Finite Group Databasebeta

← C2×#20257296 #27124650

Subgroups — C2×#20257296 #27124650

Order 12032.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257296C2132yesmaximal, direct product factor
2C2×#15689844C212yesmaximal, complemented
3C2×#15689839C211yesmaximal, characteristic, complemented
4C2×#15689838C211yesmaximal, characteristic, complemented
5C2×#15689833C211yesmaximal, characteristic, complemented
6C2×#15689826C212yesmaximal, complemented
7C2×#15689823C212yesmaximal, complemented
8C2×#15689783C214yesmaximal, complemented
9C2×#15689774C212yesmaximal, complemented
10C2×#15689743C214yesmaximal, complemented
11C2×#15689703C212yesmaximal, complemented
12C2×#15689679C212yesmaximal, complemented
13C2×#15689670C212yesmaximal, complemented
14C2×#15689670C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
16C2×#15689604C212yesmaximal, complemented
17C2×C4×#10625354C211yesmaximal, characteristic, complemented
18C2×C47×#554C211yesmaximal, characteristic, complemented
19C22×#10625354C2211yescharacteristic
20C22×#10625350C2212yes—
21C22×#10625350C2214yes—
22C22×Q8×D47C2212yes—
23#15689844C22132yescomplemented
24#15689839C22116yescomplemented
25#15689838C22116yescomplemented
26#15689833C22116yescomplemented
27#15689826C22132yescomplemented
28#15689823C22132yescomplemented
29#15689783C22164yescomplemented
30#15689774C22132yescomplemented
31#15689743C22164yescomplemented
32#15689703C22132yescomplemented
33#15689679C22132yescomplemented
34#15689670C22132yescomplemented
35#15689670C22116yescomplemented
36C2×#13094024C2211yescharacteristic
37C2×#13094023C2212yes—
38C2×#13094023C2212yes—
39C2×#13094023C2211yescharacteristic
40C2×#13094022C2212yes—
41C4⋊Q8×D47C22116yescomplemented
42C2×#13094020C2211yescharacteristic
43C2×#13094019C2214yes—
44C2×#13094017C2214yes—
45C2×#13094016C2212yes—
46C2×#13094013C2214yes—
47C2×#13094010C2214yes—
48C2×#13094010C2214yes—
49C2×#13094010C2212yes—
50C2×#13094009C2214yes—
51C2×#13094007C2214yes—
52C2×#13094002C2214yes—
53C2×#13094002C2214yes—
54C2×#13094002C2214yes—
55C2×#13094000C2212yes—
56C2×#13093999C2212yes—
57C2×#13093999C2214yes—
58C2×#13093999C2211yescharacteristic
59C2×#13093999C2212yes—
60C2×#13093998C2212yes—
61C2×#13093997C2212yes—
62C2×#13093997C2214yes—
63C2×#13093997C2214yes—
64C2×#13093995C2211yescharacteristic
65C2×#13093995C2212yes—
66#15689604C22132yescomplemented
67C4×#10625354C22116yescomplemented
68C2×Q8×Dic47C2211yescharacteristic
69C2×#13093989C2214yes—
70C2×#13093989C2214yes—
71C2×C4×D188C2212yes—
72C2×C4×D188C2211yescharacteristic
73C2×C4×D188C2212yes—
74C2×C4×D188C2211yescharacteristic
