Finite Group Databasebeta

← #11796571

Subgroups — #11796571

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#10595997C211yesmaximal, characteristic
2#10593808C212yesmaximal
3#10590144C214yesmaximal, complemented
4C2×#3828C2211yescharacteristic
5C22×#634C411yescharacteristic
6#64283—22no—
7C32×#117C411yescharacteristic
8#64106—22no—
9#64095—22no—
10#64084C412yes—
11#64078C2212yes—
12#63788—22no—
13#63780C2214yes—
14#5526—62no—
15C22×C32×C4C2×C411yescharacteristic
16C2×#638D412yes—
17C22×C3⋊Dic3—21no—
18#3828—42no—
19C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
20C2×C4×C3⋊D3D412yes—
21C2×#634—21no—
22C2×#634—42no—
23C2×#634C2×C412yes—
24C2×#634C2311yescharacteristic
25#3792—24no—
26#3788—42no—
27#3787—42no—
28C32×C4⋊C4—21no—
29C32×C22⋊C4—21no—
30C32×C42C2×C412yes—
31#3752—24no—
32C4⋊(C3⋊Dic3)—24no—
33#2135—91nomaximal, Sylow
34C2×#235—62no—
35C22×Dic6—62no—
36C3×#117—22no—
37#897—68no—
38#886—68no—
39#875—64no—
40#869—64no—
41C23×C32C22⋊C411yescharacteristic
42C22×C3⋊D3C22⋊C412yes—
43C2×C32×C4—22no—
44C2×C32×C4—22no—
45C2×C32×C4C22⋊C411yescharacteristic
46C2×C32×C4C22×C411yescharacteristic
47#638—42no—
48C2×C3⋊Dic3—22no—
49C2×C3⋊Dic3—42no—
50C2×C3⋊Dic3C2×D412yes—
51C4⋊(C3⋊D3)—41no—
52C4×C3⋊D3—22no—
53C4×C3⋊D3—22no—
54#634—41no—
55#634—42no—
56#634—42no—
57#622—44no—
58#536—91no—
59#413—92no—
60#356—94no—
61C22×C3×C4—22no—
62C2×#67—64no—
63C22×Dic3—64no—
64#235—128no—
65C2×D12—62no—
66C2×C4×D3—64no—
67C2×Dic6—62no—
68C2×Dic6—64no—
69C2×Dic6—64no—
70C2×Dic6—128no—
71C3×C4⋊C4—24no—
72C3×C22⋊C4—24no—
73C3×C42—24no—
74(C2×D3)⋊C4—616no—
75C4⋊Dic3—616no—
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—91no—
88C2×M16—182no—
89C4⋊Q8—92no—
90#124—92no—
91#123—182no—
92C22⋊Q8—182no—
93#117#15711yescharacteristic
94#101—94no—
95#100—182no—
96C23×C3—22no—
97C22×D3—64no—
98C2×C3×C4—28no—
99C2×C3×C4—28no—
100C2×C3×C4—22no—
101C2×C3×C4—22no—
102#67—128no—
103C2×Dic3—64no—
104C2×Dic3—68no—
105C2×Dic3—128no—
106D12—124no—
107C4×D3—124no—
108C4×D3—124no—
109Dic6—128no—
110Dic6—128no—
111Dic6—124no—
112C2×C32—21no—
113C2×C32—41no—
114C2×C32C2×#9911yescharacteristic
115C3⋊D3—42no—
116#41—362no—
117C2×Q8—91no—
118C2×Q8—92no—
119C2×Q8—181no—
120C2×Q8—362no—
121C2×D4—92no—
122C2×D4—91no—
123C22×C4—92no—
124C22×C4—181no—
125C22×C4C2×#15711yescharacteristic
126M16—184no—
127M16—362no—
128C2×C8—362no—
129C4⋊C4—21no—
130C4⋊C4—184no—
131C22⋊C4—21no—
132C22⋊C4—184no—
133C42C2×#15712yes—
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—361no—
148Q8—362no—
149Q8—362no—
150D4—361no—
151D4—362no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—92no—
155C2×C4—182no—
156C2×C4—182no—
157C2×C4—182no—
158C2×C4—362no—
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#6377412yes—
176C3—22no—
177C2—21no—
178C2—41no—
179C2—362no—
180C2C2×#6377411yescharacteristic
subgroupG/H
centerC2C2×#63774
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC2×C32C2×#99
prime radicalC2×#3828C22
cosocleC2×#634C23
hypercenter#117#157
hypocenterC32#2135
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10590144C2semidirect
144. C32#2135semidirect

Maximal subgroups

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

subgroupindex
#105959972
#105938082
#105901442
#21359