Finite Group Databasebeta

← #16846160

Subgroups — #16846160

Order 3968.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11758503C211yesmaximal, characteristic, complemented
2C2×#11758425C212yesmaximal, complemented
3#14521013C211yesmaximal, characteristic, complemented
4#14520808C212yesmaximal, complemented
5C31×#525C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C31×#123—21no—
9C31×C22⋊Q8C412yescomplemented
10C31×#121C412yescomplemented
11C31×#120—21no—
12C4×D4×C31—22no—
13C31×#117C2211yescharacteristic
14C2×C22⋊Dic31—21no—
15#11758503—24no—
16C2×C4⋊Dic31—21no—
17C2×C4×Dic31C2212yes—
18C2×#92474C2212yes—
19#11758425—24no—
20C22⋊(C31⋊C8)—22no—
21C24×C31D411yescharacteristic
22#41×C31—22no—
23#41×C31—22no—
24C2×Q8×C31C2×C411yescharacteristic
25C2×D4×C31—22no—
26C2×D4×C31—21no—
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31—21no—
31C22×C4×C31C2×C412yes—
32C22×C4×C31D411yescharacteristic
33C22×C4×C31D412yes—
34C22×C4×C31C2311yescharacteristic
35C22×Dic31—22no—
36C4⋊C4×C31—22no—
37C4⋊C4×C31C2×C412yes—
38C22⋊C4×C31—22no—
39C22⋊C4×C31—21no—
40C22⋊C4×C31—22no—
41C42×C31—21no—
42C22⋊Dic31—24no—
43C4⋊Dic31—24no—
44C4×Dic31—22no—
45C4×Dic31D414yescomplemented
46#92474—22no—
47#92474—22no—
48C2×C31⋊C8—22no—
49C23×C31—21no—
50C23×C31—21no—
51C23×C31—21no—
52C23×C31—42no—
53C23×C31C22⋊C412yes—
54C23×C31C2×D411yescharacteristic
55Q8×C31—22no—
56D4×C31—22no—
57D4×C31—44no—
58D4×C31—41no—
59D4×C31—41no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—24no—
63C2×C4×C31—24no—
64C2×C4×C31—22no—
65C2×C4×C31—21no—
66C2×C4×C31—42no—
67C2×C4×C31C22⋊C412yes—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D412yes—
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31#4112yes—
72C2×Dic31—24no—
73C2×Dic31—44no—
74C31⋊C8—42no—
75#1897—311nomaximal, Sylow
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—41no—
83C22×C31—42no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31#12011yescharacteristic
86C22×C31#12311yescharacteristic
87C4×C31—22no—
88C4×C31—41no—
89C4×C31—42no—
90C4×C31C4×D412yes—
91C4×C31#12112yes—
92Dic31—44no—
93#525D3111yescharacteristic
94C2×#117—311no—
95C2×#104—312no—
96#407—311no—
97#339—312no—
98C2×C31—21no—
99C2×C31—21no—
100C2×C31—42no—
101C2×C31—81no—
102C2×C31#38611yescharacteristic
103C2×C31#42112yes—
104C2×#41C2×D3111yescharacteristic
105C23×C4C2×D3111yescharacteristic
106C2×M16—312no—
107#123—21no—
108C22⋊Q8Dic3112yescomplemented
109#121Dic3112yescomplemented
110#120—21no—
111C4×D4—22no—
112#117—624no—
113#117C2×D3111yescharacteristic
114C2×C4⋊C4—621no—
115C2×C22⋊C4—621no—
116C2×C42—312no—
117#104—624no—
118C22⋊C8—622no—
119C31#189711yescharacteristic, complemented, Sylow
120C24C22⋊D3111yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic3111yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic3111yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—622no—
131C22×C4C2×Dic3112yes—
132C22×C4C22⋊D3111yescharacteristic
133C22×C4C22⋊D3112yes—
134C22×C4C22×D3111yescharacteristic
135M16—622no—
136M16—622no—
137C2×C8—622no—
138C4⋊C4—22no—
139C4⋊C4—624no—
140C4⋊C4C2×Dic3112yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—624no—
145C42—21no—
146C42—314no—
147C42—622no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic3112yes—
153C23C2×C22⋊D3111yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—624no—
167C2×C4—1244no—
168C2×C4C22⋊Dic3112yes—
169C2×C4D4×D3112yes—
170C2×C4#9249712yes—
171C2×C4C22×Dic3111yescharacteristic
172C2×C4C2×C22⋊D3111yescharacteristic
173C8—1242no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—42no—
182C22#1175851211yescharacteristic
183C22#1175851411yescharacteristic
184C22C2×C22⋊Dic3111yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—1244no—
189C4D4×Dic3112yes—
190C4#1175851612yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#1452092911yescharacteristic
196C2#1452106612yes—
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#525C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#525D31
hypocenterC31#1897
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11758503C2semidirect
2. C2×#11758425C2semidirect
3. #14521013C2semidirect
4. #14520808C2semidirect
9. C31×C22⋊Q8C4semidirect
10. C31×#121C4semidirect
45. C4×Dic31D4semidirect
108. C22⋊Q8Dic31semidirect
109. #121Dic31semidirect
119. C31#1897semidirect

Maximal subgroups

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

subgroupindex
C2×#117585032
C2×#117584252
#145210132
#145208082
C31×#5252
#189731