Finite Group Databasebeta

← C2×#20257862 #27123908

Subgroups — C2×#20257862 #27123908

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#20257862C2132yesmaximal, direct product factor
2C2×#15689871C214yesmaximal, complemented
3C2×#15689858C211yesmaximal, characteristic, complemented
4C2×#15689858C212yesmaximal, complemented
5C2×#15689829C212yesmaximal, complemented
6C2×#15689795C211yesmaximal, characteristic, complemented
7C2×#15689788C211yesmaximal, characteristic, complemented
8C2×#15689785C212yesmaximal, complemented
9C2×#15689776C212yesmaximal, complemented
10C2×#15689745C212yesmaximal, complemented
11C2×#15689745C212yesmaximal, complemented
12C2×#15689729C212yesmaximal, complemented
13C2×#15689721C214yesmaximal, complemented
14C2×#15689698C212yesmaximal, complemented
15C2×#15689677C211yesmaximal, characteristic, complemented
16C2×#15689674C211yesmaximal, characteristic, complemented
17C2×#15689660C211yesmaximal, characteristic, complemented
18C2×C47×#557C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×#10625354C2212yes—
21C22×Q8×D47C2212yes—
22#15689871C22164yescomplemented
23#15689858C22132yescomplemented
24#15689858C22116yescomplemented
25#15689829C22132yescomplemented
26#15689795C22116yescomplemented
27#15689788C22116yescomplemented
28#15689785C22132yescomplemented
29#15689776C22132yescomplemented
30#15689745C22132yescomplemented
31#15689745C22132yescomplemented
32#15689729C22132yescomplemented
33#15689721C22164yescomplemented
34#15689698C22132yescomplemented
35#15689677C22116yescomplemented
36#15689674C22116yescomplemented
37C2×#13094023C2212yes—
38C2×#13094023C2211yescharacteristic
39C2×#13094022C2211yescharacteristic
40C2×#13094021C2211yescharacteristic
41C2×#13094021C2212yes—
42#15689660C22116yescomplemented
43C2×#13094019C2212yes—
44C2×#13094018C2214yes—
45C2×#13094015C2211yescharacteristic
46C2×#13094014C2212yes—
47C2×#13094013C2211yescharacteristic
48C2×#13094013C2212yes—
49C2×#13094013C2212yes—
50C2×#13094012C2212yes—
51C2×#13094012C2214yes—
52C2×#13094012C2214yes—
53C2×#13094009C2214yes—
54C2×#13094009C2214yes—
55C2×#13094009C2212yes—
56C2×#13094009C2214yes—
57C2×#13094009C2214yes—
58C2×#13094009C2214yes—
59C2×#13094009C2214yes—
60C2×#13094004C2211yescharacteristic
61C2×#13094004C2214yes—
62C2×#13094002C2214yes—
63C2×#13094002C2214yes—
64C2×#13094002C2214yes—
65C2×#13094002C2212yes—
66C2×#13094002C2214yes—
67C2×#13094000C2211yescharacteristic
68C2×#13094000C2212yes—
69C2×#13094000C2211yescharacteristic
70C2×#13093999C2214yes—
71C2×#13093999C2212yes—
72C2×#13093999C2214yes—
73C2×#13093999C2214yes—
74C2×#13093999C2211yescharacteristic
75C2×#13093999C2212yes—
76C2×#13093999C2212yes—
77C2×C4×Dic94C2211yescharacteristic
78C2×C4×Dic94C2212yes—
