Finite Group Databasebeta

← C2×#20257361 #27124383

Subgroups — C2×#20257361 #27124383

Order 12032.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257361C2132yesmaximal, direct product factor
2C2×#15689848C211yesmaximal, characteristic, complemented
3C2×#15689834C211yesmaximal, characteristic, complemented
4C2×#15689834C211yesmaximal, characteristic, complemented
5C2×#15689817C212yesmaximal, complemented
6C2×#15689814C214yesmaximal, complemented
7C2×#15689812C212yesmaximal, complemented
8C2×#15689807C212yesmaximal, complemented
9C2×#15689776C211yesmaximal, characteristic, complemented
10C2×#15689775C212yesmaximal, complemented
11C2×#15689731C212yesmaximal, complemented
12C2×#15689719C214yesmaximal, complemented
13C2×#15689658C212yesmaximal, complemented
14C2×#15689657C211yesmaximal, characteristic, complemented
15C2×#125×D47C212yesmaximal, complemented
16C2×#15689605C212yesmaximal, complemented
17C2×C4×#10625350C211yesmaximal, characteristic, complemented
18C2×C47×#533C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×#10625350C2211yescharacteristic
21#15689848C22116yescomplemented
22#15689834C22116yescomplemented
23#15689834C22116yescomplemented
24#15689817C22132yescomplemented
25#15689814C22164yescomplemented
26#15689812C22132yescomplemented
27#15689807C22132yescomplemented
28#15689776C22116yescomplemented
29#15689775C22132yescomplemented
30#15689731C22132yescomplemented
31#15689719C22164yescomplemented
32C2×#13094022C2212yes—
33#15689658C22132yescomplemented
34#15689657C22116yescomplemented
35C2×#13094019C2214yes—
36C2×#13094018C2212yes—
37C2×#13094018C2214yes—
38C2×#13094017C2214yes—
39C2×#13094016C2211yescharacteristic
40C2×#13094016C2214yes—
41C2×#13094015C2212yes—
42C2×#13094015C2212yes—
43C2×#13094015C2212yes—
44C2×#13094014C2214yes—
45C2×#13094014C2214yes—
46C2×#13094014C2214yes—
47#125×D47C22132yescomplemented
48C2×#13094012C2211yescharacteristic
49C2×#13094009C2214yes—
50C2×#13094009C2214yes—
51C2×#13094007C2212yes—
52C2×#13094006C2214yes—
53C2×#13094006C2214yes—
54C2×#13094004C2212yes—
55C2×#13094004C2212yes—
56C2×#13094003C2211yescharacteristic
57C2×#13094000C2212yes—
58C2×#13094000C2214yes—
59C2×#13094000C2214yes—
60C2×#13093999C2212yes—
61C2×#13093998C2211yescharacteristic
62C2×#13093997C2214yes—
63#15689605C22132yescomplemented
64C4×#10625350C22116yescomplemented
65C2×Q8×Dic47C2212yes—
66C2×C4×Dic94C2211yescharacteristic
67C2×C4×Dic94C2211yescharacteristic
68C2×C4×Dic94C2211yescharacteristic
69C2×#13093989C2212yes—
70C2×C4×D188C2211yescharacteristic
71C2×C4×D188C2211yescharacteristic
72C2×C4×D188C2214yes—
73C2×C4×D188C2211yescharacteristic
74C2×#13093986C2212yes—
75C2×#13093986C2214yes—
76C2×#13093986C2212yes—
77C2×C4×C22⋊D47C2212yes—
78C2×C4×C22⋊D47C2212yes—
79C2×C4×C22⋊D47C2212yes—
80C2×#13093983C2211yescharacteristic
81C2×#13093982C2214yes—
82C2×#13093981C2212yes—
