Finite Group Databasebeta

← C2×#20257470 #27124482

Subgroups — C2×#20257470 #27124482

Order 12032.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257470C2132yesmaximal, direct product factor
2C2×#15689855C212yesmaximal, complemented
3C2×Q8×Dic94C211yesmaximal, characteristic, complemented
4C2×#15689833C211yesmaximal, characteristic, complemented
5C2×#15689832C212yesmaximal, complemented
6C2×#15689793C211yesmaximal, characteristic, complemented
7C2×#15689781C212yesmaximal, complemented
8C2×#15689778C212yesmaximal, complemented
9C2×#15689771C214yesmaximal, complemented
10C2×#15689742C212yesmaximal, complemented
11C2×#15689741C214yesmaximal, complemented
12C2×#15689671C211yesmaximal, characteristic, complemented
13C2×#15689670C212yesmaximal, complemented
14C2×#15689660C211yesmaximal, characteristic, complemented
15C2×#15689652C212yesmaximal, complemented
16C2×#15689602C212yesmaximal, complemented
17C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
18C2×C47×#559C211yesmaximal, characteristic, complemented
19C22×#10625350C2214yes—
20C22×#10625352C2212yes—
21C22×#10625352C2212yes—
22C22×Q8×D47C2211yescharacteristic
23#15689855C22132yescomplemented
24Q8×Dic94C22116yescomplemented
25#15689833C22116yescomplemented
26#15689832C22132yescomplemented
27#15689793C22116yescomplemented
28#15689781C22132yescomplemented
29#15689778C22132yescomplemented
30#15689771C22164yescomplemented
31#15689742C22132yescomplemented
32#15689741C22164yescomplemented
33#15689671C22116yescomplemented
34#15689670C22132yescomplemented
35C2×#13094024C2212yes—
36C2×#13094024C2211yescharacteristic
37C2×#13094023C2214yes—
38C2×#13094023C2212yes—
39C2×#13094020C2212yes—
40#15689660C22116yescomplemented
41#15689652C22132yescomplemented
42C2×#13094019C2212yes—
43C2×#13094017C2214yes—
44C2×#13094016C2212yes—
45C2×#13094015C2211yescharacteristic
46C2×#13094013C2211yescharacteristic
47C2×#13094011C2212yes—
48C2×#13094010C2214yes—
49C2×#13094010C2214yes—
50C2×#13094009C2212yes—
51C2×#13094008C2214yes—
52C2×#13094006C2214yes—
53C2×#13094006C2214yes—
54C2×#13094003C2214yes—
55C2×#13094002C2214yes—
56C2×#13094001C2214yes—
57C2×#13094001C2214yes—
58C2×#13094000C2212yes—
59C2×#13094000C2211yescharacteristic
60C2×#13093999C2211yescharacteristic
61C2×#13093997C2214yes—
62C2×#13093996C2214yes—
63C2×#13093995C2212yes—
64C2×#13093995C2212yes—
65C2×#13093995C2212yes—
66#15689602C22132yescomplemented
67C2×Q8×Dic47C2211yescharacteristic
68C2×Q8×Dic47C2212yes—
69C2×C4×Dic94C2211yescharacteristic
70C2×C4×Dic94C2212yes—
71C2×C4×Dic94C2212yes—
72C2×#13093989C2211yescharacteristic
