Finite Group Databasebeta

← C2×#20256156 #27096059

Subgroups — C2×#20256156 #27096059

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689858C211yesmaximal, characteristic
2#20256156C2116yesmaximal, direct product factor
3C2×#15689489C211yesmaximal, characteristic
4C2×#15689485C211yesmaximal, characteristic, complemented
5C2×#15689480C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689420C211yesmaximal, characteristic, complemented
8C2×#15689410C211yesmaximal, characteristic, complemented
9C2×#15689345C211yesmaximal, characteristic, complemented
10C2×#15689345C211yesmaximal, characteristic, complemented
11C2×#15689323C211yesmaximal, characteristic
12C2×#15689254C211yesmaximal, characteristic, complemented
13C2×#15689228C211yesmaximal, characteristic, complemented
14C2×#15689221C211yesmaximal, characteristic, complemented
15C2×C4×#10625336C211yesmaximal, characteristic, complemented
16C2×C47×#557C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625336C2211yescharacteristic
20#15689858—24no—
21#15689858C2218yes—
22C2×#13094021C2211yescharacteristic
23C2×#13094013—21no—
24C2×#13094012C2211yescharacteristic
25C2×#13094012C2211yescharacteristic
26C2×#13094009—21no—
27C2×#13094009—21no—
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×D188C2211yescharacteristic
30C2×C4×D188C2211yescharacteristic
31C2×#13093986—21no—
32#15689489C2218yes—
33#15689485C2218yescomplemented
34#15689480C2218yescomplemented
35#15689427C2218yescomplemented
36#15689420C2218yescomplemented
37#15689410C2218yescomplemented
38#15689345C2218yescomplemented
39#15689345C2218yescomplemented
40#15689323C2218yes—
41#15689254C2218yescomplemented
42#15689228C2218yescomplemented
43#15689221C2218yescomplemented
44C4×#10625336C2218yescomplemented
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×C4⋊(C47⋊C8)C2211yescharacteristic
49C2×C4⋊(C47⋊C8)C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×#13093948C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093944C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×#13093944C2211yescharacteristic
61C2×#13093935C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#557—24no—
65C47×#557C2218yescomplemented
66C2×C4⋊Q8×C47—21no—
67C2×C4⋊Q8×C47C2211yescharacteristic
68C2×#125×C47—21no—
69C2×#125×C47—21no—
70C2×#125×C47C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×C4×Q8×C47—21no—
73C2×C4×Q8×C47C2211yescharacteristic
74C2×C4×Q8×C47C2211yescharacteristic
75C2×C4×Q8×C47C2211yescharacteristic
76C2×C4×Q8×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×D188—21no—
79C22×D188—21no—
80C22×D188C2311yescharacteristic
81C22×D188C2311yescharacteristic
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C2×#10625337—24no—
85C2×#10625337C2314yes—
86C2×#10625336—24no—
87C2×#10625336—24no—
88C2×#10625336C2314yes—
89C2×#10625336C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93C22×C47⋊C8C2311yescharacteristic
94#13094021—22no—
95#13094021C2314yes—
96#13094013—28no—
97#13094012—22no—
98#13094012—22no—
99#13094012C2314yes—
100#13094012C2314yes—
101#13094009—28no—
102#13094009—28no—
103C4×Dic94—22no—
104C4×Dic94C2314yes—
105C4×D188—22no—
106C4×D188—22no—
107C4×D188C2314yes—
108C4×D188C2314yes—
109#13093986—28no—
110C2×C4⋊Dic47C2311yescharacteristic
111C2×Dic47⋊C4—21no—
112C2×(C2×D47)⋊C4—21no—
113C2×(C2×D47)⋊C4—21no—
114C2×(C2×D47)⋊C4—21no—
115C2×(C2×D47)⋊C4—21no—
116C2×(C2×D47)⋊C4—21no—
117C2×(C2×D47)⋊C4—21no—
118C2×C4×Dic47—21no—
119#13093957C2314yes—
120#13093955C2314yes—
121#13093955C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123C4⋊(C47⋊C8)C2314yes—
