Finite Group Databasebeta

← C2×#20257007 #27123373

Subgroups — C2×#20257007 #27123373

Order 12032.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257007C2132yesmaximal, direct product factor
2C2×#15689851C211yesmaximal, characteristic, complemented
3C2×#15689841C212yesmaximal, complemented
4C2×#15689814C212yesmaximal, complemented
5C2×#15689809C214yesmaximal, complemented
6C2×#15689788C211yesmaximal, characteristic, complemented
7C2×#15689781C212yesmaximal, complemented
8C2×#15689778C211yesmaximal, characteristic, complemented
9C2×#15689775C212yesmaximal, complemented
10C2×#15689678C211yesmaximal, characteristic, complemented
11C2×#15689675C212yesmaximal, complemented
12C2×#15689656C214yesmaximal, complemented
13C2×#15689652C212yesmaximal, complemented
14C2×C4×#10625354C211yesmaximal, characteristic, complemented
15C2×#15689591C212yesmaximal, complemented
16C2×C4×#10625352C211yesmaximal, characteristic, complemented
17C2×C4×Q8×D47C212yesmaximal, complemented
18C2×C47×#556C211yesmaximal, characteristic, complemented
19C22×#10625354C2211yescharacteristic
20C22×#10625350C2212yes—
21C22×#10625352C2211yescharacteristic
22C22×Q8×D47C2212yes—
23#15689851C22116yescomplemented
24#15689841C22132yescomplemented
25#15689814C22132yescomplemented
26#15689809C22164yescomplemented
27#15689788C22116yescomplemented
28#15689781C22132yescomplemented
29#15689778C22116yescomplemented
30#15689775C22132yescomplemented
31#15689678C22116yescomplemented
32#15689675C22132yescomplemented
33C2×#13094024C2211yescharacteristic
34C2×#13094023C2212yes—
35C2×#13094022C2212yes—
36#15689656C22164yescomplemented
37#15689652C22132yescomplemented
38C2×#13094018C2214yes—
39C2×#13094017C2214yes—
40C2×#13094016C2212yes—
41C2×#13094015C2212yes—
42C2×#13094014C2214yes—
43C2×#13094014C2214yes—
44C2×#13094010C2214yes—
45C2×#13094009C2214yes—
46C2×#13094006C2214yes—
47C2×#13094006C2214yes—
48C2×#13094004C2212yes—
49C2×#13094003C2212yes—
50C2×#13094002C2214yes—
51C2×#13094001C2214yes—
52C2×#13094000C2212yes—
53C2×#13094000C2212yes—
54C2×#13093997C2214yes—
55C2×#13093995C2212yes—
56C4×#10625354C22116yescomplemented
57#15689591C22132yescomplemented
58C4×#10625352C22116yescomplemented
59C2×Q8×Dic47C2212yes—
60C2×Q8×Dic47C2211yescharacteristic
61C2×C4×Dic94C2212yes—
62C2×C4×Dic94C2214yes—
63C2×C4×Dic94C2211yescharacteristic
64C2×#13093989C2211yescharacteristic
65C2×#13093989C2214yes—
66C2×#13093989C2212yes—
67C2×#13093989C2212yes—
68C4×Q8×D47C22132yescomplemented
69C2×C4×D188C2211yescharacteristic
70C2×C4×D188C2212yes—
71C2×D4×Dic47C2211yescharacteristic
72C2×#13093986C2211yescharacteristic
73C2×#13093986C2212yes—
74C2×#13093986C2212yes—
75C2×C4×C22⋊D47C2212yes—
76C2×(C22⋊D47)⋊C4C2212yes—
77C2×(C22⋊D47)⋊C4C2214yes—
78C2×(C22⋊D47)⋊C4C2214yes—
79C2×#13093982C2211yescharacteristic
80C2×#13093982C2212yes—
81C2×#13093982C2211yescharacteristic
82C2×#13093982C2212yes—
83C2×#13093981C2214yes—
84C2×#13093980C2212yes—