73C2×#13093989C2212yes—
74C4×Q8×D47C22116yescomplemented
75C2×C4×D188C2212yes—
76C2×C4×D188C2211yescharacteristic
77C2×C4×D188C2212yes—
78C2×D4×Dic47C2212yes—
79C2×D4×Dic47C2212yes—
80C2×D4×Dic47C2212yes—
81C2×C4×C22⋊D47C2214yes—
82C2×(C22⋊D47)⋊C4C2214yes—
83C2×(C22⋊D47)⋊C4C2214yes—
84C2×#13093981C2212yes—
85C2×#13093980C2214yes—
86C22×Dic47⋊C4C2214yes—
87C2×C4⋊C4×D47C2212yes—
88C2×C4⋊C4×D47C2211yescharacteristic
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#559C22116yescomplemented
93C2×#127×C47C2211yescharacteristic
94C2×#124×C47C2212yes—
95C2×#124×C47C2212yes—
96C2×#123×C47C2214yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×D4×C47C2212yes—
100C2×C4×D4×C47C2212yes—
101C2×#10625350—416no—
102C2×#10625350C23132yes—
103C2×#10625352—216no—
104C2×#10625352—48no—
105C2×#10625352C23116yes—
106C2×#10625352C23116yes—
107C22×Dic94C2312yes—
108C22×Dic94C2314yes—
109C22×Dic94C2312yes—
110C22×Dic94C2311yescharacteristic
111C2×Q8×D47—28no—
112C2×Q8×D47C2318yes—
113C22×D188C2311yescharacteristic
114C22×D188C2312yes—
115C22×C22⋊D47C2314yes—
116C22×C22⋊D47C2314yes—
117C22×C22⋊D47C2314yes—
118C23×Dic47C2314yes—
119C23×Dic47C2314yes—
120C22×C4×D47C2311yescharacteristic
121C22×C4×D47C2312yes—
122C22×C4×D47C2311yescharacteristic
123C22×C4×D47C2312yes—
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2312yes—
126C22×C4×D47C2314yes—
127#13094024C23116yes—
128#13094024C2318yes—
129#13094023C23132yes—
130#13094023C23116yes—
131#13094020C23116yes—
132#13094019C23116yes—
133#13094017C23132yes—
134#13094016C23116yes—
135#13094015C2318yes—
136#13094013C2318yes—
137#13094011C23116yes—
138#13094010C23132yes—
139#13094010C23132yes—
140#13094009C23116yes—
141#13094008C23132yes—
142#13094006C23132yes—
143#13094006C23132yes—
144#13094003C23132yes—
145#13094002C23132yes—
146#13094001C23132yes—
147#13094001C23132yes—
148#13094000C23116yes—
149#13094000C2318yes—
150#13093999C2318yes—
151#13093997C23132yes—
152#13093996C23132yes—
153#13093995C23116yes—
154#13093995C23116yes—
155#13093995C23116yes—
156Q8×Dic47C2318yes—
157Q8×Dic47C23116yes—
158C4×Dic94C23116yes—
159C4×Dic94C2318yes—
160C4×Dic94C23116yes—
161#13093989C23116yes—
162#13093989C2318yes—
163C4×D188C23116yes—
164C4×D188C2318yes—
165C4×D188C23116yes—
166D4×Dic47C23116yes—
167D4×Dic47C23116yes—
168D4×Dic47C23116yes—
169C4×C22⋊D47C23132yes—
170(C22⋊D47)⋊C4C23132yes—
171(C22⋊D47)⋊C4C23132yes—
172#13093981C23116yes—
173#13093980C23132yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2311yescharacteristic
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2312yes—
