Finite Group Databasebeta

← #14910152

Subgroups — #14910152

Order 2816.

496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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#13079186C212yesmaximal, complemented
2#13070781C212yesmaximal, complemented
3#13070774C212yesmaximal, complemented
4#13070729C212yesmaximal, complemented
5#13070724C211yesmaximal, characteristic, complemented
6#13070719C211yesmaximal, characteristic
7#13070679C212yesmaximal, complemented
8#13070672C212yesmaximal, complemented
9C11×#2150C211yesmaximal, characteristic, complemented
10#10623010—22no—
11C2×C11×M32C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622729C2212yes—
15#10622728C2212yes—
16#10622727—22no—
17C2×Dic88C2211yescharacteristic
18C2×#66864C2212yes—
19C2×D176C2211yescharacteristic
20C4×Dic44C2212yes—
21#10622310—22no—
22#10622309C2212yes—
23C4×D88C2212yes—
24C4×#4314—22no—
25#10622296C2212yes—
26C11×C4⋊C16C2212yes—
27C11×C4⋊C16C2212yes—
28#10622147C2212yes—
29#10622147C2212yes—
30#10622143C2211yescharacteristic
31#10622143C2211yescharacteristic
32#10622142C2212yes—
33#10622141C2212yes—
34#10622141C2212yes—
35C22×C8×C11D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38#66983—22no—
39#66982—42no—
40C4×C22⋊D11—42no—
41#66977—22no—
42C2×Dic44C2312yes—
43C2×D88C2312yes—
44C2×#4314—22no—
45#66929—42no—
46#66928—22no—
47C4×D44—22no—
48#66925—42no—
49#66923—22no—
50C4×Dic22—22no—
51C11×M32—41no—
52C11×M32—41no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2312yes—
55C2×C11×C16C2311yescharacteristic
56C4×C8×C11D412yes—
57C4×C8×C11C2312yes—
58#66885—22no—
59#66885—22no—
60#66882C2312yes—
61#66882C2312yes—
62#66881—22no—
63#66880—22no—
64#66880—22no—
65Dic88—41no—
66#66864—42no—
67D176—41no—
68#33822—111nomaximal, Sylow
69C22×C4×C11D812yes—
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—42no—
72C2×D44—22no—
73C2×C4×D11—42no—
74C2×Dic22—22no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—41no—
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11C2×D412yes—
80C2×C8×C11C2411yescharacteristic
81C42×C11D811yescharacteristic
82C42×C11D811yescharacteristic
83C42×C11C2×D412yes—
84C22⋊Dic11—42no—
85(C2×D11)⋊C4—42no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95C4×Dic11—42no—
96Dic44—22no—
97Dic44—22no—
98D88—22no—
99D88—22no—
100#4314—44no—
101C11×C16—21no—
102C11×C16—22no—
103C11×C16—21no—
104#3168—112no—
105#2229—112no—
106#2228—112no—
107#2220—112no—
108#2219—111no—
109#2218—111no—
110#2211—112no—
111#2210—112no—
112#2150D1111yescharacteristic, complemented
113C23×C11C2×D811yescharacteristic
114C22×D11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—42no—
118C2×C4×C11C2×D812yes—
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11C2×D812yes—
121C2×C4×C11C22×D411yescharacteristic
122C22⋊D11—84no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125C2×Dic11—42no—
126D44—42no—
127D44—42no—
128C4×D11—84no—
129Dic22—42no—
130Dic22—42no—
131C8×C11—21no—
132C8×C11—22no—
133C8×C11H(5,𝔽2)11yescharacteristic
134C8×C112−1+411yescharacteristic
135#529—222no—
136C2×Q32—111no—
137C2×SD32—112no—
138C2×D16—111no—
139C2×M32C2×D1111yescharacteristic
140C2×M32C2×D1111yescharacteristic
141#499—112no—
142#495—112no—
143#488—222no—
144#467—112no—