79C2×C4×D188C2212yes—
80C2×C4×D188C2212yes—
81C2×C4×D188C2214yes—
82C2×C4×D188C2211yescharacteristic
83C2×C4×D188C2212yes—
84C2×#13093986C2212yes—
85C2×#13093986C2212yes—
86C2×#13093986C2212yes—
87C2×#13093986C2212yes—
88C2×#13093981C2212yes—
89C2×#13093981C2212yes—
90C2×C4⋊C4×D47C2214yes—
91C2×C42×D47C2211yescharacteristic
92C47×#557C22116yescomplemented
93C2×C4⋊Q8×C47C2212yes—
94C2×C4⋊Q8×C47C2211yescharacteristic
95C2×#125×C47C2212yes—
96C2×#125×C47C2214yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×Q8×C47C2211yescharacteristic
100C2×C4×Q8×C47C2212yes—
101C2×#10625354—48no—
102C2×#10625354—48no—
103C2×#10625354C23116yes—
104C2×#10625354C23116yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2312yes—
107C22×Dic94C2314yes—
108C2×Q8×D47—48no—
109C2×Q8×D47C23116yes—
110C22×D188C2311yescharacteristic
111C22×D188C2312yes—
112C22×D188C2312yes—
113C22×D188C2312yes—
114C22×D188C2312yes—
115C22×D188C2314yes—
116C22×D188C2314yes—
117C22×D188C2314yes—
118C22×C4×D47C2311yescharacteristic
119C22×C4×D47C2311yescharacteristic
120C22×C4×D47C2312yes—
121C22×C4×D47C2311yescharacteristic
122C22×C4×D47C2314yes—
123C22×C4×D47C2314yes—
124C22×C4×D47C2314yes—
125C22×C4×D47C2314yes—
126#13094023C2318yes—
127#13094023C23116yes—
128#13094022C2318yes—
129#13094021C23116yes—
130#13094021C2318yes—
131#13094019C23116yes—
132#13094018C23132yes—
133#13094015C2318yes—
134#13094014C23116yes—
135#13094013C23116yes—
136#13094013C23116yes—
137#13094013C2318yes—
138#13094012C23132yes—
139#13094012C23132yes—
140#13094012C23116yes—
141#13094009C23132yes—
142#13094009C23132yes—
143#13094009C23132yes—
144#13094009C23132yes—
145#13094009C23132yes—
146#13094009C23132yes—
147#13094009C23116yes—
148#13094004C2318yes—
149#13094004C23132yes—
150#13094002C23132yes—
151#13094002C23132yes—
152#13094002C23132yes—
153#13094002C23132yes—
154#13094002C23116yes—
155#13094000C2318yes—
156#13094000C23116yes—
157#13094000C2318yes—
158#13093999C2318yes—
159#13093999C23116yes—
160#13093999C23132yes—
161#13093999C23132yes—
162#13093999C23116yes—
163#13093999C23132yes—
164#13093999C23116yes—
165C4×Dic94C2318yes—
166C4×Dic94C23116yes—
167C4×D188C23116yes—
168C4×D188C23116yes—
169C4×D188C23116yes—
170C4×D188C23132yes—
171C4×D188C2318yes—
172#13093986C23116yes—
173#13093986C23116yes—
174#13093986C23116yes—
175#13093986C23116yes—
176#13093981C23116yes—
177#13093981C23116yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2312yes—
190C4⋊C4×D47C23132yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2314yes—
204C2×(C2×D47)⋊C4C2314yes—
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2312yes—
209C42×D47C2318yes—
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C22×Q8×C47C2311yescharacteristic
213C4⋊Q8×C47C23116yes—
