Finite Group Databasebeta

← C2×#13066774 #14674053

Subgroups — C2×#13066774 #14674053

Order 2816.

468 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 75 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×#10622671C211yesmaximal, characteristic
2C2×#10622179C211yesmaximal, characteristic, complemented
3#13066774C214yesmaximal, direct product factor
4C2×C11×#355C211yesmaximal, characteristic, complemented
5C2×C11×#124C2211yescharacteristic
6C22×#4325—21no—
7C22×#4323—21no—
8C2×#66927C411yescharacteristic, complemented
9C2×C11×#101—21no—
10C2×#66898—21no—
11#10622671—21no—
12#10622671—21no—
13#10622671C412yescomplemented
14#10622671C2212yes—
15C2×#66867C411yescharacteristic, complemented
16C11×#355—21no—
17C11×#355C2212yescomplemented
18#10622179—21no—
19#10622179C2212yescomplemented
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11D411yescharacteristic
22C22×D44—21no—
23C22×D44—41no—
24C2×C11×M16—41no—
25C11×#124—41no—
26C11×#124C2×C411yescharacteristic
27C11×#124D411yescharacteristic
28C11×#124D411yescharacteristic
29C11×#124C2311yescharacteristic
30C2×C11×C22⋊C4—41no—
31C2×C42×C11C2×C411yescharacteristic
32C2×C22⋊Dic11—41no—
33C2×#4325—22no—
34C2×#4325—22no—
35C2×#4325—42no—
36C2×#4325—42no—
37C2×#4323—22no—
38C2×#4323—22no—
39C2×#4323—42no—
40C2×#4323—42no—
41C22×C11⋊C8—21no—
42#66927—21no—
43#66927—41no—
44#66927C2×C412yescomplemented
45C11×#101—22no—
46C11×#101—41no—
47#66898—22no—
48#66898—41no—
49#66867—21no—
50#66867C2×C412yescomplemented
51C2×#1406—111nomaximal, Sylow
52C24×C11—21no—
53C23×D11—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—41no—
61C2×D4×C11—41no—
62C2×D4×C11C22⋊C411yescharacteristic
63C2×D4×C11C2×D411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C22⋊C411yescharacteristic
67C22×Dic11—81no—
68C2×D44—22no—
69C2×D44—42no—
70C2×D44—42no—
71C2×D44—41no—
72C2×D44—41no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—84no—
77C11×M16—42no—
78C11×M16—81no—
79C2×C8×C11—81no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C42×C11—21no—
85C42×C11C22⋊C411yescharacteristic
86C42×C11C22×C411yescharacteristic
87C22⋊Dic11—42no—
88C22⋊Dic11—81no—
89#4325—44no—
90#4325—44no—
91#4323—44no—
92#4323—44no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—22no—
95C2×C11⋊C8—22no—
96C2×#496—111no—
97C2×#355D1111yescharacteristic, complemented
98C2×#354—111no—
99#1406—114no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—41no—
103C23×C11—41no—
104C23×C11—82no—
105C23×C11#9911yescharacteristic
106C22×D11—42no—
107C22×D11—84no—
108C22×D11—81no—
109C22×D11—81no—
110Q8×C11—41no—
111Q8×C11—41no—
112Q8×C11—81no—
113D4×C11—41no—
114D4×C11—41no—
115D4×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11#9911yescharacteristic
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×Dic11—82no—
128C2×Dic11—162no—
129D44—42no—
130D44—42no—
131D44—81no—
132D44—81no—
133D44—84no—
134D44—84no—
135C8×C11—82no—
136C11⋊C8—24no—
137C22×SD16—221no—
138C22×D8—221no—
139C2×#127—111no—
140C2×#124C2×D1111yescharacteristic
141#496—112no—
142#496—112no—
143#496—221no—
144#496—221no—
145C2×#101—21no—
146C2×#99—221no—
147C2×#97—111no—
148#355—21no—
149#355C2×D1112yescomplemented
150#354—112no—
151#354—221no—
152C22×C11—22no—
153C22×C11—41no—
154C22×C11—41no—
155C22×C11—81no—
156C22×C11—81no—
157C22×C11—82no—
158C22×C11—161no—
159C22×C11#35311yescharacteristic
160C22×C11#35311yescharacteristic