83C2×#13093981C2214yes—
84C2×#13093981C2212yes—
85C2×C4⋊C4×D47C2214yes—
86C2×C4⋊C4×D47C2212yes—
87C2×C4⋊C4×D47C2214yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2212yes—
91C47×#533C22116yescomplemented
92C2×C4⋊Q8×C47C2211yescharacteristic
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2212yes—
99C2×#117×C47C2212yes—
100C22×C42×C47C2211yescharacteristic
101C2×#10625354—216no—
102C2×#10625354C23116yes—
103C2×#10625350—28no—
104C2×#10625350C2318yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2311yescharacteristic
107C22×D188C2311yescharacteristic
108C22×D188C2314yes—
109C22×D188C2311yescharacteristic
110C22×C22⋊D47C2312yes—
111C22×C22⋊D47C2312yes—
112C22×C4×D47C2312yes—
113C22×C4×D47C2312yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2312yes—
116C22×C4×D47C2312yes—
117C22×C4×D47C2314yes—
118C22×C4×D47C2314yes—
119#13094022C23116yes—
120#13094019C23132yes—
121#13094018C23132yes—
122#13094018C23116yes—
123#13094017C23132yes—
124#13094016C23132yes—
125#13094016C2318yes—
126#13094015C23116yes—
127#13094015C23116yes—
128#13094015C23116yes—
129#13094014C23132yes—
130#13094014C23132yes—
131#13094014C23132yes—
132#13094012C2318yes—
133#13094009C23132yes—
134#13094009C23132yes—
135#13094007C23116yes—
136#13094006C23132yes—
137#13094006C23132yes—
138#13094004C23116yes—
139#13094004C23116yes—
140#13094003C2318yes—
141#13094000C23116yes—
142#13094000C23132yes—
143#13094000C23132yes—
144#13093999C23116yes—
145#13093998C2318yes—
146#13093997C23132yes—
147Q8×Dic47C23116yes—
148C4×Dic94C2318yes—
149C4×Dic94C2318yes—
150C4×Dic94C2318yes—
151#13093989C23116yes—
152C4×D188C2318yes—
153C4×D188C2318yes—
154C4×D188C23132yes—
155C4×D188C2318yes—
156#13093986C23116yes—
157#13093986C23116yes—
158#13093986C23132yes—
159C4×C22⋊D47C23116yes—
160C4×C22⋊D47C23116yes—
161C4×C22⋊D47C23116yes—
162#13093983C2318yes—
163#13093982C23132yes—
164#13093981C23116yes—
165#13093981C23132yes—
166#13093981C23116yes—
167C2×C4⋊Dic47C2311yescharacteristic
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2314yes—
171C2×C4⋊Dic47C2314yes—
172C2×C4⋊Dic47C2314yes—
173C2×C4⋊Dic47C2311yescharacteristic
174C2×Dic47⋊C4C2314yes—
175C2×Dic47⋊C4C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2314yes—
178C2×Dic47⋊C4C2314yes—
179C2×Dic47⋊C4C2314yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C4⋊C4×D47C23132yes—
186C4⋊C4×D47C23116yes—
187C4⋊C4×D47C23116yes—
188C4⋊C4×D47C23116yes—
189C4⋊C4×D47C23132yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2314yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2312yes—
206C42×D47C23116yes—
207C22×Q8×C47C2312yes—
208C22×Q8×C47C2312yes—
209C23×C4×C47C2311yescharacteristic
210C23×C4×C47C2311yescharacteristic
211C23×C4×C47C2311yescharacteristic
212C4⋊Q8×C47C2318yes—
213C4⋊Q8×C47C2318yes—
214#125×C47C23116yes—
215C22⋊Q8×C47C23116yes—
216C22⋊Q8×C47C23116yes—
217C4×Q8×C47C23116yes—
