Finite Group Databasebeta

← #14664223

Subgroups — #14664223

Order 2816.

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

normal subgroups only

This group has 320 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#13070419C211yesmaximal, characteristic
3#13066633C214yesmaximal
4C4×C11×#108C211yesmaximal, characteristic
5#10623001—21no—
6C2×C11×#108—21no—
7C4×C11×M16—21no—
8C2×C4×C8×C11C2211yescharacteristic
9#10622729—21no—
10#10622729C2212yes—
11#10622312C411yescharacteristic
12C4×Dic44—21no—
13C4×Dic44C412yes—
14#10622295C411yescharacteristic
15#10622294—21no—
16C11×#341C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19#10622099—21no—
20C2×C11×M16—22no—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66979—41no—
25#66977—22no—
26#66977—41no—
27C2×Dic44—21no—
28C2×Dic44C2×C412yes—
29#66923—41no—
30#66922—21no—
31#66922—21no—
32C4×Dic22—22no—
33C4×Dic22—41no—
34C11×#108—24no—
35C11×#97—41no—
36C4×C8×C11—41no—
37C4×C8×C11C2×C411yescharacteristic
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41#66882—21no—
42#66882C2×C412yes—
43#66880—22no—
44#66880—22no—
45C2×C11⋊C16—22no—
46#11752—111nomaximal, Sylow
47C22×C4×C11SD1611yescharacteristic
48C22×C4×C11SD1611yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—41no—
52C11×M16—24no—
53C11×M16—42no—
54C2×C8×C11—22no—
55C2×C8×C11—41no—
56C2×C8×C11—42no—
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C22⋊C411yescharacteristic
59C2×C8×C11C22×C411yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61C42×C11C22⋊C411yescharacteristic
62C42×C11C22⋊C411yescharacteristic
63C42×C11D811yescharacteristic
64C42×C11D811yescharacteristic
65C22⋊Dic11—42no—
66C4⋊Dic11—22no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—41no—
70Dic11⋊C4—42no—
71Dic11⋊C4—42no—
72C4×Dic11—42no—
73Dic44—42no—
74Dic44—42no—
75C11⋊C16—42no—
76#3170—111no—
77#2163—111no—
78C4×#108D1111yescharacteristic
79#1350—114no—
80C23×C11C2×SD1611yescharacteristic
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—41no—
85C2×C4×C11#10211yescharacteristic
86C2×C4×C11#10211yescharacteristic
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11C2×C22⋊C411yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×Dic11—42no—
92C2×Dic11—42no—
93Dic22—42no—
94Dic22—42no—
95Dic22—82no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11—44no—
100C8×C11#10412yes—
101#533—221no—
102#500—111no—
103#494—111no—
104#487—221no—
105#467—112no—
106#467—221no—
107C4×Q16—112no—
108C4×Q16—221no—
109C2×#108—21no—
110C4×M16—21no—
111C2×C4×C8C2×D1111yescharacteristic
112C4⋊C16—221no—
113C22⋊C16—112no—
114#346—221no—
115#341C2×D1112yes—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11C2×#10211yescharacteristic
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11#36212yes—
125C4×C11#41011yescharacteristic
126C4×C11C2×#10411yescharacteristic
127Dic11—82no—
128Dic11—82no—
129C2×Q16—112no—
130C2×Q16—221no—
131C2×M16—22no—
132C22×C8C22⋊D1111yescharacteristic
133C22×C8C22×D1111yescharacteristic
134C4⋊Q8—221no—
135C4⋊Q8—221no—
136#125—441no—
137C22⋊Q8—222no—
138C22⋊Q8—441no—
139C4×Q8—222no—
140C4×Q8—441no—
141#117—441no—
142C2×C42C22⋊D1111yescharacteristic
143C2×C16—222no—
144#108—24no—
145#107—112no—
146#107—221no—
147#103—222no—
148#103—222no—
149#97—41no—
150C4×C8—41no—
151C4×C8C4×D1111yescharacteristic
152C4×C8C4×D1111yescharacteristic
153C4×C8D4411yescharacteristic
154C4×C8D4411yescharacteristic
155C2×C11—41no—
156C2×C11#150211yescharacteristic
157C2×C11#214311yescharacteristic
158C2×C11C2×#36211yescharacteristic
159C2×Q8—222no—
160C2×Q8—441no—
161C22×C4#432511yescharacteristic
162C22×C4#432511yescharacteristic
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—442no—
165Q16—442no—
166M16—24no—
167M16—42no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8(C2×D11)⋊C411yescharacteristic
172C2×C8(C2×D11)⋊C411yescharacteristic
173C2×C8C2×C4×D1111yescharacteristic
174C2×C8C2×D4411yescharacteristic
175C4⋊C4—222no—
176C4⋊C4—441no—
177C4⋊C4—441no—
178C4⋊C4—442no—
179C4⋊C4—441no—
180C4⋊C4—442no—
181C22⋊C4—442no—
182C42—442no—
183C42(C2×D11)⋊C411yescharacteristic
184C42(C2×D11)⋊C411yescharacteristic
185C42#432311yescharacteristic
186C42#432311yescharacteristic
187C16—442no—
188C11#1175211yescharacteristic, complemented, Sylow
189C23C2×#432511yescharacteristic
190Q8—442no—
191Q8—442no—
192Q8—882no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—442no—
198C2×C4—442no—
199C2×C4#6687311yescharacteristic
200C2×C4#6687311yescharacteristic
201C2×C4#6687311yescharacteristic
202C2×C4#6687311yescharacteristic
203C2×C4C2×(C2×D11)⋊C411yescharacteristic
204C2×C4C2×#432311yescharacteristic
205C8—21no—
206C8—21no—
207C8—21no—
208C8—44no—
209C8#6686912yes—
210C22—21no—
211C22—21no—
212C22—21no—
213C22C2×#6687311yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—21no—
218C4—882no—
219C4—882no—
220C4#1062213412yes—
221C4C2×#6686911yescharacteristic
222C4#1062261911yescharacteristic
223C2—41no—
224C2#1306711011yescharacteristic
225C2#1307034311yescharacteristic
226C2C2×#1062213411yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC4×C11×#108C2
socleC22×C11C2×#102
prime radicalC23×C11C2×SD16
cosocleC22×C8×C11C23
hypercenterC4×#108D11
hypocenterC11#11752
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
188. C11#11752semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130704192
#130666332
C4×C11×#1082
#1175211