Finite Group Databasebeta

← #14722647

Subgroups — #14722647

Order 2816.

1108 conjugacy classes of subgroups; only the 323 normal subgroups are shown.

normal subgroups only

This group has 1108 conjugacy classes of subgroups — too many to draw. Only its 323 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#13077748C212yesmaximal, complemented
2#13067351C213yesmaximal, complemented
3#13067297C216yesmaximal, complemented
4#13067278C213yesmaximal, complemented
5C11×#3499C211yesmaximal, characteristic
6C2×C11×2−1+4C412yes—
7D4×Q8×C11—22no—
8C11×#547—26no—
9C11×#536C416yes—
10C11×#532C2213yes—
11C2×C11×C4⋊Q8C2213yes—
12C4×C11×#41C2211yescharacteristic
13Q8×C11⋊C8—22no—
14#10622625—26no—
15#10622538C2216yes—
16#10622537C2216yes—
17#10622184C2216yes—
18#10622184C2216yes—
19#10622182C2211yescharacteristic
20#10622182C2213yes—
21C11×2−1+4—48no—
22C2×C11×#41—26no—
23C2×C11×#41C2×C416yes—
24C2×C11×#41C2×C411yescharacteristic
25C22×Q8×C11—22no—
26C22×Q8×C11C2×C416yes—
27C11×C4⋊Q8—26no—
28C11×C4⋊Q8C2×C416yes—
29C11×C4⋊Q8C2313yes—
30C11×#127C2311yescharacteristic
31C11×#124C2×C416yes—
32C11×#123—212no—
33C11×C22⋊Q8—212no—
34C11×#121—26no—
35C4×Q8×C11D412yes—
36C4×D4×C11—26no—
37C4×D4×C11D416yes—
38C11×#117C2×C413yes—
39C2×C11×C4⋊C4—26no—
40C2×C42×C11C2313yes—
41C2×#4318—26no—
42C22⋊(C11⋊C8)—26no—
43C4⋊(C11⋊C8)—26no—
44C4⋊(C11⋊C8)C2316yes—
45C4⋊(C11⋊C8)C2312yes—
46C4×C11⋊C8—26no—
47#17773—111nomaximal, Sylow
48C11×#41—24no—
49C11×#41—412no—
50C11×#41—424no—
51C2×Q8×C11—26no—
52C2×Q8×C11—412no—
53C2×Q8×C11—48no—
54C2×Q8×C11C22⋊C411yescharacteristic
55C2×Q8×C11C22×C416yes—
56C2×D4×C11—26no—
57C2×D4×C11—22no—
58C2×D4×C11C22⋊C413yes—
59C2×D4×C11C22×C412yes—
60C22×C4×C11—26no—
61C22×C4×C11—26no—
62C22×C4×C11C22×C413yes—
63C22×C4×C11C2×D416yes—
64C11×C4⋊C4—212no—
65C11×C4⋊C4—26no—
66C11×C4⋊C4C22⋊C416yes—
67C11×C22⋊C4—212no—
68C11×C22⋊C4C22⋊C416yes—
69C42×C11C22×C413yes—
70C42×C11C2×D416yes—
71C42×C11C2411yescharacteristic
72#4318—86no—
73C2×C11⋊C8—22no—
74C2×C11⋊C8—26no—
75#3499D1111yescharacteristic
76#2991—112no—
77#1560—113no—
78#1548—116no—
79#1543—113no—
80C23×C11—22no—
81C23×C11C2×C22⋊C413yes—
82Q8×C11—46no—
83Q8×C11—412no—
84Q8×C11#10014yes—
85D4×C11—26no—
86D4×C11—42no—
87D4×C11—412no—
88D4×C11—42no—
89D4×C11—42no—
90C2×C4×C11—26no—
91C2×C4×C11—26no—
92C2×C4×C11—26no—
93C2×C4×C11—26no—
94C2×C4×C11—412no—
95C2×C4×C11—412no—
96C2×C4×C11C2×C22⋊C416yes—
97C2×C4×C11C2×C22⋊C413yes—
98C2×C4×C11C23×C411yescharacteristic
99C2×C4×C11C22×D412yes—
100C11⋊C8—46no—
101C11⋊C8—42no—
102C2×2−1+4Dic1112yes—
103D4×Q8—22no—
104#547—26no—
105#536Dic1116yes—
106#532C2×D1113yes—
107C2×C4⋊Q8C2×D1113yes—
108C4×#41C2×D1111yescharacteristic
