Finite Group Databasebeta

← C2×#20257292 #27124646

Subgroups — C2×#20257292 #27124646

Order 12032.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257292C2132yesmaximal, direct product factor
2C2×#15689846C211yesmaximal, characteristic, complemented
3C2×#15689836C212yesmaximal, complemented
4C2×#15689831C212yesmaximal, complemented
5C2×#15689824C214yesmaximal, complemented
6C2×#15689785C212yesmaximal, complemented
7C2×#15689781C212yesmaximal, complemented
8C2×#15689777C211yesmaximal, characteristic, complemented
9C2×#15689776C211yesmaximal, characteristic, complemented
10C2×#15689739C214yesmaximal, complemented
11C2×#15689703C212yesmaximal, complemented
12C2×#15689677C212yesmaximal, complemented
13C2×#15689672C212yesmaximal, complemented
14C2×#15689670C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
16C2×#15689603C212yesmaximal, complemented
17C2×C4×#10625354C211yesmaximal, characteristic, complemented
18C2×C47×#556C211yesmaximal, characteristic, complemented
19C22×#10625354C2211yescharacteristic
20C22×#10625354C2212yes—
21C22×#10625350C2212yes—
22C22×#10625352C2212yes—
23C22×Q8×D47C2212yes—
24#15689846C22116yescomplemented
25#15689836C22132yescomplemented
26#15689831C22132yescomplemented
27#15689824C22164yescomplemented
28#15689785C22132yescomplemented
29#15689781C22132yescomplemented
30#15689777C22116yescomplemented
31#15689776C22116yescomplemented
32#15689739C22164yescomplemented
33#15689703C22132yescomplemented
34#15689677C22132yescomplemented
35#15689672C22132yescomplemented
36#15689670C22116yescomplemented
37C2×#13094024C2211yescharacteristic
38C2×#13094023C2212yes—
39C2×#13094023C2212yes—
40C2×#13094023C2211yescharacteristic
41C2×#13094022C2212yes—
42C4⋊Q8×D47C22116yescomplemented
43C2×#13094020C2211yescharacteristic
44C2×#13094019C2214yes—
45C2×#13094014C2214yes—
46C2×#13094012C2212yes—
47C2×#13094012C2214yes—
48C2×#13094010C2214yes—
49C2×#13094010C2212yes—
50C2×#13094009C2214yes—
51C2×#13094008C2214yes—
52C2×#13094004C2212yes—
53C2×#13094004C2214yes—
54C2×#13094002C2214yes—
55C2×#13094001C2214yes—
56C2×#13094000C2212yes—
57C2×#13094000C2212yes—
58C2×#13093999C2212yes—
59C2×#13093999C2211yescharacteristic
60C2×#13093999C2214yes—
61C2×#13093998C2212yes—
62C2×#13093997C2214yes—
63C2×#13093997C2212yes—
64C2×#13093997C2214yes—
65C2×#13093997C2214yes—
66C2×#13093995C2211yescharacteristic
67#15689603C22132yescomplemented
68C4×#10625354C22116yescomplemented
69C2×Q8×Dic47C2211yescharacteristic
70C2×C4×Dic94C2214yes—
71C2×C4×Dic94C2212yes—
72C2×C4×D188C2211yescharacteristic
73C2×C4×D188C2212yes—
74C2×C4×D188C2214yes—
75C2×C4×D188C2211yescharacteristic
76C2×#13093986C2212yes—
