Finite Group Databasebeta

← C2×#20257860 #27123902

Subgroups — C2×#20257860 #27123902

Order 12032.

7182 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#20257860C2132yesmaximal, direct product factor
2C2×#15689869C214yesmaximal, complemented
3C2×#15689858C211yesmaximal, characteristic, complemented
4C2×#15689856C212yesmaximal, complemented
5C2×#15689848C211yesmaximal, characteristic, complemented
6C2×#15689834C212yesmaximal, complemented
7C2×#15689794C211yesmaximal, characteristic, complemented
8C2×#15689784C212yesmaximal, complemented
9C2×#15689775C212yesmaximal, complemented
10C2×#15689747C212yesmaximal, complemented
11C2×#15689746C212yesmaximal, complemented
12C2×#15689724C212yesmaximal, complemented
13C2×#15689719C214yesmaximal, complemented
14C2×#15689697C212yesmaximal, complemented
15C2×#15689677C211yesmaximal, characteristic, complemented
16C2×#15689674C211yesmaximal, characteristic, complemented
17C2×#15689655C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×#10625350C2212yes—
21#15689869C22164yescomplemented
22#15689858C22116yescomplemented
23#15689856C22132yescomplemented
24#15689848C22116yescomplemented
25#15689834C22132yescomplemented
26#15689794C22116yescomplemented
27#15689784C22132yescomplemented
28#15689775C22132yescomplemented
29#15689747C22132yescomplemented
30#15689746C22132yescomplemented
31#15689724C22132yescomplemented
32#15689719C22164yescomplemented
33#15689697C22132yescomplemented
34#15689677C22116yescomplemented
35#15689674C22116yescomplemented
36C2×#13094023C2211yescharacteristic
37C2×#13094022C2212yes—
38C2×#13094022C2211yescharacteristic
39C2×#13094021C2211yescharacteristic
40C2×#13094020C2212yes—
41#15689655C22116yescomplemented
42C2×#13094019C2214yes—
43C2×#13094017C2212yes—
44C2×#13094015C2211yescharacteristic
45C2×#13094015C2212yes—
46C2×#13094014C2212yes—
47C2×#13094014C2214yes—
48C2×#13094013C2212yes—
49C2×#13094013C2214yes—
50C2×#13094013C2212yes—
51C2×#13094012C2212yes—
52C2×#13094011C2211yescharacteristic
53C2×#13094010C2214yes—
54C2×#13094009C2214yes—
55C2×#13094009C2214yes—
56C2×#13094007C2214yes—
57C2×#13094007C2214yes—
58C2×#13094006C2214yes—
59C2×#13094006C2214yes—
60C2×#13094006C2212yes—
61C2×#13094004C2214yes—
62C2×#13094004C2211yescharacteristic
63C2×#13094004C2211yescharacteristic
64C2×#13094002C2212yes—
65C2×#13094000C2214yes—
66C2×#13094000C2211yescharacteristic
67C2×#13094000C2214yes—
68C2×#13094000C2214yes—
69C2×#13093999C2212yes—
70C2×#13093999C2212yes—
71C2×#13093998C2212yes—
72C2×#13093998C2214yes—
73C2×#13093997C2214yes—
74C2×#13093997C2214yes—
75C2×#13093995C2211yescharacteristic
76C2×Q8×Dic47C2212yes—
77C2×C4×Dic94C2211yescharacteristic
78C2×C4×Dic94C2211yescharacteristic
79C2×C4×Dic94C2212yes—
80C2×#13093989C2212yes—
81C2×C4×D188C2212yes—
82C2×#13093986C2212yes—
83C2×#13093986C2212yes—
84C2×#13093986C2212yes—
