Finite Group Databasebeta

← #11808865

Subgroups — #11808865

Order 1152.

802 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C4×#3797C212yesmaximal
2#10593733C211yesmaximal, characteristic
3#10593411C214yesmaximal
4C4×#3773C214yesmaximal
5#10593339C214yesmaximal
6C2×#3797C2212yes—
7C2×C4×#157C2212yes—
8C2×#3773C2218yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×Dic6—22no—
11C4×#627—22no—
12#63900C2212yes—
13#63883C2214yes—
14C4×#624C2214yes—
15#63843—22no—
16#63838—22no—
17#63781C2214yes—
18#63737C2214yes—
19#63737C2214yes—
20C4×D3×Q8—62no—
21C22×#157C2314yes—
22C2×C4×C3⋊D3C2312yes—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×C3×Dic6—22no—
25C2×#627—22no—
26C2×#624C2314yes—
27C2×#624C2314yes—
28#3797—28no—
29C4×#157Q818yescomplemented
30#3773—216no—
31C32×C42D411yescharacteristic
32C4×C3⋊Dic3D412yes—
33C4×C3⋊Dic3D411yescharacteristic
34C3×C4⋊Dic3—22no—
35C3×Dic3⋊C4—24no—
36C3×C4×Dic3—24no—
37#3724—22no—
38Dic3⋊Dic3—24no—
39Dic32—24no—
40#2399—91nomaximal, Sylow
41C2×D3×Q8—62no—
42C3×C4×Q8—62no—
43Q8×Dic3—62no—
44D3×C4⋊C4—64no—
45D3×C4⋊C4—62no—
46#887—64no—
47#887—62no—
48C42×D3—64no—
49C42×D3—62no—
50C4×Dic6—22no—
51C4×Dic6—64no—
52C22×C3⋊D3C2411yescharacteristic
53C2×#157—28no—
54C2×#157C2×Q818yes—
55C2×C32×C4C2×D412yes—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3C2×D412yes—
58C2×C3⋊Dic3C2×D411yescharacteristic
59C4×C3⋊D3—24no—
60C4×C3⋊D3C2×Q814yes—
61C2×C3×Dic3—24no—
62C2×C3×Dic3—24no—
63C3×Dic6—28no—
64#627—28no—
65#624—24no—
66#624—28no—
67#624#4118yes—
68C2×C4×Q8—92no—
69#398—94no—
70#395—94no—
71C4×C4⋊C4—94no—
72#376—91no—
73C2×C3×Q8—62no—
74D3×Q8—616no—
75C2×C4×D3—64no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—64no—
79C2×C4×D3—62no—
80C2×Dic6—22no—
81C2×Dic6—64no—
82C3×C4⋊C4—64no—
83C3×C4⋊C4—62no—
84C3×C42—22no—
85C3×C42—64no—
86C4⋊Dic3—22no—
87C4⋊Dic3—64no—
88Dic3⋊C4—24no—
89Dic3⋊C4—64no—
90Dic3⋊C4—64no—
91C4×Dic3—24no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—62no—
95C4×Dic3—64no—
96C4×Dic3—64no—
97C22×C32C22×D411yescharacteristic
98C2×C3⋊D3C22×Q812yes—
99C2×C3⋊D3C2×#4114yes—
100#157—28no—
101C32×C4—22no—
102C32×C4C4⋊Q812yes—
103C3⋊Dic3—22no—
104C3⋊Dic3C4⋊Q812yes—
105C3×Dic3—28no—
106C3×Dic3—44no—
107C22×Q8—92no—
108C4×Q8—62no—
109C4×Q8—182no—
110C4×Q8—182no—
111C4×Q8—182no—
112C2×C4⋊C4—94no—
113C2×C4⋊C4—92no—
114C2×C4⋊C4—98no—
115C2×C42—94no—
116C2×C42—92no—
117C2×C42—91no—
118#95—94no—
119#95—94no—
120#95—94no—
121C22×D3—62no—
122C3×Q8—68no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—64no—
127C2×C3×C4—64no—
128C2×Dic3—24no—
129C2×Dic3—24no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C4×D3—68no—
134C4×D3—68no—
135C4×D3—68no—
136C4×D3—68no—
137C4×D3—128no—
138C4×D3—124no—
139Dic6—28no—
140Dic6—616no—
141C2×C32#52512yes—
142C2×C32C2×C4⋊Q811yescharacteristic
143C3⋊D3#53314yes—
144C2×Q8—62no—
145C2×Q8—182no—
146C2×Q8—188no—
147C22×C4—94no—
148C22×C4—94no—
149C22×C4—91no—
150C22×C4—94no—
151C22×C4—92no—
152C4⋊C4—64no—
153C4⋊C4—62no—
154C4⋊C4—182no—
155C4⋊C4—184no—
156C4⋊C4—1816no—
157C42—64no—
158C42—98no—
159C42—92no—
160C42—91no—
161C42—184no—
162C42GO+(4,𝔽2)11yescharacteristic
163C22×C3—22no—
164C2×D3—64no—
165C2×D3—64no—
166C2×D3—64no—
167C3×C4—24no—
168C3×C4—24no—
169C3×C4—42no—
170C3×C4—68no—
171C3×C4—124no—
172Dic3—28no—
173Dic3—44no—
174Dic3—64no—
175Dic3—64no—
176Dic3—122no—
177C32#239911yescharacteristic, complemented, Sylow
178C23—91no—
179Q8—68no—
180Q8—188no—
181C2×C4—64no—
182C2×C4—64no—
183C2×C4—98no—
184C2×C4—91no—
185C2×C4—94no—
186C2×C4—98no—
187C2×C4—92no—
188C2×C4—184no—
189C2×C4—184no—
190C2×C4—188no—
191C2×C4—188no—
192C2×C4C2×GO+(4,𝔽2)12yes—
193C2×C4C2×GO+(4,𝔽2)11yescharacteristic
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197D3—68no—
198C22—92no—
199C22—94no—
200C22C22×GO+(4,𝔽2)11yescharacteristic
201C4—22no—
202C4—68no—
203C4—92no—
204C4—124no—
205C4—188no—
206C4—182no—
207C4#6422212yes—
208C3—22no—
209C2—94no—
210C2C2×#6422211yescharacteristic
211C2#1059651012yes—
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutator, prime radical, cosocleC22×C3⋊D3C24
FrattiniC22C22×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C22×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2399
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
29. C4×#157Q8semidirect
177. C32#2399semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105937332
#105934112
C4×#37732
#105933392
#23999