Finite Group Databasebeta

← #16846130

Subgroups — #16846130

Order 3968.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521816C211yesmaximal, characteristic, complemented
2#14521033C211yesmaximal, characteristic, complemented
3#14521013C212yesmaximal, complemented
4#14520819C212yesmaximal, complemented
5C31×#525C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C31×#123C412yes—
9C31×C22⋊Q8—21no—
10C31×#121—21no—
11C31×#120C412yes—
12C4×D4×C31—22no—
13C31×#117C2211yescharacteristic
14#11758525—24no—
15C2×#92474—22no—
16C2×#92474C2212yes—
17C2×#92474C2212yes—
18#11758424—21no—
19#11758421—21no—
20C22⋊(C31⋊C8)—24no—
21C24×C31C2×C411yescharacteristic
22#41×C31—22no—
23#41×C31—22no—
24C2×Q8×C31D411yescharacteristic
25C2×D4×C31—22no—
26C2×D4×C31C2×C412yes—
27C2×D4×C31D411yescharacteristic
28C22×C4×C31—22no—
29C22×C4×C31—21no—
30C22×C4×C31—21no—
31C22×C4×C31—22no—
32C22×C4×C31C2×C411yescharacteristic
33C22×C4×C31D412yes—
34C22×C4×C31C2311yescharacteristic
35C4⋊C4×C31—22no—
36C4⋊C4×C31—21no—
37C22⋊C4×C31—22no—
38C22⋊C4×C31—22no—
39C22⋊C4×C31C2×C412yes—
40C42×C31—21no—
41#92474—24no—
42#92474—22no—
43#92474—22no—
44#92474—22no—
45#92474—22no—
46C2×C31⋊C8—24no—
47C2×C31⋊C8—22no—
48C2×C31⋊C8D414yescomplemented
49C23×C31—21no—
50C23×C31—22no—
51C23×C31—42no—
52C23×C31C22⋊C412yes—
53C23×C31C22×C411yescharacteristic
54Q8×C31—22no—
55D4×C31—24no—
56D4×C31—22no—
57D4×C31—44no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31—21no—
62C2×C4×C31—22no—
63C2×C4×C31—41no—
64C2×C4×C31—42no—
65C2×C4×C31—41no—
66C2×C4×C31C22⋊C412yes—
67C2×C4×C31C2×D412yes—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31#4112yes—
71C31⋊C8—24no—
72C31⋊C8—42no—
73#1891—311nomaximal, Sylow
74C22×C31—22no—
75C22×C31—24no—
76C22×C31—22no—
77C22×C31—41no—
78C22×C31—42no—
79C22×C31—41no—
80C22×C31—42no—
81C22×C31—41no—
82C22×C31C2×C22⋊C411yescharacteristic
83C22×C31C4×D412yes—
84C4×C31—22no—
85C4×C31—42no—
86C4×C31—41no—
87C4×C31#12011yescharacteristic
88C4×C31#12112yes—
89C4×C31#12311yescharacteristic
90#568—311no—
91#525D3111yescharacteristic
92#413—311no—
93#407—312no—
94#344—312no—
95C2×C31—21no—
96C2×C31—22no—
97C2×C31—42no—
98C2×C31—42no—
99C2×C31#38611yescharacteristic
100C2×#41C2×D3111yescharacteristic
101C23×C4C2×D3111yescharacteristic
102#131—624no—
103C2×M16—312no—
104C2×M16—312no—
105C2×M16—622no—
106#123Dic3112yes—
107C22⋊Q8—21no—
108#121—21no—
109#120Dic3112yes—
110C4×D4—22no—
111#117C2×D3111yescharacteristic
112#101—621no—
113#100—621no—
114C22⋊C8—624no—
115C31#189111yescharacteristic, complemented, Sylow
116C24C2×Dic3111yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D3111yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic3112yes—
122C2×D4C22⋊D3111yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×Dic3111yescharacteristic
128C22×C4C22⋊D3112yes—
129C22×C4C22×D3111yescharacteristic
130M16—624no—
131M16—622no—
132M16—622no—
133M16—622no—
134M16—622no—
135C2×C8—314no—
136C2×C8—624no—
137C2×C8—622no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic3112yes—
143C42—21no—
144C23—22no—
145C23—21no—
146C23—42no—
147C23C22⋊Dic3112yes—
148C23C22×Dic3111yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4C22⋊Dic3112yes—
162C2×C4D4×D3112yes—
163C2×C4#9249712yes—
164C2×C4C2×C22⋊D3111yescharacteristic
165C2×C4C2×C22⋊D3111yescharacteristic
166C8—624no—
167C8—1242no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22D4×Dic3112yes—
177C22C2×C22⋊Dic3111yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4#1175851211yescharacteristic
182C4#1175851411yescharacteristic
183C4#1175851612yes—
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#1452092911yescharacteristic
subgroupG/H
centerC4#11758514
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#525C2
socleC2×C31#386
cosocleC22×C4×C31C23
hypercenter#525D31
hypocenterC31#1891
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14521816C2semidirect
2. #14521033C2semidirect
3. #14521013C2semidirect
4. #14520819C2semidirect
48. C2×C31⋊C8D4semidirect
115. C31#1891semidirect

Maximal subgroups

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

subgroupindex
#145218162
#145210332
#145210132
#145208192
C31×#5252
#189131