Finite Group Databasebeta

← #11796551

Subgroups — #11796551

Order 1152.

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

normal subgroups only

This group has 596 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#10595996C211yesmaximal, characteristic
2#10593808C212yesmaximal, complemented
3#10590145C214yesmaximal, complemented
4C2×#3828C2211yescharacteristic
5C22×C4⋊(C3⋊D3)C411yescharacteristic
6#64283—22no—
7C32×#117C411yescharacteristic
8#64104—22no—
9#64091—22no—
10#64084C2212yes—
11#64083C412yes—
12#63788—22no—
13#63780C2214yescomplemented
14#5525—62no—
15C23×C3⋊D3—21no—
16C22×C32×C4C2×C411yescharacteristic
17C2×#638D412yes—
18#3828—42no—
19C2×C4⋊(C3⋊D3)—21no—
20C2×C4⋊(C3⋊D3)—24no—
21C2×C4⋊(C3⋊D3)—42no—
22C2×C4⋊(C3⋊D3)C2×C412yes—
23C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
24C2×C4×C3⋊D3D412yes—
25C2×#634C2311yescharacteristic
26#3792—24no—
27#3788—42no—
28#3787—42no—
29C32×C4⋊C4—21no—
30C32×C22⋊C4—21no—
31C32×C42C2×C412yes—
32#3752—24no—
33#2134—91nomaximal, Sylow
34C2×#235—62no—
35C22×D12—62no—
36C3×#117—22no—
37#895—68no—
38#882—68no—
39#875—64no—
40#874—64no—
41C23×C32C22⋊C411yescharacteristic
42C22×C3⋊D3—22no—
43C22×C3⋊D3—42no—
44C22×C3⋊D3—82no—
45C22×C3⋊D3C22⋊C412yes—
46C2×C32×C4—22no—
47C2×C32×C4—22no—
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C22×C411yescharacteristic
50#638—42no—
51C2×C3⋊Dic3C2×D412yes—
52C4⋊(C3⋊D3)—41no—
53C4⋊(C3⋊D3)—42no—
54C4⋊(C3⋊D3)—42no—
55C4⋊(C3⋊D3)—84no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58#634—41no—
59#622—44no—
60#535—91no—
61#413—92no—
62#355—94no—
63C23×D3—64no—
64C22×C3×C4—22no—
65C2×#67—64no—
66#235—128no—
67C2×D12—62no—
68C2×D12—64no—
69C2×D12—64no—
70C2×D12—616no—
71C2×D12—128no—
72C2×C4×D3—64no—
73C2×Dic6—62no—
74C3×C4⋊C4—24no—
75C3×C22⋊C4—24no—
76C3×C42—24no—
77(C2×D3)⋊C4—616no—
78C22×C32—21no—
79C22×C32—41no—
80C22×C32C2×C22⋊C411yescharacteristic
81C2×C3⋊D3—22no—
82C2×C3⋊D3—42no—
83C2×C3⋊D3—44no—
84C2×C3⋊D3—42no—
85C2×C3⋊D3—84no—
86C32×C4—21no—
87C32×C4—42no—
88C32×C4#9912yes—
89C3⋊Dic3—22no—
90C2×#41—91no—
91C22×D4—91no—
92C2×M16—182no—
93#127—92no—
94#124—92no—
95#121—182no—
96#120—182no—
97#117#15711yescharacteristic
98#101—94no—
99#100—182no—
100C23×C3—22no—
101C22×D3—64no—
102C22×D3—68no—
103C22×D3—128no—
104C22×D3—248no—
105C2×C3×C4—28no—
106C2×C3×C4—28no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109#67—128no—
110C2×Dic3—64no—
111D12—128no—
112D12—128no—
113D12—124no—
114D12—2416no—
115C4×D3—124no—
116C4×D3—124no—
117Dic6—124no—
118C2×C32—21no—
119C2×C32—41no—
120C2×C32C2×#9911yescharacteristic
121C3⋊D3—42no—
122C3⋊D3—82no—
123C24—181no—
124#41—362no—
125C2×Q8—91no—
126C2×D4—92no—
127C2×D4—91no—
128C2×D4—92no—
129C2×D4—184no—
130C2×D4—181no—
131C2×D4—362no—
132C22×C4—92no—
133C22×C4C2×#15711yescharacteristic
134M16—184no—
135M16—362no—
136C2×C8—362no—
137C4⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—184no—
140C42C2×#15712yes—
141C22×C3—24no—
142C22×C3—22no—
143C22×C3—44no—
144C2×D3—124no—
145C2×D3—128no—
146C2×D3—128no—
147C2×D3—1216no—
148C2×D3—2416no—
149C3×C4—24no—
150C3×C4—24no—
151C3×C4—48no—
152Dic3—124no—
153C32#213411yescharacteristic, complemented, Sylow
154C23—92no—
155C23—182no—
156C23—362no—
157C23—722no—
158C23C22⋊#15711yescharacteristic
159Q8—361no—
160D4—361no—
161D4—362no—
162D4—362no—
163D4—362no—
164D4—724no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—92no—
168C2×C4—182no—
169C2×C4—182no—
170C2×C4C22⋊#15711yescharacteristic
171C2×C4C22×#15711yescharacteristic
172C8—364no—
173C2×C3—24no—
174C2×C3—22no—
175C2×C3—44no—
176D3—244no—
177D3—248no—
178C22—21no—
179C22—41no—
180C22—182no—
181C22—362no—
182C22—364no—
183C22—362no—
184C22—724no—
185C22C2×C22⋊#15711yescharacteristic
186C4—21no—
187C4—42no—
188C4—182no—
189C4#6377412yes—
190C3—22no—
191C2—21no—
192C2—41no—
193C2—362no—
194C2—722no—
195C2C2×#6377411yescharacteristic
subgroupG/H
centerC2C2×#63774
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC2×C32C2×#99
prime radical#10595996C2
cosocleC2×#634C23
hypercenter#117#157
hypocenterC32#2134
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
2. #10593808C2semidirect
3. #10590145C2semidirect
13. #63780C22semidirect
153. C32#2134semidirect

Maximal subgroups

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

subgroupindex
#105959962
#105938082
#105901452
#21349