Finite Group Databasebeta

← C2×#20257844 #27124049

Subgroups — C2×#20257844 #27124049

Order 12032.

6566 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257844C2132yesmaximal, direct product factor
2C2×C47⋊#564C211yesmaximal, characteristic, complemented
3C2×#15689877C212yesmaximal, complemented
4C2×#15689871C211yesmaximal, characteristic, complemented
5C2×#15689828C214yesmaximal, complemented
6C2×#15689821C214yesmaximal, complemented
7C2×#15689805C214yesmaximal, complemented
8C2×#15689732C214yesmaximal, complemented
9C2×#15689721C214yesmaximal, complemented
10C2×#15689720C214yesmaximal, complemented
11C2×#15689657C212yesmaximal, complemented
12C22×#125×C47C211yesmaximal, characteristic, complemented
13C47⋊#564C22116yescomplemented
14#15689877C22132yescomplemented
15#15689871C22116yescomplemented
16#15689828C22164yescomplemented
17#15689821C22164yescomplemented
18#15689805C22164yescomplemented
19#15689732C22164yescomplemented
20#15689721C22164yescomplemented
21#15689720C22164yescomplemented
22C2×#13094023C2214yes—
23#15689657C22132yescomplemented
24C2×#13094019C2214yes—
25C2×#13094019C2214yes—
26C2×#13094019C2214yes—
27C2×#13094019C2214yes—
28C2×#13094018C2214yes—
29C2×#13094016C2212yes—
30C2×#13094015C2214yes—
31C2×#13094014C2214yes—
32C2×#13094014C2214yes—
33C2×#13094014C2214yes—
34C2×#13094014C2214yes—
35C2×#13094012C2212yes—
36C2×#13094009C2214yes—
37C2×#13094009C2214yes—
38C2×#13094009C2214yes—
39C2×#13094009C2214yes—
40C2×#13094007C2214yes—
41C2×#13094004C2214yes—
42C2×#13094003C2212yes—
43C2×#13094003C2214yes—
44C2×#13094002C2214yes—
45C2×#13094002C2214yes—
46C2×#13094002C2214yes—
47C2×#13094002C2214yes—
48C2×#13093999C2214yes—
49C2×#13093998C2212yes—
50C2×#13093998C2214yes—
51C2×C4×Dic94C2212yes—
52C2×#13093989C2214yes—
53C2×C4×D188C2212yes—
54C2×#13093986C2214yes—
55C2×C4×C22⋊D47C2214yes—
56C2×C4×C22⋊D47C2214yes—
57C2×C4×C22⋊D47C2214yes—
58C2×#13093982C2214yes—
59C2×#13093981C2214yes—
60C2×C4⋊C4×D47C2214yes—
61C2×#125×C47C2212yes—
62C2×#125×C47C2214yes—
63C2×#125×C47C2211yescharacteristic
64C2×#125×C47C2211yescharacteristic
65C2×#125×C47C22116yescomplemented
66C22×C4⋊C4×C47C2214yes—
67C22×C4⋊C4×C47C2212yes—
68C22×C42×C47C2211yescharacteristic
69C22×Dic94C2314yes—
70C22×Dic94C2312yes—
71C22×D188C2314yes—
72C22×D188C2312yes—
73C22×C22⋊D47C2314yes—
74C22×C4×D47C2314yes—
75C22×C4×D47C2314yes—
76C22×C4×D47C2314yes—
77#13094023C23132yes—
78#13094019C23132yes—
79#13094019C23132yes—
80#13094019C23132yes—
81#13094019C23132yes—
82#13094018C23132yes—
83#13094016C23116yes—
84#13094015C23132yes—
85#13094014C23132yes—
86#13094014C23132yes—
87#13094014C23132yes—
88#13094014C23132yes—
89#13094012C23116yes—
90#13094009C23132yes—
91#13094009C23132yes—
92#13094009C23132yes—
93#13094009C23132yes—
