Finite Group Databasebeta

← #11783534

Subgroups — #11783534

Order 1152.

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

normal subgroups only

This group has 330 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
1#10593765C212yesmaximal
2#10592388C211yesmaximal, characteristic
3#10590186C211yesmaximal, characteristic
4#10590184C211yesmaximal, characteristic
5#10590152C212yesmaximal
6#64286C2212yes—
7#64283C2212yes—
8C2×#3743C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10#64081C2211yescharacteristic
11#63767C414yescomplemented
12C8×#157C414yescomplemented
13C32×C4×C8C411yescharacteristic, complemented
14#63642C411yescharacteristic, complemented
15C8×C3⋊Dic3C411yescharacteristic, complemented
16#63630C411yescharacteristic, complemented
17#4689—62no—
18C2×C4×C3⋊D3C2311yescharacteristic
19C22⋊#157—22no—
20#3792—22no—
21C4⋊#157—22no—
22C4×#157C2×C414yes—
23#3788—22no—
24#3787C2×C414yes—
25C2×C32×C8C2×C411yescharacteristic
26C2×C32×C8C2×C411yescharacteristic
27C32×C42C2×C411yescharacteristic
28#3752—21no—
29#3750—21no—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33#3743—22no—
34C8×C3⋊D3C2×C412yes—
35C8×C3⋊D3C2×C412yes—
36#1747—91nomaximal, Sylow
37C2×ΓL(1,𝔽25)—62no—
38C2×D3×C8—62no—
39#872—62no—
40C3×C4×C8—22no—
41#815—62no—
42C8×Dic3—62no—
43#803—62no—
44C22×C3⋊D3#4111yescharacteristic
45C2×#157—24no—
46C2×C32×C4—21no—
47C2×C32×C4C22×C411yescharacteristic
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3#4111yescharacteristic
50C4×C3⋊D3C22×C412yes—
51C4×C3⋊D3#4112yes—
52#622—24no—
53C32×C8—21no—
54C32×C8C4211yescharacteristic
55C32×C8C4211yescharacteristic
56C3⋊(C3⋊C8)—21no—
57C3⋊(C3⋊C8)C4212yes—
58#405—92no—
59#405—91no—
60#338—91no—
61H(3,ℤ/4)—92no—
62H(3,ℤ/4)—91no—
63C2×C4×D3—62no—
64C2×C3×C8—22no—
65C2×C3×C8—22no—
66C3×C42—22no—
67(C2×D3)⋊C4—64no—
68Dic3⋊C4—64no—
69C4×Dic3—62no—
70C2×C3⋊C8—62no—
71C2×C3⋊C8—62no—
72ΓL(1,𝔽25)—68no—
73D3×C8—64no—
74D3×C8—64no—
75C22×C32#11711yescharacteristic
76C2×C3⋊D3—41no—
77C2×C3⋊D3#11712yes—
78#157—44no—
79C32×C4—41no—
80C32×C4C2×C4211yescharacteristic
81C32×C4#11711yescharacteristic
82C3⋊Dic3—41no—
83C3⋊Dic3#11712yes—
84C2×M16—92no—
85C2×M16—91no—
86C22×C8—91no—
87#117—92no—
88#117—91no—
89#97—94no—
90#97—91no—
91#97—91no—
92C4×C8—94no—
93C4×C8—91no—
94C4×C8#15711yescharacteristic, complemented
95C22×D3—62no—
96C2×C3×C4—24no—
97C2×C3×C4—22no—
98C2×Dic3—62no—
99C2×Dic3—64no—
100C4×D3—64no—
101C4×D3—64no—
102C3×C8—24no—
103C3×C8—22no—
104C3×C8—22no—
105C3⋊C8—64no—
106C3⋊C8—64no—
107C2×C32—21no—
108C2×C32#37611yescharacteristic
109C3⋊D3—22no—
110C22×C4—91no—
111M16—182no—
112M16—182no—
113M16—182no—
114C2×C8—91no—
115C2×C8—92no—
116C2×C8—92no—
117C2×C8—94no—
118C2×C8—91no—
119C2×C8C2×#15711yescharacteristic
120C2×C8C2×#15711yescharacteristic
121C4⋊C4—181no—
122C4⋊C4—182no—
123C22⋊C4—181no—
124C22⋊C4—182no—
125C42—94no—
126C42—91no—
127C42C2×#15711yescharacteristic
128C22×C3—22no—
129C2×D3—64no—
130C2×D3—124no—
131C3×C4—22no—
132C3×C4—22no—
133C3×C4—44no—
134Dic3—64no—
135Dic3—124no—
136C32#174711yescharacteristic, complemented, Sylow
137C23—91no—
138C2×C4—21no—
139C2×C4—91no—
140C2×C4—92no—
141C2×C4—92no—
142C2×C4—184no—
143C2×C4—181no—
144C2×C4C22×#15711yescharacteristic
145C8—21no—
146C8—92no—
147C8—184no—
148C8—181no—
149C8C4×#15711yescharacteristic
150C8C4×#15711yescharacteristic
151C2×C3—24no—
152C2×C3—22no—
153D3—124no—
154C22—92no—
155C22—361no—
156C22#6428611yescharacteristic
157C4—41no—
158C4—92no—
159C4—361no—
160C4—364no—
161C4C2×C4×#15711yescharacteristic
162C4#6428611yescharacteristic
163C3—22no—
164C2—21no—
165C2—182no—
166C2#1059373311yescharacteristic
subgroupG/H
centerC8C4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×C8C4
socleC2×C32#376
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenterC4×C8#157
hypocenterC32#1747
LCSG ▷ C32×C4 ▷ C32
UCSC1 ◁ C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
11. #63767C4semidirect
12. C8×#157C4semidirect
13. C32×C4×C8C4semidirect
14. #63642C4semidirect
15. C8×C3⋊Dic3C4semidirect
16. #63630C4semidirect
94. C4×C8#157semidirect
136. C32#1747semidirect

Maximal subgroups

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

subgroupindex
#105937652
#105923882
#105901862
#105901842
#105901522
#17479