Finite Group Databasebeta

← C2×#20257773 #27123981

Subgroups — C2×#20257773 #27123981

Order 12032.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257773C2132yesmaximal, direct product factor
2C2×#15689869C214yesmaximal, complemented
3C2×#15689839C212yesmaximal, complemented
4C2×#15689838C211yesmaximal, characteristic, complemented
5C2×#15689833C211yesmaximal, characteristic, complemented
6C2×#15689823C212yesmaximal, complemented
7C2×#15689807C212yesmaximal, complemented
8C2×#15689784C212yesmaximal, complemented
9C2×#15689776C211yesmaximal, characteristic, complemented
10C2×#15689750C212yesmaximal, complemented
11C2×#15689743C214yesmaximal, complemented
12C2×#15689724C212yesmaximal, complemented
13C2×#15689703C212yesmaximal, complemented
14C2×#15689697C212yesmaximal, complemented
15C2×#15689678C211yesmaximal, characteristic, complemented
16C2×#15689670C211yesmaximal, characteristic, complemented
17C2×#15689660C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×#10625350C2212yes—
21#15689869C22164yescomplemented
22#15689839C22132yescomplemented
23#15689838C22116yescomplemented
24#15689833C22116yescomplemented
25#15689823C22132yescomplemented
26#15689807C22132yescomplemented
27#15689784C22132yescomplemented
28#15689776C22116yescomplemented
29#15689750C22132yescomplemented
30#15689743C22164yescomplemented
31#15689724C22132yescomplemented
32#15689703C22132yescomplemented
33#15689697C22132yescomplemented
34#15689678C22116yescomplemented
35#15689670C22116yescomplemented
36C2×#13094024C2211yescharacteristic
37C2×#13094023C2211yescharacteristic
38C2×#13094022C2214yes—
39C2×#13094020C2211yescharacteristic
40#15689660C22116yescomplemented
41C2×#13094019C2212yes—
42C2×#13094017C2214yes—
43C2×#13094016C2212yes—
44C2×#13094015C2212yes—
45C2×#13094015C2211yescharacteristic
46C2×#13094014C2214yes—
47C2×#13094013C2211yescharacteristic
48C2×#13094013C2214yes—
49C2×#13094013C2214yes—
50C2×#13094010C2212yes—
51C2×#13094010C2214yes—
52C2×#13094009C2214yes—
53C2×#13094009C2212yes—
54C2×#13094007C2214yes—
55C2×#13094007C2214yes—
56C2×#13094006C2214yes—
57C2×#13094004C2212yes—
58C2×#13094002C2214yes—
59C2×#13094002C2214yes—
60C2×#13094000C2214yes—
61C2×#13094000C2212yes—
62C2×#13094000C2212yes—
63C2×#13094000C2211yescharacteristic
64C2×#13094000C2212yes—
65C2×#13093999C2212yes—
66C2×#13093999C2211yescharacteristic
67C2×#13093999C2211yescharacteristic
68C2×#13093999C2214yes—
69C2×#13093998C2212yes—
70C2×#13093998C2214yes—
71C2×#13093997C2214yes—
72C2×#13093997C2212yes—
73C2×#13093997C2214yes—
74C2×#13093995C2211yescharacteristic
75C2×#13093995C2212yes—
76C2×Q8×Dic47C2212yes—
77C2×#13093989C2212yes—
78C2×C4×D188C2211yescharacteristic
79C2×C4×D188C2211yescharacteristic
80C2×C4×D188C2212yes—
81C2×C4×D188C2212yes—
82C2×C4×C22⋊D47C2212yes—
83C2×C4×C22⋊D47C2214yes—
84C2×#13093983C2212yes—
85C2×#13093982C2212yes—
