Finite Group Databasebeta

← #28335758

Subgroups — #28335758

Order 13696.

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

normal subgroups only

This group has 206 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
1#20293381C211yesmaximal, characteristic, complemented
2#20293014C211yesmaximal, characteristic
3#20292991C211yesmaximal, characteristic, complemented
4#20292369C211yesmaximal, characteristic, complemented
5#20292368C211yesmaximal, characteristic, complemented
6#20292366C211yesmaximal, characteristic, complemented
7#490×C107C211yesmaximal, characteristic, complemented
8C2×#13133806—21no—
9C2×#13133803—21no—
10#16812108—21no—
11#16812104—21no—
12#16812104—21no—
13#16812101C2211yescharacteristic
14#16812097C2211yescharacteristic
15#16812094—21no—
16#16812089—21no—
17#16812087—21no—
18#16812030—21no—
19#16812030—21no—
20#16812020C2211yescharacteristic
21#16812020C2211yescharacteristic
22#127×C107C2211yescharacteristic
23#125×C107C2211yescharacteristic
24#102×C107—21no—
25#102×C107—21no—
26#97×C107C2211yescharacteristic
27C2×Dic214—21no—
28C2×Dic214D411yescharacteristic
29C2×D428D411yescharacteristic
30C2×C4×D107—21no—
31#13133806—42no—
32#13133803—42no—
33C2×C107⋊C8—21no—
34C2×C107⋊C8—21no—
35C4⋊Dic107—21no—
36C4⋊Dic107D411yescharacteristic
37C4⋊Dic107D411yescharacteristic
38Dic107⋊C4—21no—
39Dic107⋊C4—21no—
40Dic107⋊C4—21no—
41(C2×D107)⋊C4—21no—
42(C2×D107)⋊C4—21no—
43(C2×D107)⋊C4—21no—
44(C2×D107)⋊C4—21no—
45(C2×D107)⋊C4—21no—
46C4×Dic107—21no—
47C2×D4×C107—21no—
48C2×D4×C107—21no—
49C2×D4×C107—21no—
50C2×C8×C107—21no—
51C4⋊C4×C107—21no—
52C4⋊C4×C107—21no—
53C4⋊C4×C107D411yescharacteristic
54C4⋊C4×C107D411yescharacteristic
55C42×C107C2311yescharacteristic
56C23×C107—41no—
57C22×D107—21no—
58D4×C107—42no—
59D4×C107—42no—
60D4×C107—41no—
61D4×C107—41no—
62C2×C4×C107—21no—
63C2×C4×C107—21no—
64C2×C4×C107C2×D411yescharacteristic
65C2×C4×C107C2×D411yescharacteristic
66C2×C4×C107C2×D411yescharacteristic
67C2×Dic107—21no—
68C2×Dic107—21no—
69C2×Dic107—21no—
70D428—41no—
71C4×D107—81no—
72Dic214—41no—
73Dic214—81no—
74C8×C107—41no—
75C107⋊C8—22no—
76C107⋊C8—41no—
77C22×C107—81no—
78C22×C107—81no—
79C22×C107—81no—
80C22×C107#12011yescharacteristic
81C2×D107—41no—
82C2×D107—41no—
83C2×D107—41no—
84C4×C107—21no—
85C4×C107—21no—
86C4×C107—21no—
87C4×C107—41no—
88C4×C107—41no—
89Dic107—41no—
90Dic107—41no—
91Dic107—41no—
92C2×C107—161no—
93C2×C107#45311yescharacteristic
94C2×C107#45411yescharacteristic
95C2×C107#45411yescharacteristic
96D107—81no—
97#1657—1071nomaximal, Sylow
98C107#165711yescharacteristic, complemented, Sylow
99#563—1071no—
100#496—1071no—
101#490—1071no—
102#490D10711yescharacteristic, complemented
103#330—1071no—
104#330—1071no—
105#329—1071no—
106C2×SD16—2141no—
107C2×D8—2141no—
108C4⋊Q8—2141no—
109#127C2×D10711yescharacteristic
110#126—2141no—
111#126—2141no—
112#125—1071no—
113#125C2×D10711yescharacteristic
114#124—1071no—
115#123—2141no—
116C22⋊Q8—2141no—
117C22⋊Q8—2141no—
118#102—21no—
119#102—21no—
120#102—2141no—
121#102—2141no—
122#97—1071no—
123#97—1071no—
124#97C2×D10711yescharacteristic
125C2×Q8—1071no—
126C2×Q8—2141no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1071no—
131C22×C4—2141no—
132SD16—4282no—
133D8—4282no—
134C2×C8—21no—
135C2×C8—2141no—
136C2×C8—2141no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—1071no—
140C4⋊C4—1071no—
141C4⋊C4—2141no—
142C4⋊C4—2141no—
143C4⋊C4—2141no—
144C4⋊C4—2141no—
145C4⋊C4C22⋊D10711yescharacteristic
146C4⋊C4C22⋊D10711yescharacteristic
147C22⋊C4—2141no—
148C22⋊C4—2141no—
149C22⋊C4—2141no—
150C22⋊C4—2141no—
151C22⋊C4—2141no—
152C42—2141no—
153C42C22×D10711yescharacteristic
154C23—41no—
155C23—2141no—
156Q8—8561no—
157Q8—4281no—
158D4—41no—
159D4—41no—
160D4—42no—
161D4—42no—
162D4—4281no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—8561no—
166C2×C4—2141no—
167C2×C4—2141no—
168C2×C4—2141no—
169C2×C4D4×D10711yescharacteristic
170C2×C4D4×D10711yescharacteristic
171C2×C4C2×C22⋊D10711yescharacteristic
172C8—41no—
173C8—4281no—
174C8—2142no—
175C22—81no—
176C22—81no—
177C22—81no—
178C22—4281no—
179C22—4281no—
180C22—4281no—
181C22#1681207711yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—4281no—
188C4—4281no—
189C4—4281no—
190C2—161no—
191C2—8561no—
192C2#2029279311yescharacteristic
193C2#2029279811yescharacteristic
194C2#2029279911yescharacteristic
subgroupG/H
centerC22#16812077
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
Fitting#490×C107C2
socleC22×C107#120
prime radical#20293014C2
hypercenter#490D107
hypocenterC107#1657
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20293381C2semidirect
3. #20292991C2semidirect
4. #20292369C2semidirect
5. #20292368C2semidirect
6. #20292366C2semidirect
7. #490×C107C2semidirect
98. C107#1657semidirect
102. #490D107semidirect

Maximal subgroups

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

subgroupindex
#202933812
#202930142
#202929912
#202923692
#202923682
#202923662
#490×C1072
#1657107