Finite Group Databasebeta

← #14653184

Subgroups — #14653184

Order 2816.

418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079202C211yesmaximal, characteristic
2#13068302C211yesmaximal, characteristic
3#13067232C212yesmaximal
4#13067129C212yesmaximal
5C11×#1568C211yesmaximal, characteristic
6#10623001C2212yes—
7C11×#432C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622729—21no—
10#10622729—21no—
11C2×#66879—21no—
12C2×C8×Dic11—21no—
13#10622545C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622312C411yescharacteristic, complemented
16C4×Dic44—21no—
17C4×Dic44—21no—
18#10622295C411yescharacteristic, complemented
19#10622294C412yescomplemented
20C11×#335—21no—
21C11×#334—21no—
22#10622105—24no—
23#10622103—24no—
24C22×C8×C11D411yescharacteristic
25C22×C8×C11D411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27#66979—22no—
28#66977—22no—
29#66977—22no—
30C2×C4×Dic11—21no—
31C22×C11⋊C8—21no—
32C2×Dic44—21no—
33C2×Dic44—21no—
34#66923—22no—
35#66922C2×C412yes—
36#66922C2×C412yes—
37C4×Dic22—22no—
38C4×Dic22—22no—
39C11×C4⋊C8—22no—
40C11×C22⋊C8—22no—
41C11×#97—22no—
42C4×C8×C11C2×C411yescharacteristic
43C4×C8×C11C2×C411yescharacteristic
44C4×C8×C11D411yescharacteristic
45C4×C8×C11D411yescharacteristic
46C11⋊#95—21no—
47C11⋊#95D412yes—
48#66882—21no—
49#66882—21no—
50#66880—22no—
51#66880—22no—
52#66879—24no—
53C8×Dic11—24no—
54#66867—21no—
55#66867D412yes—
56#9763—111nomaximal, Sylow
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11#4111yescharacteristic
60C22×Dic11—22no—
61C2×Dic22—22no—
62C2×Dic22—22no—
63C2×C8×C11—22no—
64C2×C8×C11—22no—
65C2×C8×C11—42no—
66C2×C8×C11C22⋊C411yescharacteristic
67C2×C8×C11C22⋊C411yescharacteristic
68C2×C8×C11C22⋊C411yescharacteristic
69C2×C8×C11C22⋊C411yescharacteristic
70C42×C11C22×C411yescharacteristic
71C42×C11C2×D411yescharacteristic
72C42×C11C2×D411yescharacteristic
73C42×C11#4111yescharacteristic
74C22⋊Dic11—42no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79Dic11⋊C4—42no—
80Dic11⋊C4—42no—
81C4×Dic11—22no—
82C4×Dic11—22no—
83C4×Dic11—42no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—22no—
86C2×C11⋊C8—22no—
87Dic44—42no—
88Dic44—42no—
89#3170—111no—
90#1726—111no—
91#1568D1111yescharacteristic
92#1531—112no—
93#1506—112no—
94C23×C11#12111yescharacteristic
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—41no—
99C2×C4×C11C2×C22⋊C411yescharacteristic
100C2×C4×C11C4×D411yescharacteristic
101C2×C4×C11C4×D411yescharacteristic
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12411yescharacteristic
104C2×C4×C11#12711yescharacteristic
105C2×Dic11—24no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—42no—
111Dic22—42no—
112Dic22—82no—
113C8×C11—21no—
114C8×C11—21no—
115C8×C11—82no—
116C8×C11#10412yes—
117C8×C11#10412yes—
118C11⋊C8—24no—
119#533—112no—
120#500—111no—
121#494—111no—
122#487—112no—
123#467—221no—
124#467—221no—
125C4×Q16—221no—
126C4×Q16—221no—
127#432C2×D1112yes—
128C2×#97—111no—
129C2×#97—221no—
130C2×C4×C8—221no—
131C2×C4×C8C2×D1111yescharacteristic
132#376—111no—
133#335—21no—
134#334—21no—
135#330—224no—