86C2×#13093982C2214yes—
87C2×#13093982C2212yes—
88C2×#13093981C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C4⋊C4×D47C2212yes—
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×C47C2212yes—
100C2×C4×D4×C47C2211yescharacteristic
101C2×#10625354—48no—
102C2×#10625354C23116yes—
103C2×#10625350—48no—
104C2×#10625350C23116yes—
105C22×Dic94C2312yes—
106C22×Dic94C2312yes—
107C22×D188C2311yescharacteristic
108C22×D188C2311yescharacteristic
109C22×D188C2312yes—
110C22×D188C2314yes—
111C22×D188C2312yes—
112C22×C22⋊D47C2314yes—
113C22×C22⋊D47C2312yes—
114C22×C22⋊D47C2312yes—
115C22×C22⋊D47C2312yes—
116C22×C4×D47C2311yescharacteristic
117C22×C4×D47C2311yescharacteristic
118C22×C4×D47C2312yes—
119C22×C4×D47C2312yes—
120C22×C4×D47C2311yescharacteristic
121C22×C4×D47C2314yes—
122C22×C4×D47C2314yes—
123#13094024C2318yes—
124#13094023C2318yes—
125#13094022C23132yes—
126#13094020C2318yes—
127#13094019C23116yes—
128#13094017C23132yes—
129#13094016C23116yes—
130#13094015C23116yes—
131#13094015C2318yes—
132#13094014C23132yes—
133#13094013C23132yes—
134#13094013C2318yes—
135#13094013C23132yes—
136#13094010C23116yes—
137#13094010C23132yes—
138#13094009C23132yes—
139#13094009C23116yes—
140#13094007C23132yes—
141#13094007C23132yes—
142#13094006C23132yes—
143#13094004C23116yes—
144#13094002C23132yes—
145#13094002C23132yes—
146#13094000C23132yes—
147#13094000C23116yes—
148#13094000C23116yes—
149#13094000C2318yes—
150#13094000C23116yes—
151#13093999C23116yes—
152#13093999C2318yes—
153#13093999C23132yes—
154#13093999C2318yes—
155#13093998C23116yes—
156#13093998C23132yes—
157#13093997C23132yes—
158#13093997C23132yes—
159#13093997C23116yes—
160#13093995C2318yes—
161#13093995C23116yes—
162Q8×Dic47C23116yes—
163#13093989C23116yes—
164C4×D188C2318yes—
165C4×D188C2318yes—
166C4×D188C23116yes—
167C4×D188C23116yes—
168C4×C22⋊D47C23132yes—
169C4×C22⋊D47C23116yes—
170#13093983C23116yes—
171#13093982C23132yes—
172#13093982C23116yes—
173#13093982C23116yes—
174#13093981C23116yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2311yescharacteristic
180C2×C4⋊Dic47C2314yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2314yes—
187C2×Dic47⋊C4C2314yes—
188C4⋊C4×D47C23116yes—
189C4⋊C4×D47C23116yes—
190C2×C22⋊Dic47C2314yes—
191C2×C22⋊Dic47C2312yes—
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)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2314yes—
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×C47C23132yes—
220C22⋊Q8×C47C23116yes—
221C4×Q8×C47C2318yes—
222C4×D4×C47C23116yes—
223C4×D4×C47C2318yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C4⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C22⋊C4×C47C2312yes—
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2312yes—
234C24×C47C2412yes—
235C23×D47C2412yes—
236C23×D47C2411yescharacteristic
237C23×D47C2412yes—
238C2×Q8×C47—24no—
239C2×Q8×C47—28no—
240C2×Q8×C47—48no—