180C2×C4⋊Dic47C2314yes—
181C2×Dic47⋊C4C23132yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2314yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2314yes—
190C4⋊C4×D47C23116yes—
191C4⋊C4×D47C2318yes—
192C4⋊C4×D47C23116yes—
193C2×C22⋊Dic47C2314yes—
194C2×C22⋊Dic47C2314yes—
195C2×C22⋊Dic47C2314yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2314yes—
209C42×D47C23116yes—
210C42×D47C2318yes—
211C22×Q8×C47C2311yescharacteristic
212C22×Q8×C47C2311yescharacteristic
213C22×D4×C47C2312yes—
214C22×D4×C47C2312yes—
215C22×D4×C47C2312yes—
216C23×C4×C47C2314yes—
217#127×C47C2318yes—
218#124×C47C23116yes—
219#124×C47C23116yes—
220#123×C47C23132yes—
221C4×Q8×C47C2318yes—
222C4×Q8×C47C2318yes—
223C4×D4×C47C23116yes—
224C4×D4×C47C23116yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2312yes—
229C2×C22⋊C4×C47C2314yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C22⋊C4×C47C2314yes—
232C2×C42×C47C2312yes—
233C2×C42×C47C2312yes—
234C2×C42×C47C2311yescharacteristic
235C24×C47C2414yes—
236C23×D47C2412yes—
237C23×D47C2411yescharacteristic
238C2×Q8×C47—24no—
239C2×Q8×C47—24no—
240C2×Q8×C47C2414yes—
241C2×Q8×C47C2414yes—
242C2×D4×C47—28no—
243C2×D4×C47—28no—
244C2×D4×C47—44no—
245C2×D4×C47C2418yes—
246C2×D4×C47C2418yes—
247C2×D4×C47C2418yes—
248C22×C4×C47—48no—
249C22×C4×C47C2412yes—
250C22×C4×C47C2412yes—
251C22×C4×C47C2412yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2411yescharacteristic
254C22×C4×C47C24116yes—
255C22×C4×C47C2411yescharacteristic
256C22×C4×C47C2411yescharacteristic
257C2×C22⋊D47—216no—
258C2×C22⋊D47—216no—
259C2×C22⋊D47—48no—
260C2×C22⋊D47C24116yes—
261C2×C22⋊D47C24116yes—
262C2×C22⋊D47C24116yes—
263C22×Dic47—216no—
264C22×Dic47—48no—
265C22×Dic47C2411yescharacteristic
266C22×Dic47C2411yescharacteristic
267C22×Dic47C2411yescharacteristic
268C22×Dic47C2412yes—
269C22×Dic47C2414yes—
270C22×Dic47C2412yes—
271C22×Dic47C24116yes—
272C22×Dic47C24116yes—
273C22×Dic47C2412yes—
274Q8×D47—232no—
275#10625352—264no—
276#10625352—432no—
277#10625350—464no—
278C2×D188—28no—
279C2×D188—24no—
280C2×D188C2414yes—
281C2×D188C2418yes—
282C2×C4×D47—24no—
283C2×C4×D47—28no—
284C2×C4×D47—24no—
285C2×C4×D47—28no—
286C2×C4×D47—24no—
287C2×C4×D47—28no—
288C2×C4×D47—48no—
289C2×C4×D47C2414yes—
290C2×C4×D47C2418yes—
291C2×C4×D47C2414yes—
292C2×C4×D47C2418yes—
293C2×C4×D47C2414yes—
294C2×C4×D47C2418yes—
295C2×C4×D47C24116yes—
296C2×Dic94—28no—
297C2×Dic94—44no—
298C2×Dic94—48no—
299C2×Dic94#4118yescomplemented
300C2×Dic94C2418yes—
301C2×Dic94C24116yes—
302C2×Dic94C2418yes—
303C2×Dic94C2414yes—
304C4⋊C4×C47C2414yes—
