Finite Group Databasebeta

← #11770925

Subgroups — #11770925

Order 1152.

292 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 51 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#10593805C211yesmaximal, characteristic
2#10591360C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4C2×#3792—21no—
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×#3724—21no—
7#63779—21no—
8C4⋊#622C412yescomplemented
9C3×C3⋊#95—21no—
10C3×#830—21no—
11#63579C412yes—
12#63572—21no—
13#63553C412yescomplemented
14#4718—61no—
15#4650—61no—
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3C2×C411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3×Dic3—22no—
20#3792—41no—
21#3792—41no—
22C2×#622—22no—
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C2×C3×C3⋊C8—22no—
28#3724—41no—
29#3724—41no—
30#1286—91nomaximal, Sylow
31C2×Dic3⋊C4—62no—
32C2×C4×Dic3—61no—
33C2×C4×Dic3—61no—
34C3×C22⋊C8—61no—
35C3×#95—61no—
36C3⋊#95—21no—
37C3⋊#95—62no—
38#830—21no—
39Dic3⋊C8—62no—
40C8×Dic3—62no—
41C23×C32C22⋊C411yescharacteristic
42C2×C32×C4—41no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C3⋊Dic3—41no—
46C2×C3⋊Dic3C4211yescharacteristic
47C2×C3⋊Dic3C22⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C2×C3⋊Dic3C4⋊C411yescharacteristic
50C2×C3⋊Dic3D811yescharacteristic
51C2×C3⋊Dic3SD1611yescharacteristic
52C2×C3⋊Dic3SD1611yescharacteristic
53C2×C3⋊Dic3Q1611yescharacteristic
54C2×C3×Dic3—42no—
55C2×C3×Dic3—42no—
56C2×C3×Dic3—42no—
57#622—42no—
58C3×C3⋊C8—42no—
59#431—91no—
60#423—91no—
61#382—91no—
62C22×C3×C4—21no—
63C22×C3×C4—21no—
64C22×C3×C4—62no—
65C22×Dic3—22no—
66C22×Dic3—61no—
67C22×Dic3—61no—
68C22×Dic3—61no—
69C22×Dic3—61no—
70C2×C3×C8—62no—
71Dic3⋊C4—122no—
72Dic3⋊C4—122no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C2×C3⋊C8—22no—
82C22×C32—21no—
83C22×C32—21no—
84C22×C32#9511yescharacteristic
85C22×C32#10211yescharacteristic
86C22×C32#10311yescharacteristic
87C32×C4—21no—
88C32×C4—21no—
89C3⋊Dic3—21no—
90C3⋊Dic3—21no—
91C3⋊Dic3#10211yescharacteristic
92C3⋊Dic3#10311yescharacteristic
93C3⋊Dic3#10611yescharacteristic
94C3⋊Dic3#10711yescharacteristic
95C3×Dic3—82no—
96C2×M16—181no—
97C2×C4⋊C4—181no—
98C2×C42—91no—
99C4⋊C8—92no—
100C4⋊C8—181no—
101C4⋊C8—181no—
102C22⋊C8—61no—
103C4×C8—92no—
104#95—61no—
105#95—92no—
106C23×C3—21no—
107C23×C3—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—42no—
113C2×C3×C4—42no—
114C2×C3×C4—122no—
115C2×C3×C4—122no—
116C2×C3×C4—122no—
117C2×Dic3—42no—
118C2×Dic3—42no—
119C2×Dic3—42no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—61no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C2×Dic3—122no—
137C2×Dic3—122no—
138C3×C8—122no—
139C3⋊C8—42no—
140C2×C32—21no—
141C2×C32—21no—
142C2×C32H(3,ℤ/4)11yescharacteristic
143C2×C32#34011yescharacteristic
144C2×C32#34411yescharacteristic
145C22×C4—62no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4GO+(4,𝔽2)11yescharacteristic
149M16—361no—
150M16—361no—
151C2×C8—62no—
152C2×C8—182no—
153C4⋊C4—361no—
154C4⋊C4—361no—
155C42—91no—
156C42—91no—
157C42—91no—
158C42—91no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—21no—
162C22×C3—21no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—41no—
168C22×C3—41no—
169C3×C4—22no—
170C3×C4—41no—
171C3×C4—41no—
172C3×C4—41no—
173C3×C4—242no—
174Dic3—61no—
175Dic3—61no—
176Dic3—61no—
177Dic3—61no—
178Dic3—61no—
179Dic3—61no—
180Dic3—61no—
181Dic3—61no—
182Dic3—62no—
183Dic3—82no—
184Dic3—121no—
185Dic3—121no—
186Dic3—121no—
187C32#128611yescharacteristic, complemented, Sylow
188C23D32⋊C411yescharacteristic
189C2×C4—41no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—122no—
199C2×C4—122no—
200C2×C4—122no—
201C2×C4—361no—
202C2×C4D32⋊C411yescharacteristic
203C2×C4#377311yescharacteristic
204C8—122no—
205C8—362no—
206C2×C3—22no—
207C2×C3—22no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—21no—
214C2×C3—41no—
215C2×C3—41no—
216C22—21no—
217C22—21no—
218C22#6372911yescharacteristic
219C22#6373011yescharacteristic
220C22#6373711yescharacteristic
221C4—21no—
222C4—21no—
223C4—91no—
224C4—91no—
225C4—91no—
226C4—91no—
227C4—181no—
228C4—181no—
229C4—242no—
230C3—21no—
231C3—21no—
232C2—21no—
233C2—21no—
234C2#1059004911yescharacteristic
235C2#1059005411yescharacteristic
236C2#1059007311yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C32C22⋊C4
cosocleC2×C4×C3⋊Dic3C22
hypocenterC32#1286
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C4⋊#622C4semidirect
13. #63553C4semidirect
187. C32#1286semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105913602
#105910612
#12869