Finite Group Databasebeta

← #11776967

Subgroups — #11776967

Order 1152.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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×#3788C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3#10590299C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×#3788C412yes—
7C42×C3⋊D3C2211yescharacteristic
8C2×#3712—21no—
9#63777C411yescharacteristic
10#63777C411yescharacteristic
11C4×#622C2212yes—
12C3×C4⋊(C3⋊C8)—21no—
13C3×#803—21no—
14#63572C2211yescharacteristic
15#63572C2212yes—
16#63572C2211yescharacteristic
17#63557—21no—
18#4837—61no—
19#4705—61no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3D411yescharacteristic
22C2×C4×C3⋊D3Q811yescharacteristic
23C2×#622C2×C412yes—
24C2×#622C2×C412yes—
25#3788—24no—
26C32×C42D411yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3Q811yescharacteristic
29C4×C3⋊Dic3C2311yescharacteristic
30C2×C3×C3⋊C8—21no—
31C2×C3×C3⋊C8—21no—
32C2×C3×C3⋊C8—22no—
33#3712—42no—
34#1569—91nomaximal, Sylow
35C2×ΓL(1,𝔽25)—62no—
36C42×D3—61no—
37C42×D3—61no—
38C3×C4⋊C8—61no—
39C3×#97—61no—
40(C2×D3)⋊C8—61no—
41(C2×D3)⋊C8—61no—
42Dic3⋊C8—61no—
43Dic3⋊C8—61no—
44Dic3⋊C8—62no—
45C4⋊(C3⋊C8)—21no—
46#803—21no—
47C22×C3⋊D3C4⋊C411yescharacteristic
48C2×C32×C4C4⋊C411yescharacteristic
49C2×C32×C4C4⋊C411yescharacteristic
50C2×C32×C4C2×D411yescharacteristic
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C2×C3⋊Dic3C22×C411yescharacteristic
53C2×C3⋊Dic3C2×Q811yescharacteristic
54C4×C3⋊D3—21no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—41no—
58#622—22no—
59#622M1614yescomplemented
60C3×C3⋊C8—42no—
61C3×C3⋊C8—41no—
62C3×C3⋊C8—41no—
63#432—91no—
64#423—91no—
65C4×M16—91no—
66#335—92no—
67#334—92no—
68C2×C4×D3—61no—
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C2×C4×D3—61no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C3×C8—61no—
75C2×C3×C8—61no—
76C2×C3×C8—62no—
77C3×C42—21no—
78C3×C42—21no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C4×Dic3—61no—
83C4×Dic3—61no—
84C4×Dic3—61no—
85C2×C3⋊C8—21no—
86C2×C3⋊C8—21no—
87C2×C3⋊C8—22no—
88ΓL(1,𝔽25)—124no—
89C22×C32C2×C4⋊C411yescharacteristic
90C2×C3⋊D3—21no—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—21no—
93C32×C4—21no—
94C32×C4—21no—
95C32×C4AGL(1,ℤ/8)11yescharacteristic
96C32×C4#13711yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3C2×M1612yes—
100C2×M16—92no—
101C2×M16—181no—
102C2×C42—91no—
103C4⋊C8—61no—
104C4⋊C8—91no—
105C4⋊C8—92no—
106C4⋊C8—91no—
107C22⋊C8—181no—
108#97—61no—
109#97—91no—
110#97—91no—
111C4×C8—92no—
112C22×D3—61no—
113C22×D3—61no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—21no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C4×D3—62no—
127C4×D3—62no—
128C4×D3—122no—
129C4×D3—122no—
130C4×D3—121no—
131C4×D3—121no—
132C4×D3—122no—
133C4×D3—122no—
134C3×C8—122no—
135C3×C8—121no—
136C3×C8—121no—
137C3⋊C8—42no—
138C3⋊C8—41no—
139C3⋊C8—41no—
140C2×C32#42311yescharacteristic
141C2×C32#42811yescharacteristic
142C2×C32#43011yescharacteristic
143C3⋊D3—41no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—91no—
147M16—184no—
148M16—362no—
149C2×C8—61no—
150C2×C8—61no—
151C2×C8—62no—
152C2×C8—92no—
153C2×C8—92no—
154C42—91no—
155C42—91no—
156C42—91no—
157C42GO+(4,𝔽2)11yescharacteristic
158C22×C3—21no—
159C22×C3—21no—
160C2×D3—62no—
161C2×D3—62no—
162C2×D3—121no—
163C2×D3—121no—
164C2×D3—121no—
165C2×D3—121no—
166C3×C4—22no—
167C3×C4—21no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—41no—
172C3×C4—41no—
173C3×C4—41no—
174Dic3—62no—
175Dic3—62no—
176Dic3—62no—
177Dic3—121no—
178Dic3—121no—
179Dic3—121no—
180C32#156911yescharacteristic, complemented, Sylow
181C23—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—182no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—361no—
189C2×C4#377311yescharacteristic
190C2×C4#377311yescharacteristic
191C2×C4C2×GO+(4,𝔽2)11yescharacteristic
192C8—94no—
193C8—122no—
194C8—121no—
195C8—121no—
196C8—182no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203D3—122no—
204D3—122no—
205C22—181no—
206C22—181no—
207C22—181no—
208C22C2×#377311yescharacteristic
209C4—21no—
210C4—21no—
211C4—92no—
212C4—181no—
213C4—181no—
214C4#6422411yescharacteristic
215C4#6422611yescharacteristic
216C3—21no—
217C3—21no—
218C2—361no—
219C2#1059332811yescharacteristic
220C2#1059333011yescharacteristic
221C2#1059339411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1569
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
59. #622M16semidirect
180. C32#1569semidirect

Maximal subgroups

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

subgroupindex
C4×#37882
#105903402
#105902992
#105900422
#105900412
#15699