Finite Group Databasebeta

← #14664745

Subgroups — #14664745

Order 2816.

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

normal subgroups only

This group has 304 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#13070415C211yesmaximal, characteristic
2#13068754C211yesmaximal, characteristic
3#13066634C214yesmaximal
4C11×#3170C211yesmaximal, characteristic
5C11×#533—21no—
6C11×#500C411yescharacteristic
7C11×#494C411yescharacteristic
8C11×#487—21no—
9C11×#467—21no—
10C11×#467C2212yes—
11C4×C11×Q16—21no—
12C4×C11×Q16C412yes—
13C2×C4×C8×C11C2211yescharacteristic
14#10622537—21no—
15#10622190—21no—
16#10622190C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19C4×C11⋊C16—21no—
20C2×C11×Q16—21no—
21C2×C11×Q16C2×C412yes—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11C2311yescharacteristic
24C11×C4⋊Q8—21no—
25C11×C4⋊Q8—21no—
26C11×#125—41no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—41no—
29C4×Q8×C11—22no—
30C4×Q8×C11—41no—
31C11×#117—41no—
32C2×C42×C11D411yescharacteristic
33C2×#4318—22no—
34C11×#107—21no—
35C11×#107C2×C412yes—
36C11×#103—22no—
37C11×#103—22no—
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11C2×C411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C4×C8×C11D411yescharacteristic
42C2×C11⋊C16—22no—
43C4⋊(C11⋊C8)—41no—
44C4⋊(C11⋊C8)—41no—
45#11863—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C2×Q8×C11—41no—
48C22×C4×C11SD1611yescharacteristic
49C22×C4×C11SD1611yescharacteristic
50C22×C4×C11C2×D411yescharacteristic
51C11×Q16—42no—
52C11×Q16—42no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C22×C411yescharacteristic
58C2×C8×C11C2×D411yescharacteristic
59C11×C4⋊C4—22no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—42no—
66C42×C11—42no—
67C42×C11C22⋊C411yescharacteristic
68C42×C11C22⋊C411yescharacteristic
69C42×C11D811yescharacteristic
70C42×C11D811yescharacteristic
71#4318—42no—
72#4318—42no—
73C2×C11⋊C8—42no—
74C11⋊C16—42no—
75#3170D1111yescharacteristic
76#2162—111no—
77#1837—111no—
78#1350—114no—
79C23×C11C2×SD1611yescharacteristic
80Q8×C11—42no—
81Q8×C11—42no—
82Q8×C11—82no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11#10211yescharacteristic
92C2×C4×C11#10211yescharacteristic
93C2×C4×C11C2×C22⋊C411yescharacteristic
94C2×C4×C11C2×D811yescharacteristic
95C8×C11—21no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C11⋊C8—82no—
100#533—21no—
101#500Dic1111yescharacteristic
102#494Dic1111yescharacteristic
103#487—21no—
104#467—21no—
105#467C2×D1112yes—
106C4×Q16—21no—
107C4×Q16Dic1112yes—
108#423—221no—
109C2×C4×C8C2×D1111yescharacteristic
110C4⋊C16—221no—
111C22⋊C16—112no—
112C4×C16—221no—
113#341—112no—
114#341—221no—
115C22×C11—21no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11C2×#10211yescharacteristic
119C4×C11—21no—
120C4×C11—21no—
121C4×C11—21no—
122C4×C11—82no—
123C4×C11—82no—
124C4×C11#35912yes—
125C4×C11#36212yes—
126C4×C11#41011yescharacteristic
127C4×C11#42111yescharacteristic
128C2×Q16—21no—
129C2×Q16C2×Dic1112yes—
130C2×M16—222no—
131C22×C8C22⋊D1111yescharacteristic
132C22×C8C22×D1111yescharacteristic
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135#125—41no—
136C22⋊Q8—22no—
137C22⋊Q8—41no—
138C4×Q8—22no—
139C4×Q8—41no—
140#117—41no—
141C2×C42C22⋊D1111yescharacteristic
142C2×C16—222no—
143#107—21no—
144#107C2×Dic1112yes—
145C4⋊C8—441no—
146C4⋊C8—441no—
147#103—22no—
148#103—22no—
149C4×C8C2×Dic1111yescharacteristic
150C4×C8C2×Dic1111yescharacteristic
151C4×C8C22⋊D1111yescharacteristic
152C4×C8C22⋊D1111yescharacteristic
153C2×C11—41no—
154C2×C11#151711yescharacteristic
155C2×C11C2×#35911yescharacteristic
156C2×C11C2×#36211yescharacteristic
157C2×Q8—22no—
158C2×Q8—41no—
159C22×C4#432411yescharacteristic
160C22×C4#432411yescharacteristic
161C22×C4C2×C22⋊D1111yescharacteristic
162Q16—42no—
163Q16—42no—
164M16—442no—
165M16—442no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—442no—
169C2×C8C22⋊Dic1111yescharacteristic
170C2×C8C22⋊Dic1111yescharacteristic
171C2×C8C22×Dic1111yescharacteristic
172C2×C8C2×C22⋊D1111yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C22⋊C4—42no—
180C42—42no—
181C42#432311yescharacteristic
182C42#432311yescharacteristic
183C42C22⋊Dic1111yescharacteristic
184C42C22⋊Dic1111yescharacteristic
185C16—442no—
186C11#1186311yescharacteristic, complemented, Sylow
187C23C2×#432411yescharacteristic
188Q8—42no—
189Q8—42no—
190Q8—82no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4#6689611yescharacteristic
198C2×C4#6689611yescharacteristic
199C2×C4#6689611yescharacteristic
200C2×C4#6689611yescharacteristic
201C2×C4C2×#432311yescharacteristic
202C2×C4C2×C22⋊Dic1111yescharacteristic
203C8—21no—
204C8—21no—
205C8—21no—
206C8—21no—
207C8—882no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22C2×#6689611yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—82no—
216C4—82no—
217C4#1062220312yes—
218C4#1062220512yes—
219C4#1062284911yescharacteristic
220C4#1062285311yescharacteristic
221C2—41no—
222C2#1306717611yescharacteristic
223C2C2×#1062220511yescharacteristic
224C2C2×#1062220311yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#3170C2
socleC22×C11C2×#102
prime radicalC23×C11C2×SD16
cosocleC22×C8×C11C23
hypercenter#3170D11
hypocenterC11#11863
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
186. C11#11863semidirect

Maximal subgroups

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

subgroupindex
#130704152
#130687542
#130666342
C11×#31702
#1186311