214C4⋊Q8×C47C2318yes—
215#125×C47C23116yes—
216#125×C47C23132yes—
217C4×Q8×C47C23116yes—
218C4×Q8×C47C23116yes—
219C4×Q8×C47C2318yes—
220C4×Q8×C47C2318yes—
221C2×C4⋊C4×C47C2311yescharacteristic
222C2×C4⋊C4×C47C2311yescharacteristic
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2314yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2314yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C4⋊C4×C47C2312yes—
230C2×C42×C47C2312yes—
231C2×C42×C47C2314yes—
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2312yes—
234C23×D47C2412yes—
235C23×D47C2411yescharacteristic
236C23×D47C2414yes—
237C2×Q8×C47—28no—
238C2×Q8×C47—24no—
239C2×Q8×C47—24no—
240C2×Q8×C47C2414yes—
241C2×Q8×C47C2418yes—
242C2×Q8×C47C2414yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2412yes—
245C22×C4×C47C2411yescharacteristic
246C22×C4×C47C2412yes—
247C22×C4×C47C2414yes—
248C22×C4×C47C2412yes—
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2411yescharacteristic
251C22×Dic47C2411yescharacteristic
252C22×Dic47C2411yescharacteristic
253C22×Dic47C2411yescharacteristic
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257#10625354—432no—
258#10625354—432no—
259Q8×D47—432no—
260C2×D188—28no—
261C2×D188—24no—
262C2×D188—28no—
263C2×D188—48no—
264C2×D188—44no—
265C2×D188—44no—
266C2×D188—48no—
267C2×D188—48no—
268C2×D188C2414yes—
269C2×D188C2418yes—
270C2×D188C2418yes—
271C2×D188C2418yes—
272C2×D188C2418yes—
273C2×D188C24116yes—
274C2×D188C24116yes—
275C2×D188C24116yes—
276C2×C4×D47—28no—
277C2×C4×D47—24no—
278C2×C4×D47—24no—
279C2×C4×D47—42no—
280C2×C4×D47—48no—
281C2×C4×D47—48no—
282C2×C4×D47—48no—
283C2×C4×D47—48no—
284C2×C4×D47C2414yes—
285C2×C4×D47C2414yes—
286C2×C4×D47C2418yes—
287C2×C4×D47C2414yes—
288C2×C4×D47C24116yes—
289C2×C4×D47C24116yes—
290C2×C4×D47C24116yes—
291C2×C4×D47C24116yes—
292C2×Dic94—24no—
293C2×Dic94—48no—
294C2×Dic94—44no—
295C2×Dic94C2414yes—
296C2×Dic94C2418yes—
297C2×Dic94C24116yes—
298C4⋊C4×C47C2414yes—
299C4⋊C4×C47C2414yes—
300C4⋊C4×C47C2418yes—
301C4⋊C4×C47C24116yes—
302C4⋊C4×C47C2418yes—
303C4⋊C4×C47C2418yes—
304C4⋊C4×C47C24116yes—
305C4⋊C4×C47C24116yes—
306C4⋊C4×C47C2418yes—
307C42×C47C2418yes—
308C42×C47C24116yes—
309C42×C47C2414yes—
310C42×C47C2418yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C2418yes—
313(C2×D47)⋊C4C2418yes—
314(C2×D47)⋊C4C2418yes—
315(C2×D47)⋊C4C24116yes—
316(C2×D47)⋊C4C24116yes—
317(C2×D47)⋊C4C24116yes—
318(C2×D47)⋊C4C24116yes—
319(C2×D47)⋊C4C2418yes—
320(C2×D47)⋊C4C2418yes—
321(C2×D47)⋊C4C24116yes—
322(C2×D47)⋊C4C2418yes—
323(C2×D47)⋊C4C24116yes—
324(C2×D47)⋊C4C24116yes—
325C4⋊Dic47C2418yes—
326C4⋊Dic47C2414yes—
327C4⋊Dic47C2414yes—
328C4⋊Dic47C2418yes—
329Dic47⋊C4C2418yes—
330Dic47⋊C4C24116yes—
331Dic47⋊C4C2418yes—
332Dic47⋊C4C2418yes—
