Finite Group Databasebeta

← C2×#13080532 #15630211

Subgroups — C2×#13080532 #15630211

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic
3#13080532C2116yesmaximal, direct product factor
4C2×#10622428C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622426C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622423C212yesmaximal, complemented
9C2×C4×#4314C211yesmaximal, characteristic, complemented
10C2×C8×D44C211yesmaximal, characteristic, complemented
11C2×#10622417C212yesmaximal, complemented
12C2×C11×#487C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#67000—21no—
17C2×#66999C2212yes—
18C2×Q8×Dic11—21no—
19C22×#4326C2212yes—
20C22×#4314C2211yescharacteristic
21C22×C8×D11C2212yes—
22#10623263—24no—
23#10623263C2218yescomplemented
24#10623257—24no—
25#10623257C2218yes—
26C2×#66951—22no—
27C2×#66950C2212yes—
28C2×#66948—21no—
29C2×#66947—22no—
30C2×#66945C2212yes—
31C2×C4⋊C4×D11—21no—
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#487C2218yescomplemented
36C2×C11×#103C2212yes—
37C2×C11×#103C2212yes—
38C2×C4×C8×C11C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66885C2211yescharacteristic
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66881C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622703C2218yescomplemented
45#10622700C2218yescomplemented
46C2×#66873C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622428C22116yescomplemented
50#10622426C22116yescomplemented
51#10622423C22116yescomplemented
52#10622417C22116yescomplemented
53C4×#4314C2218yescomplemented
54C8×D44C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2312yes—
57C2×#4343—24no—
58C2×#4343—28no—
59C2×#4343—44no—
60C2×#4343C2318yes—
61C22×D44—22no—
62C22×D44D411yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—22no—
66C22×C4×D11C2312yes—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×C4⋊Q8C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×C42×C11C2311yescharacteristic
79#67000—28no—
80#66999—24no—
81#66999C2318yes—
82Q8×Dic11—28no—
83C2×#4326—44no—
84C2×#4326C2318yes—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D412yes—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C22×C11⋊C8C2312yes—
99C2×#4314—24no—
100C2×#4314C2314yes—
101C2×C8×D11—44no—
102C2×C8×D11C2318yes—
103#66951—216no—
104#66950—24no—
105#66950C2318yes—
106#66948—28no—
107#66947—216no—
108#66945—24no—
109#66945C2318yes—
110C4⋊C4×D11—28no—
111C4×D44—22no—
112C4×D44D414yes—
113C4×D44C2314yes—
114C4×D44C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117C11×#103C2318yes—
118C11×#103C2318yes—
119C4×C8×C11C2314yes—
120#66899C2318yes—
121#66885C2314yes—
122(C2×D11)⋊C8C2318yes—
123#66881C2314yes—
124#66880C2314yes—
125#66873C2318yes—
126#66871C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3302—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11C2×D412yes—
131C2×Q8×C11—24no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11—24no—
135C2×Q8×C11—44no—
136C2×Q8×C11C2414yes—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D412yes—
146#4343—216no—
147#4343—48no—
148#4343—416no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—22no—
153C2×D44—48no—
154C2×D44C2×D414yes—
155C2×D44#4114yes—
156C2×D44C2412yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—48no—
162C2×C4×D11—44no—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2414yes—
165C2×Dic22—21no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22C2412yes—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11C2412yes—
