Finite Group Databasebeta

← #14662981

Subgroups — #14662981

Order 2816.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#13077256C211yesmaximal, characteristic
2#13070412C212yesmaximal, complemented
3#13066557C212yesmaximal, complemented
4#13066542C211yesmaximal, characteristic
5C11×#1315C211yesmaximal, characteristic
6#41×Dic11C411yescharacteristic
7C11×#408C2211yescharacteristic
8#10622847C411yescharacteristic
9#10622732C411yescharacteristic
10M16×Dic11C411yescharacteristic
11#10622715C2211yescharacteristic
12C2×C8×Dic11C2211yescharacteristic
13#10622333—22no—
14#10622331—22no—
15C11×C22⋊C16C2212yes—
16C22⋊(C11⋊C16)C2212yes—
17Dic11⋊C16—22no—
18C16×Dic11—22no—
19C2×C11×#41C2×C411yescharacteristic
20C2×C11×M16C2×C411yescharacteristic
21C22×C8×C11C2311yescharacteristic
22Q8×Dic11C812yes—
23D4×Dic11—22no—
24D4×Dic11C812yes—
25#66979—21no—
26#66979C2×C411yescharacteristic
27C2×C4×Dic11—21no—
28C2×C4×Dic11C2×C411yescharacteristic
29C2×#4318C2×C411yescharacteristic
30C22×C11⋊C8C2×C411yescharacteristic
31C2×C11×C16—22no—
32C11×C22⋊C8—22no—
33C22⋊(C11⋊C8)—22no—
34#66879—21no—
35Dic11⋊C8—22no—
36Dic11⋊C8—22no—
37C8×Dic11—21no—
38C8×Dic11D412yes—
39C8×Dic11D412yes—
40C2×C11⋊C16—22no—
41#11462—111nomaximal, Sylow
42C11×#41—41no—
43C11×#41—41no—
44C2×Q8×C11C2×C811yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11C2×C811yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11C22×C411yescharacteristic
49C22×Dic11—22no—
50C22×Dic11M1612yes—
51C11×M16—41no—
52C2×C8×C11—21no—
53C2×C8×C11—41no—
54C2×C8×C11C2×D412yes—
55C22⋊Dic11—22no—
56C22⋊Dic11—21no—
57C4⋊Dic11—22no—
58C4⋊Dic11C2×C812yes—
59C4×Dic11—22no—
60C4×Dic11—21no—
61C4×Dic11C22⋊C411yescharacteristic
62C4×Dic11C22⋊C411yescharacteristic
63C4×Dic11C2×C812yes—
64#4318—41no—
65C2×C11⋊C8—21no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8C22⋊C412yes—
68C11×C16—42no—
69C11⋊C16—42no—
70#2922—111no—
71#2162—112no—
72#1323—112no—
73#1315—111no—
74#1315D1111yescharacteristic
75C23×C11—21no—
76C23×C11C2×M1611yescharacteristic
77Q8×C11—41no—
78D4×C11—41no—
79D4×C11—42no—
80C2×C4×C11—21no—
81C2×C4×C11—21no—
82C2×C4×C11—21no—
83C2×C4×C11—41no—
84C2×C4×C11—41no—
85C2×C4×C11C2×C22⋊C411yescharacteristic
86C2×C4×C11C22×C811yescharacteristic
87C2×Dic11—24no—
88C2×Dic11—22no—
89C2×Dic11—44no—
90C2×Dic11C22⋊C812yes—
91C2×Dic11C22⋊C812yes—
92C8×C11—22no—
93C8×C11—41no—
94C11⋊C8—22no—
95C11⋊C8—41no—
96C4×#41—111no—
97#433—222no—
98#431—222no—
99#424—111no—
100#424—111no—
101#408—111no—
102#408C2×D1111yescharacteristic
103C4×M16—111no—
104C2×C4×C8—111no—
105C4⋊C16—222no—
106C22⋊C16—112no—
107C22⋊C16C2×D1112yes—
108C4×C16—222no—
109C22×C11—22no—
110C22×C11—21no—
111C22×C11—42no—
112C22×C11—41no—
113C22×C11C2×C22⋊C811yescharacteristic
114C4×C11—21no—
115C4×C11—41no—
116C4×C11#41011yescharacteristic
117C4×C11#41311yescharacteristic
118Dic11—22no—
119Dic11—42no—
120Dic11#35014yes—
121C2×#41C4×D1111yescharacteristic
122C2×M16—111no—
123C2×M16C4×D1111yescharacteristic
124C22×C8—111no—
125C22×C8C22×D1111yescharacteristic
126C4×Q8—112no—
127C4×D4—112no—
128C4×D4—222no—
129#117—111no—
130#117—221no—
131C2×C42—111no—
132C2×C42—221no—
133C2×C16—22no—
134C2×C16—222no—
135C4⋊C8—222no—
136C4⋊C8—222no—
137C22⋊C8—22no—
138C22⋊C8—222no—
139#97—221no—
140C4×C8—112no—
141C4×C8—112no—
142C4×C8—221no—
143C2×C11—41no—
144C2×C11—81no—
145C2×C11#145811yescharacteristic
146C2×C11C2×#35012yes—
147#41—41no—
148#41—41no—
149C2×Q8C8×D1111yescharacteristic
150C2×D4—21no—
151C2×D4C8×D1111yescharacteristic
152C22×C4—21no—
153C22×C4—112no—
154C22×C4—222no—
155C22×C4C2×C4×D1111yescharacteristic
156M16—41no—
157M16—441no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—112no—
161C2×C8—221no—
162C2×C8—441no—
163C2×C8D4×D1112yes—
164C4⋊C4—112no—
165C4⋊C4—222no—
166C22⋊C4—222no—
167C22⋊C4—221no—
168C42—111no—
169C42—111no—
170C42—112no—
171C42—222no—
172C42—221no—
173C16—42no—
174C16—442no—
175C11#1146211yescharacteristic, complemented, Sylow
176C23—21no—
177C23M16×D1111yescharacteristic
178Q8—41no—
179D4—41no—
180D4—42no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—112no—
187C2×C4—112no—
188C2×C4—224no—
189C2×C4—222no—
190C2×C4—444no—
191C2×C4C22⋊C4×D1111yescharacteristic
192C2×C4C2×C8×D1111yescharacteristic
193C8—22no—
194C8—41no—
195C8—222no—
196C8—441no—
197C22—22no—
198C22—21no—
199C22—42no—
200C22—41no—
201C22D11×C22⋊C811yescharacteristic
202C4—21no—
203C4—41no—
204C4—114no—
205C4—222no—
206C4—442no—
207C4#1062235311yescharacteristic
208C4#1062235811yescharacteristic
209C2—41no—
210C2—81no—
211C2#1306692711yescharacteristic
212C2D11×#35012yes—
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C22×C8
FrattiniC22×C8C22×D11
FittingC11×#1315C2
socleC22×C11C2×C22⋊C8
prime radicalC2×C11×#41C2×C4
cosocleC22×C8×C11C23
hypercenter#1315D11
hypocenterC11#11462
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #13070412C2semidirect
3. #13066557C2semidirect
175. C11#11462semidirect

Maximal subgroups

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

subgroupindex
#130772562
#130704122
#130665572
#130665422
C11×#13152
#1146211