333Dic47⋊C4C2418yes—
334Dic47⋊C4C2418yes—
335Dic47⋊C4C2418yes—
336Dic47⋊C4C2418yes—
337C4×Dic47C2414yes—
338C4×Dic47C2414yes—
339C4×Dic47C2414yes—
340C4×Dic47C2418yes—
341C23×C47C2511yescharacteristic
342C22×D47—24no—
343C22×D47—22no—
344C22×D47—28no—
345C22×D47—22no—
346C22×D47—24no—
347C22×D47—28no—
348C22×D47—22no—
349C22×D47—28no—
350C22×D47—24no—
351C22×D47C2514yes—
352C22×D47C2512yes—
353C22×D47C2518yes—
354Q8×C47—216no—
355Q8×C47—28no—
356Q8×C47—28no—
357C2×C4×C47—28no—
358C2×C4×C47—24no—
359C2×C4×C47—24no—
360C2×C4×C47—24no—
361C2×C4×C47—24no—
362C2×C4×C47—22no—
363C2×C4×C47H(5,𝔽2)14yes—
364C2×C4×C472−1+414yes—
365C2×C4×C47C2512yes—
366C2×C4×C47C2514yes—
367C2×C4×C47C2514yes—
368C2×C4×C47C2514yes—
369C2×C4×C47C2514yes—
370C2×C4×C47C2518yes—
371C2×C4×C47C2512yes—
372C2×C4×C47C2512yes—
373C2×Dic47—24no—
374C2×Dic47—24no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—24no—
379C2×Dic47C2512yes—
380C2×Dic47C2512yes—
381C2×Dic47C2512yes—
382C2×Dic47C2514yes—
383C2×Dic47C2514yes—
384C2×Dic47C2514yes—
385D188—216no—
386D188—28no—
387D188—216no—
388D188—416no—
389D188—48no—
390D188—48no—
391D188—416no—
392D188—416no—
393C4×D47—216no—
394C4×D47—28no—
395C4×D47—28no—
396C4×D47—44no—
397C4×D47—416no—
398C4×D47—416no—
399C4×D47—416no—
400C4×D47—416no—
401Dic94—28no—
402Dic94—48no—
403Dic94—416no—
404C2×#3554—471nomaximal, Sylow
405C22×C47C2×H(5,𝔽2)12yes—
406C22×C47C2×2−1+412yes—
407C22×C47#58512yes—
408C22×C47C2611yescharacteristic
409C2×D47—24no—
410C2×D47—22no—
411C2×D47—28no—
412C2×D47—22no—
413C2×D47—24no—
414C2×D47—28no—
415C2×D47—22no—
416C2×D47—28no—
417C2×D47—24no—
418C2×D47—48no—
419C2×D47—44no—
420C2×D47—416no—
421C4×C47—28no—
422C4×C47—24no—
423C4×C47—24no—
424C4×C47—24no—
425C4×C47—24no—
426C4×C47—22no—
427C4×C47C2×H(5,𝔽2)14yes—
428C4×C47C2×2−1+414yes—
429Dic47—24no—
430Dic47—24no—
431Dic47—22no—
432Dic47—22no—
433Dic47—22no—
434Dic47—24no—
435#3554—4732no—
436C2×#562—474no—
437C2×#559—472no—
438C2×#559—471no—
439C2×#557D4711yescharacteristic, complemented
440C2×#554—472no—
441C2×#550—471no—
442C2×D4×Q8—471no—
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#355414yescomplemented
454C2×C47C22×H(5,𝔽2)11yescharacteristic
455C2×C47C22×2−1+411yescharacteristic
456C2×C47C2×#58511yescharacteristic
457D47—44no—
458D47—42no—
459D47—48no—
460C22×#41—472no—
461C22×#41—472no—
462C23×Q8—472no—
463#562—4764no—
464#559—4732no—
465#559—4716no—
466#557C2×D47116yescomplemented
467#554—4732no—
468#550—4716no—
469D4×Q8—4716no—
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—471no—
481C2×C4⋊Q8—472no—
482C2×C4⋊Q8C2×D4711yescharacteristic
483C2×C4⋊Q8C2×D4712yes—
484C2×#127—471no—
485C2×#127—472no—
486#529—4716no—
487C2×#126—472no—
488C2×#126—474no—
489C2×#125—471no—
