Finite Group Databasebeta

← #11859530

Subgroups — #11859530

Order 1152.

794 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 162 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×#64289C212yesmaximal, complemented
2#10596196C211yesmaximal, characteristic
3#10593834C212yesmaximal, complemented
4#10593751C218yesmaximal, complemented
5#10593729C211yesmaximal, characteristic, complemented
6#10593723C211yesmaximal, characteristic, complemented
7C2×#3832C2212yes—
8#64289—28no—
9C2×#3788C2212yes—
10C2×#3788C2214yes—
11C2×#3787C2214yes—
12C2×#3787C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C32×C4⋊Q8C411yescharacteristic
15#64156C412yes—
16#64104C414yes—
17#64102C2214yes—
18#64083C411yescharacteristic
19C42×C3⋊D3C2211yescharacteristic
20#63779C2214yes—
21#63778C2218yes—
22#63777C2214yes—
23#5725—62no—
24C2×C32×Q8C2×C412yes—
25#3832—24no—
26#3832—24no—
27C2×C4⋊(C3⋊D3)C2×C412yes—
28C2×C4⋊(C3⋊D3)C2×C414yes—
29C2×C4⋊(C3⋊D3)C2×C414yes—
30C2×C4×C3⋊D3C2×C412yes—
31C2×C4×C3⋊D3C2314yes—
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×#622C2314yes—
34C2×#622C2312yes—
35C2×#622C2312yes—
36#3788—24no—
37#3788—28no—
38#3787—22no—
39#3787—28no—
40#3787D414yescomplemented
41C32×C4⋊C4C2×C414yes—
42C32×C42C2×C411yescharacteristic
43#3752C2×C418yes—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3C2312yes—
46#2932—91nomaximal, Sylow
47C2×#239—64no—
48C3×C4⋊Q8—22no—
49#947—64no—
50#895—68no—
51#893—68no—
52#874—62no—
53C42×D3—62no—
54C22×C3⋊D3C22×C414yes—
55C22×C3⋊D3C22×C411yescharacteristic
56C32×Q8—24no—
57C2×C32×C4C22×C412yes—
58C2×C32×C4C22×C414yes—
59C2×C32×C4C22×C411yescharacteristic
60C2×C3⋊Dic3C22×C412yes—
61C2×C3⋊Dic3C2411yescharacteristic
62C4⋊(C3⋊D3)—28no—
63C4⋊(C3⋊D3)—24no—
64C4⋊(C3⋊D3)—44no—
65C4×C3⋊D3—24no—
66C4×C3⋊D3—24no—
67C4×C3⋊D3—42no—
68C4×C3⋊D3C2×D412yes—
69C4×C3⋊D3#4112yes—
70#622—24no—
71#622—22no—
72#622C2×D414yes—
73C2×#131—92no—
74#532—91no—
75#435—98no—
76#423—91no—
77#408—92no—
78C2×#97—91no—
79C2×C3×Q8—24no—
80#239—128no—
81#239—128no—
82C2×D12—68no—
83C2×D12—64no—
84C2×D12—68no—
85C2×C4×D3—62no—
86C2×C4×D3—64no—
87C2×C4×D3—68no—
88C3×C4⋊C4—28no—
89C3×C42—22no—
90(C2×D3)⋊C4—616no—
91C4×Dic3—64no—
92C4×Dic3—62no—
93C22×C32C23×C411yescharacteristic
94C2×C3⋊D3—22no—
95C2×C3⋊D3—24no—
96C2×C3⋊D3—28no—
97C2×C3⋊D3C4×D412yes—
98C32×C4—22no—
99C32×C4—24no—
100C32×C4C4×D412yes—
101C3⋊Dic3—22no—
102C3⋊Dic3C22×D411yescharacteristic
103C3⋊Dic3C2×#4111yescharacteristic
104C2×#41—92no—
105#131—188no—
106C2×M16—92no—
107C2×M16—94no—
108C22×C8—91no—
109C22×C8—94no—
110C22×C8—91no—
111C4⋊Q8#15711yescharacteristic
112#127—91no—
113#124—92no—
114#121—94no—
115C4×D4—94no—
116C2×C42—91no—
117C4⋊C8—94no—
118C22⋊C8—98no—
119#97—94no—
120C22×D3—62no—
121C22×D3—68no—
122C3×Q8—48no—
123C2×C3×C4—24no—
124C2×C3×C4—22no—
125C2×C3×C4—28no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128D12—128no—
129D12—1216no—
130D12—1216no—
131C4×D3—64no—
132C4×D3—64no—
133C4×D3—128no—
134C4×D3—128no—
135C4×D3—128no—
136C2×C32C2×C4×D411yescharacteristic
137C2×C32#56812yes—
138C3⋊D3—22no—
139C3⋊D3—44no—
140#41—184no—
141#41—184no—
142C2×Q8C2×#15712yes—
143C2×D4—94no—
144C2×D4—92no—
145C2×D4—94no—
146C22×C4—91no—
147C22×C4—94no—
148C22×C4—92no—
149M16—188no—
150M16—184no—
151C2×C8—92no—
152C2×C8—94no—
153C2×C8—92no—
154C2×C8—94no—
155C2×C8—188no—
156C2×C8—182no—
157C4⋊C4C2×#15714yes—
158C22⋊C4—98no—
159C42—92no—
160C42—91no—
161C42C2×#15711yescharacteristic
162C22×C3—22no—
163C2×D3—64no—
164C2×D3—124no—
165C2×D3—128no—
166C2×D3—1216no—
167C3×C4—28no—
168C3×C4—24no—
169C3×C4—48no—
170Dic3—62no—
171Dic3—62no—
172Dic3—124no—
173C32#293211yescharacteristic, complemented, Sylow
174C23—91no—
175C23—94no—
176Q8—24no—
177D4—188no—
178D4—184no—
179D4—364no—
180C2×C4—91no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—92no—
184C2×C4—184no—
185C2×C4—184no—
186C2×C4—362no—
187C2×C4C22×#15712yes—
188C2×C4C22×#15714yes—
189C2×C4C22×#15711yescharacteristic
190C8—94no—
191C8—184no—
192C8—182no—
193C2×C3—22no—
194C2×C3—24no—
195D3—124no—
196D3—248no—
197C22—92no—
198C22—182no—
199C22—184no—
200C22—188no—
201C22C23×#15711yescharacteristic
202C4—24no—
203C4—22no—
204C4—91no—
205C4—91no—
206C4—182no—
207C4D4×#15712yes—
208C3—22no—
209C2—182no—
210C2—364no—
211C2C2×D4×#15711yescharacteristic
212C2#1059664412yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4⋊Q8C4
prime radical#10596196C2
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊Q8#157
hypocenterC32#2932
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64289C2semidirect
3. #10593834C2semidirect
4. #10593751C2semidirect
5. #10593729C2semidirect
6. #10593723C2semidirect
40. #3787D4semidirect
173. C32#2932semidirect

Maximal subgroups

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

subgroupindex
C2×#642892
#105961962
#105938342
#105937512
#105937292
#105937232
#29329