77C2×#13093986C2211yescharacteristic
78C2×C4×C22⋊D47C2212yes—
79C2×(C22⋊D47)⋊C4C2214yes—
80C2×(C22⋊D47)⋊C4C2214yes—
81C2×(C22⋊D47)⋊C4C2214yes—
82C2×#13093982C2211yescharacteristic
83C2×#13093982C2212yes—
84C2×#13093982C2212yes—
85C2×#13093981C2214yes—
86C22×C4⋊Dic47C2212yes—
87C2×C4⋊C4×D47C2212yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2211yescharacteristic
91C2×C42×D47C2212yes—
92C47×#556C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#126×C47C2214yes—
95C2×#124×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×Q8×C47C2212yes—
99C2×C4×D4×C47C2211yescharacteristic
100C2×#117×C47C2212yes—
101C2×#10625354—28no—
102C2×#10625354—48no—
103C2×#10625354C2318yes—
104C2×#10625354C23116yes—
105C2×#10625350—216no—
106C2×#10625350C23116yes—
107C2×#10625352—48no—
108C2×#10625352C23116yes—
109C22×Dic94C2312yes—
110C22×Dic94C2312yes—
111C22×Dic94C2314yes—
112C2×Q8×D47—48no—
113C2×Q8×D47C23116yes—
114C22×D188C2312yes—
115C22×D188C2311yescharacteristic
116C22×D188C2312yes—
117C22×D188C2311yescharacteristic
118C22×D188C2314yes—
119C22×C22⋊D47C2312yes—
120C22×C22⋊D47C2312yes—
121C22×C22⋊D47C2312yes—
122C22×C22⋊D47C2314yes—
123C23×Dic47C2314yes—
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2312yes—
126C22×C4×D47C2312yes—
127C22×C4×D47C2311yescharacteristic
128C22×C4×D47C2312yes—
129C22×C4×D47C2312yes—
130C22×C4×D47C2314yes—
131C22×C4×D47C2314yes—
132C22×C4×D47C2311yescharacteristic
133#13094024C2318yes—
134#13094023C23116yes—
135#13094023C23116yes—
136#13094023C2318yes—
137#13094022C23116yes—
138#13094020C2318yes—
139#13094019C23132yes—
140#13094014C23132yes—
141#13094012C23132yes—
142#13094012C23116yes—
143#13094010C23116yes—
144#13094010C23132yes—
145#13094009C23132yes—
146#13094008C23132yes—
147#13094004C23132yes—
148#13094004C23116yes—
149#13094002C23132yes—
150#13094001C23132yes—
151#13094000C23116yes—
152#13094000C23116yes—
153#13093999C23116yes—
154#13093999C2318yes—
155#13093999C23132yes—
156#13093998C23116yes—
157#13093997C23132yes—
158#13093997C23132yes—
159#13093997C23116yes—
160#13093997C23132yes—
161#13093995C2318yes—
162Q8×Dic47C2318yes—
163C4×Dic94C23132yes—
164C4×Dic94C23116yes—
165C4×D188C2318yes—
166C4×D188C2318yes—
167C4×D188C23116yes—
168C4×D188C23132yes—
169#13093986C23116yes—
170#13093986C2318yes—
171C4×C22⋊D47C23116yes—
172(C22⋊D47)⋊C4C23132yes—
173(C22⋊D47)⋊C4C23132yes—
174(C22⋊D47)⋊C4C23132yes—
175#13093982C23116yes—
176#13093982C23116yes—
177#13093982C2318yes—
178#13093981C23132yes—
179C2×C4⋊Dic47C23116yes—
180C2×C4⋊Dic47C2311yescharacteristic
181C2×C4⋊Dic47C2312yes—
182C2×C4⋊Dic47C2312yes—
183C2×C4⋊Dic47C2314yes—
184C2×C4⋊Dic47C2312yes—
