Finite Group Databasebeta

← #16847634

Subgroups — #16847634

Order 3968.

230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#11758416C211yesmaximal, characteristic, complemented
2C2×#11758414C211yesmaximal, characteristic, complemented
3#14521285C211yesmaximal, characteristic, complemented
4#14520853C211yesmaximal, characteristic, complemented
5#14520850C211yesmaximal, characteristic, complemented
6C22⋊(C31⋊C16)C211yesmaximal, characteristic, complemented
7C2×C31×#135C211yesmaximal, characteristic, complemented
8C2×#41×C31—21no—
9C31×#135—22no—
10C31×#135—22no—
11C2×Q16×C31C2211yescharacteristic
12C2×SD16×C31—21no—
13C2×D8×C31C2211yescharacteristic
14C22×C8×C31C2211yescharacteristic
15#11758507—21no—
16C2×D248C2211yescharacteristic
17#11758416—22no—
18#11758414—22no—
19#11758409—21no—
20#11758406C2211yescharacteristic
21C2×C31⋊C16C2211yescharacteristic
22C2×C31⋊C16C2211yescharacteristic
23#41×C31—24no—
24#41×C31—42no—
25C2×Q8×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31—41no—
28C22×C4×C31—41no—
29C22×C4×C31D411yescharacteristic
30C2×C22⋊D31—41no—
31C2×D124—21no—
32Q16×C31—21no—
33Q16×C31D412yescomplemented
34SD16×C31—24no—
35D8×C31—21no—
36D8×C31D412yescomplemented
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C2×C8×C31D411yescharacteristic
40C2×C8×C31C2311yescharacteristic
41(C2×D31)⋊C4—41no—
42C4⋊Dic31—21no—
43D248—21no—
44D248—21no—
45C31⋊C16—21no—
46C31⋊C16—21no—
47C23×C31—41no—
48C23×C31D811yescharacteristic
49C22×D31—41no—
50Q8×C31—22no—
51Q8×C31—41no—
52D4×C31—22no—
53D4×C31—44no—
54D4×C31—41no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—44no—
58C2×C4×C31—41no—
59C2×C4×C31D811yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C22⋊D31—82no—
62C2×Dic31—41no—
63D124—41no—
64D124—41no—
65C8×C31—21no—
66C8×C31C2×D411yescharacteristic
67C8×C31C2×D411yescharacteristic
68#2186—311nomaximal, Sylow
69C22×C31—21no—
70C22×C31—21no—
71C22×C31—21no—
72C22×C31—42no—
73C22×C31—81no—
74C22×C31—81no—
75C22×C31C2×D811yescharacteristic
76C2×D31—81no—
77C2×D31—81no—
78C2×D31—81no—
79C4×C31—21no—
80C4×C31—42no—
81C4×C31#12011yescharacteristic
82C4×C31AGL(1,ℤ/8)11yescharacteristic
83Dic31—81no—
84C2×#135D3111yescharacteristic, complemented
85C2×SD32—311no—
86C2×D16—311no—
87#466—311no—
88#358—311no—
89#357—311no—
90C22⋊C16—311no—
91C2×C31—41no—
92C2×C31—82no—
93C2×C31#44711yescharacteristic
94C2×C31#50811yescharacteristic
95C2×C31#50911yescharacteristic
96D31—161no—
97C2×#41—21no—
98#135—22no—
99#135—22no—
100C2×Q16C2×D3111yescharacteristic
101C2×SD16—21no—
102C2×D8—311no—
103C2×D8C2×D3111yescharacteristic
104C22×C8C2×D3111yescharacteristic
105#121—621no—
106SD32—622no—
107D16—622no—
108C2×C16—311no—
109C2×C16—311no—
110#107—311no—
111#102—621no—
112C31#218611yescharacteristic, complemented, Sylow
113#41—24no—
114#41—42no—
115C2×Q8—21no—
116C2×D4—21no—
117C2×D4—41no—
118C2×D4—621no—
119C2×D4—1241no—
120C22×C4—41no—
121C22×C4C22⋊D3111yescharacteristic
122Q16—21no—
123Q16C22⋊D3112yescomplemented
124SD16—24no—
125D8—21no—
126D8—621no—
127D8—621no—
128D8C22⋊D3112yescomplemented
129C2×C8—21no—
130C2×C8—21no—
131C2×C8C22⋊D3111yescharacteristic
132C2×C8C22×D3111yescharacteristic
133C4⋊C4—621no—
134C22⋊C4—1241no—
135C16—621no—
136C16—621no—
137C23—41no—
138C23—1241no—
139C23#9247911yescharacteristic
140Q8—22no—
141Q8—41no—
142D4—22no—
143D4—44no—
144D4—41no—
145D4—1241no—
146D4—1241no—
147D4—2482no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—44no—
151C2×C4—41no—
152C2×C4—1241no—
153C2×C4#9247911yescharacteristic
154C2×C4C2×C22⋊D3111yescharacteristic
155C8—21no—
156C8C2×C22⋊D3111yescharacteristic
157C8C2×C22⋊D3111yescharacteristic
158C22—21no—
159C22—21no—
160C22—21no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—2481no—
165C22—2481no—
166C22—2481no—
167C22C2×#9247911yescharacteristic
168C4—21no—
169C4—42no—
170C4—2481no—
171C4#1175850911yescharacteristic
172C4#1175853011yescharacteristic
173C2—41no—
174C2—82no—
175C2—4961no—
176C2#1452118311yescharacteristic
177C2#1452147911yescharacteristic
178C2#1452148411yescharacteristic
subgroupG/H
centerC22C2×#92479
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC2×C31×#135C2
socleC22×C31C2×D8
hypercenterC2×#135D31
hypocenterC31#2186
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#11758416C2semidirect
2. C2×#11758414C2semidirect
3. #14521285C2semidirect
4. #14520853C2semidirect
5. #14520850C2semidirect
6. C22⋊(C31⋊C16)C2semidirect
7. C2×C31×#135C2semidirect
33. Q16×C31D4semidirect
36. D8×C31D4semidirect
84. C2×#135D31semidirect
112. C31#2186semidirect
123. Q16C22⋊D31semidirect
128. D8C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584162
C2×#117584142
#145212852
#145208532
#145208502
C22⋊(C31⋊C16)2
C2×C31×#1352
#218631