Finite Group Databasebeta

← #11774705

Subgroups — #11774705

Order 1152.

756 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 257 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×C32×C4×Q8C211yesmaximal, characteristic
2#10592625C211yesmaximal, characteristic
3C4×#3748C211yesmaximal, characteristic
4#10589401C214yesmaximal, complemented
5#71623—34nomaximal
6C22×C32×Q8C411yescharacteristic
7C32×C4×Q8—21no—
8C32×C4×Q8—21no—
9C32×C4×Q8C412yes—
10C32×C4×Q8C2212yes—
11C2×C32×C4⋊C4—21no—
12C2×C32×C4⋊C4C411yescharacteristic
13C2×C32×C42—21no—
14C2×C32×C42C2211yescharacteristic
15C2×#3748—21no—
16#63657—21no—
17C4⋊(C3⋊(C3⋊C8))C2212yes—
18#63630—21no—
19#63630—21no—
20C4×C3⋊(C3⋊C8)C2212yes—
21C2×C3×C4×Q8D314yes—
22#4926—34no—
23C4×#208—34no—
24#4535—316no—
25C2×C32×Q8—24no—
26C2×C32×Q8—21no—
27C2×C32×Q8C2×C412yes—
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4C2×C411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C32×C4⋊C4—22no—
34C32×C4⋊C4—21no—
35C32×C4⋊C4—22no—
36C32×C4⋊C4C2×C412yes—
37C32×C42—22no—
38C32×C42—22no—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43#3748—24no—
44C2×C3⋊(C3⋊C8)—22no—
45C2×C3⋊(C3⋊C8)—22no—
46#1491—91noSylow
47C22×C3×Q8Dic314yes—
48C3×C4×Q8—24no—
49C3×C4×Q8—24no—
50C3×C4×Q8Dic318yes—
51C3×C4×Q8C2×D318yes—
52C2×C3×C4⋊C4—24no—
53C2×C3×C4⋊C4Dic314yes—
54C2×C3×C42—24no—
55C2×C3×C42C2×D314yes—
56C2×#208—64no—
57#830—64no—
58C4⋊(C3⋊C8)—38no—
59#803—64no—
60#803—64no—
61C4×C3⋊C8—38no—
62C23×C32C22⋊C411yescharacteristic
63C32×Q8—24no—
64C32×Q8—22no—
65C32×Q8M1614yescomplemented
66C2×C32×C4—24no—
67C2×C32×C4—22no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—42no—
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C411yescharacteristic
76C2×C32×C4C22×C411yescharacteristic
77C2×C32×C4C2×D411yescharacteristic
78C2×C32×C4C2×D411yescharacteristic
79C3⋊(C3⋊C8)—24no—
80C3⋊(C3⋊C8)—42no—
81C2×C4×Q8C3⋊D311yescharacteristic
82#432—91no—
83C4×M16—91no—
84Q8⋊C8—94no—
85C2×C3×Q8—216no—
86C2×C3×Q8—24no—
87C2×C3×Q8C2×Dic318yes—
88C22×C3×C4—24no—
89C22×C3×C4—24no—
90C22×C3×C4C2×Dic314yes—
91C22×C3×C4#6714yes—
92C22×C3×C4#6714yes—
93C3×C4⋊C4—28no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—28no—
96C3×C4⋊C4C2×Dic318yes—
97C3×C42—28no—
98C3×C42—28no—
99C3×C42C2×Dic314yes—
100C3×C42#6714yes—
101C3×C42#6714yes—
102C3×C42C22×D314yes—
103#208—616no—
104C2×C3⋊C8—68no—
105C2×C3⋊C8—68no—
106C22×C32—21no—
107C22×C32—21no—
108C22×C32#10412yes—
109C22×C32C2×C22⋊C411yescharacteristic
110C32×C4—24no—
111C32×C4—21no—
112C32×C4—21no—
113C32×C4—21no—
114C32×C4—21no—
115C32×C4—42no—
116C32×C4C2×M1612yes—
117C32×C4#13712yes—
118C22×Q8C3⋊Dic311yescharacteristic
