Finite Group Databasebeta

← C2×#13068092 #14736271

Subgroups — C2×#13068092 #14736271

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C212yesmaximal, complemented
2C2×#10622301C211yesmaximal, characteristic, complemented
3#13068092C218yesmaximal, direct product factor
4C2×#10622095C211yesmaximal, characteristic, complemented
5C2×#10622182C212yesmaximal, complemented
6C2×C11×#493C211yesmaximal, characteristic, complemented
7C22×C11×D8—21no—
8C22×C11×D8—21no—
9C2×C11×#127C2212yes—
10C22×#4323—22no—
11C22×#4313—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#493—22no—
14C11×#493C2214yescomplemented
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66896—22no—
17C2×(C2×D11)⋊C8—21no—
18#10622685—24no—
19#10622685C2218yescomplemented
20C2×C4⋊(C11⋊C8)C2212yes—
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22#10622301—22no—
23#10622301C2214yescomplemented
24#10622182C2218yescomplemented
25#10622095C2214yescomplemented
26C22×D4×C11—22no—
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D44D411yescharacteristic
30C22×C4×D11—21no—
31C2×C11×D8—24no—
32C2×C11×D8—24no—
33C2×C11×D8—44no—
34C2×C11×D8—44no—
35C22×C8×C11D411yescharacteristic
36C22×C8×C11D411yescharacteristic
37C11×#127—22no—
38C11×#127—22no—
39C11×#127—22no—
40C11×#127C2314yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4323—28no—
43C2×#4323—48no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C22×C11⋊C8—21no—
47C22×C11⋊C8—22no—
48C2×#4313—24no—
49C2×#4313—44no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44D412yes—
53C4×D44C2312yes—
54C4×C8×C11D412yes—
55C4×C8×C11C2312yes—
56#66896—28no—
57(C2×D11)⋊C8—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—22no—
60C4⋊(C11⋊C8)C2312yes—
61C4⋊(C11⋊C8)C2314yes—
62C2×#1687—111nomaximal, Sylow
63C24×C11—42no—
64C23×D11—21no—
65C2×D4×C11—24no—
66C2×D4×C11—24no—
67C2×D4×C11—24no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—44no—
74C2×D4×C11—44no—
75C2×D4×C11—84no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—21no—
80C2×D44—21no—
81C2×D44—24no—
82C2×D44C2×D412yes—
83C2×C4×D11—22no—
84C2×C4×D11—22no—
85C2×C4×D11—42no—
86C2×C4×D11—42no—
87C11×D8—48no—
88C11×D8—48no—
89C2×C8×C11—22no—
90C2×C8×C11D814yescomplemented
91C2×C8×C11C2×D412yes—
92C2×C8×C11C2×D412yes—
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11C2411yescharacteristic
97#4323—416no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11C2×D412yes—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—24no—
104C2×C11⋊C8—42no—
105C2×C11⋊C8—44no—
106#4313—48no—
107C2×#493D1111yescharacteristic, complemented
108C2×#459—112no—
109C2×#436—111no—
110#1687—118no—
111C2×#334—111no—
112C2×#331—112no—
113C23×C11—44no—
114C23×C11—84no—
115C23×C11—84no—
116C23×C11—84no—
117C23×C11#12111yescharacteristic
118C22×D11—22no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122D4×C11—44no—
123D4×C11—44no—
124D4×C11—44no—
125D4×C11—44no—
126D4×C11—84no—
127D4×C11—84no—
128D4×C11—84no—
129D4×C11—84no—
130C2×C4×C11—22no—
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11C2×D812yes—
135C2×C4×C11AGL(1,ℤ/8)14yes—
136C2×C4×C11AGL(1,ℤ/8)12yes—
137C2×C4×C11C22×D411yescharacteristic
138C2×C4×C11C22×D411yescharacteristic
139C2×C4×C11C2×#4111yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—42no—
142D44—24no—
143D44—42no—
144C4×D11—42no—
145C4×D11—42no—
146C4×D11—44no—
147C8×C11—22no—
148C8×C11C2×D814yescomplemented
149C11⋊C8—42no—
150C11⋊C8—44no—
151C22×D8—21no—
152C22×D8—21no—
153C22×D8—222no—
154C22×M16—221no—
155C2×#127C2×D1112yes—
156C2×C4×D4—111no—
157#493—22no—
158#493C2×D1114yescomplemented
159#459—118no—
160#459—224no—
161#436—114no—
162#436—222no—
163C2×C4⋊C8—111no—
164C2×C4⋊C8—112no—
165C2×#102—222no—
166C2×C22⋊C8—221no—
167C2×C4×C8C2×D1111yescharacteristic
168#334—114no—
169#331—118no—
170C22×C11—84no—
171C22×C11—84no—
172C22×C11—84no—
173C22×C11—168no—
174C22×C11#45912yes—
175C22×C11#46912yes—
176C22×C11#47212yes—
177C22×C11C2×#12111yescharacteristic
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C2×D11—84no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11#45912yes—