124C4⋊(C47⋊C8)C2314yes—
125#13093948C2314yes—
126#13093947C2314yes—
127#13093947C2314yes—
128#13093947C2314yes—
129#13093944C2314yes—
130#13093944C2314yes—
131#13093944C2314yes—
132#13093944C2314yes—
133#13093944C2314yes—
134#13093944C2314yes—
135#13093935C2314yes—
136#13093935C2314yes—
137C4×C47⋊C8C2314yes—
138C22×Q8×C47—21no—
139C22×Q8×C47D411yescharacteristic
140C22×Q8×C47C2311yescharacteristic
141C4⋊Q8×C47—28no—
142C4⋊Q8×C47—22no—
143C4⋊Q8×C47C2314yes—
144#125×C47—28no—
145#125×C47—28no—
146#125×C47—22no—
147#125×C47—22no—
148#125×C47C2314yes—
149#125×C47C2314yes—
150C4×Q8×C47—28no—
151C4×Q8×C47—22no—
152C4×Q8×C47—22no—
153C4×Q8×C47—22no—
154C4×Q8×C47D414yes—
155C4×Q8×C47C2314yes—
156C4×Q8×C47C2314yes—
157C4×Q8×C47C2314yes—
158C4×Q8×C47C2314yes—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47D411yescharacteristic
169C2×C4⋊C4×C47D411yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C42×C47—21no—
174C2×C42×C47—21no—
175C2×C42×C47—21no—
176C2×C42×C47C2311yescharacteristic
177C2×C42×C47C2311yescharacteristic
178C2×C42×C47C2311yescharacteristic
179C23×D47—21no—
180C23×D47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—24no—
183C2×Q8×C47—22no—
184C2×Q8×C47—42no—
185C2×Q8×C47—44no—
186C2×Q8×C47C2×D414yes—
187C2×Q8×C47#4114yes—
188C2×Q8×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×Dic47—21no—
201C22×Dic47—21no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—22no—
206C2×D188—24no—
207C2×D188—21no—
208C2×D188—21no—
209C2×D188—24no—
210C2×D188—44no—
211C2×D188—82no—
212C2×D188C2412yes—
213C2×D188C2412yes—
214C2×C4×D47—24no—
215C2×C4×D47—24no—
216C2×C4×D47—82no—
217C2×C4×D47—82no—
218C2×Dic94—22no—
219C2×Dic94—22no—
220C2×Dic94—21no—
221C2×Dic94C2412yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47C2×D414yes—
234C4⋊C4×C47C2×D414yes—
235C4⋊C4×C47C2×D414yes—
236C4⋊C4×C47C2412yes—
237C4⋊C4×C47C2412yes—
238C4⋊C4×C47C2412yes—
239C42×C47—24no—
240C42×C47—24no—
241C42×C47—24no—
242C42×C47C2×D412yes—
243C42×C47C2×D412yes—
244C42×C47C2×D412yes—
245C42×C47C2412yes—
246C42×C47C2412yes—
247C42×C47C2412yes—
248#10625337—28no—
249#10625336—28no—
250#10625336—28no—
251(C2×D47)⋊C4—24no—
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—
257C4⋊Dic47—21no—
258C4⋊Dic47C2412yes—
259Dic47⋊C4—24no—
260C4×Dic47—24no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C23×C47C22×D411yescharacteristic
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—24no—
279Q8×C47—22no—
280Q8×C47—44no—
281Q8×C47—48no—
282Q8×C47C2×#4114yes—
283C2×C4×C47—24no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—42no—
295C2×C4×C47—42no—
296C2×C4×C47—42no—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D412yes—
299C2×C4×C47C22×D412yes—
300C2×C4×C47C22×D412yes—
301C2×C4×C47C22×D412yes—
302C2×C4×C47C22×D412yes—
303C2×C4×C47C22×D411yescharacteristic
304C2×C4×C47C2×#4112yes—
305C2×C4×C472−1+412yes—
306C2×C4×C47C2511yescharacteristic
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311D188—22no—
312D188—22no—
313D188—22no—
314D188—22no—
315D188—48no—
316D188—42no—
317D188—42no—
318D188—84no—
319C4×D47—84no—
320C4×D47—84no—
321Dic94—22no—
322Dic94—22no—
323Dic94—42no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C2×#3371—471nomaximal, Sylow
329C22×C47#54812yes—
330C22×C47#57512yes—
331C22×C47#57712yes—
332C22×C47C23×D411yescharacteristic
333C2×D47—42no—
334C2×D47—42no—
335C2×D47—42no—
336C2×D47—42no—
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—84no—
340C2×D47—84no—
341C4×C47—24no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—22no—
346C4×C47—22no—
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47—42no—