185C2×C4⋊Dic47C2311yescharacteristic
186C2×Dic47⋊C4C2314yes—
187C2×Dic47⋊C4C2314yes—
188C2×Dic47⋊C4C2314yes—
189C2×Dic47⋊C4C2312yes—
190C2×Dic47⋊C4C2314yes—
191C4⋊C4×D47C23116yes—
192C4⋊C4×D47C23116yes—
193C4⋊C4×D47C23116yes—
194C2×C22⋊Dic47C2312yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2311yescharacteristic
209C2×C4×Dic47C2314yes—
210C42×D47C2318yes—
211C42×D47C23116yes—
212C22×Q8×C47C2311yescharacteristic
213C22×Q8×C47C2312yes—
214C22×D4×C47C2311yescharacteristic
215C23×C4×C47C2312yes—
216C4⋊Q8×C47C2318yes—
217#126×C47C23132yes—
218#124×C47C23116yes—
219C22⋊Q8×C47C23116yes—
220C4×Q8×C47C23116yes—
221C4×Q8×C47C2318yes—
222C4×D4×C47C2318yes—
223#117×C47C23116yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C4⋊C4×C47C2314yes—
228C2×C4⋊C4×C47C2312yes—
229C2×C4⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C22⋊C4×C47C2312yes—
232C2×C22⋊C4×C47C2314yes—
233C2×C42×C47C2314yes—
234C2×C42×C47C2311yescharacteristic
235C2×C42×C47C2312yes—
236C24×C47C2412yes—
237C23×D47C2412yes—
238C23×D47C2412yes—
239C23×D47C2411yescharacteristic
240C2×Q8×C47—24no—
241C2×Q8×C47—28no—
242C2×Q8×C47C2414yes—
243C2×Q8×C47C2418yes—
244C2×D4×C47—24no—
245C2×D4×C47C2414yes—
246C22×C4×C47—28no—
247C22×C4×C47C2412yes—
248C22×C4×C47C2412yes—
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2412yes—
251C22×C4×C47C2414yes—
252C22×C4×C47C2418yes—
253C22×C4×C47C2411yescharacteristic
254C22×C4×C47C2411yescharacteristic
255C2×C22⋊D47—28no—
256C2×C22⋊D47—28no—
257C2×C22⋊D47—28no—
258C2×C22⋊D47—48no—
259C2×C22⋊D47C2418yes—
260C2×C22⋊D47C2418yes—
261C2×C22⋊D47C2418yes—
262C2×C22⋊D47C24116yes—
263C22×Dic47—48no—
264C22×Dic47C2411yescharacteristic
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C22×Dic47C2414yes—
268C22×Dic47C24116yes—
269C22×Dic47C2411yescharacteristic
270C22×Dic47C2411yescharacteristic
271#10625354—232no—
272#10625354—432no—
273Q8×D47—432no—
274#10625352—432no—
275#10625350—264no—
276C2×D188—28no—
277C2×D188—28no—
278C2×D188—24no—
279C2×D188—24no—
280C2×D188—48no—
281C2×D188C2418yes—
282C2×D188C2414yes—
283C2×D188C2418yes—
284C2×D188C2414yes—
285C2×D188C24116yes—
286C2×C4×D47—28no—
287C2×C4×D47—24no—
288C2×C4×D47—28no—
289C2×C4×D47—28no—
290C2×C4×D47—24no—
291C2×C4×D47—28no—
292C2×C4×D47—48no—
293C2×C4×D47—48no—
294C2×C4×D47#4118yescomplemented
295C2×C4×D47C2414yes—
296C2×C4×D47C2418yes—
297C2×C4×D47C2418yes—
298C2×C4×D47C2414yes—
299C2×C4×D47C2418yes—
300C2×C4×D47C2418yes—
301C2×C4×D47C24116yes—
302C2×C4×D47C24116yes—
303C2×C4×D47C2414yes—
304C2×Dic94—28no—
305C2×Dic94—28no—
306C2×Dic94—48no—
307C2×Dic94C2418yes—
308C2×Dic94C2418yes—
309C2×Dic94C24116yes—
310C4⋊C4×C47C2414yes—