490C2×#125—472no—
491C2×#125C2×D4714yes—
492C2×#125C2×D4712yes—
493C2×#124—471no—
494C2×#124—472no—
495C2×#124—472no—
496C2×#124—472no—
497C2×#124—474no—
498C2×#124—474no—
499C2×#123—472no—
500C2×#123—474no—
501C2×#123—474no—
502C2×#123—474no—
503C2×#123—474no—
504C2×#123—474no—
505C2×#123—474no—
506C2×C22⋊Q8—471no—
507C2×C22⋊Q8—471no—
508C2×C22⋊Q8—472no—
509C2×C22⋊Q8—471no—
510C2×C22⋊Q8—472no—
511C2×C22⋊Q8—474no—
512C2×C22⋊Q8—474no—
513C2×C22⋊Q8—474no—
514C2×C22⋊Q8—474no—
515C2×C22⋊Q8—474no—
516C2×#121—471no—
517C2×#121—472no—
518C2×#121—472no—
519C2×#121—474no—
520C2×#121—474no—
521C2×#121—474no—
522C2×#121—472no—
523C2×C4×Q8—471no—
524C2×C4×Q8—472no—
525C2×C4×Q8C2×D4711yescharacteristic
526C2×C4×Q8C2×D4711yescharacteristic
527C2×C4×Q8C2×D4712yes—
528C2×C4×Q8C2×D4712yes—
529C2×C4×D4—472no—
530C2×C4×D4—472no—
531C2×C4×D4—472no—
532C2×C4×D4—472no—
533C2×C4×D4—472no—
534C2×C4×D4—471no—
535C2×C4×D4—474no—
536C2×C4×D4—472no—
537C2×C4×D4—472no—
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—4716no—
548C22×Q8—471no—
549C22×Q8—472no—
550C22×Q8—474no—
551C22×Q8—1888no—
552C22×Q8C22×D4711yescharacteristic
553C22×Q8C22×D4712yes—
554C22×Q8C22×D4711yescharacteristic
555C22×D4—472no—
556C22×D4—471no—
557C22×D4—472no—
558C22×D4—472no—
559C22×D4—472no—
560C22×D4—474no—
561C22×D4—474no—
562C22×D4—474no—
563C23×C4—471no—
564C23×C4—472no—
565C23×C4—471no—
566C23×C4—474no—
567C23×C4—474no—
568C23×C4—474no—
569C23×C4—474no—
570C23×C4—471no—
571C4⋊Q8—478no—
572C4⋊Q8—478no—
573C4⋊Q8—4716no—
574C4⋊Q8C22×D4718yes—
575C4⋊Q8C22×D47116yes—
576#127—478no—
577#127—4716no—
578#126—4716no—
579#126—4732no—
580#125—478no—
581#125—4716no—
582#125C22×D47132yes—
583#125C22×D47116yes—
584#124—478no—
585#124—4716no—
586#124—4716no—
587#124—4716no—
588#124—4732no—
589#124—4732no—
590#123—4716no—
591#123—4732no—
592#123—4732no—
593#123—4732no—
594#123—4732no—
595#123—4732no—
596#123—4732no—
597C22⋊Q8—478no—
598C22⋊Q8—478no—
599C22⋊Q8—4716no—
600C22⋊Q8—478no—
601C22⋊Q8—4716no—
602C22⋊Q8—4732no—
603C22⋊Q8—4732no—
604C22⋊Q8—4732no—
605C22⋊Q8—4732no—
606C22⋊Q8—4732no—
607#121—478no—
608#121—4716no—
609#121—4716no—
610#121—4732no—
611#121—4732no—
612#121—4732no—
613#121—4716no—
614C4×Q8—478no—
615C4×Q8—4716no—
616C4×Q8C22×D4718yes—
617C4×Q8C22×D4718yes—
618C4×Q8C22×D47116yes—
619C4×Q8C22×D47116yes—
620C4×D4—4716no—
621C4×D4—4716no—
622C4×D4—4716no—
623C4×D4—4716no—
624C4×D4—4716no—
625C4×D4—478no—
626C4×D4—4732no—
627C4×D4—4716no—
628C4×D4—4716no—
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—472no—
643C2×C4⋊C4—4732no—
644C2×C4⋊C4C22×D4714yes—
645C2×C4⋊C4C22×D4711yescharacteristic
646C2×C4⋊C4C22×D4712yes—
647C2×C4⋊C4C22×D4712yes—
648C2×C4⋊C4C22×D4711yescharacteristic
649C2×C4⋊C4C22×D4712yes—
650C2×C4⋊C4C22×D4714yes—
