Finite Group Databasebeta

← C2×#13076879 #14960183

Subgroups — C2×#13076879 #14960183

Order 2816.

3294 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076879C2116yesmaximal, direct product factor
2C2×#10622290C211yesmaximal, characteristic, complemented
3C2×#10622605C213yesmaximal, complemented
4C2×#10622289C211yesmaximal, characteristic, complemented
5C2×#10622561C213yesmaximal, complemented
6C2×#10622607C213yesmaximal, complemented
7C2×#10622568C213yesmaximal
8C2×C11×#396C211yesmaximal, characteristic, complemented
9C25×D11C2211yescharacteristic
10C22×C11×C4⋊C4C2213yescomplemented
11C22×C11×C22⋊C4C2213yes—
12C22×C22⋊Dic11C2213yes—
13C22×(C2×D11)⋊C4C2213yes—
14C22×(C2×D11)⋊C4C2213yes—
15C22×(C2×D11)⋊C4C2213yes—
16C22×(C2×D11)⋊C4C2213yes—
17C22×C4⋊Dic11C2213yescomplemented
18C22×Dic11⋊C4C2213yescomplemented
19C22×Dic11⋊C4C2213yescomplemented
20C11×#396C2218yescomplemented
21C2×C11×#95C2211yescharacteristic, complemented
22C2×C11⋊#95C2213yescomplemented
23#10622607C22124yescomplemented
24#10622605C22124yescomplemented
25#10622568C22124yes—
26#10622561C22124yescomplemented
27#10622290C2218yescomplemented
28#10622289C2218yescomplemented
29C25×C11C2311yescharacteristic
30C24×D11—46no—
31C24×D11—46no—
32C24×D11Q818yes—
33C24×D11C2311yescharacteristic
34C24×D11C2311yescharacteristic
35C24×D11C2314yes—
36C23×C4×C11C2313yes—
37C23×C4×C11C2313yes—
38C23×Dic11C2313yes—
39C23×Dic11C2313yes—
40C2×C11×C4⋊C4—46no—
41C2×C11×C4⋊C4C23112yescomplemented
42C2×C11×C22⋊C4—46no—
43C2×C11×C22⋊C4C23112yes—
44C2×C22⋊Dic11—46no—
45C2×C22⋊Dic11C23112yes—
46C2×(C2×D11)⋊C4—46no—
47C2×(C2×D11)⋊C4—46no—
48C2×(C2×D11)⋊C4—46no—
49C2×(C2×D11)⋊C4—46no—
50C2×(C2×D11)⋊C4C23112yes—
51C2×(C2×D11)⋊C4C23112yes—
52C2×(C2×D11)⋊C4C23112yes—
53C2×(C2×D11)⋊C4C23112yes—
54C2×C4⋊Dic11—46no—
55C2×C4⋊Dic11C23112yescomplemented
56C2×Dic11⋊C4—46no—
57C2×Dic11⋊C4—46no—
58C2×Dic11⋊C4C23112yescomplemented
59C2×Dic11⋊C4C23112yescomplemented
60C11×#95C2314yescomplemented
61C11⋊#95C23112yescomplemented
62C2×#2842—111nomaximal, Sylow
63C24×C11—26no—
64C24×C11—26no—
65C24×C11C2×Q814yes—
66C24×C11C2412yes—
67C24×C11C2411yescharacteristic
68C23×D11—26no—
69C23×D11—26no—
70C23×D11—26no—
71C23×D11—26no—
72C23×D11—448no—
73C23×D11—412no—
74C23×D11—412no—
75C23×D11—416no—
76C23×D11—448no—
77C23×D11C2×Q814yes—
78C23×D11C2×Q814yes—
79C23×D11C2×Q8116yes—
80C23×D11C2412yes—
81C23×D11C2412yes—
82C22×C4×C11—26no—
83C22×C4×C11—26no—
84C22×C4×C11—26no—
85C22×C4×C11—26no—
86C22×C4×C11—26no—
87C22×C4×C11—26no—
88C22×C4×C11C2416yes—
89C22×C4×C11C2416yes—
90C22×Dic11—26no—
91C22×Dic11—26no—
92C22×Dic11—26no—
93C22×Dic11—26no—
94C22×Dic11—26no—
95C22×Dic11—26no—
96C22×Dic11C2416yes—
97C22×Dic11C2416yes—
98C11×C4⋊C4—412no—
99C11×C22⋊C4—412no—
100C22⋊Dic11—412no—
101(C2×D11)⋊C4—412no—
102(C2×D11)⋊C4—412no—
103(C2×D11)⋊C4—412no—
104(C2×D11)⋊C4—412no—
105C4⋊Dic11—412no—
106Dic11⋊C4—412no—
107Dic11⋊C4—412no—
108#2842—1116no—
109C2×#399—111no—
110C2×#399—113no—
111C2×#396—111no—