351C4×C47#54812yes—
352C4×C47C22×#4111yescharacteristic
353C4×C47C2×2−1+411yescharacteristic
354Dic47—42no—
355Dic47—42no—
356C2×#559—471no—
357C2×#557D4711yescharacteristic, complemented
358#3371—4716no—
359C2×#490—471no—
360C2×#489—471no—
361C2×#488—471no—
362C2×#479—471no—
363C2×#478—471no—
364C2×#476—471no—
365C2×#464—471no—
366C2×#464—471no—
367C2×#460—471no—
368C2×#446—471no—
369C2×#441—471no—
370C2×#440—471no—
371C2×C4×SD16—471no—
372C2×C47#337114yescomplemented
373C2×C47C2×#54811yescharacteristic
374C2×C47C2×#57511yescharacteristic
375C2×C47C2×#57711yescharacteristic
376D47—82no—
377D47—82no—
378C22×Q16—471no—
379C22×SD16—471no—
380C22×SD16—471no—
381#559—478no—
382#559—944no—
383#557—24no—
384#557C2×D4718yescomplemented
385C2×C4⋊Q8—21no—
386C2×C4⋊Q8C2×D4711yescharacteristic
387C2×#127—471no—
388C2×#125—21no—
389C2×#125—21no—
390C2×#125C2×D4711yescharacteristic
391C2×#125C2×D4711yescharacteristic
392C2×#124—471no—
393C2×#124—471no—
394C2×#124—941no—
395C2×#123—941no—
396C2×#123—941no—
397C2×C4×Q8—21no—
398C2×C4×Q8—471no—
399C2×C4×Q8C2×D4711yescharacteristic
400C2×C4×Q8C2×D4711yescharacteristic
401C2×C4×Q8C2×D4711yescharacteristic
402C2×C4×Q8C2×D4711yescharacteristic
403C2×C4×D4—471no—
404C2×C4×D4—471no—
405C2×C4×D4—941no—
406#490—478no—
407#489—478no—
408#488—478no—
409#479—478no—
410#478—478no—
411#476—478no—
412#464—478no—
413#464—478no—
414#460—478no—
415#446—478no—
416#441—478no—
417#440—478no—
418C4×SD16—478no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×#97—471no—
436C2×#97—471no—
437C2×C4×C8—471no—
438C47C2×#337111yescharacteristic, complemented, Sylow
439C22×Q8—21no—
440C22×Q8—471no—
441C22×Q8C22⋊D4711yescharacteristic
442C22×Q8C22×D4711yescharacteristic
443C22×D4—471no—
444C22×D4—471no—
445C22×D4—941no—
446C22×D4—941no—
447C23×C4—941no—
448C23×C4—941no—
449C2×Q16—474no—
450C2×Q16—944no—
451C2×SD16—474no—
452C2×SD16—474no—
453C2×SD16—944no—
454C2×SD16—944no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8—471no—
458C22×C8—471no—
459C4⋊Q8—28no—
460C4⋊Q8—22no—
461C4⋊Q8C22×D4714yes—
462#127—474no—
463#127—942no—
464#125—28no—
465#125—28no—
466#125—22no—
467#125—22no—
468#125C22×D4714yes—
469#125C22×D4714yes—
470#124—474no—
471#124—474no—
472#124—948no—
473#124—942no—
474#124—942no—
475#123—948no—
476#123—948no—
477C4×Q8—28no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—474no—
482C4×Q8—942no—
483C4×Q8C22⋊D4714yes—
484C4×Q8C22×D4714yes—
485C4×Q8C22×D4714yes—
486C4×Q8C22×D4714yes—
487C4×Q8C22×D4714yes—
488C4×D4—474no—
489C4×D4—474no—
490C4×D4—948no—
491C4×D4—942no—
492C4×D4—942no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—471no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4C22⋊D4711yescharacteristic
504C2×C4⋊C4C22⋊D4711yescharacteristic
505C2×C4⋊C4C22⋊D4711yescharacteristic
506C2×C4⋊C4C22×D4711yescharacteristic
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—941no—
519C2×C42C22×D4711yescharacteristic
520C2×C42C22×D4711yescharacteristic
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#102—474no—
533#102—474no—
534#102—474no—
535#102—474no—
536#102—474no—
537#102—474no—
538#97—474no—
539#97—474no—
540C4×C8—474no—
541C24—941no—
542C24—941no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—472no—
549C2×Q8—941no—
550C2×Q8—942no—
551C2×Q8—942no—
552C2×Q8#1062535414yes—
553C2×Q8C2×C22⋊D4714yes—
554C2×Q8C23×D4712yes—
555C2×D4—472no—
556C2×D4—472no—
557C2×D4—944no—
558C2×D4—944no—
559C2×D4—941no—
560C2×D4—941no—
561C2×D4—942no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—942no—
565C2×D4—3762no—
