—24no—
244C4⋊Dic47—24no—
245C4⋊Dic47—21no—
246C4⋊Dic47—21no—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255C4×Dic47—24no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8—22no—
258C2×C47⋊C8—22no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8C2412yes—
261C2×C47⋊C8C2412yes—
262C2×C47⋊C8C2412yes—
263C2×C47⋊C8C2412yes—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—42no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47—42no—
274C23×C47—42no—
275C23×C47C22×D412yes—
276C23×C47C22×D411yescharacteristic
277D4×C47—22no—
278D4×C47—22no—
279D4×C47—22no—
280D4×C47—22no—
281D4×C47—42no—
282D4×C47—42no—
283D4×C47—84no—
284D4×C47—84no—
285D4×C47—84no—
286D4×C47—84no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—24no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—42no—
298C2×C4×C47—42no—
299C2×C4×C47—84no—
300C2×C4×C47—84no—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D412yes—
304C2×C4×C47C22×D412yes—
305C2×C4×C47C22×D412yes—
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C472−1+412yes—
308C2×C4×C472−1+412yes—
309C2×C4×C47C2511yescharacteristic
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—42no—
317C2×Dic47—42no—
318C2×Dic47—84no—
319Dic94—84no—
320Dic94—84no—
321C47⋊C8—22no—
322C47⋊C8—22no—
323C47⋊C8—22no—
324C47⋊C8—22no—
325C2×#3241—471nomaximal, Sylow
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—44no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—42no—
336C22×C47—84no—
337C22×C47—84no—
338C22×C47#53612yes—
339C22×C47#57612yes—
340C22×C47#57712yes—
341C22×C47C23×D411yescharacteristic
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—42no—
348C4×C47—42no—
349C4×C47#53612yes—
350C4×C47C2×2−1+411yescharacteristic
351C4×C47C2×2−1+411yescharacteristic
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#544—471no—
357C2×#540D4711yescharacteristic
358#3241—4716no—
359C2×#501—471no—
360C2×#499—471no—
361C2×#490—471no—
362C2×#486—471no—
363C2×#481—471no—
364C2×#482—471no—
365C2×#482—471no—
366C2×#480—471no—
367C2×#478—471no—
368C2×#478—471no—
369C2×#476—471no—
370C2×#474—471no—
371C2×#433—471no—
372C2×C47—42no—
373C2×C47—82no—
374C2×C47—82no—
375C2×C47#324114yescomplemented
376C2×C47C2×#53611yescharacteristic
377C2×C47C2×#57611yescharacteristic
378C2×C47C2×#57711yescharacteristic
379#544—478no—
380#544—944no—
381#540—24no—
382#540C2×D4718yes—
383C2×C4⋊Q8—471no—
384C2×C4⋊Q8—471no—
385C2×C4⋊Q8—941no—
386C2×#127C2×D4711yescharacteristic
387C2×#125—471no—
388C2×#125—471no—
389C2×#125—941no—
390C2×#125C2×D4711yescharacteristic
391C2×#123—21no—
392C2×#123—21no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×#121—21no—
396C2×#121—21no—
397C2×#121C2×D4711yescharacteristic
398C2×#121C2×D4711yescharacteristic
399C2×C4×D4C2×D4711yescharacteristic
400C2×C4×D4C2×D4711yescharacteristic
401C2×#117—471no—
402C2×#117C2×D4711yescharacteristic
403C22×C4⋊C4—471no—
404#501—478no—
405#499—478no—
406#490—478no—
407#486—478no—
408#482—478no—
409#482—478no—
410#481—478no—
411#480—478no—
412#478—478no—
413#478—478no—
414#476—478no—
415#474—478no—
416#433—478no—
417C2×#107—471no—
418C2×#107—471no—
419C2×#107—471no—
420C2×#107—471no—
421C2×#106—471no—
422C2×#106—471no—
423C2×#106—471no—
424C2×#106—471no—
425C2×C4⋊C8—471no—
426C2×C4⋊C8—471no—
427C2×#102—471no—
428C2×#102—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×C22⋊C8—471no—
436C2×C22⋊C8—471no—
437C2×#97—471no—
438C2×C4×C8—471no—
439C47C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—941no—
441C22×Q8—941no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C22×D4711yescharacteristic
447C22×D4C22×D4711yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—941no—
451C23×C4C22×D4711yescharacteristic
452C22×C8—471no—
453C22×C8—471no—
454C22×C8—471no—
455C22×C8—471no—
456C4⋊Q8—474no—
457C4⋊Q8—474no—
458C4⋊Q8—948no—
459C4⋊Q8—942no—
460C4⋊Q8—942no—
461#127—22no—
462#127C22×D4714yes—
463#125—22no—
464#125—474no—
465#125—474no—
466#125—948no—
467#125—942no—
468#125—942no—
469#125C22×D4714yes—
470#123—28no—
471#123—28no—
472C22⋊Q8—948no—
473C22⋊Q8—948no—
474#121—22no—
475#121—22no—
476#121—28no—
477#121—28no—
478#121C22×D4714yes—
479#121C22×D4714yes—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4C22×D4714yes—
483C4×D4C22×D4714yes—
484#117—474no—
485#117—942no—
486#117C22⋊D4714yes—
487#117C22×D4714yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—471no—