112C2×#396—113no—
113C2×#396—113no—
114C2×#396D1111yescharacteristic, complemented
115C2×#379—113no—
116C23×C11—224no—
117C23×C11—26no—
118C23×C11—26no—
119C23×C11—44no—
120C23×C11—412no—
121C23×C11C22×Q814yes—
122C23×C11C22×Q812yes—
123C23×C11H(5,𝔽2)16yes—
124C23×C11H(5,𝔽2)16yes—
125C23×C11C2511yescharacteristic
126C22×D11—224no—
127C22×D11—224no—
128C22×D11—26no—
129C22×D11—26no—
130C22×D11—26no—
131C22×D11—26no—
132C22×D11—448no—
133C22×D11—4128no—
134C22×D11—448no—
135C22×D11—416no—
136C22×D11—44no—
137C22×D11—44no—
138C22×D11—412no—
139C22×D11—412no—
140C22×D11C22×Q814yes—
141C22×D11C22×Q814yes—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—26no—
146C2×C4×C11—26no—
147C2×C4×C11—26no—
148C2×C4×C11—412no—
149C2×C4×C11—412no—
150C2×Dic11—26no—
151C2×Dic11—26no—
152C2×Dic11—26no—
153C2×Dic11—26no—
154C2×Dic11—26no—
155C2×Dic11—26no—
156C2×Dic11—412no—
157C2×Dic11—412no—
158C26—111no—
159C22×C4⋊C4—113no—
160C22×C4⋊C4—113no—
161C22×C4⋊C4—113no—
162C22×C4⋊C4C2×D1113yescomplemented
163C22×C22⋊C4—113no—
164C22×C22⋊C4—113no—
165C22×C22⋊C4—113no—
166C22×C22⋊C4—113no—
167C22×C22⋊C4—113no—
168C22×C22⋊C4C2×D1113yes—
169#399—1124no—
170#399—118no—
171#396—1124no—
172#396—1124no—
173#396—118no—
174#396C2×D1118yescomplemented
175#379—1124no—
176C2×#95—113no—
177C2×#95C2×D1111yescharacteristic, complemented
178C22×C11—212no—
179C22×C11—416no—
180C22×C11—46no—
181C22×C11—42no—
182C22×C11#543112yes—
183C22×C11#56014yes—
184C22×C11#560112yes—
185C22×C11C23×Q811yescharacteristic
186C22×C11C2×H(5,𝔽2)13yes—
187C22×C11C2×H(5,𝔽2)13yes—
188C2×D11—212no—
189C2×D11—212no—
190C2×D11—464no—
191C2×D11—416no—
192C2×D11—416no—
193C2×D11—46no—
194C2×D11—46no—
195C2×D11—42no—
196C2×D11—42no—
197C4×C11—46no—
198C4×C11—46no—
199Dic11—46no—
200Dic11—46no—
201C25—111no—
202C25—111no—
203C25—118no—
204C25—114no—
205C25—446no—
206C25—446no—
207C25C22×D1111yescharacteristic
208C23×C4—113no—
209C23×C4—113no—
210C23×C4C22×D1113yes—
211C23×C4C22×D1113yes—
212C2×C4⋊C4—46no—
213C2×C4⋊C4—1112no—
214C2×C4⋊C4—1112no—
215C2×C4⋊C4—1112no—
216C2×C4⋊C4—446no—
217C2×C4⋊C4—446no—
218C2×C4⋊C4—446no—
219C2×C4⋊C4C22×D11112yescomplemented
220C2×C22⋊C4—46no—
221C2×C22⋊C4—1112no—
222C2×C22⋊C4—1112no—
223C2×C22⋊C4—1112no—
224C2×C22⋊C4—1112no—
225C2×C22⋊C4—1112no—
226C2×C22⋊C4—446no—
227C2×C22⋊C4—446no—
228C2×C22⋊C4—446no—
229C2×C22⋊C4—446no—
230C2×C22⋊C4—446no—
231C2×C22⋊C4C22×D11112yes—
232#95—1112no—
233#95C22×D1114yescomplemented
234C2×C11—44no—
235C2×C11#284218yescomplemented
236C2×C11C2×#54313yes—
237C2×C11C2×#56013yes—
238C2×C11C2×#56011yescharacteristic
239D11—44no—
240D11—44no—
241C24—26no—
242C24—26no—
243C24—114no—
244C24—114no—
245C24—112no—
246C24—112no—
247C24—1116no—
248C24—226no—
249C24—226no—
250C24—226no—
251C24—226no—
252C24—4448no—
253C24—4412no—
254C24—4412no—
255C24—4416no—
256C24—4448no—
257C24Q8×D1114yes—
258C24C23×D1112yes—
259C24C23×D1111yescharacteristic
260C22×C4—26no—
261C22×C4—26no—
262C22×C4—26no—
263C22×C4—26no—