85C2×#13093986C2212yes—
86C2×C4×C22⋊D47C2212yes—
87C2×C4×C22⋊D47C2214yes—
88C2×#13093983C2212yes—
89C2×#13093981C2212yes—
90C2×C4⋊C4×D47C2214yes—
91C2×C42×D47C2211yescharacteristic
92C23×Q8×C47C2212yes—
93D4×Q8×C47C22116yescomplemented
94C2×C4⋊Q8×C47C2212yes—
95C2×C4⋊Q8×C47C2211yescharacteristic
96C2×C22⋊Q8×C47C2212yes—
97C2×C22⋊Q8×C47C2214yes—
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×D4×C47C2211yescharacteristic
100C2×C4×D4×C47C2212yes—
101C2×#10625354—48no—
102C2×#10625354C23116yes—
103C2×#10625350—48no—
104C2×#10625350C23116yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2311yescharacteristic
107C22×Dic94C2312yes—
108C22×D188C2312yes—
109C22×D188C2312yes—
110C22×D188C2312yes—
111C22×D188C2314yes—
112C22×C22⋊D47C2312yes—
113C22×C22⋊D47C2314yes—
114C22×C22⋊D47C2314yes—
115C22×C4×D47C2311yescharacteristic
116C22×C4×D47C2311yescharacteristic
117C22×C4×D47C2311yescharacteristic
118C22×C4×D47C2314yes—
119C22×C4×D47C2314yes—
120C22×C4×D47C2314yes—
121#13094023C2318yes—
122#13094022C23116yes—
123#13094022C2318yes—
124#13094021C2318yes—
125#13094020C23116yes—
126#13094019C23132yes—
127#13094017C23116yes—
128#13094015C2318yes—
129#13094015C23116yes—
130#13094014C23132yes—
131#13094014C23116yes—
132#13094013C23116yes—
133#13094013C23132yes—
134#13094013C23116yes—
135#13094012C23116yes—
136#13094011C2318yes—
137#13094010C23132yes—
138#13094009C23132yes—
139#13094009C23132yes—
140#13094007C23132yes—
141#13094007C23132yes—
142#13094006C23132yes—
143#13094006C23132yes—
144#13094006C23116yes—
145#13094004C23132yes—
146#13094004C2318yes—
147#13094004C2318yes—
148#13094002C23116yes—
149#13094000C23132yes—
150#13094000C2318yes—
151#13094000C23132yes—
152#13094000C23132yes—
153#13093999C23116yes—
154#13093999C23116yes—
155#13093998C23116yes—
156#13093998C23132yes—
157#13093997C23132yes—
158#13093997C23132yes—
159#13093995C2318yes—
160Q8×Dic47C23116yes—
161C4×Dic94C2318yes—
162C4×Dic94C23116yes—
163C4×Dic94C2318yes—
164#13093989C23116yes—
165C4×D188C23116yes—
166#13093986C23116yes—
167#13093986C23116yes—
168#13093986C23116yes—
169#13093986C23116yes—
170C4×C22⋊D47C23116yes—
171C4×C22⋊D47C23132yes—
172#13093983C23116yes—
173#13093981C23116yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2311yescharacteristic
179C2×C4⋊Dic47C2314yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C4⋊C4×D47C23132yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2314yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2314yes—
208C42×D47C2318yes—
209C22×Q8×C47—48no—
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C22×Q8×C47C23116yes—
213C22×Q8×C47C2314yes—
214C22×D4×C47C2311yescharacteristic
215C23×C4×C47C2312yes—
216C23×C4×C47C2314yes—
217C4⋊Q8×C47C23116yes—
218C4⋊Q8×C47C2318yes—
219C22⋊Q8×C47C23116yes—
220C22⋊Q8×C47C23132yes—
221C4×Q8×C47C2318yes—
222C4×D4×C47C2318yes—