75C2×#13093986C2211yescharacteristic
76C2×#13093986C2212yes—
77C2×#13093986C2214yes—
78C2×C4×C22⋊D47C2214yes—
79C2×C4×C22⋊D47C2214yes—
80C2×C4×C22⋊D47C2212yes—
81C2×#13093983C2212yes—
82C2×#13093982C2211yescharacteristic
83C2×#13093982C2212yes—
84C2×#13093982C2212yes—
85C2×#13093982C2212yes—
86C2×#13093982C2212yes—
87C2×C4⋊C4×D47C2212yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2211yescharacteristic
91C2×C42×D47C2212yes—
92C47×#554C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2214yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×D4×C47C2212yes—
99C2×C4×D4×C47C2211yescharacteristic
100C22×C4⋊C4×C47C2212yes—
101C2×#10625354—28no—
102C2×#10625354C2318yes—
103C2×#10625350—216no—
104C2×#10625350—416no—
105C2×#10625350C23116yes—
106C2×#10625350C23132yes—
107C22×Dic94C2312yes—
108C22×Dic94C2314yes—
109C22×Dic94C2312yes—
110C2×Q8×D47—48no—
111C2×Q8×D47C23116yes—
112C22×D188C2312yes—
113C22×D188C2312yes—
114C22×D188C2311yescharacteristic
115C22×D188C2311yescharacteristic
116C22×D188C2314yes—
117C22×C22⋊D47C2312yes—
118C22×C22⋊D47C2312yes—
119C22×C22⋊D47C2312yes—
120C22×C22⋊D47C2314yes—
121C22×C4×D47C2311yescharacteristic
122C22×C4×D47C2312yes—
123C22×C4×D47C2312yes—
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2312yes—
126C22×C4×D47C2312yes—
127C22×C4×D47C2314yes—
128C22×C4×D47C2314yes—
129C22×C4×D47C2311yescharacteristic
130#13094024C2318yes—
131#13094023C23116yes—
132#13094023C23116yes—
133#13094023C2318yes—
134#13094022C23116yes—
135#13094020C2318yes—
136#13094019C23132yes—
137#13094017C23132yes—
138#13094016C23116yes—
139#13094013C23132yes—
140#13094010C23116yes—
141#13094010C23132yes—
142#13094010C23132yes—
143#13094009C23132yes—
144#13094007C23132yes—
145#13094002C23132yes—
146#13094002C23132yes—
147#13094002C23132yes—
148#13094000C23116yes—
149#13093999C23116yes—
150#13093999C23132yes—
151#13093999C2318yes—
152#13093999C23116yes—
153#13093998C23116yes—
154#13093997C23132yes—
155#13093997C23116yes—
156#13093997C23132yes—
157#13093995C2318yes—
158#13093995C23116yes—
159Q8×Dic47C2318yes—
160#13093989C23132yes—
161#13093989C23132yes—
162C4×D188C23116yes—
163C4×D188C23116yes—
164C4×D188C2318yes—
165C4×D188C2318yes—
166#13093986C2318yes—
167#13093986C23116yes—
168#13093986C23132yes—
169C4×C22⋊D47C23132yes—
170C4×C22⋊D47C23116yes—
171C4×C22⋊D47C23132yes—
172#13093983C23116yes—
173#13093982C23116yes—
174#13093982C23116yes—
175#13093982C23116yes—
176#13093982C23116yes—
177#13093982C2318yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2312yes—
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2311yescharacteristic