305C4⋊C4×C47C2414yes—
306C4⋊C4×C47C2418yes—
307C4⋊C4×C47C2418yes—
308C22⋊C4×C47C24116yes—
309C22⋊C4×C47C24116yes—
310C22⋊C4×C47C24116yes—
311C42×C47C2418yes—
312C42×C47C2418yes—
313C42×C47C2414yes—
314C22⋊Dic47C24116yes—
315C22⋊Dic47C24116yes—
316C22⋊Dic47C24116yes—
317(C2×D47)⋊C4C2418yes—
318(C2×D47)⋊C4C2418yes—
319(C2×D47)⋊C4C2418yes—
320(C2×D47)⋊C4C2418yes—
321(C2×D47)⋊C4C24116yes—
322(C2×D47)⋊C4C2418yes—
323C4⋊Dic47C2418yes—
324C4⋊Dic47C2414yes—
325C4⋊Dic47C2418yes—
326C4⋊Dic47C2414yes—
327C4⋊Dic47C2418yes—
328C4⋊Dic47C2418yes—
329C4⋊Dic47C24116yes—
330Dic47⋊C4C2418yes—
331Dic47⋊C4C24116yes—
332Dic47⋊C4C2418yes—
333Dic47⋊C4C2418yes—
334Dic47⋊C4C2418yes—
335Dic47⋊C4C24116yes—
336Dic47⋊C4C2418yes—
337Dic47⋊C4C24116yes—
338C4×Dic47C2418yes—
339C4×Dic47C2414yes—
340C4×Dic47C2414yes—
341C4×Dic47C2418yes—
342C4×Dic47C2414yes—
343C4×Dic47C2418yes—
344C4×Dic47C24116yes—
345C23×C47—28no—
346C23×C47—28no—
347C23×C47—28no—
348C23×C47C2518yes—
349C23×C47C2511yescharacteristic
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—24no—
353C22×D47—24no—
354C22×D47—24no—
355C22×D47H(5,𝔽2)14yes—
356C22×D47C2514yes—
357C22×D47C2512yes—
358Q8×C47—28no—
359Q8×C47—28no—
360D4×C47—216no—
361D4×C47—216no—
362D4×C47—48no—
363C2×C4×C47—24no—
364C2×C4×C47—22no—
365C2×C4×C47—24no—
366C2×C4×C47—24no—
367C2×C4×C47—24no—
368C2×C4×C47—416no—
369C2×C4×C47C2×#4114yes—
370C2×C4×C472−1+414yes—
371C2×C4×C47C2514yes—
372C2×C4×C47C2514yes—
373C2×C4×C47C2514yes—
374C2×C4×C47C2512yes—
375C2×C4×C47C2514yes—
376C2×C4×C47C2512yes—
377C2×C4×C47C2512yes—
378C22⋊D47—232no—
379C22⋊D47—232no—
380C22⋊D47—416no—
381C2×Dic47—22no—
382C2×Dic47—24no—
383C2×Dic47—24no—
384C2×Dic47—28no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—232no—
388C2×Dic47—416no—
389C2×Dic47C2×#4118yes—
390C2×Dic47C2512yes—
391C2×Dic47C2512yes—
392C2×Dic47C2514yes—
393C2×Dic47C2512yes—
394C2×Dic47C2518yes—
395C2×Dic47C2514yes—
396C2×Dic47C2514yes—
397D188—216no—
398D188—28no—
399C4×D47—216no—
400C4×D47—28no—
401C4×D47—216no—
402C4×D47—28no—
403C4×D47—28no—
404C4×D47—216no—
405C4×D47—416no—
406Dic94—216no—
407Dic94—416no—
408Dic94—48no—
409Dic94C2×#41116yescomplemented
410C2×#3522—471nomaximal, Sylow
411C22×C47—28no—
412C22×C47—28no—
413C22×C47—28no—
414C22×C47—416no—
415C22×C47C22×#4112yes—
416C22×C47C2×H(5,𝔽2)12yes—
417C22×C47C2×2−1+412yes—
418C22×C47C2611yescharacteristic
419C2×D47—22no—
420C2×D47—22no—
421C2×D47—28no—
422C2×D47—24no—
423C2×D47—24no—
424C2×D47—24no—
425C2×D47—48no—
426C2×D47C2×H(5,𝔽2)14yes—
427C4×C47—24no—
428C4×C47—22no—
429C4×C47—24no—
430C4×C47—24no—
431C4×C47—24no—