223C4×D4×C47C23116yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C4⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2312yes—
231C2×C22⋊C4×C47C2314yes—
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2312yes—
234C24×C47C2412yes—
235C23×D47C2411yescharacteristic
236C23×D47C2414yes—
237C2×Q8×C47—24no—
238C2×Q8×C47—28no—
239C2×Q8×C47—48no—
240C2×Q8×C47—432no—
241C2×Q8×C47C2414yes—
242C2×Q8×C47C2418yes—
243C2×Q8×C47C24116yes—
244C2×D4×C47—24no—
245C2×D4×C47C2414yes—
246C22×C4×C47—28no—
247C22×C4×C47—48no—
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2412yes—
250C22×C4×C47C2412yes—
251C22×C4×C47C2414yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2418yes—
254C22×C4×C47C24116yes—
255C22×C4×C47C2411yescharacteristic
256C22×C4×C47C2411yescharacteristic
257C2×C22⋊D47—48no—
258C2×C22⋊D47—44no—
259C2×C22⋊D47—48no—
260C2×C22⋊D47C2418yes—
261C2×C22⋊D47C24116yes—
262C2×C22⋊D47C24116yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2411yescharacteristic
266C22×Dic47C2411yescharacteristic
267C22×Dic47C2411yescharacteristic
268C22×Dic47C2412yes—
269C22×Dic47C2412yes—
270#10625354—432no—
271#10625350—432no—
272C2×D188—28no—
273C2×D188—28no—
274C2×D188—44no—
275C2×D188—48no—
276C2×D188C2418yes—
277C2×D188C2418yes—
278C2×D188C2418yes—
279C2×D188C24116yes—
280C2×C4×D47—24no—
281C2×C4×D47—24no—
282C2×C4×D47—42no—
283C2×C4×D47—48no—
284C2×C4×D47—48no—
285C2×C4×D47—48no—
286C2×C4×D47C2414yes—
287C2×C4×D47C2414yes—
288C2×C4×D47C2414yes—
289C2×C4×D47C24116yes—
290C2×C4×D47C24116yes—
291C2×C4×D47C24116yes—
292C2×Dic94—24no—
293C2×Dic94—24no—
294C2×Dic94—44no—
295C2×Dic94C2414yes—
296C2×Dic94C2414yes—
297C2×Dic94C2418yes—
298C4⋊C4×C47C2414yes—
299C4⋊C4×C47C2418yes—
300C4⋊C4×C47C2414yes—
301C4⋊C4×C47C2418yes—
302C4⋊C4×C47C24116yes—
303C4⋊C4×C47C2418yes—
304C22⋊C4×C47C2418yes—
305C22⋊C4×C47C24116yes—
306C42×C47C2414yes—
307C42×C47C2418yes—
308C22⋊Dic47C2418yes—
309C22⋊Dic47C2418yes—
310C22⋊Dic47C2418yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C2418yes—
313(C2×D47)⋊C4C24116yes—
314(C2×D47)⋊C4C2418yes—
315(C2×D47)⋊C4C24116yes—
316(C2×D47)⋊C4C24116yes—
317(C2×D47)⋊C4C24116yes—
318(C2×D47)⋊C4C24116yes—
319(C2×D47)⋊C4C24116yes—
320C4⋊Dic47C2418yes—
321C4⋊Dic47C2418yes—
322C4⋊Dic47C2418yes—
323C4⋊Dic47C2414yes—
324C4⋊Dic47C2414yes—
325C4⋊Dic47C24116yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C24116yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C2418yes—
330Dic47⋊C4C2418yes—
331Dic47⋊C4C24116yes—
332Dic47⋊C4C2418yes—
333Dic47⋊C4C2418yes—
334Dic47⋊C4C2418yes—
335C4×Dic47C2414yes—
336C4×Dic47C2414yes—
337C4×Dic47C2414yes—
338C4×Dic47C2418yes—
339C4×Dic47C2418yes—
340C4×Dic47C24116yes—
341C23×C47—24no—
342C23×C47—24no—
343C23×C47—24no—
344C23×C47C2514yes—
345C23×C47C2511yescharacteristic
346C22×D47—22no—
347C22×D47—28no—
348C22×D47—22no—
349C22×D47—28no—
350C22×D47—28no—
351C22×D47—22no—