182C2×C4⋊Dic47C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2314yes—
188C4⋊C4×D47C23116yes—
189C4⋊C4×D47C23116yes—
190C4⋊C4×D47C23116yes—
191C2×C22⋊Dic47C2314yes—
192C2×C22⋊Dic47C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2314yes—
208C2×C4×Dic47C2314yes—
209C42×D47C2318yes—
210C42×D47C23116yes—
211C22×Q8×C47C2311yescharacteristic
212C22×Q8×C47C2312yes—
213C22×D4×C47C2311yescharacteristic
214C23×C4×C47C2312yes—
215C23×C4×C47C2314yes—
216C4⋊Q8×C47C2318yes—
217#125×C47C23116yes—
218C22⋊Q8×C47C23132yes—
219C22⋊Q8×C47C23116yes—
220C4×Q8×C47C2318yes—
221C4×D4×C47C23116yes—
222C4×D4×C47C2318yes—
223C2×C4⋊C4×C47C23116yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2314yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2311yescharacteristic
228C2×C4⋊C4×C47C2312yes—
229C2×C4⋊C4×C47C2312yes—
230C2×C4⋊C4×C47C2314yes—
231C2×C22⋊C4×C47C2314yes—
232C2×C22⋊C4×C47C2312yes—
233C2×C42×C47C2312yes—
234C2×C42×C47C2311yescharacteristic
235C24×C47C2412yes—
236C23×D47C2412yes—
237C23×D47C2412yes—
238C23×D47C2411yescharacteristic
239C2×Q8×C47—24no—
240C2×Q8×C47—44no—
241C2×Q8×C47C2414yes—
242C2×Q8×C47C2418yes—
243C2×D4×C47—24no—
244C2×D4×C47C2414yes—
245C22×C4×C47—28no—
246C22×C4×C47—48no—
247C22×C4×C47C2412yes—
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2412yes—
250C22×C4×C47C2412yes—
251C22×C4×C47C2414yes—
252C22×C4×C47C2418yes—
253C22×C4×C47C24116yes—
254C22×C4×C47C2411yescharacteristic
255C22×C4×C47C2411yescharacteristic
256C2×C22⋊D47—28no—
257C2×C22⋊D47—28no—
258C2×C22⋊D47—28no—
259C2×C22⋊D47—48no—
260C2×C22⋊D47C2418yes—
261C2×C22⋊D47C2418yes—
262C2×C22⋊D47C2418yes—
263C2×C22⋊D47C24116yes—
264C22×Dic47C2412yes—
265C22×Dic47C2411yescharacteristic
266C22×Dic47C2412yes—
267C22×Dic47C2414yes—
268C22×Dic47C2411yescharacteristic
269C22×Dic47C2411yescharacteristic
270#10625354—232no—
271Q8×D47—432no—
272#10625350—264no—
273#10625350—464no—
274C2×D188—28no—
275C2×D188—28no—
276C2×D188—24no—
277C2×D188—24no—
278C2×D188—48no—
279C2×D188C2418yes—
280C2×D188C2418yes—
281C2×D188C2414yes—
282C2×D188C2414yes—
283C2×D188C24116yes—
284C2×C4×D47—28no—
285C2×C4×D47—24no—
286C2×C4×D47—28no—
287C2×C4×D47—28no—
288C2×C4×D47—24no—
289C2×C4×D47—28no—
290C2×C4×D47—48no—
291C2×C4×D47—48no—
292C2×C4×D47#4118yescomplemented
293C2×C4×D47C2414yes—
294C2×C4×D47C2418yes—
295C2×C4×D47C2418yes—
296C2×C4×D47C2414yes—
297C2×C4×D47C2418yes—
298C2×C4×D47C2418yes—
299C2×C4×D47C24116yes—
300C2×C4×D47C24116yes—
301C2×C4×D47C2414yes—
302C2×Dic94—28no—
303C2×Dic94—216no—
304C2×Dic94—44no—
305C2×Dic94C2418yes—
306C2×Dic94C24116yes—
307C2×Dic94C2418yes—
308C4⋊C4×C47C2414yes—