218C4×Q8×C47C23116yes—
219#117×C47C23116yes—
220C2×C4⋊C4×C47C2312yes—
221C2×C4⋊C4×C47C2312yes—
222C2×C4⋊C4×C47C2314yes—
223C2×C4⋊C4×C47C2314yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C22⋊C4×C47C2314yes—
227C2×C42×C47C2311yescharacteristic
228C2×C42×C47C2311yescharacteristic
229C2×C42×C47C2311yescharacteristic
230C2×C42×C47C2311yescharacteristic
231C2×C42×C47C2318yes—
232C2×C42×C47C2314yes—
233C24×C47C2411yescharacteristic
234C23×D47C2412yes—
235C23×D47C2412yes—
236C2×Q8×C47—28no—
237C2×Q8×C47—44no—
238C2×Q8×C47C2418yes—
239C2×Q8×C47C2418yes—
240C22×C4×C47—24no—
241C22×C4×C47—24no—
242C22×C4×C47—42no—
243C22×C4×C47C2411yescharacteristic
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C2411yescharacteristic
246C22×C4×C47C2411yescharacteristic
247C22×C4×C47C2414yes—
248C22×C4×C47C2414yes—
249C22×C4×C47C2414yes—
250C22×C4×C47C2414yes—
251C22×C4×C47C2414yes—
252C22×C4×C47C2411yescharacteristic
253C22×C4×C47C2411yescharacteristic
254C2×C22⋊D47—28no—
255C2×C22⋊D47—44no—
256C2×C22⋊D47C2418yes—
257C2×C22⋊D47C2418yes—
258C22×Dic47C2412yes—
259C22×Dic47C2412yes—
260C22×Dic47C2412yes—
261C22×Dic47C2412yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264#10625354—264no—
265#10625350—232no—
266C2×D188—216no—
267C2×D188—24no—
268C2×D188#4118yes—
269C2×D188C2414yes—
270C2×D188C24116yes—
271C2×D188C2414yes—
272C2×C4×D47—28no—
273C2×C4×D47—216no—
274C2×C4×D47—28no—
275C2×C4×D47—28no—
276C2×C4×D47—44no—
277C2×C4×D47—48no—
278C2×C4×D47—48no—
279C2×C4×D47C2418yes—
280C2×C4×D47C2418yes—
281C2×C4×D47C24116yes—
282C2×C4×D47C2418yes—
283C2×C4×D47C2418yes—
284C2×C4×D47C24116yes—
285C2×C4×D47C24116yes—
286C2×Dic94—24no—
287C2×Dic94—24no—
288C2×Dic94C2414yes—
289C2×Dic94C2414yes—
290C4⋊C4×C47C2418yes—
291C4⋊C4×C47C2418yes—
292C4⋊C4×C47C24116yes—
293C4⋊C4×C47C24116yes—
294C4⋊C4×C47C2418yes—
295C4⋊C4×C47C2418yes—
296C22⋊C4×C47C24116yes—
297C42×C47C2414yes—
298C42×C47C2414yes—
299C42×C47C2414yes—
300C42×C47C2414yes—
301C42×C47C24116yes—
302C22⋊Dic47C2418yes—
303C22⋊Dic47C2418yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C2418yes—
306(C2×D47)⋊C4C24116yes—
307(C2×D47)⋊C4C2418yes—
308(C2×D47)⋊C4C2418yes—
309(C2×D47)⋊C4C2418yes—
310(C2×D47)⋊C4C24116yes—
311(C2×D47)⋊C4C24116yes—
312(C2×D47)⋊C4C2418yes—
313C4⋊Dic47C2414yes—
314C4⋊Dic47C2414yes—
315C4⋊Dic47C2414yes—
316C4⋊Dic47C24116yes—
317C4⋊Dic47C24116yes—
318C4⋊Dic47C24116yes—
319C4⋊Dic47C2414yes—
320Dic47⋊C4C24116yes—
321Dic47⋊C4C2418yes—
322Dic47⋊C4C2418yes—
323Dic47⋊C4C24116yes—
324Dic47⋊C4C24116yes—
325Dic47⋊C4C24116yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C2418yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C24116yes—
330Dic47⋊C4C2418yes—
331C4×Dic47C2418yes—
332C4×Dic47C2418yes—
333C4×Dic47C2418yes—
334C4×Dic47C24116yes—
335C4×Dic47C2418yes—
336C23×C47—22no—
337C23×C47—22no—
338C23×C47—22no—
339C23×C47C2512yes—