651C2×C4⋊C4C22×D4714yes—
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—472no—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—474no—
663C2×C22⋊C4—474no—
664C2×C22⋊C4—472no—
665C2×C22⋊C4—474no—
666C2×C22⋊C4—474no—
667C2×C42—471no—
668C2×C42—472no—
669C2×C42—471no—
670C2×C42—471no—
671C2×C42—478no—
672C2×C42C22×D4712yes—
673C2×C42C22×D4712yes—
674C2×C42C22×D4711yescharacteristic
675C2×C42C22×D4714yes—
676C24—472no—
677C24—471no—
678C24—474no—
679#41—18832no—
680#41—18832no—
681C2×Q8—28no—
682C2×Q8—24no—
683C2×Q8—24no—
684C2×Q8—474no—
685C2×Q8—478no—
686C2×Q8—4716no—
687C2×Q8—944no—
688C2×Q8—1884no—
689C2×Q8—1888no—
690C2×Q8—18832no—
691C2×Q8C23×D4714yes—
692C2×Q8C23×D4718yes—
693C2×Q8C23×D4714yes—
694C2×D4—478no—
695C2×D4—474no—
696C2×D4—478no—
697C2×D4—478no—
698C2×D4—478no—
699C2×D4—4716no—
700C2×D4—4716no—
701C2×D4—4716no—
702C2×D4—948no—
703C2×D4—948no—
704C2×D4—944no—
705C2×D4—1884no—
706C2×D4—1884no—
707C2×D4—1888no—
708C2×D4—1888no—
709C2×D4—1888no—
710C22×C4—471no—
711C22×C4—471no—
712C22×C4—471no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—474no—
717C22×C4—474no—
718C22×C4—478no—
719C22×C4—474no—
720C22×C4—4716no—
721C22×C4—4716no—
722C22×C4—4716no—
723C22×C4—4716no—
724C22×C4—948no—
725C22×C4—944no—
726C22×C4—944no—
727C22×C4—1888no—
728C22×C4—1882no—
729C22×C4—1888no—
730C22×C4—1888no—
731C22×C4—1888no—
732C22×C4C23×D4711yescharacteristic
733C22×C4C23×D4712yes—
734C22×C4C23×D4712yes—
735C22×C4C23×D4712yes—
736C22×C4C23×D4714yes—
737C22×C4C23×D4712yes—
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—478no—
748C4⋊C4—478no—
749C4⋊C4—474no—
750C4⋊C4—478no—
751C4⋊C4—474no—
752C4⋊C4C23×D47116yes—
753C4⋊C4C23×D4714yes—
754C4⋊C4C23×D4718yes—
755C4⋊C4C23×D4718yes—
756C4⋊C4C23×D4714yes—
757C4⋊C4C23×D4718yes—
758C4⋊C4C23×D47116yes—
759C4⋊C4C23×D47116yes—
760C4⋊C4C23×D4718yes—
761C22⋊C4—478no—
762C22⋊C4—478no—
763C22⋊C4—478no—
764C22⋊C4—478no—
765C22⋊C4—478no—
766C22⋊C4—478no—
767C22⋊C4—4716no—
768C22⋊C4—4716no—
769C22⋊C4—4716no—
770C22⋊C4—4716no—
771C22⋊C4—4716no—
772C22⋊C4—478no—
773C22⋊C4—4716no—
774C22⋊C4—4716no—
775C42—474no—
776C42—474no—
777C42—474no—
778C42—478no—
779C42C23×D4714yes—
780C42C23×D4718yes—
781C42C23×D4718yes—
782C42C23×D47116yes—
783C23—474no—
784C23—472no—
785C23—478no—
786C23—944no—
787C23—942no—
788C23—948no—
789C23—942no—
790C23—944no—
791C23—948no—
792C23—942no—
793C23—948no—
794C23—944no—
795C23C24×D4711yescharacteristic
796Q8—216no—
797Q8—28no—
798Q8—28no—
799Q8—948no—
800Q8—1888no—
801Q8—18816no—
802D4—9416no—
803D4—9416no—
804D4—948no—
805D4—1888no—
806D4—1888no—
807D4—18816no—
808D4—18816no—
809D4—18816no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—472no—
817C2×C4—472no—
818C2×C4—472no—
819C2×C4—474no—