432C4×C47C22×#4114yes—
433C4×C47C2×2−1+414yes—
434Dic47—22no—
435Dic47—24no—
436Dic47—24no—
437Dic47—28no—
438Dic47—22no—
439Dic47—22no—
440Dic47C22×#4118yes—
441#3522—4732no—
442C2×#559—472no—
443C2×#559D4711yescharacteristic, complemented
444C2×Q82—471no—
445C2×#554—471no—
446C2×#554—472no—
447C2×#550—471no—
448C2×#548—472no—
449C2×#547—474no—
450C2×#547—472no—
451C2×#542—472no—
452C2×#542—474no—
453C2×#532—471no—
454C2×#532—472no—
455C2×#529—472no—
456C2×#529—471no—
457C2×#520—472no—
458C22×C4×Q8—471no—
459C2×C47—48no—
460C2×C47#352214yescomplemented
461C2×C47C23×#4111yescharacteristic
462C2×C47C22×H(5,𝔽2)11yescharacteristic
463C2×C47C22×2−1+411yescharacteristic
464D47—24no—
465D47—44no—
466C22×#41—472no—
467C22×#41—472no—
468C22×#41—474no—
469C23×Q8—471no—
470#559—4732no—
471#559C2×D47116yescomplemented
472Q82—4716no—
473#554—4716no—
474#554—4732no—
475#550—4716no—
476#548—4732no—
477#547—4764no—
478#547—4732no—
479#542—4732no—
480#542—4764no—
481#532—4716no—
482#532—4732no—
483C2×C4⋊Q8—472no—
484C2×C4⋊Q8—474no—
485C2×C4⋊Q8—471no—
486C2×C4⋊Q8—472no—
487C2×#127—472no—
488C2×#127C2×D4711yescharacteristic
489#529—4732no—
490#529—4716no—
491C2×#126—472no—
492C2×#126—474no—
493C2×#125—471no—
494C2×#125—472no—
495C2×#124—471no—
496C2×#124—472no—
497C2×#124—474no—
498C2×#124—474no—
499C2×#124C2×D4712yes—
500C2×#124C2×D4712yes—
501C2×#123—472no—
502C2×#123—474no—
503C2×#123—474no—
504C2×#123—474no—
505C2×#123C2×D4714yes—
506C2×C22⋊Q8—471no—
507C2×C22⋊Q8—472no—
508C2×C22⋊Q8—474no—
509C2×C22⋊Q8—474no—
510C2×C22⋊Q8—474no—
511C2×C22⋊Q8—474no—
512C2×#121—472no—
513C2×#121—472no—
514C2×#121—472no—
515C2×#121—474no—
516C2×#121—471no—
517C2×#121—474no—
518#520—4732no—
519C2×C4×Q8—471no—
520C2×C4×Q8—472no—
521C2×C4×Q8—4716no—
522C2×C4×Q8—471no—
523C2×C4×Q8—472no—
524C2×C4×Q8—471no—
525C2×C4×Q8—472no—
526C2×C4×Q8—472no—
527C2×C4×Q8C2×D4711yescharacteristic
528C2×C4×Q8C2×D4711yescharacteristic
529C2×C4×D4—472no—
530C2×C4×D4—472no—
531C2×C4×D4—472no—
532C2×C4×D4—474no—
533C2×C4×D4—474no—
534C2×C4×D4—474no—
535C2×C4×D4—472no—
536C2×C4×D4—471no—
537C2×C4×D4—472no—
538C2×C4×D4C2×D4712yes—
539C2×C4×D4C2×D4712yes—
540C2×#117—474no—
541C2×#117—472no—
542C22×C4⋊C4—474no—
543C22×C4⋊C4—472no—
544C22×C4⋊C4—471no—
545C22×C4⋊C4—472no—
546C22×C42—471no—
547C22×C42—472no—
548C47C2×#352211yescharacteristic, complemented, Sylow
549C2×#41—4716no—
550C2×#41—4716no—
551C2×#41—4732no—
552C2×#41—9416no—
553C2×#41—18816no—
554C2×#41—1888no—
555C22×Q8—478no—
556C22×Q8—471no—
557C22×Q8—472no—
558C22×Q8—474no—
559C22×Q8—472no—
560C22×Q8—948no—