172C2×C8×C11C2412yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4C2414yes—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180#4326—48no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4C2×D418yes—
186C4⋊Dic11—28no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2×D414yes—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2412yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—24no—
194C4×Dic11—28no—
195C4×Dic11—24no—
196C2×C11⋊C8—24no—
197C2×C11⋊C8C2414yes—
198#4314—28no—
199C8×D11—48no—
200C2×#556—111no—
201C2×#547—111no—
202#3302—1116no—
203C2×#487D1111yescharacteristic, complemented
204C2×#485—112no—
205C2×#474—111no—
206C2×#467—112no—
207C2×#462—111no—
208C2×#452—112no—
209C2×C4×SD16—111no—
210C2×C8×D4—111no—
211C2×#416—112no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11C22×D414yes—
221Q8×C11—24no—
222Q8×C11—24no—
223Q8×C11—44no—
224Q8×C11—48no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—44no—
229C2×C4×C11—44no—
230C2×C4×C11#13514yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C2×C4×C11C2511yescharacteristic
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11C22×D414yes—
245D44—24no—
246D44—28no—
247D44—22no—
248D44—416no—
249D44C2×#4114yes—
250C4×D11—28no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—416no—
254C4×D11—48no—
255Dic22—22no—
256Dic22—22no—
257Dic22—42no—
258C8×C11—22no—
259C8×C11—22no—
260C11⋊C8—24no—
261C22×#41—112no—
262C22×Q16—112no—
263C22×SD16—111no—
264C23×C8—112no—
265#556—118no—
266#556—224no—
267#547—118no—
268#547—224no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×#126—222no—
272C2×#124—221no—
273C2×#123—222no—
274C2×C22⋊Q8—112no—
275C2×C22⋊Q8—112no—
276C2×#121—221no—
277C2×C4×Q8—111no—
278C2×C4×Q8—221no—
279C2×C4×D4—111no—
280C2×C4×D4—111no—
281C2×#117—112no—
282C22×C4⋊C4—221no—
283#487C2×D1118yescomplemented
284#485—1116no—
285#474—118no—
286#467—1116no—
287#462—118no—
288#452—1116no—
289C4×SD16—118no—
290C8×D4—118no—
291C2×#107—112no—
292C2×#106—111no—
293C2×C4⋊C8—111no—
294#416—1116no—
295C2×#103—112no—
296C2×#103—111no—
297C2×#103C2×D1112yes—
298C2×#103C2×D1112yes—
299C2×#102—111no—
300C2×#102—112no—
301C2×C22⋊C8—112no—
302C2×C4×C8C2×D1111yescharacteristic
303C22×C11#54612yes—
304C22×C11C2×#13512yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—48no—
312C2×D11—48no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11—44no—
318C4×C11#54612yes—
319C4×C11C2×#13514yes—
320C4×C11C22×#4111yescharacteristic
321C4×C11C2×H(5,𝔽2)11yescharacteristic
322Dic11—24no—
323Dic11—42no—
324Dic11—42no—
325Dic11—42no—
326C2×#41—118no—
327C2×#41—224no—
328C2×#41—228no—
329C2×#41—444no—
330C22×Q8—21no—
331C22×Q8—111no—
332C22×Q8C22×D1112yes—
333C22×D4—111no—
334C22×D4—111no—
335C22×D4—222no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4—221no—
339C2×Q16—118no—
340C2×Q16—444no—
341C2×SD16—114no—
342C2×SD16—224no—
343C22×C8—112no—
344C22×C8—118no—
345C22×C8—444no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8C22×D1114yes—
351C4⋊Q8C22×D1114yes—
352#126—2216no—
353#124—228no—
354#123—2216no—
355C22⋊Q8—118no—
356C22⋊Q8—118no—
357C22⋊Q8—224no—
358C22⋊Q8—224no—
359#121—228no—
360C4×Q8—114no—
361C4×Q8—228no—
362C4×Q8—222no—
363C4×D4—114no—
364C4×D4—114no—
365C4×D4—114no—
366C4×D4—222no—
367#117—118no—
368#117—224no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1112yes—
380C2×C22⋊C4—112no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—221no—
385C2×C42—222no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#107—118no—
389#106—114no—
390C4⋊C8—114no—
391#103—118no—
392#103—114no—
393#103C22×D1118yes—
394#103C22×D1118yes—
395#102—114no—
