Finite Group Databasebeta

← C2×#13080972 #15632195

Subgroups — C2×#13080972 #15632195

Order 2816.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic
3#13080972C2116yesmaximal, direct product factor
4C2×#10622476C212yesmaximal, complemented
5C2×#10622475C212yesmaximal, complemented
6C2×#10622707C211yesmaximal, characteristic, complemented
7C2×#10622697C211yesmaximal, characteristic, complemented
8C2×#10622477C212yesmaximal, complemented
9C2×C4×#4314C211yesmaximal, characteristic, complemented
10C2×C8×D44C211yesmaximal, characteristic, complemented
11C2×D11×#106C212yesmaximal, complemented
12C2×C11×#498C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#66999—22no—
17C2×#66999—21no—
18C22×#4314C2211yescharacteristic
19C22×C8×D11C2212yes—
20#10623261—24no—
21#10623261C2218yescomplemented
22#10623257—24no—
23#10623257C2218yes—
24C2×#66950C2212yes—
25C2×#66948C2212yes—
26C2×#66947—22no—
27C2×#66946—21no—
28C2×C4⋊C4×D11C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66943—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#498C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×#106C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66881C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622707C2218yescomplemented
43#10622697C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66873C2212yes—
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622477C22116yescomplemented
50#10622476C22116yescomplemented
51#10622475C22116yescomplemented
52D11×#106C22116yescomplemented
53C4×#4314C2218yescomplemented
54C8×D44C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C2×#4343—28no—
58C2×#4343—48no—
59C22×D44—22no—
60C22×D44D411yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—21no—
64C22×C4×D11—22no—
65C22×C4×D11C2312yes—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C11×C4⋊Q8C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C42×C11C2311yescharacteristic
78#66999—216no—
79#66999—28no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4D412yes—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2312yes—
93C2×#4314—24no—
94C2×#4314C2314yes—
95C2×C8×D11—28no—
96C2×C8×D11C2318yes—
97#66950—24no—
98#66950C2318yes—
99#66948—24no—
100#66948C2318yes—
101#66947—216no—
102#66946—28no—
103C4⋊C4×D11—24no—
104C4⋊C4×D11—24no—
105C4⋊C4×D11C2318yes—
106C4⋊C4×D11C2318yes—
107#66943—28no—
108C4×D44—22no—
109C4×D44D414yes—
110C4×D44C2314yes—
111C4×D44C2314yes—
112C4×Dic22—22no—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×#106C2318yes—
116C4×C8×C11C2314yes—
117#66885C2314yes—
118(C2×D11)⋊C8C2318yes—
119#66881C2314yes—
120#66880C2314yes—
121#66874C2318yes—
122#66873C2318yes—
123#66872C2318yes—
124#66872C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3335—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11C2×D412yes—
129C2×Q8×C11—24no—
130C2×Q8×C11—24no—
131C2×Q8×C11—44no—
132C2×Q8×C11—82no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142#4343—432no—
143C2×D44—28no—
144C2×D44—21no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—48no—
148C2×D44SD1618yescomplemented
149C2×D44C2×D414yes—
150C2×D44C2412yes—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—48no—
157C2×C4×D11—44no—
158C2×C4×D11—84no—
159C2×C4×D11C2×D414yes—
160C2×C4×D11C2414yes—
161C2×Dic22—21no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22C2412yes—
165C2×C8×C11—22no—
166C2×C8×C11#4114yescomplemented
167C2×C8×C11C2412yes—
168C2×C8×C11C2412yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4C2414yes—
174C11×C4⋊C4C2414yes—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4C2×D418yes—
