Finite Group Databasebeta

← #11797324

Subgroups — #11797324

Order 1152.

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

normal subgroups only

This group has 314 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
1C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C22⋊#3708C212yesmaximal
3#10590148C212yesmaximal, complemented
4C4⋊#3708C212yesmaximal, complemented
5C2×C32×C42C411yescharacteristic
6C22×C3⋊(C3⋊C8)C411yescharacteristic
7C22×C3⋊(C3⋊C8)C2211yescharacteristic
8C2×#3708C2214yes—
9C4×C3⋊(C3⋊C8)C411yescharacteristic
10C4×C3⋊(C3⋊C8)C411yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C4×C3⋊C8—62no—
14C22×C32×C4C811yescharacteristic
15C22×C32×C4C811yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C32×C42C811yescharacteristic
18C32×C42C811yescharacteristic
19C32×C42C2×C411yescharacteristic
20C32×C42C2×C411yescharacteristic
21C2×C3⋊(C3⋊C8)—22no—
22C2×C3⋊(C3⋊C8)—22no—
23C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
24C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
25C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
26C2×C3⋊(C3⋊C8)C2311yescharacteristic
27#3708—24no—
28#2163—91nomaximal, Sylow
29C2×C3×C42—22no—
30C22×C3⋊C8—62no—
31C22×C3⋊C8—62no—
32C4×C3⋊C8—62no—
33C4×C3⋊C8—62no—
34C4×C3⋊C8—62no—
35C4×C3⋊C8—62no—
36C23×C32C2×C811yescharacteristic
37C2×C32×C4—22no—
38C2×C32×C4—22no—
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4C2×C811yescharacteristic
42C2×C32×C4C2×C811yescharacteristic
43C2×C32×C4C2×C811yescharacteristic
44C2×C32×C4C2×C811yescharacteristic
45C2×C32×C4C2×C811yescharacteristic
46C2×C32×C4C22×C411yescharacteristic
47C3⋊(C3⋊C8)—21no—
48C3⋊(C3⋊C8)—21no—
49C3⋊(C3⋊C8)M1612yes—
50C3⋊(C3⋊C8)#4112yes—
51C2×C4×C8—91no—
52C4⋊C16—92no—
53C22⋊C16—92no—
54#346—92no—
55C22×C3×C4—22no—
56C22×C3×C4—22no—
57C22×C3×C4—22no—
58C3×C42—22no—
59C3×C42—22no—
60C3×C42—22no—
61C3×C42—22no—
62C2×C3⋊C8—62no—
63C2×C3⋊C8—62no—
64C2×C3⋊C8—62no—
65C2×C3⋊C8—62no—
66C2×C3⋊C8—68no—
67C2×C3⋊C8—68no—
68C22×C32—21no—
69C22×C32—21no—
70C22×C32M3212yes—
71C22×C32C22×C811yescharacteristic
72C32×C4—21no—
73C32×C4—21no—
74C32×C4—21no—
75C32×C4—21no—
76C32×C4M3212yes—
77C32×C4#11711yescharacteristic
78C32×C4C2×M1611yescharacteristic
79C22×C8—91no—
80C22×C8—91no—
81C2×C42#15711yescharacteristic
82C2×C16—94no—
83C4×C8—91no—
84C4×C8—91no—
85C4×C8—91no—
86C4×C8—91no—
87C23×C3—22no—
88C2×C3×C4—24no—
89C2×C3×C4—24no—
90C2×C3×C4—28no—
91C2×C3×C4—28no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—22no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C3⋊C8—64no—
99C3⋊C8—64no—
100C3⋊C8—64no—
101C3⋊C8—64no—
102C2×C32—22no—
103C2×C32#43111yescharacteristic
104C2×C32C2×M3211yescharacteristic
105C2×C32C2×M3211yescharacteristic
106C22×C4#62211yescharacteristic
107C22×C4#62211yescharacteristic
108C22×C4C2×#15711yescharacteristic
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—91no—
112C2×C8—91no—
113C2×C8—182no—
114C2×C8—182no—
115C42#62211yescharacteristic
116C42#62211yescharacteristic
117C42C2×#15711yescharacteristic
118C42C2×#15711yescharacteristic
119C16—184no—
120C22×C3—24no—
121C22×C3—24no—
122C22×C3—24no—
123C22×C3—22no—
124C3×C4—24no—
125C3×C4—24no—
126C3×C4—24no—
127C3×C4—24no—
128C3×C4—22no—
129C3×C4—24no—
130C3×C4—22no—
131C32#216311yescharacteristic, complemented, Sylow
132C23C2×#62211yescharacteristic
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4C2×#62211yescharacteristic
138C2×C4C2×#62211yescharacteristic
139C2×C4C2×#62211yescharacteristic
140C2×C4C2×#62211yescharacteristic
141C2×C4C2×#62211yescharacteristic
142C2×C4C22×#15711yescharacteristic
143C8—92no—
144C8—92no—
145C8—181no—
146C8—181no—
147C2×C3—28no—
148C2×C3—22no—
149C2×C3—22no—
150C2×C3—22no—
151C22—21no—
152C22—21no—
153C22#6377312yes—
154C22C22×#62211yescharacteristic
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4#6377312yes—
160C4#6428311yescharacteristic
161C4#6428611yescharacteristic
162C3—22no—
163C2—22no—
164C2C2×#6377311yescharacteristic
165C2C2×#6377311yescharacteristic
166C2#1059379511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C22×C8
FittingC2×C32×C42C4
prime radicalC23×C32C2×C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C42#157
hypocenterC32#2163
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. #10590148C2semidirect
4. C4⋊#3708C2semidirect
131. C32#2163semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊(C3⋊C8)2
C22⋊#37082
#105901482
C4⋊#37082
#21639