311C4⋊C4×C47C2418yes—
312C4⋊C4×C47C2414yes—
313C4⋊C4×C47C24116yes—
314C4⋊C4×C47C2418yes—
315C4⋊C4×C47C2418yes—
316C22⋊C4×C47C24116yes—
317C22⋊C4×C47C2418yes—
318C22⋊C4×C47C24116yes—
319C42×C47C24116yes—
320C42×C47C2414yes—
321C42×C47C2418yes—
322C22⋊Dic47C2418yes—
323(C2×D47)⋊C4C24116yes—
324(C2×D47)⋊C4C24116yes—
325(C2×D47)⋊C4C2418yes—
326(C2×D47)⋊C4C24116yes—
327(C2×D47)⋊C4C2418yes—
328(C2×D47)⋊C4C2418yes—
329(C2×D47)⋊C4C24116yes—
330(C2×D47)⋊C4C2418yes—
331(C2×D47)⋊C4C2418yes—
332C4⋊Dic47C2414yes—
333C4⋊Dic47C2418yes—
334C4⋊Dic47C2418yes—
335C4⋊Dic47C24116yes—
336C4⋊Dic47C2418yes—
337C4⋊Dic47C2414yes—
338Dic47⋊C4C24116yes—
339Dic47⋊C4C24116yes—
340Dic47⋊C4C24116yes—
341Dic47⋊C4C2418yes—
342Dic47⋊C4C24116yes—
343C4×Dic47C2414yes—
344C4×Dic47C2418yes—
345C4×Dic47C2414yes—
346C4×Dic47C2418yes—
347C4×Dic47C2414yes—
348C4×Dic47C24116yes—
349C23×C47—24no—
350C23×C47—24no—
351C23×C47—24no—
352C23×C47C2514yes—
353C23×C47C2511yescharacteristic
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—24no—
357C22×D47—24no—
358C22×D47—24no—
359C22×D47—24no—
360C22×D47—24no—
361C22×D47—24no—
362C22×D47C2×#4114yes—
363C22×D47C2514yes—
364C22×D47C2514yes—
365C22×D47C2512yes—
366Q8×C47—28no—
367Q8×C47—216no—
368D4×C47—28no—
369C2×C4×C47—24no—
370C2×C4×C47—24no—
371C2×C4×C47—28no—
372C2×C4×C47—24no—
373C2×C4×C47—22no—
374C2×C4×C47—216no—
375C2×C4×C47C2×#4114yes—
376C2×C4×C47H(5,𝔽2)14yes—
377C2×C4×C47C2514yes—
378C2×C4×C47C2514yes—
379C2×C4×C47C2512yes—
380C2×C4×C47C2518yes—
381C2×C4×C47C2514yes—
382C2×C4×C47C2512yes—
383C2×C4×C47C2512yes—
384C22⋊D47—216no—
385C22⋊D47—216no—
386C22⋊D47—216no—
387C22⋊D47—416no—
388C2×Dic47—24no—
389C2×Dic47—28no—
390C2×Dic47—22no—
391C2×Dic47—24no—
392C2×Dic47—416no—
393C2×Dic47C2×#4114yes—
394C2×Dic472−1+414yes—
395C2×Dic47C2514yes—
396C2×Dic47C2514yes—
397C2×Dic47C2512yes—
398C2×Dic47C2518yes—
399C2×Dic47C2512yes—
400C2×Dic47C2512yes—
401D188—216no—
402D188—216no—
403D188—28no—
404D188—28no—
405D188—416no—
406C4×D47—216no—
407C4×D47—216no—
408C4×D47—28no—
409C4×D47—216no—
410C4×D47—28no—
411C4×D47—216no—
412C4×D47—416no—
413C4×D47—416no—
414C4×D47C2×#41116yescomplemented
415Dic94—216no—
416Dic94—216no—
417Dic94—416no—
418C2×#3511—471nomaximal, Sylow
419C22×C47—24no—
420C22×C47—24no—
421C22×C47—24no—
422C22×C47—48no—
423C22×C47C22×#4112yes—
424C22×C47C2×H(5,𝔽2)12yes—
425C22×C47C2×2−1+412yes—
426C22×C47C2611yescharacteristic
427C2×D47—22no—
428C2×D47—22no—
429C2×D47—28no—
430C2×D47—24no—
431C2×D47—24no—
432C2×D47—24no—
433C2×D47—24no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—48no—
437C2×D47—48no—
438C2×D47C22×#4114yes—
439C4×C47—24no—