136#328—224no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11#39011yescharacteristic
140C22×C11#47312yes—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11C2×#10411yescharacteristic
147C4×C11C2×#10411yescharacteristic
148Dic11—44no—
149Dic11—82no—
150Dic11—82no—
151C2×Q16—221no—
152C2×Q16—221no—
153C22×C8—221no—
154C22×C8D4411yescharacteristic
155C22×C8D4411yescharacteristic
156C4⋊Q8—112no—
157C4⋊Q8—112no—
158#125—222no—
159C22⋊Q8—222no—
160C22⋊Q8—222no—
161C4×Q8—222no—
162C4×Q8—222no—
163#117—222no—
164C2×C42—221no—
165C2×C42C22×D1111yescharacteristic
166#107—221no—
167#107—221no—
168C4⋊C8—22no—
169#103—222no—
170#103—222no—
171C22⋊C8—22no—
172#97—22no—
173#97—112no—
174#97—224no—
175#97—221no—
176C4×C8—224no—
177C4×C8C4×D1111yescharacteristic
178C4×C8C4×D1111yescharacteristic
179C4×C8C22⋊D1111yescharacteristic
180C4×C8C22⋊D1111yescharacteristic
181#95—112no—
182#95—221no—
183C2×C11—22no—
184C2×C11#196211yescharacteristic
185C2×C11#197611yescharacteristic
186C2×C11#197911yescharacteristic
187C2×Q8—222no—
188C2×Q8—222no—
189C22×C4—222no—
190C22×C4C2×D4411yescharacteristic
191C22×C4D4×D1111yescharacteristic
192C22×C4#434311yescharacteristic
193Q16—442no—
194Q16—442no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—42no—
198C2×C8—222no—
199C2×C8—222no—
200C2×C8—222no—
201C2×C8(C2×D11)⋊C411yescharacteristic
202C2×C8(C2×D11)⋊C411yescharacteristic
203C2×C8(C2×D11)⋊C411yescharacteristic
204C2×C8(C2×D11)⋊C411yescharacteristic
205C4⋊C4—222no—
206C4⋊C4—222no—
207C4⋊C4—222no—
208C4⋊C4—222no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C22⋊C4—442no—
212C42—222no—
213C42—222no—
214C42—442no—
215C42C2×C4×D1111yescharacteristic
216C42D4×D1111yescharacteristic
217C42#434311yescharacteristic
218C42C2×C22⋊D1111yescharacteristic
219C11#976311yescharacteristic, complemented, Sylow
220C23#6694811yescharacteristic
221Q8—442no—
222Q8—442no—
223Q8—882no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—224no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—442no—
233C2×C4#6694611yescharacteristic
234C2×C4#6694611yescharacteristic
235C2×C4#6694811yescharacteristic
236C2×C4C2×(C2×D11)⋊C411yescharacteristic
237C2×C4#6699311yescharacteristic
238C2×C4#6700011yescharacteristic
239C8—21no—
240C8—21no—
241C8—82no—
242C8—224no—
243C8#6688912yes—
244C8#6688912yes—
245C22—21no—
246C22—21no—
247C22#1062250912yes—
248C22#1062260111yescharacteristic
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—444no—
255C4—882no—
256C4—882no—
257C4C2×#6688911yescharacteristic
258C4C2×#6688911yescharacteristic
259C2—22no—
260C2#1306944311yescharacteristic
261C2#1306951211yescharacteristic
262C2#1306952911yescharacteristic
subgroupG/H
centerC22#10622601
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1568C2
socleC22×C11#390
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1568D11
hypocenterC11#9763
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
15. #10622312C4semidirect
18. #10622295C4semidirect
19. #10622294C4semidirect
219. C11#9763semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130683022
#130672322
#130671292
C11×#15682
#976311