Finite Group Databasebeta

← #14665131

Subgroups — #14665131

Order 2816.

306 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 103 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
2C2×#10622096C211yesmaximal, characteristic
3#13066670C212yesmaximal, complemented
4#13066666C212yesmaximal, complemented
5C11×#2163C211yesmaximal, characteristic
6#10623001—21no—
7C2×C4×C8×C11C2211yescharacteristic
8#10622729—21no—
9#10622729C412yes—
10C2×C4⋊(C11⋊C8)—21no—
11#10622312C2211yescharacteristic
12C4×Dic44—21no—
13C4×Dic44C412yes—
14#10622295C2211yescharacteristic
15#10622294—21no—
16C11×C4⋊C16C2212yes—
17C11×C22⋊C16—21no—
18C11×#346—21no—
19#10622096—21no—
20#10622096C2212yes—
21C22×C8×C11C2×C411yescharacteristic
22C22×C8×C11D411yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66979—41no—
25#66977—22no—
26#66977—41no—
27C22×C11⋊C8—41no—
28C2×Dic44—21no—
29C2×Dic44C2×C412yes—
30#66923—41no—
31#66922—21no—
32#66922—21no—
33C4×Dic22—22no—
34C4×Dic22—41no—
35C2×C11×C16—22no—
36C4×C8×C11C2×C411yescharacteristic
37C4×C8×C11D411yescharacteristic
38C4×C8×C11D411yescharacteristic
39C4×C8×C11C2311yescharacteristic
40#66882—21no—
41#66882C2×C412yes—
42#66880—22no—
43#66880—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)—41no—
46#11954—111nomaximal, Sylow
47C22×C4×C11C22⋊C411yescharacteristic
48C22×C4×C11D811yescharacteristic
49C22×C4×C11SD1611yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—41no—
52C2×C8×C11—22no—
53C2×C8×C11—41no—
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22×C411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C42×C11C22⋊C411yescharacteristic
59C42×C11D811yescharacteristic
60C42×C11SD1611yescharacteristic
61C42×C11C2×D411yescharacteristic
62C22⋊Dic11—42no—
63C4⋊Dic11—22no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—41no—
67Dic11⋊C4—42no—
68Dic11⋊C4—42no—
69C4×Dic11—42no—
70C2×C11⋊C8—42no—
71C2×C11⋊C8—82no—
72Dic44—42no—
73Dic44—42no—
74C11×C16—42no—
75#3170—111no—
76#2163D1111yescharacteristic
77C2×#335—111no—
78#1364—112no—
79#1362—112no—
80C23×C11#10211yescharacteristic
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11#10211yescharacteristic
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11C2×C22⋊C411yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C2×Dic11—42no—
93C2×Dic11—42no—
94Dic22—42no—
95Dic22—42no—
96Dic22—81no—
97Dic22—81no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—21no—
101C8×C11#13512yes—
102C11⋊C8—82no—
103#533—221no—
104#500—111no—
105#494—111no—
106#487—221no—
107#467—112no—
108#467—221no—
109C4×Q16—112no—
110C4×Q16—221no—
111C2×C4⋊C8—221no—
112C2×C4×C8C2×D1111yescharacteristic
113C4⋊C16C2×D1112yes—
114C22⋊C16—21no—
115#346—21no—
116#335—112no—
117#335—221no—
118C22×C11—21no—
119C22×C11—21no—
120C22×C11#36212yes—
121C22×C11C2×#10211yescharacteristic
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11#41311yescharacteristic
127C4×C11#41611yescharacteristic
128C4×C11#50911yescharacteristic
129C4×C11#51011yescharacteristic
130Dic11—82no—
131Dic11—82no—
132C2×Q16—112no—
133C2×Q16—221no—
134C22×C8—441no—
135C22×C8C4×D1111yescharacteristic
136C22×C8C22⋊D1111yescharacteristic
137C4⋊Q8—221no—
138C4⋊Q8—221no—
139#125—441no—
140C22⋊Q8—222no—
141C22⋊Q8—441no—
142C4×Q8—222no—
143C4×Q8—441no—
144#117—441no—
145C2×C42D4411yescharacteristic
146C2×C16—22no—
147#107—112no—
148#107—221no—
149C4⋊C8—222no—
150C4⋊C8—441no—
151#103—222no—
152#103—222no—
153C4×C8C4×D1111yescharacteristic
154C4×C8D4411yescharacteristic
155C4×C8C22⋊D1111yescharacteristic
156C4×C8C22×D1111yescharacteristic
157C2×C11—22no—
158C2×C11#154011yescharacteristic
159C2×C11#213911yescharacteristic
160C2×C11C2×#36211yescharacteristic
161C2×Q8—222no—
162C2×Q8—441no—
163C22×C4#431411yescharacteristic
164C22×C4D8811yescharacteristic
165C22×C4(C2×D11)⋊C411yescharacteristic
166Q16—442no—
167Q16—442no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—442no—
171C2×C8—882no—
172C2×C8(C2×D11)⋊C411yescharacteristic
173C2×C8(C2×D11)⋊C411yescharacteristic
174C2×C8C2×C4×D1111yescharacteristic
175C2×C8C2×C22⋊D1111yescharacteristic
176C4⋊C4—222no—
177C4⋊C4—442no—
178C4⋊C4—442no—
179C4⋊C4—441no—
180C4⋊C4—441no—
181C4⋊C4—441no—
182C22⋊C4—442no—
183C42—442no—
184C42#431411yescharacteristic
185C42D8811yescharacteristic
186C42(C2×D11)⋊C411yescharacteristic
187C42C2×D4411yescharacteristic
188C16—42no—
189C11#1195411yescharacteristic, complemented, Sylow
190C23#6688511yescharacteristic
191Q8—442no—
192Q8—442no—
193Q8—881no—
194Q8—881no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—442no—
201C2×C4—442no—
202C2×C4#6688511yescharacteristic
203C2×C4#6688511yescharacteristic
204C2×C4#6688511yescharacteristic
205C2×C4C2×#431411yescharacteristic
206C2×C4C2×D8811yescharacteristic
207C2×C4C2×(C2×D11)⋊C411yescharacteristic
208C8—21no—
209C8—21no—
210C8—21no—
211C8—882no—
212C8#6700312yes—
213C22—21no—
214C22—21no—
215C22#1062215512yes—
216C22C2×#6688511yescharacteristic
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—882no—
222C4—882no—
223C4#1062252111yescharacteristic
224C4#1062252211yescharacteristic
225C4#1062261511yescharacteristic
226C4#1062274511yescharacteristic
227C2—22no—
228C2#1306726311yescharacteristic
229C2#1307032911yescharacteristic
230C2C2×#1062215511yescharacteristic
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#2163C2
socleC22×C11C2×#102
prime radicalC23×C11#102
cosocleC4×C8×C11C23
hypercenter#2163D11
hypocenterC11#11954
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
3. #13066670C2semidirect
4. #13066666C2semidirect
189. C11#11954semidirect

Maximal subgroups

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

subgroupindex
#130792022
C2×#106220962
#130666702
#130666662
C11×#21632
#1195411