Finite Group Databasebeta

← #11772634

Subgroups — #11772634

Order 1152.

320 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 40 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#10593808C211yesmaximal, characteristic
2#10593792C211yesmaximal, characteristic
3#10592828C211yesmaximal, characteristic
4C2×#3828C2211yescharacteristic
5#64286—21no—
6#64283—21no—
7C2×C32×M16C411yescharacteristic, complemented
8C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
9#63788—21no—
10#63786—21no—
11#63780C412yescomplemented
12#63774C412yes—
13#63647—21no—
14#63647—21no—
15#5129—62no—
16C22×C32×C4C2×C411yescharacteristic
17C2×#638D411yescharacteristic
18C2×#638Q811yescharacteristic
19#3828—41no—
20#3828—41no—
21C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×#634C2×C411yescharacteristic
25C22⋊#157—22no—
26#3792—22no—
27C4⋊#157—41no—
28C4×#157—41no—
29#3788—41no—
30#3787—41no—
31C32×M16—41no—
32C2×C32×C8—21no—
33C2×C3⋊(C3⋊C8)—21no—
34C2×C3⋊(C3⋊C8)—41no—
35#1395—91nomaximal, Sylow
36C2×#235—62no—
37C2×C3×M16—22no—
38C22×C3⋊C8—62no—
39(C2×D3)⋊C8—64no—
40(C2×D3)⋊C8—64no—
41C23×C32C4⋊C411yescharacteristic
42C22×C3⋊D3C22⋊C411yescharacteristic
43C22×C3⋊D3C4⋊C411yescharacteristic
44C2×#157—42no—
45C2×C32×C4—21no—
46C2×C32×C4—21no—
47C2×C32×C4C4211yescharacteristic
48C2×C32×C4C22⋊C411yescharacteristic
49#638—41no—
50#638—41no—
51C2×C3⋊Dic3C22⋊C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C4⋊(C3⋊D3)—41no—
54C4×C3⋊D3—21no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3—21no—
58#634—41no—
59#622—42no—
60C32×C8—41no—
61C3⋊(C3⋊C8)—41no—
62#413—91no—
63#410—91no—
64#408—91no—
65C22×C3×C4—22no—
66C2×#67—62no—
67C2×#67—62no—
68#235—124no—
69#235—124no—
70C2×D12—62no—
71C2×C4×D3—62no—
72C2×C4×D3—62no—
73C2×Dic6—62no—
74C3×M16—44no—
75C2×C3×C8—24no—
76C2×C3⋊C8—64no—
77C2×C3⋊C8—124no—
78C22×C32—21no—
79C22×C32—41no—
80C22×C32#9511yescharacteristic
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—41no—
84C2×C3⋊D3—41no—
85#157—82no—
86C32×C4—21no—
87C32×C4#9911yescharacteristic
88C32×C4#9911yescharacteristic
89C3⋊Dic3—21no—
90C3⋊Dic3—21no—
91C2×#41—91no—
92C2×M16—181no—
93C2×M16#15711yescharacteristic, complemented
94C22×C8—91no—
95#117—181no—
96#101—92no—
97#100—181no—
98#99—92no—
99#99—181no—
100C22⋊C8—181no—
101C22⋊C8—181no—
102C23×C3—22no—
103C22×D3—62no—
104C22×D3—62no—
105C2×C3×C4—24no—
106C2×C3×C4—24no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109#67—124no—
110#67—124no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113D12—124no—
114C4×D3—122no—
115C4×D3—122no—
116C4×D3—122no—
117C4×D3—122no—
118Dic6—124no—
119C3×C8—44no—
120C3⋊C8—124no—
121C2×C32—21no—
122C2×C32—41no—
123C2×C32#34211yescharacteristic
124C3⋊D3—41no—
125C3⋊D3—41no—
126#41—361no—
127#41—361no—
128C2×Q8—91no—
129C2×D4—91no—
130C2×D4—91no—
131C2×D4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4C2×#15711yescharacteristic
135M16—41no—
136M16—182no—
137M16—361no—
138C2×C8—21no—
139C2×C8—181no—
140C2×C8—361no—
141C2×C8—361no—
142C4⋊C4—361no—
143C22⋊C4—182no—
144C42—361no—
145C22×C3—24no—
146C22×C3—22no—
147C22×C3—44no—
148C2×D3—122no—
149C2×D3—122no—
150C2×D3—124no—
151C2×D3—124no—
152C3×C4—24no—
153C3×C4—22no—
154C3×C4—22no—
155Dic3—122no—
156Dic3—122no—
157C32#139511yescharacteristic, complemented, Sylow
158C23—91no—
159C23—91no—
160C23C4⋊#15711yescharacteristic
161Q8—361no—
162D4—361no—
163D4—361no—
164D4—361no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—181no—
172C2×C4—181no—
173C2×C4—362no—
174C2×C4C4×#15711yescharacteristic
175C2×C4C22⋊#15711yescharacteristic
176C8—41no—
177C8—362no—
178C8—361no—
179C2×C3—24no—
180C2×C3—22no—
181C2×C3—44no—
182D3—242no—
183D3—242no—
184C22—21no—
185C22—41no—
186C22—181no—
187C22—181no—
188C22—361no—
189C22—361no—
190C22#6378111yescharacteristic
191C4—21no—
192C4—181no—
193C4—181no—
194C4—722no—
195C4#6377411yescharacteristic
196C4#6378611yescharacteristic
197C3—22no—
198C2—21no—
199C2—41no—
200C2—361no—
201C2—361no—
202C2#1059020611yescharacteristic
subgroupG/H
centerC4#63786
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC2×C32#342
prime radical, cosocleC2×#3828C22
hypercenterC2×M16#157
hypocenterC32#1395
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
7. C2×C32×M16C4semidirect
8. C22×C3⋊(C3⋊C8)C4semidirect
11. #63780C4semidirect
93. C2×M16#157semidirect
157. C32#1395semidirect

Maximal subgroups

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

subgroupindex
#105938082
#105937922
#105928282
#13959