Finite Group Databasebeta

← C2×#20257801 #27124089

Subgroups — C2×#20257801 #27124089

Order 12032.

7074 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257801C2132yesmaximal, direct product factor
2C2×#15689875C214yesmaximal, complemented
3C2×#15689855C212yesmaximal, complemented
4C2×Q8×Dic94C212yesmaximal, complemented
5C2×#15689847C211yesmaximal, characteristic, complemented
6C2×#15689841C212yesmaximal, complemented
7C2×Q8×D188C211yesmaximal, characteristic, complemented
8C2×D4×Dic94C211yesmaximal, characteristic, complemented
9C2×#15689786C212yesmaximal, complemented
10C2×#15689745C212yesmaximal, complemented
11C2×#15689742C212yesmaximal, complemented
12C2×#15689739C214yesmaximal, complemented
13C2×#15689699C212yesmaximal, complemented
14C2×#15689696C212yesmaximal, complemented
15C2×#15689678C211yesmaximal, characteristic, complemented
16C2×#15689677C211yesmaximal, characteristic, complemented
17C2×#15689670C211yesmaximal, characteristic
18C2×C47×#556C211yesmaximal, characteristic, complemented
19C22×#10625350C2212yes—
20C23×Dic94C2212yes—
21C22×Q8×D47C2212yes—
22#15689875C22164yescomplemented
23#15689855C22132yescomplemented
24Q8×Dic94C22132yescomplemented
25#15689847C22116yescomplemented
26#15689841C22132yescomplemented
27Q8×D188C22116yescomplemented
28D4×Dic94C22116yescomplemented
29#15689786C22132yescomplemented
30#15689745C22132yescomplemented
31#15689742C22132yescomplemented
32#15689739C22164yescomplemented
33#15689699C22132yescomplemented
34#15689696C22132yescomplemented
35#15689678C22116yescomplemented
36#15689677C22116yescomplemented
37#15689670C22116yes—
38C2×#13094024C2211yescharacteristic
39C2×#13094024C2212yes—
40C2×#13094024C2214yes—
41C2×#13094023C2214yes—
42C2×#13094023C2212yes—
43C2×#13094023C2211yescharacteristic
44C2×#13094023C2211yescharacteristic
45C2×#13094023C2214yes—
46C2×#13094022C2211yescharacteristic
47C2×#13094020C2211yescharacteristic
48C2×#13094019C2214yes—
49C2×#13094018C2214yes—
50C2×#13094017C2214yes—
51C2×#13094015C2212yes—
52C2×#13094014C2212yes—
53C2×#13094013C2212yes—
54C2×#13094012C2214yes—
55C2×#13094010C2212yes—
56C2×#13094010C2214yes—
57C2×#13094010C2214yes—
58C2×#13094009C2214yes—
59C2×#13094008C2214yes—
60C2×#13094008C2214yes—
61C2×#13094006C2214yes—
62C2×#13094004C2212yes—
63C2×#13094004C2212yes—
64C2×#13094004C2214yes—
65C2×#13094004C2211yescharacteristic
66C2×#13094004C2212yes—
67C2×#13094003C2212yes—
68C2×#13094002C2214yes—
69C2×#13094002C2212yes—
70C2×#13094001C2214yes—
71C2×#13094001C2214yes—
72C2×#13094000C2211yescharacteristic
73C2×#13094000C2212yes—
74C2×#13093999C2211yescharacteristic
75C2×#13093997C2212yes—
76C2×#13093995C2211yescharacteristic
77C2×Q8×Dic47C2212yes—
78C2×Q8×Dic47C2212yes—
79C2×C4×Dic94C2211yescharacteristic
80C2×C4×Dic94C2212yes—
81C2×C4×Dic94C2214yes—
82C2×#13093989C2212yes—
83C2×C4×D188C2211yescharacteristic
84C2×C4×D188C2212yes—
85C2×D4×Dic47C2212yes—