85C2×#13093980C2214yes—
86C2×C4⋊C4×D47C2214yes—
87C2×C4⋊C4×D47C2212yes—
88C22×C4×Dic47C2212yes—
89C2×C42×D47C2214yes—
90C2×C42×D47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#556C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#126×C47C2214yes—
95C2×#124×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×D4×C47C2211yescharacteristic
100C2×#117×C47C2212yes—
101C2×#10625354—28no—
102C2×#10625354C2318yes—
103C2×#10625350—216no—
104C2×#10625350C23116yes—
105C2×#10625352—28no—
106C2×#10625352C2318yes—
107C22×Dic94C2312yes—
108C22×Dic94C2314yes—
109C22×Dic94C2311yescharacteristic
110C2×Q8×D47—216no—
111C2×Q8×D47C23116yes—
112C22×D188C2312yes—
113C22×D188C2311yescharacteristic
114C22×C22⋊D47C2314yes—
115C22×C22⋊D47C2312yes—
116C23×Dic47C2312yes—
117C23×Dic47C2312yes—
118C22×C4×D47C2312yes—
119C22×C4×D47C2314yes—
120C22×C4×D47C2312yes—
121C22×C4×D47C2314yes—
122C22×C4×D47C2312yes—
123C22×C4×D47C2311yescharacteristic
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2311yescharacteristic
126#13094024C2318yes—
127#13094023C23116yes—
128#13094022C23116yes—
129#13094018C23132yes—
130#13094017C23132yes—
131#13094016C23116yes—
132#13094015C23116yes—
133#13094014C23132yes—
134#13094014C23132yes—
135#13094010C23132yes—
136#13094009C23132yes—
137#13094006C23132yes—
138#13094006C23132yes—
139#13094004C23116yes—
140#13094003C23116yes—
141#13094002C23132yes—
142#13094001C23132yes—
143#13094000C23116yes—
144#13094000C23116yes—
145#13093997C23132yes—
146#13093995C23116yes—
147Q8×Dic47C23116yes—
148Q8×Dic47C2318yes—
149C4×Dic94C23116yes—
150C4×Dic94C2318yes—
151C4×Dic94C23132yes—
152#13093989C23116yes—
153#13093989C2318yes—
154#13093989C23132yes—
155#13093989C23116yes—
156C4×D188C2318yes—
157C4×D188C23116yes—
158D4×Dic47C2318yes—
159#13093986C23116yes—
160#13093986C2318yes—
161#13093986C23116yes—
162C4×C22⋊D47C23116yes—
163(C22⋊D47)⋊C4C23132yes—
164(C22⋊D47)⋊C4C23116yes—
165(C22⋊D47)⋊C4C23132yes—
166#13093982C23116yes—
167#13093982C2318yes—
168#13093982C2318yes—
169#13093982C23116yes—
170#13093981C23132yes—
171#13093980C23116yes—
172#13093980C23132yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2314yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2314yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2314yes—
187C4⋊C4×D47C23132yes—
188C4⋊C4×D47C23116yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2314yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2314yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×C4×Dic47C2311yescharacteristic
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2314yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C23116yes—
208C42×D47C23132yes—
209C42×D47C23116yes—
210C42×D47C2318yes—
211C22×Q8×C47C2311yescharacteristic
212C22×Q8×C47C2312yes—
213C22×D4×C47C2311yescharacteristic
214C23×C4×C47C2312yes—
215C4⋊Q8×C47C2318yes—
216#126×C47C23132yes—
217#124×C47C23116yes—
218C22⋊Q8×C47C23116yes—
219C4×Q8×C47C23116yes—
220C4×Q8×C47C2318yes—
