Finite Group Databasebeta

← #14656916

Subgroups — #14656916

Order 2816.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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#13071921C211yesmaximal, characteristic
2#13067115C212yesmaximal
3#13066517C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#1995C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C11×#423C2211yescharacteristic
8C11×#376C2211yescharacteristic
9C4×C4⋊Dic11C2212yes—
10C4×Dic11⋊C4—22no—
11#10622538C2212yes—
12#10622273—22no—
13#10622270—22no—
14C11×#339—22no—
15#10622176—22no—
16#10622176—22no—
17C2×C11×M16—21no—
18C11×C4⋊Q8Q812yes—
19C11×#125—21no—
20C11×C22⋊Q8—22no—
21C4×Q8×C11—22no—
22C11×#117—21no—
23C2×C42×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11—22no—
26C2×Dic11⋊C4—22no—
27C2×Dic11⋊C4—22no—
28C2×C4×Dic11—22no—
29C11×C4⋊C8—22no—
30C11×#95—22no—
31C11⋊#95—22no—
32C11⋊#95—22no—
33C11⋊#95D412yes—
34C11⋊#95D412yes—
35C22⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4×C11⋊C8—22no—
38#10373—111nomaximal, Sylow
39C2×Q8×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11C2×D412yes—
42C22×C4×C11C2×D411yescharacteristic
43C22×Dic11—22no—
44C22×Dic11—22no—
45C11×M16—42no—
46C2×C8×C11—41no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—22no—
49C11×C4⋊C4—42no—
50C11×C22⋊C4—41no—
51C42×C11—22no—
52C42×C11—22no—
53C42×C11—41no—
54C42×C11C2×Q811yescharacteristic
55C42×C11#4111yescharacteristic
56C42×C11#4112yes—
57C4⋊Dic11—44no—
58Dic11⋊C4—44no—
59Dic11⋊C4—44no—
60C4×Dic11—42no—
61C4×Dic11—42no—
62C2×C11⋊C8—42no—
63#2402—111no—
64#1995D1111yescharacteristic
65#1503—112no—
66#1303—112no—
67#1274—111no—
68C23×C11#12011yescharacteristic
69Q8×C11—82no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11—42no—
75C2×C4×C11C22⋊Q812yes—
76C2×C4×C11C22⋊Q811yescharacteristic
77C2×C4×C11#12412yes—
78C2×C4×C11#12411yescharacteristic
79C2×C4×C11#13512yes—
80C2×C4×C11#13712yes—
81C2×Dic11—24no—
82C2×Dic11—42no—
83C2×Dic11—42no—
84C2×Dic11—42no—
85C2×Dic11—42no—
86C2×Dic11—42no—
87C8×C11—81no—
88C11⋊C8—82no—
89#533C2×D1111yescharacteristic
90#431—112no—
91#423C2×D1111yescharacteristic
92#400—222no—
93#398—222no—
94C4×C4⋊C4—112no—
95C4×C4⋊C4—222no—
96#376C2×D1111yescharacteristic
97#339—22no—
98#328—222no—
99#328—222no—
100C22×C11—22no—
101C22×C11#39311yescharacteristic
102C22×C11#45212yes—
103C4×C11—22no—
104C4×C11—22no—
105C4×C11—82no—
106C4×C11—82no—
107C4×C11#47912yes—
108C4×C11#48811yescharacteristic
109C4×C11#49111yescharacteristic
110Dic11—44no—
111Dic11—82no—
112C2×M16—21no—
113C4⋊Q8Dic2212yes—
114#125—21no—
115C22⋊Q8—22no—
116C4×Q8—22no—
117#117—21no—
118C2×C4⋊C4—222no—
119C2×C4⋊C4—222no—
120C2×C4⋊C4—222no—
121C2×C42—222no—
122C2×C42C22⋊D1112yes—
123C2×C42C22×D1111yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—222no—
126C22⋊C8—222no—
127C4×C8—222no—
128#95—22no—
129#95—112no—
130#95—112no—
131#95—222no—
132#95—222no—
133C2×C11—22no—
134C2×C11#202611yescharacteristic
135C2×C11#203112yes—
136C2×Q8—22no—
137C22×C4—22no—
138C22×C4—222no—
139C22×C4—222no—
140C22×C4D4×D1112yes—
141C22×C4C2×C22⋊D1111yescharacteristic
142M16—42no—
143C2×C8—41no—
144C2×C8—442no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C4⋊C4—42no—
148C4⋊C4—444no—
149C4⋊C4—444no—
150C4⋊C4—444no—
151C22⋊C4—41no—
152C42—22no—
153C42—22no—
154C42—41no—
155C42—442no—
156C42—442no—
157C42C2×Dic2211yescharacteristic
158C42#433911yescharacteristic
159C42#434112yes—
160C11#1037311yescharacteristic, complemented, Sylow
161C23#6699011yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—224no—
169C2×C4—442no—
170C2×C4—442no—
171C2×C4—442no—
172C2×C4—442no—
173C2×C4—442no—
174C2×C4#6693112yes—
175C2×C4#6693812yes—
176C2×C4#6697711yescharacteristic
177C2×C4#6698911yescharacteristic
178C2×C4#6699512yes—
179C2×C4#6700312yes—
180C8—81no—
181C8—882no—
182C22—22no—
183C22#1062256011yescharacteristic
184C22#1062266012yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—444no—
190C4—882no—
191C4#1062263512yes—
192C4#1062266911yescharacteristic
193C4#1062269511yescharacteristic
194C2—22no—
195C2#1306976711yescharacteristic
196C2#1306978612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1995D11
hypocenterC11#10373
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
160. C11#10373semidirect

Maximal subgroups

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

subgroupindex
#130719212
#130671152
#130665172
#130664452
C11×#19952
#1037311