241C2×Q8×C47—432no—
242C2×Q8×C47C2414yes—
243C2×Q8×C47C2418yes—
244C2×Q8×C47C24116yes—
245C2×D4×C47—24no—
246C2×D4×C47C2414yes—
247C22×C4×C47—28no—
248C22×C4×C47—48no—
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2412yes—
251C22×C4×C47C2412yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2414yes—
254C22×C4×C47C2418yes—
255C22×C4×C47C24116yes—
256C22×C4×C47C2411yescharacteristic
257C22×C4×C47C2411yescharacteristic
258C2×C22⋊D47—48no—
259C2×C22⋊D47—44no—
260C2×C22⋊D47—44no—
261C2×C22⋊D47—44no—
262C2×C22⋊D47C24116yes—
263C2×C22⋊D47C2418yes—
264C2×C22⋊D47C2418yes—
265C2×C22⋊D47C2418yes—
266C22×Dic47C2411yescharacteristic
267C22×Dic47C2412yes—
268C22×Dic47C2414yes—
269C22×Dic47C2411yescharacteristic
270C22×Dic47C2411yescharacteristic
271C22×Dic47C2412yes—
272#10625354—432no—
273#10625350—432no—
274C2×D188—24no—
275C2×D188—24no—
276C2×D188—44no—
277C2×D188—44no—
278C2×D188—48no—
279C2×D188C2414yes—
280C2×D188C2414yes—
281C2×D188C2418yes—
282C2×D188C24116yes—
283C2×D188C2418yes—
284C2×C4×D47—24no—
285C2×C4×D47—28no—
286C2×C4×D47—24no—
287C2×C4×D47—28no—
288C2×C4×D47—48no—
289C2×C4×D47—42no—
290C2×C4×D47—48no—
291C2×C4×D47C2414yes—
292C2×C4×D47C2414yes—
293C2×C4×D47C2418yes—
294C2×C4×D47C2418yes—
295C2×C4×D47C2414yes—
296C2×C4×D47C24116yes—
297C2×C4×D47C24116yes—
298C2×Dic94—44no—
299C2×Dic94—44no—
300C2×Dic94C2418yes—
301C2×Dic94C2418yes—
302C4⋊C4×C47C2418yes—
303C4⋊C4×C47C2414yes—
304C4⋊C4×C47C2414yes—
305C4⋊C4×C47C2418yes—
306C4⋊C4×C47C24116yes—
307C4⋊C4×C47C2418yes—
308C22⋊C4×C47C24116yes—
309C22⋊C4×C47C2418yes—
310C42×C47C2414yes—
311C42×C47C2418yes—
312C22⋊Dic47C24116yes—
313C22⋊Dic47C2418yes—
314(C2×D47)⋊C4C2418yes—
315(C2×D47)⋊C4C2418yes—
316(C2×D47)⋊C4C2418yes—
317(C2×D47)⋊C4C24116yes—
318(C2×D47)⋊C4C24116yes—
319(C2×D47)⋊C4C24116yes—
320(C2×D47)⋊C4C2418yes—
321(C2×D47)⋊C4C2418yes—
322(C2×D47)⋊C4C24116yes—
323(C2×D47)⋊C4C2418yes—
324(C2×D47)⋊C4C2418yes—
325C4⋊Dic47C2414yes—
326C4⋊Dic47C2418yes—
327C4⋊Dic47C2418yes—
328C4⋊Dic47C2418yes—
329C4⋊Dic47C2414yes—
330C4⋊Dic47C24116yes—
331Dic47⋊C4C24116yes—
332Dic47⋊C4C24116yes—
333Dic47⋊C4C2418yes—
334Dic47⋊C4C2418yes—
335Dic47⋊C4C2418yes—
336Dic47⋊C4C24116yes—
337Dic47⋊C4C24116yes—
338C4×Dic47C2414yes—
339C4×Dic47C2414yes—
340C4×Dic47C2414yes—
341C4×Dic47C24116yes—
342C4×Dic47C24116yes—
343C23×C47—24no—
344C23×C47—24no—
345C23×C47—24no—
346C23×C47C2514yes—
347C23×C47C2511yescharacteristic
348C22×D47—24no—
349C22×D47—22no—
350C22×D47—24no—
351C22×D47—22no—
352C22×D47—24no—
353C22×D47—24no—
354C22×D47—24no—
355C22×D47—22no—
356C22×D47—24no—
357C22×D47C2514yes—
358C22×D47C2512yes—
359C22×D47C2514yes—
360Q8×C47—216no—
361Q8×C47—28no—
362Q8×C47—416no—
363D4×C47—28no—
364C2×C4×C47—24no—
365C2×C4×C47—28no—
366C2×C4×C47—24no—
367C2×C4×C47—22no—
368C2×C4×C47—24no—
369C2×C4×C47—216no—
370C2×C4×C47—416no—
371C2×C4×C47H(5,𝔽2)14yes—
372C2×C4×C472−1+414yes—