221C4×D4×C47C2318yes—
222#117×C47C23116yes—
223C2×C4⋊C4×C47C2311yescharacteristic
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2314yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2312yes—
229C2×C22⋊C4×C47C2314yes—
230C2×C22⋊C4×C47C2312yes—
231C2×C22⋊C4×C47C2314yes—
232C2×C42×C47C2314yes—
233C2×C42×C47C2311yescharacteristic
234C2×C42×C47C2312yes—
235C24×C47C2412yes—
236C23×D47C2411yescharacteristic
237C23×D47C2412yes—
238C2×Q8×C47—28no—
239C2×Q8×C47—24no—
240C2×Q8×C47C2414yes—
241C2×Q8×C47C2418yes—
242C2×D4×C47—24no—
243C2×D4×C47C2414yes—
244C22×C4×C47—28no—
245C22×C4×C47C2412yes—
246C22×C4×C47C2412yes—
247C22×C4×C47C2411yescharacteristic
248C22×C4×C47C2414yes—
249C22×C4×C47C2412yes—
250C22×C4×C47C2418yes—
251C22×C4×C47C2411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253C2×C22⋊D47—216no—
254C2×C22⋊D47—28no—
255C2×C22⋊D47C24116yes—
256C2×C22⋊D47C2418yes—
257C22×Dic47—28no—
258C22×Dic47—28no—
259C22×Dic47C2411yescharacteristic
260C22×Dic47C2411yescharacteristic
261C22×Dic47C2412yes—
262C22×Dic47C2412yes—
263C22×Dic47C2414yes—
264C22×Dic47C2418yes—
265C22×Dic47C2418yes—
266C22×Dic47C2412yes—
267C22×Dic47C2411yescharacteristic
268#10625354—232no—
269Q8×D47—264no—
270#10625352—232no—
271#10625350—264no—
272C2×D188—28no—
273C2×D188#4118yescomplemented
274C2×D188C2418yes—
275C2×D188C2414yes—
276C2×C4×D47—216no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—24no—
280C2×C4×D47—24no—
281C2×C4×D47—216no—
282C2×C4×D47—28no—
283C2×C4×D47—24no—
284C2×C4×D47C2418yes—
285C2×C4×D47C24116yes—
286C2×C4×D47C2418yes—
287C2×C4×D47C24116yes—
288C2×C4×D47C2418yes—
289C2×C4×D47C2414yes—
290C2×C4×D47C2414yes—
291C2×C4×D47C2414yes—
292C2×Dic94—28no—
293C2×Dic94—216no—
294C2×Dic94#4118yescomplemented
295C2×Dic94C2418yes—
296C2×Dic94C24116yes—
297C2×Dic94C2414yes—
298C4⋊C4×C47C2414yes—
299C4⋊C4×C47C2418yes—
300C4⋊C4×C47C2414yes—
301C4⋊C4×C47C24116yes—
302C4⋊C4×C47C2418yes—
303C4⋊C4×C47C2418yes—
304C22⋊C4×C47C24116yes—
305C22⋊C4×C47C2418yes—
306C22⋊C4×C47C24116yes—
307C42×C47C24116yes—
308C42×C47C2414yes—
309C42×C47C2418yes—
310C22⋊Dic47C2418yes—
311C22⋊Dic47C24116yes—
312(C2×D47)⋊C4C2418yes—
313(C2×D47)⋊C4C24116yes—
314(C2×D47)⋊C4C2418yes—
315(C2×D47)⋊C4C2418yes—
316(C2×D47)⋊C4C2418yes—
317(C2×D47)⋊C4C24116yes—
318C4⋊Dic47C2418yes—
319C4⋊Dic47C24116yes—
320C4⋊Dic47C2414yes—
321C4⋊Dic47C2418yes—
322C4⋊Dic47C2414yes—
323C4⋊Dic47C2418yes—
324Dic47⋊C4C2418yes—
325Dic47⋊C4C24116yes—
326Dic47⋊C4C24116yes—
327Dic47⋊C4C2418yes—
328Dic47⋊C4C24116yes—
329Dic47⋊C4C24116yes—
330Dic47⋊C4C24116yes—
331Dic47⋊C4C24116yes—
332C4×Dic47C2414yes—
333C4×Dic47C2418yes—
334C4×Dic47C2414yes—
335C4×Dic47C2414yes—
336C4×Dic47C2418yes—
337C4×Dic47C24116yes—
338C4×Dic47C2418yes—
339C4×Dic47C24116yes—
340C4×Dic47C2418yes—
341C4×Dic47C2418yes—
342C23×C47—24no—
343C23×C47—24no—
344C23×C47—24no—
345C23×C47C2514yes—
346C23×C47C2511yescharacteristic
347C22×D47—24no—
348C22×D47—24no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47C2×#4118yes—