119C2×M16—181no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8C3⋊Dic312yes—
123C4×Q8C2×C3⋊D312yes—
124C2×C4⋊C4—21no—
125C2×C4⋊C4C3⋊Dic311yescharacteristic
126C2×C42—21no—
127C2×C42C2×C3⋊D311yescharacteristic
128C4⋊C8—92no—
129C22⋊C8—181no—
130#97—181no—
131#97—181no—
132C4×C8—92no—
133C23×C3#21714yes—
134C3×Q8—216no—
135C3×Q8—28no—
136C3×Q8#208116yescomplemented
137C2×C3×C4—216no—
138C2×C3×C4—28no—
139C2×C3×C4—28no—
140C2×C3×C4—28no—
141C2×C3×C4—28no—
142C2×C3×C4—28no—
143C2×C3×C4—48no—
144C2×C3×C4#21714yes—
145C2×C3×C4#21714yes—
146C2×C3×C4#21714yes—
147C2×C3×C4C22×Dic314yes—
148C2×C3×C4C2×#6714yes—
149C2×C3×C4C2×#6714yes—
150C3⋊C8—616no—
151C3⋊C8—128no—
152C2×C32—22no—
153C2×C32#40711yescharacteristic
154C2×C32#41911yescharacteristic
155C2×C32C2×#10411yescharacteristic
156C2×Q8—24no—
157C2×Q8—21no—
158C2×Q8C2×C3⋊Dic312yes—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4C2×C3⋊Dic311yescharacteristic
162C22×C4#63811yescharacteristic
163C22×C4#63811yescharacteristic
164M16—184no—
165C2×C8—182no—
166C2×C8—182no—
167C4⋊C4—22no—
168C4⋊C4—21no—
169C4⋊C4—22no—
170C4⋊C4C2×C3⋊Dic312yes—
171C42—22no—
172C42—22no—
173C42C2×C3⋊Dic311yescharacteristic
174C42#63811yescharacteristic
175C42#63811yescharacteristic
176C42C22×C3⋊D311yescharacteristic
177C22×C3—24no—
178C22×C3—24no—
179C22×C3#83718yes—
180C22×C3C2×#21714yes—
181C3×C4—216no—
182C3×C4—24no—
183C3×C4—24no—
184C3×C4—24no—
185C3×C4—24no—
186C3×C4—48no—
187C3×C4C2×#20818yes—
188C3×C4#94218yes—
189C32#149111yescharacteristic, complemented, Sylow
190C23#375711yescharacteristic
191Q8—24no—
192Q8—22no—
193Q8#374814yescomplemented
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4#375711yescharacteristic
202C2×C4#375711yescharacteristic
203C2×C4#375711yescharacteristic
204C2×C4C22×C3⋊Dic311yescharacteristic
205C2×C4C2×#63811yescharacteristic
206C2×C4C2×#63811yescharacteristic
207C8—184no—
208C8—362no—
209C2×C3—28no—
210C2×C3#520714yes—
211C2×C3#522514yes—
212C2×C3C2×#83714yes—
213C22—21no—
214C22—21no—
215C22#6366412yes—
216C22C2×#375711yescharacteristic
217C4—24no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—21no—
222C4—42no—
223C4C2×#374812yes—
224C4#6415112yes—
225C3#7162314yescomplemented
226C2—22no—
227C2#1059290611yescharacteristic
228C2#1059292411yescharacteristic
229C2C2×#6366411yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC2×C32×C4×Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32#1491
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
4. #10589401C2semidirect
65. C32×Q8M16semidirect
136. C3×Q8#208semidirect
189. C32#1491semidirect
193. Q8#3748semidirect
225. C3#71623semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
#105926252
C4×#37482
#105894012
#716233