Finite Group Databasebeta

← #49093832

Subgroups — #49093832

Order 35968.

326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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#31823427C211yesmaximal, characteristic, complemented
2#31823326C211yesmaximal, characteristic, complemented
3#31823197C214yesmaximal, complemented
4C2×#121×C281C211yesmaximal, characteristic
5C2×#17985122—21no—
6C2×C22⋊Dic281—21no—
7C22⋊#14555886—21no—
8C22⋊#14555886C2212yescomplemented
9#22582786—21no—
10#22582786C2212yescomplemented
11C22×D4×C281—21no—
12C22×D4×C281C411yescharacteristic, complemented
13C23×C4×C281C2211yescharacteristic
14#121×C281—21no—
15#121×C281—21no—
16#121×C281C412yescomplemented
17#121×C281C2212yes—
18C2×C4⋊C4×C281C411yescharacteristic, complemented
19C2×C22⋊C4×C281—21no—
20C22×Dic281—22no—
21#17985122—42no—
22C2×#14555886—22no—
23C22⋊Dic281—42no—
24C24×C281—21no—
25C24×C281D411yescharacteristic
26C2×D4×C281—22no—
27C2×D4×C281—22no—
28C2×D4×C281—21no—
29C2×D4×C281—42no—
30C2×D4×C281—44no—
31C2×D4×C281C2×C412yes—
32C22×C4×C281—21no—
33C22×C4×C281—42no—
34C22×C4×C281C2×C411yescharacteristic
35C22×C4×C281C2×C411yescharacteristic
36C22×C4×C281D411yescharacteristic
37C22×C4×C281D411yescharacteristic
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C4⋊C4×C281—21no—
41C4⋊C4×C281C2×C412yes—
42C22⋊C4×C281—22no—
43C22⋊C4×C281—22no—
44C2×Dic281—42no—
45C2×Dic281—42no—
46C2×Dic281—42no—
47#14555886—42no—
48C23×C281—22no—
49C23×C281—22no—
50C23×C281—22no—
51C23×C281—41no—
52C23×C281—42no—
53C23×C281—42no—
54C23×C281—42no—
55C23×C281C22⋊C411yescharacteristic
56C23×C281C22⋊C411yescharacteristic
57C23×C281C2×D411yescharacteristic
58D4×C281—42no—
59D4×C281—42no—
60D4×C281—44no—
61D4×C281—44no—
62C2×C4×C281—22no—
63C2×C4×C281—22no—
64C2×C4×C281—22no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281—42no—
70C2×C4×C281C22⋊C411yescharacteristic
71C2×C4×C281C22⋊C411yescharacteristic
72C2×C4×C281C22×C411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C22×C281—21no—
75C22×C281—21no—
76C22×C281—21no—
77C22×C281—21no—
78C22×C281—21no—
79C22×C281—21no—
80C22×C281—21no—
81C22×C281—44no—
82C22×C281—42no—
83C22×C281—42no—
84C22×C281—42no—
85C22×C281—84no—
86C22×C281#9912yes—
87C22×C281C2×C22⋊C411yescharacteristic
88C22×C281AGL(1,ℤ/8)12yes—
89C4×C281—21no—
90C4×C281—21no—
91C4×C281—21no—
92C4×C281—21no—
93C4×C281—42no—
94Dic281—82no—
95C2×C281—22no—
96C2×C281—22no—
97C2×C281—41no—
98C2×C281—82no—
99C2×C281C2×#9911yescharacteristic
100C2×C281#41811yescharacteristic
101C2×C281#42111yescharacteristic
102C281#151011yescharacteristic, complemented, Sylow
103#1510—2811nomaximal, Sylow
104C2×#121D28111yescharacteristic
105#407—2811no—
106#381—2811no—
107#327—2814no—
108C22×D4—21no—
109C22×D4Dic28111yescharacteristic, complemented
110C23×C4C2×D28111yescharacteristic
111C2×M16—5621no—
112#121—21no—
113#121—21no—
114#121Dic28112yescomplemented
115#121C2×D28112yes—
116C2×C4⋊C4Dic28111yescharacteristic, complemented
117C2×C22⋊C4—21no—
118C2×C22⋊C4—5621no—
119C22⋊C8—2812no—
120C22⋊C8—5621no—
121#95—2812no—
122#95—5621no—
123C24—21no—
124C24C22⋊D28111yescharacteristic
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—21no—
128C2×D4—42no—
129C2×D4—44no—
130C2×D4C2×Dic28112yes—
131C22×C4—21no—
132C22×C4—42no—
133C22×C4—5622no—
134C22×C4C2×Dic28111yescharacteristic
135C22×C4C2×Dic28111yescharacteristic
136C22×C4C22⋊D28111yescharacteristic
137C22×C4C22⋊D28111yescharacteristic
138C22×C4C22⋊D28111yescharacteristic
139C22×C4C22×D28111yescharacteristic
140M16—11242no—
141C2×C8—5622no—
142C4⋊C4—21no—
143C4⋊C4C2×Dic28112yes—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—11242no—
147C23—22no—
148C23—22no—
149C23—22no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23—42no—
154C23C22⋊Dic28111yescharacteristic
155C23C22⋊Dic28111yescharacteristic
156C23C2×C22⋊D28111yescharacteristic
157D4—42no—
158D4—42no—
159D4—44no—
160D4—44no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—11242no—
170C2×C4—11242no—
171C2×C4—11242no—
172C2×C4C22⋊Dic28111yescharacteristic
173C2×C4C22⋊Dic28111yescharacteristic
174C2×C4C22×Dic28111yescharacteristic
175C2×C4C2×C22⋊D28111yescharacteristic
176C8—11242no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—44no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—84no—
189C22#2258279412yes—
190C22C2×C22⋊Dic28111yescharacteristic
191C22#2258290512yes—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—42no—
197C4—22482no—
198C2—22no—
199C2—22no—
200C2—41no—
201C2—82no—
202C2C2×#2258279411yescharacteristic
203C2#3182346811yescharacteristic
204C2#3182348011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic281
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting, prime radicalC2×#121×C281C2
socleC22×C281C2×C22⋊C4
cosocleC22×C4×C281C23
hypercenterC2×#121D281
hypocenterC281#1510
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #31823427C2semidirect
2. #31823326C2semidirect
3. #31823197C2semidirect
8. C22⋊#14555886C22semidirect
10. #22582786C22semidirect
12. C22×D4×C281C4semidirect
16. #121×C281C4semidirect
18. C2×C4⋊C4×C281C4semidirect
102. C281#1510semidirect
109. C22×D4Dic281semidirect
114. #121Dic281semidirect
116. C2×C4⋊C4Dic281semidirect

Maximal subgroups

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

subgroupindex
#318234272
#318233262
#318231972
C2×#121×C2812
#1510281