353C22×D47C2512yes—
354C22×D47C2514yes—
355Q8×C47—216no—
356Q8×C47—28no—
357D4×C47—28no—
358C2×C4×C47—28no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—24no—
362C2×C4×C47—22no—
363C2×C4×C47—216no—
364C2×C4×C47C2×#4114yes—
365C2×C4×C47C2×#4114yes—
366C2×C4×C47C2514yes—
367C2×C4×C47C2514yes—
368C2×C4×C47C2514yes—
369C2×C4×C47C2512yes—
370C2×C4×C47C2518yes—
371C2×C4×C47C2512yes—
372C2×C4×C47C2512yes—
373C22⋊D47—232no—
374C22⋊D47—216no—
375C2×Dic47—24no—
376C2×Dic47—28no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—24no—
380C2×Dic47—216no—
381C2×Dic47—216no—
382C2×Dic47C2×#4118yes—
383C2×Dic472−1+414yes—
384C2×Dic47C2512yes—
385C2×Dic47C2512yes—
386C2×Dic47C2514yes—
387C2×Dic47C2518yes—
388C2×Dic47C2514yes—
389C2×Dic47C2514yes—
390C2×Dic47C2512yes—
391D188—216no—
392D188C2×#41116yescomplemented
393C4×D47—232no—
394C4×D47—216no—
395C4×D47—28no—
396C4×D47—216no—
397C4×D47—28no—
398C4×D47—232no—
399C4×D47—216no—
400C4×D47—28no—
401Dic94—216no—
402Dic94—232no—
403Dic94C2×#41116yescomplemented
404C2×#3482—471nomaximal, Sylow
405C22×C47—24no—
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—48no—
409C22×C47C22×#4112yes—
410C22×C47C22×#4112yes—
411C22×C47C2×2−1+412yes—
412C22×C47C2611yescharacteristic
413C2×D47—24no—
414C2×D47—24no—
415C2×D47—216no—
416C2×D47—22no—
417C2×D47—22no—
418C2×D47—22no—
419C2×D47—44no—
420C2×D47C22×#4118yes—
421C4×C47—28no—
422C4×C47—24no—
423C4×C47—24no—
424C4×C47—24no—
425C4×C47—22no—
426C4×C47C22×#4114yes—
427C4×C47C22×#4114yes—
428Dic47—24no—
429Dic47—28no—
430Dic47—22no—
431Dic47—22no—
432Dic47—24no—
433Dic47C22×#4118yes—
434Dic47C2×2−1+414yes—
435#3482—4732no—
436C2×#557—471no—
437C2×#556—472no—
438C2×#556D4711yescharacteristic, complemented
439C2×#552—474no—
440C2×#552—472no—
441C2×D4×Q8—471no—
442C2×#548—472no—
443C2×#547—472no—
444C2×#547—471no—
445C2×#533—471no—
446C2×#533—472no—
447C2×#529—474no—
448C2×#529—472no—
449C2×C4×#41—471no—
450C2×C4×#41—471no—
451C2×C4×#41—472no—
452C22×C4×Q8—472no—
453C2×C47—44no—
454C2×C47#348214yescomplemented
455C2×C47C23×#4111yescharacteristic
456C2×C47C23×#4111yescharacteristic
457C2×C47C22×2−1+411yescharacteristic
458D47—28no—
459D47—42no—
460C22×#41—471no—
461C22×#41—471no—
462C22×#41—472no—
463C23×Q8—472no—
464#557—4716no—
465#556—4732no—
466#556C2×D47116yescomplemented
467#552—4764no—
468#552—4732no—
469D4×Q8—4716no—
470#548—4732no—
471#547—4732no—
472#547—4716no—
473#533—4716no—
474#533—4732no—
475C2×C4⋊Q8—472no—
476C2×C4⋊Q8—472no—
477C2×C4⋊Q8—471no—
478C2×C4⋊Q8C2×D4711yescharacteristic
479#529—4764no—
480#529—4732no—
481C2×#126—474no—
482C2×#126—474no—
483C2×#126C2×D4714yes—
484C2×#125—474no—
485C2×#125—474no—
486C2×#125—472no—
487C2×#125—472no—
488C2×#124—474no—
489C2×#124C2×D4712yes—
490C2×#123—474no—
491C2×#123—474no—
492C2×#123—474no—
493C2×C22⋊Q8—472no—
494C2×C22⋊Q8—472no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—474no—
497C2×C22⋊Q8—472no—
