Finite Group Databasebeta

← #11858311

Subgroups — #11858311

Order 1152.

814 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 202 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×#64283C212yesmaximal
2C2×#64101C211yesmaximal, characteristic
3#10593805C214yesmaximal, complemented
4#10593755C218yesmaximal, complemented
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2214yes—
7#64283—28no—
8C2×#3788C2214yes—
9C2×#3787C2214yes—
10C2×C32×C4⋊C4C411yescharacteristic
11C2×#3752C412yes—
12C2×C4⋊(C3⋊Dic3)C411yescharacteristic
13C2×C4×C3⋊Dic3C2212yes—
14#64101C414yes—
15#64101C2214yes—
16#63779C2218yescomplemented
17C4⋊#622C2218yescomplemented
18C2×#892—62no—
19C23×C3⋊D3C2×C411yescharacteristic
20C22×C32×C4C2×C412yes—
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3C2×C412yes—
23C22×C3⋊Dic3C2311yescharacteristic
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3D414yes—
26C2×C4×C3⋊D3Q814yes—
27C2×C4×C3⋊D3C2312yes—
28#3792—28no—
29C2×#622C2318yes—
30#3788—28no—
31#3787—28no—
32C32×C4⋊C4C2×C414yes—
33#3752C2×C418yes—
34C4⋊(C3⋊Dic3)C2×C414yes—
35C4×C3⋊Dic3C2×C414yes—
36C4×C3⋊Dic3C2314yes—
37#2905—91nomaximal, Sylow
38C22×C4×D3—62no—
39C2×C3×C4⋊C4—22no—
40C2×(C2×D3)⋊C4—64no—
41C2×C4⋊Dic3—62no—
42C2×C4×Dic3—64no—
43#892—68no—
44#892—68no—
45C23×C32C22×C411yescharacteristic
46C22×C3⋊D3—41no—
47C22×C3⋊D3—41no—
48C22×C3⋊D3C4⋊C414yes—
49C22×C3⋊D3C22×C412yes—
50C2×C32×C4—42no—
51C2×C32×C4C4⋊C414yes—
52C2×C32×C4C22×C414yes—
53C2×C32×C4C22×C412yes—
54C2×C3⋊Dic3—42no—
55C2×C3⋊Dic3C22×C414yes—
56C2×C3⋊Dic3C22×C411yescharacteristic
57C2×C3⋊Dic3C2×D412yes—
58C2×C3⋊Dic3C2×Q812yes—
59C2×C3⋊Dic3C2411yescharacteristic
60C4×C3⋊D3C4⋊C418yes—
61C4×C3⋊D3C2×D414yes—
62C4×C3⋊D3C2×Q814yes—
63#622—28no—
64C22×M16—92no—
65C2×#117—91no—
66#424—98no—
67#423—94no—
68C23×D3—62no—
69C22×C3×C4—22no—
70C22×C3×C4—24no—
71C22×Dic3—62no—
72C22×Dic3—64no—
73C2×C4×D3—64no—
74C2×C4×D3—64no—
75C2×C4×D3—68no—
76C2×C4×D3—68no—
77C3×C4⋊C4—28no—
78(C2×D3)⋊C4—616no—
79C4⋊Dic3—68no—
80C4×Dic3—68no—
81C4×Dic3—68no—
82C22×C32—21no—
83C22×C32—21no—
84C22×C32C2×C4⋊C412yes—
85C22×C32C23×C411yescharacteristic
86C2×C3⋊D3—22no—
87C2×C3⋊D3—22no—
88C2×C3⋊D3—44no—
89C2×C3⋊D3C2×C4⋊C414yes—
90C32×C4—24no—
91C32×C4C2×C4⋊C414yes—
92C3⋊Dic3—24no—
93C3⋊Dic3C2×C4⋊C412yes—
94C3⋊Dic3C22×D411yescharacteristic
95C3⋊Dic3C22×Q811yescharacteristic
96C23×C4—91no—
97C2×M16—94no—
98C2×M16—94no—
99C2×M16—188no—
100C22×C8—94no—
101#117—94no—
102#117—94no—
103C2×C4⋊C4—91no—
104C2×C4⋊C4#15711yescharacteristic
105C2×C22⋊C4—92no—
106C2×C42—92no—
107C4⋊C8—98no—
108C4⋊C8—98no—
109C23×C3—22no—
110C22×D3—68no—
111C22×D3—64no—
112C22×D3—124no—
113C22×D3—124no—
114C2×C3×C4—24no—
115C2×C3×C4—28no—
116C2×C3×C4—28no—
117C2×C3×C4—48no—
118C2×Dic3—62no—
119C2×Dic3—64no—
120C2×Dic3—64no—
121C2×Dic3—62no—
122C2×Dic3—68no—
123C2×Dic3—128no—
124C4×D3—616no—
125C4×D3—68no—
126C4×D3—68no—
127C2×C32—22no—
128C2×C32C22×C4⋊C411yescharacteristic
129C2×C32#56811yescharacteristic
130C2×C32#56811yescharacteristic
131C3⋊D3—24no—
132C24—91no—
133C22×C4—91no—
134C22×C4—92no—
135C22×C4—92no—
136C22×C4—94no—
137C22×C4—94no—
138C22×C4—92no—
139C22×C4C2×#15712yes—
140C22×C4C2×#15711yescharacteristic
141M16—188no—
142M16—188no—
143C2×C8—98no—
144C2×C8—188no—
145C4⋊C4—94no—
146C4⋊C4C2×#15714yes—
147C22⋊C4—98no—
148C42—94no—
149C42—94no—
150C22×C3—24no—
151C22×C3—24no—
152C22×C3—24no—
153C22×C3—22no—
154C2×D3—68no—
155C2×D3—124no—
156C2×D3—124no—
157C2×D3—1216no—
158C3×C4—28no—
159C3×C4—48no—
160Dic3—64no—
161Dic3—62no—
162Dic3—62no—
163Dic3—128no—
164C32#290511yescharacteristic, complemented, Sylow
165C23—92no—
166C23—94no—
167C23—361no—
168C23—361no—
169C23C22×#15711yescharacteristic
170C2×C4—42no—
171C2×C4—92no—
172C2×C4—92no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—94no—
176C2×C4—94no—
177C2×C4—98no—
178C2×C4—94no—
179C2×C4—362no—
180C2×C4C4⋊#15714yes—
181C2×C4C22×#15714yes—
182C2×C4C22×#15712yes—
183C8—188no—
184C2×C3—28no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—22no—
188D3—128no—
189C22—21no—
190C22—21no—
191C22—94no—
192C22—182no—
193C22—182no—
194C22—364no—
195C22C2×C4⋊#15712yes—
196C22C23×#15711yescharacteristic
197C4—24no—
198C4—91no—
199C4—92no—
200C4—91no—
201C4—184no—
202C4C2×C4⋊#15714yes—
203C3—22no—
204C2—22no—
205C2—184no—
206C2C22×C4⋊#15711yescharacteristic
207C2#1059664011yescharacteristic
208C2#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#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10593805C2semidirect
4. #10593755C2semidirect
16. #63779C22semidirect
17. C4⋊#622C22semidirect
164. C32#2905semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C2×#641012
#105938052
#105937552
#29059