86C2×C4×C22⋊D47C2212yes—
87C2×(C22⋊D47)⋊C4C2214yes—
88C2×#13093982C2212yes—
89C2×#13093982C2212yes—
90C2×#13093981C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#556C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#126×C47C2214yes—
95C2×#124×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×Q8×C47C2212yes—
99C2×C4×D4×C47C2211yescharacteristic
100C2×#117×C47C2212yes—
101C2×#10625350—48no—
102C2×#10625350C23116yes—
103C22×Dic94—48no—
104C22×Dic94C2312yes—
105C22×Dic94C2312yes—
106C22×Dic94C2311yescharacteristic
107C22×Dic94C23116yes—
108C22×Dic94C2314yes—
109C22×Dic94C2314yes—
110C22×Dic94C2312yes—
111C2×Q8×D47—48no—
112C2×Q8×D47C23116yes—
113C22×D188C2311yescharacteristic
114C22×D188C2312yes—
115C22×C22⋊D47C2312yes—
116C22×C22⋊D47C2312yes—
117C22×C22⋊D47C2312yes—
118C23×Dic47C2314yes—
119C22×C4×D47C2311yescharacteristic
120C22×C4×D47C2311yescharacteristic
121C22×C4×D47C2311yescharacteristic
122C22×C4×D47C2312yes—
123C22×C4×D47C2314yes—
124#13094024C23116yes—
125#13094024C2318yes—
126#13094024C23132yes—
127#13094023C23132yes—
128#13094023C23116yes—
129#13094023C2318yes—
130#13094023C2318yes—
131#13094023C23132yes—
132#13094022C2318yes—
133#13094020C2318yes—
134#13094019C23132yes—
135#13094018C23132yes—
136#13094017C23132yes—
137#13094015C23116yes—
138#13094014C23116yes—
139#13094013C23116yes—
140#13094012C23132yes—
141#13094010C23132yes—
142#13094010C23132yes—
143#13094010C23116yes—
144#13094009C23132yes—
145#13094008C23132yes—
146#13094008C23132yes—
147#13094006C23132yes—
148#13094004C23132yes—
149#13094004C23116yes—
150#13094004C23116yes—
151#13094004C2318yes—
152#13094004C23116yes—
153#13094003C23116yes—
154#13094002C23116yes—
155#13094002C23132yes—
156#13094001C23132yes—
157#13094001C23132yes—
158#13094000C23116yes—
159#13094000C2318yes—
160#13093999C2318yes—
161#13093997C23116yes—
162#13093995C2318yes—
163Q8×Dic47C23116yes—
164Q8×Dic47C23116yes—
165C4×Dic94C23132yes—
166C4×Dic94C2318yes—
167C4×Dic94C23116yes—
168#13093989C23116yes—
169C4×D188C23116yes—
170C4×D188C2318yes—
171D4×Dic47C23116yes—
172C4×C22⋊D47C23116yes—
173(C22⋊D47)⋊C4C23132yes—
174#13093982C23116yes—
175#13093982C23116yes—
176#13093981C23116yes—
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2312yes—
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2314yes—
182C2×C4⋊Dic47C2312yes—
183C2×C4⋊Dic47C2314yes—
184C2×C4⋊Dic47C2314yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2314yes—
190C2×Dic47⋊C4C2312yes—
191C2×Dic47⋊C4C2312yes—
192C2×Dic47⋊C4C2314yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2314yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2314yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2314yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2314yes—
208C2×C4×Dic47C2314yes—
209C42×D47C2318yes—
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C22×D4×C47C2311yescharacteristic
213C23×C4×C47C2312yes—
214C4⋊Q8×C47C2318yes—