498C2×C22⋊Q8—474no—
499C2×C22⋊Q8C2×D4712yes—
500C2×#121—472no—
501C2×#121—474no—
502C4×#41—4716no—
503C4×#41—4716no—
504C4×#41—4732no—
505C2×C4×Q8—472no—
506C2×C4×Q8—471no—
507C2×C4×Q8—4732no—
508C2×C4×Q8—471no—
509C2×C4×Q8—474no—
510C2×C4×Q8—472no—
511C2×C4×Q8—472no—
512C2×C4×Q8—472no—
513C2×C4×Q8—474no—
514C2×C4×Q8—471no—
515C2×C4×Q8C2×D4712yes—
516C2×C4×Q8C2×D4711yescharacteristic
517C2×C4×D4—471no—
518C2×C4×D4—472no—
519C2×C4×D4—471no—
520C2×C4×D4—472no—
521C2×C4×D4—472no—
522C2×C4×D4—474no—
523C2×C4×D4—472no—
524C2×C4×D4—474no—
525C2×C4×D4—471no—
526C2×C4×D4—472no—
527C2×C4×D4C2×D4711yescharacteristic
528C2×#117—471no—
529C2×#117—472no—
530C2×#117—471no—
531C2×#117—472no—
532C2×#117—472no—
533C2×#117—474no—
534C2×#117—474no—
535C2×#117C2×D4712yes—
536C22×C4⋊C4—474no—
537C22×C4⋊C4—472no—
538C22×C42—472no—
539C22×C42—472no—
540C22×C42—474no—
541C22×C42—471no—
542C47C2×#348211yescharacteristic, complemented, Sylow
543C2×#41—478no—
544C2×#41—478no—
545C2×#41—4716no—
546C2×#41—9416no—
547C2×#41—948no—
548C2×#41—948no—
549C22×Q8—4716no—
550C22×Q8—471no—
551C22×Q8—474no—
552C22×Q8—472no—
553C22×Q8—9416no—
554C22×Q8C22×D4712yes—
555C22×Q8C22×D4711yescharacteristic
556C22×D4—474no—
557C22×D4—472no—
558C22×D4—471no—
559C22×D4—472no—
560C22×D4C22×D4711yescharacteristic
561C23×C4—472no—
562C23×C4—472no—
563C23×C4—472no—
564C23×C4—474no—
565C23×C4—474no—
566C23×C4—472no—
567C23×C4—471no—
568C23×C4—471no—
569C23×C4—471no—
570C23×C4—472no—
571C23×C4C22×D4712yes—
572C4⋊Q8—4716no—
573C4⋊Q8—4716no—
574C4⋊Q8—478no—
575C4⋊Q8C22×D4718yes—
576#126—4732no—
577#126—4732no—
578#126C22×D47132yes—
579#125—4732no—
580#125—4732no—
581#125—4716no—
582#125—4716no—
583#124—4732no—
584#124C22×D47116yes—
585#123—4732no—
586#123—4732no—
587#123—4732no—
588C22⋊Q8—4716no—
589C22⋊Q8—4716no—
590C22⋊Q8—4716no—
591C22⋊Q8—4732no—
592C22⋊Q8—4716no—
593C22⋊Q8—4732no—
594C22⋊Q8C22×D47116yes—
595#121—4716no—
596#121—4732no—
597C4×Q8—4716no—
598C4×Q8—478no—
599C4×Q8—478no—
600C4×Q8—4732no—
601C4×Q8—4716no—
602C4×Q8—4716no—
603C4×Q8—4716no—
604C4×Q8—4732no—
605C4×Q8—478no—
606C4×Q8C22×D47116yes—
607C4×Q8C22×D4718yes—
608C4×D4—478no—
609C4×D4—4716no—
610C4×D4—478no—
611C4×D4—4716no—
612C4×D4—4716no—
613C4×D4—4716no—
614C4×D4—4732no—
615C4×D4—4732no—
616C4×D4—478no—
617C4×D4—4716no—
618C4×D4C22×D4718yes—
619#117—478no—
620#117—4716no—
621#117—478no—
622#117—4716no—
623#117—4716no—
624#117—4732no—
625#117—4732no—
626#117C22×D47116yes—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—474no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—472no—
635C2×C4⋊C4—471no—
636C2×C4⋊C4—471no—
637C2×C4⋊C4—474no—
638C2×C4⋊C4—474no—
639C2×C4⋊C4—474no—
640C2×C4⋊C4—472no—
641C2×C4⋊C4—4732no—
642C2×C4⋊C4—4716no—
643C2×C4⋊C4C22×D4711yescharacteristic
644C2×C4⋊C4C22×D4714yes—
645C2×C4⋊C4C22×D4711yescharacteristic
646C2×C4⋊C4C22×D4712yes—
647C2×C4⋊C4C22×D4712yes—
648C2×C4⋊C4C22×D4712yes—
649C2×C22⋊C4—472no—
650C2×C22⋊C4—474no—
