Finite Group Databasebeta

← #11797239

Subgroups — #11797239

Order 1152.

278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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×#63773C211yesmaximal, characteristic
2#10591138C211yesmaximal, characteristic
3C2×#63576C211yesmaximal, characteristic
4#10590069C212yesmaximal, complemented
5#10590068C212yesmaximal, complemented
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C3×#926—21no—
8C2×C3×C4⋊Dic3—21no—
9#63773C414yescomplemented
10C2×#3708C2212yes—
11#63576—21no—
12#63576C2211yescharacteristic
13#63576C2212yes—
14#63576C2211yescharacteristic
15#63574—21no—
16#4998—61no—
17C2×#807—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3×Dic3—41no—
20C2×C3⋊(C3⋊C8)C2×C412yes—
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)Q812yes—
23C2×C3⋊(C3⋊C8)C2311yescharacteristic
24C3×#217—41no—
25C3×C4⋊Dic3—22no—
26C3×C4⋊Dic3—21no—
27C3×C4⋊Dic3—21no—
28C3×C4⋊Dic3—41no—
29C3×C4×Dic3—41no—
30#3708C2×C414yescomplemented
31#2159—91nomaximal, Sylow
32C3×#117—61no—
33C2×C3×C4⋊C4—61no—
34#926—21no—
35C2×C4⋊Dic3—21no—
36C22×C3⋊C8—61no—
37C22×C3⋊C8—61no—
38#808—61no—
39#808—61no—
40#807—62no—
41#807—61no—
42#807—61no—
43#807—62no—
44C23×C32D811yescharacteristic
45C2×C32×C4C4⋊C412yes—
46C2×C32×C4D811yescharacteristic
47C2×C32×C4Q1612yes—
48C2×C32×C4C2×D411yescharacteristic
49C2×C3×Dic3—41no—
50C2×C3×Dic3—41no—
51C2×C3×Dic3—42no—
52C2×C3×Dic3—82no—
53C3⋊(C3⋊C8)C4⋊C412yes—
54C3⋊(C3⋊C8)C22×C411yescharacteristic
55C3⋊(C3⋊C8)C2×Q811yescharacteristic
56C2×M32—91no—
57#427—91no—
58C2×#107—91no—
59#367—92no—
60#366—92no—
61C22×C3×C4—21no—
62C22×C3×C4—21no—
63C22×C3×C4—121no—
64C22×Dic3—41no—
65C3×C4⋊C4—62no—
66C3×C4⋊C4—61no—
67C3×C4⋊C4—61no—
68C3×C4⋊C4—121no—
69C3×C22⋊C4—121no—
70C3×C42—121no—
71#217—41no—
72C4⋊Dic3—22no—
73C4⋊Dic3—21no—
74C4⋊Dic3—21no—
75C4⋊Dic3—41no—
76C4×Dic3—41no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—62no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8—62no—
84C2×C3⋊C8—62no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32#10712yes—
88C22×C32C2×D811yescharacteristic
89C32×C4#10712yes—
90C32×C4C2×C4⋊C411yescharacteristic
91C32×C4C2×Q1611yescharacteristic
92C3×Dic3—81no—
93C3×Dic3—82no—
94C3×Dic3—81no—
95C22×C8—91no—
96#117—61no—
97C2×C4⋊C4—61no—
98M32—94no—
99C2×C16—92no—
100#107—91no—
101#107—92no—
102#107—91no—
103#107—181no—
104#106—181no—
105C23×C3—21no—
106C23×C3—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—22no—
114C2×C3×C4—22no—
115C2×C3×C4—121no—
116C2×C3×C4—121no—
117C2×C3×C4—122no—
118C2×C3×C4—242no—
119C2×Dic3—41no—
120C2×Dic3—41no—
121C2×Dic3—42no—
122C2×Dic3—82no—
123C3⋊C8—62no—
124C3⋊C8—62no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C3⋊C8—61no—
129C2×C32—22no—
130C2×C32C2×#10711yescharacteristic
131C2×C32#50911yescharacteristic
132C2×C32#51011yescharacteristic
133C22×C4—121no—
134C22×C4GO+(4,𝔽2)11yescharacteristic
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—92no—
138C2×C8—92no—
139C4⋊C4—61no—
140C4⋊C4—61no—
141C4⋊C4—62no—
142C4⋊C4—121no—
143C22⋊C4—121no—
144C42—121no—
145C16—94no—
146C22×C3—22no—
147C22×C3—22no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—41no—
153C22×C3—41no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—22no—
159C3×C4—22no—
160C3×C4—242no—
161C3×C4—241no—
162C3×C4—241no—
163Dic3—82no—
164Dic3—81no—
165Dic3—81no—
166C32#215911yescharacteristic, complemented, Sylow
167C23#377411yescharacteristic
168C2×C4—121no—
169C2×C4—121no—
170C2×C4—122no—
171C2×C4—242no—
172C2×C4#377312yes—
173C2×C4#377411yescharacteristic
174C2×C4#377612yes—
175C2×C4C2×GO+(4,𝔽2)11yescharacteristic
176C8—91no—
177C8—92no—
178C8—91no—
179C2×C3—24no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—42no—
187C22—21no—
188C22—21no—
189C22#6374312yes—
190C22C2×#377411yescharacteristic
191C4—242no—
192C4—241no—
193C4—241no—
194C4#6374312yes—
195C4C2×#377311yescharacteristic
196C4C2×#377611yescharacteristic
197C3—21no—
198C3—21no—
199C2—22no—
200C2#1059333411yescharacteristic
201C2#1059333611yescharacteristic
202C2C2×#6374311yescharacteristic
subgroupG/H
centerC22C2×#3774
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
prime radicalC23×C32D8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2159
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590069C2semidirect
5. #10590068C2semidirect
9. #63773C4semidirect
30. #3708C2×C4semidirect
166. C32#2159semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
#105911382
C2×#635762
#105900692
#105900682
#21599