94#13094007C23132yes—
95#13094004C23132yes—
96#13094003C23116yes—
97#13094003C23132yes—
98#13094002C23132yes—
99#13094002C23132yes—
100#13094002C23132yes—
101#13094002C23132yes—
102#13093999C23132yes—
103#13093998C23116yes—
104#13093998C23132yes—
105C4×Dic94C23116yes—
106#13093989C23132yes—
107C4×D188C23116yes—
108#13093986C23132yes—
109C4×C22⋊D47C23132yes—
110C4×C22⋊D47C23132yes—
111C4×C22⋊D47C23132yes—
112#13093982C23132yes—
113#13093981C23132yes—
114C2×C4⋊Dic47C2314yes—
115C2×C4⋊Dic47C2314yes—
116C2×C4⋊Dic47C2312yes—
117C2×C4⋊Dic47C2312yes—
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2314yes—
121C2×Dic47⋊C4C2314yes—
122C2×Dic47⋊C4C2314yes—
123C2×Dic47⋊C4C2314yes—
124C2×Dic47⋊C4C2314yes—
125C2×Dic47⋊C4C2314yes—
126C4⋊C4×D47C23132yes—
127C2×C22⋊Dic47C2314yes—
128C2×(C2×D47)⋊C4C2314yes—
129C2×(C2×D47)⋊C4C2314yes—
130C2×(C2×D47)⋊C4C2314yes—
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×C4×Dic47C2314yes—
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2314yes—
139C23×C4×C47C2311yescharacteristic
140C23×C4×C47C2312yes—
141C23×C4×C47C2314yes—
142#125×C47C23132yes—
143#125×C47C23116yes—
144#125×C47C2318yes—
145#125×C47C2318yes—
146C2×C4⋊C4×C47C2314yes—
147C2×C4⋊C4×C47C2314yes—
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2312yes—
150C2×C4⋊C4×C47C2314yes—
151C2×C4⋊C4×C47C2314yes—
152C2×C4⋊C4×C47C2312yes—
153C2×C4⋊C4×C47C23132yes—
154C2×C4⋊C4×C47C23116yes—
155C2×C42×C47C2311yescharacteristic
156C2×C42×C47C2312yes—
157C2×C42×C47C2311yescharacteristic
158C2×C42×C47C2318yes—
159C24×C47C2411yescharacteristic
160C23×D47C2414yes—
161C22×C4×C47—24no—
162C22×C4×C47—48no—
163C22×C4×C47—44no—
164C22×C4×C47C2412yes—
165C22×C4×C47C2411yescharacteristic
166C22×C4×C47C2411yescharacteristic
167C22×C4×C47C2412yes—
168C22×C4×C47C2414yes—
169C22×C4×C47C2414yes—
170C22×C4×C47C2414yes—
171C22×C4×C47C2418yes—
172C22×C4×C47C24116yes—
173C2×C22⋊D47—216no—
174C2×C22⋊D47C24116yes—
175C22×Dic47C2414yes—
176C22×Dic47C2414yes—
177C22×Dic47C2414yes—
178C2×D188—44no—
179C2×D188—48no—
180C2×D188C24116yes—
181C2×D188C2418yes—
182C2×C4×D47—48no—
183C2×C4×D47—48no—
184C2×C4×D47—48no—
185C2×C4×D47C24116yes—
186C2×C4×D47C24116yes—
187C2×C4×D47C24116yes—
188C2×Dic94—44no—
189C2×Dic94—48no—
190C2×Dic94C24116yes—
191C2×Dic94C2418yes—
192C4⋊C4×C47C24116yes—
193C4⋊C4×C47C24116yes—
194C4⋊C4×C47C24116yes—
195C4⋊C4×C47C2418yes—
196C4⋊C4×C47C24116yes—
197C4⋊C4×C47C24116yes—
198C4⋊C4×C47C2418yes—
199C42×C47C2414yes—
200C42×C47C2418yes—
201C42×C47C2414yes—
202C22⋊Dic47C24116yes—
203(C2×D47)⋊C4C24116yes—
204(C2×D47)⋊C4C24116yes—
205(C2×D47)⋊C4C24116yes—
206(C2×D47)⋊C4C24116yes—
207(C2×D47)⋊C4C24116yes—
208(C2×D47)⋊C4C24116yes—
209(C2×D47)⋊C4C24116yes—
210(C2×D47)⋊C4C24116yes—
211C4⋊Dic47C24116yes—
212C4⋊Dic47C24116yes—
