Finite Group Databasebeta

← #28346699

Subgroups — #28346699

Order 13696.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#20293101C211yesmaximal, characteristic, complemented
2#20292948C212yesmaximal, complemented
3#20292924C212yesmaximal, complemented
4#20292819C212yesmaximal, complemented
5#20292760C212yesmaximal, complemented
6#20292737C212yesmaximal, complemented
7C4×#13133803C212yesmaximal, complemented
8#20292688C211yesmaximal, characteristic, complemented
9#540×C107C211yesmaximal, characteristic, complemented
10C22×D428C2211yescharacteristic
11C2×#13133803C2212yes—
12C2×#13133803C2212yes—
13C4×D428C2212yes—
14C4×D428C2212yes—
15#16812071—22no—
16#16812068C2211yescharacteristic
17C22⋊C4×D107—22no—
18#16812042C2212yescomplemented
19#16812040C2212yescomplemented
20C4⋊(C107⋊C8)C2212yescomplemented
21#16812030C2212yescomplemented
22#16812030C2212yescomplemented
23#16812029C2212yes—
24#16812029C2212yes—
25C22⋊(C107⋊C8)C2212yes—
26#16812020C2211yescharacteristic, complemented
27C4×C107⋊C8C2211yescharacteristic, complemented
28#127×C107C2211yescharacteristic, complemented
29#125×C107C2211yescharacteristic, complemented
30#123×C107—22no—
31#121×C107—22no—
32#121×C107C2212yes—
33C4×D4×C107C2212yescomplemented
34#117×C107C2211yescharacteristic
35C23×D107—21no—
36C2×D428—21no—
37C2×D428—24no—
38C2×D428C2312yes—
39C2×C4×D107—22no—
40C2×C4×D107—22no—
41#13133803—24no—
42#13133803—24no—
43C2×C107⋊C8C2312yes—
44C2×C107⋊C8C2312yes—
45C4⋊Dic107C2312yes—
46C22⋊Dic107—21no—
47(C2×D107)⋊C4—22no—
48(C2×D107)⋊C4—22no—
49C4×Dic107—21no—
50C2×D4×C107—22no—
51C2×D4×C107—22no—
52C2×D4×C107C2312yes—
53C22×C4×C107—22no—
54C22×C4×C107C2311yescharacteristic
55C4⋊C4×C107—22no—
56C4⋊C4×C107D412yes—
57C4⋊C4×C107C2312yes—
58C22⋊C4×C107—22no—
59C22⋊C4×C107—22no—
60C22⋊C4×C107D412yes—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107—22no—
64C23×C107C2×D411yescharacteristic
65C22×D107—22no—
66C22×D107—24no—
67C22×D107—82no—
68D4×C107—22no—
69D4×C107—22no—
70D4×C107—82no—
71D4×C107—82no—
72C2×C4×C107—22no—
73C2×C4×C107—22no—
74C2×C4×C107—82no—
75C2×C4×C107C2×D412yes—
76C2×C4×C107C2×D412yes—
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2411yescharacteristic
79C2×Dic107—22no—
80D428—24no—
81D428—22no—
82D428#4114yes—
83C4×D107—82no—
84C4×D107—82no—
85C107⋊C8—22no—
86C107⋊C8—22no—
87C22×C107—21no—
88C22×C107—22no—
89C22×C107—42no—
90C22×C107—42no—
91C22×C107—42no—
92C22×C107C22×D411yescharacteristic
93C2×D107—24no—
94C2×D107—42no—
95C2×D107—42no—
96C2×D107—84no—
97C4×C107—21no—
98C4×C107—22no—
99C4×C107—22no—
100C4×C107—42no—
101C4×C107C2×#4112yes—
102Dic107—42no—
103C2×C107—41no—
104C2×C107—82no—
105C2×C107#52511yescharacteristic
106C2×C107#57612yes—
107D107—44no—
108#3122—1071nomaximal, Sylow
109C107#312211yescharacteristic, complemented, Sylow
110#540D10711yescharacteristic, complemented
111#518—1071no—
112#482—1072no—
113#478—1072no—
114#459—1072no—
115#447—1072no—
116#442—1072no—
117C4×D8—1072no—
118#433—1071no—
119C22×D4—1071no—
120C2×D8—1072no—
121C2×D8—1072no—
122#127C2×D10711yescharacteristic, complemented
123#125C2×D10711yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D10712yes—
127C4×D4—1072no—
128C4×D4—1072no—
129C4×D4—2142no—
130C4×D4C2×D10712yescomplemented
131#117—1071no—
132#117C2×D10711yescharacteristic
133C2×C22⋊C4—2142no—
134#107—1072no—
135#106—1072no—
136C4⋊C8—1072no—
137#102—1072no—
138#102—1072no—
139#102—1072no—
140#102—1072no—
141C22⋊C8—1072no—
142#97—1071no—
143C4×C8—1071no—
144C24—2141no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—1072no—
148C2×D4—2144no—
149C2×D4—2141no—
150C2×D4C22×D10712yes—
151C22×C4—22no—
152C22×C4—2142no—
153C22×C4—2142no—
154C22×C4C22×D10711yescharacteristic
155D8—2144no—
156D8—2144no—
157C2×C8—1072no—
158C2×C8—1072no—
159C4⋊C4—22no—
160C4⋊C4—1072no—
161C4⋊C4C22⋊D10712yes—
162C4⋊C4C22×D10712yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—2141no—
166C22⋊C4—2142no—
167C22⋊C4—2142no—
168C22⋊C4C22⋊D10712yes—
169C42—2141no—
170C42C22×D10711yescharacteristic
171C42C22×D10711yescharacteristic
172C23—22no—
173C23—8562no—
174C23—2144no—
175C23—2142no—
176C23C2×C22⋊D10711yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—1074no—
182D4—2144no—
183D4—2142no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—8562no—
188C2×C4—8562no—
189C2×C4—2142no—
190C2×C4C2×C22⋊D10711yescharacteristic
191C2×C4C2×C22⋊D10712yes—
192C2×C4C2×C22⋊D10712yes—
193C2×C4C23×D10711yescharacteristic
194C8—2142no—
195C8—2142no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—8564no—
202C22—4282no—
203C22—4282no—
204C22—2144no—
205C22C22×C22⋊D10711yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—4282no—
211C4#41×D10712yes—
212C2—41no—
213C2—82no—
214C2—4284no—
215C2#2029313411yescharacteristic
216C2#2029343012yes—
subgroupG/H
centerC22C22×C22⋊D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#540×C107C2
socleC22×C107C22×D4
hypercenter#540D107
hypocenterC107#3122
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20293101C2semidirect
2. #20292948C2semidirect
3. #20292924C2semidirect
4. #20292819C2semidirect
5. #20292760C2semidirect
6. #20292737C2semidirect
7. C4×#13133803C2semidirect
8. #20292688C2semidirect
9. #540×C107C2semidirect
18. #16812042C22semidirect
19. #16812040C22semidirect
20. C4⋊(C107⋊C8)C22semidirect
21. #16812030C22semidirect
22. #16812030C22semidirect
26. #16812020C22semidirect
27. C4×C107⋊C8C22semidirect
28. #127×C107C22semidirect
29. #125×C107C22semidirect
33. C4×D4×C107C22semidirect
109. C107#3122semidirect
110. #540D107semidirect
122. #127C2×D107semidirect
123. #125C2×D107semidirect
130. C4×D4C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202931012
#202929482
#202929242
#202928192
#202927602
#202927372
C4×#131338032
#202926882
#540×C1072
#3122107