Finite Group Databasebeta

← #11796570

Subgroups — #11796570

Order 1152.

500 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 54 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#10596287C211yesmaximal, characteristic
2#10593808C212yesmaximal
3#10590218C214yesmaximal, complemented
4C22×C32×Q8C411yescharacteristic
5C2×#3828C2211yescharacteristic
6#64283—22no—
7#64156C412yes—
8#64155—22no—
9#64153C2212yes—
10#64138—22no—
11#64135C411yescharacteristic
12#63788—22no—
13#63780C2214yes—
14#5816—62no—
15C2×C32×Q8—21no—
16C2×C32×Q8—42no—
17C2×C32×Q8C2×C412yes—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C2×#638D412yes—
21#3828—42no—
22C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
23C2×C4×C3⋊D3D412yes—
24C2×#634C2311yescharacteristic
25#3792—24no—
26#3788—42no—
27#3787—42no—
28#3757—21no—
29#3752—24no—
30C4⋊(C3⋊Dic3)—21no—
31#3750—24no—
32C4×C3⋊Dic3C2×C412yes—
33#2135—91nomaximal, Sylow
34C22×C3×Q8—22no—
35C2×#235—62no—
36#947—64no—
37#946—68no—
38#944—64no—
39#929—68no—
40#926—62no—
41C23×C32C22⋊C411yescharacteristic
42C22×C3⋊D3C22⋊C412yes—
43C32×Q8—42no—
44C32×Q8—42no—
45C2×C32×C4—22no—
46C2×C32×C4—22no—
47C2×C32×C4—42no—
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C22×C411yescharacteristic
50#638—42no—
51C2×C3⋊Dic3—22no—
52C2×C3⋊Dic3C2×D412yes—
53C4⋊(C3⋊D3)—41no—
54C4×C3⋊D3—22no—
55C4×C3⋊D3—22no—
56#634—41no—
57#622—44no—
58#536—91no—
59#413—92no—
60#356—94no—
61C2×C3×Q8—24no—
62C2×C3×Q8—24no—
63C2×C3×Q8—48no—
64C22×C3×C4—24no—
65C22×C3×C4—22no—
66C2×#67—64no—
67#235—128no—
68C2×D12—62no—
69C2×C4×D3—64no—
70C2×Dic6—62no—
71#217—64no—
72(C2×D3)⋊C4—616no—
73C4⋊Dic3—64no—
74Dic3⋊C4—616no—
75C4×Dic3—64no—
76C22×C32—21no—
77C22×C32—41no—
78C22×C32C2×C22⋊C411yescharacteristic
79C2×C3⋊D3—22no—
80C2×C3⋊D3—42no—
81C32×C4—21no—
82C32×C4—42no—
83C32×C4#9912yes—
84C3⋊Dic3—22no—
85C3⋊Dic3—42no—
86C2×#41—91no—
87C22×Q8#15711yescharacteristic
88C2×M16—182no—
89C4⋊Q8—92no—
90#124—92no—
91#123—182no—
92C22⋊Q8—182no—
93#117—91no—
94#101—94no—
95#100—182no—
96C23×C3—22no—
97C22×D3—64no—
98C3×Q8—48no—
99C3×Q8—48no—
100C2×C3×C4—28no—
101C2×C3×C4—28no—
102C2×C3×C4—22no—
103C2×C3×C4—22no—
104C2×C3×C4—48no—
105#67—128no—
106C2×Dic3—64no—
107C2×Dic3—68no—
108D12—124no—
109C4×D3—124no—
110C4×D3—124no—
111Dic6—124no—
112C2×C32—21no—
113C2×C32—41no—
114C2×C32C2×#9911yescharacteristic
115C3⋊D3—42no—
116#41—362no—
117C2×Q8—21no—
118C2×Q8—42no—
119C2×Q8—91no—
120C2×Q8C2×#15712yes—
121C2×D4—92no—
122C2×D4—91no—
123C22×C4—21no—
124C22×C4—92no—
125C22×C4C2×#15711yescharacteristic
126M16—184no—
127M16—362no—
128C2×C8—362no—
129C4⋊C4—184no—
130C4⋊C4—181no—
131C22⋊C4—184no—
132C22⋊C4—181no—
133C42—92no—
134C22×C3—24no—
135C22×C3—22no—
136C22×C3—44no—
137C2×D3—124no—
138C2×D3—128no—
139C3×C4—24no—
140C3×C4—24no—
141C3×C4—48no—
142Dic3—124no—
143Dic3—128no—
144C32#213511yescharacteristic, complemented, Sylow
145C23—92no—
146C23C22⋊#15711yescharacteristic
147Q8—42no—
148Q8—42no—
149Q8—361no—
150D4—361no—
151D4—362no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—92no—
156C2×C4—182no—
157C2×C4—182no—
158C2×C4—182no—
159C2×C4C22⋊#15711yescharacteristic
160C2×C4C22×#15711yescharacteristic
161C8—364no—
162C2×C3—24no—
163C2×C3—22no—
164C2×C3—44no—
165D3—244no—
166C22—21no—
167C22—41no—
168C22—182no—
169C22—362no—
170C22C2×C22⋊#15711yescharacteristic
171C4—21no—
172C4—42no—
173C4—182no—
174C4—362no—
175C4#6378612yes—
176C3—22no—
177C2—21no—
178C2—41no—
179C2—362no—
180C2C2×#6378611yescharacteristic
subgroupG/H
centerC2C2×#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC2×C32C2×#99
prime radicalC2×#3828C22
cosocleC2×#634C23
hypercenterC22×Q8#157
hypocenterC32#2135
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10590218C2semidirect
144. C32#2135semidirect

Maximal subgroups

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

subgroupindex
#105962872
#105938082
#105902182
#21359