Finite Group Databasebeta

← C2×#13078790 #15621924

Subgroups — C2×#13078790 #15621924

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623155C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13078790C2116yesmaximal, direct product factor
4C2×#10622581C211yesmaximal, characteristic
5C2×#10622490C212yesmaximal, complemented
6C2×#10622411C212yesmaximal, complemented
7C2×#10622663C211yesmaximal, characteristic, complemented
8C2×#10622351C211yesmaximal, characteristic
9C2×#10622402C212yesmaximal, complemented
10C2×#10622502C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#484C211yesmaximal, characteristic, complemented
13C23×Dic22C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#67000C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4326C2212yes—
19C2×#66983C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11—21no—
22C22×C4×Dic11C2211yescharacteristic
23C22×#4314C2212yes—
24#10623155—24no—
25#10623155C2218yes—
26C2×#66951—21no—
27C2×#66946C2211yescharacteristic
28C2×#66945—21no—
29C2×#66943C2211yescharacteristic
30C2×#66940—24no—
31C2×#66940—21no—
32C2×#66940—21no—
33C2×#66940C2212yes—
34C2×#66940C2212yes—
35C2×#66940C2218yescomplemented
36C2×#66939—21no—
37C2×(C22⋊D11)⋊C4—21no—
38C11×#484C2218yescomplemented
39C2×C11×#107C2212yes—
40C2×C11×#103C2212yes—
41C2×C11×C22⋊C8C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622663C2218yescomplemented
47C2×#66874C2212yes—
48#10622581C2218yes—
49C2×#66873C2212yes—
50C2×#66872C2212yes—
51#10622502C22116yescomplemented
52#10622490C22116yescomplemented
53#10622411C22116yescomplemented
54#10622402C22116yescomplemented
55#10622351C2218yes—
56#10622332C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—28no—
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C22×C8×C11C2312yes—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81#67000—22no—
82#67000C2314yes—
83Q8×Dic11—22no—
84Q8×Dic11C2314yes—
85C2×#4326—28no—
86C2×#4326C2318yes—
87#66983—22no—
88#66983C2314yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—28no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—28no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D414yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2314yes—
110C22×C11⋊C8C2312yes—
111C2×#4314—28no—
112C2×#4314C2318yes—
113#66951—28no—
114#66946—22no—
115#66946C2314yes—
116#66945—28no—
117#66943—22no—
118#66943C2314yes—
119#66940—24no—
120#66940—24no—
121#66940—28no—
122#66940—28no—
123#66940C2318yes—
124#66940C2318yes—
125#66939—28no—
126(C22⋊D11)⋊C4—28no—
127C11×#107C2318yes—
128C11×#103C2318yes—
129C11×C22⋊C8C2314yes—
130C22⋊(C11⋊C8)C2314yes—
131#66880C2318yes—
132#66879C2318yes—
133Dic11⋊C8C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66872C2318yes—
137C2×#3117—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—24no—
142C2×Q8×C11C2412yes—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—44no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—44no—
155C22×Dic11—28no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—42no—
161C22×Dic11C2×D414yes—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D414yes—
167C2×D44—21no—
168C2×D44—24no—
169C2×D44C2412yes—
170C2×C4×D11—24no—
171C2×C4×D11—44no—
172C2×Dic22—28no—
173C2×Dic22—216no—
174C2×Dic22—216no—
175C2×Dic22—24no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22#4118yes—
179C2×Dic22C2414yes—
180C2×C8×C11—24no—
181C2×C8×C11C2414yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4C2414yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189#4326—216no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—28no—
200Dic11⋊C4—28no—
201C4×Dic11—24no—
202C4×Dic11—28no—
203C4×Dic11—28no—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2×D412yes—
207C4×Dic11C2×D414yes—
208C4×Dic11C2412yes—
209C4×Dic11C2412yes—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212#4314—216no—
213C2×#529—111no—
214C22×C4×Q8—111no—
215#3117—1116no—
216C2×#484D1111yescharacteristic, complemented
217C2×#481—111no—
218C2×#479—112no—
219C2×#464—112no—
220C2×#451—111no—
221C2×#448—111no—
222C2×#441—112no—
223C2×#440—112no—
224C2×#432—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11#13714yes—
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234Q8×C11—24no—
235Q8×C11—42no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—48no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—44no—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4114yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—48no—
251C2×Dic11—216no—
252C2×Dic11—28no—
253C2×Dic11—28no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11C22×D412yes—
263C2×Dic11C22×D412yes—
264C2×Dic11C22×D412yes—
265C2×Dic11C22×D412yes—
266D44—24no—
267D44—42no—
268C4×D11—48no—
269Dic22—216no—
270Dic22—28no—
271Dic22—24no—
272Dic22C2×#4118yes—
273C8×C11—24no—
274C11⋊C8—24no—
275C23×Q8—111no—
276C22×Q16—112no—
277C22×SD16—112no—
278#529—118no—
279#529—224no—
280C2×#126—221no—
281C2×#125—111no—
282C2×#124—111no—
283C2×#123—221no—
284C2×C22⋊Q8C2×D1111yescharacteristic
285C2×#121—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—112no—
288C2×C4×Q8—118no—
289C2×C4×Q8—112no—
290C2×C4×Q8—221no—
291C2×C4×Q8—221no—
292C2×C4×Q8—224no—
293C2×C4×D4—111no—
294C2×C4×D4—221no—
295C2×#117—221no—
296C22×C4⋊C4—221no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C42—111no—