340C23×C47C2511yescharacteristic
341C22×D47—24no—
342C22×D47—24no—
343C22×D47—24no—
344C22×D47—24no—
345C22×D47—24no—
346C22×D47C2×#4118yes—
347C22×D47C2514yes—
348C22×D47C2514yes—
349Q8×C47—216no—
350Q8×C47—48no—
351C2×C4×C47—22no—
352C2×C4×C47—28no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—28no—
356C2×C4×C47—22no—
357C2×C4×C47—28no—
358C2×C4×C47—28no—
359C2×C4×C47—44no—
360C2×C4×C47C2×#4114yes—
361C2×C4×C472−1+414yes—
362C2×C4×C47C2512yes—
363C2×C4×C47C2512yes—
364C2×C4×C47C2518yes—
365C2×C4×C47C2512yes—
366C2×C4×C47C2512yes—
367C2×C4×C47C2518yes—
368C2×C4×C47C2512yes—
369C2×C4×C47C2512yes—
370C22⋊D47—216no—
371C22⋊D47—48no—
372C2×Dic47—24no—
373C2×Dic47—24no—
374C2×Dic47—24no—
375C2×Dic47—24no—
376C2×Dic47—24no—
377C2×Dic47—24no—
378C2×Dic47C2514yes—
379C2×Dic47C2514yes—
380C2×Dic47C2514yes—
381C2×Dic47C2514yes—
382C2×Dic47C2514yes—
383C2×Dic47C2514yes—
384D188—232no—
385D188—28no—
386D188C2×#41116yes—
387C4×D47—216no—
388C4×D47—232no—
389C4×D47—216no—
390C4×D47—216no—
391C4×D47—48no—
392C4×D47—416no—
393C4×D47—416no—
394Dic94—28no—
395Dic94—28no—
396C2×#3515—471nomaximal, Sylow
397C22×C47—22no—
398C22×C47—22no—
399C22×C47—22no—
400C22×C47—44no—
401C22×C47C22×#4112yes—
402C22×C47C2×2−1+412yes—
403C22×C47#58512yes—
404C22×C47C2611yescharacteristic
405C2×D47—24no—
406C2×D47—24no—
407C2×D47—216no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—48no—
412C2×D47C22×#4118yes—
413C4×C47—22no—
414C4×C47—28no—
415C4×C47—22no—
416C4×C47—22no—
417C4×C47—28no—
418C4×C47—22no—
419C4×C47C22×#4114yes—
420C4×C47C2×2−1+414yes—
421Dic47—24no—
422Dic47—24no—
423Dic47—24no—
424Dic47—24no—
425Dic47—24no—
426Dic47—24no—
427#3515—4732no—
428C2×#557—471no—
429C2×#554—471no—
430C2×#554—471no—
431C2×#553—472no—
432C2×#552—472no—
433C2×#552—474no—
434C2×#552—472no—
435C2×#547—471no—
436C2×#547—472no—
437C2×#541—472no—
438C2×#539—474no—
439C2×#533D4711yescharacteristic, complemented
440C2×#529—471no—
441C2×#529—472no—
442C22×#125—472no—
443C2×#520—472no—
444C2×C4×#41—471no—
445C2×C47—42no—
446C2×C47#351514yescomplemented
447C2×C47C23×#4111yescharacteristic
448C2×C47C22×2−1+411yescharacteristic
449C2×C47C2×#58511yescharacteristic
450D47—28no—
451D47—44no—
452C22×#41—472no—
453C22×#41—471no—
454#557—4716no—
455#554—4716no—
456#554—4716no—
457#553—4732no—
458#552—4732no—
459#552—4764no—
460#552—4732no—
461#547—4716no—
462#547—4732no—
463#541—4732no—
464#539—4764no—
465#533C2×D47116yescomplemented
466C2×C4⋊Q8—472no—
467C2×C4⋊Q8C2×D4711yescharacteristic
468C2×C4⋊Q8C2×D4711yescharacteristic
469#529—4732no—
470#529—4716no—
471C2×#126—474no—
472C2×#126—474no—
473C2×#126—472no—
474C2×#126—474no—
475C2×#125—4732no—
476C2×#125—474no—
477C2×#125—474no—
478C2×#125—472no—
479C2×#125—472no—
480C2×#125—474no—
481C2×#125—472no—
482C2×#125—471no—
483C2×#125—474no—
484C2×#125C2×D4712yes—
485C2×#124—471no—
486C2×#123—472no—
