Finite Group Databasebeta

← C2×#13080986 #15632210

Subgroups — C2×#13080986 #15632210

Order 2816.

1866 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623112C212yesmaximal
2#13080986C2116yesmaximal, direct product factor
3C2×#10622296C211yesmaximal, characteristic, complemented
4C2×#10622428C212yesmaximal, complemented
5C2×#10622418C212yesmaximal, complemented
6C2×#10622635C212yesmaximal, complemented
7C2×#10622801C211yesmaximal, characteristic, complemented
8C2×#10622801C211yesmaximal, characteristic, complemented
9C2×C8×D44C211yesmaximal, characteristic
10C2×#10622493C211yesmaximal, characteristic, complemented
11C2×D11×#107C211yesmaximal, characteristic, complemented
12C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2211yescharacteristic
14C2×C4×Q8×C11C2212yes—
15C2×#66999C2212yes—
16C2×#66999C2212yes—
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623112—28no—
20#10623112C22116yes—
21C2×#66947—22no—
22C2×#66945C2212yes—
23C2×C4⋊C4×D11C2212yes—
24C2×#66942—22no—
25C2×#66929—22no—
26C2×C4×D44C2211yescharacteristic
27C2×#66925—22no—
28C2×#66923C2212yes—
29C4×C11×Q16C2218yescomplemented
30C2×C11×#107C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C2×#66899C2212yes—
34C2×#66899C2212yes—
35#10622801C2218yescomplemented
36#10622801C2218yescomplemented
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×#66882C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66881C2212yes—
42#10622635C22116yescomplemented
43C2×#66872C2212yes—
44C2×#66871C2212yes—
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46#10622493C2218yescomplemented
47D11×#107C2218yescomplemented
48#10622428C22116yescomplemented
49#10622418C22116yescomplemented
50C8×D44C2218yes—
51#10622296C2218yescomplemented
52C22×Q8×C11C2312yes—
53C22×D44D411yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11C2311yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C2×C11×Q16—24no—
58C2×C11×Q16C2314yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×Q8×C11—24no—
62C4×Q8×C11C2318yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11—22no—
66C2×C42×C11C2311yescharacteristic
67#66999—24no—
68#66999—24no—
69#66999C2318yes—
70#66999C2318yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—22no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C2×C8×D11—24no—
88C2×C8×D11—24no—
89C2×C8×D11C2314yes—
90C2×C8×D11C2314yes—
91#66947—216no—
92#66945—24no—
93#66945C2318yes—
94C4⋊C4×D11—24no—
95C4⋊C4×D11C2318yes—
96#66942—216no—
97#66929—216no—
98C4×D44D414yes—
99C4×D44C2314yes—
100#66925—216no—
101#66923—24no—
102#66923C2318yes—
103C11×#107C2314yes—
104C11×#103C2318yes—
105C4×C8×C11C2314yes—
106#66899C2318yes—
107#66899C2318yes—
108(C2×D11)⋊C8C2314yes—
109(C2×D11)⋊C8C2314yes—
110#66882C2314yes—
111#66882C2314yes—
112#66881C2318yes—
113#66872C2318yes—
114#66871C2318yes—
115C4⋊(C11⋊C8)C2314yes—
116C2×#3336—111nomaximal, Sylow
117C23×D11C2×D411yescharacteristic
118C23×D11C2×D411yescharacteristic
119C2×Q8×C11—22no—
120C2×Q8×C11—24no—
121C2×Q8×C11—24no—
122C2×Q8×C11C2414yes—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C2×D44—24no—
133C2×D44C2×D414yes—
134C2×C4×D11—28no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—48no—
140C2×C4×D11C2×D412yes—
141C2×C4×D11C2×D412yes—
142C2×C4×D11C2412yes—
143C2×C4×D11C2412yes—
144C11×Q16—28no—
145C2×C8×C11—22no—
146C2×C8×C11#4114yes—
147C2×C8×C11C2412yes—
148C2×C8×C11C2412yes—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2414yes—
152C42×C11—28no—
153C42×C11C2×D412yes—
