Finite Group Databasebeta

← #14674151

Subgroups — #14674151

Order 2816.

334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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#13079002C211yesmaximal, characteristic
2C2×#10622179C211yesmaximal, characteristic
3#13066792C214yesmaximal, complemented
4C2×C11×#355C211yesmaximal, characteristic
5C2×C11×#124C2211yescharacteristic
6#10623001C411yescharacteristic, complemented
7C2×C11×#101—21no—
8#10622838—21no—
9C2×#66898—21no—
10#10622828—21no—
11#10622669C412yescomplemented
12#10622669C2212yes—
13#10622668—21no—
14#10622668—21no—
15C4×#4318C411yescharacteristic, complemented
16C11×#355—21no—
17C11×#355C2212yes—
18#10622179—21no—
19#10622179C2212yes—
20C22×Q8×C11D411yescharacteristic
21C22×D4×C11D411yescharacteristic
22C2×C11×M16—41no—
23C11×#124—41no—
24C11×#124C2×C411yescharacteristic
25C11×#124D411yescharacteristic
26C11×#124D411yescharacteristic
27C11×#124C2311yescharacteristic
28C2×C11×C22⋊C4—41no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C22⋊Dic11—41no—
31#66979—21no—
32#66977—41no—
33C2×#4318—21no—
34#66923C2×C412yescomplemented
35#66922—21no—
36C4×Dic22—41no—
37C11×#101—22no—
38C11×#101—41no—
39#66899—22no—
40#66899—22no—
41#66898—22no—
42#66898—41no—
43#66896—22no—
44#66896—22no—
45#66867—21no—
46C4×C11⋊C8C2×C412yescomplemented
47#13603—111nomaximal, Sylow
48C24×C11—21no—
49C2×Q8×C11—21no—
50C2×Q8×C11—41no—
51C2×Q8×C11—41no—
52C2×Q8×C11C22⋊C411yescharacteristic
53C2×Q8×C11C2×D411yescharacteristic
54C2×D4×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11C22⋊C411yescharacteristic
58C2×D4×C11C2×D411yescharacteristic
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22⋊C411yescharacteristic
62C22×Dic11—81no—
63C2×Dic22—41no—
64C11×M16—42no—
65C11×M16—81no—
66C2×C8×C11—81no—
67C11×C22⋊C4—41no—
68C11×C22⋊C4—41no—
69C11×C22⋊C4—41no—
70C11×C22⋊C4—41no—
71C42×C11—21no—
72C42×C11C22⋊C411yescharacteristic
73C42×C11C22×C411yescharacteristic
74C22⋊Dic11—42no—
75C22⋊Dic11—41no—
76C22⋊Dic11—81no—
77C4⋊Dic11—22no—
78C4⋊Dic11—41no—
79Dic11⋊C4—42no—
80C4×Dic11—41no—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—22no—
84#3140—111no—
85C2×#355D1111yescharacteristic
86C2×#354—111no—
87#1414—114no—
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—41no—
91C23×C11—41no—
92C23×C11—82no—
93C23×C11#9911yescharacteristic
94Q8×C11—41no—
95Q8×C11—41no—
96Q8×C11—81no—
97D4×C11—41no—
98D4×C11—41no—
99D4×C11—81no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—81no—
109C2×C4×C11#9911yescharacteristic
110C2×C4×C11C2×C22⋊C411yescharacteristic
111C2×Dic11—42no—
112C2×Dic11—82no—
113C2×Dic11—162no—
114Dic22—82no—
115C8×C11—82no—
116C11⋊C8—42no—
117#533—111no—
118C2×#124C2×D1111yescharacteristic
119#489—221no—
120#489—221no—
121#488—112no—
122#488—112no—
123#419—221no—
124#418—221no—
125C2×#101—21no—
126C2×#99—221no—
127C4×M16—111no—
128#355—21no—
129#355C2×D1112yes—
130#354—112no—
131#354—221no—
132C22×C11—41no—
133C22×C11—41no—
134C22×C11—41no—
135C22×C11—81no—
136C22×C11—81no—
137C22×C11—82no—
138C22×C11—161no—
139C22×C11#35411yescharacteristic
140C22×C11#35411yescharacteristic
141C22×C11C2×#9911yescharacteristic
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—41no—
145C4×C11—41no—
146C4×C11—41no—
147C4×C11—41no—
148Dic11—82no—
149Dic11—162no—
150C22×Q8C22⋊D1111yescharacteristic
151C22×D4D4411yescharacteristic
152C2×M16—41no—
153C2×M16—221no—
154C4⋊Q8—221no—
155#125—112no—
156#124—41no—
157#124C4×D1111yescharacteristic
158#124D4411yescharacteristic
159#124C22⋊D1111yescharacteristic
160#124C22×D1111yescharacteristic
161C22⋊Q8—441no—
162C4×Q8—441no—
163#117—221no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—441no—
166C2×C42C4×D1111yescharacteristic
167#103—222no—
168#103—222no—
169#102—222no—
170#102—222no—
171#101—22no—
172#101—41no—
173#99—222no—
174#99—441no—
175#97—221no—
176C4×C8—112no—
177C2×C11—21no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—81no—
181C2×C11—81no—
182C2×C11C2×#35411yescharacteristic
183C24—21no—
184C2×Q8—21no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—441no—
188C2×Q8(C2×D11)⋊C411yescharacteristic
189C2×Q8C2×C22⋊D1111yescharacteristic
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4(C2×D11)⋊C411yescharacteristic
194C2×D4C2×D4411yescharacteristic
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—881no—
198C22×C4(C2×D11)⋊C411yescharacteristic
199M16—42no—
200M16—81no—
201M16—441no—
202M16—441no—
203C2×C8—81no—
204C2×C8—222no—
205C4⋊C4—222no—
206C4⋊C4—442no—
207C4⋊C4—441no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—441no—
213C22⋊C4—442no—
214C22⋊C4—881no—
215C42—21no—
216C42—441no—
217C42(C2×D11)⋊C411yescharacteristic
218C42C2×C4×D1111yescharacteristic
219C11#1360311yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—41no—
223C23—41no—
224C23—82no—
225C23#6687011yescharacteristic
226Q8—41no—
227Q8—41no—
228Q8—81no—
229Q8—882no—
230D4—41no—
231D4—41no—
232D4—81no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—442no—
243C2×C4—882no—
244C2×C4—1762no—
245C2×C4#6687011yescharacteristic
246C2×C4C2×(C2×D11)⋊C411yescharacteristic
247C8—82no—
248C8—442no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—81no—
253C22—81no—
254C22—82no—
255C22—161no—
256C22#1062211111yescharacteristic
257C22#1062211111yescharacteristic
258C22C2×#6687011yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—882no—
266C4—1762no—
267C2—21no—
268C2—21no—
269C2—21no—
270C2—81no—
271C2—81no—
272C2C2×#1062211111yescharacteristic
subgroupG/H
centerC2C2×#10622111
commutatorC42×C11C22×C4
Frattini#124C22×D11
FittingC2×C11×#355C2
socleC2×C11C2×#354
prime radicalC22×D4×C11D4
cosocleC11×#124C23
hypercenterC2×#355D11
hypocenterC11#13603
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
3. #13066792C2semidirect
6. #10623001C4semidirect
11. #10622669C4semidirect
15. C4×#4318C4semidirect
34. #66923C2×C4semidirect
46. C4×C11⋊C8C2×C4semidirect
219. C11#13603semidirect

Maximal subgroups

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

subgroupindex
#130790022
C2×#106221792
#130667922
C2×C11×#3552
#1360311