309C4⋊C4×C47C24116yes—
310C4⋊C4×C47C2418yes—
311C4⋊C4×C47C2414yes—
312C4⋊C4×C47C2418yes—
313C4⋊C4×C47C2418yes—
314C4⋊C4×C47C24116yes—
315C22⋊C4×C47C24116yes—
316C22⋊C4×C47C2418yes—
317C42×C47C2418yes—
318C42×C47C2414yes—
319C22⋊Dic47C24116yes—
320C22⋊Dic47C2418yes—
321(C2×D47)⋊C4C2418yes—
322(C2×D47)⋊C4C24116yes—
323(C2×D47)⋊C4C2418yes—
324(C2×D47)⋊C4C2418yes—
325(C2×D47)⋊C4C24116yes—
326(C2×D47)⋊C4C24116yes—
327(C2×D47)⋊C4C2418yes—
328(C2×D47)⋊C4C24116yes—
329(C2×D47)⋊C4C2418yes—
330C4⋊Dic47C2418yes—
331C4⋊Dic47C2418yes—
332C4⋊Dic47C2414yes—
333C4⋊Dic47C2414yes—
334C4⋊Dic47C2418yes—
335Dic47⋊C4C24116yes—
336Dic47⋊C4C24116yes—
337Dic47⋊C4C24116yes—
338Dic47⋊C4C2418yes—
339Dic47⋊C4C24116yes—
340C4×Dic47C2414yes—
341C4×Dic47C2418yes—
342C4×Dic47C2414yes—
343C4×Dic47C2414yes—
344C4×Dic47C2418yes—
345C4×Dic47C24116yes—
346C4×Dic47C24116yes—
347C23×C47—24no—
348C23×C47—24no—
349C23×C47—24no—
350C23×C47C2514yes—
351C23×C47C2511yescharacteristic
352C22×D47—22no—
353C22×D47—22no—
354C22×D47—24no—
355C22×D47—24no—
356C22×D47—24no—
357C22×D47—24no—
358C22×D47—24no—
359C22×D47—24no—
360C22×D47C2×#4114yes—
361C22×D47C2514yes—
362C22×D47C2514yes—
363C22×D47C2512yes—
364Q8×C47—28no—
365Q8×C47—48no—
366D4×C47—28no—
367C2×C4×C47—24no—
368C2×C4×C47—24no—
369C2×C4×C47—28no—
370C2×C4×C47—22no—
371C2×C4×C47—24no—
372C2×C4×C47—216no—
373C2×C4×C47—416no—
374C2×C4×C47C2×#4114yes—
375C2×C4×C472−1+414yes—
376C2×C4×C47C2514yes—
377C2×C4×C47C2514yes—
378C2×C4×C47C2514yes—
379C2×C4×C47C2518yes—
380C2×C4×C47C2512yes—
381C2×C4×C47C2512yes—
382C2×C4×C47C2512yes—
383C22⋊D47—216no—
384C22⋊D47—216no—
385C22⋊D47—216no—
386C22⋊D47—416no—
387C2×Dic47—24no—
388C2×Dic47—28no—
389C2×Dic47—24no—
390C2×Dic47—22no—
391C2×Dic47C2×#4114yes—
392C2×Dic47H(5,𝔽2)14yes—
393C2×Dic47C2514yes—
394C2×Dic47C2514yes—
395C2×Dic47C2512yes—
396C2×Dic47C2518yes—
397C2×Dic47C2512yes—
398C2×Dic47C2512yes—
399D188—216no—
400D188—216no—
401D188—28no—
402D188—28no—
403D188—416no—
404C4×D47—216no—
405C4×D47—28no—
406C4×D47—216no—
407C4×D47—216no—
408C4×D47—216no—
409C4×D47—28no—
410C4×D47—416no—
411C4×D47—416no—
412C4×D47C2×#41116yescomplemented
413Dic94—216no—
414Dic94—232no—
415Dic94—48no—
416C2×#3511—471nomaximal, Sylow
417C22×C47—24no—
418C22×C47—24no—
419C22×C47—24no—
420C22×C47—48no—
421C22×C47C22×#4112yes—
422C22×C47C2×H(5,𝔽2)12yes—
423C22×C47C2×2−1+412yes—
424C22×C47C2611yescharacteristic
425C2×D47—22no—
426C2×D47—22no—
427C2×D47—28no—
428C2×D47—24no—
429C2×D47—24no—
430C2×D47—24no—
431C2×D47—24no—
432C2×D47—24no—
433C2×D47—24no—
434C2×D47—48no—
435C2×D47—48no—
436C2×D47C22×#4114yes—
437C4×C47—24no—
438C4×C47—24no—