440C4×C47—24no—
441C4×C47—28no—
442C4×C47—24no—
443C4×C47—22no—
444C4×C47C22×#4114yes—
445C4×C47C2×H(5,𝔽2)14yes—
446Dic47—24no—
447Dic47—28no—
448Dic47—22no—
449Dic47—24no—
450Dic47C22×#4114yes—
451Dic47C2×2−1+414yes—
452#3511—4732no—
453C2×#556—471no—
454C2×#556D4711yescharacteristic, complemented
455C2×#555—472no—
456C2×#554—472no—
457C2×#553—474no—
458C2×#548—472no—
459C2×#548—472no—
460C2×#547—471no—
461C2×#547—471no—
462C2×#542—474no—
463C2×#537—472no—
464C2×#533—472no—
465C2×#532—472no—
466C2×#532—471no—
467C22×C4⋊Q8—471no—
468C2×#520—472no—
469C2×C4×#41—471no—
470C2×C47—44no—
471C2×C47#351114yescomplemented
472C2×C47C23×#4111yescharacteristic
473C2×C47C22×H(5,𝔽2)11yescharacteristic
474C2×C47C22×2−1+411yescharacteristic
475D47—24no—
476D47—44no—
477D47—44no—
478C22×#41—471no—
479C22×#41—472no—
480C22×#41—472no—
481C22×#41—472no—
482C23×Q8—472no—
483#556—4716no—
484#556C2×D47116yescomplemented
485#555—4732no—
486#554—4732no—
487#553—4764no—
488#548—4732no—
489#548—4732no—
490#547—4716no—
491#547—4716no—
492#542—4764no—
493#537—4732no—
494#533—4732no—
495#532—4732no—
496#532—4716no—
497C2×C4⋊Q8—472no—
498C2×C4⋊Q8—4716no—
499C2×C4⋊Q8—472no—
500C2×C4⋊Q8—472no—
501C2×C4⋊Q8—471no—
502C2×C4⋊Q8—471no—
503C2×C4⋊Q8C2×D4711yescharacteristic
504C2×#127—471no—
505C2×#126—474no—
506C2×#126C2×D4714yes—
507C2×#125—474no—
508C2×#124—472no—
509C2×#124—474no—
510C2×#124—472no—
511C2×#124—474no—
512C2×#124C2×D4712yes—
513C2×#123—474no—
514C2×#123—474no—
515C2×C22⋊Q8—472no—
516C2×C22⋊Q8—472no—
517C2×C22⋊Q8—474no—
518C2×C22⋊Q8—472no—
519C2×C22⋊Q8—474no—
520C2×C22⋊Q8—474no—
521C2×C22⋊Q8C2×D4712yes—
522C2×#121—471no—
523C2×#121—472no—
524C2×#121—471no—
525C2×#121—472no—
526C2×#121—474no—
527C2×#121—474no—
528C2×#121—472no—
529C2×#121—474no—
530C2×#121—474no—
531#520—4732no—
532C4×#41—4716no—
533C2×C4×Q8—471no—
534C2×C4×Q8—474no—
535C2×C4×Q8—472no—
536C2×C4×Q8C2×D4711yescharacteristic
537C2×C4×Q8C2×D4712yes—
538C2×C4×D4—472no—
539C2×C4×D4—472no—
540C2×C4×D4—471no—
541C2×C4×D4—474no—
542C2×C4×D4—474no—
543C2×C4×D4—474no—
544C2×C4×D4—471no—
545C2×C4×D4—472no—
546C2×C4×D4—474no—
547C2×C4×D4—471no—
548C2×C4×D4C2×D4711yescharacteristic
549C2×#117—471no—
550C2×#117—472no—
551C2×#117—472no—
552C2×#117—474no—
553C2×#117C2×D4712yes—
554C22×C4⋊C4—472no—
555C22×C4⋊C4—472no—
556C22×C4⋊C4—472no—
557C22×C4⋊C4—472no—
558C22×C42—471no—
559C22×C42—472no—
560C47C2×#351111yescharacteristic, complemented, Sylow
561C2×#41—478no—
562C2×#41—4716no—
563C2×#41—4716no—
564C2×#41—4716no—
565C2×#41—9416no—
566C2×#41—948no—
567C2×#41—1888no—
568C2×#41—1888no—
569C22×Q8—4716no—
570C22×Q8—472no—
571C22×Q8—472no—
572C22×Q8—474no—
