Finite Group Databasebeta

← #14653194

Subgroups — #14653194

Order 2816.

374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 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#13068367C211yesmaximal, characteristic
3#13067232C212yesmaximal
4#13067129C212yesmaximal
5C11×#1568C211yesmaximal, characteristic
6#10623001C2212yes—
7C11×#432C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622729—21no—
10#10622729—21no—
11#10622545C2211yescharacteristic
12C2×#66867C2211yescharacteristic
13#10622312C411yescharacteristic, complemented
14C4×Dic44—21no—
15C4×Dic44—21no—
16#10622295C411yescharacteristic, complemented
17#10622294C412yescomplemented
18C11×#335—21no—
19C11×#334—21no—
20#10622188—21no—
21#10622188—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#66867—21no—
53#66867D412yes—
54#9765—111nomaximal, Sylow
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—22no—
59C2×Dic22—22no—
60C2×Dic22—22no—
61C2×C8×C11—41no—
62C2×C8×C11—41no—
63C2×C8×C11—42no—
64C2×C8×C11C22⋊C411yescharacteristic
65C2×C8×C11C22⋊C411yescharacteristic
66C2×C8×C11C22⋊C411yescharacteristic
67C2×C8×C11C22⋊C411yescharacteristic
68C42×C11C22×C411yescharacteristic
69C42×C11C2×D411yescharacteristic
70C42×C11C2×D411yescharacteristic
71C42×C11#4111yescharacteristic
72C22⋊Dic11—42no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75C4⋊Dic11—22no—
76C4⋊Dic11—22no—
77Dic11⋊C4—42no—
78Dic11⋊C4—42no—
79C4×Dic11—41no—
80C4×Dic11—41no—
81C4×Dic11—42no—
82C2×C11⋊C8—22no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85Dic44—42no—
86Dic44—42no—
87#3170—111no—
88#1746—111no—
89#1568D1111yescharacteristic
90#1531—112no—
91#1506—112no—
92C23×C11#12111yescharacteristic
93C2×C4×C11—22no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—41no—
97C2×C4×C11C2×C22⋊C411yescharacteristic
98C2×C4×C11C4×D411yescharacteristic
99C2×C4×C11C4×D411yescharacteristic
100C2×C4×C11#12111yescharacteristic
101C2×C4×C11#12411yescharacteristic
102C2×C4×C11#12711yescharacteristic
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108Dic22—42no—
109Dic22—42no—
110Dic22—82no—
111C8×C11—21no—
112C8×C11—21no—
113C8×C11—21no—
114C8×C11—21no—
115C8×C11—82no—
116C11⋊C8—42no—
117#533—112no—
118#500—111no—
119#494—111no—
120#487—112no—
121#467—221no—
122#467—221no—
123C4×Q16—221no—
124C4×Q16—221no—
125#432C2×D1112yes—
126C2×#97—111no—
127C2×C4×C8C2×D1111yescharacteristic
128#376—111no—
129#336—221no—
130#336—221no—
131#335—21no—
132#334—21no—
133#330—224no—
134#328—224no—
135C22×C11—21no—
136C22×C11—21no—
137C22×C11#39011yescharacteristic
138C22×C11#47312yes—
139C4×C11—21no—
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11#42111yescharacteristic
145C4×C11#42111yescharacteristic
146Dic11—82no—
147Dic11—82no—
148Dic11—82no—
149C2×Q16—221no—
150C2×Q16—221no—
151C22×C8—221no—
152C22×C8D4411yescharacteristic
153C22×C8D4411yescharacteristic
154C4⋊Q8—112no—
155C4⋊Q8—112no—
156#125—222no—
157C22⋊Q8—222no—
158C22⋊Q8—222no—
159C4×Q8—222no—
160C4×Q8—222no—
161#117—222no—
162C2×C42—221no—
163C2×C42C22×D1111yescharacteristic
164#107—221no—
165#107—221no—
166C4⋊C8—22no—
167#103—222no—
168#103—222no—
169C22⋊C8—22no—
170#97—22no—
171#97—112no—
172#97—221no—
173C4×C8C4×D1111yescharacteristic
174C4×C8C4×D1111yescharacteristic
175C4×C8C22⋊D1111yescharacteristic
176C4×C8C22⋊D1111yescharacteristic
177#95—112no—
178#95—221no—
179C2×C11—22no—
180C2×C11#196311yescharacteristic
181C2×C11#197611yescharacteristic
182C2×C11#197911yescharacteristic
183C2×Q8—222no—
184C2×Q8—222no—
185C22×C4—222no—
186C22×C4C2×D4411yescharacteristic
187C22×C4D4×D1111yescharacteristic
188C22×C4#434311yescharacteristic
189Q16—442no—
190Q16—442no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—222no—
195C2×C8—441no—
196C2×C8—441no—
197C2×C8(C2×D11)⋊C411yescharacteristic
198C2×C8(C2×D11)⋊C411yescharacteristic
199C2×C8(C2×D11)⋊C411yescharacteristic
200C2×C8(C2×D11)⋊C411yescharacteristic
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C22⋊C4—442no—
208C42—441no—
209C42—441no—
210C42—442no—
211C42C2×C4×D1111yescharacteristic
212C42D4×D1111yescharacteristic
213C42#434311yescharacteristic
214C42C2×C22⋊D1111yescharacteristic
215C11#976511yescharacteristic, complemented, Sylow
216C23#6694811yescharacteristic
217Q8—442no—
218Q8—442no—
219Q8—882no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—442no—
225C2×C4—442no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4#6694611yescharacteristic
230C2×C4#6694611yescharacteristic
231C2×C4#6694811yescharacteristic
232C2×C4C2×(C2×D11)⋊C411yescharacteristic
233C2×C4#6699311yescharacteristic
234C2×C4#6700011yescharacteristic
235C8—21no—
236C8—21no—
237C8—21no—
238C8—21no—
239C8—82no—
240C8—442no—
241C22—21no—
242C22—21no—
243C22#1062250912yes—
244C22#1062260111yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—21no—
249C4—21no—
250C4—882no—
251C4—882no—
252C4—882no—
253C4#1062275211yescharacteristic
254C4#1062275211yescharacteristic
255C2—22no—
256C2#1306944711yescharacteristic
257C2#1306951211yescharacteristic
258C2#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#9765
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
13. #10622312C4semidirect
16. #10622295C4semidirect
17. #10622294C4semidirect
215. C11#9765semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130683672
#130672322
#130671292
C11×#15682
#976511