Finite Group Databasebeta

← C2×#13067908 #14734898

Subgroups — C2×#13067908 #14734898

Order 2816.

1138 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623231C211yesmaximal, characteristic, complemented
2C2×#10622687C212yesmaximal, complemented
3#13067908C218yesmaximal, direct product factor
4C2×#10622181C211yesmaximal, characteristic, complemented
5C2×#10622102C212yesmaximal, complemented
6C2×C11×#490C211yesmaximal, characteristic, complemented
7C2×C11×#127C2211yescharacteristic
8C2×C11×#125C2211yescharacteristic
9C22×#4324—22no—
10C22×#4323—22no—
11#10623231—22no—
12#10623231—24no—
13#10623231C2214yescomplemented
14C2×#66949—22no—
15C2×#66948—22no—
16C2×#66947—22no—
17C2×#66928C2212yes—
18C11×#490—22no—
19C11×#490C2214yescomplemented
20C2×C11×#102—22no—
21C2×C11×#97C2211yescharacteristic
22#10622687—24no—
23#10622687C2218yescomplemented
24C2×#66867C2212yes—
25#10622181C2214yescomplemented
26#10622102C2218yescomplemented
27C22×D4×C11—22no—
28C22×D4×C11—21no—
29C22×D44—22no—
30C22×D44D412yes—
31C22×C4×D11—22no—
32C22×Dic22D412yes—
33C22×C8×C11—21no—
34C11×#127—21no—
35C11×#127—22no—
36C11×#127C2312yes—
37C11×#125—22no—
38C11×#125D412yes—
39C11×#125C2312yes—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D412yes—
42C2×C42×C11C2311yescharacteristic
43C2×#4324—28no—
44C2×#4324—48no—
45C2×#4323—28no—
46C2×#4323—48no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×Dic11⋊C4—22no—
51C22×C11⋊C8—22no—
52#66949—28no—
53#66949—28no—
54#66948—28no—
55#66948—28no—
56#66947—28no—
57#66947—28no—
58#66928—22no—
59#66928—22no—
60#66928D414yes—
61#66928C2314yes—
62C11×#102—28no—
63C11×#97—21no—
64C11×#97C2312yes—
65#66867—22no—
66#66867C2314yes—
67C2×#1656—111nomaximal, Sylow
68C24×C11—41no—
69C23×D11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—24no—
72C2×D4×C11—44no—
73C2×D4×C11—44no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C22×C4×C11—22no—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—22no—
81C2×D44—28no—
82C2×D44—22no—
83C2×D44—44no—
84C2×D44—84no—
85C2×D44C2×D414yes—
86C2×C4×D11—28no—
87C2×C4×D11—84no—
88C2×Dic22—22no—
89C2×Dic22—44no—
90C2×Dic22C2×D414yes—
91C2×C8×C11—22no—
92C2×C8×C11—42no—
93C11×C4⋊C4—22no—
94C11×C4⋊C4—24no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4C2×D414yes—
97C42×C11C2×D412yes—
98C42×C11C2×D411yescharacteristic
99C42×C11C2411yescharacteristic
100#4324—416no—
101#4323—416no—
102(C2×D11)⋊C4—28no—
103(C2×D11)⋊C4—24no—
104(C2×D11)⋊C4—24no—
105(C2×D11)⋊C4—24no—
106(C2×D11)⋊C4—24no—
107Dic11⋊C4—28no—
108C2×C11⋊C8—28no—
109C2×C11⋊C8—24no—
110C2×#562—111no—
111C2×#496—112no—
112C2×#490D1111yescharacteristic, complemented
113#1656—118no—
114C2×#330—111no—
115C2×#329—112no—
116C23×C11—42no—
117C23×C11—84no—
118C23×C11—82no—
119C23×C11#12011yescharacteristic
120C22×D11—24no—
121C22×D11—44no—
122C22×D11—44no—
123C22×D11—44no—
124D4×C11—44no—
125D4×C11—44no—
126D4×C11—44no—
127D4×C11—84no—
128D4×C11—82no—
129C2×C4×C11—24no—
130C2×C4×C11—22no—
131C2×C4×C11—24no—
132C2×C4×C11—44no—
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12012yes—
135C2×C4×C11C22×D412yes—
136C2×C4×C11C22×D411yescharacteristic
137C2×Dic11—24no—
138C2×Dic11—44no—
139D44—44no—
140D44—82no—
141D44—88no—
142C4×D11—88no—
143Dic22—44no—
144Dic22—82no—
145C8×C11—42no—
146C11⋊C8—28no—
147C22×SD16—222no—
148C22×D8—222no—
149#562—114no—
150#562—224no—
151#562—222no—
152C2×#127C2×D1111yescharacteristic
153C2×#125C2×D1111yescharacteristic
154C2×#124—112no—
155C2×#123—222no—
156C2×C22⋊Q8—222no—
157C2×#121—222no—
158#496—118no—
159#496—224no—
160#490—22no—
161#490C2×D1114yescomplemented
162C2×#102—22no—
163C2×#97—112no—