373C2×C4×C47C2514yes—
374C2×C4×C47C2518yes—
375C2×C4×C47C2512yes—
376C2×C4×C47C2514yes—
377C2×C4×C47C2514yes—
378C2×C4×C47C2512yes—
379C2×C4×C47C2512yes—
380C22⋊D47—48no—
381C22⋊D47—48no—
382C22⋊D47—416no—
383C22⋊D47—48no—
384C2×Dic47—22no—
385C2×Dic47—24no—
386C2×Dic47—22no—
387C2×Dic47—24no—
388C2×Dic47—28no—
389C2×Dic47—22no—
390C2×Dic47C2512yes—
391C2×Dic47C2512yes—
392C2×Dic47C2512yes—
393C2×Dic47C2514yes—
394C2×Dic47C2518yes—
395C2×Dic47C2514yes—
396D188—28no—
397D188—28no—
398D188—48no—
399D188—48no—
400D188—416no—
401C4×D47—28no—
402C4×D47—216no—
403C4×D47—28no—
404C4×D47—216no—
405C4×D47—416no—
406C4×D47—44no—
407C4×D47—416no—
408Dic94—48no—
409Dic94—48no—
410C2×#3547—471nomaximal, Sylow
411C22×C47—24no—
412C22×C47—24no—
413C22×C47—24no—
414C22×C47—48no—
415C22×C47C2×H(5,𝔽2)12yes—
416C22×C47C2×2−1+412yes—
417C22×C47#58512yes—
418C22×C47C2611yescharacteristic
419C2×D47—24no—
420C2×D47—22no—
421C2×D47—24no—
422C2×D47—22no—
423C2×D47—24no—
424C2×D47—24no—
425C2×D47—24no—
426C2×D47—22no—
427C2×D47—24no—
428C2×D47—48no—
429C2×D47—44no—
430C2×D47—48no—
431C4×C47—24no—
432C4×C47—28no—
433C4×C47—24no—
434C4×C47—22no—
435C4×C47—24no—
436C4×C47C2×H(5,𝔽2)14yes—
437C4×C47C2×2−1+414yes—
438Dic47—22no—
439Dic47—24no—
440Dic47—22no—
441Dic47—24no—
442Dic47—28no—
443Dic47—22no—
444#3547—4732no—
445C2×#562—474no—
446C2×#555—472no—
447C2×#555—471no—
448C2×#554—471no—
449C2×#553—472no—
450C2×#552—472no—
451C2×D4×Q8D4711yescharacteristic, complemented
452C2×#548—472no—
453C2×#547—471no—
454C2×#544—472no—
455C2×#542—474no—
456C2×#540—472no—
457C2×#537—472no—
458C2×#536—472no—
459C2×#533—471no—
460C2×#532—471no—
461C2×#529—471no—
462C2×C47—44no—
463C2×C47#354714yescomplemented
464C2×C47C22×H(5,𝔽2)11yescharacteristic
465C2×C47C22×2−1+411yescharacteristic
466C2×C47C2×#58511yescharacteristic
467D47—44no—
468D47—42no—
469D47—44no—
470C22×#41—472no—
471C22×#41—472no—
472C23×Q8C2×D4712yes—
473#562—4764no—
474#555—4732no—
475#555—4716no—
476#554—4716no—
477#553—4732no—
478#552—4732no—
479D4×Q8C2×D47116yescomplemented
480#548—4732no—
481#547—4716no—
482#544—4732no—
483#542—4764no—
484#540—4732no—
485#537—4732no—
486#536—4732no—
487#533—4716no—
488#532—4716no—
489C2×C4⋊Q8—474no—
490C2×C4⋊Q8—471no—
491C2×C4⋊Q8—471no—
492C2×C4⋊Q8C2×D4711yescharacteristic
493C2×C4⋊Q8C2×D4712yes—
494C2×#127—471no—
495#529—4716no—
496C2×#126—472no—
497C2×#126—474no—
498C2×#125—471no—
499C2×#125—472no—
500C2×#125—474no—
501C2×#125—472no—
502C2×#124—471no—
503C2×#124—474no—
504C2×#124—474no—
505C2×#124—472no—
506C2×#124—474no—
507C2×#123—474no—
508C2×#123—474no—
509C2×#123—472no—
510C2×#123—474no—
511C2×#123—474no—
512C2×C22⋊Q8—471no—
513C2×C22⋊Q8—472no—
514C2×C22⋊Q8—472no—
515C2×C22⋊Q8—472no—
516C2×C22⋊Q8—474no—
517C2×C22⋊Q8—472no—
518C2×C22⋊Q8—474no—
519C2×C22⋊Q8—474no—
520C2×C22⋊Q8C2×D4712yes—
521C2×C22⋊Q8C2×D4714yes—
522C2×#121—471no—
