Finite Group Databasebeta

← #14664321

Subgroups — #14664321

Order 2816.

292 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 65 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#13079270C211yesmaximal, characteristic
2#13070429C211yesmaximal, characteristic
3#13068372C211yesmaximal, characteristic
4#13066609C211yesmaximal, characteristic
5#13066605C211yesmaximal, characteristic
6#13066604C211yesmaximal, characteristic
7C11×#1342C211yesmaximal, characteristic
8#10623156—21no—
9C11×#470C2211yescharacteristic
10#10622797C411yescharacteristic, complemented
11#10622794C411yescharacteristic, complemented
12#10622750C2211yescharacteristic
13#10622735—21no—
14#10622735C2211yescharacteristic
15#10622664—21no—
16#10622471C411yescharacteristic, complemented
17#10622466C411yescharacteristic, complemented
18#10622410—21no—
19#10622403—21no—
20C11×#349C2211yescharacteristic
21C11×#338C2211yescharacteristic
22#10622195—21no—
23#10622195C2211yescharacteristic
24#10622191C2211yescharacteristic
25#10622150—21no—
26#10622149—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×M16C2311yescharacteristic
30C11×C22⋊Q8—21no—
31Q8×Dic11—21no—
32#66997—21no—
33C2×#4326—21no—
34#66979—21no—
35#66979D411yescharacteristic
36#66977—21no—
37C22×C11⋊C8D411yescharacteristic
38C2×Dic44C2×C411yescharacteristic
39#66943—21no—
40#66943—41no—
41#66942—41no—
42#66940—21no—
43#66932—41no—
44#66932—41no—
45C11×M32—21no—
46C11×#106C2×C411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49#66881C2×C411yescharacteristic
50#66880—21no—
51#66879—22no—
52#66879C2×C411yescharacteristic
53#66879D411yescharacteristic
54C8×Dic11—22no—
55C8×Dic11C2×C411yescharacteristic
56C8×Dic11D411yescharacteristic
57#66876—21no—
58#66874—21no—
59#66871—21no—
60#11771—111nomaximal, Sylow
61C2×Q8×C11—21no—
62C22×C4×C11C2×D411yescharacteristic
63C2×Dic22—21no—
64C11×Q16—41no—
65C11×M16—41no—
66C11×M16—41no—
67C11×M16—41no—
68C2×C8×C11—22no—
69C2×C8×C11C22×C411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C11×C22⋊C4—41no—
74C22⋊Dic11—21no—
75C22⋊Dic11—41no—
76C22⋊Dic11—41no—
77#4326—41no—
78#4326—41no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C4⋊Dic11—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89C4×Dic11—22no—
90C4×Dic11—41no—
91C4×Dic11—41no—
92C4×Dic11C22⋊C411yescharacteristic
93C4×Dic11C22⋊C411yescharacteristic
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98Dic44—41no—
99C11×C16—41no—
100C11⋊C16—41no—
101#3177—111no—
102#2166—111no—
103#1747—111no—
104#1342—111no—
105#1342D1111yescharacteristic
106#1340—111no—
107#1340—111no—
108C23×C11AGL(1,ℤ/8)11yescharacteristic
109Q8×C11—41no—
110Q8×C11—41no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122Dic22—41no—
123Dic22—41no—
124C8×C11—21no—
125C8×C11—21no—
126C8×C11—42no—
127C11⋊C8—21no—
128C11⋊C8#10411yescharacteristic
129C11⋊C8#10411yescharacteristic
130#541—221no—
131#499—111no—
132#494—111no—
133#491—221no—
134#470—111no—
135#470C2×D1111yescharacteristic
136#467—221no—
137#441—111no—
138#441—111no—
139C4×Q16—221no—
140#405—111no—
141#405—221no—
142#364—221no—
143#349—111no—
144#349C2×D1111yescharacteristic
145#347—221no—
146#338C2×D1111yescharacteristic
147H(3,ℤ/4)—111no—
148H(3,ℤ/4)—221no—
149C22×C11—21no—
150C22×C11—41no—
151C22×C11#41811yescharacteristic
152C4×C11—21no—
153C4×C11—81no—
154C4×C11—81no—
155C4×C11#41011yescharacteristic
156C4×C11C2×#10411yescharacteristic
157Dic11—41no—
158Dic11—41no—
159Dic11—81no—
160Dic11—82no—
161Dic11—81no—
162C2×Q16—111no—
163C2×Q16—221no—
164C2×Q16C4×D1111yescharacteristic
165C2×M16—21no—
166C2×M16C22×D1111yescharacteristic
167C22×C8—111no—
168C4⋊Q8—221no—
169#126—441no—
170#126—441no—
171#125—221no—
172#125—441no—
173#125—441no—
174C22⋊Q8—21no—
175C22⋊Q8—221no—
176C4×Q8—221no—
177C4×Q8—221no—
178#117—111no—
179#117—221no—
180M32—21no—
181M32—221no—
182#107—221no—
183#106—111no—
184#106C4×D1111yescharacteristic
185#103—21no—
186#103—221no—
187#103—221no—
188#103—221no—
189#97—111no—
190#97—111no—
191#97—222no—
192C4×C8—111no—
193C4×C8—111no—
194C4×C8—222no—
195C2×C11—21no—
196C2×C11—41no—
197C2×C11#150511yescharacteristic
198C2×Q8—21no—
199C2×Q8—221no—
200C22×C4D4×D1111yescharacteristic
201Q16—41no—
202Q16—441no—
203Q16—441no—
204Q16—441no—
205M16—41no—
206M16—41no—
207M16—41no—
208C2×C8—22no—
209C2×C8—111no—
210C2×C8—111no—
211C2×C8—221no—
212C2×C8—221no—
213C2×C8C2×C4×D1111yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—221no—
218C4⋊C4—221no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C22⋊C4—41no—
228C22⋊C4—221no—
229C22⋊C4—441no—
230C22⋊C4—441no—
231C42—111no—
232C42—111no—
233C42—222no—
234C42—441no—
235C42—441no—
236C16—41no—
237C16—441no—
238C11#1177111yescharacteristic, complemented, Sylow
239C23#6696711yescharacteristic
240Q8—41no—
241Q8—41no—
242Q8—441no—
243Q8—441no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—442no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4C22⋊C4×D1111yescharacteristic
254C2×C4#6696411yescharacteristic
255C8—21no—
256C8—21no—
257C8—42no—
258C8—111no—
259C8—111no—
260C8—221no—
261C22—21no—
262C22—41no—
263C22#1062238311yescharacteristic
264C4—21no—
265C4—81no—
266C4—81no—
267C4—441no—
268C4—441no—
269C4—881no—
270C4—882no—
271C4—881no—
272C4#1062235311yescharacteristic
273C4D11×#10411yescharacteristic
274C2—21no—
275C2—41no—
276C2#1306712211yescharacteristic
subgroupG/H
centerC2#13067122
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1342C2
socleC2×C11#1505
prime radicalC23×C11AGL(1,ℤ/8)
cosocleC2×C11×M16C23
hypercenter#1342D11
hypocenterC11#11771
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1342

Complements

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

NH ≅ G/Ntype
10. #10622797C4semidirect
11. #10622794C4semidirect
16. #10622471C4semidirect
17. #10622466C4semidirect
238. C11#11771semidirect

Maximal subgroups

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

subgroupindex
#130792702
#130704292
#130683722
#130666092
#130666052
#130666042
C11×#13422
#1177111