Finite Group Databasebeta

← C2×#13066773 #14674052

Subgroups — C2×#13066773 #14674052

Order 2816.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10622180C211yesmaximal, characteristic, complemented
2C2×#10622179C211yesmaximal, characteristic, complemented
3#13066773C214yesmaximal, direct product factor
4C2×C11×#496C211yesmaximal, characteristic
5C22×C11×SD16—21no—
6C22×C11×D8—21no—
7C2×C11×#127C411yescharacteristic, complemented
8C2×C11×#124C2211yescharacteristic
9C11×#496—21no—
10C11×#496—21no—
11C11×#496C412yescomplemented
12C11×#496C2212yes—
13C2×C11×#97C411yescharacteristic, complemented
14C2×#66900—21no—
15C2×#66898—21no—
16#10622180—21no—
17#10622180C2212yescomplemented
18#10622179—21no—
19#10622179C2212yescomplemented
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11—21no—
22C22×D4×C11—41no—
23C22×D4×C11D411yescharacteristic
24C2×C11×SD16—22no—
25C2×C11×SD16—22no—
26C2×C11×SD16—42no—
27C2×C11×SD16—42no—
28C2×C11×D8—22no—
29C2×C11×D8—22no—
30C2×C11×D8—42no—
31C2×C11×D8—42no—
32C22×C8×C11—21no—
33C11×#127—21no—
34C11×#127—41no—
35C11×#127C2×C412yescomplemented
36C11×#124—41no—
37C11×#124C2×C411yescharacteristic
38C11×#124D411yescharacteristic
39C11×#124D411yescharacteristic
40C11×#124C2311yescharacteristic
41C2×C11×C22⋊C4—41no—
42C2×C42×C11C2×C411yescharacteristic
43C2×C22⋊Dic11—41no—
44C2×#4318—41no—
45C11×#97—21no—
46C11×#97C2×C412yescomplemented
47#66900—22no—
48#66900—41no—
49#66898—22no—
50#66898—41no—
51C2×#1406—111nomaximal, Sylow
52C24×C11—21no—
53C24×C11—41no—
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Q8×C11—41no—
57C2×Q8×C11C22⋊C411yescharacteristic
58C2×Q8×C11C2×D411yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—42no—
68C2×D4×C11—42no—
69C2×D4×C11—41no—
70C2×D4×C11—84no—
71C2×D4×C11C22⋊C411yescharacteristic
72C2×D4×C11C2×D411yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×Dic11—81no—
77C11×SD16—44no—
78C11×SD16—44no—
79C11×D8—44no—
80C11×D8—44no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11—22no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11C22⋊C411yescharacteristic
90C42×C11C22×C411yescharacteristic
91C22⋊Dic11—42no—
92C22⋊Dic11—81no—
93#4318—42no—
94#4318—81no—
95C2×C11⋊C8—81no—
96C2×#496D1111yescharacteristic
97C2×#355—111no—
98C2×#354—111no—
99#1406—114no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—42no—
105C23×C11—82no—
106C23×C11—84no—
107C23×C11—81no—
108C23×C11—81no—
109C23×C11#9911yescharacteristic
110Q8×C11—41no—
111Q8×C11—41no—
112Q8×C11—81no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—42no—
116D4×C11—42no—
117D4×C11—81no—
118D4×C11—81no—
119D4×C11—81no—
120D4×C11—84no—
121D4×C11—84no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—42no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×Dic11—82no—
134C2×Dic11—162no—
135C8×C11—24no—
136C11⋊C8—82no—
137C22×SD16—21no—
138C22×D8—21no—
139C2×#127Dic1111yescharacteristic, complemented
140C2×#124C2×D1111yescharacteristic
141#496—21no—
142#496—21no—
143#496Dic1112yescomplemented
144#496C2×D1112yes—
145C2×#101—221no—
146C2×#99—221no—
147C2×#97Dic1111yescharacteristic, complemented
148#355—112no—
149#355—221no—
150#354—112no—
151#354—221no—
152C22×C11—22no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11—84no—
158C22×C11—82no—
159C22×C11—82no—
160C22×C11—161no—
161C22×C11—162no—
162C22×C11—162no—
163C22×C11#35311yescharacteristic
164C22×C11#35311yescharacteristic
165C22×C11C2×#9911yescharacteristic