154C42×C11C2412yes—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—28no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4C2×D414yes—
159(C2×D11)⋊C4C2×D414yes—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11C2×D414yes—
163C4⋊Dic11C2414yes—
164C4⋊Dic11C2414yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167Dic11⋊C4—28no—
168Dic11⋊C4—28no—
169Dic11⋊C4—28no—
170C4×Dic11—28no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C2412yes—
174C2×C11⋊C8C2412yes—
175C8×D11—28no—
176C8×D11—28no—
177C2×#552—112no—
178#3336—1116no—
179C2×#499—111no—
180C2×#485—112no—
181C2×#483—112no—
182C2×#479—112no—
183C2×#467—111no—
184C2×#467—111no—
185C2×C4×Q16D1111yescharacteristic, complemented
186C2×C8×D4—111no—
187C2×#427—111no—
188C22×#107—111no—
189C23×C11C22×D411yescharacteristic
190C22×D11—22no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11#13514yes—
196C22×D11C22×D412yes—
197C22×D11C22×D412yes—
198Q8×C11—24no—
199Q8×C11—24no—
200Q8×C11—44no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—44no—
206C2×C4×C11—44no—
207C2×C4×C11C22×D412yes—
208C2×C4×C11C22×D412yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4112yes—
211C2×C4×C112−1+412yes—
212C2×C4×C11C2511yescharacteristic
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—24no—
216C2×Dic11—24no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11C22×D412yes—
220C2×Dic11C22×D412yes—
221D44—28no—
222C4×D11—24no—
223C4×D11—24no—
224C4×D11—22no—
225C4×D11—22no—
226C4×D11—22no—
227C4×D11—22no—
228C4×D11—416no—
229C8×C11—22no—
230C8×C11C2×#4114yes—
231C11⋊C8—22no—
232C11⋊C8—22no—
233C22×Q16C2×D1111yescharacteristic
234C23×C8—111no—
235C23×C8—111no—
236#552—1116no—
237#552—228no—
238C2×#126—222no—
239C2×#125—112no—
240C2×#125—222no—
241C2×#123—222no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C4×Q8C2×D1112yes—
245C2×C4×D4—111no—
246C2×#117—112no—
247C2×#117—222no—
248C22×C4⋊C4—112no—
249#499—118no—
250#485—1116no—
251#483—1116no—
252#479—1116no—
253#467—118no—
254#467—118no—
255C4×Q16C2×D1118yescomplemented
256C8×D4—118no—
257#427—118no—
258C2×#107—111no—
259C2×#107—111no—
260C2×#107—112no—
261C2×#107—118no—
262C2×#107C2×D1111yescharacteristic
263C2×#106—112no—
264C2×#106—112no—
265C2×C4⋊C8—111no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103C2×D1112yes—
269C2×C22⋊C8—111no—
270C2×C22⋊C8—111no—
271C2×C4×C8C2×D1111yescharacteristic
272C22×C11#54712yes—
273C22×C11C2×#13512yes—
274C22×C11#57812yes—
275C22×C11C23×D411yescharacteristic
276C2×D11—28no—
277C2×D11—22no—
278C2×D11—22no—
279C2×D11—22no—
280C2×D11—22no—
281C2×D11—22no—
282C2×D11—44no—
283C2×D11C2×#13514yes—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—44no—
287C4×C11—44no—
288C4×C11#54712yes—
289C4×C11C22×#4111yescharacteristic
290C4×C11C2×2−1+411yescharacteristic
291Dic11—22no—
292Dic11—22no—
293Dic11—44no—
294Dic11—44no—
295C22×Q8C22×D1112yes—
296C22×D4—111no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—222no—
300C2×Q16—24no—
301C2×Q16C22×D1114yes—
302C22×C8—111no—
303C22×C8—111no—
304C22×C8—114no—
305C22×C8—114no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#126—2216no—
311#125—118no—
312#125—2216no—
313#125—224no—
314#123—2216no—
315C22⋊Q8—118no—
316C22⋊Q8—118no—
317C22⋊Q8—224no—
318C22⋊Q8—224no—
319C4×Q8—24no—
320C4×Q8C22×D1118yes—
321C4×D4—114no—
322C4×D4—114no—
323#117—118no—
324#117—2216no—
325#117—224no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—112no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4C22×D1112yes—
338C2×C22⋊C4—111no—