213C4⋊Dic47C2418yes—
214C4⋊Dic47C2418yes—
215Dic47⋊C4C24116yes—
216Dic47⋊C4C24116yes—
217Dic47⋊C4C24116yes—
218Dic47⋊C4C24116yes—
219Dic47⋊C4C24116yes—
220Dic47⋊C4C24116yes—
221Dic47⋊C4C24116yes—
222Dic47⋊C4C24116yes—
223C4×Dic47C24116yes—
224C4×Dic47C24116yes—
225C4×Dic47C24116yes—
226C23×C47—24no—
227C23×C472−1+414yes—
228C23×C47C2512yes—
229C23×C47C2511yescharacteristic
230C22×D47—28no—
231C22×D47—28no—
232C22×D47—28no—
233C22×D47C2518yes—
234C2×C4×C47—28no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—28no—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—28no—
241C2×C4×C47—416no—
242C2×C4×C47—48no—
243C2×C4×C47C2514yes—
244C2×C4×C47C2518yes—
245C2×C4×C47C2518yes—
246C2×C4×C47C2512yes—
247C2×C4×C47C2512yes—
248C2×C4×C47C2514yes—
249C22⋊D47—232no—
250C2×Dic47—28no—
251C2×Dic47—28no—
252C2×Dic47—28no—
253C2×Dic47C2518yes—
254C2×Dic47C2518yes—
255C2×Dic47C2518yes—
256D188—48no—
257D188—416no—
258C4×D47—416no—
259C4×D47—416no—
260C4×D47—416no—
261Dic94—48no—
262Dic94—416no—
263C2×#3553—471nomaximal, Sylow
264C22×C47—24no—
265C22×C47—28no—
266C22×C47C2×2−1+414yes—
267C22×C47C2×2−1+412yes—
268C22×C47#58514yes—
269C22×C47C2611yescharacteristic
270C2×D47—28no—
271C2×D47—28no—
272C2×D47—28no—
273C2×D47—416no—
274C4×C47—22no—
275C4×C47—22no—
276C4×C47—28no—
277C4×C47—24no—
278C4×C47—24no—
279C4×C47—28no—
280Dic47—28no—
281Dic47—28no—
282Dic47—28no—
283#3553—4732no—
284C2×#564—471no—
285C2×#563—472no—
286C2×#562—471no—
287C2×#554—474no—
288C2×#553—474no—
289C2×#552—474no—
290C2×#541—474no—
291C2×#539—474no—
292C2×#539—474no—
293C2×#529—472no—
294C22×#125D4711yescharacteristic, complemented
295C2×C47—24no—
296C2×C47#355314yescomplemented
297C2×C47C22×2−1+411yescharacteristic
298C2×C47C2×#58512yes—
299D47—48no—
300#564—4716no—
301#563—4732no—
302#562—4716no—
303#554—4764no—
304#553—4764no—
305#552—4764no—
306#541—4764no—
307#539—4764no—
308#539—4764no—
309C2×C4⋊Q8—474no—
310#529—4732no—
311C2×#126—474no—
312C2×#126—474no—
313C2×#126—474no—
314C2×#126—474no—
315C2×#126—474no—
316C2×#125—474no—
317C2×#125—474no—
318C2×#125—474no—
319C2×#125—474no—
320C2×#125—474no—
321C2×#125—472no—
322C2×#125C2×D4714yes—
323C2×#125C2×D4712yes—
324C2×#125C2×D4711yescharacteristic
325C2×#125C2×D4711yescharacteristic
326C2×#125C2×D47116yescomplemented
327C2×#124—472no—
328C2×#123—474no—
329C2×#123—474no—
330C2×#123—474no—
331C2×#123—474no—
332C2×#123—474no—
333C2×C22⋊Q8—472no—
334C2×C22⋊Q8—474no—
335C2×C22⋊Q8—474no—
336C2×C22⋊Q8—474no—
337C2×C22⋊Q8—474no—
338C2×C22⋊Q8—474no—
339C2×C22⋊Q8—474no—
340C2×#121—472no—
341C2×#121—474no—
342C2×#121—474no—
343C2×C4×Q8—474no—
344C2×C4×Q8—472no—
345C2×C4×D4—474no—
346C2×C4×D4—474no—
347C2×C4×D4—474no—
348C2×C4×D4—474no—
349C2×C4×D4—472no—
350C2×#117—474no—