523C2×#121—472no—
524C2×#121—472no—
525C2×#121—474no—
526C2×#121—471no—
527C2×#121—471no—
528C2×#121—474no—
529C2×#121—472no—
530C2×#121—472no—
531C2×#121—474no—
532C2×#121—474no—
533C2×C4×Q8—472no—
534C2×C4×Q8—472no—
535C2×C4×Q8C2×D4711yescharacteristic
536C2×C4×D4—472no—
537C2×C4×D4—474no—
538C2×C4×D4—471no—
539C2×C4×D4—472no—
540C2×C4×D4—471no—
541C2×C4×D4—472no—
542C2×C4×D4C2×D4711yescharacteristic
543C2×C4×D4C2×D4712yes—
544C2×#117—472no—
545C2×#117—472no—
546C2×#117—474no—
547C2×#117—472no—
548C2×#117—472no—
549C22×C4⋊C4—472no—
550C22×C4⋊C4—472no—
551C22×C42—471no—
552C47C2×#354711yescharacteristic, complemented, Sylow
553C2×#41—4716no—
554C2×#41—4716no—
555C2×#41—1888no—
556C2×#41—1888no—
557C22×Q8—48no—
558C22×Q8—472no—
559C22×Q8—472no—
560C22×Q8C22×D4712yes—
561C22×Q8C22×D4711yescharacteristic
562C22×Q8C22×D4714yes—
563C22×Q8C22×D47116yes—
564C22×D4—474no—
565C22×D4—472no—
566C22×D4—472no—
567C22×D4—472no—
568C22×D4—471no—
569C22×D4—471no—
570C22×D4—472no—
571C22×D4—474no—
572C22×D4—472no—
573C22×D4C22×D4711yescharacteristic
574C23×C4—472no—
575C23×C4—472no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—474no—
579C23×C4—474no—
580C23×C4—471no—
581C23×C4C22×D4712yes—
582C23×C4C22×D4714yes—
583C4⋊Q8—4732no—
584C4⋊Q8—478no—
585C4⋊Q8—478no—
586C4⋊Q8C22×D4718yes—
587C4⋊Q8C22×D47116yes—
588#127—478no—
589#126—4716no—
590#126—4732no—
591#125—478no—
592#125—4716no—
593#125—4732no—
594#125—4716no—
595#124—478no—
596#124—4732no—
597#124—4732no—
598#124—4716no—
599#124—4732no—
600#123—4732no—
601#123—4732no—
602#123—4716no—
603#123—4732no—
604#123—4732no—
605C22⋊Q8—478no—
606C22⋊Q8—4716no—
607C22⋊Q8—4716no—
608C22⋊Q8—4716no—
609C22⋊Q8—4732no—
610C22⋊Q8—4716no—
611C22⋊Q8—4732no—
612C22⋊Q8—4732no—
613C22⋊Q8C22×D47116yes—
614C22⋊Q8C22×D47132yes—
615#121—478no—
616#121—4716no—
617#121—4716no—
618#121—4732no—
619#121—478no—
620#121—478no—
621#121—4732no—
622#121—4716no—
623#121—4716no—
624#121—4732no—
625#121—4732no—
626C4×Q8—4716no—
627C4×Q8—4716no—
628C4×Q8C22×D4718yes—
629C4×D4—4716no—
630C4×D4—4732no—
631C4×D4—478no—
632C4×D4—4716no—
633C4×D4—478no—
634C4×D4—4716no—
635C4×D4C22×D4718yes—
636C4×D4C22×D47116yes—
637#117—4716no—
638#117—4716no—
639#117—4732no—
640#117—4716no—
641#117—4716no—
642C2×C4⋊C4—471no—
643C2×C4⋊C4—472no—
644C2×C4⋊C4—474no—
645C2×C4⋊C4—474no—
646C2×C4⋊C4—472no—
647C2×C4⋊C4—471no—
648C2×C4⋊C4—472no—
649C2×C4⋊C4—472no—
650C2×C4⋊C4—472no—
651C2×C4⋊C4—472no—
652C2×C4⋊C4—474no—
653C2×C4⋊C4—474no—
654C2×C4⋊C4—474no—
655C2×C4⋊C4—4716no—
656C2×C4⋊C4—4716no—
657C2×C4⋊C4C22×D4711yescharacteristic
658C2×C4⋊C4C22×D4712yes—
659C2×C4⋊C4C22×D4711yescharacteristic
660C2×C4⋊C4C22×D4714yes—
661C2×C4⋊C4C22×D4712yes—
662C2×C4⋊C4C22×D4712yes—
663C2×C22⋊C4—474no—
664C2×C22⋊C4—472no—
665C2×C22⋊C4—472no—
666C2×C22⋊C4—472no—
667C2×C22⋊C4—474no—
668C2×C22⋊C4—472no—
669C2×C22⋊C4—474no—
670C2×C22⋊C4—474no—
