Finite Group Databasebeta

← C2×#13081468 #15634186

Subgroups — C2×#13081468 #15634186

Order 2816.

2286 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C212yesmaximal, complemented
2#13081468C2116yesmaximal, direct product factor
3C2×#10622487C212yesmaximal, complemented
4C2×#10622503C214yesmaximal, complemented
5C2×#10622700C212yesmaximal, complemented
6C2×C8×Dic22C211yesmaximal, characteristic, complemented
7C2×C4×D88C211yesmaximal, characteristic
8C2×#10622485C212yesmaximal
9C2×C11×#500C211yesmaximal, characteristic, complemented
10C22×Q8×D11—22no—
11C2×C11×C4⋊Q8C2212yes—
12C2×#66999—22no—
13C22×D88C2211yescharacteristic
14#10623258—28no—
15#10623258C22116yescomplemented
16C2×#66949—24no—
17C2×#66946C2214yes—
18C2×#66941C2214yes—
19C2×C4×D44C2212yes—
20C2×C4×Dic22C2211yescharacteristic
21C11×#500C2218yescomplemented
22C2×C11×#107C2212yes—
23C2×C11×#107C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66885C2212yes—
26C2×#66882C2211yescharacteristic
27C2×Dic11⋊C8C2212yes—
28C2×C8×Dic11C2212yes—
29#10622700C22116yescomplemented
30C2×#66873C2214yes—
31C2×#66871C2214yes—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622503C22132yescomplemented
34#10622487C22116yescomplemented
35#10622485C22116yes—
36C4×D88C2218yes—
37C8×Dic22C2218yescomplemented
38C22×Q8×C11—22no—
39C2×Q8×D11—216no—
40C2×Q8×D11—416no—
41C22×D44C2312yes—
42C22×C4×D11—22no—
43C22×C4×D11—24no—
44C22×Dic22—24no—
45C22×Dic22D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8C2318yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2314yes—
52C2×C42×C11C2311yescharacteristic
53#66999—216no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—24no—
56C2×C4⋊Dic11D411yescharacteristic
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4D412yes—
60C2×C4×Dic11C2312yes—
61C22×C11⋊C8C2312yes—
62C2×D88Q818yescomplemented
63C2×D88C2314yes—
64#66949—232no—
65#66946—28no—
66#66946C23116yes—
67#66941—28no—
68#66941C23116yes—
69C4×D44—24no—
70C4×D44C2318yes—
71C4×Dic22D414yes—
72C4×Dic22C2314yes—
73C11×#107C2318yes—
74C11×#107C2318yes—
75C4×C8×C11C2314yes—
76#66885C2318yes—
77#66882C2314yes—
78Dic11⋊C8C2318yes—
79C8×Dic11C2318yes—
80#66873C23116yes—
81#66871C23116yes—
82C4⋊(C11⋊C8)C2314yes—
83C2×Q8×D8—111nomaximal, Sylow
84C23×D11—22no—
85C2×Q8×C11—28no—
86C2×Q8×C11—48no—
87C22×C4×C11—24no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—22no—
92C22×Dic11C2×D412yes—
93C22×Dic11C2×D412yes—
94Q8×D11—464no—
95C2×D44—22no—
96C2×D44—24no—
97C2×D44C2×Q818yescomplemented
98C2×D44C2414yes—
99C2×C4×D11—216no—
100C2×C4×D11—28no—
101C2×C4×D11—416no—
102C2×C4×D11—48no—
103C2×Dic22—216no—
104C2×Dic22—416no—
105C2×Dic22D818yescomplemented
106C2×Dic22C2×D414yes—
107C2×C8×C11—22no—
108C2×C8×C11C2×Q814yescomplemented
109C2×C8×C11C2412yes—
110C2×C8×C11C2412yes—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4C2418yes—
114C42×C11C2×D412yes—
115C42×C11C2412yes—
116(C2×D11)⋊C4—216no—
117(C2×D11)⋊C4—28no—
118C4⋊Dic11—22no—
119C4⋊Dic11C2×D414yes—