215#126×C47C23132yes—
216#124×C47C23116yes—
217C22⋊Q8×C47C23116yes—
218C4×Q8×C47C23116yes—
219C4×Q8×C47C2318yes—
220C4×D4×C47C2318yes—
221#117×C47C23116yes—
222C2×C4⋊C4×C47C2311yescharacteristic
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2314yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C22⋊C4×C47C2314yes—
229C2×C22⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C42×C47C2314yes—
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2312yes—
234C24×C47C2412yes—
235C23×D47C2412yes—
236C23×D47C2411yescharacteristic
237C2×Q8×C47—24no—
238C2×Q8×C47—28no—
239C2×Q8×C47C2414yes—
240C2×Q8×C47C2418yes—
241C2×D4×C47—24no—
242C2×D4×C47C2414yes—
243C22×C4×C47—28no—
244C22×C4×C47C2412yes—
245C22×C4×C47C2412yes—
246C22×C4×C47C2411yescharacteristic
247C22×C4×C47C2414yes—
248C22×C4×C47C2412yes—
249C22×C4×C47C2418yes—
250C22×C4×C47C2411yescharacteristic
251C22×C4×C47C2411yescharacteristic
252C2×C22⋊D47—28no—
253C2×C22⋊D47—44no—
254C2×C22⋊D47—44no—
255C2×C22⋊D47C2418yes—
256C2×C22⋊D47C2418yes—
257C2×C22⋊D47C2418yes—
258C22×Dic47—48no—
259C22×Dic47C2412yes—
260C22×Dic47C2411yescharacteristic
261C22×Dic47C2412yes—
262C22×Dic47C2411yescharacteristic
263C22×Dic47C2412yes—
264C22×Dic47C2414yes—
265C22×Dic47C24116yes—
266C22×Dic47C2411yescharacteristic
267Q8×D47—432no—
268#10625350—432no—
269C2×D188—24no—
270C2×D188—44no—
271C2×D188C2414yes—
272C2×D188C2418yes—
273C2×C4×D47—28no—
274C2×C4×D47—24no—
275C2×C4×D47—24no—
276C2×C4×D47—24no—
277C2×C4×D47—48no—
278C2×C4×D47C2414yes—
279C2×C4×D47C2414yes—
280C2×C4×D47C2414yes—
281C2×C4×D47C2418yes—
282C2×C4×D47C24116yes—
283C2×Dic94—28no—
284C2×Dic94—24no—
285C2×Dic94—28no—
286C2×Dic94—432no—
287C2×Dic94—48no—
288C2×Dic94—48no—
289C2×Dic94—44no—
290C2×Dic94C2418yes—
291C2×Dic94C2418yes—
292C2×Dic94C2414yes—
293C2×Dic94C24116yes—
294C2×Dic94C24116yes—
295C2×Dic94C2418yes—
296C4⋊C4×C47C2414yes—
297C4⋊C4×C47C2418yes—
298C4⋊C4×C47C2414yes—
299C4⋊C4×C47C24116yes—
300C4⋊C4×C47C2418yes—
301C4⋊C4×C47C2418yes—
302C22⋊C4×C47C24116yes—
303C22⋊C4×C47C2418yes—
304C22⋊C4×C47C24116yes—
305C42×C47C24116yes—
306C42×C47C2414yes—
307C42×C47C2418yes—
308C22⋊Dic47C2418yes—
309C22⋊Dic47C24116yes—
310(C2×D47)⋊C4C2418yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C24116yes—
313(C2×D47)⋊C4C24116yes—
314(C2×D47)⋊C4C24116yes—
315(C2×D47)⋊C4C2418yes—
316(C2×D47)⋊C4C2418yes—
317(C2×D47)⋊C4C24116yes—
318C4⋊Dic47C2414yes—
319C4⋊Dic47C2418yes—
320C4⋊Dic47C2418yes—
321C4⋊Dic47C2414yes—
322C4⋊Dic47C24116yes—
323C4⋊Dic47C2418yes—
324C4⋊Dic47C24116yes—
325C4⋊Dic47C24116yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C2418yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C2418yes—
330Dic47⋊C4C24116yes—
331Dic47⋊C4C2418yes—
332Dic47⋊C4C2418yes—
333Dic47⋊C4C24116yes—
334C4×Dic47C2414yes—
335C4×Dic47C2414yes—
336C4×Dic47C2414yes—
337C4×Dic47C2418yes—
338C4×Dic47C24116yes—
339C4×Dic47C24116yes—
340C23×C47—24no—
341C23×C47—24no—