109C8×Q8—222no—
110#436—226no—
111#431—116no—
112#423—116no—
113#333—116no—
114#333—116no—
115#331—111no—
116#331—113no—
117C22×C11—23no—
118C22×C11—26no—
119C22×C11—42no—
120C22×C11—44no—
121C22×C11C22×C22⋊C411yescharacteristic
122C4×C11—21no—
123C4×C11—26no—
124C4×C11—46no—
125C4×C11C2×#10016yes—
126C4×C11#57712yes—
127C4×C11#57812yes—
1282−1+4—48no—
129C2×#41—26no—
130C2×#41C2×Dic1116yes—
131C2×#41C2×Dic1111yescharacteristic
132C22×Q8—22no—
133C22×Q8C2×Dic1116yes—
134C2×M16—226no—
135C4⋊Q8—26no—
136C4⋊Q8C2×Dic1116yes—
137C4⋊Q8C22×D1113yes—
138#127C22×D1111yescharacteristic
139#124C2×Dic1116yes—
140#123—212no—
141C22⋊Q8—212no—
142#121—26no—
143C4×Q8C22⋊D1112yes—
144C4×D4—26no—
145C4×D4C22⋊D1116yes—
146#117C2×Dic1113yes—
147C2×C4⋊C4—26no—
148C2×C42C22×D1113yes—
149C4⋊C8—116no—
150C4⋊C8—112no—
151C4⋊C8—226no—
152C22⋊C8—226no—
153C4×C8—226no—
154C2×C11—43no—
155C2×C11—82no—
156C2×C11C22×#10011yescharacteristic
157C2×C11#289812yes—
158#41—24no—
159#41—412no—
160#41—424no—
161C2×Q8—26no—
162C2×Q8—412no—
163C2×Q8—48no—
164C2×Q8C22⋊Dic1111yescharacteristic
165C2×Q8C22×Dic1116yes—
166C2×D4—26no—
167C2×D4—22no—
168C2×D4C22⋊Dic1113yes—
169C2×D4C22×Dic1112yes—
170C22×C4—26no—
171C22×C4—26no—
172C22×C4C22×Dic1113yes—
173C22×C4C2×C22⋊D1116yes—
174M16—886no—
175C2×C8—222no—
176C2×C8—226no—
177C4⋊C4—212no—
178C4⋊C4—26no—
179C4⋊C4C22⋊Dic1116yes—
180C22⋊C4—212no—
181C22⋊C4C22⋊Dic1116yes—
182C42C22×Dic1113yes—
183C42C2×C22⋊D1116yes—
184C42C23×D1111yescharacteristic
185C11#1777311yescharacteristic, complemented, Sylow
186C23—22no—
187C23C2×C22⋊Dic1113yes—
188Q8—46no—
189Q8—412no—
190Q8#6689714yes—
191D4—26no—
192D4—42no—
193D4—412no—
194D4—42no—
195D4—42no—
196C2×C4—26no—
197C2×C4—26no—
198C2×C4—26no—
199C2×C4—26no—
200C2×C4—412no—
201C2×C4—412no—
202C2×C4C2×C22⋊Dic1116yes—
203C2×C4C2×C22⋊Dic1113yes—
204C2×C4C23×Dic1111yescharacteristic
205C2×C4C22×C22⋊D1112yes—
206C8—446no—
207C8—442no—
208C22—23no—
209C22—26no—
210C22—42no—
211C22—44no—
212C22C22×C22⋊Dic1111yescharacteristic
213C4—21no—
214C4—26no—
215C4—46no—
216C4C2×#6689716yes—
217C4#1062336812yes—
218C4#1062336912yes—
219C2—43no—
220C2—82no—
221C2C22×#6689711yescharacteristic
222C2#1307714912yes—
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3499C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3499D11
hypocenterC11#17773
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13077748C2semidirect
2. #13067351C2semidirect
3. #13067297C2semidirect
4. #13067278C2semidirect
185. C11#17773semidirect

Maximal subgroups

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

subgroupindex
#130777482
#130673512
#130672972
#130672782
C11×#34992
#1777311