Finite Group Databasebeta

← #16844273

Subgroups — #16844273

Order 3968.

220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521601C211yesmaximal, characteristic
2#14521099C211yesmaximal, characteristic
3#14520913C211yesmaximal, characteristic
4#14520787C211yesmaximal, characteristic
5#14520786C211yesmaximal, characteristic
6#14520785C211yesmaximal, characteristic
7C31×#328C211yesmaximal, characteristic
8C31×C22⋊Q8C2211yescharacteristic
9Q8×Dic31C411yescharacteristic, complemented
10#11758521C411yescharacteristic, complemented
11#11758501C2211yescharacteristic
12C2×Dic31⋊C4—21no—
13C2×C4×Dic31C2211yescharacteristic
14#11758466—21no—
15#11758465C411yescharacteristic, complemented
16#11758464—21no—
17#11758464C411yescharacteristic, complemented
18#11758455—21no—
19#11758454—21no—
20C31×C22⋊C8C2211yescharacteristic
21C31×#95C2211yescharacteristic
22C31⋊#95—21no—
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25Dic31⋊C8—21no—
26C8×Dic31—21no—
27C2×Q8×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31D411yescharacteristic
32C22×Dic31D411yescharacteristic
33C2×Dic62—21no—
34C2×Dic62C2×C411yescharacteristic
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31C2×C411yescharacteristic
38C22⋊C4×C31—21no—
39C22⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31C2×C411yescharacteristic
42Dic31⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47Dic31⋊C4—42no—
48C4×Dic31—21no—
49C4×Dic31—21no—
50C4×Dic31C2×C411yescharacteristic
51C4×Dic31C2×C411yescharacteristic
52C4×Dic31D411yescharacteristic
53C4×Dic31D411yescharacteristic
54C2×C31⋊C8—21no—
55C23×C31C2×D411yescharacteristic
56Q8×C31—41no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—41no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×Dic31—21no—
66C2×Dic31—21no—
67C2×Dic31—41no—
68C2×Dic31—41no—
69C2×Dic31—41no—
70C2×Dic31—41no—
71C2×Dic31C22⋊C411yescharacteristic
72C2×Dic31C22⋊C411yescharacteristic
73C2×Dic31C22⋊C411yescharacteristic
74C2×Dic31C22⋊C411yescharacteristic
75C2×Dic31SD1612yes—
76C2×Dic31Q1612yes—
77Dic62—42no—
78Dic62—41no—
79C8×C31—41no—
80C31⋊C8—41no—
81#1518—311nomaximal, Sylow
82C22×C31—21no—
83C22×C31—21no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31C2×SD1611yescharacteristic
86C22×C31C2×Q1611yescharacteristic
87C4×C31—21no—
88C4×C31—21no—
89C4×C31—41no—
90C4×C31—41no—
91C4×C31—81no—
92Dic31—21no—
93Dic31—21no—
94Dic31—41no—
95Dic31—41no—
96Dic31—81no—
97Dic31#10312yes—
98Dic31#10312yes—
99#533—311no—
100#431—311no—
101#382—311no—
102#328—311no—
103#328—311no—
104#328—311no—
105#328D3111yescharacteristic
106C2×C31—21no—
107C2×C31—21no—
108C2×C31#41011yescharacteristic
109C2×C31C2×#10311yescharacteristic
110C2×C31#42111yescharacteristic
111C4⋊Q8—311no—
112C4⋊Q8—311no—
113#125—621no—
114C22⋊Q8—311no—
115C22⋊Q8—621no—
116C22⋊Q8C2×D3111yescharacteristic
117C4×Q8—311no—
118C4×Q8—311no—
119C4×Q8—621no—
120#117—621no—
121C2×C4⋊C4—621no—
122C2×C42—311no—
123C4⋊C8—621no—
124C22⋊C8—311no—
125C22⋊C8C2×D3111yescharacteristic
126C4×C8—621no—
127#95—311no—
128#95—621no—
129#95C2×D3111yescharacteristic
130C31#151811yescharacteristic, complemented, Sylow
131C2×Q8—311no—
132C2×Q8—621no—
133C2×Q8C4×D3111yescharacteristic
134C22×C4—21no—
135C22×C4—311no—
136C22×C4—311no—
137C22×C4—621no—
138C22×C4C22×D3111yescharacteristic
139C2×C8—21no—
140C2×C8—621no—
141C4⋊C4—21no—
142C4⋊C4—311no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C4⋊C4—1242no—
150C4⋊C4C4×D3111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—621no—
153C42—311no—
154C42—311no—
155C42—311no—
156C42—311no—
157C42—621no—
158C42—621no—
159C23D4×D3111yescharacteristic
160Q8—41no—
161Q8—1241no—
162Q8—1242no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—311no—
170C2×C4—311no—
171C2×C4—312no—
172C2×C4—312no—
173C2×C4—311no—
174C2×C4—311no—
175C2×C4—621no—
176C2×C4—621no—
177C2×C4—1241no—
178C2×C4—1241no—
179C2×C4—1241no—
180C2×C4—1241no—
181C2×C4C2×C4×D3111yescharacteristic
182C2×C4D4×D3111yescharacteristic
183C8—41no—
184C8—1241no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D3111yescharacteristic
188C22SD16×D3111yescharacteristic
189C22Q16×D3111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—312no—
196C4—312no—
197C4—621no—
198C4—621no—
199C4—1241no—
200C4—1241no—
201C4—2481no—
202C2—21no—
203C2—21no—
204C2#1452102111yescharacteristic
205C2#103×D3111yescharacteristic
206C2#1452106411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#328D31
hypocenterC31#1518
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
9. Q8×Dic31C4semidirect
10. #11758521C4semidirect
15. #11758465C4semidirect
17. #11758464C4semidirect
130. C31#1518semidirect

Maximal subgroups

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

subgroupindex
#145216012
#145210992
#145209132
#145207872
#145207862
#145207852
C31×#3282
#151831