491C2×C4⋊C4—471no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—471no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—942no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22⋊D4711yescharacteristic
504C2×C4⋊C4C22⋊D4711yescharacteristic
505C2×C4⋊C4C22×D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4C22⋊D4711yescharacteristic
513C2×C22⋊C4C22⋊D4711yescharacteristic
514C2×C42—941no—
515C2×C42C22×D4711yescharacteristic
516C2×C42C22×D4711yescharacteristic
517#107—474no—
518#107—474no—
519#107—474no—
520#107—474no—
521#106—474no—
522#106—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527#102—474no—
528#102—474no—
529#102—474no—
530#102—474no—
531#102—474no—
532#102—474no—
533#102—474no—
534#102—474no—
535C22⋊C8—474no—
536C22⋊C8—474no—
537#97—474no—
538C4×C8—474no—
539C24—21no—
540C24—21no—
541C24C2×C22⋊D4711yescharacteristic
542C2×Q8—944no—
543C2×Q8—944no—
544C2×Q8—3762no—
545C2×Q8—3762no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C23×D4712yes—
561C2×D4C23×D4712yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—944no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—3762no—
576C22×C4C2×C22⋊D4712yes—
577C22×C4C2×C22⋊D4711yescharacteristic
578C22×C4C2×C22⋊D4711yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580C22×C4C2×C22⋊D4711yescharacteristic
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C23×D4712yes—
583C22×C4C23×D4711yescharacteristic
584C2×C8—472no—
585C2×C8—472no—
586C2×C8—472no—
587C2×C8—472no—
588C2×C8—942no—
589C2×C8—942no—
590C2×C8—942no—
591C2×C8—942no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—472no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—472no—
600C4⋊C4—944no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—941no—
606C4⋊C4—941no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4C2×C22⋊D4714yes—
612C4⋊C4C2×C22⋊D4714yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—944no—
620C22⋊C4C2×C22⋊D4714yes—
621C22⋊C4C2×C22⋊D4714yes—
622C42—944no—
623C42C2×C22⋊D4712yes—
624C42C2×C22⋊D4712yes—
625C42C23×D4712yes—
626C42C23×D4712yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D4712yes—
639C23C22×C22⋊D4711yescharacteristic
640Q8—3764no—
641Q8—3764no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—3764no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4C22×C22⋊D4712yes—
676C2×C4C22×C22⋊D4712yes—
677C2×C4C22×C22⋊D4712yes—
678C2×C4C22×C22⋊D4712yes—
679C2×C4C22×C22⋊D4712yes—
680C2×C4C22×C22⋊D4711yescharacteristic
681C2×C4#1309407112yes—
682C2×C4#1309407112yes—
683C2×C4C24×D4711yescharacteristic
684C8—942no—
685C8—942no—
686C8—942no—
687C8—942no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1568969412yes—
701C22#1568992612yes—
702C22#1568993412yes—
703C22C23×C22⋊D4711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4—1882no—
715C4#1568969412yes—
716C4C2×#1309407111yescharacteristic
717C4C2×#1309407111yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#2025463514yesdirect product factor
722C2C2×#1568969411yescharacteristic
723C2C2×#1568992611yescharacteristic
724C2C2×#1568993411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
Fitting, prime radicalC2×C47×#540C2
socleC23×C47C22×D4
hypercenterC2×#540D47
hypocenterC47C2×#3241
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#15689751C2semidirect
2. #20254635C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689522C2semidirect
5. C2×#15689487C2semidirect
6. C2×#15689469C2semidirect
7. C2×#15689439C2semidirect
8. C2×#15689444C2semidirect
9. C2×#15689444C2semidirect
10. C2×#15689434C2semidirect
11. C2×#15689423C2semidirect
12. C2×#15689423C2semidirect
13. C2×#15689413C2semidirect
14. C2×#15689403C2semidirect
15. C2×#15689184C2semidirect
18. #15689751C22semidirect
29. #15689533C22semidirect
30. #15689522C22semidirect
31. #15689487C22semidirect
32. #15689469C22semidirect
33. #15689444C22semidirect
34. #15689444C22semidirect
35. #15689439C22semidirect
36. #15689434C22semidirect
37. #15689423C22semidirect
38. #15689423C22semidirect
39. #15689413C22semidirect
40. #15689403C22semidirect
41. #15689184C22semidirect
375. C2×C47#3241semidirect
439. C47C2×#3241semidirect
721. C2#20254635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897512
#202546352
C2×#156895332
C2×#156895222
C2×#156894872
C2×#156894692
C2×#156894392
C2×#156894442
C2×#156894342
C2×#156894232
C2×#156894132
C2×#156894032
C2×#156891842
C2×C47×#5402
C2×#324147