342C23×C47—24no—
343C23×C47C2514yes—
344C23×C47C2511yescharacteristic
345C22×D47—24no—
346C22×D47—22no—
347C22×D47—22no—
348C22×D47—22no—
349C22×D47—24no—
350C22×D47—24no—
351C22×D47C2514yes—
352C22×D47C2512yes—
353Q8×C47—28no—
354Q8×C47—216no—
355D4×C47—28no—
356C2×C4×C47—24no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—22no—
360C2×C4×C47—28no—
361C2×C4×C47—216no—
362C2×C4×C47H(5,𝔽2)14yes—
363C2×C4×C472−1+414yes—
364C2×C4×C47C2518yes—
365C2×C4×C47C2512yes—
366C2×C4×C47C2514yes—
367C2×C4×C47C2514yes—
368C2×C4×C47C2514yes—
369C2×C4×C47C2512yes—
370C2×C4×C47C2512yes—
371C22⋊D47—216no—
372C22⋊D47—48no—
373C22⋊D47—48no—
374C2×Dic47—28no—
375C2×Dic47—24no—
376C2×Dic47—24no—
377C2×Dic47—22no—
378C2×Dic47—24no—
379C2×Dic47—22no—
380C2×Dic47—416no—
381C2×Dic472−1+414yes—
382C2×Dic47C2514yes—
383C2×Dic47C2512yes—
384C2×Dic47C2512yes—
385C2×Dic47C2514yes—
386C2×Dic47C2514yes—
387C2×Dic47C2518yes—
388C2×Dic47C2512yes—
389D188—28no—
390D188—48no—
391C4×D47—28no—
392C4×D47—216no—
393C4×D47—28no—
394C4×D47—28no—
395C4×D47—416no—
396Dic94—28no—
397Dic94—216no—
398Dic94—216no—
399Dic94—416no—
400Dic94—48no—
401Dic94—416no—
402C2×#3550—471nomaximal, Sylow
403C22×C47—24no—
404C22×C47—24no—
405C22×C47—24no—
406C22×C47—48no—
407C22×C47C2×H(5,𝔽2)12yes—
408C22×C47C2×2−1+412yes—
409C22×C47C2×2−1+412yes—
410C22×C47C2611yescharacteristic
411C2×D47—24no—
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—24no—
416C2×D47—24no—
417C2×D47—48no—
418C2×D47—44no—
419C4×C47—24no—
420C4×C47—24no—
421C4×C47—24no—
422C4×C47—22no—
423C4×C47—28no—
424C4×C47C2×H(5,𝔽2)14yes—
425C4×C47C2×2−1+414yes—
426Dic47—28no—
427Dic47—24no—
428Dic47—24no—
429Dic47—22no—
430Dic47—24no—
431Dic47—22no—
432Dic47C2×2−1+414yes—
433#3550—4732no—
434C2×#563—474no—
435C2×#559—472no—
436C2×Q82—472no—
437C2×#556—471no—
438C2×#556—472no—
439C2×#556D4711yescharacteristic, complemented
440C2×D4×Q8—472no—
441C2×D4×Q8—471no—
442C2×D4×Q8—471no—
443C2×#542—474no—
444C2×#542—472no—
445C2×#542—472no—
446C2×#536—472no—
447C2×#536—472no—
448C2×#533—471no—
449C2×#533—471no—
450C2×#532—471no—
451C2×C47—44no—
452C2×C47#355014yescomplemented
453C2×C47C22×H(5,𝔽2)11yescharacteristic
454C2×C47C22×2−1+411yescharacteristic
455C2×C47C22×2−1+411yescharacteristic
456D47—44no—
457D47—42no—
458C22×#41—472no—
459C23×Q8—472no—
460C23×Q8—472no—
461#563—4764no—
462#559—4732no—
463Q82—4732no—
464#556—4716no—
465#556—4732no—
466#556C2×D47116yescomplemented
467D4×Q8—4732no—
468D4×Q8—4716no—
469D4×Q8—4716no—
470#542—4764no—
471#542—4732no—
472#542—4732no—
473#536—4732no—
474#536—4732no—
475#533—4716no—
476#533—4716no—
477#532—4716no—
478C2×C4⋊Q8—471no—
479C2×C4⋊Q8—471no—
480C2×C4⋊Q8—471no—
481C2×C4⋊Q8—474no—
482C2×C4⋊Q8—474no—
483C2×C4⋊Q8—472no—
484C2×C4⋊Q8—471no—
485C2×C4⋊Q8—474no—
486C2×C4⋊Q8—472no—
487C2×C4⋊Q8C2×D4711yescharacteristic
488C2×#127—471no—
489C2×#126—474no—
490C2×#126—474no—
491C2×#126—474no—
492C2×#126C2×D4714yes—
