Finite Group Databasebeta

← #14664224

Subgroups — #14664224

Order 2816.

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

normal subgroups only

This group has 320 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#13070419C211yesmaximal, characteristic
2C4×#66883C211yesmaximal, 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
14C2×#66883—21no—
15C4×#4318—21no—
16#10622190C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19#10622099—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
42#66883—24no—
43C2×C11⋊C16—22no—
44#66867—41no—
45C4×C11⋊C8—41no—
46#11752—111nomaximal, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—41no—
49C22×C4×C11SD1611yescharacteristic
50C22×C4×C11SD1611yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C11×Q16—42no—
53C11×Q16—42no—
54C2×C8×C11—22no—
55C2×C8×C11—41no—
56C2×C8×C11C22⋊C411yescharacteristic
57C2×C8×C11C22⋊C411yescharacteristic
58C2×C8×C11C22×C411yescharacteristic
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—22no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—42no—
66C11×C22⋊C4—42no—
67C42×C11—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11C22⋊C411yescharacteristic
70C42×C11D811yescharacteristic
71C42×C11D811yescharacteristic
72#4318—24no—
73#4318—42no—
74C2×C11⋊C8—42no—
75C11⋊C16—42no—
76#3170D1111yescharacteristic
77#2163—111no—
78C4×#108—111no—
79#1350—114no—
80C23×C11C2×SD1611yescharacteristic
81Q8×C11—42no—
82Q8×C11—42no—
83Q8×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11#10211yescharacteristic
92C2×C4×C11#10211yescharacteristic
93C2×C4×C11#10211yescharacteristic
94C2×C4×C11C2×C22⋊C411yescharacteristic
95C2×C4×C11C2×D811yescharacteristic
96C8×C11—21no—
97C8×C11—21no—
98C8×C11—21no—
99C8×C11#10412yes—
100C11⋊C8—44no—
101#533—21no—
102#500Dic1111yescharacteristic
103#494Dic1111yescharacteristic
104#487—21no—
105#467—21no—
106#467C2×D1112yes—
107C4×Q16—21no—
108C4×Q16Dic1112yes—
109C2×#108—221no—
110C4×M16—221no—
111C2×C4×C8C2×D1111yescharacteristic
112C4⋊C16—221no—
113C22⋊C16—112no—
114#346—221no—
115#341—112no—
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—82no—
125C4×C11—82no—
126C4×C11#36212yes—
127C4×C11#41011yescharacteristic
128C4×C11C2×#10411yescharacteristic
129C2×Q16—21no—
130C2×Q16C2×Dic1112yes—
131C2×M16—222no—
132C22×C8C22⋊D1111yescharacteristic
133C22×C8C22×D1111yescharacteristic
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136#125—41no—
137C22⋊Q8—22no—
138C22⋊Q8—41no—
139C4×Q8—22no—
140C4×Q8—41no—
141#117—41no—
142C2×C42C22⋊D1111yescharacteristic
143C2×C16—222no—
144#108—224no—
145#107—21no—
146#107C2×Dic1112yes—
147#103—22no—
148#103—22no—
149#97—441no—
150C4×C8—441no—
151C4×C8C2×Dic1111yescharacteristic
152C4×C8C2×Dic1111yescharacteristic
153C4×C8C22⋊D1111yescharacteristic
154C4×C8C22⋊D1111yescharacteristic
155C2×C11—41no—
156C2×C11#150211yescharacteristic
157C2×C11#214311yescharacteristic
158C2×C11C2×#36211yescharacteristic
159C2×Q8—22no—
160C2×Q8—41no—
161C22×C4#432411yescharacteristic
162C22×C4#432411yescharacteristic
163C22×C4C2×C22⋊D1111yescharacteristic
164Q16—42no—
165Q16—42no—
166M16—224no—
167M16—442no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—442no—
171C2×C8C22⋊Dic1111yescharacteristic
172C2×C8C22⋊Dic1111yescharacteristic
173C2×C8C22×Dic1111yescharacteristic
174C2×C8C2×C22⋊D1111yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C22⋊C4—42no—
182C42—42no—
183C42#432311yescharacteristic
184C42#432311yescharacteristic
185C42C22⋊Dic1111yescharacteristic
186C42C22⋊Dic1111yescharacteristic
187C16—442no—
188C11#1175211yescharacteristic, complemented, Sylow
189C23C2×#432411yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4#6689611yescharacteristic
200C2×C4#6689611yescharacteristic
201C2×C4#6689611yescharacteristic
202C2×C4#6689611yescharacteristic
203C2×C4C2×#432311yescharacteristic
204C2×C4C2×C22⋊Dic1111yescharacteristic
205C8—21no—
206C8—21no—
207C8—21no—
208C8—444no—
209C8#6690112yes—
210C22—21no—
211C22—21no—
212C22—21no—
213C22C2×#6689611yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4#1062220312yes—
221C4C2×#6690111yescharacteristic
222C4#1062285311yescharacteristic
223C2—41no—
224C2#1306711111yescharacteristic
225C2#1307034411yescharacteristic
226C2C2×#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#11752
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
188. C11#11752semidirect

Maximal subgroups

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

subgroupindex
#130704192
C4×#668832
#130666342
C11×#31702
#1175211