573C22×Q8—1888no—
574C22×Q8C22×D4711yescharacteristic
575C22×Q8C22×D4712yes—
576C22×D4—472no—
577C22×D4—472no—
578C22×D4—472no—
579C22×D4—474no—
580C22×D4—472no—
581C22×D4—472no—
582C22×D4—471no—
583C22×D4—471no—
584C22×D4—474no—
585C22×D4C22×D4711yescharacteristic
586C23×C4—471no—
587C23×C4—474no—
588C23×C4—471no—
589C23×C4—472no—
590C23×C4—472no—
591C23×C4—472no—
592C23×C4—471no—
593C23×C4—472no—
594C23×C4—474no—
595C23×C4—474no—
596C23×C4C22×D4712yes—
597C4⋊Q8—4716no—
598C4⋊Q8—4716no—
599C4⋊Q8—4716no—
600C4⋊Q8—478no—
601C4⋊Q8—478no—
602C4⋊Q8C22×D4718yes—
603#127—478no—
604#126—4732no—
605#126C22×D47132yes—
606#125—4732no—
607#124—4716no—
608#124—4732no—
609#124—4716no—
610#124—4732no—
611#124C22×D47116yes—
612#123—4732no—
613#123—4732no—
614C22⋊Q8—4716no—
615C22⋊Q8—4716no—
616C22⋊Q8—4732no—
617C22⋊Q8—4716no—
618C22⋊Q8—4732no—
619C22⋊Q8—4732no—
620C22⋊Q8C22×D47116yes—
621#121—478no—
622#121—4716no—
623#121—478no—
624#121—4716no—
625#121—4732no—
626#121—4732no—
627#121—4716no—
628#121—4732no—
629#121—4732no—
630C4×Q8—478no—
631C4×Q8—4732no—
632C4×Q8—4716no—
633C4×Q8C22×D4718yes—
634C4×Q8C22×D47116yes—
635C4×D4—4716no—
636C4×D4—4716no—
637C4×D4—478no—
638C4×D4—4732no—
639C4×D4—4732no—
640C4×D4—4732no—
641C4×D4—478no—
642C4×D4—4716no—
643C4×D4—4732no—
644C4×D4—478no—
645C4×D4C22×D4718yes—
646#117—478no—
647#117—4716no—
648#117—4716no—
649#117—4732no—
650#117C22×D47116yes—
651C2×C4⋊C4—471no—
652C2×C4⋊C4—472no—
653C2×C4⋊C4—474no—
654C2×C4⋊C4—474no—
655C2×C4⋊C4—474no—
656C2×C4⋊C4—474no—
657C2×C4⋊C4—4716no—
658C2×C4⋊C4—472no—
659C2×C4⋊C4—472no—
660C2×C4⋊C4—472no—
661C2×C4⋊C4—471no—
662C2×C4⋊C4—474no—
663C2×C4⋊C4—4716no—
664C2×C4⋊C4—4716no—
665C2×C4⋊C4—4716no—
666C2×C4⋊C4C22×D4712yes—
667C2×C4⋊C4C22×D4712yes—
668C2×C4⋊C4C22×D4711yescharacteristic
669C2×C4⋊C4C22×D4712yes—
670C2×C4⋊C4C22×D4711yescharacteristic
671C2×C4⋊C4C22×D4714yes—
672C2×C22⋊C4—472no—
673C2×C22⋊C4—472no—
674C2×C22⋊C4—474no—
675C2×C22⋊C4—472no—
676C2×C22⋊C4—472no—
677C2×C22⋊C4—474no—
678C2×C22⋊C4—474no—
679C2×C22⋊C4—474no—
680C2×C22⋊C4—472no—
681C2×C22⋊C4—472no—
682C2×C22⋊C4C22×D4714yes—
683C2×C22⋊C4C22×D4714yes—
684C2×C22⋊C4C22×D4712yes—
685C2×C42—472no—
686C2×C42—474no—
687C2×C42—471no—
688C2×C42—472no—
689C2×C42—471no—
690C2×C42—471no—
691C2×C42—478no—
692C2×C42—4716no—
693C2×C42C22×D4714yes—
694C2×C42C22×D4711yescharacteristic
695C2×C42C22×D4712yes—
696C24—471no—
697C24—472no—
698C24—472no—
699C24C23×D4712yes—
700#41—9464no—
701#41—9432no—
702#41—18832no—
703#41—18832no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—478no—
707C2×Q8—478no—
708C2×Q8—4716no—
709C2×Q8—948no—
710C2×Q8—948no—
711C2×Q8—1888no—