439C4×C47—28no—
440C4×C47—22no—
441C4×C47—24no—
442C4×C47C22×#4114yes—
443C4×C47C2×2−1+414yes—
444Dic47—24no—
445Dic47—28no—
446Dic47—24no—
447Dic47—22no—
448Dic47C22×#4114yes—
449Dic47C2×H(5,𝔽2)14yes—
450#3511—4732no—
451C2×#556—472no—
452C2×#555—471no—
453C2×#555—471no—
454C2×#554—471no—
455C2×#554D4711yescharacteristic, complemented
456C2×#553—472no—
457C2×#553—472no—
458C2×#548—474no—
459C2×#547—472no—
460C2×#542—474no—
461C2×#537—472no—
462C2×#533—472no—
463C2×#532—472no—
464C2×#532—471no—
465C22×C4⋊Q8—471no—
466C2×#520—472no—
467C2×C4×#41—471no—
468C2×C47—44no—
469C2×C47#351114yescomplemented
470C2×C47C23×#4111yescharacteristic
471C2×C47C22×H(5,𝔽2)11yescharacteristic
472C2×C47C22×2−1+411yescharacteristic
473D47—24no—
474D47—44no—
475D47—44no—
476C22×#41—471no—
477C22×#41—472no—
478C22×#41—474no—
479C23×Q8—472no—
480#556—4732no—
481#555—4716no—
482#555—4716no—
483#554—4716no—
484#554C2×D47116yescomplemented
485#553—4732no—
486#553—4732no—
487#548—4764no—
488#547—4732no—
489#542—4764no—
490#537—4732no—
491#533—4732no—
492#532—4716no—
493#532—4732no—
494C2×C4⋊Q8—472no—
495C2×C4⋊Q8—4716no—
496C2×C4⋊Q8—472no—
497C2×C4⋊Q8—472no—
498C2×C4⋊Q8—471no—
499C2×C4⋊Q8—471no—
500C2×C4⋊Q8C2×D4711yescharacteristic
501C2×#127—471no—
502C2×#126—474no—
503C2×#126—474no—
504C2×#125—472no—
505C2×#125C2×D4712yes—
506C2×#124—474no—
507C2×#124—472no—
508C2×#124—474no—
509C2×#124—474no—
510C2×#123—474no—
511C2×#123—474no—
512C2×C22⋊Q8—472no—
513C2×C22⋊Q8—474no—
514C2×C22⋊Q8—474no—
515C2×C22⋊Q8—474no—
516C2×C22⋊Q8C2×D4712yes—
517C2×C22⋊Q8C2×D4714yes—
518C2×#121—471no—
519C2×#121—472no—
520C2×#121—472no—
521C2×#121—471no—
522C2×#121—472no—
523C2×#121—472no—
524C2×#121—474no—
525C2×#121—474no—
526C2×#121—472no—
527C2×#121—474no—
528#520—4732no—
529C4×#41—4716no—
530C2×C4×Q8—471no—
531C2×C4×Q8—474no—
532C2×C4×Q8—474no—
533C2×C4×Q8C2×D4711yescharacteristic
534C2×C4×D4—474no—
535C2×C4×D4—474no—
536C2×C4×D4—472no—
537C2×C4×D4—471no—
538C2×C4×D4—472no—
539C2×C4×D4—474no—
540C2×C4×D4—472no—
541C2×C4×D4—471no—
542C2×C4×D4—472no—
543C2×C4×D4—471no—
544C2×C4×D4C2×D4712yes—
545C2×C4×D4C2×D4711yescharacteristic
546C2×#117—472no—
547C2×#117—471no—
548C2×#117—472no—
549C2×#117—472no—
550C2×#117—472no—
551C2×#117—472no—
552C22×C4⋊C4—472no—
553C22×C4⋊C4—472no—
554C22×C4⋊C4—472no—
555C22×C4⋊C4C2×D4712yes—
556C22×C42—471no—
557C22×C42—472no—
558C47C2×#351111yescharacteristic, complemented, Sylow
559C2×#41—478no—
560C2×#41—4716no—
561C2×#41—4732no—
562C2×#41—9416no—
563C2×#41—948no—
564C2×#41—18816no—
565C22×Q8—4716no—
566C22×Q8—472no—
567C22×Q8—474no—
568C22×Q8—472no—
569C22×Q8—1888no—
