Finite Group Databasebeta

← #14664726

Subgroups — #14664726

Order 2816.

314 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 95 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#13066627C214yesmaximal
4C11×#1835C211yesmaximal, characteristic
5#10623001—21no—
6C2×C4×C8×C11C2211yescharacteristic
7C11×#382—21no—
8#10622729—21no—
9#10622729C2212yes—
10#10622312C411yescharacteristic, complemented
11C4×Dic44—21no—
12C4×Dic44C412yescomplemented
13#10622295C411yescharacteristic, complemented
14#10622294—21no—
15C11×#340—21no—
16C11×#340C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19#10622099—21no—
20C22×C8×C11D411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22C2×C11×C4⋊C4—22no—
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—
34C4×C8×C11C2×C411yescharacteristic
35C4×C8×C11C2×C411yescharacteristic
36C4×C8×C11D411yescharacteristic
37C4×C8×C11D411yescharacteristic
38C11×#95—41no—
39C11×#95—41no—
40#66882—21no—
41#66882C2×C412yes—
42#66880—22no—
43#66880—22no—
44C2×C11⋊C16—22no—
45#11859—111nomaximal, Sylow
46C22×C4×C11—42no—
47C22×C4×C11D811yescharacteristic
48C22×C4×C11D811yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11C22⋊C411yescharacteristic
55C2×C8×C11C22⋊C411yescharacteristic
56C2×C8×C11C22×C411yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C11×C4⋊C4—42no—
59C11×C4⋊C4—42no—
60C42×C11C22⋊C411yescharacteristic
61C42×C11C22⋊C411yescharacteristic
62C42×C11SD1611yescharacteristic
63C42×C11SD1611yescharacteristic
64C22⋊Dic11—42no—
65C4⋊Dic11—22no—
66C4⋊Dic11—41no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69Dic11⋊C4—42no—
70Dic11⋊C4—42no—
71C4×Dic11—42no—
72Dic44—42no—
73Dic44—42no—
74C11⋊C16—42no—
75#3170—111no—
76#2163—111no—
77#1835D1111yescharacteristic
78#1348—114no—
79C23×C11C2×D811yescharacteristic
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11—82no—
85C2×C4×C11—82no—
86C2×C4×C11—82no—
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11C2×C22⋊C411yescharacteristic
92C2×C4×C11C2×SD1611yescharacteristic
93C2×Dic11—42no—
94C2×Dic11—42no—
95Dic22—42no—
96Dic22—42no—
97Dic22—82no—
98C8×C11—21no—
99C8×C11—21no—
100C8×C11—21no—
101C8×C11—21no—
102#533—221no—
103#500—111no—
104#494—111no—
105#487—221no—
106#467—112no—
107#467—221no—
108C4×Q16—112no—
109C4×Q16—221no—
110C2×C4×C8C2×D1111yescharacteristic
111#382—21no—
112C4⋊C16—221no—
113C22⋊C16—112no—
114#346—221no—
115#340—21no—
116#340C2×D1112yes—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11C2×#10211yescharacteristic
120C22×C11#51012yes—
121C4×C11—21no—
122C4×C11—21no—
123C4×C11—21no—
124C4×C11—21no—
125C4×C11—21no—
126C4×C11—162no—
127C4×C11#41011yescharacteristic
128C4×C11#42111yescharacteristic
129Dic11—82no—
130Dic11—82no—
131C2×Q16—112no—
132C2×Q16—221no—
133C22×C8C22⋊D1111yescharacteristic
134C22×C8C22×D1111yescharacteristic
135C4⋊Q8—221no—
136C4⋊Q8—221no—
137#125—441no—
138C22⋊Q8—222no—
139C22⋊Q8—441no—
140C4×Q8—222no—
141C4×Q8—441no—
142#117—441no—
143C2×C4⋊C4—22no—
144C2×C42C22⋊D1111yescharacteristic
145C2×C16—222no—
146#107—112no—
147#107—221no—
148#103—222no—
149#103—222no—
150C4×C8C4×D1111yescharacteristic
151C4×C8C4×D1111yescharacteristic
152C4×C8D4411yescharacteristic
153C4×C8D4411yescharacteristic
154#95—41no—
155#95—41no—
156C2×C11—22no—
157C2×C11#151711yescharacteristic
158C2×C11#214111yescharacteristic
159C2×C11#214511yescharacteristic
160C2×Q8—222no—
161C2×Q8—441no—
162C22×C4—42no—
163C22×C4#432311yescharacteristic
164C22×C4#432311yescharacteristic
165C22×C4C2×C22⋊D1111yescharacteristic
166Q16—442no—
167Q16—442no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8(C2×D11)⋊C411yescharacteristic
171C2×C8(C2×D11)⋊C411yescharacteristic
172C2×C8C2×C4×D1111yescharacteristic
173C2×C8C2×D4411yescharacteristic
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—222no—
177C4⋊C4—441no—
178C4⋊C4—441no—
179C4⋊C4—442no—
180C4⋊C4—441no—
181C4⋊C4—442no—
182C22⋊C4—442no—
183C42—442no—
184C42(C2×D11)⋊C411yescharacteristic
185C42(C2×D11)⋊C411yescharacteristic
186C42#432511yescharacteristic
187C42#432511yescharacteristic
188C16—442no—
189C11#1185911yescharacteristic, complemented, Sylow
190C23C2×#432311yescharacteristic
191Q8—442no—
192Q8—442no—
193Q8—882no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—82no—
199C2×C4—82no—
200C2×C4—82no—
201C2×C4—442no—
202C2×C4—442no—
203C2×C4#6687311yescharacteristic
204C2×C4#6687311yescharacteristic
205C2×C4#6687311yescharacteristic
206C2×C4#6687311yescharacteristic
207C2×C4C2×(C2×D11)⋊C411yescharacteristic
208C2×C4C2×#432511yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—21no—
213C22—21no—
214C22—21no—
215C22C2×#6687311yescharacteristic
216C22#1062280812yes—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—162no—
223C4—882no—
224C4—882no—
225C4#1062261811yescharacteristic
226C4#1062261911yescharacteristic
227C2—22no—
228C2#1306717511yescharacteristic
229C2#1307033511yescharacteristic
230C2#1307035111yescharacteristic
subgroupG/H
centerC22C2×#66873
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1835C2
socleC22×C11C2×#102
prime radicalC23×C11C2×D8
cosocleC22×C8×C11C23
hypercenter#1835D11
hypocenterC11#11859
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1835

Complements

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

NH ≅ G/Ntype
10. #10622312C4semidirect
12. C4×Dic44C4semidirect
13. #10622295C4semidirect
189. C11#11859semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130704192
#130666272
C11×#18352
#1185911