352C22×D47C2512yes—
353C22×D47C2518yes—
354Q8×C47—216no—
355Q8×C47—28no—
356Q8×C47—416no—
357D4×C47—28no—
358C2×C4×C47—24no—
359C2×C4×C47—28no—
360C2×C4×C47—24no—
361C2×C4×C47—24no—
362C2×C4×C47—22no—
363C2×C4×C47—216no—
364C2×C4×C47—416no—
365C2×C4×C47H(5,𝔽2)14yes—
366C2×C4×C472−1+414yes—
367C2×C4×C47C2512yes—
368C2×C4×C47C2518yes—
369C2×C4×C47C2514yes—
370C2×C4×C47C2514yes—
371C2×C4×C47C2514yes—
372C2×C4×C47C2512yes—
373C2×C4×C47C2512yes—
374C22⋊D47—416no—
375C22⋊D47—416no—
376C22⋊D47—48no—
377C2×Dic47—24no—
378C2×Dic47—22no—
379C2×Dic47—24no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—24no—
383C2×Dic47—24no—
384C2×Dic47C2514yes—
385C2×Dic47C2514yes—
386C2×Dic47C2512yes—
387C2×Dic47C2512yes—
388C2×Dic47C2512yes—
389C2×Dic47C2514yes—
390C2×Dic47C2514yes—
391D188—216no—
392D188—216no—
393D188—48no—
394D188—416no—
395C4×D47—28no—
396C4×D47—28no—
397C4×D47—44no—
398C4×D47—416no—
399C4×D47—416no—
400C4×D47—416no—
401Dic94—28no—
402Dic94—28no—
403Dic94—48no—
404C2×#3554—471nomaximal, Sylow
405C22×C47—24no—
406C22×C47—24no—
407C22×C47—24no—
408C22×C47—48no—
409C22×C47C2×H(5,𝔽2)12yes—
410C22×C47C2×2−1+412yes—
411C22×C47#58512yes—
412C22×C47C2611yescharacteristic
413C2×D47—22no—
414C2×D47—28no—
415C2×D47—22no—
416C2×D47—28no—
417C2×D47—28no—
418C2×D47—22no—
419C2×D47—44no—
420C2×D47—416no—
421C4×C47—24no—
422C4×C47—28no—
423C4×C47—24no—
424C4×C47—24no—
425C4×C47—22no—
426C4×C47C2×H(5,𝔽2)14yes—
427C4×C47C2×2−1+414yes—
428Dic47—24no—
429Dic47—22no—
430Dic47—24no—
431Dic47—22no—
432Dic47—22no—
433Dic47—24no—
434Dic47—24no—
435#3554—4732no—
436C2×#562—474no—
437C2×#559—471no—
438C2×#559—472no—
439C2×#557—471no—
440C2×#554—472no—
441C2×#550—471no—
442C2×D4×Q8D4711yescharacteristic, complemented
443C2×#548—472no—
444C2×#547—472no—
445C2×#542—472no—
446C2×#542—472no—
447C2×#540—472no—
448C2×#539—474no—
449C2×#536—472no—
450C2×#533—471no—
451C2×#532—471no—
452C2×#529—471no—
453C2×C47—44no—
454C2×C47#355414yescomplemented
455C2×C47C22×H(5,𝔽2)11yescharacteristic
456C2×C47C22×2−1+411yescharacteristic
457C2×C47C2×#58511yescharacteristic
458D47—42no—
459D47—48no—
460C22×#41—472no—
461C22×#41—472no—
462C23×Q8C2×D4712yes—
463#562—4764no—
464#559—4716no—
465#559—4732no—
466#557—4716no—
467#554—4732no—
468#550—4716no—
469D4×Q8C2×D47116yescomplemented
470#548—4732no—
471#547—4732no—
472#542—4732no—
473#542—4732no—
474#540—4732no—
475#539—4764no—
476#536—4732no—
477#533—4716no—
478#532—4716no—
479C2×C4⋊Q8—471no—
480C2×C4⋊Q8—472no—
481C2×C4⋊Q8—471no—
482C2×C4⋊Q8C2×D4711yescharacteristic
483C2×C4⋊Q8C2×D4712yes—
484C2×#127—472no—
485C2×#127—471no—
486#529—4716no—
487C2×#126—474no—
488C2×#126—472no—
489C2×#125—471no—
490C2×#125—472no—
491C2×#125—474no—
492C2×#125—472no—
493C2×#124—472no—
494C2×#124—472no—
495C2×#124—474no—
496C2×#124—471no—
497C2×#124—474no—
498C2×#124—472no—
499C2×#123—474no—