561C22×Q8C22×D4711yescharacteristic
562C22×Q8C22×D4711yescharacteristic
563C22×D4—474no—
564C22×D4—474no—
565C22×D4—474no—
566C22×D4—471no—
567C22×D4—472no—
568C22×D4C22×D4712yes—
569C22×D4C22×D4712yes—
570C22×D4C22×D4712yes—
571C23×C4—474no—
572C23×C4—474no—
573C23×C4—471no—
574C23×C4—472no—
575C23×C4—472no—
576C23×C4—472no—
577C23×C4—471no—
578C23×C4—471no—
579C23×C4—474no—
580C23×C4C22×D4714yes—
581C4⋊Q8—4716no—
582C4⋊Q8—4732no—
583C4⋊Q8—478no—
584C4⋊Q8—4716no—
585#127—4716no—
586#127C22×D4718yes—
587#126—4716no—
588#126—4732no—
589#125—478no—
590#125—4716no—
591#124—478no—
592#124—4716no—
593#124—4732no—
594#124—4732no—
595#124C22×D47116yes—
596#124C22×D47116yes—
597#123—4716no—
598#123—4732no—
599#123—4732no—
600#123—4732no—
601#123C22×D47132yes—
602C22⋊Q8—478no—
603C22⋊Q8—4716no—
604C22⋊Q8—4732no—
605C22⋊Q8—4732no—
606C22⋊Q8—4732no—
607C22⋊Q8—4732no—
608#121—4716no—
609#121—4716no—
610#121—4716no—
611#121—4732no—
612#121—478no—
613#121—4732no—
614C4×Q8—478no—
615C4×Q8—4716no—
616C4×Q8—478no—
617C4×Q8—4716no—
618C4×Q8—478no—
619C4×Q8—4716no—
620C4×Q8—4716no—
621C4×Q8C22×D4718yes—
622C4×Q8C22×D4718yes—
623C4×D4—4716no—
624C4×D4—4716no—
625C4×D4—4716no—
626C4×D4—4732no—
627C4×D4—4732no—
628C4×D4—4732no—
629C4×D4—4716no—
630C4×D4—478no—
631C4×D4—4716no—
632C4×D4C22×D47116yes—
633C4×D4C22×D47116yes—
634#117—4732no—
635#117—4716no—
636C2×C4⋊C4—472no—
637C2×C4⋊C4—472no—
638C2×C4⋊C4—474no—
639C2×C4⋊C4—474no—
640C2×C4⋊C4—472no—
641C2×C4⋊C4—472no—
642C2×C4⋊C4—471no—
643C2×C4⋊C4—472no—
644C2×C4⋊C4—472no—
645C2×C4⋊C4—4732no—
646C2×C4⋊C4—472no—
647C2×C4⋊C4—471no—
648C2×C4⋊C4—472no—
649C2×C4⋊C4—474no—
650C2×C4⋊C4—472no—
651C2×C4⋊C4—474no—
652C2×C4⋊C4—4716no—
653C2×C4⋊C4—478no—
654C2×C4⋊C4—4716no—
655C2×C4⋊C4C22×D4711yescharacteristic
656C2×C4⋊C4C22×D4712yes—
657C2×C4⋊C4C22×D4711yescharacteristic
658C2×C4⋊C4C22×D4712yes—
659C2×C22⋊C4—474no—
660C2×C22⋊C4—474no—
661C2×C22⋊C4—474no—
662C2×C22⋊C4—472no—
663C2×C22⋊C4—472no—
664C2×C22⋊C4—472no—
665C2×C22⋊C4—472no—
666C2×C22⋊C4—474no—
667C2×C22⋊C4—472no—
668C2×C22⋊C4C22×D4714yes—
669C2×C22⋊C4C22×D4714yes—
670C2×C22⋊C4C22×D4714yes—
671C2×C42—472no—
672C2×C42—471no—
673C2×C42—474no—
674C2×C42—471no—
675C2×C42—472no—
676C2×C42—471no—
677C2×C42—472no—
678C2×C42—478no—
679C2×C42—4716no—
680C2×C42C22×D4712yes—
681C2×C42C22×D4712yes—
682C2×C42C22×D4711yescharacteristic
683C24—471no—
684C24—472no—
685C24C23×D4714yes—
686#41—9464no—
687#41—18864no—
688#41—18832no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—478no—
692C2×Q8—474no—
693C2×Q8—478no—
694C2×Q8—4716no—
695C2×Q8—478no—
696C2×Q8—948no—