339C2×C22⋊C4—111no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C42—22no—
344C2×C42—222no—
345C2×C42C22×D1111yescharacteristic
346#107—114no—
347#107—114no—
348#107—118no—
349#107C22×D1114yes—
350#106—118no—
351#106—118no—
352C4⋊C8—114no—
353#103—118no—
354#103—118no—
355#103C22×D1118yes—
356C22⋊C8—114no—
357C22⋊C8—114no—
358C4×C8C22×D1114yes—
359C2×C11#333614yescomplemented
360C2×C11C2×#54711yescharacteristic
361C2×C11C22×#13511yescharacteristic
362C2×C11C2×#57811yescharacteristic
363D11—24no—
364D11—42no—
365C24—111no—
366C24—111no—
367C2×Q8—22no—
368C2×Q8—24no—
369C2×Q8—24no—
370C2×Q8C23×D1114yes—
371C2×D4—114no—
372C2×D4—224no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—448no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—28no—
393C2×C8—22no—
394C2×C8—112no—
395C2×C8—112no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—228no—
399C2×C8—228no—
400C2×C8#433914yes—
401C2×C8C23×D1112yes—
402C2×C8C23×D1112yes—
403C4⋊C4—28no—
404C4⋊C4—22no—
405C4⋊C4—114no—
406C4⋊C4—114no—
407C4⋊C4—114no—
408C4⋊C4—228no—
409C4⋊C4—228no—
410C4⋊C4—228no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—228no—
414C4⋊C4—228no—
415C4⋊C4C23×D1114yes—
416C22⋊C4—114no—
417C22⋊C4—114no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C42—28no—
422C42—228no—
423C42D4×D1112yes—
424C42C23×D1112yes—
425C11C2×#333611yescharacteristic, complemented, Sylow
426C23—114no—
427C23—112no—
428C23—112no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23C2×D4×D1111yescharacteristic
435Q8—24no—
436Q8—24no—
437Q8—44no—
438D4—228no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—112no—
446C2×C4—112no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—4416no—
458C2×C4—444no—
459C2×C4—444no—
460C2×C4C2×#433912yes—
461C2×C4C2×D4×D1112yes—
462C2×C4C2×D4×D1112yes—
463C2×C4C2×D4×D1111yescharacteristic
464C2×C4#6704312yes—
465C2×C4C24×D1111yescharacteristic
466C8—22no—
467C8—222no—
468C8—222no—
469C8C2×#433914yes—
470C22—114no—
471C22—228no—
472C22—222no—
473C22—222no—
474C22—222no—
475C22—222no—
476C22—222no—
477C22—444no—
478C22#1062308212yes—
479C22#1062329712yes—
480C22D11×#13512yes—
481C22C22×D4×D1111yescharacteristic
482C4—22no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—222no—
487C4—222no—
488C4—444no—
489C4—444no—
490C4#1062308212yes—
491C4C22×#433911yescharacteristic
492C4C2×#6704311yescharacteristic
493C2—224no—
494C2—442no—
495C2#1308098614yesdirect product factor
496C2C2×#1062308211yescharacteristic
497C2C2×D11×#13511yescharacteristic
498C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×C4×Q16D11
hypocenterC11C2×#3336
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. #13080986C2direct (N × H)
3. C2×#10622296C2semidirect
4. C2×#10622428C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622801C2semidirect
8. C2×#10622801C2semidirect
10. C2×#10622493C2semidirect
11. C2×D11×#107C2semidirect
12. C2×C4×C11×Q16C2semidirect
29. C4×C11×Q16C22semidirect
35. #10622801C22semidirect
36. #10622801C22semidirect
42. #10622635C22semidirect
46. #10622493C22semidirect
47. D11×#107C22semidirect
48. #10622428C22semidirect
49. #10622418C22semidirect
51. #10622296C22semidirect
185. C2×C4×Q16D11semidirect
255. C4×Q16C2×D11semidirect
359. C2×C11#3336semidirect
425. C11C2×#3336semidirect
495. C2#13080986direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231122
#130809862
C2×#106222962
C2×#106224282
C2×#106224182
C2×#106226352
C2×#106228012
C2×C8×D442
C2×#106224932
C2×D11×#1072
C2×C4×C11×Q162
C2×#333611