Finite Group Databasebeta

← #11783258

Subgroups — #11783258

Order 1152.

762 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 138 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×#64286C212yesmaximal
2C22×C8×C3⋊D3C211yesmaximal, characteristic
3#10590182C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157—22no—
6#64286—24no—
7#64286C418yescomplemented
8C2×C4⋊#157C2214yes—
9C2×C4×#157—22no—
10C22×C32×C8C411yescharacteristic, complemented
11C22×C3⋊(C3⋊C8)C411yescharacteristic, complemented
12C2×C8×C3⋊D3—24no—
13C2×C8×C3⋊D3C412yescomplemented
14C2×C8×C3⋊D3C2212yes—
15C22×D3×C8—62no—
16C23×C3⋊D3D411yescharacteristic
17C22×#157—24no—
18C22×C32×C4C2×C411yescharacteristic
19C22×C3⋊Dic3Q811yescharacteristic
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C414yes—
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D414yes—
24C2×C4×C3⋊D3Q811yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C22⋊#157—28no—
27C4⋊#157—24no—
28C4⋊#157C2×C418yes—
29C4×#157—28no—
30C2×C32×C8—22no—
31C2×C32×C8C2×C412yes—
32C2×C3⋊(C3⋊C8)—22no—
33C2×C3⋊(C3⋊C8)C2×C412yes—
34C8×C3⋊D3—24no—
35C8×C3⋊D3—24no—
36#1735—91nomaximal, Sylow
37C22×C4×D3—62no—
38C22×C3×C8—22no—
39C22×C3⋊C8—62no—
40C2×D3×C8—64no—
41C2×D3×C8—64no—
42C2×D3×C8—616no—
43C23×C32C4⋊C411yescharacteristic
44C22×C3⋊D3—24no—
45C22×C3⋊D3C22⋊C414yes—
46C22×C3⋊D3C4⋊C411yescharacteristic
47C22×C3⋊D3C2×D411yescharacteristic
48C2×#157—28no—
49C2×#157—48no—
50C2×C32×C4C4212yes—
51C2×C32×C4C22⋊C412yes—
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C414yes—
56C2×C3⋊Dic3C2×Q811yescharacteristic
57C4×C3⋊D3C4212yes—
58C4×C3⋊D3C22⋊C414yes—
59C4×C3⋊D3C22⋊C412yes—
60C4×C3⋊D3C4⋊C414yes—
61C4×C3⋊D3C22×C412yes—
62C4×C3⋊D3C2×D412yes—
63C32×C8—22no—
64C3⋊(C3⋊C8)—22no—
65C23×C8—91no—
66C2×#117—92no—
67#340—94no—
68C23×D3—62no—
69C22×C3×C4—22no—
70C22×Dic3—62no—
71C2×C4×D3—62no—
72C2×C4×D3—68no—
73C2×C4×D3—62no—
74C2×C4×D3—68no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×C3×C8—28no—
78C2×C3×C8—24no—
79C2×C3⋊C8—64no—
80C2×C3⋊C8—68no—
81D3×C8—616no—
82D3×C8—616no—
83C22×C32—22no—
84C22×C32#9512yes—
85C22×C32C2×C4⋊C411yescharacteristic
86C2×C3⋊D3—22no—
87C2×C3⋊D3—28no—
88C2×C3⋊D3#9512yes—
89C2×C3⋊D3C2×C22⋊C412yes—
90C2×C3⋊D3#13514yes—
91#157—48no—
92C32×C4#9512yes—
93C32×C4C2×C4211yescharacteristic
94C32×C4C2×C22⋊C411yescharacteristic
95C3⋊Dic3#9512yes—
96C3⋊Dic3C2×C4⋊C412yes—
97C23×C4—91no—
98C22×C8—91no—
99C22×C8—92no—
100C22×C8—92no—
101C22×C8—184no—
102C22×C8#15711yescharacteristic, complemented
103#117—98no—
104#117—184no—
105C2×C4⋊C4—94no—
106C2×C22⋊C4—182no—
107C2×C42—182no—
108C23×C3—22no—
109C22×D3—68no—
110C22×D3—62no—
111C22×D3—62no—
112C22×D3—616no—
113C2×C3×C4—22no—
114C2×C3×C4—24no—
115C2×C3×C4—22no—
116C2×C3×C4—24no—
117C2×Dic3—62no—
118C2×Dic3—68no—
119C2×Dic3—62no—
120C4×D3—64no—
121C4×D3—64no—
122C4×D3—68no—
123C4×D3—68no—
124C4×D3—64no—
125C4×D3—64no—
126C3×C8—28no—
127C3⋊C8—68no—
128C2×C32—22no—
129C2×C32C2×#9511yescharacteristic
130C2×C32#42712yes—
131C3⋊D3—22no—
132C3⋊D3#41614yes—
133C24—91no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—94no—
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—94no—
141C22×C4—184no—
142C22×C4C2×#15711yescharacteristic
143C2×C8—22no—
144C2×C8—92no—
145C2×C8—184no—
146C2×C8—184no—
147C2×C8—182no—
148C2×C8C2×#15712yes—
149C4⋊C4—98no—
150C4⋊C4—184no—
151C22⋊C4—188no—
152C42—188no—
153C22×C3—28no—
154C22×C3—22no—
155C22×C3—24no—
156C2×D3—64no—
157C2×D3—64no—
158C2×D3—68no—
159C2×D3—632no—
160C2×D3—68no—
161C3×C4—22no—
162C3×C4—24no—
163C3×C4—22no—
164Dic3—64no—
165Dic3—64no—
166C32#173511yescharacteristic, complemented, Sylow
167C23—91no—
168C23—91no—
169C23—94no—
170C23—184no—
171C23C4⋊#15711yescharacteristic
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—94no—
175C2×C4—92no—
176C2×C4—92no—
177C2×C4—94no—
178C2×C4—94no—
179C2×C4—92no—
180C2×C4—92no—
181C2×C4—188no—
182C2×C4—368no—
183C2×C4C4×#15712yes—
184C2×C4C4⋊#15711yescharacteristic
185C2×C4C22⋊#15712yes—
186C2×C4C22×#15711yescharacteristic
187C8—22no—
188C8—182no—
189C2×C3—28no—
190C2×C3—22no—
191C2×C3—24no—
192D3—68no—
193D3—68no—
194C22—22no—
195C22—92no—
196C22—94no—
197C22—92no—
198C22—188no—
199C22—182no—
200C22#6378112yes—
201C22C2×C4⋊#15711yescharacteristic
202C4—92no—
203C4—92no—
204C4—368no—
205C4#6378112yes—
206C4C2×C4×#15711yescharacteristic
207C4C2×C22⋊#15711yescharacteristic
208C3—22no—
209C2—22no—
210C2—94no—
211C2—182no—
212C2#1059376812yes—
213C2C2×#6378111yescharacteristic
subgroupG/H
centerC2×C4C4⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C8#157
hypocenterC32#1735
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10590182C2semidirect
7. #64286C4semidirect
10. C22×C32×C8C4semidirect
11. C22×C3⋊(C3⋊C8)C4semidirect
13. C2×C8×C3⋊D3C4semidirect
102. C22×C8#157semidirect
166. C32#1735semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
C22×C8×C3⋊D32
#105901822
#17359