712C2×Q8—18832no—
713C2×Q8C23×D4714yes—
714C2×Q8C23×D4718yes—
715C2×D4—24no—
716C2×D4—478no—
717C2×D4—478no—
718C2×D4—478no—
719C2×D4—4716no—
720C2×D4—478no—
721C2×D4—478no—
722C2×D4—474no—
723C2×D4—474no—
724C2×D4—4716no—
725C2×D4—948no—
726C2×D4—948no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—948no—
730C2×D4—944no—
731C2×D4—944no—
732C2×D4—1888no—
733C2×D4—1888no—
734C2×D4C23×D4714yes—
735C22×C4—28no—
736C22×C4—471no—
737C22×C4—471no—
738C22×C4—478no—
739C22×C4—474no—
740C22×C4—471no—
741C22×C4—472no—
742C22×C4—472no—
743C22×C4—474no—
744C22×C4—4716no—
745C22×C4—474no—
746C22×C4—478no—
747C22×C4—478no—
748C22×C4—474no—
749C22×C4—478no—
750C22×C4—478no—
751C22×C4—4716no—
752C22×C4—4716no—
753C22×C4—944no—
754C22×C4—948no—
755C22×C4—948no—
756C22×C4—948no—
757C22×C4—944no—
758C22×C4—948no—
759C22×C4—1888no—
760C22×C4—1888no—
761C22×C4—1888no—
762C22×C4C23×D4718yes—
763C22×C4C23×D4712yes—
764C22×C4C23×D4711yescharacteristic
765C22×C4C23×D4712yes—
766C22×C4C23×D4712yes—
767C22×C4C23×D4714yes—
768C22×C4C23×D4711yescharacteristic
769C22×C4C23×D4711yescharacteristic
770C4⋊C4—4716no—
771C4⋊C4—4716no—
772C4⋊C4—4716no—
773C4⋊C4—478no—
774C4⋊C4—4716no—
775C4⋊C4—474no—
776C4⋊C4—478no—
777C4⋊C4—4716no—
778C4⋊C4—478no—
779C4⋊C4—478no—
780C4⋊C4—474no—
781C4⋊C4C23×D4718yes—
782C4⋊C4C23×D4718yes—
783C4⋊C4C23×D4714yes—
784C4⋊C4C23×D4718yes—
785C4⋊C4C23×D4714yes—
786C4⋊C4C23×D47116yes—
787C22⋊C4—478no—
788C22⋊C4—478no—
789C22⋊C4—4716no—
790C22⋊C4—478no—
791C22⋊C4—478no—
792C22⋊C4—4716no—
793C22⋊C4—4716no—
794C22⋊C4—4716no—
795C22⋊C4—478no—
796C22⋊C4—478no—
797C22⋊C4C23×D47116yes—
798C22⋊C4C23×D47116yes—
799C22⋊C4C23×D4718yes—
800C42—474no—
801C42—478no—
802C42—474no—
803C42—478no—
804C42—474no—
805C42—4716no—
806C42C23×D4714yes—
807C42C23×D4718yes—
808C42C23×D47116yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—474no—
813C23—472no—
814C23—474no—
815C23—474no—
816C23—942no—
817C23—942no—
818C23—944no—
819C23—944no—
820C23—944no—
821C23—944no—
822C23—944no—
823C23—944no—
824C23C24×D4714yes—
825C23C24×D4711yescharacteristic
826Q8—28no—
827Q8—216no—
828Q8—9416no—
829Q8—9416no—
830Q8—18816no—
831D4—28no—
832D4—9416no—
833D4—9416no—
834D4—9416no—
835D4—9416no—
836D4—9416no—
837D4—948no—
838D4—948no—
839D4—18816no—
840D4—18816no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—216no—
847C2×C4—474no—
848C2×C4—474no—
849C2×C4—472no—
850C2×C4—472no—
851C2×C4—4716no—
852C2×C4—472no—
853C2×C4—474no—
854C2×C4—474no—
855C2×C4—478no—
856C2×C4—948no—
857C2×C4—9416no—
858C2×C4—9416no—
859C2×C4—944no—
860C2×C4—944no—
861C2×C4—942no—
862C2×C4—948no—
863C2×C4—9416no—
864C2×C4—948no—
865C2×C4—9416no—
