Finite Group Databasebeta

← #11770850

Subgroups — #11770850

Order 1152.

346 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 57 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×C22⋊#157C211yesmaximal, characteristic
2#10593800C211yesmaximal, characteristic
3C2×#63778C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C22×#622—21no—
7C2×C4×#157—21no—
8C2×#3787C412yescomplemented
9C22⋊#622—21no—
10#63781—21no—
11#63778—21no—
12#63778—21no—
13#63778C412yescomplemented
14C23×C3⋊D3C2×C411yescharacteristic
15C22×#157—22no—
16C22×C32×C4Q811yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C2×C4×C3⋊D3—42no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C22⋊#157—22no—
24C22⋊#157C814yescomplemented
25C2×#622—22no—
26C2×#622—22no—
27C2×#622—42no—
28C4×#157—42no—
29#3787—42no—
30#1282—91nomaximal, Sylow
31C22×C4×D3—121no—
32C23×C32C4⋊C411yescharacteristic
33C22×C3⋊D3—41no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3C4211yescharacteristic
36C22×C3⋊D3C22⋊C411yescharacteristic
37C22×C3⋊D3C2×C812yes—
38C22×C3⋊D3M1612yes—
39C2×#157—24no—
40C2×#157—42no—
41C2×#157—42no—
42C2×C32×C4—41no—
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3C22⋊C411yescharacteristic
47C2×C3⋊Dic3C22⋊C411yescharacteristic
48C4×C3⋊D3—22no—
49C4×C3⋊D3—22no—
50C4×C3⋊D3—41no—
51C4×C3⋊D3—41no—
52#622—42no—
53#622—42no—
54C2×C22⋊C8—91no—
55C2×C22⋊C8—91no—
56C4×C22⋊C4—91no—
57C23×D3—121no—
58C22×C3×C4—41no—
59C22×Dic3—121no—
60C2×C4×D3—121no—
61C2×C4×D3—121no—
62C2×C4×D3—121no—
63C2×C4×D3—121no—
64C2×C4×D3—128no—
65C22×C32—21no—
66C22×C32—21no—
67C22×C32#9511yescharacteristic
68C22×C32C4⋊C812yes—
69C2×C3⋊D3—21no—
70C2×C3⋊D3—21no—
71C2×C3⋊D3—21no—
72C2×C3⋊D3—21no—
73C2×C3⋊D3—42no—
74C2×C3⋊D3—42no—
75C2×C3⋊D3C4×C811yescharacteristic
76C2×C3⋊D3#9711yescharacteristic
77C2×C3⋊D3C22⋊C812yes—
78#157—44no—
79C32×C4—21no—
80C32×C4—21no—
81C3⋊Dic3—21no—
82C3⋊Dic3#9912yes—
83C23×C4—91no—
84C22×C8—92no—
85C22×C8—181no—
86C2×C22⋊C4—92no—
87C2×C42—181no—
88C22⋊C8—92no—
89C22⋊C8—181no—
90C22⋊C8—181no—
91C22⋊C8—181no—
92#95—181no—
93C23×C3—41no—
94C22×D3—121no—
95C22×D3—121no—
96C22×D3—122no—
97C22×D3—122no—
98C22×D3—124no—
99C22×D3—124no—
100C2×C3×C4—44no—
101C2×C3×C4—41no—
102C2×C3×C4—41no—
103C2×Dic3—121no—
104C2×Dic3—121no—
105C2×Dic3—124no—
106C4×D3—124no—
107C4×D3—124no—
108C4×D3—124no—
109C4×D3—124no—
110C2×C32—22no—
111C2×C32#33611yescharacteristic
112C2×C32#34211yescharacteristic
113C2×C32#34411yescharacteristic
114C3⋊D3—22no—
115C3⋊D3—21no—
116C3⋊D3—21no—
117C24—91no—
118C22×C4—91no—
119C22×C4—91no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—91no—
123C22×C4—182no—
124C22×C4—362no—
125C22×C4PSU(3,𝔽2)11yescharacteristic
126C2×C8—182no—
127C2×C8—182no—
128C2×C8—362no—
129C2×C8—362no—
130C22⋊C4—94no—
131C22⋊C4—182no—
132C42—362no—
133C22×C3—42no—
134C22×C3—42no—
135C22×C3—42no—
136C22×C3—41no—
137C2×D3—121no—
138C2×D3—121no—
139C2×D3—122no—
140C2×D3—122no—
141C2×D3—122no—
142C2×D3—122no—
143C2×D3—122no—
144C2×D3—128no—
145C2×D3—128no—
146C3×C4—42no—
147C3×C4—42no—
148Dic3—122no—
149Dic3—122no—
150C32#128211yescharacteristic, complemented, Sylow
151C23—91no—
152C23—91no—
153C23—92no—
154C23—92no—
155C23—361no—
156C23—361no—
157C23#377711yescharacteristic
158C2×C4—41no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—182no—
162C2×C4—182no—
163C2×C4—182no—
164C2×C4—184no—
165C2×C4—361no—
166C2×C4—361no—
167C2×C4—362no—
168C2×C4—362no—
169C2×C4#377711yescharacteristic
170C2×C4#377711yescharacteristic
171C8—362no—
172C8—362no—
173C2×C3—44no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—41no—
177D3—124no—
178D3—122no—
179D3—122no—
180C22—21no—
181C22—21no—
182C22—92no—
183C22—91no—
184C22—91no—
185C22—181no—
186C22—181no—
187C22—181no—
188C22—181no—
189C22—362no—
190C22—362no—
191C22#6374412yes—
192C22#6374711yescharacteristic
193C4—21no—
194C4—21no—
195C4—92no—
196C4—181no—
197C4—364no—
198C3—41no—
199C2—22no—
200C2—182no—
201C2—181no—
202C2—181no—
203C2#1059009011yescharacteristic
204C2#1059009511yescharacteristic
205C2#1059009811yescharacteristic
subgroupG/H
centerC22#63747
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC22×C4PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1282
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×#3787C4semidirect
13. #63778C4semidirect
24. C22⋊#157C8semidirect
150. C32#1282semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105938002
C2×#637782
#12829