Finite Group Databasebeta

← #14665113

Subgroups — #14665113

Order 2816.

300 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 111 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#13067364C211yesmaximal, characteristic
3#13066671C212yesmaximal, complemented
4#13066665C212yesmaximal, complemented
5C11×#3170C211yesmaximal, characteristic
6C11×#533—21no—
7C11×#500C2211yescharacteristic
8C11×#494C2211yescharacteristic
9C11×#487—21no—
10C11×#467—21no—
11C11×#467C412yes—
12C4×C11×Q16—21no—
13C4×C11×Q16C412yes—
14C2×C4×C8×C11C2211yescharacteristic
15#10622538—21no—
16C22⋊(C11⋊C16)—21no—
17C4⋊(C11⋊C16)C2212yes—
18C4×C11⋊C16—21no—
19#10622096C2212yes—
20#10622095—21no—
21C2×C11×Q16—21no—
22C2×C11×Q16C2×C412yes—
23C22×C8×C11C2×C411yescharacteristic
24C22×C8×C11D411yescharacteristic
25C11×C4⋊Q8—21no—
26C11×C4⋊Q8—21no—
27C11×#125—41no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—41no—
30C4×Q8×C11—22no—
31C4×Q8×C11—41no—
32C11×#117—41no—
33C2×C42×C11D411yescharacteristic
34C11×#107—21no—
35C11×#107C2×C412yes—
36C11×#103—22no—
37C11×#103—22no—
38C4×C8×C11C2×C411yescharacteristic
39C4×C8×C11D411yescharacteristic
40C4×C8×C11D411yescharacteristic
41C4×C8×C11C2311yescharacteristic
42C22⋊(C11⋊C8)—41no—
43C2×C11⋊C16—22no—
44C4⋊(C11⋊C8)—22no—
45C4×C11⋊C8—41no—
46#11950—111nomaximal, Sylow
47C2×Q8×C11—22no—
48C2×Q8×C11—41no—
49C22×C4×C11C22⋊C411yescharacteristic
50C22×C4×C11D811yescharacteristic
51C22×C4×C11SD1611yescharacteristic
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—42no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C11×C4⋊C4—41no—
66C11×C22⋊C4—42no—
67C42×C11—42no—
68C42×C11C22⋊C411yescharacteristic
69C42×C11D811yescharacteristic
70C42×C11SD1611yescharacteristic
71C42×C11C2×D411yescharacteristic
72C2×C11⋊C8—42no—
73C11⋊C16—42no—
74#3170D1111yescharacteristic
75#2162—111no—
76#1564—111no—
77#1364—112no—
78#1362—112no—
79C23×C11#10211yescharacteristic
80Q8×C11—42no—
81Q8×C11—42no—
82Q8×C11—82no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11#10211yescharacteristic
92C2×C4×C11C2×C22⋊C411yescharacteristic
93C2×C4×C11C2×D811yescharacteristic
94C2×C4×C11C2×SD1611yescharacteristic
95C8×C11—21no—
96C8×C11—21no—
97C8×C11—21no—
98C8×C11#13512yes—
99C11⋊C8—82no—
100#533—21no—
101#500C2×D1111yescharacteristic
102#494C2×D1111yescharacteristic
103#487—21no—
104#467—21no—
105#467Dic1112yes—
106C4×Q16—21no—
107C4×Q16Dic1112yes—
108#431—221no—
109C2×C4×C8C2×D1111yescharacteristic
110C4⋊C16—112no—
111C22⋊C16—221no—
112C4×C16—221no—
113#335—112no—
114#334—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#36212yes—
125C4×C11#41311yescharacteristic
126C4×C11#41611yescharacteristic
127C4×C11#50812yes—
128C2×Q16—21no—
129C2×Q16C2×Dic1112yes—
130C22×C8C2×Dic1111yescharacteristic
131C22×C8C22⋊D1111yescharacteristic
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134#125—41no—
135C22⋊Q8—22no—
136C22⋊Q8—41no—
137C4×Q8—22no—
138C4×Q8—41no—
139#117—41no—
140C2×C42C22⋊D1111yescharacteristic
141C2×C16—222no—
142#107—21no—
143#107C2×Dic1112yes—
144C4⋊C8—222no—
145#103—22no—
146#103—22no—
147C22⋊C8—441no—
148C4×C8—441no—
149C4×C8C2×Dic1111yescharacteristic
150C4×C8C22⋊D1111yescharacteristic
151C4×C8C22⋊D1111yescharacteristic
152C4×C8C22×D1111yescharacteristic
153C2×C11—41no—
154C2×C11#154011yescharacteristic
155C2×C11#213811yescharacteristic
156C2×C11C2×#36211yescharacteristic
157C2×Q8—22no—
158C2×Q8—41no—
159C22×C4#432311yescharacteristic
160C22×C4#432411yescharacteristic
161C22×C4C22⋊Dic1111yescharacteristic
162Q16—42no—
163Q16—42no—
164C2×C8—22no—
165C2×C8—41no—
166C2×C8—442no—
167C2×C8C22⋊Dic1111yescharacteristic
168C2×C8C22⋊Dic1111yescharacteristic
169C2×C8C22×Dic1111yescharacteristic
170C2×C8C2×C22⋊D1111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C22⋊C4—42no—
178C42—42no—
179C42#432311yescharacteristic
180C42#432411yescharacteristic
181C42C22⋊Dic1111yescharacteristic
182C42C2×C22⋊D1111yescharacteristic
183C16—442no—
184C11#1195011yescharacteristic, complemented, Sylow
185C23#6689611yescharacteristic
186Q8—42no—
187Q8—42no—
188Q8—82no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4#6689611yescharacteristic
196C2×C4#6689611yescharacteristic
197C2×C4#6689611yescharacteristic
198C2×C4C2×#432311yescharacteristic
199C2×C4C2×#432411yescharacteristic
200C2×C4C2×C22⋊Dic1111yescharacteristic
201C8—21no—
202C8—21no—
203C8—21no—
204C8—882no—
205C8#6700312yes—
206C22—21no—
207C22—21no—
208C22—21no—
209C22C2×#6689611yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—82no—
214C4—82no—
215C4#1062220312yes—
216C4#1062280712yes—
217C4#1062284611yescharacteristic
218C4#1062285011yescharacteristic
219C2—41no—
220C2#1306726511yescharacteristic
221C2#1307032311yescharacteristic
222C2C2×#1062220311yescharacteristic
subgroupG/H
centerC2×C4#66896
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#3170C2
socleC22×C11C2×#102
prime radicalC23×C11#102
cosocleC4×C8×C11C23
hypercenter#3170D11
hypocenterC11#11950
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13066671C2semidirect
4. #13066665C2semidirect
184. C11#11950semidirect

Maximal subgroups

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

subgroupindex
#130704152
#130673642
#130666712
#130666652
C11×#31702
#1195011