Finite Group Databasebeta

← #14663210

Subgroups — #14663210

Order 2816.

280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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#13077263C211yesmaximal, characteristic
2#13070425C212yesmaximal, complemented
3#13066568C212yesmaximal, complemented
4#13066554C211yesmaximal, characteristic
5C11×#1321C211yesmaximal, characteristic
6#41×Dic11C411yescharacteristic
7C11×#408C2211yescharacteristic
8#10622847C411yescharacteristic
9#10622732C2211yescharacteristic
10M16×Dic11C2211yescharacteristic
11#10622715C411yescharacteristic
12C2×#66879C411yescharacteristic
13#10622333—22no—
14#10622332—22no—
15C11×#349C2212yes—
16#10622191C2212yes—
17#10622150—22no—
18#10622149—22no—
19C2×C11×#41C2×C411yescharacteristic
20C2×C11×M16C2311yescharacteristic
21C22×C8×C11C2×C411yescharacteristic
22Q8×Dic11—21no—
23D4×Dic11—21no—
24D4×Dic11—22no—
25#66979—21no—
26#66979C2×C411yescharacteristic
27C2×C4×Dic11—21no—
28C2×C4×Dic11C2×C411yescharacteristic
29C2×#4318C2×C411yescharacteristic
30C22×C11⋊C8C2×C411yescharacteristic
31C11×M32—22no—
32C11×C22⋊C8—22no—
33C22⋊(C11⋊C8)—22no—
34#66879—21no—
35#66879—21no—
36#66879D412yes—
37Dic11⋊C8—22no—
38Dic11⋊C8—22no—
39C8×Dic11D412yes—
40#66876—22no—
41#11523—111nomaximal, Sylow
42C11×#41—41no—
43C11×#41—41no—
44C2×Q8×C11M1611yescharacteristic
45C2×D4×C11—21no—
46C2×D4×C11M1611yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11C22×C411yescharacteristic
49C22×Dic11—22no—
50C22×Dic11—21no—
51C11×M16—41no—
52C2×C8×C11—21no—
53C2×C8×C11—41no—
54C2×C8×C11C2×D412yes—
55C22⋊Dic11—22no—
56C22⋊Dic11M1612yes—
57C4⋊Dic11—22no—
58C4⋊Dic11—21no—
59C4×Dic11—22no—
60C4×Dic11—21no—
61C4×Dic11—21no—
62C4×Dic11C22⋊C411yescharacteristic
63C4×Dic11C22⋊C411yescharacteristic
64#4318—41no—
65C2×C11⋊C8—21no—
66C2×C11⋊C8—41no—
67C2×C11⋊C8C22⋊C412yes—
68C11×C16—42no—
69C11⋊C16—42no—
70#2923—111no—
71#2165—112no—
72#1328—112no—
73#1321—111no—
74#1321D1111yescharacteristic
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×C11C2×M1611yescharacteristic
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11—21no—
90C2×Dic11—81no—
91C2×Dic11—82no—
92C8×C11—22no—
93C8×C11—41no—
94C11⋊C8—22no—
95C11⋊C8—41no—
96C4×#41—111no—
97#433—222no—
98#432—222no—
99#424—111no—
100#424—111no—
101#408—111no—
102#408C2×D1111yescharacteristic
103C4×M16—111no—
104C2×#97—111no—
105#364—222no—
106#349—112no—
107#349C2×D1112yes—
108#347—222no—
109C22×C11—21no—
110C22×C11—41no—
111C22×C11—42no—
112C22×C11—41no—
113C22×C11#40711yescharacteristic
114C4×C11—21no—
115C4×C11—41no—
116C4×C11#41011yescharacteristic
117C4×C11#41311yescharacteristic
118Dic11—42no—
119Dic11—41no—
120Dic11—41no—
121C2×#41C4×D1111yescharacteristic
122C2×M16—111no—
123C2×M16C22×D1111yescharacteristic
124C22×C8—111no—
125C22×C8C4×D1111yescharacteristic
126C4×Q8—221no—
127C4×D4—222no—
128C4×D4—221no—
129#117—111no—
130#117—221no—
131C2×C42—111no—
132C2×C42—221no—
133M32—22no—
134M32—222no—
135C4⋊C8—222no—
136C4⋊C8—222no—
137C22⋊C8—22no—
138C22⋊C8—222no—
139#97—112no—
140#97—221no—
141#97—221no—
142C4×C8—112no—
143C2×C11—21no—
144C2×C11—41no—
145C2×C11—81no—
146C2×C11#146411yescharacteristic
147#41—41no—
148#41—41no—
149C2×Q8#431311yescharacteristic
150C2×D4—21no—
151C2×D4#431311yescharacteristic
152C22×C4—21no—
153C22×C4—222no—
154C22×C4—221no—
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—222no—
165C4⋊C4—221no—
166C22⋊C4—112no—
167C22⋊C4—222no—
168C42—111no—
169C42—111no—
170C42—222no—
171C42—221no—
172C42—221no—
173C16—42no—
174C16—442no—
175C11#1152311yescharacteristic, 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—221no—
187C2×C4—221no—
188C2×C4—222no—
189C2×C4—881no—
190C2×C4—882no—
191C2×C4C22⋊C4×D1111yescharacteristic
192C2×C4C2×#431311yescharacteristic
193C8—22no—
194C8—41no—
195C8—222no—
196C8—441no—
197C22—21no—
198C22—41no—
199C22—42no—
200C22—41no—
201C22#1062233911yescharacteristic
202C4—21no—
203C4—41no—
204C4—441no—
205C4—441no—
206C4—442no—
207C4#1062235311yescharacteristic
208C4#1062235811yescharacteristic
209C2—21no—
210C2—41no—
211C2—81no—
212C2#1306694711yescharacteristic
subgroupG/H
centerC4#10622353
commutatorC22×C4×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1321C2
socleC2×C11#1464
prime radicalC2×C11×#41C2×C4
cosocleC2×C11×M16C23
hypercenter#1321D11
hypocenterC11#11523
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #13070425C2semidirect
3. #13066568C2semidirect
175. C11#11523semidirect

Maximal subgroups

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

subgroupindex
#130772632
#130704252
#130665682
#130665542
C11×#13212
#1152311