671C2×C22⋊C4—472no—
672C2×C22⋊C4—472no—
673C2×C22⋊C4—474no—
674C2×C22⋊C4—472no—
675C2×C22⋊C4—472no—
676C2×C22⋊C4C22×D4714yes—
677C2×C22⋊C4C22×D4712yes—
678C2×C42—474no—
679C2×C42—474no—
680C2×C42—471no—
681C2×C42—471no—
682C2×C42—471no—
683C2×C42—478no—
684C2×C42C22×D4712yes—
685C2×C42C22×D4711yescharacteristic
686C24—471no—
687C24—472no—
688C24—472no—
689C24C23×D4712yes—
690#41—18832no—
691#41—18832no—
692C2×Q8—24no—
693C2×Q8—28no—
694C2×Q8—48no—
695C2×Q8—432no—
696C2×Q8—478no—
697C2×Q8—478no—
698C2×Q8—1884no—
699C2×Q8—1884no—
700C2×Q8C23×D4718yes—
701C2×Q8C23×D4714yes—
702C2×Q8C23×D47116yes—
703C2×D4—24no—
704C2×D4—4716no—
705C2×D4—478no—
706C2×D4—478no—
707C2×D4—478no—
708C2×D4—474no—
709C2×D4—474no—
710C2×D4—478no—
711C2×D4—4716no—
712C2×D4—478no—
713C2×D4—944no—
714C2×D4—944no—
715C2×D4—1884no—
716C2×D4—1884no—
717C2×D4—1888no—
718C2×D4—1884no—
719C2×D4—1888no—
720C2×D4—1884no—
721C2×D4—1884no—
722C2×D4C23×D4714yes—
723C22×C4—28no—
724C22×C4—48no—
725C22×C4—471no—
726C22×C4—472no—
727C22×C4—474no—
728C22×C4—471no—
729C22×C4—471no—
730C22×C4—472no—
731C22×C4—474no—
732C22×C4—474no—
733C22×C4—478no—
734C22×C4—478no—
735C22×C4—474no—
736C22×C4—4716no—
737C22×C4—4716no—
738C22×C4—948no—
739C22×C4—944no—
740C22×C4—948no—
741C22×C4—944no—
742C22×C4—1888no—
743C22×C4—1882no—
744C22×C4—1888no—
745C22×C4C23×D4718yes—
746C22×C4C23×D4712yes—
747C22×C4C23×D4711yescharacteristic
748C22×C4C23×D4714yes—
749C22×C4C23×D4712yes—
750C22×C4C23×D4712yes—
751C22×C4C23×D47116yes—
752C22×C4C23×D4711yescharacteristic
753C22×C4C23×D4711yescharacteristic
754C4⋊C4—4716no—
755C4⋊C4—4716no—
756C4⋊C4—478no—
757C4⋊C4—478no—
758C4⋊C4—478no—
759C4⋊C4—4716no—
760C4⋊C4—4716no—
761C4⋊C4—474no—
762C4⋊C4—478no—
763C4⋊C4—478no—
764C4⋊C4—474no—
765C4⋊C4—478no—
766C4⋊C4—4716no—
767C4⋊C4C23×D4714yes—
768C4⋊C4C23×D4718yes—
769C4⋊C4C23×D4714yes—
770C4⋊C4C23×D47116yes—
771C4⋊C4C23×D4718yes—
772C4⋊C4C23×D4718yes—
773C22⋊C4—4716no—
774C22⋊C4—478no—
775C22⋊C4—478no—
776C22⋊C4—478no—
777C22⋊C4—4716no—
778C22⋊C4—478no—
779C22⋊C4—4716no—
780C22⋊C4—4716no—
781C22⋊C4—478no—
782C22⋊C4—478no—
783C22⋊C4—4716no—
784C22⋊C4—478no—
785C22⋊C4—478no—
786C22⋊C4C23×D47116yes—
787C22⋊C4C23×D4718yes—
788C42—474no—
789C42—474no—
790C42—474no—
791C42—4716no—
792C42—4716no—
793C42C23×D4714yes—
794C42C23×D4718yes—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—472no—
799C23—474no—
800C23—474no—
801C23—944no—
802C23—942no—
803C23—944no—
804C23—942no—
805C23—944no—
806C23—944no—
807C23—944no—
808C23—942no—
809C23—944no—
810C23C24×D4714yes—
811C23C24×D4711yescharacteristic
812Q8—28no—
813Q8—216no—
814Q8—416no—
815Q8—1888no—
816Q8—1888no—
817D4—28no—
818D4—948no—
819D4—948no—
820D4—1888no—
821D4—1888no—
822D4—18816no—
823D4—1888no—
824D4—18816no—
825D4—1888no—
826D4—1888no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—28no—
830C2×C4—24no—
831C2×C4—22no—