487C2×#123—474no—
488C2×#123—474no—
489C2×#123—474no—
490C2×#123—474no—
491C2×C22⋊Q8—474no—
492C2×C22⋊Q8—474no—
493C2×C22⋊Q8—472no—
494C2×C22⋊Q8—471no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—472no—
497C2×C22⋊Q8C2×D4712yes—
498C2×C22⋊Q8C2×D4712yes—
499C2×#121—471no—
500C2×#121—472no—
501C2×#121—474no—
502#520—4732no—
503C4×#41—4716no—
504C2×C4×Q8—472no—
505C2×C4×Q8—472no—
506C2×C4×Q8—471no—
507C2×C4×Q8—471no—
508C2×C4×Q8—471no—
509C2×C4×Q8C2×D4712yes—
510C2×C4×Q8C2×D4712yes—
511C2×C4×D4—472no—
512C2×C4×D4—472no—
513C2×C4×D4—472no—
514C2×C4×D4—474no—
515C2×C4×D4—472no—
516C2×C4×D4—472no—
517C2×C4×D4—471no—
518C2×C4×D4—471no—
519C2×C4×D4—474no—
520C2×C4×D4—471no—
521C2×#117—471no—
522C2×#117—474no—
523C2×#117—472no—
524C2×#117—472no—
525C2×#117—474no—
526C2×#117C2×D4712yes—
527C22×C4⋊C4—474no—
528C22×C4⋊C4—472no—
529C22×C4⋊C4—472no—
530C22×C4⋊C4—474no—
531C22×C4⋊C4—472no—
532C22×C42—472no—
533C22×C42C2×D4711yescharacteristic
534C47C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—4716no—
536C2×#41—478no—
537C2×#41—948no—
538C2×#41—9416no—
539C22×Q8—471no—
540C22×Q8—471no—
541C22×Q8C22×D4712yes—
542C22×Q8C22×D4712yes—
543C22×D4—472no—
544C22×D4—472no—
545C22×D4—471no—
546C22×D4—471no—
547C22×D4—474no—
548C23×C4—474no—
549C23×C4—472no—
550C23×C4—472no—
551C23×C4—472no—
552C23×C4—474no—
553C23×C4—472no—
554C23×C4—474no—
555C23×C4C22×D4711yescharacteristic
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C4⋊Q8—4716no—
559C4⋊Q8C22×D4718yes—
560C4⋊Q8C22×D4718yes—
561#126—4732no—
562#126—4732no—
563#126—4716no—
564#126—4732no—
565#125—4732no—
566#125—4732no—
567#125—4716no—
568#125—4716no—
569#125—4732no—
570#125—4716no—
571#125—478no—
572#125—4732no—
573#125C22×D47116yes—
574#124—478no—
575#123—4716no—
576#123—4732no—
577#123—4732no—
578#123—4732no—
579#123—4732no—
580C22⋊Q8—4732no—
581C22⋊Q8—4732no—
582C22⋊Q8—4716no—
583C22⋊Q8—478no—
584C22⋊Q8—4716no—
585C22⋊Q8—4716no—
586C22⋊Q8C22×D47116yes—
587C22⋊Q8C22×D47116yes—
588#121—478no—
589#121—4716no—
590#121—4732no—
591C4×Q8—4716no—
592C4×Q8—4716no—
593C4×Q8—478no—
594C4×Q8—478no—
595C4×Q8—478no—
596C4×Q8C22×D47116yes—
597C4×Q8C22×D47116yes—
598C4×D4—4716no—
599C4×D4—4716no—
600C4×D4—4716no—
601C4×D4—4732no—
602C4×D4—4716no—
603C4×D4—4716no—
604C4×D4—478no—
605C4×D4—478no—
606C4×D4—4732no—
607C4×D4—478no—
608#117—478no—
609#117—4732no—
610#117—4716no—
611#117—4716no—
612#117—4732no—
613#117C22×D47116yes—
614C2×C4⋊C4—471no—
615C2×C4⋊C4—474no—
616C2×C4⋊C4—472no—
617C2×C4⋊C4—471no—
618C2×C4⋊C4—472no—
619C2×C4⋊C4—471no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—472no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—472no—
629C2×C4⋊C4—474no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—4732no—
633C2×C4⋊C4—4716no—
634C2×C4⋊C4—4732no—
635C2×C4⋊C4—4716no—
636C2×C4⋊C4—4716no—
637C2×C4⋊C4C22×D4714yes—
638C2×C4⋊C4C22×D4712yes—
