Finite Group Databasebeta

← #16856012

Subgroups — #16856012

Order 3968.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#14521661C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic
3#14521391C212yesmaximal
4#14521357C212yesmaximal, complemented
5#14521260C212yesmaximal, complemented
6#14521207C212yesmaximal
7#14521157C212yesmaximal, complemented
8C4×Dic124C212yesmaximal, complemented
9C31×#433C211yesmaximal, characteristic
10C22×Dic62C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758503C2211yescharacteristic
13#11758501C2212yes—
14C2×Dic124C2212yes—
15C2×Dic124C2212yes—
16#11758466—22no—
17#11758464—22no—
18#11758456—22no—
19#11758454—22no—
20#11758447C2211yescharacteristic
21#11758446C2211yescharacteristic
22C4×Dic62C2212yes—
23C4×Dic62C2212yes—
24C4×Dic62C2212yes—
25C31×C4⋊C8C2212yes—
26C31×C22⋊C8C2212yes—
27C31×#97C2211yescharacteristic
28C4×C8×C31C2211yescharacteristic
29#11758406C2212yes—
30#11758405C2212yes—
31#11758404C2212yes—
32#11758404C2212yes—
33#11758404C2212yes—
34#11758404C2212yes—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31—21no—
37C2×Dic62—21no—
38C2×Dic62—24no—
39C2×Dic62C2312yes—
40C2×Dic62C2312yes—
41C2×C8×C31C2312yes—
42C2×C8×C31C2312yes—
43C4⋊C4×C31D412yes—
44C22⋊C4×C31D412yes—
45C42×C31C2311yescharacteristic
46C42×C31C2311yescharacteristic
47C22⋊Dic31—21no—
48C22⋊Dic31—22no—
49C4⋊Dic31—22no—
50C4⋊Dic31C2312yes—
51C4⋊Dic31C2312yes—
52Dic31⋊C4—22no—
53Dic31⋊C4—22no—
54Dic31⋊C4—22no—
55Dic31⋊C4—22no—
56Dic31⋊C4—22no—
57C4×Dic31—22no—
58C4×Dic31—22no—
59C4×Dic31—22no—
60C4×Dic31—21no—
61Dic124—24no—
62Dic124—24no—
63C23×C31C2×D411yescharacteristic
64C2×C4×C31—22no—
65C2×C4×C31C2×D412yes—
66C2×C4×C31C2×D412yes—
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2411yescharacteristic
69C2×Dic31—24no—
70C2×Dic31—22no—
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74Dic62—24no—
75Dic62—22no—
76Dic62—22no—
77Dic62—22no—
78Dic62#4114yes—
79C8×C31—22no—
80C8×C31—22no—
81#3127—311nomaximal, Sylow
82C22×C31—21no—
83C22×C31—22no—
84C22×C31C22×D411yescharacteristic
85C4×C31—21no—
86C4×C31—22no—
87C4×C31—22no—
88C4×C31C2×#4112yes—
89Dic31—24no—
90Dic31—42no—
91Dic31—42no—
92Dic31—42no—
93#541—311no—
94#519—311no—
95#485—312no—
96#479—312no—
97#462—312no—
98#451—312no—
99#441—312no—
100C4×Q16—312no—
101#433D3111yescharacteristic
102C2×C31—41no—
103C2×C31#52511yescharacteristic
104C2×C31#57812yes—
105C22×Q8—311no—
106C2×Q16—312no—
107C2×Q16—312no—
108C4⋊Q8—311no—
109#126—622no—
110#125—311no—
111#125—622no—
112C22⋊Q8—312no—
113C4×Q8—312no—
114C4×Q8—312no—
115C4×Q8—312no—
116C4×Q8—622no—
117#117—311no—
118#117—622no—
119#117C2×D3111yescharacteristic
120#107—312no—
121#106—312no—
122C4⋊C8C2×D3112yes—
123#103—312no—
124#103—312no—
125#103—312no—
126#103—312no—
127C22⋊C8C2×D3112yes—
128#97C2×D3111yescharacteristic
129C4×C8C2×D3111yescharacteristic
130C31#312711yescharacteristic, complemented, Sylow
131C2×Q8—312no—
132C2×Q8—312no—
133C2×Q8—624no—
134C2×Q8—621no—
135C22×C4—621no—
136C22×C4C22×D3111yescharacteristic
137Q16—624no—
138Q16—624no—
139C2×C8C22×D3112yes—
140C2×C8C22×D3112yes—
141C4⋊C4—312no—
142C4⋊C4—312no—
143C4⋊C4—622no—
144C4⋊C4—622no—
145C4⋊C4—622no—
146C4⋊C4—622no—
147C4⋊C4—622no—
148C4⋊C4—622no—
149C4⋊C4D12412yes—
150C22⋊C4—621no—
151C22⋊C4—622no—
152C22⋊C4D12412yes—
153C42—621no—
154C42—622no—
155C42—622no—
156C42—622no—
157C42C22×D3111yescharacteristic
158C42C22×D3111yescharacteristic
159C23C2×D12411yescharacteristic
160Q8—314no—
161Q8—624no—
162Q8—622no—
163Q8—622no—
164Q8—622no—
165C2×C4—22no—
166C2×C4—624no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4C2×D12412yes—
172C2×C4C2×D12412yes—
173C2×C4C2×D12411yescharacteristic
174C2×C4C23×D3111yescharacteristic
175C8—22no—
176C8—22no—
177C22—22no—
178C22—21no—
179C22C22×D12411yescharacteristic
180C4—22no—
181C4—22no—
182C4—21no—
183C4—624no—
184C4—1242no—
185C4—1242no—
186C4—1242no—
187C4#41×D3112yes—
188C2—41no—
189C2#1452156111yescharacteristic
190C2#1452186612yes—
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#433C2
socleC22×C31C22×D4
prime radicalC23×C31C2×D4
hypercenter#433D31
hypocenterC31#3127
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
4. #14521357C2semidirect
5. #14521260C2semidirect
7. #14521157C2semidirect
8. C4×Dic124C2semidirect
130. C31#3127semidirect

Maximal subgroups

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

subgroupindex
#145216612
#145215262
#145213912
#145213572
#145212602
#145212072
#145211572
C4×Dic1242
C31×#4332
#312731