Finite Group Databasebeta

← #11790732

Subgroups — #11790732

Order 1152.

598 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C2×#63784C214yesmaximal
3#10593736C211yesmaximal, characteristic
4#10593723C211yesmaximal, characteristic
5C2×Q8×C3⋊D3C2212yes—
6C2×C4⋊#157C2212yes—
7C2×#3787C2212yes—
8C32×C4⋊Q8C411yescharacteristic, complemented
9#64153C412yescomplemented
10C4⋊C4×C3⋊D3—22no—
11#64097—22no—
12C42×C3⋊D3C2211yescharacteristic
13#64078C411yescharacteristic, complemented
14#63784—28no—
15#63781—22no—
16#63777—22no—
17D3×C4⋊Q8—62no—
18C22×#157—22no—
19C2×C32×Q8C2×C412yes—
20Q8×C3⋊D3—24no—
21Q8×C3⋊D3—24no—
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×#634—22no—
26C2×#634C2×C412yes—
27C2×#622—22no—
28C4⋊#157—24no—
29#3787—22no—
30#3787D414yes—
31C32×C4⋊C4—22no—
32C32×C42C2×C411yescharacteristic
33C4⋊(C3⋊Dic3)—22no—
34#3750—24no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D412yes—
37#1960—91nomaximal, Sylow
38C2×D3×Q8—64no—
39C3×C4⋊Q8—22no—
40#944—64no—
41D3×C4⋊C4—68no—
42#888—68no—
43C42×D3—62no—
44#869—62no—
45C22×C3⋊D3C2×D411yescharacteristic
46C2×#157—42no—
47C2×#157—44no—
48C32×Q8—24no—
49C2×C32×C4—22no—
50C2×C32×C4C22⋊C412yes—
51C2×C32×C4C22×C411yescharacteristic
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3C22⋊C412yes—
54C2×C3⋊Dic3C2×D411yescharacteristic
55C4×C3⋊D3—24no—
56C4×C3⋊D3—42no—
57C4×C3⋊D3—42no—
58C4×C3⋊D3C2×D412yes—
59C4×C3⋊D3#4112yes—
60#634—24no—
61#634—44no—
62#622—24no—
63C2×C4⋊Q8—91no—
64C2×#103—94no—
65C2×#97—91no—
66#382—91no—
67C2×C3×Q8—24no—
68D3×Q8—128no—
69D3×Q8—128no—
70C2×C4×D3—64no—
71C2×C4×D3—62no—
72C2×C4×D3—68no—
73C2×Dic6—64no—
74C2×Dic6—68no—
75C3×C4⋊C4—28no—
76C3×C42—22no—
77C4⋊Dic3—68no—
78Dic3⋊C4—616no—
79C4×Dic3—64no—
80C4×Dic3—62no—
81C22×C32C2×C22⋊C411yescharacteristic
82C2×C3⋊D3#12411yescharacteristic
83C2×C3⋊D3#12711yescharacteristic
84C2×C3⋊D3#13714yes—
85#157—82no—
86C32×C4—22no—
87C32×C4—42no—
88C32×C4C4×D412yes—
89C3⋊Dic3—22no—
90C3⋊Dic3—42no—
91C3⋊Dic3#12112yes—
92C22×Q8—92no—
93C22×C8—92no—
94C4⋊Q8—92no—
95C4⋊Q8—91no—
96C4⋊Q8—182no—
97C4⋊Q8#15711yescharacteristic, complemented
98C2×C4⋊C4—92no—
99C2×C4⋊C4—182no—
100C2×C42—91no—
101#103—188no—
102#97—182no—
103#95—182no—
104C22×D3—62no—
105C3×Q8—48no—
106C2×C3×C4—28no—
107C2×C3×C4—22no—
108C2×C3×C4—24no—
109C2×Dic3—64no—
110C2×Dic3—62no—
111C2×Dic3—68no—
112C4×D3—64no—
113C4×D3—64no—
114C4×D3—616no—
115C4×D3—128no—
116C4×D3—128no—
117Dic6—128no—
118Dic6—1216no—
119C2×C32#39011yescharacteristic
120C2×C32#41912yes—
121C3⋊D3#49112yes—
122C3⋊D3#49712yes—
123C2×Q8—92no—
124C2×Q8—182no—
125C2×Q8—184no—
126C2×Q8—184no—
127C2×Q8C2×#15712yes—
128C22×C4—91no—
129C22×C4—92no—
130C22×C4—182no—
131C22×C4—182no—
132C2×C8—94no—
133C2×C8—182no—
134C2×C8—182no—
135C4⋊C4—22no—
136C4⋊C4—184no—
137C4⋊C4—184no—
138C4⋊C4—182no—
139C42—91no—
140C42—92no—
141C42C2×#15711yescharacteristic
142C22×C3—22no—
143C2×D3—62no—
144C2×D3—62no—
145C2×D3—68no—
146C3×C4—28no—
147C3×C4—24no—
148C3×C4—48no—
149Dic3—64no—
150Dic3—68no—
151Dic3—128no—
152C32#196011yescharacteristic, complemented, Sylow
153C23—91no—
154Q8—24no—
155Q8—184no—
156Q8—364no—
157C2×C4—22no—
158C2×C4—91no—
159C2×C4—92no—
160C2×C4—92no—
161C2×C4—92no—
162C2×C4—184no—
163C2×C4—182no—
164C2×C4—362no—
165C2×C4—362no—
166C2×C4—362no—
167C2×C4—364no—
168C2×C4C22⋊#15712yes—
169C2×C4C22×#15711yescharacteristic
170C8—184no—
171C2×C3—22no—
172C2×C3—24no—
173D3—64no—
174D3—64no—
175C22—91no—
176C22—91no—
177C22—94no—
178C22C2×C22⋊#15711yescharacteristic
179C4—22no—
180C4—42no—
181C4—92no—
182C4—182no—
183C4—362no—
184C4—722no—
185C4D4×#15712yes—
186C3—22no—
187C2—92no—
188C2—92no—
189C2#1059382711yescharacteristic
190C2#1059382912yes—
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#1960
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
8. C32×C4⋊Q8C4semidirect
9. #64153C4semidirect
13. #64078C4semidirect
97. C4⋊Q8#157semidirect
152. C32#1960semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C2×#637842
#105937362
#105937232
#19609