Finite Group Databasebeta

← #28335791

Subgroups — #28335791

Order 13696.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C107⋊#564C211yesmaximal, characteristic
2#20293037C211yesmaximal, characteristic
3#20293036C211yesmaximal, characteristic
4#20292996C211yesmaximal, characteristic
5#20292368C211yesmaximal, characteristic
6#20292368C211yesmaximal, characteristic
7#330×C107C211yesmaximal, characteristic
8#16812109C2211yescharacteristic
9#16812101C2211yescharacteristic
10#16812101C2211yescharacteristic
11#16812100—21no—
12#16812100—21no—
13#16812099—21no—
14#16812099—21no—
15#16812099—21no—
16#16812099—21no—
17#16812043—21no—
18#16812042—21no—
19#16812041—21no—
20#16812040—21no—
21#16812034—21no—
22#16812034—21no—
23#16812020C2211yescharacteristic
24#125×C107C2211yescharacteristic
25#97×C107C2211yescharacteristic
26#97×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×C107⋊C8—21no—
29C4⋊Dic107—21no—
30C4⋊Dic107—21no—
31C4⋊Dic107—21no—
32C4⋊Dic107—21no—
33C4⋊Dic107D411yescharacteristic
34C4⋊Dic107D411yescharacteristic
35C4⋊Dic107D411yescharacteristic
36C4⋊Dic107D411yescharacteristic
37Dic107⋊C4—21no—
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41Dic107⋊C4—21no—
42Dic107⋊C4—21no—
43Dic107⋊C4—21no—
44Dic107⋊C4—21no—
45C4×Dic107—21no—
46C4×Dic107—21no—
47C2×C8×C107—21no—
48C2×C8×C107—21no—
49C4⋊C4×C107—21no—
50C4⋊C4×C107—21no—
51C4⋊C4×C107D411yescharacteristic
52C4⋊C4×C107D411yescharacteristic
53C42×C107C2311yescharacteristic
54C2×C4×C107—21no—
55C2×C4×C107—21no—
56C2×C4×C107C2×D411yescharacteristic
57C2×C4×C107C2×D411yescharacteristic
58C2×C4×C107C2×D411yescharacteristic
59C2×Dic107—21no—
60C2×Dic107—21no—
61C2×Dic107—21no—
62C2×Dic107—21no—
63C2×Dic107—41no—
64Dic214—42no—
65C8×C107—22no—
66C8×C107—41no—
67C107⋊C8—22no—
68C22×C107#12011yescharacteristic
69C4×C107—21no—
70C4×C107—21no—
71C4×C107—21no—
72C4×C107—41no—
73C4×C107—41no—
74Dic107—41no—
75Dic107—41no—
76Dic107—41no—
77Dic107—41no—
78Dic107—81no—
79C2×C107#45411yescharacteristic
80C2×C107#45611yescharacteristic
81C2×C107#45611yescharacteristic
82#1663—1071nomaximal, Sylow
83C107#166311yescharacteristic, complemented, Sylow
84#564—1071no—
85#501—1071no—
86#501—1071no—
87#491—1071no—
88#330—1071no—
89#330—1071no—
90#330D10711yescharacteristic
91C4⋊Q8—1071no—
92#125—1071no—
93#125—1071no—
94#125—2141no—
95#125—2141no—
96#125—2141no—
97#125—2141no—
98#125—2141no—
99#125—2141no—
100#125C2×D10711yescharacteristic
101#107—2141no—
102#107—2141no—
103#106—2141no—
104#106—2141no—
105#103—2141no—
106#103—2141no—
107#97—1071no—
108#97C2×D10711yescharacteristic
109#97C2×D10711yescharacteristic
110C2×Q8—2141no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—2141no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—1071no—
117C4⋊C4—1071no—
118C4⋊C4—1071no—
119C4⋊C4—1071no—
120C4⋊C4—2141no—
121C4⋊C4—2141no—
122C4⋊C4—2141no—
123C4⋊C4—2141no—
124C4⋊C4—2141no—
125C4⋊C4—2141no—
126C4⋊C4—2141no—
127C4⋊C4—2141no—
128C4⋊C4—2141no—
129C4⋊C4—2141no—
130C4⋊C4—2141no—
131C4⋊C4—2141no—
132C4⋊C4D42811yescharacteristic
133C4⋊C4D42811yescharacteristic
134C42—2141no—
135C42—2141no—
136C42C22×D10711yescharacteristic
137Q8—4282no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—4281no—
141C2×C4—2141no—
142C2×C4—2141no—
143C2×C4—2141no—
144C2×C4—2141no—
145C2×C4D4×D10711yescharacteristic
146C2×C4D4×D10711yescharacteristic
147C2×C4C2×D42811yescharacteristic
148C8—22no—
149C8—41no—
150C8—2142no—
151C22#1681207911yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—8561no—
158C4—4281no—
159C4—4281no—
160C4—4281no—
161C4—4281no—
162C2#2029280111yescharacteristic
163C2#2029281111yescharacteristic
164C2#2029281211yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#330×C107C2
socle, prime radicalC22×C107#120
hypercenter#330D107
hypocenterC107#1663
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
83. C107#1663semidirect

Maximal subgroups

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

subgroupindex
C107⋊#5642
#202930372
#202930362
#202929962
#202923682
#330×C1072
#1663107