164C2×#97C2×D1111yescharacteristic
165#330—114no—
166#329—118no—
167C22×C11—84no—
168C22×C11—82no—
169C22×C11—164no—
170C22×C11#45314yes—
171C22×C11#45412yes—
172C22×C11C2×#12011yescharacteristic
173C2×D11—44no—
174C2×D11—44no—
175C2×D11—44no—
176C2×D11—88no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—44no—
182Dic11—44no—
183C22×Q8—112no—
184C22×D4—22no—
185C22×D4—21no—
186C22×D4—112no—
187C22×D4—222no—
188C23×C4—222no—
189C2×SD16—228no—
190C2×SD16—448no—
191C2×D8—228no—
192C2×D8—448no—
193C22×C8—21no—
194C22×C8—222no—
195#127—22no—
196#127—21no—
197#127C22×D1112yes—
198#125—22no—
199#125C22⋊D1112yes—
200#125C22×D1112yes—
201#124—114no—
202#124—114no—
203#124—222no—
204#124—222no—
205#123—228no—
206#123—228no—
207C22⋊Q8—228no—
208C22⋊Q8—228no—
209#121—228no—
210#121—228no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—222no—
213C2×C4⋊C4C22⋊D1112yes—
214C2×C22⋊C4—222no—
215C2×C22⋊C4—222no—
216C2×C22⋊C4—222no—
217C2×C42C22×D1111yescharacteristic
218#102—28no—
219#97—21no—
220#97—114no—
221#97—222no—
222#97C22×D1112yes—
223C2×C11—162no—
224C2×C11#165614yescomplemented
225C2×C11C2×#45312yes—
226C2×C11C2×#45411yescharacteristic
227D11—84no—
228C24—41no—
229C24—222no—
230C2×Q8—114no—
231C2×Q8—222no—
232C2×Q8—444no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—44no—
236C2×D4—44no—
237C2×D4—44no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—114no—
241C2×D4—228no—
242C2×D4—222no—
243C2×D4—444no—
244C2×D4—884no—
245C22×C4—22no—
246C22×C4—228no—
247C22×C4—222no—
248C22×C4—884no—
249C22×C4D4×D1112yes—
250C22×C4C2×C22⋊D1111yescharacteristic
251SD16—4416no—
252D8—4416no—
253C2×C8—22no—
254C2×C8—42no—
255C2×C8—228no—
256C2×C8—224no—
257C4⋊C4—24no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—228no—
261C4⋊C4C2×C22⋊D1114yes—
262C22⋊C4—228no—
263C22⋊C4—224no—
264C22⋊C4—224no—
265C22⋊C4—224no—
266C22⋊C4—224no—
267C42D4×D1112yes—
268C42C2×C22⋊D1111yescharacteristic
269C42C23×D1111yescharacteristic
270C11C2×#165611yescharacteristic, complemented, Sylow
271C23—42no—
272C23—84no—
273C23—82no—
274C23—224no—
275C23—444no—
276C23—444no—
277C23—444no—
278C23#6699011yescharacteristic
279Q8—444no—
280Q8—882no—
281D4—44no—
282D4—44no—
283D4—44no—
284D4—84no—
285D4—82no—
286D4—444no—
287D4—882no—
288D4—888no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—24no—
292C2×C4—44no—
293C2×C4—224no—
294C2×C4—444no—
295C2×C4—888no—
296C2×C4#6699011yescharacteristic
297C2×C4#6699012yes—
298C2×C4C2×D4×D1112yes—
299C2×C4C22×C22⋊D1111yescharacteristic
300C8—42no—
301C8—228no—
302C22—84no—
303C22—82no—
304C22—164no—
305C22—444no—
306C22—444no—
307C22—444no—
308C22—888no—
309C22#1062267512yes—
310C22#1062281114yes—
311C22C2×#6699011yescharacteristic
312C4—22no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—444no—
318C2—162no—
319C2—884no—
320C2#1306790814yesdirect product factor
321C2C2×#1062281112yes—
322C2C2×#1062267511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#490C2
socleC23×C11#120
hypercenterC2×#490D11
hypocenterC11C2×#1656
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#10623231C2semidirect
2. C2×#10622687C2semidirect
3. #13067908C2direct (N × H)
4. C2×#10622181C2semidirect
5. C2×#10622102C2semidirect
6. C2×C11×#490C2semidirect
13. #10623231C22semidirect
19. C11×#490C22semidirect
23. #10622687C22semidirect
25. #10622181C22semidirect
26. #10622102C22semidirect
112. C2×#490D11semidirect
161. #490C2×D11semidirect
224. C2×C11#1656semidirect
270. C11C2×#1656semidirect
320. C2#13067908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232312
C2×#106226872
#130679082
C2×#106221812
C2×#106221022
C2×C11×#4902
C2×#165611