145#466—112no—
146#465—222no—
147C4×Q16—112no—
148C4×SD16—222no—
149C4×D8—112no—
150C2×C4×C8C2×D1111yescharacteristic
151#367—111no—
152#367—111no—
153#366—112no—
154C4⋊C16C2×D1112yes—
155C4⋊C16C2×D1112yes—
156#358—112no—
157#358—112no—
158#357—112no—
159#357—112no—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11C22×D811yescharacteristic
163C2×D11—82no—
164C2×D11—82no—
165C2×D11—82no—
166C4×C11—22no—
167C4×C11—22no—
168C4×C11—21no—
169C4×C11#53711yescharacteristic
170C4×C11#57511yescharacteristic
171Dic11—82no—
172Dic11—82no—
173Dic11—82no—
174C2×Q16—112no—
175C2×SD16—222no—
176C2×D8—112no—
177C22×C8D4411yescharacteristic
178C22×C8C22×D1111yescharacteristic
179#126—442no—
180#125—222no—
181#124—222no—
182#123—442no—
183C22⋊Q8—222no—
184#121—222no—
185C4×Q8—222no—
186C4×D4—222no—
187C4×D4—442no—
188#117—442no—
189C2×C42D4411yescharacteristic
190Q32—441no—
191SD32—442no—
192D16—441no—
193M32—41no—
194M32—41no—
195C2×C16C22×D1111yescharacteristic
196C2×C16C22×D1112yes—
197C2×C16C22×D1111yescharacteristic
198#107—112no—
199#107—112no—
200#106—222no—
201#103—222no—
202#103—222no—
203#102—222no—
204#102—222no—
205C4×C8D4412yes—
206C4×C8C22×D1112yes—
207C2×C11—41no—
208C2×C11#324511yescharacteristic
209C2×C11#341412yes—
210D11—162no—
211C2×Q8—222no—
212C2×D4—222no—
213C2×D4—442no—
214C22×C4—442no—
215C22×C4D8812yes—
216C22×C4C2×D4411yescharacteristic
217Q16—222no—
218Q16—222no—
219SD16—444no—
220D8—222no—
221D8—222no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8C2×D4412yes—
226C2×C8C2×D4411yescharacteristic
227C2×C8C23×D1111yescharacteristic
228C4⋊C4—222no—
229C4⋊C4—222no—
230C4⋊C4—442no—
231C4⋊C4—442no—
232C4⋊C4—442no—
233C4⋊C4—442no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C22⋊C4—442no—
239C42—442no—
240C42D8811yescharacteristic
241C42D8811yescharacteristic
242C42C2×D4412yes—
243C16—21no—
244C16—22no—
245C16—21no—
246C11#3382211yescharacteristic, complemented, Sylow
247C23—442no—
248C23C2×D8811yescharacteristic
249Q8—442no—
250Q8—442no—
251D4—442no—
252D4—442no—
253D4—884no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4—884no—
261C2×C4C2×D8812yes—
262C2×C4C2×D8811yescharacteristic
263C2×C4C2×D8812yes—
264C2×C4C22×D4411yescharacteristic
265C8—22no—
266C8—21no—
267C8#6703711yescharacteristic
268C8#6704011yescharacteristic
269C22—21no—
270C22—22no—
271C22—882no—
272C22—882no—
273C22—882no—
274C22C22×D8811yescharacteristic
275C4—21no—
276C4—22no—
277C4—22no—
278C4—882no—
279C4—882no—
280C4—882no—
281C4#1062304111yescharacteristic
282C4#1062327911yescharacteristic
283C2—41no—
284C2—1762no—
285C2#1307992611yescharacteristic
286C2#1308175212yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2150C2
socleC22×C11C22×D8
prime radical#13070719C2
hypercenter#2150D11
hypocenterC11#33822
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2150

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070781C2semidirect
3. #13070774C2semidirect
4. #13070729C2semidirect
5. #13070724C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. C11×#2150C2semidirect
112. #2150D11semidirect
246. C11#33822semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130707812
#130707742
#130707292
#130707242
#130707192
#130706792
#130706722
C11×#21502
#3382211