185C4×C11#46912yes—
186C4×C11C22×D811yescharacteristic
187C4×C11C2×AGL(1,ℤ/8)12yes—
188C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
189Dic11—42no—
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—111no—
194C23×C4—221no—
195C2×D8—24no—
196C2×D8—24no—
197C2×D8—44no—
198C2×D8—44no—
199C2×D8—228no—
200C2×D8—448no—
201C2×M16—224no—
202C2×M16—444no—
203C22×C8—222no—
204C22×C8—221no—
205C22×C8C22⋊D1111yescharacteristic
206C22×C8C22⋊D1111yescharacteristic
207#127—22no—
208#127—22no—
209#127—22no—
210#127C22×D1114yes—
211C4×D4—112no—
212C4×D4—112no—
213C4×D4—221no—
214C4×D4—221no—
215C2×C4⋊C4—111no—
216C2×C22⋊C4—221no—
217C2×C42C22×D1111yescharacteristic
218C4⋊C8—112no—
219C4⋊C8—114no—
220C4⋊C8—222no—
221C4⋊C8—221no—
222#102—228no—
223C22⋊C8—224no—
224C4×C8C22⋊D1112yes—
225C4×C8C22×D1112yes—
226C2×C11—164no—
227C2×C11#168714yescomplemented
228C2×C11C2×#45911yescharacteristic
229C2×C11C2×#46911yescharacteristic
230C2×C11C2×#47211yescharacteristic
231D11—82no—
232C24—42no—
233C24—221no—
234C2×D4—24no—
235C2×D4—24no—
236C2×D4—24no—
237C2×D4—44no—
238C2×D4—44no—
239C2×D4—44no—
240C2×D4—44no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—42no—
244C2×D4—84no—
245C2×D4—112no—
246C2×D4—224no—
247C2×D4—221no—
248C22×C4—221no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4—442no—
252C22×C4—442no—
253C22×C4D4×D1111yescharacteristic
254C22×C4#434111yescharacteristic
255C22×C4C2×C22⋊D1111yescharacteristic
256D8—48no—
257D8—48no—
258D8—4416no—
259M16—448no—
260C2×C8—22no—
261C2×C8—224no—
262C2×C8—222no—
263C2×C8—444no—
264C2×C8—442no—
265C2×C8#432314yescomplemented
266C2×C8C2×C22⋊D1112yes—
267C2×C8C2×C22⋊D1112yes—
268C4⋊C4—112no—
269C4⋊C4—221no—
270C22⋊C4—222no—
271C22⋊C4—222no—
272C42D4×D1111yescharacteristic
273C42#434111yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C42C23×D1111yescharacteristic
276C11C2×#168711yescharacteristic, complemented, Sylow
277C23—44no—
278C23—84no—
279C23—84no—
280C23—84no—
281C23—222no—
282C23—442no—
283C23—442no—
284C23—442no—
285C23#6699111yescharacteristic
286D4—44no—
287D4—44no—
288D4—44no—
289D4—44no—
290D4—84no—
291D4—84no—
292D4—84no—
293D4—84no—
294D4—224no—
295D4—442no—
296C2×C4—22no—
297C2×C4—222no—
298C2×C4—442no—
299C2×C4—442no—
300C2×C4—442no—
301C2×C4—444no—
302C2×C4#6696414yes—
303C2×C4C2×#432312yes—
304C2×C4#6698512yes—
305C2×C4#6699111yescharacteristic
306C2×C4#6699111yescharacteristic
307C2×C4#6699111yescharacteristic
308C2×C4C2×D4×D1111yescharacteristic
309C2×C4C2×#434111yescharacteristic
310C2×C4C22×C22⋊D1111yescharacteristic
311C8—22no—
312C8—444no—
313C8—442no—
314C8C2×#432314yescomplemented
315C22—84no—
316C22—84no—
317C22—84no—
318C22—168no—
319C22—442no—
320C22—442no—
321C22—442no—
322C22—884no—
323C22#1062268512yes—
324C22#1062277212yes—
325C22#1062277312yes—
326C22C2×#6699111yescharacteristic
327C4—21no—
328C4—21no—
329C4—442no—
330C4#1062268512yes—
331C4#1062277212yes—
332C4C2×#6696412yes—
333C4C22×#432311yescharacteristic
334C4C2×#6698511yescharacteristic
335C2—164no—
336C2—882no—
337C2#1306809214yesdirect product factor
338C2C2×#1062268511yescharacteristic
339C2C2×#1062277211yescharacteristic
340C2C2×#1062277311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#493C2
socleC23×C11#121
hypercenterC2×#493D11
hypocenterC11C2×#1687
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10622685C2semidirect
2. C2×#10622301C2semidirect
3. #13068092C2direct (N × H)
4. C2×#10622095C2semidirect
5. C2×#10622182C2semidirect
6. C2×C11×#493C2semidirect
14. C11×#493C22semidirect
19. #10622685C22semidirect
23. #10622301C22semidirect
24. #10622182C22semidirect
25. #10622095C22semidirect
90. C2×C8×C11D8semidirect
107. C2×#493D11semidirect
148. C8×C11C2×D8semidirect
158. #493C2×D11semidirect
227. C2×C11#1687semidirect
265. C2×C8#4323semidirect
276. C11C2×#1687semidirect
314. C8C2×#4323semidirect
337. C2#13068092direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226852
C2×#106223012
#130680922
C2×#106220952
C2×#106221822
C2×C11×#4932
C2×#168711