351C2×#117—474no—
352C22×C4⋊C4—474no—
353C22×C4⋊C4C2×D4712yes—
354C22×C4⋊C4C2×D4714yes—
355C22×C42C2×D4711yescharacteristic
356C47C2×#355311yescharacteristic, complemented, Sylow
357C22×Q8—474no—
358C22×Q8—472no—
359C22×D4—474no—
360C22×D4—474no—
361C22×D4—472no—
362C23×C4—474no—
363C23×C4—474no—
364C23×C4—474no—
365C23×C4C22×D4711yescharacteristic
366C23×C4C22×D4714yes—
367C23×C4C22×D4712yes—
368C4⋊Q8—4732no—
369#126—4732no—
370#126—4732no—
371#126—4732no—
372#126—4732no—
373#126—4732no—
374#125—4732no—
375#125—4732no—
376#125—4732no—
377#125—4732no—
378#125—4732no—
379#125—4716no—
380#125C22×D47132yes—
381#125C22×D47116yes—
382#125C22×D4718yes—
383#125C22×D4718yes—
384#124—4716no—
385#123—4732no—
386#123—4732no—
387#123—4732no—
388#123—4732no—
389#123—4732no—
390C22⋊Q8—4716no—
391C22⋊Q8—4732no—
392C22⋊Q8—4732no—
393C22⋊Q8—4732no—
394C22⋊Q8—4732no—
395C22⋊Q8—4732no—
396C22⋊Q8—4732no—
397#121—4716no—
398#121—4732no—
399#121—4732no—
400C4×Q8—4732no—
401C4×Q8—4716no—
402C4×D4—4732no—
403C4×D4—4732no—
404C4×D4—4732no—
405C4×D4—4732no—
406C4×D4—4716no—
407#117—4732no—
408#117—4732no—
409C2×C4⋊C4—474no—
410C2×C4⋊C4—474no—
411C2×C4⋊C4—474no—
412C2×C4⋊C4—474no—
413C2×C4⋊C4—474no—
414C2×C4⋊C4—472no—
415C2×C4⋊C4—474no—
416C2×C4⋊C4—474no—
417C2×C4⋊C4—474no—
418C2×C4⋊C4—472no—
419C2×C4⋊C4—474no—
420C2×C4⋊C4—474no—
421C2×C4⋊C4—4732no—
422C2×C4⋊C4C22×D4714yes—
423C2×C4⋊C4C22×D4714yes—
424C2×C4⋊C4C22×D4714yes—
425C2×C4⋊C4C22×D4712yes—
426C2×C4⋊C4C22×D4714yes—
427C2×C4⋊C4C22×D4714yes—
428C2×C4⋊C4C22×D4712yes—
429C2×C4⋊C4C22×D47116yes—
430C2×C4⋊C4C22×D47132yes—
431C2×C22⋊C4—474no—
432C2×C22⋊C4—474no—
433C2×C22⋊C4—474no—
434C2×C22⋊C4—474no—
435C2×C22⋊C4—474no—
436C2×C22⋊C4—474no—
437C2×C22⋊C4—474no—
438C2×C22⋊C4—474no—
439C2×C22⋊C4—474no—
440C2×C42—474no—
441C2×C42—474no—
442C2×C42—474no—
443C2×C42C22×D4711yescharacteristic
444C2×C42C22×D4712yes—
445C2×C42C22×D4711yescharacteristic
446C2×C42C22×D4718yes—
447C24—474no—
448C24C23×D4711yescharacteristic
449C2×Q8—4716no—
450C2×Q8—478no—
451C2×Q8—1888no—
452C2×Q8—1884no—
453C2×D4—4716no—
454C2×D4—4716no—
455C2×D4—478no—
456C2×D4—9416no—
457C2×D4—1888no—
458C2×D4—1884no—
459C22×C4—24no—
460C22×C4—44no—
461C22×C4—48no—
462C22×C4—474no—
463C22×C4—474no—
464C22×C4—474no—
465C22×C4—4716no—
466C22×C4—4716no—
467C22×C4—4716no—
468C22×C4—1888no—
469C22×C4—1888no—
470C22×C4—1888no—
471C22×C4C23×D4714yes—
472C22×C4C23×D4712yes—
473C22×C4C23×D4714yes—
474C22×C4C23×D4714yes—
475C22×C4C23×D4711yescharacteristic
476C22×C4C23×D4711yescharacteristic
477C22×C4C23×D4712yes—
478C22×C4C23×D4718yes—
479C22×C4C23×D47116yes—
480C4⋊C4—4716no—
481C4⋊C4—4716no—
482C4⋊C4—4716no—
483C4⋊C4—4716no—
484C4⋊C4—4716no—
485C4⋊C4—4716no—
486C4⋊C4—4716no—
487C4⋊C4—4716no—
488C4⋊C4—4716no—
489C4⋊C4—4716no—