697C2×Q8—9432no—
698C2×Q8—1888no—
699C2×Q8—1884no—
700C2×Q8C23×D4714yes—
701C2×Q8C23×D4714yes—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—44no—
705C2×D4—4716no—
706C2×D4—4716no—
707C2×D4—4716no—
708C2×D4—474no—
709C2×D4—478no—
710C2×D4—948no—
711C2×D4—9416no—
712C2×D4—9416no—
713C2×D4—944no—
714C2×D4—1888no—
715C2×D4C23×D4718yes—
716C2×D4C23×D4718yes—
717C2×D4C23×D4718yes—
718C22×C4—48no—
719C22×C4—472no—
720C22×C4—4716no—
721C22×C4—471no—
722C22×C4—471no—
723C22×C4—471no—
724C22×C4—472no—
725C22×C4—474no—
726C22×C4—472no—
727C22×C4—4716no—
728C22×C4—474no—
729C22×C4—474no—
730C22×C4—478no—
731C22×C4—478no—
732C22×C4—474no—
733C22×C4—478no—
734C22×C4—4716no—
735C22×C4—948no—
736C22×C4—948no—
737C22×C4—944no—
738C22×C4—9416no—
739C22×C4—944no—
740C22×C4—948no—
741C22×C4—944no—
742C22×C4—1888no—
743C22×C4—1888no—
744C22×C4C23×D4712yes—
745C22×C4C23×D4712yes—
746C22×C4C23×D4711yescharacteristic
747C22×C4C23×D4712yes—
748C22×C4C23×D4712yes—
749C22×C4C23×D47116yes—
750C22×C4C23×D4711yescharacteristic
751C22×C4C23×D4711yescharacteristic
752C4⋊C4—478no—
753C4⋊C4—478no—
754C4⋊C4—4716no—
755C4⋊C4—4716no—
756C4⋊C4—478no—
757C4⋊C4—478no—
758C4⋊C4—478no—
759C4⋊C4—4716no—
760C4⋊C4—478no—
761C4⋊C4—474no—
762C4⋊C4—478no—
763C4⋊C4—474no—
764C4⋊C4—478no—
765C4⋊C4—478no—
766C4⋊C4—4716no—
767C4⋊C4C23×D4714yes—
768C4⋊C4C23×D4718yes—
769C4⋊C4C23×D4714yes—
770C4⋊C4C23×D4718yes—
771C22⋊C4—4716no—
772C22⋊C4—4716no—
773C22⋊C4—4716no—
774C22⋊C4—478no—
775C22⋊C4—478no—
776C22⋊C4—478no—
777C22⋊C4—478no—
778C22⋊C4—4716no—
779C22⋊C4—478no—
780C22⋊C4C23×D47116yes—
781C22⋊C4C23×D47116yes—
782C22⋊C4C23×D47116yes—
783C42—478no—
784C42—474no—
785C42—474no—
786C42—478no—
787C42—474no—
788C42—478no—
789C42—4716no—
790C42C23×D4718yes—
791C42C23×D4714yes—
792C42C23×D4718yes—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—474no—
797C23—472no—
798C23—474no—
799C23—942no—
800C23—942no—
801C23—944no—
802C23—944no—
803C23—944no—
804C23C24×D4718yes—
805C23C24×D4711yescharacteristic
806Q8—28no—
807Q8—28no—
808Q8—4716no—
809Q8—9416no—
810Q8—18816no—
811Q8—1888no—
812D4—216no—
813D4—216no—
814D4—48no—
815D4—9416no—
816D4—9432no—
817D4—9432no—
818D4—948no—
819D4—18816no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—416no—
826C2×C4—478no—
827C2×C4—474no—
828C2×C4—472no—
829C2×C4—472no—
830C2×C4—472no—
831C2×C4—474no—
832C2×C4—478no—
833C2×C4—474no—
834C2×C4—9416no—
835C2×C4—9416no—
836C2×C4—948no—
837C2×C4—9432no—
838C2×C4—944no—
839C2×C4—942no—
840C2×C4—942no—
841C2×C4—944no—
842C2×C4—948no—
843C2×C4—942no—
844C2×C4—948no—
845C2×C4—9416no—