566C2×D4—1884no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—944no—
574C22×C4—944no—
575C22×C4—3762no—
576C22×C4—3762no—
577C22×C4C2×C22⋊D4711yescharacteristic
578C22×C4C2×C22⋊D4711yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580C22×C4C2×C22⋊D4711yescharacteristic
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584Q16—948no—
585SD16—948no—
586SD16—948no—
587C2×C8—472no—
588C2×C8—472no—
589C2×C8—472no—
590C2×C8—472no—
591C2×C8—942no—
592C2×C8—942no—
593C2×C8—942no—
594C2×C8—942no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—472no—
607C4⋊C4—944no—
608C4⋊C4—941no—
609C4⋊C4C2×C22⋊D4714yes—
610C4⋊C4C2×C22⋊D4714yes—
611C4⋊C4C2×C22⋊D4714yes—
612C4⋊C4C23×D4712yes—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—944no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—944no—
625C42C2×C22⋊D4712yes—
626C42C2×C22⋊D4712yes—
627C42C2×C22⋊D4712yes—
628C42C23×D4712yes—
629C42C23×D4712yes—
630C42C23×D4712yes—
631C23—942no—
632C23—942no—
633C23—1882no—
634C23—1882no—
635C23—1882no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C22×C22⋊D4711yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—942no—
645Q8—942no—
646Q8—1882no—
647Q8C2×#1062535414yes—
648D4—942no—
649D4—942no—
650D4—942no—
651D4—942no—
652D4—3764no—
653D4—1888no—
654D4—1882no—
655D4—1882no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—3764no—
673C2×C4—3764no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4C22×C22⋊D4712yes—
677C2×C4C22×C22⋊D4712yes—
678C2×C4C22×C22⋊D4712yes—
679C2×C4C22×C22⋊D4712yes—
680C2×C4C22×C22⋊D4712yes—
681C2×C4C22×C22⋊D4712yes—
682C2×C4C22×C22⋊D4711yescharacteristic
683C2×C4C2×#1062535412yes—
684C2×C4#1309407212yes—
685C2×C4C24×D4711yescharacteristic
686C8—942no—
687C8—942no—
688C8—942no—
689C8—942no—
690C22—3764no—
691C22—3764no—
692C22—1882no—
693C22—1882no—
694C22—1882no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22#1568978412yes—
699C22#1568992112yes—
700C22#1568993112yes—
701C22C23×C22⋊D4711yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—1882no—
713C4—1882no—
714C4#1568978412yes—
715C4C22×#1062535411yescharacteristic
716C4C2×#1309407211yescharacteristic
717C2—3762no—
718C2—3762no—
719C2#2025615614yesdirect product factor
720C2C2×#1568978411yescharacteristic
721C2C2×#1568992111yescharacteristic
722C2C2×#1568993111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#557C2
socleC23×C47C22×D4
prime radicalC2×#13094021C22
hypercenterC2×#557D47
hypocenterC47C2×#3371
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #20256156C2direct (N × H)
4. C2×#15689485C2semidirect
5. C2×#15689480C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689420C2semidirect
8. C2×#15689410C2semidirect
9. C2×#15689345C2semidirect
10. C2×#15689345C2semidirect
12. C2×#15689254C2semidirect
13. C2×#15689228C2semidirect
14. C2×#15689221C2semidirect
15. C2×C4×#10625336C2semidirect
16. C2×C47×#557C2semidirect
33. #15689485C22semidirect
34. #15689480C22semidirect
35. #15689427C22semidirect
36. #15689420C22semidirect
37. #15689410C22semidirect
38. #15689345C22semidirect
39. #15689345C22semidirect
41. #15689254C22semidirect
42. #15689228C22semidirect
43. #15689221C22semidirect
44. C4×#10625336C22semidirect
65. C47×#557C22semidirect
357. C2×#557D47semidirect
372. C2×C47#3371semidirect
384. #557C2×D47semidirect
438. C47C2×#3371semidirect
719. C2#20256156direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898582
#202561562
C2×#156894892
C2×#156894852
C2×#156894802
C2×#156894272
C2×#156894202
C2×#156894102
C2×#156893452
C2×#156893232
C2×#156892542
C2×#156892282
C2×#156892212
C2×C4×#106253362
C2×C47×#5572
C2×#337147