Finite Group Databasebeta

← #14960196

Subgroups — #14960196

Order 2816.

1778 conjugacy classes of subgroups; only the 539 normal subgroups are shown.

normal subgroups only

This group has 1778 conjugacy classes of subgroups — too many to draw. Only its 539 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#13076880C213yesmaximal
2#13076876C2112yesmaximal, complemented
3#13071883C2112yesmaximal, complemented
4#13070994C213yesmaximal
5C11×#2840C211yesmaximal, characteristic
6C24×Dic11C2211yescharacteristic
7C2×Q8×Dic11C2214yescomplemented
8C2×#66930C2216yes—
9C11×#393C22112yes—
10C11×#379C2213yes—
11#10622860C2213yes—
12#10622842C22112yescomplemented
13#10622562C22112yes—
14#10622561C22124yes—
15#10622556C2216yes—
16#10622555C22112yes—
17C22⋊C4×Dic11C22112yes—
18#10622272C22112yescomplemented
19#10622270C22124yescomplemented
20#10622262C22112yescomplemented
21C25×C11C2311yescharacteristic
22C22×Q8×C11C2314yes—
23C23×Dic11—44no—
24C23×Dic11Q818yescomplemented
25C23×Dic11C2313yes—
26C23×Dic11C2313yes—
27C2×C11×C22⋊C4C2316yes—
28C2×C11×C22⋊C4C23112yes—
29C2×C22⋊Dic11C2316yes—
30C2×C22⋊Dic11C23112yes—
31Q8×Dic11—48no—
32C2×C4⋊Dic11C23112yes—
33C2×Dic11⋊C4C23112yes—
34C2×Dic11⋊C4C23124yes—
35C2×C4×Dic11C23112yes—
36#66930—412no—
37C11×#95C23112yes—
38C11⋊#95C23112yes—
39C11⋊#95C23124yes—
40#36674—111nomaximal, Sylow
41C24×C11—42no—
42C24×C11—44no—
43C24×C11C2×Q814yes—
44C24×C11C2413yes—
45C2×Q8×C11—44no—
46C2×Q8×C11—48no—
47C22×C4×C11C24112yes—
48C22×Dic11—212no—
49C22×Dic11—46no—
50C22×Dic11—416no—
51C22×Dic11C2×Q8112yes—
52C22×Dic11C2×Q8112yes—
53C22×Dic11C24112yes—
54C22×Dic11C2413yes—
55C22×Dic11C2411yescharacteristic
56C11×C22⋊C4—46no—
57C11×C22⋊C4—412no—
58C22⋊Dic11—46no—
59C22⋊Dic11—412no—
60C4⋊Dic11—412no—
61Dic11⋊C4—412no—
62Dic11⋊C4—424no—
63C4×Dic11—224no—
64#2842—113no—
65#2841—1112no—
66#2840D1111yescharacteristic
67#2396—1112no—
68#2280—113no—
69C23×C11—26no—
70C23×C11—212no—
71C23×C11—44no—
72C23×C11—48no—
73C23×C11—416no—
74C23×C11C22×Q816yes—
75C23×C11C2511yescharacteristic
76Q8×C11—416no—
77C2×C4×C11—212no—
78C2×C4×C11—224no—
79C2×Dic11—26no—
80C2×Dic11—224no—
81C2×Dic11—212no—
82C2×Dic11—224no—
83C2×Dic11—412no—
84C2×Dic11C22×Q816yes—
85C2×Dic11C22×Q812yes—
86C2×Dic11H(5,𝔽2)14yes—
87C24×C4—111no—
88C2×C4×Q8—114no—
89C2×#117—116no—
90#400—1112no—
91#399—1112no—
92#398—1124no—
93#396—1124no—
94#395—1112no—
95#393C2×D11112yes—
96#381—116no—
97#380—1112no—
98#379—113no—
99#379C2×D1113yes—
100C4×C4⋊C4—1112no—
101C4×C22⋊C4—1112no—
102C22×C11—26no—
103C22×C11—212no—
104C22×C11—416no—
105C22×C11—412no—
106C22×C11C23×Q811yescharacteristic
107C22×C11C2×H(5,𝔽2)12yes—
108C22×C11#58514yes—
109C4×C11—412no—
110Dic11—26no—
111Dic11—412no—
112Dic11#54314yes—
113C25C22×D1111yescharacteristic
114C22×Q8C22×D1114yes—
115C23×C4—113no—
116C23×C4—118no—
117C23×C4—113no—
118C23×C4—444no—
119C4×Q8—448no—
120#117—4412no—
121C2×C4⋊C4—1112no—
122C2×C4⋊C4—1112no—
123C2×C4⋊C4—1124no—
124C2×C22⋊C4—116no—
125C2×C22⋊C4—1112no—
126C2×C22⋊C4C22×D1116yes—
127C2×C22⋊C4C22×D11112yes—
128C2×C42—1112no—
129#95—1124no—
130#95—1112no—
131#95C22×D11112yes—
132C2×C11—46no—
133C2×C11C2×#54311yescharacteristic
134C2×C11#345812yes—
135C2×C11#352914yes—
136C24—42no—
137C24—44no—
138C24Q8×D1114yes—
139C24C23×D1113yes—
140C2×Q8—44no—
141C2×Q8—48no—
142C22×C4—111no—
143C22×C4—1112no—
144C22×C4—113no—
145C22×C4—1112no—
146C22×C4—1112no—
147C22×C4—2212no—
148C22×C4—4416no—
149C22×C4—446no—
150C22×C4C23×D11112yes—
151C4⋊C4—4412no—
152C4⋊C4—4412no—
153C4⋊C4—4424no—
154C22⋊C4—46no—
155C22⋊C4—412no—
156C22⋊C4—446no—
157C22⋊C4—4412no—
158C42—2224no—
159C11#3667411yescharacteristic, complemented, Sylow
160C23—26no—
161C23—212no—
162C23—44no—
163C23—48no—
164C23—416no—
165C23C2×Q8×D1116yes—
166C23C24×D1111yescharacteristic
167Q8—416no—
168C2×C4—212no—
169C2×C4—224no—
170C2×C4—112no—
171C2×C4—114no—
172C2×C4—116no—
173C2×C4—2224no—
174C2×C4—226no—
175C2×C4—2212no—
176C2×C4—2224no—
177C2×C4—4412no—
178C22—26no—
179C22—212no—
180C22—416no—
181C22—412no—
182C22C22×Q8×D1111yescharacteristic
183C22D11×H(5,𝔽2)12yes—
184C22#1062345514yes—
185C4—412no—
186C4—114no—
187C4—226no—
188C4—4412no—
189C2—46no—
190C2D11×#54311yescharacteristic
191C2#1308201812yes—
192C2#1308275614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2840C2
prime radicalC25×C11C23
hypercenter#2840D11
hypocenterC11#36674
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2840

Complements

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

NH ≅ G/Ntype
2. #13076876C2semidirect
3. #13071883C2semidirect
7. C2×Q8×Dic11C22semidirect
12. #10622842C22semidirect
18. #10622272C22semidirect
19. #10622270C22semidirect
20. #10622262C22semidirect
24. C23×Dic11Q8semidirect
159. C11#36674semidirect

Maximal subgroups

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

subgroupindex
#130768802
#130768762
#130718832
#130709942
C11×#28402
#3667411