490C4⋊C4—478no—
491C4⋊C4—478no—
492C4⋊C4C23×D47116yes—
493C4⋊C4C23×D47116yes—
494C4⋊C4C23×D47116yes—
495C4⋊C4C23×D4718yes—
496C4⋊C4C23×D47116yes—
497C4⋊C4C23×D47116yes—
498C4⋊C4C23×D4718yes—
499C22⋊C4—4716no—
500C22⋊C4—4716no—
501C22⋊C4—4716no—
502C22⋊C4—4716no—
503C22⋊C4—4716no—
504C22⋊C4—4716no—
505C22⋊C4—4716no—
506C22⋊C4—4716no—
507C22⋊C4—4716no—
508C42—4716no—
509C42—4716no—
510C42—4716no—
511C42C23×D4714yes—
512C42C23×D4718yes—
513C42C23×D4714yes—
514C23—24no—
515C23—478no—
516C23—948no—
517C23—948no—
518C23—948no—
519C23#1309407214yes—
520C23C24×D4712yes—
521C23C24×D4711yescharacteristic
522Q8—18816no—
523Q8—1888no—
524D4—9432no—
525D4—18816no—
526D4—1888no—
527C2×C4—28no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—28no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—416no—
536C2×C4—478no—
537C2×C4—478no—
538C2×C4—478no—
539C2×C4—948no—
540C2×C4—948no—
541C2×C4—948no—
542C2×C4—18816no—
543C2×C4—18816no—
544C2×C4—18816no—
545C2×C4C24×D4714yes—
546C2×C4C24×D4718yes—
547C2×C4C24×D4718yes—
548C2×C4C24×D4712yes—
549C2×C4C24×D4712yes—
550C2×C4C24×D4714yes—
551C22—28no—
552C22—24no—
553C22—948no—
554C22—948no—
555C22—948no—
556C22—18816no—
557C22C2×#1309407214yes—
558C22C2×#1309407212yes—
559C22#1568995914yes—
560C22C25×D4711yescharacteristic
561C4—22no—
562C4—22no—
563C4—24no—
564C4—28no—
565C4—28no—
566C4—24no—
567C4—948no—
568C4—948no—
569C4—948no—
570C2—24no—
571C2—1888no—
572C2#2025784414yesdirect product factor
573C2C22×#1309407211yescharacteristic
574C2C2×#1568995912yes—
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×#125×C47C2
socleC23×C47C25
hypercenterC22×#125D47
hypocenterC47C2×#3553
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #20257844C2direct (N × H)
2. C2×C47⋊#564C2semidirect
3. C2×#15689877C2semidirect
4. C2×#15689871C2semidirect
5. C2×#15689828C2semidirect
6. C2×#15689821C2semidirect
7. C2×#15689805C2semidirect
8. C2×#15689732C2semidirect
9. C2×#15689721C2semidirect
10. C2×#15689720C2semidirect
11. C2×#15689657C2semidirect
12. C22×#125×C47C2semidirect
13. C47⋊#564C22semidirect
14. #15689877C22semidirect
15. #15689871C22semidirect
16. #15689828C22semidirect
17. #15689821C22semidirect
18. #15689805C22semidirect
19. #15689732C22semidirect
20. #15689721C22semidirect
21. #15689720C22semidirect
23. #15689657C22semidirect
65. C2×#125×C47C22semidirect
294. C22×#125D47semidirect
296. C2×C47#3553semidirect
326. C2×#125C2×D47semidirect
356. C47C2×#3553semidirect
572. C2#20257844direct (N × H)

Maximal subgroups

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

subgroupindex
#202578442
C2×C47⋊#5642
C2×#156898772
C2×#156898712
C2×#156898282
C2×#156898212
C2×#156898052
C2×#156897322
C2×#156897212
C2×#156897202
C2×#156896572
C22×#125×C472
C2×#355347