500C2×#123—474no—
501C2×#123—474no—
502C2×#123—474no—
503C2×#123—472no—
504C2×#123—474no—
505C2×#123—474no—
506C2×C22⋊Q8—471no—
507C2×C22⋊Q8—474no—
508C2×C22⋊Q8—474no—
509C2×C22⋊Q8—474no—
510C2×C22⋊Q8—471no—
511C2×C22⋊Q8—471no—
512C2×C22⋊Q8—472no—
513C2×C22⋊Q8—474no—
514C2×C22⋊Q8C2×D4714yes—
515C2×C22⋊Q8C2×D4712yes—
516C2×#121—471no—
517C2×#121—474no—
518C2×#121—472no—
519C2×#121—472no—
520C2×#121—472no—
521C2×#121—474no—
522C2×#121—474no—
523C2×C4×Q8—472no—
524C2×C4×Q8—472no—
525C2×C4×Q8—471no—
526C2×C4×Q8—471no—
527C2×C4×Q8—472no—
528C2×C4×Q8C2×D4711yescharacteristic
529C2×C4×D4—472no—
530C2×C4×D4—474no—
531C2×C4×D4—472no—
532C2×C4×D4—472no—
533C2×C4×D4—472no—
534C2×C4×D4—472no—
535C2×C4×D4—472no—
536C2×C4×D4C2×D4711yescharacteristic
537C2×C4×D4C2×D4712yes—
538C2×#117—472no—
539C2×#117—472no—
540C22×C4⋊C4—474no—
541C22×C42—471no—
542C47C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—4716no—
544C2×#41—4716no—
545C2×#41—1888no—
546C2×#41—1888no—
547C22×Q8—48no—
548C22×Q8—471no—
549C22×Q8—471no—
550C22×Q8—472no—
551C22×Q8C22×D4712yes—
552C22×Q8C22×D4711yescharacteristic
553C22×Q8C22×D4714yes—
554C22×Q8C22×D47116yes—
555C22×D4—472no—
556C22×D4—474no—
557C22×D4—474no—
558C22×D4—472no—
559C22×D4—472no—
560C22×D4—472no—
561C22×D4—474no—
562C22×D4C22×D4711yescharacteristic
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—474no—
566C23×C4—474no—
567C23×C4—474no—
568C23×C4—471no—
569C23×C4C22×D4712yes—
570C23×C4C22×D4714yes—
571C4⋊Q8—478no—
572C4⋊Q8—4716no—
573C4⋊Q8—478no—
574C4⋊Q8C22×D4718yes—
575C4⋊Q8C22×D47116yes—
576#127—4716no—
577#127—478no—
578#126—4732no—
579#126—4716no—
580#125—478no—
581#125—4716no—
582#125—4732no—
583#125—4716no—
584#124—4716no—
585#124—4716no—
586#124—4732no—
587#124—478no—
588#124—4732no—
589#124—4716no—
590#123—4732no—
591#123—4732no—
592#123—4732no—
593#123—4732no—
594#123—4716no—
595#123—4732no—
596#123—4732no—
597C22⋊Q8—478no—
598C22⋊Q8—4732no—
599C22⋊Q8—4732no—
600C22⋊Q8—4732no—
601C22⋊Q8—478no—
602C22⋊Q8—478no—
603C22⋊Q8—4716no—
604C22⋊Q8—4732no—
605C22⋊Q8C22×D47132yes—
606C22⋊Q8C22×D47116yes—
607#121—478no—
608#121—4732no—
609#121—4716no—
610#121—4716no—
611#121—4716no—
612#121—4732no—
613#121—4732no—
614C4×Q8—4716no—
615C4×Q8—4716no—
616C4×Q8—478no—
617C4×Q8—478no—
618C4×Q8—4716no—
619C4×Q8C22×D4718yes—
620C4×D4—4716no—
621C4×D4—4732no—
622C4×D4—4716no—
623C4×D4—4716no—
624C4×D4—4716no—
625C4×D4—4716no—
626C4×D4—4716no—
627C4×D4C22×D4718yes—
628C4×D4C22×D47116yes—
629#117—4716no—
630#117—4716no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—472no—
635C2×C4⋊C4—472no—
636C2×C4⋊C4—472no—
637C2×C4⋊C4—472no—
638C2×C4⋊C4—471no—
639C2×C4⋊C4—472no—
640C2×C4⋊C4—471no—
641C2×C4⋊C4—472no—
642C2×C4⋊C4—474no—
643C2×C4⋊C4—472no—
644C2×C4⋊C4—474no—
645C2×C4⋊C4—472no—
646C2×C4⋊C4—4732no—
647C2×C4⋊C4C22×D4714yes—
648C2×C4⋊C4C22×D4711yescharacteristic
