Finite Group Databasebeta

← #14664749

Subgroups — #14664749

Order 2816.

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

normal subgroups only

This group has 344 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#13070419C211yesmaximal, characteristic, complemented
2#13068754C211yesmaximal, characteristic, complemented
3#13066631C214yesmaximal, complemented
4C11×#3169C211yesmaximal, characteristic
5C11×#532—21no—
6C11×#500C411yescharacteristic
7C11×#493C411yescharacteristic
8C11×#486—21no—
9C11×#466—21no—
10C11×#466C2212yes—
11C4×C11×D8—21no—
12C4×C11×D8C412yes—
13C2×C4×C8×C11C2211yescharacteristic
14#10622537—21no—
15#10622190—21no—
16#10622190C2212yes—
17C22⋊(C11⋊C16)C2212yes—
18C4⋊(C11⋊C16)—21no—
19#10622099—21no—
20C2×C11×#41—41no—
21C2×C11×D8—21no—
22C2×C11×D8C2×C412yes—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C11×C4⋊Q8—21no—
26C11×#127—21no—
27C11×#124—41no—
28C11×#121—22no—
29C11×#121—41no—
30C4×D4×C11—22no—
31C4×D4×C11—41no—
32C2×C42×C11D411yescharacteristic
33C2×#4318—22no—
34C11×#107—21no—
35C11×#107C2×C412yes—
36C11×#102—22no—
37C11×#102—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#11864—111nomaximal, Sylow
46C11×#41—84no—
47C2×Q8×C11—41no—
48C2×D4×C11—22no—
49C2×D4×C11—42no—
50C2×D4×C11—41no—
51C2×D4×C11—41no—
52C22×C4×C11—42no—
53C22×C4×C11SD1611yescharacteristic
54C22×C4×C11SD1611yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C11×D8—42no—
57C11×D8—42no—
58C2×C8×C11—41no—
59C2×C8×C11—41no—
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C22⋊C411yescharacteristic
62C2×C8×C11C22×C411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—22no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—42no—
67C11×C22⋊C4—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11C22⋊C411yescharacteristic
70C42×C11D811yescharacteristic
71C42×C11D811yescharacteristic
72#4318—42no—
73#4318—42no—
74C2×C11⋊C8—42no—
75C11⋊C16—42no—
76#3169D1111yescharacteristic
77#2163—111no—
78#1837—111no—
79#1349—114no—
80C23×C11—42no—
81C23×C11C2×SD1611yescharacteristic
82Q8×C11—82no—
83D4×C11—42no—
84D4×C11—42no—
85D4×C11—82no—
86D4×C11—82no—
87D4×C11—84no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—84no—
94C2×C4×C11#10211yescharacteristic
95C2×C4×C11#10211yescharacteristic
96C2×C4×C11#10211yescharacteristic
97C2×C4×C11#10211yescharacteristic
98C2×C4×C11C2×C22⋊C411yescharacteristic
99C2×C4×C11C2×D811yescharacteristic
100C8×C11—21no—
101C8×C11—21no—
102C8×C11—21no—
103C8×C11—21no—
104C11⋊C8—82no—
105#532—21no—
106#500Dic1111yescharacteristic
107#493Dic1111yescharacteristic
108#486—21no—
109#466—21no—
110#466C2×D1112yes—
111C4×D8—21no—
112C4×D8Dic1112yes—
113#423—221no—
114C2×C4×C8C2×D1111yescharacteristic
115C4⋊C16—221no—
116C22⋊C16—112no—
117#346—221no—
118#341—112no—
119#341—221no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—21no—
123C22×C11—82no—
124C22×C11—82no—
125C22×C11—82no—
126C22×C11C2×#10211yescharacteristic
127C4×C11—21no—
128C4×C11—21no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—82no—
132C4×C11#36112yes—
133C4×C11#41011yescharacteristic
134C4×C11#42111yescharacteristic
135C2×#41—41no—
136C2×D8—21no—
137C2×D8C2×Dic1112yes—
138C2×M16—222no—
139C22×C8C22⋊D1111yescharacteristic
140C22×C8C22×D1111yescharacteristic
141C4⋊Q8—21no—
142#127—21no—
143#124—41no—
144#121—22no—
145#121—41no—
146C4×D4—22no—
147C4×D4—41no—
148C2×C42C22⋊D1111yescharacteristic
149C2×C16—222no—
150#107—21no—
151#107C2×Dic1112yes—
152C4⋊C8—441no—
153C4⋊C8—441no—
154#102—22no—
155#102—22no—
156C4×C8C2×Dic1111yescharacteristic
157C4×C8C2×Dic1111yescharacteristic
158C4×C8C22⋊D1111yescharacteristic
159C4×C8C22⋊D1111yescharacteristic
160C2×C11—41no—
161C2×C11—162no—
162C2×C11#151711yescharacteristic
163C2×C11#214311yescharacteristic
164C2×C11C2×#36111yescharacteristic
165#41—84no—
166C2×Q8—41no—
167C2×D4—22no—
168C2×D4—42no—
169C2×D4—41no—
170C2×D4—41no—
171C22×C4—42no—
172C22×C4#432411yescharacteristic
173C22×C4#432411yescharacteristic
174C22×C4C2×C22⋊D1111yescharacteristic
175D8—42no—
176D8—42no—
177M16—442no—
178M16—442no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—442no—
182C2×C8C22⋊Dic1111yescharacteristic
183C2×C8C22⋊Dic1111yescharacteristic
184C2×C8C22×Dic1111yescharacteristic
185C2×C8C2×C22⋊D1111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—41no—
188C22⋊C4—42no—
189C22⋊C4—42no—
190C42#432311yescharacteristic
191C42#432311yescharacteristic
192C42C22⋊Dic1111yescharacteristic
193C42C22⋊Dic1111yescharacteristic
194C16—442no—
195C11#1186411yescharacteristic, complemented, Sylow
196C23—42no—
197C23C2×#432411yescharacteristic
198Q8—82no—
199D4—42no—
200D4—42no—
201D4—82no—
202D4—82no—
203D4—84no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—84no—
210C2×C4#6689611yescharacteristic
211C2×C4#6689611yescharacteristic
212C2×C4#6689611yescharacteristic
213C2×C4#6689611yescharacteristic
214C2×C4C2×#432311yescharacteristic
215C2×C4C2×C22⋊Dic1111yescharacteristic
216C8—21no—
217C8—21no—
218C8—21no—
219C8—21no—
220C8—882no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—82no—
225C22—82no—
226C22—82no—
227C22C2×#6689611yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—82no—
233C4#1062220112yes—
234C4#1062284911yescharacteristic
235C4#1062285311yescharacteristic
236C2—41no—
237C2—162no—
238C2#1306717611yescharacteristic
239C2#1307034411yescharacteristic
240C2C2×#1062220111yescharacteristic
subgroupG/H
centerC22C2×#66896
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
Fitting, prime radicalC11×#3169C2
socleC22×C11C2×#102
cosocleC22×C8×C11C23
hypercenter#3169D11
hypocenterC11#11864
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13070419C2semidirect
2. #13068754C2semidirect
3. #13066631C2semidirect
195. C11#11864semidirect

Maximal subgroups

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

subgroupindex
#130704192
#130687542
#130666312
C11×#31692
#1186411