Finite Group Databasebeta

← #14910222

Subgroups — #14910222

Order 2816.

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

normal subgroups only

This group has 488 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#13079255C212yesmaximal, complemented
2#13070764C212yesmaximal, complemented
3#13070759C212yesmaximal, complemented
4#13070724C211yesmaximal, characteristic, complemented
5#13070719C211yesmaximal, characteristic
6#13070712C212yesmaximal, complemented
7#13070679C212yesmaximal, complemented
8#13070672C212yesmaximal, complemented
9C11×#2151C211yesmaximal, characteristic, complemented
10#10623065—22no—
11C2×C11×M32C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C11×#405C2211yescharacteristic
14#10622747—22no—
15#10622729C2212yes—
16#10622728C2212yes—
17C2×Dic88C2211yescharacteristic
18C2×#66864C2212yes—
19C2×D176C2211yescharacteristic
20#10622327—22no—
21#10622323—22no—
22C4×Dic44C2212yes—
23#10622309C2212yes—
24C4×D88C2212yes—
25#10622295C2212yes—
26C11×C4⋊C16C2212yes—
27C11×C4⋊C16C2212yes—
28#10622147C2212yes—
29#10622147C2212yes—
30#10622143C2212yes—
31#10622143C2211yescharacteristic
32#10622143C2211yescharacteristic
33#10622141C2212yes—
34#10622141C2212yes—
35C2×C11×M16D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C11×#117D411yescharacteristic
38#66983—22no—
39#66977—22no—
40C2×Dic44C2312yes—
41C2×D88C2312yes—
42C2×#4314—22no—
43#66951—42no—
44#66949—42no—
45#66938—42no—
46#66936—42no—
47#66928—22no—
48C4×D44—22no—
49#66922—22no—
50C4×Dic22—22no—
51C11×M32—41no—
52C2×C11×C16—41no—
53C2×C11×C16C2312yes—
54C2×C11×C16C2311yescharacteristic
55C2×C11×C16C2311yescharacteristic
56C11×#97D412yes—
57C4×C8×C11C2312yes—
58#66885—22no—
59#66885—22no—
60#66882—22no—
61#66882C2312yes—
62#66882C2312yes—
63#66880—22no—
64#66880—22no—
65Dic88—41no—
66#66864—42no—
67D176—41no—
68#33829—111nomaximal, Sylow
69C22×C4×C11C2×D411yescharacteristic
70C2×C22⋊D11—42no—
71C2×D44—22no—
72C2×C4×D11—42no—
73C2×Dic22—22no—
74C2×Dic22—42no—
75C11×M16—41no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11C2×D411yescharacteristic
79C2×C8×C11C2×D412yes—
80C2×C8×C11C2411yescharacteristic
81C11×C4⋊C4D812yes—
82C11×C22⋊C4D811yescharacteristic
83C11×C22⋊C4D811yescharacteristic
84C42×C11C2×D412yes—
85C22⋊Dic11—42no—
86(C2×D11)⋊C4—42no—
87(C2×D11)⋊C4—42no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—42no—
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—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#3175—112no—
105#2226—112no—
106#2225—112no—
107#2219—111no—
108#2218—111no—
109#2217—112no—
110#2211—112no—
111#2210—112no—
112#2151D1111yescharacteristic, complemented
113C23×C11C2×D811yescharacteristic
114C22×D11—42no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D812yes—
118C2×C4×C11C2×D811yescharacteristic
119C2×C4×C11C2×D812yes—
120C2×C4×C11C22×D411yescharacteristic
121C22⋊D11—162no—
122C2×Dic11—42no—
123C2×Dic11—42no—
124C2×Dic11—42no—
125D44—42no—
126D44—42no—
127C4×D11—162no—
128Dic22—42no—
129Dic22—42no—
130Dic22—162no—
131C8×C11—21no—
132C8×C11—22no—
133C8×C11H(5,𝔽2)11yescharacteristic
134C8×C112−1+411yescharacteristic
135#542—222no—
136C2×Q32—111no—
137C2×SD32—112no—
138C2×D16—111no—
139C2×M32C2×D1111yescharacteristic
140C22×C16C2×D1111yescharacteristic
141#500—112no—
142#495—112no—
143#489—222no—
144#468—222no—
145#467—112no—
146#466—112no—
147#440—222no—
148C4×Q16—112no—
149C4×D8—112no—
150#405C2×D1111yescharacteristic
151#367—112no—
152#367—111no—
153#367—111no—
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—
177C2×M16D4411yescharacteristic
178C22×C8C22×D1111yescharacteristic
179C4⋊Q8—222no—
180#126—442no—
181#124—222no—
182#124—442no—
183#123—442no—
184C22⋊Q8—222no—
185C22⋊Q8—442no—
186#121—222no—
187C4×Q8—222no—
188C4×D4—222no—
189#117D4411yescharacteristic
190Q32—441no—
191SD32—442no—
192D16—441no—
193M32—41no—
194C2×C16—41no—
195C2×C16C22×D1111yescharacteristic
196C2×C16C22×D1112yes—
197C2×C16C22×D1111yescharacteristic
198#107—112no—
199#107—112no—
200#107—222no—
201#103—222no—
202#103—222no—
203#102—222no—
204#102—222no—
205#97D4412yes—
206C4×C8C22×D1112yes—
207C2×C11—41no—
208C2×C11#324511yescharacteristic
209C2×C11#341612yes—
210D11—162no—
211C2×Q8—222no—
212C2×Q8—442no—
213C2×D4—222no—
214C2×D4—442no—
215C22×C4—442no—
216C22×C4C2×D4411yescharacteristic
217Q16—222no—
218Q16—222no—
219SD16—444no—
220D8—222no—
221D8—222no—
222M16—41no—
223C2×C8—21no—
224C2×C8—21no—
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⋊C4D8812yes—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C22⋊C4—442no—
239C22⋊C4D8811yescharacteristic
240C22⋊C4D8811yescharacteristic
241C42—442no—
242C42C2×D4412yes—
243C16—22no—
244C16—21no—
245C16—21no—
246C11#3382911yescharacteristic, complemented, Sylow
247C23—442no—
248C23C2×D8811yescharacteristic
249Q8—442no—
250Q8—442no—
251Q8—1762no—
252D4—442no—
253D4—442no—
254D4—1762no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—442no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4—1762no—
261C2×C4C2×D8812yes—
262C2×C4C2×D8812yes—
263C2×C4C2×D8811yescharacteristic
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#1308176412yes—
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2151C2
socleC22×C11C22×D8
prime radical#13070719C2
hypercenter#2151D11
hypocenterC11#33829
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2151

Complements

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

NH ≅ G/Ntype
1. #13079255C2semidirect
2. #13070764C2semidirect
3. #13070759C2semidirect
4. #13070724C2semidirect
6. #13070712C2semidirect
7. #13070679C2semidirect
8. #13070672C2semidirect
9. C11×#2151C2semidirect
112. #2151D11semidirect
246. C11#33829semidirect

Maximal subgroups

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

subgroupindex
#130792552
#130707642
#130707592
#130707242
#130707192
#130707122
#130706792
#130706722
C11×#21512
#3382911