639C2×C4⋊C4C22×D4712yes—
640C2×C4⋊C4C22×D4712yes—
641C2×C4⋊C4C22×D4714yes—
642C2×C4⋊C4C22×D4712yes—
643C2×C22⋊C4—472no—
644C2×C22⋊C4—472no—
645C2×C22⋊C4—472no—
646C2×C22⋊C4—472no—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—472no—
650C2×C22⋊C4—472no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—474no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4C22×D4714yes—
655C2×C42—472no—
656C2×C42—474no—
657C2×C42—472no—
658C2×C42—472no—
659C2×C42—472no—
660C2×C42—4716no—
661C2×C42C22×D4711yescharacteristic
662C2×C42C22×D4711yescharacteristic
663C2×C42C22×D4714yes—
664C2×C42C22×D4711yescharacteristic
665C2×C42C22×D4718yes—
666C2×C42C22×D4711yescharacteristic
667C24—472no—
668C24—472no—
669C24C23×D4711yescharacteristic
670#41—9432no—
671#41—9464no—
672C2×Q8—28no—
673C2×Q8—44no—
674C2×Q8—474no—
675C2×Q8—474no—
676C2×Q8—944no—
677C2×Q8—944no—
678C2×Q8C23×D4718yes—
679C2×Q8C23×D4718yes—
680C2×D4—478no—
681C2×D4—478no—
682C2×D4—478no—
683C2×D4—474no—
684C2×D4—474no—
685C2×D4—4716no—
686C2×D4—9416no—
687C2×D4—948no—
688C2×D4—944no—
689C2×D4—1884no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—42no—
693C22×C4—472no—
694C22×C4—472no—
695C22×C4—472no—
696C22×C4—472no—
697C22×C4—472no—
698C22×C4—472no—
699C22×C4—478no—
700C22×C4—478no—
701C22×C4—4716no—
702C22×C4—478no—
703C22×C4—478no—
704C22×C4—4716no—
705C22×C4—4716no—
706C22×C4—948no—
707C22×C4—9416no—
708C22×C4—948no—
709C22×C4—948no—
710C22×C4—1884no—
711C22×C4—1888no—
712C22×C4—1888no—
713C22×C4C23×D4714yes—
714C22×C4C23×D4714yes—
715C22×C4C23×D4711yescharacteristic
716C22×C4C23×D4711yescharacteristic
717C22×C4C23×D4714yes—
718C22×C4C23×D4711yescharacteristic
719C22×C4C23×D4711yescharacteristic
720C22×C4C23×D4714yes—
721C22×C4C23×D4714yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C4⋊C4—4716no—
725C4⋊C4—478no—
726C4⋊C4—478no—
727C4⋊C4—4716no—
728C4⋊C4—4716no—
729C4⋊C4—4716no—
730C4⋊C4—478no—
731C4⋊C4—478no—
732C4⋊C4—478no—
733C4⋊C4—478no—
734C4⋊C4—4716no—
735C4⋊C4—474no—
736C4⋊C4—474no—
737C4⋊C4—474no—
738C4⋊C4—4716no—
739C4⋊C4—4716no—
740C4⋊C4—474no—
741C4⋊C4—4716no—
742C4⋊C4C23×D47116yes—
743C4⋊C4C23×D4718yes—
744C4⋊C4C23×D4718yes—
745C4⋊C4C23×D4718yes—
746C4⋊C4C23×D47116yes—
747C4⋊C4C23×D4718yes—
748C22⋊C4—478no—
749C22⋊C4—478no—
750C22⋊C4—478no—
751C22⋊C4—478no—
752C22⋊C4—478no—
753C22⋊C4—4716no—
754C22⋊C4—478no—
755C22⋊C4—478no—
756C22⋊C4—4716no—
757C22⋊C4—4716no—
758C22⋊C4—478no—
759C22⋊C4C23×D47116yes—
760C42—478no—
761C42—478no—
762C42—478no—
763C42—4716no—
764C42—478no—
765C42C23×D4714yes—
766C42C23×D4714yes—
767C42C23×D4714yes—
768C42C23×D4714yes—
769C42C23×D47116yes—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—478no—
774C23—474no—
775C23—474no—
776C23—944no—
777C23—944no—
778C23—944no—
779C23—944no—
780C23—944no—
781C23C24×D4712yes—
782C23C24×D4711yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—948no—