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11—41no—
172Dic11—162no—
173C22×Q8C22⋊D1111yescharacteristic
174C22×D4—21no—
175C22×D4—41no—
176C22×D4C22⋊D1111yescharacteristic
177C2×SD16—22no—
178C2×SD16—22no—
179C2×SD16—42no—
180C2×SD16—42no—
181C2×D8—22no—
182C2×D8—22no—
183C2×D8—42no—
184C2×D8—42no—
185C2×M16—441no—
186C22×C8—21no—
187#127—21no—
188#127—41no—
189#127C2×Dic1112yescomplemented
190#124—41no—
191#124C2×Dic1111yescharacteristic
192#124C22⋊D1111yescharacteristic
193#124C22⋊D1111yescharacteristic
194#124C22×D1111yescharacteristic
195C2×C22⋊C4—41no—
196C2×C22⋊C4—441no—
197C2×C42C2×Dic1111yescharacteristic
198#101—222no—
199#101—441no—
200#99—222no—
201#99—441no—
202#97—21no—
203#97C2×Dic1112yescomplemented
204C2×C11—21no—
205C2×C11—21no—
206C2×C11—81no—
207C2×C11—81no—
208C2×C11—162no—
209C2×C11#140612yescomplemented
210C2×C11C2×#35311yescharacteristic
211C24—21no—
212C24—41no—
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8C22⋊Dic1111yescharacteristic
217C2×Q8C2×C22⋊D1111yescharacteristic
218C2×D4—21no—
219C2×D4—22no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—41no—
229C2×D4—84no—
230C2×D4C22⋊Dic1111yescharacteristic
231C2×D4C2×C22⋊D1111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—881no—
235C22×C4C22⋊Dic1111yescharacteristic
236SD16—44no—
237SD16—44no—
238D8—44no—
239D8—44no—
240M16—442no—
241M16—881no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—881no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—442no—
251C22⋊C4—881no—
252C42—21no—
253C42C22⋊Dic1111yescharacteristic
254C42C22×Dic1111yescharacteristic
255C11C2×#140611yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—42no—
261C23—82no—
262C23—84no—
263C23—81no—
264C23—81no—
265C23#6689811yescharacteristic
266Q8—41no—
267Q8—41no—
268Q8—81no—
269D4—41no—
270D4—41no—
271D4—42no—
272D4—42no—
273D4—81no—
274D4—81no—
275D4—81no—
276D4—84no—
277D4—84no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—882no—
288C2×C4—1762no—
289C2×C4#6689811yescharacteristic
290C2×C4C2×C22⋊Dic1111yescharacteristic
291C8—24no—
292C8—882no—
293C22—22no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22—84no—
299C22—82no—
300C22—82no—
301C22—161no—
302C22—162no—
303C22—162no—
304C22#1062218311yescharacteristic
305C22#1062218311yescharacteristic
306C22C2×#6689811yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1762no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—81no—
318C2—162no—
319C2#1306677312yesdirect product factor
320C2C2×#1062218311yescharacteristic
subgroupG/H
centerC22#10622183
commutatorC42×C11C22×C4
Frattini#124C22×D11
Fitting, prime radicalC2×C11×#496C2
socleC22×C11#353
cosocleC11×#124C23
hypercenterC2×#496D11
hypocenterC11C2×#1406
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#496

Complements

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

NH ≅ G/Ntype
1. C2×#10622180C2semidirect
2. C2×#10622179C2semidirect
3. #13066773C2direct (N × H)
7. C2×C11×#127C4semidirect
11. C11×#496C4semidirect
13. C2×C11×#97C4semidirect
17. #10622180C22semidirect
19. #10622179C22semidirect
35. C11×#127C2×C4semidirect
46. C11×#97C2×C4semidirect
139. C2×#127Dic11semidirect
143. #496Dic11semidirect
147. C2×#97Dic11semidirect
189. #127C2×Dic11semidirect
203. #97C2×Dic11semidirect
209. C2×C11#1406semidirect
255. C11C2×#1406semidirect
319. C2#13066773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221802
C2×#106221792
#130667732
C2×C11×#4962
C2×#140611