570C22×Q8C22×D4711yescharacteristic
571C22×Q8C22×D4712yes—
572C22×D4—472no—
573C22×D4—472no—
574C22×D4—472no—
575C22×D4—474no—
576C22×D4—471no—
577C22×D4—472no—
578C22×D4—472no—
579C22×D4—471no—
580C22×D4—474no—
581C22×D4C22×D4711yescharacteristic
582C23×C4—471no—
583C23×C4—471no—
584C23×C4—472no—
585C23×C4—472no—
586C23×C4—472no—
587C23×C4—471no—
588C23×C4—472no—
589C23×C4—474no—
590C23×C4—474no—
591C23×C4C22×D4712yes—
592C23×C4C22×D4714yes—
593C4⋊Q8—4716no—
594C4⋊Q8—4716no—
595C4⋊Q8—4716no—
596C4⋊Q8—478no—
597C4⋊Q8—478no—
598C4⋊Q8C22×D4718yes—
599#127—478no—
600#126—4732no—
601#126—4732no—
602#125—4716no—
603#125C22×D47116yes—
604#124—4732no—
605#124—4716no—
606#124—4732no—
607#124—4732no—
608#123—4732no—
609#123—4732no—
610C22⋊Q8—4716no—
611C22⋊Q8—4732no—
612C22⋊Q8—4732no—
613C22⋊Q8—4732no—
614C22⋊Q8C22×D47116yes—
615C22⋊Q8C22×D47132yes—
616#121—478no—
617#121—4716no—
618#121—4716no—
619#121—478no—
620#121—4716no—
621#121—4716no—
622#121—4732no—
623#121—4732no—
624#121—4716no—
625#121—4732no—
626C4×Q8—478no—
627C4×Q8—4732no—
628C4×Q8—4732no—
629C4×Q8C22×D4718yes—
630C4×D4—4732no—
631C4×D4—4732no—
632C4×D4—4716no—
633C4×D4—478no—
634C4×D4—4716no—
635C4×D4—4732no—
636C4×D4—4716no—
637C4×D4—478no—
638C4×D4—4716no—
639C4×D4—478no—
640C4×D4C22×D47116yes—
641C4×D4C22×D4718yes—
642#117—4716no—
643#117—478no—
644#117—4716no—
645#117—4716no—
646#117—4716no—
647#117—4716no—
648C2×C4⋊C4—472no—
649C2×C4⋊C4—472no—
650C2×C4⋊C4—474no—
651C2×C4⋊C4—474no—
652C2×C4⋊C4—474no—
653C2×C4⋊C4—471no—
654C2×C4⋊C4—471no—
655C2×C4⋊C4—472no—
656C2×C4⋊C4—472no—
657C2×C4⋊C4—474no—
658C2×C4⋊C4—4716no—
659C2×C4⋊C4—4716no—
660C2×C4⋊C4—4716no—
661C2×C4⋊C4C22×D4711yescharacteristic
662C2×C4⋊C4C22×D4712yes—
663C2×C4⋊C4C22×D4712yes—
664C2×C4⋊C4C22×D4714yes—
665C2×C4⋊C4C22×D47116yes—
666C2×C4⋊C4C22×D4711yescharacteristic
667C2×C4⋊C4C22×D4712yes—
668C2×C4⋊C4C22×D4714yes—
669C2×C22⋊C4—474no—
670C2×C22⋊C4—472no—
671C2×C22⋊C4—472no—
672C2×C22⋊C4—474no—
673C2×C22⋊C4—472no—
674C2×C22⋊C4—472no—
675C2×C22⋊C4—474no—
676C2×C22⋊C4—474no—
677C2×C22⋊C4—474no—
678C2×C22⋊C4—472no—
679C2×C22⋊C4—472no—
680C2×C22⋊C4C22×D4714yes—
681C2×C22⋊C4C22×D4712yes—
682C2×C42—472no—
683C2×C42—474no—
684C2×C42—474no—
685C2×C42—471no—
686C2×C42—471no—
687C2×C42—472no—
688C2×C42—471no—
689C2×C42—478no—
690C2×C42—4716no—
691C2×C42C22×D4712yes—
692C2×C42C22×D4711yescharacteristic
693C24—471no—
694C24—472no—
695C24—472no—
696C24C23×D4712yes—
697#41—9464no—
698#41—9432no—
699#41—18864no—
700C2×Q8—24no—
701C2×Q8—44no—
702C2×Q8—478no—
703C2×Q8—4716no—
704C2×Q8—478no—
705C2×Q8—9416no—
706C2×Q8—948no—
707C2×Q8—1884no—