786Q8—948no—
787D4—4716no—
788D4—9432no—
789D4—9416no—
790D4—948no—
791D4—1888no—
792C2×C4—22no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—44no—
801C2×C4—474no—
802C2×C4—474no—
803C2×C4—474no—
804C2×C4—474no—
805C2×C4—474no—
806C2×C4—474no—
807C2×C4—9416no—
808C2×C4—9432no—
809C2×C4—944no—
810C2×C4—944no—
811C2×C4—944no—
812C2×C4—944no—
813C2×C4—944no—
814C2×C4—944no—
815C2×C4—9416no—
816C2×C4—9416no—
817C2×C4—1888no—
818C2×C4—18816no—
819C2×C4—18816no—
820C2×C4#41×D4714yes—
821C2×C4#1309407214yes—
822C2×C4C24×D4712yes—
823C2×C4C24×D4712yes—
824C2×C4C24×D4718yes—
825C2×C4C24×D4712yes—
826C2×C4C24×D4712yes—
827C2×C4C24×D4718yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—478no—
835C22—9416no—
836C22—944no—
837C22—944no—
838C22—944no—
839C22—944no—
840C22—944no—
841C22—1888no—
842C22C2×#41×D4712yes—
843C22C2×#1309407212yes—
844C22#1568995912yes—
845C22C25×D4711yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—944no—
853C4—944no—
854C4—944no—
855C4—944no—
856C4—944no—
857C4—944no—
858C4C2×#41×D4714yes—
859C4C2×#1309407214yes—
860C2—42no—
861C2—948no—
862C2—1884no—
863C2#2025736114yesdirect product factor
864C2C22×#41×D4711yescharacteristic
865C2C22×#1309407211yescharacteristic
866C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#533C2
socleC23×C47C25
hypercenterC2×#533D47
hypocenterC47C2×#3515
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20257361C2direct (N × H)
2. C2×#15689848C2semidirect
3. C2×#15689834C2semidirect
4. C2×#15689834C2semidirect
5. C2×#15689817C2semidirect
6. C2×#15689814C2semidirect
7. C2×#15689812C2semidirect
8. C2×#15689807C2semidirect
9. C2×#15689776C2semidirect
10. C2×#15689775C2semidirect
11. C2×#15689731C2semidirect
12. C2×#15689719C2semidirect
13. C2×#15689658C2semidirect
14. C2×#15689657C2semidirect
15. C2×#125×D47C2semidirect
16. C2×#15689605C2semidirect
17. C2×C4×#10625350C2semidirect
18. C2×C47×#533C2semidirect
21. #15689848C22semidirect
22. #15689834C22semidirect
23. #15689834C22semidirect
24. #15689817C22semidirect
25. #15689814C22semidirect
26. #15689812C22semidirect
27. #15689807C22semidirect
28. #15689776C22semidirect
29. #15689775C22semidirect
30. #15689731C22semidirect
31. #15689719C22semidirect
33. #15689658C22semidirect
34. #15689657C22semidirect
47. #125×D47C22semidirect
63. #15689605C22semidirect
64. C4×#10625350C22semidirect
91. C47×#533C22semidirect
439. C2×#533D47semidirect
446. C2×C47#3515semidirect
465. #533C2×D47semidirect
534. C47C2×#3515semidirect
863. C2#20257361direct (N × H)

Maximal subgroups

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

subgroupindex
#202573612
C2×#156898482
C2×#156898342
C2×#156898172
C2×#156898142
C2×#156898122
C2×#156898072
C2×#156897762
C2×#156897752
C2×#156897312
C2×#156897192
C2×#156896582
C2×#156896572
C2×#125×D472
C2×#156896052
C2×C4×#106253502
C2×C47×#5332
C2×#351547