493C2×#125—472no—
494C2×#125—472no—
495C2×#124—472no—
496C2×#124—472no—
497C2×#124—474no—
498C2×#124—474no—
499C2×#124—474no—
500C2×#124C2×D4712yes—
501C2×#123—474no—
502C2×#123—474no—
503C2×#123—474no—
504C2×#123—474no—
505C2×C22⋊Q8—471no—
506C2×C22⋊Q8—472no—
507C2×C22⋊Q8—472no—
508C2×C22⋊Q8—472no—
509C2×C22⋊Q8—471no—
510C2×C22⋊Q8—472no—
511C2×C22⋊Q8—472no—
512C2×C22⋊Q8—472no—
513C2×C22⋊Q8—474no—
514C2×C22⋊Q8—474no—
515C2×C22⋊Q8—474no—
516C2×C22⋊Q8—474no—
517C2×C22⋊Q8C2×D4712yes—
518C2×#121—471no—
519C2×#121—471no—
520C2×#121—472no—
521C2×C4×Q8—472no—
522C2×C4×Q8—472no—
523C2×C4×Q8—472no—
524C2×C4×Q8—471no—
525C2×C4×Q8—472no—
526C2×C4×Q8—474no—
527C2×C4×Q8C2×D4711yescharacteristic
528C2×C4×Q8C2×D4712yes—
529C2×C4×D4—472no—
530C2×C4×D4—472no—
531C2×C4×D4—474no—
532C2×C4×D4—471no—
533C2×C4×D4—472no—
534C2×C4×D4C2×D4711yescharacteristic
535C2×#117—472no—
536C2×#117—472no—
537C2×#117—472no—
538C2×#117C2×D4712yes—
539C22×C42—471no—
540C47C2×#355011yescharacteristic, complemented, Sylow
541C2×#41—4716no—
542C2×#41—1888no—
543C22×Q8—4716no—
544C22×Q8—472no—
545C22×Q8—472no—
546C22×Q8—471no—
547C22×Q8—474no—
548C22×Q8—474no—
549C22×Q8—472no—
550C22×Q8—4716no—
551C22×Q8—1888no—
552C22×Q8—1888no—
553C22×Q8C22×D4712yes—
554C22×Q8C22×D4711yescharacteristic
555C22×D4—472no—
556C22×D4—472no—
557C22×D4—472no—
558C22×D4—471no—
559C22×D4—472no—
560C22×D4C22×D4711yescharacteristic
561C23×C4—474no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—472no—
565C23×C4—471no—
566C23×C4—474no—
567C23×C4C22×D4712yes—
568C4⋊Q8—478no—
569C4⋊Q8—478no—
570C4⋊Q8—478no—
571C4⋊Q8—4732no—
572C4⋊Q8—4732no—
573C4⋊Q8—4716no—
574C4⋊Q8—478no—
575C4⋊Q8—4732no—
576C4⋊Q8—4716no—
577C4⋊Q8C22×D4718yes—
578#127—478no—
579#126—4732no—
580#126—4732no—
581#126—4732no—
582#126C22×D47132yes—
583#125—4716no—
584#125—4716no—
585#124—4716no—
586#124—4716no—
587#124—4732no—
588#124—4732no—
589#124—4732no—
590#124C22×D47116yes—
591#123—4732no—
592#123—4732no—
593#123—4732no—
594#123—4732no—
595C22⋊Q8—478no—
596C22⋊Q8—4716no—
597C22⋊Q8—4716no—
598C22⋊Q8—4716no—
599C22⋊Q8—478no—
600C22⋊Q8—4716no—
601C22⋊Q8—4716no—
602C22⋊Q8—4716no—
603C22⋊Q8—4732no—
604C22⋊Q8—4732no—
605C22⋊Q8—4732no—
606C22⋊Q8—4732no—
607C22⋊Q8C22×D47116yes—
608#121—478no—
609#121—478no—
610#121—4716no—
611C4×Q8—4716no—
612C4×Q8—4716no—
613C4×Q8—4716no—
614C4×Q8—478no—
615C4×Q8—4716no—
616C4×Q8—4732no—
617C4×Q8C22×D4718yes—
618C4×Q8C22×D47116yes—
619C4×D4—4716no—
620C4×D4—4716no—
621C4×D4—4732no—
622C4×D4—478no—
623C4×D4—4716no—
624C4×D4C22×D4718yes—
625#117—4716no—
626#117—4716no—
627#117—4716no—
628#117C22×D47116yes—
629C2×C4⋊C4—471no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—472no—
634C2×C4⋊C4—472no—
635C2×C4⋊C4—472no—
636C2×C4⋊C4—471no—
637C2×C4⋊C4—472no—
638C2×C4⋊C4—474no—
639C2×C4⋊C4—474no—
640C2×C4⋊C4—474no—
641C2×C4⋊C4—474no—
642C2×C4⋊C4—472no—
643C2×C4⋊C4—474no—
644C2×C4⋊C4—472no—
645C2×C4⋊C4C22×D4712yes—