649C2×C4⋊C4C22×D4711yescharacteristic
650C2×C4⋊C4C22×D4712yes—
651C2×C4⋊C4C22×D4712yes—
652C2×C4⋊C4C22×D4712yes—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—472no—
655C2×C22⋊C4—472no—
656C2×C22⋊C4—472no—
657C2×C22⋊C4—472no—
658C2×C22⋊C4—474no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—472no—
663C2×C22⋊C4—474no—
664C2×C22⋊C4—474no—
665C2×C22⋊C4C22×D4712yes—
666C2×C22⋊C4C22×D4714yes—
667C2×C42—471no—
668C2×C42—472no—
669C2×C42—472no—
670C2×C42—471no—
671C2×C42—471no—
672C2×C42—474no—
673C2×C42—478no—
674C2×C42C22×D4712yes—
675C2×C42C22×D4711yescharacteristic
676C24—471no—
677C24—474no—
678C24C23×D4712yes—
679#41—18832no—
680#41—18832no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—474no—
686C2×Q8—474no—
687C2×Q8—478no—
688C2×Q8—944no—
689C2×Q8—944no—
690C2×Q8—1884no—
691C2×Q8C23×D4718yes—
692C2×Q8C23×D4714yes—
693C2×Q8C23×D47116yes—
694C2×D4—24no—
695C2×D4—478no—
696C2×D4—4716no—
697C2×D4—4716no—
698C2×D4—478no—
699C2×D4—478no—
700C2×D4—478no—
701C2×D4—4716no—
702C2×D4—948no—
703C2×D4—948no—
704C2×D4—1884no—
705C2×D4—1888no—
706C2×D4—1884no—
707C2×D4—1888no—
708C2×D4—1888no—
709C2×D4C23×D4714yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—471no—
715C22×C4—471no—
716C22×C4—471no—
717C22×C4—472no—
718C22×C4—472no—
719C22×C4—474no—
720C22×C4—474no—
721C22×C4—474no—
722C22×C4—4716no—
723C22×C4—4716no—
724C22×C4—4716no—
725C22×C4—944no—
726C22×C4—944no—
727C22×C4—1888no—
728C22×C4—1882no—
729C22×C4—1888no—
730C22×C4—1888no—
731C22×C4C23×D4718yes—
732C22×C4C23×D4711yescharacteristic
733C22×C4C23×D4714yes—
734C22×C4C23×D4712yes—
735C22×C4C23×D4712yes—
736C22×C4C23×D4712yes—
737C22×C4C23×D47116yes—
738C22×C4C23×D4711yescharacteristic
739C22×C4C23×D4711yescharacteristic
740C4⋊C4—478no—
741C4⋊C4—4716no—
742C4⋊C4—478no—
743C4⋊C4—478no—
744C4⋊C4—478no—
745C4⋊C4—478no—
746C4⋊C4—478no—
747C4⋊C4—4716no—
748C4⋊C4—478no—
749C4⋊C4—478no—
750C4⋊C4—478no—
751C4⋊C4—478no—
752C4⋊C4—474no—
753C4⋊C4—474no—
754C4⋊C4—4716no—
755C4⋊C4C23×D47116yes—
756C4⋊C4C23×D4714yes—
757C4⋊C4C23×D4714yes—
758C4⋊C4C23×D4718yes—
759C4⋊C4C23×D4718yes—
760C4⋊C4C23×D4718yes—
761C22⋊C4—478no—
762C22⋊C4—478no—
763C22⋊C4—478no—
764C22⋊C4—478no—
765C22⋊C4—478no—
766C22⋊C4—4716no—
767C22⋊C4—4716no—
768C22⋊C4—4716no—
769C22⋊C4—4716no—
770C22⋊C4—478no—
771C22⋊C4—4716no—
772C22⋊C4—4716no—
773C22⋊C4C23×D4718yes—
774C22⋊C4C23×D47116yes—
775C42—474no—
776C42—474no—
777C42—474no—
778C42—478no—
779C42—478no—
780C42—4716no—
781C42C23×D4714yes—
782C42C23×D4718yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—472no—
787C23—478no—
788C23—942no—
789C23—948no—
790C23—942no—
791C23—948no—
792C23—948no—
793C23—942no—
794C23C24×D4714yes—
795C23C24×D4711yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—948no—
800Q8—948no—
801Q8—1888no—
802D4—28no—
803D4—9416no—
804D4—9416no—
805D4—1888no—
806D4—18816no—
807D4—1888no—
