Finite Group Databasebeta

← #28338536

Subgroups — #28338536

Order 13696.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#20293065C211yesmaximal, characteristic, complemented
2#20293063C211yesmaximal, characteristic, complemented
3#20293002C211yesmaximal, characteristic, complemented
4#20292743C211yesmaximal, characteristic, complemented
5#20292447C211yesmaximal, characteristic, complemented
6#20292439C211yesmaximal, characteristic, complemented
7#361×C107C211yesmaximal, characteristic, complemented
8#16812131C2211yescharacteristic
9C2×D856C2211yescharacteristic
10C2×#13133803—21no—
11#16812117—21no—
12#16812105—21no—
13#16812054—21no—
14#16812053—21no—
15D1712—21no—
16#16812050—21no—
17#16812049C2211yescharacteristic
18#16812035—21no—
19C8×Dic107C2211yescharacteristic
20C2×D8×C107C2211yescharacteristic
21M32×C107C2211yescharacteristic
22#108×C107C2211yescharacteristic
23#13133818—21no—
24C2×D428—21no—
25C2×C22⋊D107—42no—
26Dic428D411yescharacteristic, complemented
27#13133807—21no—
28D856—21no—
29D856—21no—
30D856D411yescharacteristic, complemented
31#13133803—41no—
32#13133803—41no—
33#13133801—41no—
34C2×C107⋊C8D411yescharacteristic
35C8×D107—41no—
36C4×Dic107D411yescharacteristic
37C107⋊C16—21no—
38C2×D4×C107—21no—
39D8×C107—21no—
40D8×C107—21no—
41M16×C107—21no—
42C2×C8×C107C2311yescharacteristic
43C16×C107—21no—
44C23×C107—41no—
45C22×D107—41no—
46D4×C107—41no—
47D4×C107—41no—
48C2×C4×C107C2×D411yescharacteristic
49C22⋊D107—41no—
50C22⋊D107—84no—
51C2×Dic107—21no—
52D428—21no—
53D428—41no—
54D428—41no—
55C4×D107—41no—
56Dic214—21no—
57C8×C107—41no—
58C8×C107C2×D411yescharacteristic
59C8×C107#4111yescharacteristic
60C107⋊C8D811yescharacteristic
61C107⋊C8D811yescharacteristic
62C22×C107—82no—
63C22×C107—81no—
64C22×C107AGL(1,ℤ/8)11yescharacteristic
65C2×D107—41no—
66C2×D107—82no—
67C2×D107—81no—
68C4×C107#12111yescharacteristic
69C4×C107C2×D811yescharacteristic
70Dic107—22no—
71Dic107—41no—
72C2×C107—21no—
73C2×C107—161no—
74C2×C107#45911yescharacteristic
75D107—81no—
76D107—161no—
77#2213—1071nomaximal, Sylow
78C107#221311yescharacteristic, complemented, Sylow
79#509—1071no—
80#509—1071no—
81#493—1071no—
82#443—1071no—
83#364—1071no—
84#361—1071no—
85#361D10711yescharacteristic, complemented
86#135—1071no—
87C2×D8—1071no—
88C2×D8—2141no—
89C2×D8C2×D10711yescharacteristic
90#131—2141no—
91#127—2141no—
92SD32—2141no—
93SD32—2141no—
94D16—2141no—
95D16—2141no—
96M32—1071no—
97M32C2×D10711yescharacteristic
98#108C2×D10711yescharacteristic
99#104—2141no—
100C4×C8—1071no—
101#41—2141no—
102C2×D4—21no—
103C2×D4—4282no—
104C2×D4—2141no—
105Q16—1071no—
106SD16—2141no—
107D8—21no—
108D8—21no—
109D8—1071no—
110D8—4281no—
111D8—4281no—
112D8—2141no—
113D8—2141no—
114M16—21no—
115M16—4281no—
116C2×C8—1071no—
117C2×C8—4281no—
118C2×C8C22×D10711yescharacteristic
119C42—1071no—
120C16—21no—
121C16—2141no—
122C23—41no—
123C23—4281no—
124Q8—2141no—
125D4—41no—
126D4—41no—
127D4—8564no—
128D4—4281no—
129D4—4281no—
130D4—4281no—
131D4—2141no—
132C2×C4—4281no—
133C2×C4—2141no—
134C2×C4D4×D10711yescharacteristic
135C8—41no—
136C8—1071no—
137C8—1071no—
138C8D4×D10711yescharacteristic
139C8#1313381811yescharacteristic
140C22—82no—
141C22—81no—
142C22—8562no—
143C22—8561no—
144C22—4281no—
145C22#1681213611yescharacteristic
146C4—4281no—
147C4—2142no—
148C4#1681208211yescharacteristic
149C4D8×D10711yescharacteristic
150C2—21no—
151C2—161no—
152C2—8561no—
153C2—17121no—
154C2#2029282111yescharacteristic
subgroupG/H
centerC2#20292821
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
Fitting#361×C107C2
socleC2×C107#459
hypercenter#361D107
hypocenterC107#2213
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #20293065C2semidirect
2. #20293063C2semidirect
3. #20293002C2semidirect
4. #20292743C2semidirect
5. #20292447C2semidirect
6. #20292439C2semidirect
7. #361×C107C2semidirect
26. Dic428D4semidirect
30. D856D4semidirect
78. C107#2213semidirect
85. #361D107semidirect

Maximal subgroups

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

subgroupindex
#202930652
#202930632
#202930022
#202927432
#202924472
#202924392
#361×C1072
#2213107