646C2×C4⋊C4C22×D4712yes—
647C2×C4⋊C4C22×D4711yescharacteristic
648C2×C4⋊C4C22×D4711yescharacteristic
649C2×C4⋊C4C22×D4712yes—
650C2×C4⋊C4C22×D4714yes—
651C2×C22⋊C4—472no—
652C2×C22⋊C4—474no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—474no—
655C2×C22⋊C4—472no—
656C2×C22⋊C4—474no—
657C2×C22⋊C4—472no—
658C2×C22⋊C4—472no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4C22×D4714yes—
662C2×C22⋊C4C22×D4714yes—
663C2×C22⋊C4C22×D4712yes—
664C2×C42—474no—
665C2×C42—472no—
666C2×C42—474no—
667C2×C42—471no—
668C2×C42—471no—
669C2×C42—471no—
670C2×C42—478no—
671C2×C42C22×D4712yes—
672C2×C42C22×D4714yes—
673C2×C42C22×D4711yescharacteristic
674C24—472no—
675C24—471no—
676C24C23×D4712yes—
677#41—18832no—
678C2×Q8—24no—
679C2×Q8—28no—
680C2×Q8—478no—
681C2×Q8—478no—
682C2×Q8—474no—
683C2×Q8—4716no—
684C2×Q8—4716no—
685C2×Q8—478no—
686C2×Q8—948no—
687C2×Q8—948no—
688C2×Q8—944no—
689C2×Q8—1888no—
690C2×Q8—1888no—
691C2×Q8—1884no—
692C2×Q8—18832no—
693C2×Q8—18832no—
694C2×Q8C23×D4718yes—
695C2×Q8C23×D4714yes—
696C2×D4—24no—
697C2×D4—478no—
698C2×D4—478no—
699C2×D4—478no—
700C2×D4—474no—
701C2×D4—478no—
702C2×D4—948no—
703C2×D4—944no—
704C2×D4—1884no—
705C2×D4—1884no—
706C2×D4—1884no—
707C2×D4C23×D4714yes—
708C22×C4—28no—
709C22×C4—471no—
710C22×C4—472no—
711C22×C4—471no—
712C22×C4—472no—
713C22×C4—471no—
714C22×C4—472no—
715C22×C4—474no—
716C22×C4—4716no—
717C22×C4—474no—
718C22×C4—474no—
719C22×C4—474no—
720C22×C4—478no—
721C22×C4—4716no—
722C22×C4—944no—
723C22×C4—948no—
724C22×C4—944no—
725C22×C4—944no—
726C22×C4—1888no—
727C22×C4—1888no—
728C22×C4C23×D4718yes—
729C22×C4C23×D4714yes—
730C22×C4C23×D4711yescharacteristic
731C22×C4C23×D4712yes—
732C22×C4C23×D4712yes—
733C22×C4C23×D4712yes—
734C22×C4C23×D4711yescharacteristic
735C22×C4C23×D4711yescharacteristic
736C4⋊C4—478no—
737C4⋊C4—478no—
738C4⋊C4—478no—
739C4⋊C4—478no—
740C4⋊C4—478no—
741C4⋊C4—4716no—
742C4⋊C4—4716no—
743C4⋊C4—478no—
744C4⋊C4—474no—
745C4⋊C4—478no—
746C4⋊C4—478no—
747C4⋊C4—474no—
748C4⋊C4—4716no—
749C4⋊C4—4716no—
750C4⋊C4—4716no—
751C4⋊C4—478no—
752C4⋊C4C23×D4718yes—
753C4⋊C4C23×D4718yes—
754C4⋊C4C23×D4714yes—
755C4⋊C4C23×D4714yes—
756C4⋊C4C23×D4718yes—
757C4⋊C4C23×D47116yes—
758C22⋊C4—478no—
759C22⋊C4—4716no—
760C22⋊C4—478no—
761C22⋊C4—4716no—
762C22⋊C4—478no—
763C22⋊C4—4716no—
764C22⋊C4—478no—
765C22⋊C4—478no—
766C22⋊C4—4716no—
767C22⋊C4—4716no—
768C22⋊C4C23×D47116yes—
769C22⋊C4C23×D47116yes—
770C22⋊C4C23×D4718yes—
771C42—474no—
772C42—474no—
773C42—474no—
774C42—4716no—
775C42—478no—
776C42—4716no—
777C42C23×D4714yes—
778C42C23×D4718yes—
779C42C23×D47116yes—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—474no—
784C23—472no—
785C23—944no—
786C23—942no—
787C23—942no—
788C23—944no—
789C23—942no—
790C23—944no—
791C23C24×D4714yes—
792C23C24×D4711yescharacteristic
793Q8—28no—
794Q8—216no—
795Q8—9416no—
796Q8—948no—
797Q8—9416no—
798Q8—18816no—
799Q8—18816no—