808D4—18816no—
809D4—18816no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—474no—
818C2×C4—474no—
819C2×C4—472no—
820C2×C4—472no—
821C2×C4—472no—
822C2×C4—474no—
823C2×C4—474no—
824C2×C4—942no—
825C2×C4—944no—
826C2×C4—942no—
827C2×C4—944no—
828C2×C4—944no—
829C2×C4—942no—
830C2×C4—944no—
831C2×C4—948no—
832C2×C4—948no—
833C2×C4—18816no—
834C2×C4—1884no—
835C2×C4—18816no—
836C2×C4—18816no—
837C2×C4#1309406914yes—
838C2×C4#1309407214yes—
839C2×C4C24×D4712yes—
840C2×C4C24×D4718yes—
841C2×C4C24×D4714yes—
842C2×C4C24×D4714yes—
843C2×C4C24×D4714yes—
844C2×C4C24×D4712yes—
845C2×C4C24×D4712yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—942no—
851C22—948no—
852C22—942no—
853C22—948no—
854C22—948no—
855C22—942no—
856C22—1884no—
857C22—18816no—
858C22C2×#1309406912yes—
859C22C2×#1309407212yes—
860C22#1568996012yes—
861C22C25×D4711yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—942no—
868C4—944no—
869C4—942no—
870C4—944no—
871C4—944no—
872C4—942no—
873C4—944no—
874C4C2×#1309406914yes—
875C4C2×#1309407214yes—
876C2—44no—
877C2—1882no—
878C2—1888no—
879C2#2025786014yesdirect product factor
880C2C22×#1309406911yescharacteristic
881C2C22×#1309407211yescharacteristic
882C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×D4×Q8×C47C2
socleC23×C47C25
hypercenterC2×D4×Q8D47
hypocenterC47C2×#3554
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257860C2direct (N × H)
2. C2×#15689869C2semidirect
3. C2×#15689858C2semidirect
4. C2×#15689856C2semidirect
5. C2×#15689848C2semidirect
6. C2×#15689834C2semidirect
7. C2×#15689794C2semidirect
8. C2×#15689784C2semidirect
9. C2×#15689775C2semidirect
10. C2×#15689747C2semidirect
11. C2×#15689746C2semidirect
12. C2×#15689724C2semidirect
13. C2×#15689719C2semidirect
14. C2×#15689697C2semidirect
15. C2×#15689677C2semidirect
16. C2×#15689674C2semidirect
17. C2×#15689655C2semidirect
18. C2×D4×Q8×C47C2semidirect
21. #15689869C22semidirect
22. #15689858C22semidirect
23. #15689856C22semidirect
24. #15689848C22semidirect
25. #15689834C22semidirect
26. #15689794C22semidirect
27. #15689784C22semidirect
28. #15689775C22semidirect
29. #15689747C22semidirect
30. #15689746C22semidirect
31. #15689724C22semidirect
32. #15689719C22semidirect
33. #15689697C22semidirect
34. #15689677C22semidirect
35. #15689674C22semidirect
41. #15689655C22semidirect
93. D4×Q8×C47C22semidirect
442. C2×D4×Q8D47semidirect
454. C2×C47#3554semidirect
469. D4×Q8C2×D47semidirect
542. C47C2×#3554semidirect
879. C2#20257860direct (N × H)

Maximal subgroups

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

subgroupindex
#202578602
C2×#156898692
C2×#156898582
C2×#156898562
C2×#156898482
C2×#156898342
C2×#156897942
C2×#156897842
C2×#156897752
C2×#156897472
C2×#156897462
C2×#156897242
C2×#156897192
C2×#156896972
C2×#156896772
C2×#156896742
C2×#156896552
C2×D4×Q8×C472
C2×#355447