Finite Group Databasebeta

← #16844720

Subgroups — #16844720

Order 3968.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521678C211yesmaximal, characteristic
2#14521380C211yesmaximal, characteristic
3#14521377C211yesmaximal, characteristic
4#14520981C211yesmaximal, characteristic
5#14520785C211yesmaximal, characteristic
6#14520774C211yesmaximal, characteristic
7C31×#328C211yesmaximal, characteristic
8C31×C22⋊Q8C2211yescharacteristic
9#11758521—21no—
10C2×C4⋊Dic31—21no—
11C2×C4⋊Dic31C2211yescharacteristic
12#11758501C2211yescharacteristic
13C2×Dic31⋊C4C2211yescharacteristic
14#11758466—21no—
15#11758466—21no—
16#11758465—21no—
17#11758455—21no—
18#11758454—21no—
19C31×C22⋊C8C2211yescharacteristic
20C31×#95C2211yescharacteristic
21#11758423—21no—
22C31⋊#95—21no—
23C22⋊(C31⋊C8)C2211yescharacteristic
24#11758405—21no—
25#11758404—21no—
26#11758396—21no—
27C2×Q8×C31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31D411yescharacteristic
32C22×Dic31D411yescharacteristic
33C2×Dic62—21no—
34C2×Dic62D411yescharacteristic
35C2×C8×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31D411yescharacteristic
38C22⋊C4×C31—21no—
39C22⋊Dic31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42C4⋊Dic31—21no—
43C4⋊Dic31—42no—
44C4⋊Dic31D411yescharacteristic
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48Dic31⋊C4—21no—
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51Dic31⋊C4—21no—
52C4×Dic31—21no—
53C4×Dic31—21no—
54C2×C31⋊C8—21no—
55C23×C31C2×D411yescharacteristic
56Q8×C31—41no—
57C2×C4×C31—22no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×Dic31—21no—
66C2×Dic31—21no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31—21no—
70C2×Dic31—41no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73C2×Dic31—41no—
74C2×Dic31SD1612yes—
75Dic62—41no—
76Dic62—81no—
77C8×C31—41no—
78C31⋊C8—41no—
79#1611—311nomaximal, Sylow
80C22×C31—21no—
81C22×C31—21no—
82C22×C31#12011yescharacteristic
83C22×C31C2×SD1611yescharacteristic
84C22×C31#13711yescharacteristic
85C4×C31—21no—
86C4×C31—21no—
87C4×C31—42no—
88C4×C31—41no—
89C4×C31—41no—
90Dic31—22no—
91Dic31—41no—
92Dic31—41no—
93Dic31—41no—
94Dic31—81no—
95#544—311no—
96#483—311no—
97#483—311no—
98#398—311no—
99#328—311no—
100#328D3111yescharacteristic
101#324—311no—
102C2×C31—21no—
103C2×C31—21no—
104C2×C31#44811yescharacteristic
105C2×C31#45611yescharacteristic
106C2×C31#45811yescharacteristic
107C4⋊Q8—621no—
108C4⋊Q8—621no—
109#125—621no—
110#125—621no—
111C22⋊Q8—311no—
112C22⋊Q8—621no—
113C22⋊Q8C2×D3111yescharacteristic
114#117—621no—
115C2×C4⋊C4—311no—
116C2×C4⋊C4—311no—
117C2×C4⋊C4—621no—
118#106—621no—
119#106—621no—
120#103—621no—
121#103—621no—
122C22⋊C8—311no—
123C22⋊C8C2×D3111yescharacteristic
124#95—621no—
125#95C2×D3111yescharacteristic
126C31#161111yescharacteristic, complemented, Sylow
127C2×Q8—311no—
128C2×Q8—621no—
129C2×Q8D12411yescharacteristic
130C22×C4—21no—
131C22×C4—311no—
132C22×C4—311no—
133C22×C4—621no—
134C22×C4C22×D3111yescharacteristic
135C2×C8—21no—
136C2×C8—621no—
137C4⋊C4—21no—
138C4⋊C4—311no—
139C4⋊C4—621no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4—621no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C4⋊C4—621no—
148C4⋊C4—621no—
149C4⋊C4—1242no—
150C4⋊C4D12411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—621no—
153C42—621no—
154C42—621no—
155C23D4×D3111yescharacteristic
156Q8—41no—
157Q8—1241no—
158Q8—2481no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—312no—
166C2×C4—621no—
167C2×C4—621no—
168C2×C4—621no—
169C2×C4—621no—
170C2×C4—621no—
171C2×C4—1241no—
172C2×C4—1241no—
173C2×C4—1241no—
174C2×C4—1241no—
175C2×C4C2×D12411yescharacteristic
176C2×C4D4×D3111yescharacteristic
177C8—41no—
178C8—1241no—
179C22—21no—
180C22—21no—
181C22#1175845911yescharacteristic
182C22SD16×D3111yescharacteristic
183C22#1175849511yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—622no—
190C4—1241no—
191C4—1241no—
192C4—1241no—
193C4—2481no—
194C2—21no—
195C2—21no—
196C2#1452118911yescharacteristic
197C2#1452123311yescharacteristic
198C2#1452124011yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#328D31
hypocenterC31#1611
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
126. C31#1611semidirect

Maximal subgroups

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

subgroupindex
#145216782
#145213802
#145213772
#145209812
#145207852
#145207742
C31×#3282
#161131