161C22×C11C2×#9911yescharacteristic
162C2×D11—84no—
163C2×D11—82no—
164C2×D11—162no—
165C2×D11—162no—
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—221no—
175C22×D4—441no—
176C22×D4D4411yescharacteristic
177C2×SD16—222no—
178C2×SD16—222no—
179C2×SD16—442no—
180C2×SD16—442no—
181C2×D8—222no—
182C2×D8—222no—
183C2×D8—442no—
184C2×D8—442no—
185C2×M16—41no—
186C22×C8—221no—
187#127—112no—
188#127—221no—
189#127—441no—
190#124—41no—
191#124C4×D1111yescharacteristic
192#124D4411yescharacteristic
193#124C22⋊D1111yescharacteristic
194#124C22×D1111yescharacteristic
195C2×C22⋊C4—41no—
196C2×C22⋊C4—441no—
197C2×C42C4×D1111yescharacteristic
198#101—22no—
199#101—41no—
200#99—222no—
201#99—441no—
202#97—112no—
203#97—221no—
204C2×C11—21no—
205C2×C11—21no—
206C2×C11—81no—
207C2×C11—81no—
208C2×C11#140612yescomplemented
209C2×C11C2×#35311yescharacteristic
210D11—162no—
211C24—21no—
212C24—441no—
213C2×Q8—21no—
214C2×Q8—41no—
215C2×Q8—41no—
216C2×Q8(C2×D11)⋊C411yescharacteristic
217C2×Q8C2×C22⋊D1111yescharacteristic
218C2×D4—21no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—222no—
222C2×D4—441no—
223C2×D4—441no—
224C2×D4—441no—
225C2×D4—441no—
226C2×D4—442no—
227C2×D4—442no—
228C2×D4—441no—
229C2×D4—884no—
230C2×D4(C2×D11)⋊C411yescharacteristic
231C2×D4C2×D4411yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—881no—
235C22×C4(C2×D11)⋊C411yescharacteristic
236SD16—444no—
237SD16—444no—
238D8—444no—
239D8—444no—
240M16—42no—
241M16—81no—
242C2×C8—81no—
243C2×C8—222no—
244C2×C8—222no—
245C2×C8—222no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—442no—
251C22⋊C4—881no—
252C42—21no—
253C42(C2×D11)⋊C411yescharacteristic
254C42C2×C4×D1111yescharacteristic
255C11C2×#140611yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—82no—
261C23—442no—
262C23—884no—
263C23—881no—
264C23—881no—
265C23#6687011yescharacteristic
266Q8—41no—
267Q8—41no—
268Q8—81no—
269D4—41no—
270D4—41no—
271D4—81no—
272D4—442no—
273D4—442no—
274D4—881no—
275D4—881no—
276D4—884no—
277D4—884no—
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#6687011yescharacteristic
290C2×C4C2×(C2×D11)⋊C411yescharacteristic
291C8—82no—
292C8—224no—
293C22—22no—
294C22—41no—
295C22—41no—
296C22—81no—
297C22—81no—
298C22—82no—
299C22—161no—
300C22—884no—
301C22—882no—
302C22—1762no—
303C22—1762no—
304C22#1062211211yescharacteristic
305C22#1062211211yescharacteristic
306C22C2×#6687011yescharacteristic
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—1762no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—81no—
318C2—1762no—
319C2#1306677412yesdirect product factor
320C2C2×#1062211211yescharacteristic
subgroupG/H
centerC22#10622112
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC2×C11×#355C2
socleC22×C11#353
prime radicalC2×#10622671C2
cosocleC11×#124C23
hypercenterC2×#355D11
hypocenterC11C2×#1406
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
2. C2×#10622179C2semidirect
3. #13066774C2direct (N × H)
4. C2×C11×#355C2semidirect
8. C2×#66927C4semidirect
13. #10622671C4semidirect
15. C2×#66867C4semidirect
17. C11×#355C22semidirect
19. #10622179C22semidirect
44. #66927C2×C4semidirect
50. #66867C2×C4semidirect
97. C2×#355D11semidirect
149. #355C2×D11semidirect
208. C2×C11#1406semidirect
255. C11C2×#1406semidirect
319. C2#13066774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226712
C2×#106221792
#130667742
C2×C11×#3552
C2×#140611