181C4⋊Dic11—28no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C2×D414yes—
185C4⋊Dic11C2412yes—
186C4⋊Dic11C2412yes—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—24no—
190C4×Dic11—24no—
191C2×C11⋊C8—24no—
192C2×C11⋊C8C2414yes—
193#4314—28no—
194C8×D11—216no—
195C2×#554—111no—
196C2×#547—111no—
197#3335—1116no—
198C2×#498D1111yescharacteristic, complemented
199C2×#481—112no—
200C2×#483—112no—
201C2×#475—111no—
202C2×#476—111no—
203C2×#465—112no—
204C2×C4×SD16—111no—
205C2×C8×D4—111no—
206C22×#106—112no—
207C23×C11C22×D411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11C2×SD1618yes—
215C22×D11C22×D414yes—
216Q8×C11—48no—
217Q8×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11C2×SD1614yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11C22×D414yes—
238D44—22no—
239D44—22no—
240D44—416no—
241D44—42no—
242D44C2×SD16116yescomplemented
243C4×D11—28no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—416no—
247C4×D11—48no—
248C4×D11—88no—
249Dic22—22no—
250Dic22—22no—
251Dic22—42no—
252C8×C11—22no—
253C8×C11C2×#4114yescomplemented
254C11⋊C8—24no—
255C22×#41—221no—
256C22×SD16—111no—
257C23×C8—112no—
258#554—118no—
259#554—224no—
260#547—118no—
261#547—224no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#125—221no—
265C2×#123—222no—
266C2×C22⋊Q8—112no—
267C2×C22⋊Q8—222no—
268C2×C22⋊Q8—221no—
269C2×#121—112no—
270C2×C4×Q8—111no—
271C2×C4×D4—111no—
272C2×C4×D4—111no—
273C2×C4×D4—221no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—112no—
276#498C2×D1118yescomplemented
277#483—1116no—
278#481—1116no—
279#476—118no—
280#475—118no—
281#465—1116no—
282C4×SD16—118no—
283C8×D4—118no—
284C2×#106—111no—
285C2×#106—112no—
286C2×#106—112no—
287C2×#106—1116no—
288C2×#106C2×D1112yes—
289C2×#106C2×D1112yes—
290C2×C4⋊C8—111no—
291C2×#103—111no—
292C2×#103—112no—
293C2×#102—111no—
294C2×#102—112no—
295C2×C22⋊C8—112no—
296C2×C4×C8C2×D1111yescharacteristic
297C22×C11#54712yes—
298C22×C11C22×SD1612yes—
299C22×C11#57712yes—
300C22×C11C23×D411yescharacteristic
301C2×D11—216no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—84no—
308C2×D11C22×SD1618yes—
309C4×C11—22no—
310C4×C11—44no—
311C4×C11—44no—
312C4×C11#54712yes—
313C4×C11C22×SD1614yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×2−1+411yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—42no—
320C2×#41—228no—
321C2×#41—448no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—111no—
325C22×D4—111no—
326C22×D4—111no—
327C22×D4—222no—
328C23×C4—112no—
329C23×C4—222no—
330C23×C4—222no—
331C23×C4—221no—
332C2×SD16—114no—
333C2×SD16—224no—
334C22×C8—112no—
335C22×C8—118no—
336C22×C8—228no—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339C4⋊Q8—22no—
340C4⋊Q8—22no—
341C4⋊Q8C22×D1114yes—
342C4⋊Q8C22×D1114yes—
343#125—228no—
344#123—2216no—
345C22⋊Q8—118no—
346C22⋊Q8—2216no—
347C22⋊Q8—224no—
348C22⋊Q8—228no—
349#121—118no—
350#121—224no—
351C4×Q8—114no—
352C4×Q8—222no—
353C4×D4—114no—
354C4×D4—114no—
355C4×D4—114no—
356C4×D4—228no—
357C4×D4—222no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1112yes—
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—221no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#106—114no—
380#106—118no—
381#106—118no—
382#106C22×D1118yes—
383#106C22×D1118yes—
384C4⋊C8—114no—
385#103—114no—
386#103—118no—
387#102—114no—
388#102—118no—
389C22⋊C8—118no—
390C4×C8C22×D1114yes—
391C2×C11#333514yescomplemented
392C2×C11C2×#54711yescharacteristic
393C2×C11C23×SD1611yescharacteristic
394C2×C11C2×#57711yescharacteristic
395D11—28no—
396D11—82no—
397C24—112no—
398C24—221no—