820C2×C4—474no—
821C2×C4—474no—
822C2×C4—942no—
823C2×C4—944no—
824C2×C4—944no—
825C2×C4—942no—
826C2×C4—944no—
827C2×C4—942no—
828C2×C4—9416no—
829C2×C4—948no—
830C2×C4—948no—
831C2×C4—18816no—
832C2×C4—1884no—
833C2×C4—18816no—
834C2×C4—18816no—
835C2×C4—18816no—
836C2×C4#1309407014yes—
837C2×C4#1309407214yes—
838C2×C4C24×D4712yes—
839C2×C4C24×D4714yes—
840C2×C4C24×D4714yes—
841C2×C4C24×D4714yes—
842C2×C4C24×D4718yes—
843C2×C4C24×D4714yes—
844C2×C4C24×D4712yes—
845C2×C4C24×D4712yes—
846C22—944no—
847C22—942no—
848C22—948no—
849C22—942no—
850C22—944no—
851C22—948no—
852C22—942no—
853C22—948no—
854C22—944no—
855C22—1888no—
856C22—1884no—
857C22—18816no—
858C22C2×#1309407012yes—
859C22C2×#1309407212yes—
860C22#1568996012yes—
861C22C25×D4711yescharacteristic
862C4—24no—
863C4—28no—
864C4—24no—
865C4—24no—
866C4—22no—
867C4—24no—
868C4—942no—
869C4—944no—
870C4—944no—
871C4—942no—
872C4—944no—
873C4—942no—
874C4C2×#1309407014yes—
875C4C2×#1309407214yes—
876C2—1884no—
877C2—1882no—
878C2—1888no—
879C2#2025786214yesdirect product factor
880C2C22×#1309407011yescharacteristic
881C2C22×#1309407211yescharacteristic
882C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#557C2
socleC23×C47C25
hypercenterC2×#557D47
hypocenterC47C2×#3554
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20257862C2direct (N × H)
2. C2×#15689871C2semidirect
3. C2×#15689858C2semidirect
4. C2×#15689858C2semidirect
5. C2×#15689829C2semidirect
6. C2×#15689795C2semidirect
7. C2×#15689788C2semidirect
8. C2×#15689785C2semidirect
9. C2×#15689776C2semidirect
10. C2×#15689745C2semidirect
11. C2×#15689745C2semidirect
12. C2×#15689729C2semidirect
13. C2×#15689721C2semidirect
14. C2×#15689698C2semidirect
15. C2×#15689677C2semidirect
16. C2×#15689674C2semidirect
17. C2×#15689660C2semidirect
18. C2×C47×#557C2semidirect
22. #15689871C22semidirect
23. #15689858C22semidirect
24. #15689858C22semidirect
25. #15689829C22semidirect
26. #15689795C22semidirect
27. #15689788C22semidirect
28. #15689785C22semidirect
29. #15689776C22semidirect
30. #15689745C22semidirect
31. #15689745C22semidirect
32. #15689729C22semidirect
33. #15689721C22semidirect
34. #15689698C22semidirect
35. #15689677C22semidirect
36. #15689674C22semidirect
42. #15689660C22semidirect
92. C47×#557C22semidirect
439. C2×#557D47semidirect
453. C2×C47#3554semidirect
466. #557C2×D47semidirect
542. C47C2×#3554semidirect
879. C2#20257862direct (N × H)

Maximal subgroups

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

subgroupindex
#202578622
C2×#156898712
C2×#156898582
C2×#156898292
C2×#156897952
C2×#156897882
C2×#156897852
C2×#156897762
C2×#156897452
C2×#156897292
C2×#156897212
C2×#156896982
C2×#156896772
C2×#156896742
C2×#156896602
C2×C47×#5572
C2×#355447