800Q8—1888no—
801D4—28no—
802D4—9416no—
803D4—948no—
804D4—1888no—
805D4—1888no—
806D4—1888no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—216no—
813C2×C4—474no—
814C2×C4—472no—
815C2×C4—474no—
816C2×C4—472no—
817C2×C4—474no—
818C2×C4—472no—
819C2×C4—474no—
820C2×C4—478no—
821C2×C4—948no—
822C2×C4—942no—
823C2×C4—944no—
824C2×C4—948no—
825C2×C4—944no—
826C2×C4—944no—
827C2×C4—942no—
828C2×C4—9416no—
829C2×C4—948no—
830C2×C4—948no—
831C2×C4—18816no—
832C2×C4—18816no—
833C2×C4#1309407014yes—
834C2×C4#1309407114yes—
835C2×C4C24×D4718yes—
836C2×C4C24×D4712yes—
837C2×C4C24×D4714yes—
838C2×C4C24×D4714yes—
839C2×C4C24×D4714yes—
840C2×C4C24×D4712yes—
841C2×C4C24×D4712yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—48no—
846C22—944no—
847C22—942no—
848C22—942no—
849C22—944no—
850C22—942no—
851C22—944no—
852C22—1888no—
853C22—1884no—
854C22C2×#1309407012yes—
855C222−1+4×D4712yes—
856C22C2×#1309407112yes—
857C22C25×D4711yescharacteristic
858C4—24no—
859C4—24no—
860C4—22no—
861C4—24no—
862C4—28no—
863C4—474no—
864C4—942no—
865C4—944no—
866C4—948no—
867C4—944no—
868C4—944no—
869C4—942no—
870C4C2×#1309407014yes—
871C4C2×#1309407114yes—
872C2—44no—
873C2—1884no—
874C2—1882no—
875C2#2025780114yesdirect product factor
876C2C22×#1309407011yescharacteristic
877C2C2×2−1+4×D4711yescharacteristic
878C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#556C2
socleC23×C47C25
prime radicalC2×#15689670C2
hypercenterC2×#556D47
hypocenterC47C2×#3550
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20257801C2direct (N × H)
2. C2×#15689875C2semidirect
3. C2×#15689855C2semidirect
4. C2×Q8×Dic94C2semidirect
5. C2×#15689847C2semidirect
6. C2×#15689841C2semidirect
7. C2×Q8×D188C2semidirect
8. C2×D4×Dic94C2semidirect
9. C2×#15689786C2semidirect
10. C2×#15689745C2semidirect
11. C2×#15689742C2semidirect
12. C2×#15689739C2semidirect
13. C2×#15689699C2semidirect
14. C2×#15689696C2semidirect
15. C2×#15689678C2semidirect
16. C2×#15689677C2semidirect
18. C2×C47×#556C2semidirect
22. #15689875C22semidirect
23. #15689855C22semidirect
24. Q8×Dic94C22semidirect
25. #15689847C22semidirect
26. #15689841C22semidirect
27. Q8×D188C22semidirect
28. D4×Dic94C22semidirect
29. #15689786C22semidirect
30. #15689745C22semidirect
31. #15689742C22semidirect
32. #15689739C22semidirect
33. #15689699C22semidirect
34. #15689696C22semidirect
35. #15689678C22semidirect
36. #15689677C22semidirect
92. C47×#556C22semidirect
439. C2×#556D47semidirect
452. C2×C47#3550semidirect
466. #556C2×D47semidirect
540. C47C2×#3550semidirect
875. C2#20257801direct (N × H)

Maximal subgroups

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

subgroupindex
#202578012
C2×#156898752
C2×#156898552
C2×Q8×Dic942
C2×#156898472
C2×#156898412
C2×Q8×D1882
C2×D4×Dic942
C2×#156897862
C2×#156897452
C2×#156897422
C2×#156897392
C2×#156896992
C2×#156896962
C2×#156896782
C2×#156896772
C2×#156896702
C2×C47×#5562
C2×#355047