399#41—4432no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—44no—
403C2×Q8—82no—
404C2×Q8—112no—
405C2×Q8—221no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×D4—118no—
409C2×D4—114no—
410C2×D4—112no—
411C2×D4—228no—
412C2×D4—221no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—448no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—112no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—228no—
422C22×C4—228no—
423C22×C4—224no—
424C22×C4—224no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—224no—
429C22×C4—448no—
430C22×C4—444no—
431C22×C4—884no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435SD16—228no—
436C2×C8—22no—
437C2×C8—114no—
438C2×C8—224no—
439C2×C8—2216no—
440C2×C8#434314yescomplemented
441C2×C8C23×D1112yes—
442C2×C8C23×D1112yes—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—114no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—224no—
456C4⋊C4C23×D1114yes—
457C4⋊C4C23×D1114yes—
458C22⋊C4—118no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—224no—
462C42—224no—
463C42D4×D1112yes—
464C42C23×D1112yes—
465C11C2×#333511yescharacteristic, complemented, Sylow
466C23—118no—
467C23—114no—
468C23—224no—
469C23—224no—
470C23—222no—
471C23—442no—
472C23—442no—
473C23—442no—
474C23C2×D4×D1111yescharacteristic
475Q8—48no—
476Q8—84no—
477Q8—222no—
478Q8—222no—
479Q8—442no—
480D4—1116no—
481D4—222no—
482D4—222no—
483D4—4416no—
484D4—442no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—114no—
491C2×C4—224no—
492C2×C4—228no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—4416no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—448no—
503C2×C4—888no—
504C2×C4SD16×D1114yes—
505C2×C4C2×D4×D1112yes—
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×D4×D1112yes—
508C2×C4C2×#434312yes—
509C2×C4#6704012yes—
510C2×C4C24×D1111yescharacteristic
511C8—22no—
512C8—224no—
513C8C2×#434314yescomplemented
514C22—118no—
515C22—2216no—
516C22—224no—
517C22—224no—
518C22—442no—
519C22—442no—
520C22—442no—
521C22—884no—
522C22#1062325712yes—
523C22C2×SD16×D1112yes—
524C22#1062329312yes—
525C22C22×D4×D1111yescharacteristic
526C4—22no—
527C4—44no—
528C4—44no—
529C4—224no—
530C4—442no—
531C4—442no—
532C4—442no—
533C4#1062325712yes—
534C4C2×SD16×D1114yes—
535C4C22×#434311yescharacteristic
536C4C2×#6704011yescharacteristic
537C2—228no—
538C2—882no—
539C2#1308097214yesdirect product factor
540C2C2×#1062325711yescharacteristic
541C2C22×SD16×D1111yescharacteristic
542C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#498D11
hypocenterC11C2×#3335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13080972C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622475C2semidirect
6. C2×#10622707C2semidirect
7. C2×#10622697C2semidirect
8. C2×#10622477C2semidirect
9. C2×C4×#4314C2semidirect
10. C2×C8×D44C2semidirect
11. C2×D11×#106C2semidirect
12. C2×C11×#498C2semidirect
21. #10623261C22semidirect
34. C11×#498C22semidirect
42. #10622707C22semidirect
43. #10622697C22semidirect
49. #10622477C22semidirect
50. #10622476C22semidirect
51. #10622475C22semidirect
52. D11×#106C22semidirect
53. C4×#4314C22semidirect
54. C8×D44C22semidirect
148. C2×D44SD16semidirect
166. C2×C8×C11#41semidirect
198. C2×#498D11semidirect
242. D44C2×SD16semidirect
253. C8×C11C2×#41semidirect
276. #498C2×D11semidirect
391. C2×C11#3335semidirect
440. C2×C8#4343semidirect
465. C11C2×#3335semidirect
513. C8C2×#4343semidirect
539. C2#13080972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106232572
#130809722
C2×#106224762
C2×#106224752
C2×#106227072
C2×#106226972
C2×#106224772
C2×C4×#43142
C2×C8×D442
C2×D11×#1062
C2×C11×#4982
C2×#333511