120C4⋊Dic11C2414yes—
121Dic11⋊C4—216no—
122Dic11⋊C4C2×D418yes—
123C4×Dic11C2×D414yes—
124C4×Dic11C2414yes—
125C2×C11⋊C8—24no—
126C2×C11⋊C8C2414yes—
127D88C2×Q8116yescomplemented
128C2×D4×Q8—112no—
129Q8×D8—1116no—
130C2×#500—112no—
131C2×#500D1111yescharacteristic, complemented
132C2×#474—114no—
133C2×#474—112no—
134C2×C8×Q8—111no—
135C2×C4×D8—112no—
136C2×C4×D8—111no—
137C23×C11C22×D411yescharacteristic
138C22×D11—28no—
139C22×D11—24no—
140C22×D11—44no—
141C22×D11—44no—
142Q8×C11—416no—
143C2×C4×C11—22no—
144C2×C4×C11—28no—
145C2×C4×C11—48no—
146C2×C4×C11C2×D814yes—
147C2×C4×C11C22×D412yes—
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C22×D412yes—
150C2×C4×C11C22×Q812yes—
151C2×C4×C112−1+412yes—
152C2×C4×C11C2511yescharacteristic
153C2×Dic11—24no—
154C2×Dic11—24no—
155C2×Dic11—44no—
156C2×Dic11C2×D818yes—
157C2×Dic11C22×D414yes—
158C2×Dic11C22×D414yes—
159D44—28no—
160D44—24no—
161D44C22×Q818yescomplemented
162C4×D11—416no—
163C4×D11—432no—
164Dic22—432no—
165Dic22C2×D8116yescomplemented
166C8×C11—22no—
167C8×C11C22×Q814yescomplemented
168C11⋊C8—24no—
169C23×Q8—222no—
170C22×D8—111no—
171D4×Q8—1116no—
172D4×Q8—228no—
173C2×C4⋊Q8—114no—
174C2×C4⋊Q8C2×D1112yes—
175C2×C22⋊Q8—224no—
176C2×C22⋊Q8—222no—
177C2×C4×Q8—111no—
178C2×C4×D4—114no—
179C2×C4×D4—112no—
180#500—1116no—
181#500C2×D1118yescomplemented
182#474—1116no—
183#474—1132no—
184C8×Q8—118no—
185C4×D8—1116no—
186C4×D8—118no—
187C2×#107—111no—
188C2×#107—114no—
189C2×#107C2×D1112yes—
190C2×#107C2×D1112yes—
191C2×C4⋊C8—112no—
192C2×C4⋊C8—111no—
193C2×#102—112no—
194C2×#102—114no—
195C2×C4×C8—112no—
196C2×C4×C8C2×D1111yescharacteristic
197C22×C11D4×Q812yes—
198C22×C11C22×D812yes—
199C22×C11#57812yes—
200C22×C11C23×D411yescharacteristic
201C2×D11—28no—
202C2×D11—416no—
203C2×D11—44no—
204C2×D11—44no—
205C4×C11—22no—
206C4×C11—48no—
207C4×C11D4×Q812yes—
208C4×C11C22×D814yes—
209C4×C11C23×Q811yescharacteristic
210C4×C11C2×2−1+411yescharacteristic
211Dic11—24no—
212Dic11—44no—
213Dic11C22×D818yes—
214C22×Q8—22no—
215C22×Q8—111no—
216C22×Q8—224no—
217C22×Q8—2216no—
218C22×Q8—4416no—
219C22×D4—112no—
220C23×C4—224no—
221C23×C4—222no—
222C2×D8—118no—
223C2×D8—114no—
224C22×C8—112no—
225C22×C8C22×D1111yescharacteristic
226C22×C8C22×D1111yescharacteristic
227C4⋊Q8—24no—
228C4⋊Q8—1116no—
229C4⋊Q8—228no—
230C4⋊Q8C22×D1118yes—
231C22⋊Q8—2232no—
232C22⋊Q8—2216no—
233C4×Q8—114no—
234C4×Q8—114no—
235C4×D4—1116no—
236C4×D4—118no—
237C4×D4—228no—
238C4×D4—224no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—112no—
243C2×C4⋊C4—224no—
244C2×C4⋊C4C22×D1114yes—
245C2×C22⋊C4—224no—
246C2×C22⋊C4—222no—
247C2×C42—112no—
248C2×C42C22×D1111yescharacteristic
249#107—114no—
250#107—1116no—
251#107C22×D1118yes—
252#107C22×D1118yes—
253C4⋊C8—118no—
254C4⋊C8—114no—
255#102—118no—
256#102—1116no—
257C4×C8—118no—
258C4×C8C22×D1114yes—
259C2×C11Q8×D814yescomplemented
260C2×C11C2×D4×Q811yescharacteristic
261C2×C11C23×D811yescharacteristic
262C2×C11C2×#57811yescharacteristic