396#102—118no—
397C22⋊C8—118no—
398C4×C8C22×D1114yes—
399C2×C11#330214yescomplemented
400C2×C11C2×#54611yescharacteristic
401C2×C11C22×#13511yescharacteristic
402C2×C11C2×#57811yescharacteristic
403D11—44no—
404D11—44no—
405C24—112no—
406C24—221no—
407#41—2216no—
408#41—448no—
409#41—4416no—
410C2×Q8—24no—
411C2×Q8—22no—
412C2×Q8—24no—
413C2×Q8—24no—
414C2×Q8—44no—
415C2×Q8—112no—
416C2×Q8—221no—
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8C23×D1114yes—
420C2×D4—114no—
421C2×D4—114no—
422C2×D4—112no—
423C2×D4—228no—
424C2×D4—224no—
425C2×D4—221no—
426C2×D4—222no—
427C2×D4—448no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—224no—
440C22×C4—448no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445Q16—448no—
446SD16—228no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—114no—
450C2×C8—224no—
451C2×C8—448no—
452C2×C8C23×D1112yes—
453C2×C8C23×D1112yes—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—114no—
459C4⋊C4—112no—
460C4⋊C4—112no—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—224no—
466C4⋊C4C23×D1114yes—
467C22⋊C4—118no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C42—228no—
473C42—224no—
474C42D4×D1112yes—
475C42C23×D1112yes—
476C11C2×#330211yescharacteristic, complemented, Sylow
477C23—114no—
478C23—224no—
479C23—224no—
480C23—222no—
481C23—224no—
482C23—224no—
483C23—442no—
484C23—442no—
485C23C2×D4×D1111yescharacteristic
486Q8—24no—
487Q8—24no—
488Q8—48no—
489Q8—44no—
490Q8—222no—
491Q8—222no—
492Q8—442no—
493D4—114no—
494D4—228no—
495D4—222no—
496D4—224no—
497D4—4416no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—114no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—228no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—4416no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—448no—
516C2×C4#6696914yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#41×D1112yes—
521C2×C4#6704212yes—
522C2×C4C24×D1111yescharacteristic
523C8—22no—
524C8—22no—
525C8—224no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—224no—
530C22—442no—
531C22—448no—
532C22—448no—
533C22—442no—
534C22#1062320712yes—
535C22C2×#6696912yes—
536C22#1062329712yes—
537C22C22×D4×D1111yescharacteristic
538C4—22no—
539C4—44no—
540C4—44no—
541C4—224no—
542C4—442no—
543C4—442no—
544C4—442no—
545C4#1062320712yes—
546C4C2×#6696914yes—
547C4C2×#41×D1111yescharacteristic
548C4C2×#6704211yescharacteristic
549C2—444no—
550C2—444no—
551C2#1308053214yesdirect product factor
552C2C2×#1062320711yescharacteristic
553C2C22×#6696911yescharacteristic
554C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#487D11
hypocenterC11C2×#3302
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
3. #13080532C2direct (N × H)
4. C2×#10622428C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622426C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622423C2semidirect
9. C2×C4×#4314C2semidirect
10. C2×C8×D44C2semidirect
11. C2×#10622417C2semidirect
12. C2×C11×#487C2semidirect
23. #10623263C22semidirect
35. C11×#487C22semidirect
44. #10622703C22semidirect
45. #10622700C22semidirect
49. #10622428C22semidirect
50. #10622426C22semidirect
51. #10622423C22semidirect
52. #10622417C22semidirect
53. C4×#4314C22semidirect
54. C8×D44C22semidirect
203. C2×#487D11semidirect
283. #487C2×D11semidirect
399. C2×C11#3302semidirect
476. C11C2×#3302semidirect
551. C2#13080532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106232572
#130805322
C2×#106224282
C2×#106227002
C2×#106224262
C2×#106227032
C2×#106224232
C2×C4×#43142
C2×C8×D442
C2×#106224172
C2×C11×#4872
C2×#330211