Finite Group Databasebeta

← #28347039

Subgroups — #28347039

Order 13696.

456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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#20293178C211yesmaximal, characteristic, complemented
2#20293175C211yesmaximal, characteristic, complemented
3#20293030C211yesmaximal, characteristic, complemented
4#20293003C211yesmaximal, characteristic, complemented
5#20292974C211yesmaximal, characteristic, complemented
6#20292862C214yesmaximal, complemented
7#20292707C214yesmaximal, complemented
8C4×C8×D107C211yesmaximal, characteristic, complemented
9#486×C107C211yesmaximal, characteristic, complemented
10C2×#13133819—21no—
11C2×#13133817—21no—
12C2×#13133803C2214yes—
13C2×C8×D107C2212yes—
14#16812109C2211yescharacteristic
15#16812106C2211yescharacteristic
16#16812098—21no—
17#16812096—21no—
18#16812084—21no—
19#16812084C2212yes—
20#16812080—21no—
21#16812080C2212yes—
22D4×Dic107—21no—
23D4×Dic107C2212yes—
24#16812071—21no—
25#16812071C2212yes—
26C42×D107C2211yescharacteristic
27#16812042C2214yes—
28#16812031C2214yes—
29C4×C107⋊C8C2211yescharacteristic
30C8×Dic107C2212yes—
31C4⋊Q8×C107C2211yescharacteristic
32#127×C107C2211yescharacteristic
33#102×C107C2214yes—
34C4×C8×C107C2211yescharacteristic
35#13133819—44no—
36#13133817—44no—
37C2×Dic214—21no—
38C2×D428—22no—
39C2×D428—21no—
40C2×D428—21no—
41C2×D428C2312yes—
42C2×C22⋊D107—22no—
43C22×Dic107—22no—
44C2×C4×D107—22no—
45C2×C4×D107D411yescharacteristic
46C2×C4×D107D411yescharacteristic
47C2×C4×D107C2311yescharacteristic
48#13133803—28no—
49C2×C107⋊C8C2312yes—
50C8×D107—24no—
51C4⋊Dic107—21no—
52C4⋊Dic107C2312yes—
53C22⋊Dic107—22no—
54C22⋊Dic107—22no—
55(C2×D107)⋊C4—22no—
56(C2×D107)⋊C4—22no—
57C4×Dic107D411yescharacteristic
58C4×Dic107D411yescharacteristic
59C4×Dic107C2311yescharacteristic
60C2×Q8×C107—21no—
61C2×D4×C107—21no—
62C2×D4×C107—21no—
63C2×D4×C107C2312yes—
64C2×C8×C107C2312yes—
65C4⋊C4×C107—21no—
66C4⋊C4×C107C2312yes—
67C42×C107C2311yescharacteristic
68C23×C107—22no—
69C22×D107—22no—
70C22×D107C2×D411yescharacteristic
71Q8×C107—42no—
72D4×C107—24no—
73D4×C107—42no—
74D4×C107—42no—
75C2×C4×C107—22no—
76C2×C4×C107C2×D411yescharacteristic
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2411yescharacteristic
79C22⋊D107—44no—
80C2×Dic107—22no—
81C2×Dic107—44no—
82C2×Dic107C2×D411yescharacteristic
83C2×Dic107C2×D411yescharacteristic
84C2×Dic107C2×D411yescharacteristic
85D428—24no—
86D428—44no—
87D428—42no—
88D428—42no—
89C4×D107—22no—
90C4×D107—22no—
91C4×D107—44no—
92C4×D107D814yescomplemented
93Dic214—42no—
94C8×C107—22no—
95C107⋊C8#4114yescomplemented
96C22×C107—42no—
97C22×C107—42no—
98C22×C107—42no—
99C22×C107C22×D411yescharacteristic
100C2×D107—21no—
101C2×D107—21no—
102C2×D107—42no—
103C2×D107—42no—
104C2×D107—42no—
105C2×D107C2×D812yes—
106C4×C107—42no—
107C4×C107C2×D812yes—
108C4×C107#13512yes—
109C4×C107C2×#4112yes—
110Dic107—21no—
111Dic107—21no—
112Dic107—42no—
113Dic107C2×D812yes—
114C2×C107—82no—
115C2×C107#53211yescharacteristic
116C2×C107C22×D811yescharacteristic
