Finite Group Databasebeta

← #11772410

Subgroups — #11772410

Order 1152.

234 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593768C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3C2×#63542C211yesmaximal, characteristic
4#64286—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63818—21no—
7#63769C412yes—
8#63768—21no—
9C3×#819—21no—
10C2×C3×C3⋊C16—21no—
11#63578C412yescomplemented
12#63542—21no—
13#63542C412yescomplemented
14C2×D3×C16—61no—
15D3×#108—61no—
16C2×C4×C3⋊D3D411yescharacteristic
17C22⋊#157—41no—
18C4⋊#157—22no—
19C4×#157—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
22C8×C3⋊D3C2×C411yescharacteristic
23C8×C3⋊D3C2×C411yescharacteristic
24C8×C3⋊D3D411yescharacteristic
25C8×C3⋊D3Q811yescharacteristic
26C3×#208—22no—
27#3712—41no—
28#3710—41no—
29C3×C3⋊C16—22no—
30#1382—91nomaximal, Sylow
31D3×M16—62no—
32C2×D3×C8—61no—
33C2×D3×C8—61no—
34C2×C3×C16—61no—
35C3×#108—61no—
36#822—62no—
37#819—21no—
38C2×C3⋊C16—21no—
39D3×C16—62no—
40D3×C16—62no—
41C22×C3⋊D3SD1611yescharacteristic
42C2×#157—42no—
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C3⋊Dic3Q1611yescharacteristic
45C4×C3⋊D3C22⋊C411yescharacteristic
46C4×C3⋊D3C4⋊C411yescharacteristic
47C4×C3⋊D3D811yescharacteristic
48C4×C3⋊D3SD1611yescharacteristic
49C32×C8C22⋊C411yescharacteristic
50C32×C8C4⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4211yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C3×C3⋊C8—42no—
54C22×C16—91no—
55C2×#108—91no—
56#427—91no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C3×M16—62no—
60C2×C3×C8—21no—
61C2×C3×C8—21no—
62#208—22no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65ΓL(1,𝔽25)—122no—
66D3×C8—61no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—122no—
75C3×C16—62no—
76C3⋊C16—22no—
77C22×C32#10311yescharacteristic
78C2×C3⋊D3—22no—
79C2×C3⋊D3#10211yescharacteristic
80C2×C3⋊D3#10611yescharacteristic
81#157—82no—
82C32×C4#9511yescharacteristic
83C32×C4#10211yescharacteristic
84C3⋊Dic3#10311yescharacteristic
85C3⋊Dic3#10711yescharacteristic
86C2×M16—181no—
87C22×C8—91no—
88#117—181no—
89C2×C16—61no—
90C2×C16—92no—
91C2×C16—181no—
92#108—61no—
93#108—92no—
94#107—92no—
95#106—181no—
96C22×D3—61no—
97C22×D3—61no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102C4×D3—61no—
103C4×D3—61no—
104C4×D3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C3×C8—21no—
111C3×C8—21no—
112C3×C8—21no—
113C3×C8—21no—
114C3×C8—122no—
115C3⋊C8—42no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C2×C32—21no—
121C2×C32#34011yescharacteristic
122C3⋊D3—21no—
123C3⋊D3#35912yes—
124C22×C4—91no—
125M16—62no—
126M16—361no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—361no—
133C2×C8GO+(4,𝔽2)11yescharacteristic
134C4⋊C4—182no—
135C22⋊C4—361no—
136C42—361no—
137C16—62no—
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—61no—
141C2×D3—61no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—64no—
145C2×D3—122no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150Dic3—61no—
151Dic3—61no—
152Dic3—61no—
153Dic3—61no—
154C32#138211yescharacteristic, complemented, Sylow
155C23—91no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—362no—
162C2×C4D32⋊C411yescharacteristic
163C8—91no—
164C8—91no—
165C8—122no—
166C8D32⋊C411yescharacteristic
167C8#377311yescharacteristic
168C2×C3—22no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—41no—
172D3—62no—
173D3—62no—
174D3—62no—
175D3—121no—
176C22—91no—
177C22—91no—
178C22—182no—
179C22#6373011yescharacteristic
180C4—91no—
181C4—91no—
182C4—722no—
183C4#6372911yescharacteristic
184C4#6373711yescharacteristic
185C3—21no—
186C3—21no—
187C2—21no—
188C2—92no—
189C2—181no—
190C2#1059004911yescharacteristic
subgroupG/H
centerC4#63729
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#340
prime radicalC22×C3⋊D3SD16
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1382
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
11. #63578C4semidirect
13. #63542C4semidirect
154. C32#1382semidirect

Maximal subgroups

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

subgroupindex
#105937682
#105909132
C2×#635422
#13829