Finite Group Databasebeta

← #11858868

Subgroups — #11858868

Order 1152.

722 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 722 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C2×#64101C211yesmaximal, characteristic
2#10593805C212yesmaximal, complemented
3#10593802C212yesmaximal
4C4×#3792C212yesmaximal, complemented
5#10593753C218yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3792C2214yes—
8C2×C32×C4⋊C4C411yescharacteristic
9C2×#3752C411yescharacteristic
10C2×#3752C411yescharacteristic
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64101C414yes—
15#64101C2214yes—
16#63779C2214yescomplemented
17#63778C2218yes—
18#63777C2214yescomplemented
19C4⋊#622C2214yescomplemented
20C4×#622C2214yescomplemented
21C2×#892—62no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×C4×C3⋊D3—24no—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2312yes—
32#3792—28no—
33C2×#622C2318yes—
34C32×C4⋊C4C2×C414yes—
35#3752C2×C414yes—
36#3752C2×C414yes—
37C4⋊(C3⋊Dic3)C2×C414yes—
38C4×C3⋊Dic3C2×C412yes—
39C4×C3⋊Dic3C2×C412yes—
40C4×C3⋊Dic3C2312yes—
41C4×C3⋊Dic3C2312yes—
42#2921—91nomaximal, Sylow
43C22×C4×D3—62no—
44C2×C3×C4⋊C4—22no—
45C2×(C2×D3)⋊C4—62no—
46C2×(C2×D3)⋊C4—62no—
47C2×C4⋊Dic3—62no—
48C2×C4×Dic3—62no—
49C2×C4×Dic3—62no—
50#892—68no—
51#892—68no—
52C23×C32C22×C411yescharacteristic
53C22×C3⋊D3—22no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3—41no—
56C22×C3⋊D3C22×C412yes—
57C2×C32×C4—22no—
58C2×C32×C4—41no—
59C2×C32×C4—41no—
60C2×C32×C4C22×C412yes—
61C2×C32×C4C22×C412yes—
62C2×C32×C4C22×C412yes—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22×C412yes—
66C2×C3⋊Dic3C22×C412yes—
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3#4114yes—
69C2×C3⋊Dic3C2411yescharacteristic
70C4×C3⋊D3—24no—
71C4×C3⋊D3—24no—
72#622—28no—
73C2×#117—91no—
74#433—98no—
75#423—92no—
76#407—92no—
77C4×M16—92no—
78C23×D3—62no—
79C22×C3×C4—22no—
80C22×C3×C4—22no—
81C22×C3×C4—22no—
82C22×Dic3—62no—
83C22×Dic3—62no—
84C22×Dic3—62no—
85C2×C4×D3—64no—
86C2×C4×D3—64no—
87C2×C4×D3—616no—
88C3×C4⋊C4—28no—
89(C2×D3)⋊C4—68no—
90(C2×D3)⋊C4—68no—
91C4⋊Dic3—68no—
92C4×Dic3—64no—
93C4×Dic3—64no—
94C4×Dic3—64no—
95C4×Dic3—64no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32#11712yes—
99C22×C32C23×C411yescharacteristic
100C2×C3⋊D3—22no—
101C2×C3⋊D3—22no—
102C2×C3⋊D3—22no—
103C2×C3⋊D3—44no—
104C32×C4—22no—
105C32×C4—22no—
106C32×C4—22no—
107C3⋊Dic3—22no—
108C3⋊Dic3—22no—
109C3⋊Dic3#11712yes—
110C3⋊Dic3C2×#4112yes—
111C23×C4—91no—
112C2×M16—94no—
113#117—94no—
114#117—94no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4#15711yescharacteristic
117C2×C22⋊C4—91no—
118C2×C22⋊C4—91no—
119C2×C42—91no—
120C2×C42—91no—
121C4⋊C8—94no—
122C4⋊C8—94no—
123C22⋊C8—98no—
124#97—94no—
125C4×C8—94no—
126C23×C3—22no—
127C22×D3—64no—
128C22×D3—68no—
129C22×D3—124no—
130C22×D3—124no—
131C2×C3×C4—28no—
132C2×C3×C4—24no—
133C2×C3×C4—24no—
134C2×C3×C4—24no—
135C2×C3×C4—44no—
136C2×C3×C4—44no—
137C2×Dic3—62no—
138C2×Dic3—68no—
139C2×Dic3—62no—
140C2×Dic3—64no—
141C2×Dic3—64no—
142C2×Dic3—124no—
143C2×Dic3—124no—
144C4×D3—616no—
145C4×D3—616no—
146C2×C32—22no—
147C2×C32C2×#11711yescharacteristic
148C2×C32#56811yescharacteristic
149C2×C32#56811yescharacteristic
150C3⋊D3—42no—
151C24—91no—
152C22×C4—91no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—92no—
156C22×C4—92no—
157C22×C4—184no—
158C22×C4C2×#15711yescharacteristic
159C22×C4C2×#15711yescharacteristic
160C22×C4C2×#15711yescharacteristic
161M16—188no—
162C2×C8—98no—
163C4⋊C4—94no—
164C4⋊C4C2×#15714yes—
165C22⋊C4—94no—
166C22⋊C4—94no—
167C42—92no—
168C42—92no—
169C42—92no—
170C42—92no—
171C22×C3—24no—
172C22×C3—24no—
173C22×C3—24no—
174C22×C3—22no—
175C2×D3—68no—
176C2×D3—124no—
177C2×D3—124no—
178C2×D3—1216no—
179C3×C4—28no—
180C3×C4—44no—
181C3×C4—44no—
182Dic3—64no—
183Dic3—64no—
184Dic3—124no—
185Dic3—124no—
186C32#292111yescharacteristic, complemented, Sylow
187C23—92no—
188C23—182no—
189C23—361no—
190C23—361no—
191C23C22×#15711yescharacteristic
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—94no—
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—92no—
199C2×C4—92no—
200C2×C4—184no—
201C2×C4—184no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4C22×#15712yes—
205C2×C4C22×#15712yes—
206C2×C4C22×#15712yes—
207C8—188no—
208C2×C3—28no—
209C2×C3—22no—
210C2×C3—22no—
211C2×C3—22no—
212D3—128no—
213C22—21no—
214C22—21no—
215C22—182no—
216C22—182no—
217C22—182no—
218C22—364no—
219C22#6428612yes—
220C22C23×#15711yescharacteristic
221C4—22no—
222C4—22no—
223C4—22no—
224C4—92no—
225C4—92no—
226C4—182no—
227C4—182no—
228C3—22no—
229C2—22no—
230C2—362no—
231C2C2×#6428611yescharacteristic
232C2#1059664011yescharacteristic
233C2#1059664411yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C4⋊C4C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenterC2×C4⋊C4#157
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
4. C4×#3792C2semidirect
5. #10593753C2semidirect
16. #63779C22semidirect
18. #63777C22semidirect
19. C4⋊#622C22semidirect
20. C4×#622C22semidirect
186. C32#2921semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
#105938052
#105938022
C4×#37922
#105937532
#29219