Finite Group Databasebeta

← #11771110

Subgroups — #11771110

Order 1152.

392 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 48 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#10593803C211yesmaximal, characteristic
2C2×#63778C211yesmaximal, characteristic
3C3⋊D3×C22⋊C8C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C22×#622—21no—
6C2×#3788C412yes—
7C2×C8×C3⋊D3—21no—
8C22⋊#622—21no—
9#63778—21no—
10#63778—21no—
11#63778C412yes—
12C32×C22⋊C8C411yescharacteristic
13#63657C411yescharacteristic
14#63647—21no—
15D3×C22⋊C8—62no—
16C23×C3⋊D3Q811yescharacteristic
17C22×C32×C4C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×#622—22no—
25C2×#622—22no—
26C2×#622—42no—
27#3788—42no—
28C2×C32×C8—21no—
29C2×C3⋊(C3⋊C8)—21no—
30C8×C3⋊D3—42no—
31#1298—91nomaximal, Sylow
32C22×C4×D3—62no—
33C2×D3×C8—64no—
34C3×C22⋊C8—22no—
35#830—62no—
36(C2×D3)⋊C8—64no—
37C23×C32C4⋊C411yescharacteristic
38C22×C3⋊D3—21no—
39C22×C3⋊D3—21no—
40C22×C3⋊D3—22no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3C4⋊C411yescharacteristic
43C22×C3⋊D3C4⋊C411yescharacteristic
44C2×C32×C4—41no—
45C2×C32×C4C4211yescharacteristic
46C2×C32×C4C22⋊C411yescharacteristic
47C2×C3⋊Dic3—22no—
48C2×C3⋊Dic3C22⋊C411yescharacteristic
49C2×C3⋊Dic3C22⋊C411yescharacteristic
50C4×C3⋊D3—22no—
51C4×C3⋊D3—22no—
52C4×C3⋊D3—41no—
53C4×C3⋊D3—41no—
54#622—42no—
55#622—42no—
56C32×C8—41no—
57C3⋊(C3⋊C8)—41no—
58#407—91no—
59C2×C22⋊C8—91no—
60C2×C22⋊C8—91no—
61C23×D3—62no—
62C22×C3×C4—22no—
63C22×Dic3—62no—
64C2×C4×D3—62no—
65C2×C4×D3—62no—
66C2×C4×D3—62no—
67C2×C4×D3—62no—
68C2×C4×D3—128no—
69C2×C3×C8—24no—
70C2×C3⋊C8—64no—
71D3×C8—128no—
72C22×C32—21no—
73C22×C32—21no—
74C22×C32#9511yescharacteristic
75C22×C32#10811yescharacteristic
76C22×C32#10811yescharacteristic
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—42no—
83C2×C3⋊D3—42no—
84C2×C3⋊D3#10812yes—
85C32×C4—21no—
86C32×C4—21no—
87C3⋊Dic3—21no—
88C3⋊Dic3#9912yes—
89C23×C4—91no—
90C2×M16—92no—
91C22×C8—181no—
92C22×C8—181no—
93C22⋊C8—92no—
94C22⋊C8—91no—
95C22⋊C8—181no—
96C22⋊C8—181no—
97C22⋊C8—181no—
98C22⋊C8—181no—
99C22⋊C8#15711yescharacteristic
100C23×C3—22no—
101C22×D3—62no—
102C22×D3—62no—
103C22×D3—64no—
104C22×D3—64no—
105C22×D3—124no—
106C22×D3—124no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×C3×C4—44no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—124no—
113C4×D3—68no—
114C4×D3—124no—
115C4×D3—124no—
116C4×D3—124no—
117C3×C8—44no—
118C3⋊C8—124no—
119C2×C32—21no—
120C2×C32—21no—
121C2×C32#34111yescharacteristic
122C2×C32#34111yescharacteristic
123C2×C32#34211yescharacteristic
124C3⋊D3—22no—
125C3⋊D3—41no—
126C24—91no—
127C22×C4—91no—
128C22×C4—91no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—362no—
133C22×C4C2×#15711yescharacteristic
134M16—362no—
135C2×C8—21no—
136C2×C8—182no—
137C2×C8—182no—
138C2×C8—181no—
139C2×C8—362no—
140C2×C8—362no—
141C22×C3—22no—
142C22×C3—22no—
143C22×C3—22no—
144C22×C3—42no—
145C22×C3—42no—
146C2×D3—64no—
147C2×D3—64no—
148C2×D3—64no—
149C2×D3—64no—
150C2×D3—122no—
151C2×D3—122no—
152C2×D3—128no—
153C2×D3—128no—
154C3×C4—24no—
155C3×C4—42no—
156Dic3—64no—
157Dic3—122no—
158C32#129811yescharacteristic, complemented, Sylow
159C23—91no—
160C23—91no—
161C23—182no—
162C23—181no—
163C23—181no—
164C23—361no—
165C23C4⋊#15711yescharacteristic
166C2×C4—41no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—182no—
170C2×C4—182no—
171C2×C4—182no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4C4×#15711yescharacteristic
175C2×C4C22⋊#15711yescharacteristic
176C8—41no—
177C8—361no—
178C8—362no—
179C8—362no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—42no—
184C2×C3—42no—
185D3—68no—
186D3—124no—
187C22—21no—
188C22—21no—
189C22—92no—
190C22—181no—
191C22—181no—
192C22—181no—
193C22—181no—
194C22—181no—
195C22—362no—
196C22—362no—
197C22#6377011yescharacteristic
198C22#6377111yescharacteristic
199C22#6378111yescharacteristic
200C4—21no—
201C4—21no—
202C4—92no—
203C4—181no—
204C3—22no—
205C2—21no—
206C2—21no—
207C2—182no—
208C2—361no—
209C2#1059015511yescharacteristic
210C2#1059018511yescharacteristic
211C2#1059019011yescharacteristic
subgroupG/H
centerC22#63781
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC32×C22⋊C8C4
socleC22×C32#95
prime radicalC23×C3⋊D3Q8
cosocleC22×C4×C3⋊D3C22
hypercenterC22⋊C8#157
hypocenterC32#1298
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
158. C32#1298semidirect

Maximal subgroups

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

subgroupindex
#105938032
C2×#637782
C3⋊D3×C22⋊C82
#12989