708C2×Q8—18832no—
709C2×Q8C23×D4714yes—
710C2×Q8C23×D4718yes—
711C2×D4—24no—
712C2×D4—478no—
713C2×D4—478no—
714C2×D4—478no—
715C2×D4—4716no—
716C2×D4—474no—
717C2×D4—478no—
718C2×D4—478no—
719C2×D4—474no—
720C2×D4—4716no—
721C2×D4—948no—
722C2×D4—948no—
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—944no—
727C2×D4—944no—
728C2×D4—1888no—
729C2×D4—1888no—
730C2×D4C23×D4714yes—
731C22×C4—28no—
732C22×C4—48no—
733C22×C4—471no—
734C22×C4—471no—
735C22×C4—478no—
736C22×C4—474no—
737C22×C4—472no—
738C22×C4—471no—
739C22×C4—472no—
740C22×C4—474no—
741C22×C4—474no—
742C22×C4—478no—
743C22×C4—478no—
744C22×C4—474no—
745C22×C4—478no—
746C22×C4—478no—
747C22×C4—4716no—
748C22×C4—4716no—
749C22×C4—944no—
750C22×C4—948no—
751C22×C4—948no—
752C22×C4—948no—
753C22×C4—944no—
754C22×C4—948no—
755C22×C4—1888no—
756C22×C4—1888no—
757C22×C4C23×D4718yes—
758C22×C4C23×D4712yes—
759C22×C4C23×D4711yescharacteristic
760C22×C4C23×D4712yes—
761C22×C4C23×D4712yes—
762C22×C4C23×D4714yes—
763C22×C4C23×D47116yes—
764C22×C4C23×D4711yescharacteristic
765C22×C4C23×D4711yescharacteristic
766C4⋊C4—4716no—
767C4⋊C4—4716no—
768C4⋊C4—4716no—
769C4⋊C4—478no—
770C4⋊C4—4716no—
771C4⋊C4—478no—
772C4⋊C4—478no—
773C4⋊C4—474no—
774C4⋊C4—474no—
775C4⋊C4—478no—
776C4⋊C4C23×D4714yes—
777C4⋊C4C23×D4718yes—
778C4⋊C4C23×D4718yes—
779C4⋊C4C23×D47116yes—
780C4⋊C4C23×D4714yes—
781C4⋊C4C23×D4718yes—
782C4⋊C4C23×D47116yes—
783C22⋊C4—4716no—
784C22⋊C4—478no—
785C22⋊C4—478no—
786C22⋊C4—4716no—
787C22⋊C4—478no—
788C22⋊C4—478no—
789C22⋊C4—4716no—
790C22⋊C4—4716no—
791C22⋊C4—4716no—
792C22⋊C4—478no—
793C22⋊C4—478no—
794C22⋊C4C23×D47116yes—
795C22⋊C4C23×D4718yes—
796C42—474no—
797C42—478no—
798C42—474no—
799C42—474no—
800C42—478no—
801C42—4716no—
802C42—4716no—
803C42C23×D4718yes—
804C42C23×D4714yes—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—474no—
809C23—472no—
810C23—474no—
811C23—474no—
812C23—942no—
813C23—942no—
814C23—944no—
815C23—944no—
816C23—944no—
817C23—944no—
818C23—944no—
819C23—944no—
820C23C24×D4714yes—
821C23C24×D4711yescharacteristic
822Q8—28no—
823Q8—48no—
824Q8—9432no—
825Q8—9416no—
826Q8—1888no—
827D4—28no—
828D4—9416no—
829D4—9416no—
830D4—9416no—
831D4—9416no—
832D4—9416no—
833D4—948no—
834D4—948no—
835D4—18816no—
836D4—18816no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—216no—
843C2×C4—416no—
844C2×C4—474no—
845C2×C4—474no—
846C2×C4—472no—
847C2×C4—472no—
848C2×C4—4716no—
849C2×C4—474no—
850C2×C4—472no—
851C2×C4—474no—
852C2×C4—478no—
853C2×C4—948no—
854C2×C4—9416no—
855C2×C4—9416no—
856C2×C4—944no—
857C2×C4—948no—
858C2×C4—944no—
859C2×C4—942no—
