Finite Group Databasebeta

← #11790742

Subgroups — #11790742

Order 1152.

526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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#10593909C211yesmaximal, characteristic
2#10593736C211yesmaximal, characteristic
3C2×#63730C214yesmaximal
4#10590322C211yesmaximal, characteristic
5C2×#3797C2212yes—
6C2×C4⋊#157C2212yes—
7C42×C3⋊D3C2211yescharacteristic
8C3×#869—21no—
9#63919C414yescomplemented
10#63900—22no—
11#63873—21no—
12C2×#3710C2212yes—
13#63781—22no—
14#63730—28no—
15C3×#803—21no—
16#63555—21no—
17D3×C4⋊Q8—61no—
18D3×#97—61no—
19C22×#157—22no—
20C2×C4×C3⋊D3D412yes—
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×C3×Dic6—22no—
23C2×#627C2×C414yes—
24C2×#624—22no—
25#3797—24no—
26#3797—24no—
27C4⋊#157—24no—
28C32×C42D411yescharacteristic
29C4×C3⋊Dic3C2×C412yes—
30C4×C3⋊Dic3D411yescharacteristic
31C3×C4⋊Dic3—24no—
32C2×C3×C3⋊C8—22no—
33#3724—24no—
34#3710—22no—
35#3710D414yes—
36#1960—91nomaximal, Sylow
37C2×D3×Q8—62no—
38C3×C4⋊Q8—61no—
39#944—62no—
40C2×D3×C8—62no—
41D3×C4⋊C4—64no—
42#888—64no—
43C42×D3—61no—
44C42×D3—61no—
45#869—21no—
46C3×#97—61no—
47#815—62no—
48#803—21no—
49C22×C3⋊D3C2×D411yescharacteristic
50C2×#157—42no—
51C2×#157—44no—
52C2×C32×C4C22⋊C412yes—
53C2×C32×C4C2×D411yescharacteristic
54C2×C3⋊Dic3C22⋊C412yes—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C4×C3⋊D3—24no—
57C4×C3⋊D3C2×D412yes—
58C4×C3⋊D3#4112yes—
59C2×C3×Dic3—24no—
60C3×Dic6—44no—
61#627—28no—
62#624—42no—
63#624—42no—
64C3×C3⋊C8—24no—
65C2×C4⋊Q8—91no—
66C2×#103—94no—
67C2×#97—91no—
68#382—91no—
69C2×C3×Q8—62no—
70D3×Q8—124no—
71D3×Q8—124no—
72C2×C4×D3—62no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—62no—
76C2×C4×D3—64no—
77C2×Dic6—22no—
78C2×Dic6—64no—
79C2×C3×C8—62no—
80C3×C4⋊C4—64no—
81C3×C42—21no—
82C3×C42—21no—
83C4⋊Dic3—24no—
84Dic3⋊C4—68no—
85C4×Dic3—61no—
86C4×Dic3—62no—
87C4×Dic3—62no—
88C4×Dic3—61no—
89C2×C3⋊C8—22no—
90D3×C8—64no—
91D3×C8—64no—
92C22×C32C2×C22⋊C411yescharacteristic
93C2×C3⋊D3#12411yescharacteristic
94C2×C3⋊D3#12711yescharacteristic
95C2×C3⋊D3#13714yes—
96#157—82no—
97C32×C4—22no—
98C32×C4#12112yes—
99C3⋊Dic3—22no—
100C3⋊Dic3C4×D412yes—
101C3×Dic3—44no—
102C22×Q8—92no—
103C22×C8—92no—
104C4⋊Q8—61no—
105C4⋊Q8—94no—
106C4⋊Q8—181no—
107C2×C4⋊C4—92no—
108C2×C4⋊C4—182no—
109C2×C42—91no—
110#103—188no—
111#97—61no—
112#97—181no—
113#95—182no—
114C22×D3—61no—
115C22×D3—61no—
116C3×Q8—124no—
117C2×C3×C4—21no—
118C2×C3×C4—21no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—64no—
122C2×Dic3—24no—
123C2×Dic3—62no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—62no—
127C4×D3—62no—
128C4×D3—62no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—68no—
132C4×D3—124no—
133C4×D3—124no—
134C4×D3—124no—
135Dic6—44no—
136Dic6—128no—
137C3×C8—64no—
138C3⋊C8—24no—
139C2×C32#39011yescharacteristic
140C2×C32#41912yes—
141C3⋊D3#49112yes—
142C3⋊D3#49712yes—
143C2×Q8—62no—
144C2×Q8—94no—
145C2×Q8—184no—
146C2×Q8—184no—
147C22×C4—91no—
148C22×C4—92no—
149C22×C4—182no—
150C22×C4—182no—
151C2×C8—62no—
152C2×C8—94no—
153C2×C8—182no—
154C4⋊C4—64no—
155C4⋊C4—184no—
156C4⋊C4—184no—
157C42—91no—
158C42—92no—
159C42GO+(4,𝔽2)11yescharacteristic
160C22×C3—21no—
161C22×C3—21no—
162C2×D3—61no—
163C2×D3—61no—
164C2×D3—61no—
165C2×D3—61no—
166C2×D3—64no—
167C2×D3—64no—
168C3×C4—24no—
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—42no—
172C3×C4—124no—
173Dic3—44no—
174Dic3—62no—
175Dic3—62no—
176Dic3—64no—
177Dic3—122no—
178C32#196011yescharacteristic, complemented, Sylow
179C23—91no—
180Q8—124no—
181Q8—188no—
182C2×C4—64no—
183C2×C4—91no—
184C2×C4—92no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—184no—
188C2×C4—362no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4—364no—
192C2×C4D32⋊C412yes—
193C2×C4C2×GO+(4,𝔽2)11yescharacteristic
194C8—64no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3—21no—
199D3—62no—
200D3—62no—
201D3—62no—
202D3—62no—
203C22—94no—
204C22—91no—
205C22—91no—
206C22C2×D32⋊C411yescharacteristic
207C4—22no—
208C4—92no—
209C4—124no—
210C4—182no—
211C4—722no—
212C4#6423012yes—
213C3—21no—
214C3—21no—
215C2—92no—
216C2—92no—
217C2#1059332112yes—
218C2#1059340511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1960
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
9. #63919C4semidirect
178. C32#1960semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105937362
C2×#637302
#105903222
#19609