866C2×C4—18816no—
867C2×C4—18816no—
868C2×C4—18816no—
869C2×C4#41×D4714yes—
870C2×C4#1309407014yes—
871C2×C4C24×D4714yes—
872C2×C4C24×D4712yes—
873C2×C4C24×D4714yes—
874C2×C4C24×D4714yes—
875C2×C4C24×D4718yes—
876C2×C4C24×D4712yes—
877C2×C4C24×D4712yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—48no—
882C22—474no—
883C22—948no—
884C22—942no—
885C22—942no—
886C22—944no—
887C22—944no—
888C22—944no—
889C22—944no—
890C22—944no—
891C22—944no—
892C22—1888no—
893C22—1888no—
894C22C2×#41×D4712yes—
895C22C2×#1309407012yes—
896C222−1+4×D4712yes—
897C22C25×D4711yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—24no—
902C4—22no—
903C4—474no—
904C4—474no—
905C4—944no—
906C4—944no—
907C4—942no—
908C4—948no—
909C4C2×#41×D4714yes—
910C4C2×#1309407014yes—
911C2—44no—
912C2—944no—
913C2—1884no—
914C2—1884no—
915C2#2025729214yesdirect product factor
916C2C22×#41×D4711yescharacteristic
917C2C22×#1309407011yescharacteristic
918C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#556C2
socleC23×C47C25
hypercenterC2×#556D47
hypocenterC47C2×#3511
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20257292C2direct (N × H)
2. C2×#15689846C2semidirect
3. C2×#15689836C2semidirect
4. C2×#15689831C2semidirect
5. C2×#15689824C2semidirect
6. C2×#15689785C2semidirect
7. C2×#15689781C2semidirect
8. C2×#15689777C2semidirect
9. C2×#15689776C2semidirect
10. C2×#15689739C2semidirect
11. C2×#15689703C2semidirect
12. C2×#15689677C2semidirect
13. C2×#15689672C2semidirect
14. C2×#15689670C2semidirect
15. C2×C4⋊Q8×D47C2semidirect
16. C2×#15689603C2semidirect
17. C2×C4×#10625354C2semidirect
18. C2×C47×#556C2semidirect
24. #15689846C22semidirect
25. #15689836C22semidirect
26. #15689831C22semidirect
27. #15689824C22semidirect
28. #15689785C22semidirect
29. #15689781C22semidirect
30. #15689777C22semidirect
31. #15689776C22semidirect
32. #15689739C22semidirect
33. #15689703C22semidirect
34. #15689677C22semidirect
35. #15689672C22semidirect
36. #15689670C22semidirect
42. C4⋊Q8×D47C22semidirect
67. #15689603C22semidirect
68. C4×#10625354C22semidirect
92. C47×#556C22semidirect
294. C2×C4×D47#41semidirect
414. C4×D47C2×#41semidirect
454. C2×#556D47semidirect
471. C2×C47#3511semidirect
484. #556C2×D47semidirect
560. C47C2×#3511semidirect
915. C2#20257292direct (N × H)

Maximal subgroups

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

subgroupindex
#202572922
C2×#156898462
C2×#156898362
C2×#156898312
C2×#156898242
C2×#156897852
C2×#156897812
C2×#156897772
C2×#156897762
C2×#156897392
C2×#156897032
C2×#156896772
C2×#156896722
C2×#156896702
C2×C4⋊Q8×D472
C2×#156896032
C2×C4×#106253542
C2×C47×#5562
C2×#351147