651C2×C22⋊C4—472no—
652C2×C22⋊C4—474no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—472no—
655C2×C22⋊C4—472no—
656C2×C22⋊C4—474no—
657C2×C22⋊C4C22×D4712yes—
658C2×C22⋊C4C22×D4714yes—
659C2×C22⋊C4C22×D4714yes—
660C2×C42—471no—
661C2×C42—472no—
662C2×C42—472no—
663C2×C42—474no—
664C2×C42—472no—
665C2×C42—472no—
666C2×C42—474no—
667C2×C42—472no—
668C2×C42—471no—
669C2×C42—471no—
670C2×C42—4716no—
671C2×C42—4716no—
672C2×C42—4732no—
673C2×C42—478no—
674C2×C42C22×D4714yes—
675C2×C42C22×D4711yescharacteristic
676C2×C42C22×D4712yes—
677C24—472no—
678C24—471no—
679C24C23×D4712yes—
680#41—9464no—
681#41—9432no—
682#41—9432no—
683C2×Q8—28no—
684C2×Q8—24no—
685C2×Q8—478no—
686C2×Q8—474no—
687C2×Q8—4716no—
688C2×Q8—478no—
689C2×Q8—9416no—
690C2×Q8—9464no—
691C2×Q8—948no—
692C2×Q8C23×D4718yes—
693C2×Q8C23×D4714yes—
694C2×D4—24no—
695C2×D4—4716no—
696C2×D4—478no—
697C2×D4—478no—
698C2×D4—474no—
699C2×D4—478no—
700C2×D4—948no—
701C2×D4—948no—
702C2×D4—9416no—
703C2×D4C23×D4714yes—
704C22×C4—28no—
705C22×C4—471no—
706C22×C4—472no—
707C22×C4—478no—
708C22×C4—478no—
709C22×C4—471no—
710C22×C4—471no—
711C22×C4—472no—
712C22×C4—472no—
713C22×C4—474no—
714C22×C4—478no—
715C22×C4—478no—
716C22×C4—4716no—
717C22×C4—4716no—
718C22×C4—478no—
719C22×C4—474no—
720C22×C4—474no—
721C22×C4—474no—
722C22×C4—948no—
723C22×C4—944no—
724C22×C4—9416no—
725C22×C4—9416no—
726C22×C4—948no—
727C22×C4—948no—
728C22×C4—948no—
729C22×C4—948no—
730C22×C4—944no—
731C22×C4—944no—
732C22×C4C23×D4718yes—
733C22×C4C23×D4712yes—
734C22×C4C23×D4712yes—
735C22×C4C23×D4711yescharacteristic
736C22×C4C23×D4714yes—
737C22×C4C23×D4712yes—
738C22×C4C23×D4711yescharacteristic
739C22×C4C23×D4711yescharacteristic
740C4⋊C4—478no—
741C4⋊C4—4716no—
742C4⋊C4—4716no—
743C4⋊C4—478no—
744C4⋊C4—4716no—
745C4⋊C4—4716no—
746C4⋊C4—4716no—
747C4⋊C4—4716no—
748C4⋊C4—478no—
749C4⋊C4—4716no—
750C4⋊C4—478no—
751C4⋊C4—474no—
752C4⋊C4—474no—
753C4⋊C4—478no—
754C4⋊C4C23×D4714yes—
755C4⋊C4C23×D47116yes—
756C4⋊C4C23×D4714yes—
757C4⋊C4C23×D4718yes—
758C4⋊C4C23×D4718yes—
759C4⋊C4C23×D4718yes—
760C22⋊C4—478no—
761C22⋊C4—4716no—
762C22⋊C4—478no—
763C22⋊C4—4716no—
764C22⋊C4—478no—
765C22⋊C4—478no—
766C22⋊C4—478no—
767C22⋊C4—4716no—
768C22⋊C4C23×D4718yes—
769C22⋊C4C23×D47116yes—
770C22⋊C4C23×D47116yes—
771C42—478no—
772C42—474no—
773C42—474no—
774C42—474no—
775C42—478no—
776C42—478no—
777C42—4716no—
778C42—478no—
779C42—478no—
780C42—4716no—
781C42C23×D47116yes—
782C42C23×D4714yes—
783C42C23×D4718yes—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—478no—
788C23—474no—
789C23—472no—
790C23—944no—
791C23—944no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23C24×D4714yes—
796C23C24×D4711yescharacteristic
797Q8—216no—
798Q8—28no—
799Q8—4716no—
800Q8—9432no—
801Q8—9416no—
802D4—28no—
803D4—4716no—
804D4—9416no—
805D4—9416no—
806D4—9432no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—28no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—216no—