263D11—48no—
264C24—222no—
265C2×Q8—28no—
266C2×Q8—48no—
267C2×Q8—118no—
268C2×Q8—114no—
269C2×Q8—2216no—
270C2×Q8—4416no—
271C2×Q8—4464no—
272C2×D4—118no—
273C2×D4—114no—
274C2×D4—222no—
275C2×D4—224no—
276C22×C4—24no—
277C22×C4—112no—
278C22×C4—112no—
279C22×C4—2216no—
280C22×C4—222no—
281C22×C4—228no—
282C22×C4—4416no—
283C22×C4—448no—
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286C22×C4C23×D1111yescharacteristic
287D8—1116no—
288C2×C8—22no—
289C2×C8—114no—
290C2×C8—224no—
291C2×C8Q8×D1114yescomplemented
292C2×C8C23×D1112yes—
293C2×C8C23×D1112yes—
294C4⋊C4—28no—
295C4⋊C4—24no—
296C4⋊C4—118no—
297C4⋊C4—114no—
298C4⋊C4—114no—
299C4⋊C4—2216no—
300C4⋊C4—222no—
301C4⋊C4C23×D1118yes—
302C22⋊C4—2216no—
303C22⋊C4—228no—
304C42—114no—
305C42—114no—
306C42D4×D1112yes—
307C42C23×D1112yes—
308C11C2×Q8×D811yescharacteristic, complemented, Sylow
309C23—228no—
310C23—224no—
311C23—444no—
312C23—444no—
313C23C2×D4×D1111yescharacteristic
314Q8—416no—
315Q8—1116no—
316Q8—4432no—
317D4—118no—
318D4—228no—
319D4—224no—
320C2×C4—22no—
321C2×C4—28no—
322C2×C4—48no—
323C2×C4—118no—
324C2×C4—114no—
325C2×C4—114no—
326C2×C4—224no—
327C2×C4—224no—
328C2×C4—4432no—
329C2×C4—444no—
330C2×C4—4416no—
331C2×C4D8×D1114yes—
332C2×C4C2×D4×D1112yes—
333C2×C4C2×D4×D1111yescharacteristic
334C2×C4C2×D4×D1112yes—
335C2×C4C2×Q8×D1112yes—
336C2×C4#6704012yes—
337C2×C4C24×D1111yescharacteristic
338C8—22no—
339C8—224no—
340C8C2×Q8×D1114yescomplemented
341C22—228no—
342C22—4416no—
343C22—444no—
344C22—444no—
345C22#1062325812yes—
346C22C2×D8×D1112yes—
347C22#1062329712yes—
348C22C22×D4×D1111yescharacteristic
349C4—22no—
350C4—48no—
351C4—118no—
352C4—224no—
353C4—444no—
354C4#1062325812yes—
355C4C2×D8×D1114yes—
356C4C22×Q8×D1111yescharacteristic
357C4C2×#6704011yescharacteristic
358C2—448no—
359C2#1308146814yesdirect product factor
360C2C2×#1062325811yescharacteristic
361C2C22×D8×D1111yescharacteristic
362C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenterC2×#500D11
hypocenterC11C2×Q8×D8
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
1. C2×#10623258C2semidirect
2. #13081468C2direct (N × H)
3. C2×#10622487C2semidirect
4. C2×#10622503C2semidirect
5. C2×#10622700C2semidirect
6. C2×C8×Dic22C2semidirect
9. C2×C11×#500C2semidirect
15. #10623258C22semidirect
21. C11×#500C22semidirect
29. #10622700C22semidirect
33. #10622503C22semidirect
34. #10622487C22semidirect
37. C8×Dic22C22semidirect
62. C2×D88Q8semidirect
97. C2×D44C2×Q8semidirect
105. C2×Dic22D8semidirect
108. C2×C8×C11C2×Q8semidirect
127. D88C2×Q8semidirect
131. C2×#500D11semidirect
161. D44C22×Q8semidirect
165. Dic22C2×D8semidirect
167. C8×C11C22×Q8semidirect
181. #500C2×D11semidirect
259. C2×C11Q8×D8semidirect
291. C2×C8Q8×D11semidirect
308. C11C2×Q8×D8semidirect
340. C8C2×Q8×D11semidirect
359. C2#13081468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232582
#130814682
C2×#106224872
C2×#106225032
C2×#106227002
C2×C8×Dic222
C2×C4×D882
C2×#106224852
C2×C11×#5002
C2×Q8×D811