832C2×C4—216no—
833C2×C4—416no—
834C2×C4—472no—
835C2×C4—474no—
836C2×C4—478no—
837C2×C4—472no—
838C2×C4—472no—
839C2×C4—474no—
840C2×C4—944no—
841C2×C4—942no—
842C2×C4—942no—
843C2×C4—944no—
844C2×C4—942no—
845C2×C4—948no—
846C2×C4—9416no—
847C2×C4—948no—
848C2×C4—948no—
849C2×C4—9416no—
850C2×C4—18816no—
851C2×C4—1884no—
852C2×C4—18816no—
853C2×C4#1309406914yes—
854C2×C4#1309407214yes—
855C2×C4C24×D4714yes—
856C2×C4C24×D4712yes—
857C2×C4C24×D4718yes—
858C2×C4C24×D4714yes—
859C2×C4C24×D4714yes—
860C2×C4C24×D4712yes—
861C2×C4C24×D4712yes—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—48no—
866C22—944no—
867C22—942no—
868C22—944no—
869C22—942no—
870C22—944no—
871C22—944no—
872C22—944no—
873C22—942no—
874C22—944no—
875C22—1884no—
876C22—1888no—
877C22—1888no—
878C22C2×#1309406912yes—
879C22C2×#1309407212yes—
880C22#1568996012yes—
881C22C25×D4711yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—22no—
887C4—944no—
888C4—942no—
889C4—942no—
890C4—944no—
891C4—942no—
892C4—948no—
893C4C2×#1309406914yes—
894C4C2×#1309407214yes—
895C2—44no—
896C2—1882no—
897C2—1884no—
898C2—1884no—
899C2#2025777314yesdirect product factor
900C2C22×#1309406911yescharacteristic
901C2C22×#1309407211yescharacteristic
902C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×D4×Q8×C47C2
socleC23×C47C25
hypercenterC2×D4×Q8D47
hypocenterC47C2×#3547
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20257773C2direct (N × H)
2. C2×#15689869C2semidirect
3. C2×#15689839C2semidirect
4. C2×#15689838C2semidirect
5. C2×#15689833C2semidirect
6. C2×#15689823C2semidirect
7. C2×#15689807C2semidirect
8. C2×#15689784C2semidirect
9. C2×#15689776C2semidirect
10. C2×#15689750C2semidirect
11. C2×#15689743C2semidirect
12. C2×#15689724C2semidirect
13. C2×#15689703C2semidirect
14. C2×#15689697C2semidirect
15. C2×#15689678C2semidirect
16. C2×#15689670C2semidirect
17. C2×#15689660C2semidirect
18. C2×D4×Q8×C47C2semidirect
21. #15689869C22semidirect
22. #15689839C22semidirect
23. #15689838C22semidirect
24. #15689833C22semidirect
25. #15689823C22semidirect
26. #15689807C22semidirect
27. #15689784C22semidirect
28. #15689776C22semidirect
29. #15689750C22semidirect
30. #15689743C22semidirect
31. #15689724C22semidirect
32. #15689703C22semidirect
33. #15689697C22semidirect
34. #15689678C22semidirect
35. #15689670C22semidirect
40. #15689660C22semidirect
93. D4×Q8×C47C22semidirect
451. C2×D4×Q8D47semidirect
463. C2×C47#3547semidirect
479. D4×Q8C2×D47semidirect
552. C47C2×#3547semidirect
899. C2#20257773direct (N × H)

Maximal subgroups

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

subgroupindex
#202577732
C2×#156898692
C2×#156898392
C2×#156898382
C2×#156898332
C2×#156898232
C2×#156898072
C2×#156897842
C2×#156897762
C2×#156897502
C2×#156897432
C2×#156897242
C2×#156897032
C2×#156896972
C2×#156896782
C2×#156896702
C2×#156896602
C2×D4×Q8×C472
C2×#354747