264C22×C4—26no—
265C22×C4—26no—
266C22×C4—116no—
267C22×C4—116no—
268C22×C4—226no—
269C22×C4—226no—
270C22×C4—226no—
271C22×C4—226no—
272C22×C4—226no—
273C22×C4—226no—
274C22×C4C23×D1116yes—
275C22×C4C23×D1116yes—
276C4⋊C4—412no—
277C4⋊C4—4412no—
278C4⋊C4—4412no—
279C4⋊C4—4412no—
280C22⋊C4—412no—
281C22⋊C4—4412no—
282C22⋊C4—4412no—
283C22⋊C4—4412no—
284C22⋊C4—4412no—
285C22⋊C4—4412no—
286C11C2×#284211yescharacteristic, complemented, Sylow
287C23—224no—
288C23—26no—
289C23—26no—
290C23—44no—
291C23—412no—
292C23—114no—
293C23—114no—
294C23—2224no—
295C23—2224no—
296C23—226no—
297C23—226no—
298C23—226no—
299C23—226no—
300C23—4448no—
301C23—4448no—
302C23—4416no—
303C23—44128no—
304C23—444no—
305C23—444no—
306C23—4412no—
307C23—4412no—
308C23#6703716yes—
309C23C2×Q8×D1114yes—
310C23C2×Q8×D1112yes—
311C23#6704216yes—
312C23C24×D1111yescharacteristic
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—412no—
320C2×C4—412no—
321C2×C4—226no—
322C2×C4—226no—
323C2×C4—226no—
324C2×C4—226no—
325C2×C4—226no—
326C2×C4—226no—
327C2×C4—4412no—
328C2×C4—4412no—
329C22—212no—
330C22—46no—
331C22—42no—
332C22—416no—
333C22—2212no—
334C22—2212no—
335C22—4464no—
336C22—446no—
337C22—446no—
338C22—442no—
339C22—442no—
340C22—4416no—
341C22—4416no—
342C22#10623151112yes—
343C22#10623165112yes—
344C22#1062324214yes—
345C22C2×#6703713yes—
346C22C22×Q8×D1111yescharacteristic
347C22C2×#6704213yes—
348C4—46no—
349C4—46no—
350C4—446no—
351C4—446no—
352C2—44no—
353C2—444no—
354C2—444no—
355C2#1307687918yesdirect product factor
356C2C2×#1062316513yes—
357C2C2×#1062315113yes—
358C2C2×#1062324211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#396C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#396D11
hypocenterC11C2×#2842
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #13076879C2direct (N × H)
2. C2×#10622290C2semidirect
3. C2×#10622605C2semidirect
4. C2×#10622289C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622607C2semidirect
8. C2×C11×#396C2semidirect
10. C22×C11×C4⋊C4C22semidirect
17. C22×C4⋊Dic11C22semidirect
18. C22×Dic11⋊C4C22semidirect
19. C22×Dic11⋊C4C22semidirect
20. C11×#396C22semidirect
21. C2×C11×#95C22semidirect
22. C2×C11⋊#95C22semidirect
23. #10622607C22semidirect
24. #10622605C22semidirect
26. #10622561C22semidirect
27. #10622290C22semidirect
28. #10622289C22semidirect
41. C2×C11×C4⋊C4C23semidirect
55. C2×C4⋊Dic11C23semidirect
58. C2×Dic11⋊C4C23semidirect
59. C2×Dic11⋊C4C23semidirect
60. C11×#95C23semidirect
61. C11⋊#95C23semidirect
114. C2×#396D11semidirect
162. C22×C4⋊C4C2×D11semidirect
174. #396C2×D11semidirect
177. C2×#95C2×D11semidirect
219. C2×C4⋊C4C22×D11semidirect
233. #95C22×D11semidirect
235. C2×C11#2842semidirect
286. C11C2×#2842semidirect
355. C2#13076879direct (N × H)

Maximal subgroups

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

subgroupindex
#130768792
C2×#106222902
C2×#106226052
C2×#106222892
C2×#106225612
C2×#106226072
C2×#106225682
C2×C11×#3962
C2×#284211