Finite Group Databasebeta

← #14674124

Subgroups — #14674124

Order 2816.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#10622183C212yesmaximal
2#13066787C214yesmaximal, complemented
3C11×#3138C211yesmaximal, characteristic
4C11×#533C411yescharacteristic, complemented
5C2×C11×#127C2211yescharacteristic
6C11×#490C412yescomplemented
7C11×#490C2212yes—
8C11×#486—22no—
9C11×#418—22no—
10C4×C11×M16C411yescharacteristic, complemented
11C2×#66898—22no—
12#10622183—22no—
13#10622183C2214yes—
14C22×D4×C11—41no—
15C22×D4×C11D412yes—
16C2×C11×M16—21no—
17C11×C4⋊Q8—21no—
18C11×#127—41no—
19C11×#127C2×C411yescharacteristic
20C11×#127D412yes—
21C11×#127C2311yescharacteristic
22C11×#125C2×C412yescomplemented
23C11×C22⋊Q8—41no—
24C4×Q8×C11—41no—
25C11×#117—21no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C22⋊Dic11—42no—
28C11×#102—24no—
29C11×#102—24no—
30C11×#97C2×C412yescomplemented
31C4×C8×C11—21no—
32#66898—24no—
33#66898—42no—
34#13595—111nomaximal, Sylow
35C24×C11—22no—
36C2×Q8×C11—41no—
37C2×D4×C11—22no—
38C2×D4×C11—42no—
39C2×D4×C11—42no—
40C2×D4×C11—41no—
41C2×D4×C11—42no—
42C2×D4×C11—41no—
43C2×D4×C11—84no—
44C2×D4×C11C22⋊C412yes—
45C2×D4×C11C2×D412yes—
46C22×C4×C11—21no—
47C22×C4×C11C22⋊C411yescharacteristic
48C22×Dic11—82no—
49C11×M16—42no—
50C2×C8×C11—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—41no—
53C11×C4⋊C4—42no—
54C11×C22⋊C4—41no—
55C42×C11—21no—
56C42×C11—41no—
57C42×C11C22⋊C411yescharacteristic
58C42×C11C22×C411yescharacteristic
59C22⋊Dic11—44no—
60C22⋊Dic11—82no—
61#3138D1111yescharacteristic
62C2×#353—112no—
63#1412—114no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—42no—
67C23×C11—42no—
68C23×C11—84no—
69C23×C11#9911yescharacteristic
70Q8×C11—82no—
71D4×C11—42no—
72D4×C11—42no—
73D4×C11—82no—
74D4×C11—84no—
75D4×C11—82no—
76D4×C11—82no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—42no—
81C2×C4×C11—42no—
82C2×C4×C11#9911yescharacteristic
83C2×C4×C11C2×C22⋊C411yescharacteristic
84C2×Dic11—84no—
85C2×Dic11—164no—
86C8×C11—42no—
87#533Dic1111yescharacteristic, complemented
88C2×#127C2×D1111yescharacteristic
89#490Dic1112yescomplemented
90#490C2×D1112yes—
91#486—22no—
92#418—22no—
93C2×#99—222no—
94C4×M16Dic1111yescharacteristic, complemented
95#353—114no—
96#353—222no—
97C22×C11—41no—
98C22×C11—42no—
99C22×C11—42no—
100C22×C11—82no—
101C22×C11—82no—
102C22×C11—84no—
103C22×C11—162no—
104C22×C11#35412yes—
105C22×C11C2×#9911yescharacteristic
106C4×C11—22no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—41no—
110C4×C11—82no—
111Dic11—164no—
112C22×D4—41no—
113C22×D4C22⋊D1112yes—
114C2×M16—21no—
115C4⋊Q8—21no—
116#127—41no—
117#127C2×Dic1111yescharacteristic
118#127C22⋊D1112yes—
119#127C22×D1111yescharacteristic
120#125C2×Dic1112yescomplemented
121C22⋊Q8—41no—
122C4×Q8—41no—
123#117—21no—
124C2×C22⋊C4—442no—
125C2×C42C2×Dic1111yescharacteristic
126#102—24no—
127#102—24no—
128#99—224no—
129#99—442no—
130#97C2×Dic1112yescomplemented
131C4×C8—21no—
132C2×C11—21no—
133C2×C11—22no—
134C2×C11—82no—
135C2×C11—82no—
136C2×C11C2×#35411yescharacteristic
137C24—22no—
138C2×Q8—41no—
139C2×D4—22no—
140C2×D4—42no—
141C2×D4—42no—
142C2×D4—41no—
143C2×D4—41no—
144C2×D4—42no—
145C2×D4—84no—
146C2×D4C22⋊Dic1112yes—
147C2×D4C2×C22⋊D1112yes—
148C22×C4—21no—
149C22×C4—882no—
150C22×C4C22⋊Dic1111yescharacteristic
151M16—42no—
152C2×C8—22no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—41no—
156C22⋊C4—41no—
157C22⋊C4—444no—
158C22⋊C4—882no—
159C42—21no—
160C42—41no—
161C42C22⋊Dic1111yescharacteristic
162C42C22×Dic1111yescharacteristic
163C11#1359511yescharacteristic, complemented, Sylow
164C23—22no—
165C23—22no—
166C23—42no—
167C23—42no—
168C23—84no—
169C23#6689811yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—84no—
175D4—82no—
176D4—82no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—884no—
183C2×C4—1764no—
184C2×C4#6689811yescharacteristic
185C2×C4C2×C22⋊Dic1111yescharacteristic
186C8—42no—
187C22—41no—
188C22—42no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—84no—
193C22—162no—
194C22#1062217912yes—
195C22C2×#6689811yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—82no—
201C4—1764no—
202C2—21no—
203C2—22no—
204C2—82no—
205C2—82no—
206C2C2×#1062217911yescharacteristic
subgroupG/H
centerC2C2×#10622179
commutatorC42×C11C22×C4
Frattini#127C22×D11
FittingC11×#3138C2
socleC2×C11C2×#354
prime radicalC2×C11×#127C22
cosocleC11×#127C23
hypercenter#3138D11
hypocenterC11#13595
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#127 ◁ #3138

Complements

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

NH ≅ G/Ntype
2. #13066787C2semidirect
4. C11×#533C4semidirect
6. C11×#490C4semidirect
10. C4×C11×M16C4semidirect
22. C11×#125C2×C4semidirect
30. C11×#97C2×C4semidirect
87. #533Dic11semidirect
89. #490Dic11semidirect
94. C4×M16Dic11semidirect
120. #125C2×Dic11semidirect
130. #97C2×Dic11semidirect
163. C11#13595semidirect

Maximal subgroups

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

subgroupindex
C2×#106221832
#130667872
C11×#31382
#1359511