117C2×C107C2×#13511yescharacteristic
118D107—22no—
119D107—82no—
120#3169—1071nomaximal, Sylow
121C107#316911yescharacteristic, complemented, Sylow
122#532—1071no—
123#532—1071no—
124#500—1071no—
125#493—1071no—
126#486—1071no—
127#486D10711yescharacteristic, complemented
128#466—1074no—
129C4×D8—1074no—
130C2×C4×C8—1071no—
131C2×#41—2141no—
132C2×#41—2141no—
133C2×D8—1074no—
134C22×C8—1072no—
135C4⋊Q8—1071no—
136C4⋊Q8C2×D10711yescharacteristic
137#127—1071no—
138#127C2×D10711yescharacteristic
139#124—2141no—
140#124—2141no—
141#121—1072no—
142#121—1072no—
143#121—2141no—
144#121—2141no—
145C4×D4—1072no—
146C4×D4—1072no—
147C4×D4—2141no—
148C4×D4—2141no—
149C2×C42—1071no—
150#107—1074no—
151#102—1074no—
152#102C2×D10714yes—
153C4×C8—1072no—
154C4×C8—1071no—
155C4×C8C2×D10711yescharacteristic
156#41—4284no—
157#41—4284no—
158C2×Q8—21no—
159C2×Q8—2141no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—1072no—
163C2×D4—2142no—
164C2×D4—2142no—
165C2×D4—2141no—
166C2×D4—2141no—
167C2×D4C22×D10712yes—
168C22×C4—1071no—
169C22×C4—1071no—
170C22×C4—1071no—
171C22×C4—2142no—
172C22×C4—2142no—
173D8—2148no—
174C2×C8—1072no—
175C2×C8—2144no—
176C2×C8C22×D10712yes—
177C4⋊C4—21no—
178C4⋊C4—1072no—
179C4⋊C4—2141no—
180C4⋊C4C22×D10712yes—
181C22⋊C4—2142no—
182C22⋊C4—2142no—
183C22⋊C4—2142no—
184C22⋊C4—2142no—
185C42—1071no—
186C42—1071no—
187C42—1071no—
188C42C22×D10711yescharacteristic
189C23—22no—
190C23—1071no—
191C23—2142no—
192Q8—42no—
193Q8—4282no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—4284no—
198D4—4284no—
199D4—4282no—
200D4—4282no—
201D4—2144no—
202C2×C4—22no—
203C2×C4—1071no—
204C2×C4—1074no—
205C2×C4—1071no—
206C2×C4—1071no—
207C2×C4—4284no—
208C2×C4—4284no—
209C2×C4—2142no—
210C2×C4—2142no—
211C2×C4—2142no—
212C2×C4D4×D10711yescharacteristic
213C2×C4D4×D10711yescharacteristic
214C2×C4C23×D10711yescharacteristic
215C8—22no—
216C8—1074no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—1072no—
221C22—4282no—
222C22—4282no—
223C22—4282no—
224C22—2141no—
225C22—2141no—
226C22C2×D4×D10711yescharacteristic
227C4—42no—
228C4—1072no—
229C4—4282no—
230C4—2141no—
231C4—2141no—
232C4D8×D10712yes—
233C4#1681213012yes—
234C4#41×D10712yes—
235C2—82no—
236C2—8562no—
237C2—2142no—
238C2#2029317611yescharacteristic
239C2C2×D8×D10711yescharacteristic
240C2C2×#1681213011yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#486×C107C2
socleC22×C107C22×D4
hypercenter#486D107
hypocenterC107#3169
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20293178C2semidirect
2. #20293175C2semidirect
3. #20293030C2semidirect
4. #20293003C2semidirect
5. #20292974C2semidirect
6. #20292862C2semidirect
7. #20292707C2semidirect
8. C4×C8×D107C2semidirect
9. #486×C107C2semidirect
92. C4×D107D8semidirect
95. C107⋊C8#41semidirect
121. C107#3169semidirect
127. #486D107semidirect

Maximal subgroups

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

subgroupindex
#202931782
#202931752
#202930302
#202930032
#202929742
#202928622
#202927072
C4×C8×D1072
#486×C1072
#3169107