Finite Group Databasebeta

← #14910202

Subgroups — #14910202

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#13070783C212yesmaximal, complemented
3#13070778C212yesmaximal, complemented
4#13070724C211yesmaximal, characteristic
5#13070705C212yesmaximal
6#13070665C212yesmaximal, complemented
7#13070664C212yesmaximal, complemented
8#13070376C211yesmaximal, characteristic
9C11×#2219C211yesmaximal, characteristic
10#10623156—22no—
11C2×C11×Q32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#467C2212yes—
14Q16×Dic11C2212yes—
15#10622794C2212yes—
16C2×#66893C2212yes—
17#10622729C2212yes—
18#10622714C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20#10622665—22no—
21C2×Dic88C2211yescharacteristic
22#10622491C2212yes—
23#10622486C2212yes—
24#10622410—22no—
25#10622402—22no—
26C11×#367C2211yescharacteristic
27C11×#358C2212yes—
28#10622202C2212yes—
29#10622143C2211yescharacteristic
30#10622141C2212yes—
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622130C2212yes—
34#10622127C2212yes—
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—
52C11×M32—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—
63C2×C11⋊C16—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⋊Dic11D811yescharacteristic
83C22⋊Dic11D811yescharacteristic
84#4326—44no—
85C4⋊Dic11—22no—
86C4⋊Dic11—42no—
87C4⋊Dic11—42no—
88C4⋊Dic11D812yes—
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—111no—
108#2219D1111yescharacteristic
109#2216—112no—
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×M32C2×D1111yescharacteristic
137C22×C16—111no—
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—111no—
149#367C2×D1111yescharacteristic
150#366—112no—
151C4⋊C16—112no—
152C4⋊C16—112no—
153#358—112no—
154#358—112no—
155#358—112no—
156#358C2×D1112yes—
157C22×C11—22no—
158C22×C11—21no—
159C22×C11C22×D811yescharacteristic
160C4×C11—21no—
161C4×C11—82no—
162C4×C11—82no—
163C4×C11#53711yescharacteristic
164C4×C11#57511yescharacteristic
165Dic11—22no—
166Dic11—22no—
167Dic11—82no—
168Dic11—82no—
169C2×Q16—112no—
170C2×Q16—222no—
171C2×Q16C22×D1112yes—
172C2×M16—111no—
173C22×C8C22×D1111yescharacteristic
174C4⋊Q8—222no—
175#126—442no—
176#126—442no—
177#125—222no—
178#125—442no—
179#125—442no—
180C22⋊Q8—22no—
181C22⋊Q8—222no—
182C4×Q8—222no—
183C4×Q8—222no—
184#117—111no—
185Q32—41no—
186Q32—441no—
187Q32—442no—
188M32—41no—
189C2×C16—112no—
190C2×C16—441no—
191C2×C16C22×D1111yescharacteristic
192C2×C16C22×D1111yescharacteristic
193#107—112no—
194#107C22×D1112yes—
195#106—222no—
196#103—22no—
197#103—222no—
198#103—222no—
199#103—222no—
200#97—112no—
201C4×C8—112no—
202C2×C11—41no—
203C2×C11#324511yescharacteristic
204C2×C11#341712yes—
205C2×Q8—22no—
206C2×Q8—222no—
207C22×C4D4×D1111yescharacteristic
208Q16—22no—
209Q16—22no—
210Q16—222no—
211Q16—222no—
212Q16—444no—
213M16—441no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—112no—
217C2×C8D4×D1111yescharacteristic
218C2×C8C23×D1111yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—112no—
222C4⋊C4—222no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C4⋊C4—442no—
226C4⋊C4—442no—
227C4⋊C4—442no—
228C4⋊C4—442no—
229C4⋊C4—442no—
230C22⋊C4—42no—
231C22⋊C4—111no—
232C22⋊C4—111no—
233C22⋊C4—442no—
234C42—112no—
235C42—442no—
236C42—442no—
237C16—21no—
238C16—21no—
239C16—222no—
240C11#3382711yescharacteristic, complemented, Sylow
241C23D8×D1111yescharacteristic
242Q8—42no—
243Q8—42no—
244Q8—442no—
245Q8—442no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—112no—
251C2×C4—112no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4D8×D1111yescharacteristic
255C2×C4C2×D4×D1111yescharacteristic
256C8—21no—
257C8—222no—
258C8#6703711yescharacteristic
259C8#6704311yescharacteristic
260C22—21no—
261C22—22no—
262C22C2×D8×D1111yescharacteristic
263C4—21no—
264C4—82no—
265C4—82no—
266C4—222no—
267C4—222no—
268C4—882no—
269C4—882no—
270C4#1062312811yescharacteristic
271C4#1062329911yescharacteristic
272C2—41no—
273C2#1307992211yescharacteristic
274C2#1308176812yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2219C2
socleC22×C11C22×D8
prime radicalC23×C11C2×D8
hypercenter#2219D11
hypocenterC11#33827
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2219

Complements

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

NH ≅ G/Ntype
2. #13070783C2semidirect
3. #13070778C2semidirect
6. #13070665C2semidirect
7. #13070664C2semidirect
240. C11#33827semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130707832
#130707782
#130707242
#130707052
#130706652
#130706642
#130703762
C11×#22192
#3382711