Finite Group Databasebeta

← #11798026

Subgroups — #11798026

Order 1152.

228 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592529C211yesmaximal, characteristic
2#10590177C211yesmaximal, characteristic
3#10590177C211yesmaximal, characteristic
4#10590175C211yesmaximal, characteristic
5#10590174C211yesmaximal, characteristic
6#10590148C211yesmaximal, characteristic
7C4⋊#3708C211yesmaximal, characteristic
8C4×#634C411yescharacteristic
9C2×#3708C2211yescharacteristic
10C2×#3708C2211yescharacteristic
11C2×#3708C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13C32×C4⋊C8C411yescharacteristic
14#63641C411yescharacteristic
15#63641C411yescharacteristic
16C8×C3⋊Dic3C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19#4830—62no—
20C2×#634C811yescharacteristic
21C2×C32×C8C2×C411yescharacteristic
22C2×C32×C8C2×C411yescharacteristic
23C32×C42C2×C411yescharacteristic
24C4⋊(C3⋊Dic3)C811yescharacteristic
25#3750C811yescharacteristic
26#3750C811yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C4×C3⋊Dic3C2×C411yescharacteristic
29C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)C2311yescharacteristic
31#3708—21no—
32#3708—21no—
33#3708—21no—
34#3708Q812yescomplemented
35#2183—91nomaximal, Sylow
36C4×Dic6—62no—
37C3×C4⋊C8—22no—
38Dic3⋊C8—62no—
39Dic3⋊C8—62no—
40C8×Dic3—62no—
41C8×Dic3—62no—
42C4×C3⋊C8—62no—
43C2×C32×C4C2×C811yescharacteristic
44C2×C32×C4C2×C811yescharacteristic
45C2×C32×C4C22×C411yescharacteristic
46C2×C3⋊Dic3C2×C811yescharacteristic
47C2×C3⋊Dic3C2×C811yescharacteristic
48C2×C3⋊Dic3C2×C811yescharacteristic
49C2×C3⋊Dic3C2×C811yescharacteristic
50#634—22no—
51C32×C8—21no—
52C32×C8—21no—
53C3⋊(C3⋊C8)—21no—
54C3⋊(C3⋊C8)C2×Q811yescharacteristic
55C3⋊(C3⋊C8)#4111yescharacteristic
56C8×Q8—91no—
57C4⋊C16—91no—
58C4⋊C16—91no—
59C4⋊C16—91no—
60#346—91no—
61#346—91no—
62C4×C16—91no—
63C2×Dic6—62no—
64C2×C3×C8—22no—
65C2×C3×C8—22no—
66C3×C42—22no—
67C4⋊Dic3—62no—
68Dic3⋊C4—62no—
69Dic3⋊C4—62no—
70C4×Dic3—62no—
71C4×Dic3—62no—
72C2×C3⋊C8—62no—
73C2×C3⋊C8—62no—
74C22×C32C22×C811yescharacteristic
75C32×C4—21no—
76C32×C4—21no—
77C32×C4C4×Q811yescharacteristic
78C32×C4#13111yescharacteristic
79C3⋊Dic3—21no—
80C3⋊Dic3—21no—
81C3⋊Dic3—21no—
82C3⋊Dic3M3212yes—
83C4×Q8—91no—
84C2×C16—91no—
85C2×C16—91no—
86C2×C16—91no—
87C2×C16—91no—
88C4⋊C8—91no—
89C4⋊C8—91no—
90C4⋊C8#15711yescharacteristic
91C4×C8—91no—
92C4×C8—91no—
93C4×C8—91no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×Dic3—62no—
98C2×Dic3—62no—
99C2×Dic3—62no—
100C2×Dic3—62no—
101Dic6—68no—
102C3×C8—42no—
103C3×C8—42no—
104C3⋊C8—62no—
105C3⋊C8—62no—
106C3⋊C8—122no—
107C2×C32C8×Q811yescharacteristic
108C2×C32C2×M3211yescharacteristic
109C2×C32#50411yescharacteristic
110C2×Q8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8C2×#15711yescharacteristic
114C2×C8C2×#15711yescharacteristic
115C4⋊C4—91no—
116C4⋊C4—91no—
117C4⋊C4—91no—
118C42—91no—
119C42—91no—
120C42C2×#15711yescharacteristic
121C16—92no—
122C16—181no—
123C16—181no—
124C16—181no—
125C22×C3—22no—
126C3×C4—24no—
127C3×C4—22no—
128C3×C4—22no—
129C3×C4—42no—
130Dic3—64no—
131Dic3—64no—
132Dic3—122no—
133Dic3—122no—
134C32#218311yescharacteristic, complemented, Sylow
135Q8—182no—
136C2×C4—91no—
137C2×C4—91no—
138C2×C4—91no—
139C2×C4—91no—
140C2×C4#378711yescharacteristic
141C2×C4#378711yescharacteristic
142C2×C4C22×#15711yescharacteristic
143C8—21no—
144C8—21no—
145C8—91no—
146C8—91no—
147C8—181no—
148C2×C3—22no—
149C2×C3—22no—
150C2×C3—22no—
151C22C2×#378711yescharacteristic
152C4—21no—
153C4—21no—
154C4—92no—
155C4—181no—
156C4—181no—
157C4—181no—
158C4#6428711yescharacteristic
159C4Q8×#15711yescharacteristic
160C3—22no—
161C2#1059375011yescharacteristic
162C2#1059376211yescharacteristic
163C2#1059377211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socle, prime radicalC22×C32C22×C8
FittingC32×C4⋊C8C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC4⋊C8#157
hypocenterC32#2183
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
34. #3708Q8semidirect
134. C32#2183semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105901772
#105901752
#105901742
#105901482
C4⋊#37082
#21839