Finite Group Databasebeta

← #14910200

Subgroups — #14910200

Order 2816.

464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#13079268C212yesmaximal
2#13070782C212yesmaximal, complemented
3#13070779C212yesmaximal, complemented
4#13070722C212yesmaximal
5#13070707C211yesmaximal, characteristic
6#13070665C212yesmaximal, complemented
7#13070664C212yesmaximal, complemented
8#13070374C211yesmaximal, characteristic
9C11×#2216C211yesmaximal, characteristic
10#10623156—22no—
11C2×C11×Q32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#467C2212yes—
14Q16×Dic11C2212yes—
15#10622794C2212yes—
16C2×#66893C2212yes—
17#10622729C2212yes—
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622665—22no—
21C2×Dic88C2211yescharacteristic
22#10622491C2212yes—
23#10622486C2212yes—
24#10622410—22no—
25#10622402—22no—
26C11×#366C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29#10622142C2211yescharacteristic
30#10622141C2212yes—
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622130C2212yes—
34#10622128C2212yes—
35C2×C11×Q16C2312yes—
36C22×C8×C11C2311yescharacteristic
37C11×C22⋊Q8—22no—
38Q8×Dic11—22no—
39#66997—22no—
40C2×#4326—22no—
41#66979D411yescharacteristic
42#66977—22no—
43C2×#4318D411yescharacteristic
44C2×Dic44C2312yes—
45#66943—22no—
46#66943—42no—
47#66942—42no—
48#66940—22no—
49#66932—42no—
50#66932—42no—
51C11×Q32—41no—
52C2×C11×C16—41no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2311yescharacteristic
55C11×#107C2312yes—
56C11×#103—22no—
57#66899—22no—
58#66893—42no—
59#66882C2312yes—
60#66880—22no—
61#66879D412yes—
62C8×Dic11C2312yes—
63#66876—41no—
64C2×C11⋊C16C2312yes—
65#66874—22no—
66#66872—22no—
67Dic88—41no—
68#33827—111nomaximal, Sylow
69C2×Q8×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C2×Dic22—22no—
72C11×Q16—22no—
73C11×Q16—22no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11C2×D411yescharacteristic
77C2×C8×C11C2411yescharacteristic
78C11×C4⋊C4—22no—
79C11×C4⋊C4—42no—
80C11×C22⋊C4—42no—
81C22⋊Dic11—42no—
82C22⋊Dic11D812yes—
83#4326—44no—
84C4⋊Dic11—22no—
85C4⋊Dic11—42no—
86C4⋊Dic11—42no—
87C4⋊Dic11D811yescharacteristic
88C4⋊Dic11D811yescharacteristic
89Dic11⋊C4—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94C4×Dic11—42no—
95C4×Dic11—42no—
96C4×Dic11C2×D412yes—
97#4318—41no—
98C2×C11⋊C8C2×D412yes—
99Dic44—22no—
100Dic44—22no—
101C11×C16—21no—
102C11×C16—21no—
103C11⋊C16—22no—
104#3177—112no—
105#2229—112no—
106#2229—112no—
107#2219—112no—
108#2216—111no—
109#2216D1111yescharacteristic
110#2209—112no—
111#2209—112no—
112#2151—111no—
113C23×C11C2×D811yescharacteristic
114Q8×C11—42no—
115Q8×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11C22×D411yescharacteristic
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11C2×D812yes—
125C2×Dic11C2×D812yes—
126Dic22—42no—
127Dic22—42no—
128C8×C11—21no—
129C8×C11H(5,𝔽2)11yescharacteristic
130C8×C112−1+411yescharacteristic
131C11⋊C8—22no—
132#541—222no—
133C2×Q32—112no—
134C2×Q32—111no—
135C2×Q32C2×D1111yescharacteristic
136C2×M32—111no—
137C22×C16C2×D1111yescharacteristic
138#499—112no—
139#494—112no—
140#491—222no—
141#470—222no—
142#467—112no—
143#467C2×D1112yes—
144#441—222no—
145C4×Q16—112no—
146C4×Q16—112no—
147#405—111no—
148#367—112no—
149#366—111no—
150#366C2×D1111yescharacteristic
151C4⋊C16—112no—
152C4⋊C16—112no—
153#358—112no—
154#358—112no—
155#358—112no—
156#358C2×D1112yes—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11C22×D811yescharacteristic
161C4×C11—21no—
162C4×C11—82no—
163C4×C11—82no—
164C4×C11#53711yescharacteristic
165C4×C11#57511yescharacteristic
166Dic11—22no—
167Dic11—22no—
168Dic11—82no—
169Dic11—82no—
170C2×Q16—112no—
171C2×Q16—222no—
172C2×Q16C22×D1112yes—
173C2×M16—111no—
174C22×C8C22×D1111yescharacteristic
175C4⋊Q8—222no—
176#126—442no—
177#126—442no—
178#125—222no—
179#125—442no—
180#125—442no—
181C22⋊Q8—22no—
182C22⋊Q8—222no—
183C4×Q8—222no—
184C4×Q8—222no—
185#117—111no—
186Q32—41no—
187Q32—441no—
188Q32—442no—
189M32—441no—
190C2×C16—41no—
191C2×C16—112no—
192C2×C16C22×D1111yescharacteristic
193C2×C16C22×D1111yescharacteristic
194#107—112no—
195#107C22×D1112yes—
196#106—222no—
197#103—22no—
198#103—222no—
199#103—222no—
200#103—222no—
201#97—112no—
202C4×C8—112no—
203C2×C11—41no—
204C2×C11#324511yescharacteristic
205C2×C11#341711yescharacteristic
206C2×C11#341711yescharacteristic
207C2×Q8—22no—
208C2×Q8—222no—
209C22×C4D4×D1111yescharacteristic
210Q16—22no—
211Q16—22no—
212Q16—222no—
213Q16—222no—
214Q16—444no—
215M16—441no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—112no—
219C2×C8D4×D1111yescharacteristic
220C2×C8C23×D1111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—42no—
223C4⋊C4—111no—
224C4⋊C4—111no—
225C4⋊C4—222no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C4⋊C4—442no—
230C4⋊C4—442no—
231C4⋊C4—442no—
232C4⋊C4—442no—
233C22⋊C4—42no—
234C22⋊C4—112no—
235C22⋊C4—442no—
236C42—112no—
237C42—442no—
238C42—442no—
239C16—21no—
240C16—21no—
241C16—222no—
242C11#3382711yescharacteristic, complemented, Sylow
243C23D8×D1111yescharacteristic
244Q8—42no—
245Q8—42no—
246Q8—442no—
247Q8—442no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—112no—
253C2×C4—112no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4D8×D1111yescharacteristic
257C2×C4C2×D4×D1111yescharacteristic
258C8—21no—
259C8—222no—
260C8#6703711yescharacteristic
261C8#6704311yescharacteristic
262C22—21no—
263C22—21no—
264C22—21no—
265C22C2×D8×D1111yescharacteristic
266C4—21no—
267C4—82no—
268C4—82no—
269C4—222no—
270C4—222no—
271C4—882no—
272C4—882no—
273C4#1062312811yescharacteristic
274C4#1062329911yescharacteristic
275C2—41no—
276C2#1307992211yescharacteristic
277C2#1308176511yescharacteristic
278C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2216D11
hypocenterC11#33827
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
2. #13070782C2semidirect
3. #13070779C2semidirect
6. #13070665C2semidirect
7. #13070664C2semidirect
242. C11#33827semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130707822
#130707792
#130707222
#130707072
#130706652
#130706642
#130703742
C11×#22162
#3382711