Finite Group Databasebeta

← #16846183

Subgroups — #16846183

Order 3968.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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×#11758486C211yesmaximal, characteristic
2#14521815C211yesmaximal, characteristic
3#14521067C211yesmaximal, characteristic
4#14521057C211yesmaximal, characteristic, complemented
5C2×#11758412C211yesmaximal, characteristic, complemented
6C31⋊#338C211yesmaximal, characteristic, complemented
7C31×#344C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C31×#117C2211yescharacteristic
13C2×#92474C2211yescharacteristic
14C2×#92474C2211yescharacteristic
15#11758486—22no—
16#11758486—22no—
17#11758484—22no—
18M16×D31—22no—
19C2×Dic124C412yescomplemented
20C2×#92470C412yescomplemented
21#11758478—22no—
22#11758412—22no—
23#11758398—22no—
24#11758393—22no—
25C22×C4×C31C2311yescharacteristic
26C2×C22⋊D31—21no—
27C22×Dic31—21no—
28#92495—21no—
29#92495—21no—
30#92495D412yes—
31#92495D412yes—
32C2×D124C2×C411yescharacteristic
33C2×C4×D31—21no—
34C2×Dic62—21no—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62—21no—
38C2×Dic62—21no—
39C2×Dic62C2×C412yes—
40C2×Dic62C2×C411yescharacteristic
41M16×C31—21no—
42M16×C31—21no—
43M16×C31—21no—
44M16×C31D412yes—
45C2×C8×C31—21no—
46C2×C8×C31C2×C412yes—
47C4⋊C4×C31—21no—
48C22⋊C4×C31—21no—
49C42×C31—21no—
50#92474—21no—
51#92474—21no—
52#92474—21no—
53#92474—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8D412yes—
56Dic124—24no—
57#92470—24no—
58#92469—24no—
59C8×D31—24no—
60C23×C31#4111yescharacteristic
61C22×D31—21no—
62C2×C4×C31—41no—
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31#4111yescharacteristic
69C22⋊D31—22no—
70C22⋊D31—22no—
71C2×Dic31—21no—
72C2×Dic31—22no—
73C2×Dic31—41no—
74C2×Dic31—41no—
75D124—21no—
76D124C22⋊C412yes—
77C4×D31—22no—
78C4×D31—22no—
79Dic62—21no—
80Dic62—22no—
81Dic62—22no—
82Dic62—41no—
83Dic62—41no—
84Dic62C22⋊C412yes—
85C8×C31—22no—
86C8×C31—22no—
87C31⋊C8—22no—
88C31⋊C8—41no—
89#1902—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31C4×D411yescharacteristic
92C22×C31#12111yescharacteristic
93C22×C31#12311yescharacteristic
94C2×D31—22no—
95C2×D31—81no—
96C4×C31—81no—
97C4×C31C2×C22⋊C411yescharacteristic
98C4×C31C4×D411yescharacteristic
99C4×C31#12011yescharacteristic
100C4×C31#12111yescharacteristic
101Dic31—22no—
102Dic31—42no—
103C2×#137—311no—
104#568—311no—
105#421—311no—
106#419—311no—
107C2×#101—311no—
108#344D3111yescharacteristic, complemented
109#338—311no—
110C2×C31—21no—
111C2×C31—21no—
112C2×C31—21no—
113C2×C31#38611yescharacteristic
114D31—42no—
115C2×#41—311no—
116C22×Q8—311no—
117#137—622no—
118#137—622no—
119C2×Q16—312no—
120C2×SD16—312no—
121#131—622no—
122#131—622no—
123C2×M16—311no—
124C2×M16—311no—
125C2×M16—622no—
126C2×M16C2×D3111yescharacteristic
127C2×M16C2×D3111yescharacteristic
128#117C2×D3111yescharacteristic
129#104—622no—
130#103—622no—
131#101—622no—
132C31#190211yescharacteristic, complemented, Sylow
133#41—312no—
134#41—312no—
135#41—621no—
136#41—621no—
137C2×Q8—311no—
138C2×Q8—312no—
139C2×Q8—621no—
140C2×Q8—621no—
141C2×Q8—621no—
142C2×Q8—621no—
143C2×Q8—621no—
144C2×D4—311no—
145C2×D4—621no—
146C22×C4—621no—
147C22×C4—621no—
148C22×C4C22×D3111yescharacteristic
149Q16—624no—
150SD16—624no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—624no—
155M16—621no—
156M16—621no—
157M16—621no—
158M16—621no—
159M16D12412yes—
160C2×C8—21no—
161C2×C8—312no—
162C2×C8—624no—
163C2×C8—621no—
164C2×C8C4×D3112yes—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—621no—
169C23#9249511yescharacteristic
170Q8—312no—
171Q8—621no—
172Q8—622no—
173Q8—622no—
174Q8—1241no—
175Q8—1241no—
176D4—312no—
177D4—622no—
178D4—622no—
179D4—621no—
180C2×C4—41no—
181C2×C4—621no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4—1241no—
186C2×C4—1241no—
187C2×C4C2×C4×D3111yescharacteristic
188C2×C4C2×D12411yescharacteristic
189C2×C4D4×D3111yescharacteristic
190C2×C4D4×D3111yescharacteristic
191C2×C4D4×D3111yescharacteristic
192C2×C4#9249911yescharacteristic
193C8—22no—
194C8—22no—
195C8—622no—
196C8—1241no—
197C22—41no—
198C22—622no—
199C22—2481no—
200C22C4×D12411yescharacteristic
201C22#1175846111yescharacteristic
202C22#1175847111yescharacteristic
203C4—81no—
204C4—622no—
205C4—1242no—
206C4C22⋊C4×D3111yescharacteristic
207C4#1175845911yescharacteristic
208C4#1175847011yescharacteristic
209C4#1175847211yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—1242no—
214C2#1452092711yescharacteristic
subgroupG/H
centerC2#14520927
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#344C2
socleC2×C31#386
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenter#344D31
hypocenterC31#1902
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. #14521057C2semidirect
5. C2×#11758412C2semidirect
6. C31⋊#338C2semidirect
7. C31×#344C2semidirect
19. C2×Dic124C4semidirect
20. C2×#92470C4semidirect
108. #344D31semidirect
132. C31#1902semidirect

Maximal subgroups

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

subgroupindex
C2×#117584862
#145218152
#145210672
#145210572
C2×#117584122
C31⋊#3382
C31×#3442
#190231