Finite Group Databasebeta

← Dic11×H(3,𝔽4) #14916479

Subgroups — Dic11×H(3,𝔽4) #14916479

Order 2816.

2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.

normal subgroups only

This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 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#13071790C219yesmaximal, complemented
2#13071757C216yesmaximal, complemented
3#124×Dic11C219yesmaximal, complemented
4#120×Dic11C216yesmaximal, complemented
5C2×C11×H(3,𝔽4)C211yesmaximal, characteristic
6C24×Dic11C2212yescomplemented
7C11×H(3,𝔽4)C4116yescomplemented
8C2×C11×#124C2219yes—
9C2×C11×#120C2216yes—
10C2×Q8×Dic11C2213yescomplemented
11C2×D4×Dic11C2219yes—
12#10622860C2216yescomplemented
13#10622843C2219yescomplemented
14#10622834C2219yes—
15#10622833C22118yes—
16#10622564C22136yescomplemented
17#10622563C22118yescomplemented
18C22⋊C4×Dic11C22118yescomplemented
19#10622549C2219yescomplemented
20C42×Dic11C2213yescomplemented
21C25×C11C2312yes—
22C22×Q8×C11C2313yes—
23C22×D4×C11C2319yes—
24C23×Dic11—412no—
25C23×Dic11C2316yes—
26C23×Dic11C2316yes—
27C11×#124C2×C4172yescomplemented
28C11×#120C2×C4148yescomplemented
29C2×C11×C22⋊C4C23118yes—
30C2×C42×C11C2313yes—
31C2×C22⋊Dic11C23118yes—
32C2×C22⋊Dic11C23118yes—
33Q8×Dic11—46no—
34D4×Dic11—418no—
35C2×C4⋊Dic11C2319yes—
36C2×C4⋊Dic11C2319yes—
37C2×C4×Dic11C2319yes—
38C2×C4×Dic11C2319yes—
39C11⋊#95C23136yes—
40C4×H(3,𝔽4)—111nomaximal, Sylow
41C24×C11—46no—
42C24×C11—46no—
43C24×C11C22×C418yescomplemented
44C24×C11C2416yes—
45C2×Q8×C11—43no—
46C2×Q8×C11—43no—
47C2×Q8×C11C22×C4112yescomplemented
48C2×D4×C11—49no—
49C2×D4×C11—49no—
50C2×D4×C11C22×C4136yes—
51C22×C4×C11C2419yes—
52C22×Dic11—236no—
53C22×Dic11—418no—
54C22×Dic11—432no—
55C22×Dic11C2416yes—
56C22×Dic11C2419yes—
57C22×Dic11C2411yescharacteristic
58C11×C22⋊C4C22×C4172yescomplemented
59C42×C11C22×C4112yescomplemented
60C22⋊Dic11—418no—
61C22⋊Dic11—418no—
62C4⋊Dic11—49no—
63C4⋊Dic11—49no—
64C4×Dic11—218no—
65C4×Dic11—49no—
66C2×H(3,𝔽4)D1111yescharacteristic
67#2379—119no—
68#2375—116no—
69C4×#124—119no—
70C4×#120—116no—
71C23×C11—218no—
72C23×C11—218no—
73C23×C11—424no—
74C23×C11—48no—
75C23×C11—424no—
76C23×C11C23×C4112yes—
77C23×C11C2511yescharacteristic
78Q8×C11—412no—
79D4×C11—436no—
80C2×C4×C11—29no—
81C2×C4×C11—29no—
82C2×C4×C11C23×C4118yes—
83C2×Dic11—29no—
84C2×Dic11—218no—
85C2×Dic11—218no—
86C2×Dic11—424no—
87C2×Dic11—424no—
88C2×Dic11H(5,𝔽2)16yes—
89C24×C4—112no—
90H(3,𝔽4)Dic11116yesdirect product factor
91C2×#124C2×D1119yes—
92C2×#120C2×D1116yes—
93C2×C4×Q8—113no—
94C2×C4×D4—119no—
95#391—119no—
96#390—119no—
97#388—1136no—
98#386—1118no—
99#385—1118no—
100#382—119no—
101#379—116no—
102C4×C22⋊C4—1118no—
103C43—113no—
104C22×C11—236no—
105C22×C11—432no—
106C22×C11—46no—
107C22×C11—418no—
108C22×C11C24×C411yescharacteristic
109C22×C11C2×H(5,𝔽2)13yes—
110C22×C11#58513yes—
111C4×C11—218no—
112Dic11—46no—
