Finite Group Databasebeta

← #11771925

Subgroups — #11771925

Order 1152.

364 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592930C211yesmaximal, characteristic
2#10590206C211yesmaximal, characteristic
3#10590204C211yesmaximal, characteristic
4C22×C32×Q8C411yescharacteristic, complemented
5C2×C22⋊#157—21no—
6C2×#3752—21no—
7C2×#3752C2211yescharacteristic
8C22⋊#622—21no—
9#63658—21no—
10#63658C411yescharacteristic, complemented
11#5231—62no—
12C23×C3⋊D3D411yescharacteristic
13C22×#157—41no—
14C2×C32×Q8—42no—
15C2×C32×Q8—41no—
16C22×C32×C4—21no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3D411yescharacteristic
20C22⋊#157—22no—
21C22⋊#157—41no—
22C2×#622—41no—
23#3752—41no—
24#3752—42no—
25#1351—91nomaximal, Sylow
26C22×C3×Q8—22no—
27C2×(C2×D3)⋊C4—62no—
28C2×(C2×D3)⋊C4—64no—
29C3⋊#95—62no—
30C3⋊#95—64no—
31C23×C32C22⋊C411yescharacteristic
32C22×C3⋊D3—21no—
33C22×C3⋊D3—21no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3—41no—
36C22×C3⋊D3SD1611yescharacteristic
37C22×C3⋊D3Q1611yescharacteristic
38C2×#157—42no—
39C2×#157—81no—
40C2×#157—81no—
41C32×Q8—42no—
42C32×Q8—42no—
43C2×C32×C4—22no—
44C2×C32×C4—21no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C32×C4—41no—
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51C2×C3⋊Dic3—41no—
52C2×C3⋊Dic3—41no—
53#622—81no—
54#393—91no—
55#342—91no—
56#323—91no—
57C23×D3—62no—
58C2×C3×Q8—48no—
59C2×C3×Q8—44no—
60C22×C3×C4—24no—
61C22×C3×C4—22no—
62C22×Dic3—62no—
63C22×Dic3—64no—
64(C2×D3)⋊C4—124no—
65(C2×D3)⋊C4—128no—
66C22×C32—21no—
67C22×C32—21no—
68C22×C32#9911yescharacteristic
69C22×C32#10311yescharacteristic
70C22×C32#10411yescharacteristic
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3—41no—
74C2×C3⋊D3—41no—
75C2×C3⋊D3—41no—
76C2×C3⋊D3—41no—
77C2×C3⋊D3—81no—
78#157—82no—
79C32×C4—42no—
80C32×C4—41no—
81C3⋊Dic3—41no—
82C3⋊Dic3—81no—
83C22×Q8#15711yescharacteristic, complemented
84C2×C22⋊C4—91no—
85C2×C22⋊C4—181no—
86C2×C22⋊C4—181no—
87C22⋊C8—181no—
88#95—91no—
89#95—181no—
90C23×C3—22no—
91C22×D3—62no—
92C22×D3—62no—
93C22×D3—122no—
94C22×D3—122no—
95C22×D3—124no—
96C22×D3—124no—
97C3×Q8—48no—
98C3×Q8—48no—
99C2×C3×C4—28no—
100C2×C3×C4—24no—
101C2×C3×C4—44no—
102C2×C3×C4—44no—
103C2×C3×C4—44no—
104C2×Dic3—122no—
105C2×Dic3—124no—
106C2×Dic3—124no—
107C2×Dic3—124no—
108C2×Dic3—124no—
109C2×C32—21no—
110C2×C32—21no—
111C2×C32#32811yescharacteristic
112C2×C32AΣL(1,𝔽16)11yescharacteristic
113C2×C32#35411yescharacteristic
114C3⋊D3—41no—
115C3⋊D3—41no—
116C24—91no—
117C2×Q8—42no—
118C2×Q8—41no—
119C22×C4—21no—
120C22×C4—91no—
121C22×C4—181no—
122C22×C4—361no—
123C22×C4C2×#15711yescharacteristic
124C2×C8—361no—
125C22⋊C4—182no—
126C22⋊C4—361no—
127C22⋊C4—362no—
128C22⋊C4—361no—
129C22×C3—24no—
130C22×C3—24no—
131C22×C3—22no—
132C22×C3—22no—
133C22×C3—22no—
134C2×D3—122no—
135C2×D3—122no—
136C2×D3—124no—
137C2×D3—124no—
138C2×D3—242no—
139C2×D3—242no—
140C2×D3—244no—
141C3×C4—48no—
142C3×C4—44no—
143Dic3—242no—
144Dic3—244no—
145C32#135111yescharacteristic, complemented, Sylow
146C23—91no—
147C23—91no—
148C23—181no—
149C23—181no—
150C23—361no—
151C23—361no—
152C23C22⋊#15711yescharacteristic
153Q8—42no—
154Q8—42no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—181no—
161C2×C4—361no—
162C2×C4—361no—
163C2×C4—361no—
164C2×C4—362no—
165C2×C4—361no—
166C2×C4—721no—
167C2×C4—721no—
168C8—721no—
169C2×C3—24no—
170C2×C3—24no—
171C2×C3—22no—
172C2×C3—22no—
173C2×C3—22no—
174D3—242no—
175D3—242no—
176C22—21no—
177C22—21no—
178C22—181no—
179C22—181no—
180C22—361no—
181C22—361no—
182C22—361no—
183C22—361no—
184C22—721no—
185C22#6378411yescharacteristic
186C22#6378511yescharacteristic
187C22#6378611yescharacteristic
188C4—42no—
189C4—41no—
190C4—361no—
191C4—721no—
192C4—722no—
193C3—22no—
194C2—21no—
195C2—21no—
196C2—361no—
197C2—361no—
198C2#1059021511yescharacteristic
199C2#1059021711yescharacteristic
200C2#1059022311yescharacteristic
subgroupG/H
centerC22#63786
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC22×C32×Q8C4
socleC22×C32#99
prime radicalC23×C3⋊D3D4
cosocleC2×#3752C22
hypercenterC22×Q8#157
hypocenterC32#1351
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. C22×C32×Q8C4semidirect
10. #63658C4semidirect
83. C22×Q8#157semidirect
145. C32#1351semidirect

Maximal subgroups

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

subgroupindex
#105929302
#105902062
#105902042
#13519