Finite Group Databasebeta

← #11775084

Subgroups — #11775084

Order 1152.

462 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596199C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10593727C211yesmaximal, characteristic
4#10590158C214yesmaximal
5C2×C4⋊#157—21no—
6C2×C4×#157—21no—
7C32×C4⋊Q8C411yescharacteristic, complemented
8#64155—21no—
9Q8×C3⋊Dic3—21no—
10#64106C2212yes—
11#64101—21no—
12#64099—21no—
13#64096C412yescomplemented
14C42×C3⋊D3C2211yescharacteristic
15#64078C411yescharacteristic, complemented
16#63781C2212yes—
17#63778C2212yes—
18C4⋊#622—21no—
19C4×#622—21no—
20#5728—62no—
21C22×#157—22no—
22C2×C32×Q8—21no—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×#634C2×C412yes—
27C2×#622—22no—
28C4⋊#157—24no—
29C4×#157—42no—
30C32×C4⋊C4—21no—
31C32×C4⋊C4C2×C412yes—
32C32×C42C2×C411yescharacteristic
33#3752—22no—
34C4⋊(C3⋊Dic3)—21no—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—22no—
37#3750—22no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42#1503—91nomaximal, Sylow
43C3×C4⋊Q8—22no—
44#946—64no—
45Q8×Dic3—64no—
46#897—64no—
47#892—64no—
48#890—64no—
49#887—64no—
50C42×D3—62no—
51#869—62no—
52C22×C3⋊D3C2×D411yescharacteristic
53C2×#157—24no—
54C2×#157—42no—
55C2×#157—42no—
56C32×Q8—42no—
57C2×C32×C4—22no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22⋊C411yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C2×D411yescharacteristic
65C4×C3⋊D3—22no—
66C4×C3⋊D3—41no—
67C4×C3⋊D3SD1612yes—
68C4×C3⋊D3Q1612yes—
69#634—42no—
70#622—42no—
71#533—91no—
72#431—91no—
73C4×C4⋊C4—91no—
74#328—94no—
75C2×C3×Q8—24no—
76C2×C4×D3—62no—
77C2×C4×D3—62no—
78C2×C4×D3—62no—
79C2×Dic6—64no—
80C3×C4⋊C4—24no—
81C3×C4⋊C4—24no—
82C3×C42—22no—
83(C2×D3)⋊C4—68no—
84C4⋊Dic3—64no—
85C4⋊Dic3—64no—
86C4⋊Dic3—68no—
87Dic3⋊C4—68no—
88C4×Dic3—62no—
89C4×Dic3—62no—
90C4×Dic3—62no—
91C4×Dic3—68no—
92C22×C32C2×C22⋊C411yescharacteristic
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3C2×SD1611yescharacteristic
96C2×C3⋊D3C2×Q1611yescharacteristic
97#157—44no—
98C32×C4—21no—
99C32×C4—42no—
100C32×C4#10312yes—
101C32×C4#10412yes—
102C3⋊Dic3—21no—
103C3⋊Dic3—21no—
104C3⋊Dic3—42no—
105C3⋊Dic3#10312yes—
106C4⋊Q8—91no—
107C4⋊Q8#15711yescharacteristic, complemented
108#125—181no—
109C22⋊Q8—92no—
110C22⋊Q8—181no—
111C4×Q8—92no—
112C4×Q8—181no—
113#117—181no—
114C2×C4⋊C4—181no—
115C2×C42—91no—
116C2×C42—181no—
117C4⋊C8—181no—
118C22⋊C8—92no—
119C4×C8—181no—
120#95—92no—
121C22×D3—62no—
122C3×Q8—48no—
123C2×C3×C4—28no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—68no—
131C4×D3—64no—
132C4×D3—64no—
133C4×D3—124no—
134C4×D3—124no—
135Dic6—128no—
136C2×C32#41011yescharacteristic
137C2×C32C2×#10311yescharacteristic
138C2×C32C2×#10411yescharacteristic
139C3⋊D3—21no—
140C3⋊D3—21no—
141C2×Q8—21no—
142C2×Q8—92no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—182no—
147C2×C8—182no—
148C4⋊C4—21no—
149C4⋊C4—182no—
150C4⋊C4—182no—
151C4⋊C4—184no—
152C4⋊C4—181no—
153C4⋊C4—181no—
154C4⋊C4C2×#15712yes—
155C22⋊C4—182no—
156C42—91no—
157C42—91no—
158C42—91no—
159C42—182no—
160C42—362no—
161C42C2×#15711yescharacteristic
162C22×C3—22no—
163C2×D3—62no—
164C2×D3—62no—
165C2×D3—122no—
166C2×D3—122no—
167C3×C4—24no—
168C3×C4—24no—
169C3×C4—24no—
170C3×C4—48no—
171Dic3—64no—
172Dic3—122no—
173Dic3—122no—
174Dic3—128no—
175C32#150311yescharacteristic, complemented, Sylow
176C23—91no—
177Q8—42no—
178Q8—362no—
179C2×C4—22no—
180C2×C4—91no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—182no—
186C2×C4—184no—
187C2×C4—182no—
188C2×C4—361no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4C22⋊#15711yescharacteristic
192C2×C4C22⋊#15711yescharacteristic
193C2×C4C22×#15711yescharacteristic
194C8—362no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—22no—
198D3—122no—
199D3—122no—
200C22—91no—
201C22—91no—
202C22—181no—
203C22—181no—
204C22C2×C22⋊#15711yescharacteristic
205C4—21no—
206C4—42no—
207C4—92no—
208C4—181no—
209C4—181no—
210C4—364no—
211C4—362no—
212C4#6378312yes—
213C4#6378412yes—
214C3—22no—
215C2—181no—
216C2—181no—
217C2C2×#6378311yescharacteristic
218C2C2×#6378411yescharacteristic
219C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1503
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
7. C32×C4⋊Q8C4semidirect
13. #64096C4semidirect
15. #64078C4semidirect
107. C4⋊Q8#157semidirect
175. C32#1503semidirect

Maximal subgroups

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

subgroupindex
#105961992
C4×C4⋊#1572
#105937272
#105901582
#15039