Finite Group Databasebeta

← #16858287

Subgroups — #16858287

Order 3968.

336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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#14521740C212yesmaximal
2#14521451C211yesmaximal, characteristic, complemented
3#14521389C212yesmaximal, complemented
4#14521383C212yesmaximal, complemented
5#14521356C212yesmaximal, complemented
6#14521304C212yesmaximal, complemented
7#14521128C211yesmaximal, characteristic
8#14521090C212yesmaximal, complemented
9C4×Q16×C31C211yesmaximal, characteristic, complemented
10C2×Q16×C31C2211yescharacteristic
11C4×Q8×C31C2212yes—
12#11758523C2212yes—
13#11758523C2212yes—
14C2×#92469C2212yes—
15#11758471—22no—
16#11758469C2212yes—
17C4⋊C4×D31C2212yes—
18#11758466—22no—
19#11758453—22no—
20C4×D124C2211yescharacteristic
21#11758449—22no—
22#11758447C2212yes—
23C31×#107C2211yescharacteristic
24C31×#103C2212yes—
25C4×C8×C31C2211yescharacteristic
26#11758423C2212yes—
27#11758423C2212yes—
28(C2×D31)⋊C8C2212yes—
29#11758406C2211yescharacteristic
30#11758406C2211yescharacteristic
31#11758405C2212yes—
32#11758396C2212yes—
33#11758395C2212yes—
34C4⋊(C31⋊C8)C2211yescharacteristic
35C2×Q8×C31C2312yes—
36C2×D124D411yescharacteristic
37C2×C4×D31—22no—
38C2×C4×D31C2312yes—
39Q16×C31—22no—
40C2×C8×C31C2311yescharacteristic
41C2×C8×C31C2311yescharacteristic
42C4⋊C4×C31—22no—
43C4⋊C4×C31C2312yes—
44C42×C31—22no—
45C42×C31C2311yescharacteristic
46(C2×D31)⋊C4—22no—
47(C2×D31)⋊C4—22no—
48(C2×D31)⋊C4—22no—
49(C2×D31)⋊C4D412yes—
50C4⋊Dic31D411yescharacteristic
51C4⋊Dic31C2312yes—
52C4⋊Dic31C2312yes—
53Dic31⋊C4—22no—
54Dic31⋊C4—22no—
55Dic31⋊C4—22no—
56Dic31⋊C4—22no—
57Dic31⋊C4—22no—
58C4×Dic31—22no—
59C2×C31⋊C8C2312yes—
60#92469—24no—
61C22×D31C2×D412yes—
62Q8×C31—22no—
63Q8×C31—22no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2411yescharacteristic
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31C2×D412yes—
72D124—41no—
73C4×D31—22no—
74C4×D31—22no—
75C4×D31—44no—
76C8×C31—21no—
77C8×C31#4112yes—
78C31⋊C8—22no—
79#3352—311nomaximal, Sylow
80C22×C31C22×D411yescharacteristic
81C2×D31—22no—
82C2×D31—22no—
83C2×D31—22no—
84C4×C31—21no—
85C4×C31—21no—
86C4×C31—42no—
87C4×C31—42no—
88C4×C31C2×#4111yescharacteristic
89C4×C312−1+411yescharacteristic
90Dic31—22no—
91Dic31—42no—
92Dic31—42no—
93#552—312no—
94#499—311no—
95#485—312no—
96#484—312no—
97#479—312no—
98#470—312no—
99C4×Q16D3111yescharacteristic, complemented
100#436—311no—
101#428—312no—
102C2×C31#54711yescharacteristic
103C2×C31#57511yescharacteristic
104C2×C31#57811yescharacteristic
105D31—42no—
106C2×Q16C2×D3111yescharacteristic
107C2×M16—312no—
108#126—622no—
109#125—312no—
110#125—622no—
111#123—622no—
112C22⋊Q8—312no—
113C22⋊Q8—312no—
114C4×Q8C2×D3112yes—
115C4×D4—311no—
116#117—312no—
117#117—622no—
118C2×C4⋊C4—312no—
119#107—311no—
120#107—311no—
121#107—312no—
122#107C2×D3111yescharacteristic
123#106—312no—
124#106—312no—
125C4⋊C8—311no—
126#103—312no—
127#103—312no—
128#103C2×D3112yes—
129C22⋊C8—312no—
130C4×C8C2×D3111yescharacteristic
131C31#335211yescharacteristic, complemented, Sylow
132C2×Q8C22×D3112yes—
133C2×D4—311no—
134C22×C4—312no—
135C22×C4—622no—
136Q16—22no—
137M16—624no—
138C2×C8—312no—
139C2×C8C22×D3111yescharacteristic
140C2×C8C22×D3111yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—311no—
143C4⋊C4—312no—
144C4⋊C4—312no—
145C4⋊C4—622no—
146C4⋊C4—622no—
147C4⋊C4—622no—
148C4⋊C4—622no—
149C4⋊C4—622no—
150C4⋊C4C22×D3112yes—
151C22⋊C4—312no—
152C22⋊C4—622no—
153C22⋊C4—622no—
154C22⋊C4—622no—
155C42—22no—
156C42—622no—
157C42C22×D3111yescharacteristic
158C23—312no—
159Q8—22no—
160Q8—22no—
161D4—1241no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—312no—
165C2×C4—622no—
166C2×C4—622no—
167C2×C4—622no—
168C2×C4—622no—
169C2×C4—1244no—
170C2×C4D4×D3111yescharacteristic
171C2×C4D4×D3111yescharacteristic
172C2×C4C23×D3111yescharacteristic
173C8—21no—
174C8—622no—
175C8#9249512yes—
176C22—622no—
177C22—622no—
178C22—622no—
179C22C2×D4×D3111yescharacteristic
180C4—21no—
181C4—21no—
182C4—42no—
183C4—42no—
184C4—622no—
185C4—1242no—
186C4—1242no—
187C4C2×#9249511yescharacteristic
188C4#1175856711yescharacteristic
189C2—1242no—
190C2#1452170411yescharacteristic
191C2#1452184611yescharacteristic
192C2#1452186211yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×Q16×C31C2
socleC22×C31C22×D4
prime radicalC2×D124D4
hypercenterC4×Q16D31
hypocenterC31#3352
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #14521451C2semidirect
3. #14521389C2semidirect
4. #14521383C2semidirect
5. #14521356C2semidirect
6. #14521304C2semidirect
8. #14521090C2semidirect
9. C4×Q16×C31C2semidirect
99. C4×Q16D31semidirect
131. C31#3352semidirect

Maximal subgroups

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

subgroupindex
#145217402
#145214512
#145213892
#145213832
#145213562
#145213042
#145211282
#145210902
C4×Q16×C312
#335231