Finite Group Databasebeta

← #11771210

Subgroups — #11771210

Order 1152.

298 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 55 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×C4⋊#157C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C4×#157—21no—
6C42×C3⋊D3C2211yescharacteristic
7C2×#3712—21no—
8#63781C412yes—
9C3×C4⋊(C3⋊C8)—21no—
10C3×C4×C3⋊C8—21no—
11#63572C412yescomplemented
12#63572C412yescomplemented
13#63557—21no—
14#4837—61no—
15#4685—61no—
16C22×#157—22no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3D411yescharacteristic
20C4⋊#157—24no—
21C4×#157—41no—
22C4×#157—41no—
23C32×C42D411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C2×C3×C3⋊C8—22no—
28C2×C3×C3⋊C8—22no—
29#3712—41no—
30#3712—41no—
31#1303—91nomaximal, Sylow
32C2×ΓL(1,𝔽25)—62no—
33C42×D3—61no—
34C42×D3—61no—
35C3×C4⋊C8—61no—
36C3×C4×C8—61no—
37(C2×D3)⋊C8—62no—
38Dic3⋊C8—62no—
39Dic3⋊C8—62no—
40C4⋊(C3⋊C8)—21no—
41C4×C3⋊C8—21no—
42C22×C3⋊D3C22⋊C411yescharacteristic
43C2×#157—24no—
44C2×#157—42no—
45C2×#157—42no—
46C2×C32×C4C22⋊C411yescharacteristic
47C2×C32×C4C22⋊C411yescharacteristic
48C2×C32×C4C4⋊C411yescharacteristic
49C2×C3⋊Dic3C4211yescharacteristic
50C2×C3⋊Dic3C4⋊C411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C4×C3⋊D3—22no—
53C4×C3⋊D3—41no—
54C4×C3⋊D3D811yescharacteristic
55C4×C3⋊D3SD1611yescharacteristic
56C4×C3⋊D3SD1611yescharacteristic
57C4×C3⋊D3Q1611yescharacteristic
58C3×C3⋊C8—42no—
59C3×C3⋊C8—42no—
60#431—91no—
61#423—91no—
62C4×C4⋊C4—91no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×C4×D3—61no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—61no—
69C2×C3×C8—62no—
70C2×C3×C8—62no—
71C3×C42—21no—
72C3×C42—21no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C2×C3⋊C8—22no—
80C2×C3⋊C8—22no—
81ΓL(1,𝔽25)—122no—
82ΓL(1,𝔽25)—122no—
83C22×C32#9511yescharacteristic
84C2×C3⋊D3—21no—
85C2×C3⋊D3—21no—
86C2×C3⋊D3#10211yescharacteristic
87C2×C3⋊D3#10311yescharacteristic
88#157—44no—
89C32×C4—21no—
90C32×C4#10211yescharacteristic
91C32×C4#10311yescharacteristic
92C32×C4#10412yes—
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3#10611yescharacteristic
96C3⋊Dic3#10711yescharacteristic
97C2×M16—181no—
98C2×C4⋊C4—181no—
99C2×C42—91no—
100C2×C42—181no—
101C4⋊C8—61no—
102C4⋊C8—92no—
103C4⋊C8—92no—
104C22⋊C8—181no—
105C4×C8—61no—
106#95—92no—
107C22×D3—61no—
108C22×D3—61no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C4×D3—61no—
122C4×D3—61no—
123C4×D3—61no—
124C4×D3—61no—
125C4×D3—61no—
126C4×D3—61no—
127C4×D3—61no—
128C4×D3—61no—
129C4×D3—122no—
130C4×D3—122no—
131C4×D3—122no—
132C4×D3—122no—
133C3×C8—122no—
134C3×C8—122no—
135C3⋊C8—42no—
136C3⋊C8—42no—
137C2×C32#33911yescharacteristic
138C2×C32#34011yescharacteristic
139C2×C32#34411yescharacteristic
140C3⋊D3—21no—
141C3⋊D3—21no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—182no—
146M16—361no—
147M16—361no—
148C2×C8—62no—
149C2×C8—62no—
150C4⋊C4—184no—
151C42—91no—
152C42—91no—
153C42—91no—
154C42—361no—
155C42—361no—
156C42GO+(4,𝔽2)11yescharacteristic
157C22×C3—21no—
158C22×C3—21no—
159C2×D3—61no—
160C2×D3—61no—
161C2×D3—61no—
162C2×D3—61no—
163C2×D3—121no—
164C2×D3—121no—
165C2×D3—121no—
166C2×D3—121no—
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—22no—
173C3×C4—22no—
174C3×C4—41no—
175Dic3—61no—
176Dic3—61no—
177Dic3—61no—
178Dic3—61no—
179Dic3—62no—
180Dic3—121no—
181Dic3—121no—
182Dic3—121no—
183C32#130311yescharacteristic, complemented, Sylow
184C23—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—182no—
193C2×C4—184no—
194C2×C4—361no—
195C2×C4—362no—
196C2×C4—362no—
197C2×C4D32⋊C411yescharacteristic
198C2×C4D32⋊C411yescharacteristic
199C2×C4#377311yescharacteristic
200C8—122no—
201C8—122no—
202C2×C3—21no—
203C2×C3—21no—
204C2×C3—21no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—21no—
208D3—121no—
209D3—121no—
210D3—121no—
211D3—121no—
212C22—91no—
213C22—91no—
214C22—181no—
215C22—181no—
216C22#6373711yescharacteristic
217C4—21no—
218C4—91no—
219C4—91no—
220C4—181no—
221C4—181no—
222C4—364no—
223C4#6372911yescharacteristic
224C4#6373011yescharacteristic
225C4#6373112yes—
226C3—21no—
227C3—21no—
228C2—181no—
229C2—181no—
230C2#1059004711yescharacteristic
231C2#1059004911yescharacteristic
232C2#1059005511yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
prime radicalC22×C3⋊D3C22⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1303
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #63572C4semidirect
12. #63572C4semidirect
183. C32#1303semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#1572
#105903402
#105902972
#13039