860C2×C4—9416no—
861C2×C4—948no—
862C2×C4—9416no—
863C2×C4—18816no—
864C2×C4—18816no—
865C2×C4#41×D4714yes—
866C2×C4#1309407214yes—
867C2×C4C24×D4714yes—
868C2×C4C24×D4712yes—
869C2×C4C24×D4714yes—
870C2×C4C24×D4714yes—
871C2×C4C24×D4718yes—
872C2×C4C24×D4712yes—
873C2×C4C24×D4712yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—48no—
878C22—474no—
879C22—948no—
880C22—942no—
881C22—942no—
882C22—944no—
883C22—944no—
884C22—944no—
885C22—944no—
886C22—944no—
887C22—944no—
888C22—1888no—
889C22—1888no—
890C22C2×#41×D4712yes—
891C22H(5,𝔽2)×D4712yes—
892C22C2×#1309407212yes—
893C22C25×D4711yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—474no—
900C4—474no—
901C4—944no—
902C4—948no—
903C4—944no—
904C4—942no—
905C4C2×#41×D4714yes—
906C4C2×#1309407214yes—
907C2—44no—
908C2—944no—
909C2—1884no—
910C2—1884no—
911C2#2025729614yesdirect product factor
912C2C22×#41×D4711yescharacteristic
913C2C2×H(5,𝔽2)×D4711yescharacteristic
914C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
hypercenterC2×#554D47
hypocenterC47C2×#3511
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257296C2direct (N × H)
2. C2×#15689844C2semidirect
3. C2×#15689839C2semidirect
4. C2×#15689838C2semidirect
5. C2×#15689833C2semidirect
6. C2×#15689826C2semidirect
7. C2×#15689823C2semidirect
8. C2×#15689783C2semidirect
9. C2×#15689774C2semidirect
10. C2×#15689743C2semidirect
11. C2×#15689703C2semidirect
12. C2×#15689679C2semidirect
13. C2×#15689670C2semidirect
14. C2×#15689670C2semidirect
15. C2×C4⋊Q8×D47C2semidirect
16. C2×#15689604C2semidirect
17. C2×C4×#10625354C2semidirect
18. C2×C47×#554C2semidirect
23. #15689844C22semidirect
24. #15689839C22semidirect
25. #15689838C22semidirect
26. #15689833C22semidirect
27. #15689826C22semidirect
28. #15689823C22semidirect
29. #15689783C22semidirect
30. #15689774C22semidirect
31. #15689743C22semidirect
32. #15689703C22semidirect
33. #15689679C22semidirect
34. #15689670C22semidirect
35. #15689670C22semidirect
41. C4⋊Q8×D47C22semidirect
66. #15689604C22semidirect
67. C4×#10625354C22semidirect
92. C47×#554C22semidirect
292. C2×C4×D47#41semidirect
412. C4×D47C2×#41semidirect
455. C2×#554D47semidirect
469. C2×C47#3511semidirect
484. #554C2×D47semidirect
558. C47C2×#3511semidirect
911. C2#20257296direct (N × H)

Maximal subgroups

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

subgroupindex
#202572962
C2×#156898442
C2×#156898392
C2×#156898382
C2×#156898332
C2×#156898262
C2×#156898232
C2×#156897832
C2×#156897742
C2×#156897432
C2×#156897032
C2×#156896792
C2×#156896702
C2×C4⋊Q8×D472
C2×#156896042
C2×C4×#106253542
C2×C47×#5542
C2×#351147