846C2×C4—948no—
847C2×C4—18816no—
848C2×C4—18816no—
849C2×C4#41×D4714yes—
850C2×C4#1309407114yes—
851C2×C4C24×D4714yes—
852C2×C4C24×D4714yes—
853C2×C4C24×D4712yes—
854C2×C4C24×D4714yes—
855C2×C4C24×D4714yes—
856C2×C4C24×D4712yes—
857C2×C4C24×D4712yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—416no—
862C22—474no—
863C22—942no—
864C22—942no—
865C22—948no—
866C22—944no—
867C22—944no—
868C22—944no—
869C22—1888no—
870C22C2×#41×D4712yes—
871C22H(5,𝔽2)×D4712yes—
872C22C2×#1309407112yes—
873C22C25×D4711yescharacteristic
874C4—24no—
875C4—24no—
876C4—24no—
877C4—22no—
878C4—24no—
879C4—478no—
880C4—944no—
881C4—942no—
882C4—942no—
883C4—944no—
884C4—948no—
885C4—942no—
886C4C2×#41×D4714yes—
887C4C2×#1309407114yes—
888C2—48no—
889C2—944no—
890C2—1884no—
891C2#2025747014yesdirect product factor
892C2C22×#41×D4711yescharacteristic
893C2C2×H(5,𝔽2)×D4711yescharacteristic
894C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#559C2
socleC23×C47C25
hypercenterC2×#559D47
hypocenterC47C2×#3522
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #20257470C2direct (N × H)
2. C2×#15689855C2semidirect
3. C2×Q8×Dic94C2semidirect
4. C2×#15689833C2semidirect
5. C2×#15689832C2semidirect
6. C2×#15689793C2semidirect
7. C2×#15689781C2semidirect
8. C2×#15689778C2semidirect
9. C2×#15689771C2semidirect
10. C2×#15689742C2semidirect
11. C2×#15689741C2semidirect
12. C2×#15689671C2semidirect
13. C2×#15689670C2semidirect
14. C2×#15689660C2semidirect
15. C2×#15689652C2semidirect
16. C2×#15689602C2semidirect
17. C2×C4×Q8×D47C2semidirect
18. C2×C47×#559C2semidirect
23. #15689855C22semidirect
24. Q8×Dic94C22semidirect
25. #15689833C22semidirect
26. #15689832C22semidirect
27. #15689793C22semidirect
28. #15689781C22semidirect
29. #15689778C22semidirect
30. #15689771C22semidirect
31. #15689742C22semidirect
32. #15689741C22semidirect
33. #15689671C22semidirect
34. #15689670C22semidirect
40. #15689660C22semidirect
41. #15689652C22semidirect
66. #15689602C22semidirect
74. C4×Q8×D47C22semidirect
92. C47×#559C22semidirect
299. C2×Dic94#41semidirect
409. Dic94C2×#41semidirect
443. C2×#559D47semidirect
460. C2×C47#3522semidirect
471. #559C2×D47semidirect
548. C47C2×#3522semidirect
891. C2#20257470direct (N × H)

Maximal subgroups

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

subgroupindex
#202574702
C2×#156898552
C2×Q8×Dic942
C2×#156898332
C2×#156898322
C2×#156897932
C2×#156897812
C2×#156897782
C2×#156897712
C2×#156897422
C2×#156897412
C2×#156896712
C2×#156896702
C2×#156896602
C2×#156896522
C2×#156896022
C2×C4×Q8×D472
C2×C47×#5592
C2×#352247