813C2×C4—478no—
814C2×C4—474no—
815C2×C4—472no—
816C2×C4—474no—
817C2×C4—472no—
818C2×C4—472no—
819C2×C4—474no—
820C2×C4—474no—
821C2×C4—478no—
822C2×C4—9416no—
823C2×C4—948no—
824C2×C4—9432no—
825C2×C4—9432no—
826C2×C4—9416no—
827C2×C4—9416no—
828C2×C4—9416no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—948no—
832C2×C4—944no—
833C2×C4—944no—
834C2×C4—9416no—
835C2×C4—948no—
836C2×C4—948no—
837C2×C4#41×D4714yes—
838C2×C4#41×D4714yes—
839C2×C4C24×D4714yes—
840C2×C4C24×D4714yes—
841C2×C4C24×D4712yes—
842C2×C4C24×D4718yes—
843C2×C4C24×D4714yes—
844C2×C4C24×D4712yes—
845C2×C4C24×D4712yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—478no—
851C22—944no—
852C22—944no—
853C22—9416no—
854C22—942no—
855C22—942no—
856C22—942no—
857C22—1884no—
858C22C2×#41×D4712yes—
859C22C2×#41×D4712yes—
860C222−1+4×D4712yes—
861C22C25×D4711yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—478no—
868C4—474no—
869C4—942no—
870C4—942no—
871C4—948no—
872C4—944no—
873C4—944no—
874C4C2×#41×D4714yes—
875C4C2×#41×D4714yes—
876C2—44no—
877C2—948no—
878C2—1882no—
879C2#2025700714yesdirect product factor
880C2C22×#41×D4711yescharacteristic
881C2C22×#41×D4711yescharacteristic
882C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#556C2
socleC23×C47C25
hypercenterC2×#556D47
hypocenterC47C2×#3482
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20257007C2direct (N × H)
2. C2×#15689851C2semidirect
3. C2×#15689841C2semidirect
4. C2×#15689814C2semidirect
5. C2×#15689809C2semidirect
6. C2×#15689788C2semidirect
7. C2×#15689781C2semidirect
8. C2×#15689778C2semidirect
9. C2×#15689775C2semidirect
10. C2×#15689678C2semidirect
11. C2×#15689675C2semidirect
12. C2×#15689656C2semidirect
13. C2×#15689652C2semidirect
14. C2×C4×#10625354C2semidirect
15. C2×#15689591C2semidirect
16. C2×C4×#10625352C2semidirect
17. C2×C4×Q8×D47C2semidirect
18. C2×C47×#556C2semidirect
23. #15689851C22semidirect
24. #15689841C22semidirect
25. #15689814C22semidirect
26. #15689809C22semidirect
27. #15689788C22semidirect
28. #15689781C22semidirect
29. #15689778C22semidirect
30. #15689775C22semidirect
31. #15689678C22semidirect
32. #15689675C22semidirect
36. #15689656C22semidirect
37. #15689652C22semidirect
56. C4×#10625354C22semidirect
57. #15689591C22semidirect
58. C4×#10625352C22semidirect
68. C4×Q8×D47C22semidirect
92. C47×#556C22semidirect
273. C2×D188#41semidirect
294. C2×Dic94#41semidirect
392. D188C2×#41semidirect
403. Dic94C2×#41semidirect
438. C2×#556D47semidirect
454. C2×C47#3482semidirect
466. #556C2×D47semidirect
542. C47C2×#3482semidirect
879. C2#20257007direct (N × H)

Maximal subgroups

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

subgroupindex
#202570072
C2×#156898512
C2×#156898412
C2×#156898142
C2×#156898092
C2×#156897882
C2×#156897812
C2×#156897782
C2×#156897752
C2×#156896782
C2×#156896752
C2×#156896562
C2×#156896522
C2×C4×#106253542
C2×#156895912
C2×C4×#106253522
C2×C4×Q8×D472
C2×C47×#5562
C2×#348247