299C22×C42—221no—
300#484C2×D1118yescomplemented
301#481—118no—
302#479—1116no—
303#464—1116no—
304#451—118no—
305#448—118no—
306#441—1116no—
307#440—1116no—
308#432—118no—
309C2×#107C2×D1112yes—
310C2×#106—112no—
311C2×C4⋊C8—112no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103C2×D1112yes—
315C2×#102—112no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—112no—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11#52512yes—
323C22×C11C2×#13714yes—
324C22×C11C2×#13712yes—
325C22×C11#57512yes—
326C22×C11C23×D411yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11—42no—
335C4×C11#52512yes—
336C4×C11C22×#4112yes—
337Dic11—28no—
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—42no—
343C22×Q8—112no—
344C22×Q8—114no—
345C22×Q8—228no—
346C22×Q8—222no—
347C22×Q8—221no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C2×Q16—118no—
358C2×Q16—228no—
359C2×SD16—118no—
360C2×SD16—228no—
361C22×C8—112no—
362C22×C8C22×D1112yes—
363#126—228no—
364#125—114no—
365#125—222no—
366#124—114no—
367#124—222no—
368#123—228no—
369C22⋊Q8—22no—
370C22⋊Q8C22×D1114yes—
371#121—114no—
372#121—222no—
373C4×Q8—114no—
374C4×Q8—118no—
375C4×Q8—118no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—224no—
379C4×Q8—228no—
380C4×Q8—222no—
381C4×D4—114no—
382C4×D4—222no—
383C4×D4—228no—
384#117—228no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—228no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1112yes—
396C2×C4⋊C4C22×D1114yes—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—114no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—114no—
409C2×C42—221no—
410C2×C42—228no—
411C2×C42—222no—
412C2×C42—222no—
413#107C22×D1118yes—
414#106—118no—
415C4⋊C8—118no—
416#103—118no—
417#103—118no—
418#103C22×D1118yes—
419#102—118no—
420C22⋊C8—114no—
421C22⋊C8C22×D1114yes—
422#97—118no—
423C2×C11—24no—
424C2×C11#311714yescomplemented
425C2×C11C2×#52511yescharacteristic
426C2×C11C22×#13711yescharacteristic
427C2×C11C2×#57511yescharacteristic
428D11—82no—
429C24—221no—
430C24D4×D1111yescharacteristic
431C2×Q8—21no—
432C2×Q8—24no—
433C2×Q8—118no—
434C2×Q8—114no—
435C2×Q8—2216no—
436C2×Q8—228no—
437C2×Q8—2216no—
438C2×Q8—224no—
439C2×Q8—222no—
440C2×Q8—224no—
441C2×Q8C23×D1112yes—
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—221no—
445C2×D4—224no—
446C2×D4—444no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—44no—
453C22×C4—114no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—114no—
459C22×C4—224no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—444no—
466C22×C4—442no—
467C22×C4D4×D1112yes—
468C22×C4D4×D1111yescharacteristic
469C22×C4C23×D1112yes—
470C22×C4C23×D1111yescharacteristic
471Q16—2216no—
472SD16—2216no—
473C2×C8—24no—
474C2×C8—114no—
475C2×C8—224no—
476C2×C8C23×D1114yes—
477C4⋊C4—24no—
478C4⋊C4—22no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—228no—
483C4⋊C4—228no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4C23×D1114yes—
489C4⋊C4C23×D1112yes—
490C22⋊C4—24no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C42—114no—
496C42—112no—
497C42—112no—
498C42—114no—
499C42—112no—
500C42—112no—
501C42—228no—
502C42—228no—
503C42—224no—
504C11C2×#311711yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—222no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23#6697114yes—
512C23C2×D4×D1112yes—
513C23C2×D4×D1111yescharacteristic
514Q8—24no—
515Q8—42no—
516Q8—118no—
517Q8—2216no—
518Q8—228no—
519Q8—224no—
520D4—224no—
521D4—448no—
522D4—442no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—48no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—2216no—
538C2×C4—228no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—228no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—448no—
547C2×C4—444no—
548C2×C4—442no—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4#41×D1114yes—
552C2×C4C24×D1111yescharacteristic
553C8—24no—
554C8—224no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062318712yes—
563C22C2×#6697114yes—
564C22C2×#6697112yes—
565C22#1062330412yes—
566C22C22×D4×D1111yescharacteristic
567C4—22no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—222no—
572C4—222no—
573C4—222no—
574C4—222no—
575C4—228no—
576C4—442no—
577C4#1062318712yes—
578C4C2×#41×D1112yes—
579C2—24no—
580C2—882no—
581C2#1307879014yesdirect product factor
582C2C2×#1062318711yescharacteristic
583C2C22×#6697111yescharacteristic
584C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#484D11
hypocenterC11C2×#3117
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13078790C2direct (N × H)
5. C2×#10622490C2semidirect
6. C2×#10622411C2semidirect
7. C2×#10622663C2semidirect
9. C2×#10622402C2semidirect
10. C2×#10622502C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#484C2semidirect
35. C2×#66940C22semidirect
38. C11×#484C22semidirect
46. #10622663C22semidirect
51. #10622502C22semidirect
52. #10622490C22semidirect
53. #10622411C22semidirect
54. #10622402C22semidirect
56. #10622332C22semidirect
216. C2×#484D11semidirect
300. #484C2×D11semidirect
424. C2×C11#3117semidirect
504. C11C2×#3117semidirect
581. C2#13078790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231552
C22×#669402
#130787902
C2×#106225812
C2×#106224902
C2×#106224112
C2×#106226632
C2×#106223512
C2×#106224022
C2×#106225022
C2×#106223322
C2×C11×#4842
C2×#311711