113Dic11—49no—
114Dic11H(3,𝔽4)14yesdirect product factor
115C25C22×D1112yes—
116C22×Q8C22×D1113yes—
117C22×D4C22×D1119yes—
118C23×C4—116no—
119C23×C4—116no—
120C23×C4—4412no—
121#124C2×Dic11172yescomplemented
122#120C2×Dic11148yescomplemented
123C4×Q8—446no—
124C4×D4—4418no—
125C2×C4⋊C4—119no—
126C2×C4⋊C4—119no—
127C2×C22⋊C4—1118no—
128C2×C22⋊C4—1118no—
129C2×C22⋊C4C22×D11118yes—
130C2×C42—119no—
131C2×C42—119no—
132C2×C42C22×D1113yes—
133#95—1136no—
134C2×C11—412no—
135C2×C11C4×H(5,𝔽2)13yes—
136C2×C11C2×H(3,𝔽4)11yescharacteristic
137C2×C11#352913yes—
138C24—46no—
139C24—46no—
140C24C22×Dic1118yescomplemented
141C24C23×D1116yes—
142C2×Q8—43no—
143C2×Q8—43no—
144C2×Q8C22×Dic11112yescomplemented
145C2×D4—49no—
146C2×D4—49no—
147C2×D4C22×Dic11136yes—
148C22×C4—111no—
149C22×C4—116no—
150C22×C4—119no—
151C22×C4—2236no—
152C22×C4—4418no—
153C22×C4—4432no—
154C22×C4C23×D1119yes—
155C4⋊C4—449no—
156C4⋊C4—449no—
157C22⋊C4—4418no—
158C22⋊C4—4418no—
159C22⋊C4C22×Dic11172yescomplemented
160C42—2218no—
161C42—449no—
162C42C22×Dic11112yescomplemented
163C11C4×H(3,𝔽4)11yescharacteristic, complemented, Sylow
164C23—218no—
165C23—218no—
166C23—424no—
167C23—48no—
168C23—424no—
169C23C23×Dic11112yes—
170C23C24×D1111yescharacteristic
171Q8—412no—
172D4—436no—
173C2×C4—29no—
174C2×C4—29no—
175C2×C4—116no—
176C2×C4—229no—
177C2×C4—2218no—
178C2×C4—2218no—
179C2×C4—4424no—
180C2×C4—4424no—
181C2×C4C23×Dic11118yes—
182C22—236no—
183C22—432no—
184C22—46no—
185C22—418no—
186C22D11×H(5,𝔽2)13yes—
187C22#1062345513yes—
188C22C24×Dic1111yescharacteristic
189C4—218no—
190C4—114no—
191C4—446no—
192C4—449no—
193C2—412no—
194C2H(5,𝔽2)×Dic1113yes—
195C2D11×H(3,𝔽4)11yescharacteristic
196C2#1308275613yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×H(3,𝔽4)C2
socle, cosocleC23×C11C25
hypercenterC2×H(3,𝔽4)D11
hypocenterC11C4×H(3,𝔽4)
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #13071790C2semidirect
2. #13071757C2semidirect
3. #124×Dic11C2semidirect
4. #120×Dic11C2semidirect
6. C24×Dic11C22semidirect
7. C11×H(3,𝔽4)C4semidirect
10. C2×Q8×Dic11C22semidirect
12. #10622860C22semidirect
13. #10622843C22semidirect
16. #10622564C22semidirect
17. #10622563C22semidirect
18. C22⋊C4×Dic11C22semidirect
19. #10622549C22semidirect
20. C42×Dic11C22semidirect
27. C11×#124C2×C4semidirect
28. C11×#120C2×C4semidirect
43. C24×C11C22×C4semidirect
47. C2×Q8×C11C22×C4semidirect
58. C11×C22⋊C4C22×C4semidirect
59. C42×C11C22×C4semidirect
90. H(3,𝔽4)Dic11direct (N × H)
114. Dic11H(3,𝔽4)direct (N × H)
121. #124C2×Dic11semidirect
122. #120C2×Dic11semidirect
140. C24C22×Dic11semidirect
144. C2×Q8C22×Dic11semidirect
159. C22⋊C4C22×Dic11semidirect
162. C42C22×Dic11semidirect
163. C11C4×H(3,𝔽4)semidirect

Maximal subgroups

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

subgroupindex
#130717902
#130717572
#124×Dic112
#120×Dic112
C2×C11×H(3,𝔽4)2
C4×H(3,𝔽4)11