Finite Group Databasebeta

← #28346705

Subgroups — #28346705

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#20293232C211yesmaximal, characteristic, complemented
2#20293101C211yesmaximal, characteristic, complemented
3#20292952C212yesmaximal, complemented
4#20292928C212yesmaximal, complemented
5#20292823C212yesmaximal, complemented
6#20292763C212yesmaximal, complemented
7#20292740C212yesmaximal, complemented
8C4×D856C212yesmaximal, complemented
9#433×C107C211yesmaximal, characteristic, complemented
10C22×D428C2211yescharacteristic
11C2×D856C2212yes—
12C2×D856C2212yes—
13#16812106C2211yescharacteristic, complemented
14#16812101C2211yescharacteristic, complemented
15#16812094—22no—
16#16812083C2212yes—
17#16812082—22no—
18C4×D428C2212yes—
19C4×D428C2212yes—
20C4×D428C2212yescomplemented
21#16812071—22no—
22#16812068C2211yescharacteristic
23C22⋊C4×D107—22no—
24#16812043C2212yescomplemented
25#16812041C2212yescomplemented
26#16812031C2212yes—
27#16812031C2212yes—
28#16812031C2212yescomplemented
29#16812031C2212yescomplemented
30#117×C107C2211yescharacteristic
31C4⋊C8×C107C2212yescomplemented
32C22⋊C8×C107C2212yes—
33#97×C107C2211yescharacteristic, complemented
34C4×C8×C107C2211yescharacteristic, complemented
35C23×D107—21no—
36C2×D428—21no—
37C2×D428—24no—
38C2×D428—22no—
39C2×D428C2312yes—
40C2×D428C2312yes—
41C2×C22⋊D107—22no—
42C2×C4×D107—22no—
43C2×C4×D107—22no—
44C2×C4×D107—22no—
45D856—24no—
46D856—24no—
47C4⋊Dic107C2312yes—
48C4⋊Dic107C2312yes—
49Dic107⋊C4—22no—
50C22⋊Dic107—21no—
51(C2×D107)⋊C4—22no—
52(C2×D107)⋊C4—22no—
53(C2×D107)⋊C4—22no—
54(C2×D107)⋊C4—22no—
55C4×Dic107—21no—
56C22×C4×C107C2311yescharacteristic
57C2×C8×C107C2312yes—
58C2×C8×C107C2312yes—
59C4⋊C4×C107D412yes—
60C22⋊C4×C107D412yes—
61C42×C107C2311yescharacteristic
62C42×C107C2311yescharacteristic
63C23×C107C2×D411yescharacteristic
64C22×D107—22no—
65C22×D107—24no—
66C22×D107—22no—
67C22×D107—82no—
68C2×C4×C107—22no—
69C2×C4×C107C2×D412yes—
70C2×C4×C107C2×D412yes—
71C2×C4×C107C2×D411yescharacteristic
72C2×C4×C107C2411yescharacteristic
73C22⋊D107—82no—
74C2×Dic107—22no—
75C2×Dic107—22no—
76D428—24no—
77D428—22no—
78D428—22no—
79D428—22no—
80D428—82no—
81D428#4114yes—
82C4×D107—82no—
83C4×D107—82no—
84C4×D107—82no—
85C8×C107—22no—
86C8×C107—22no—
87C22×C107—21no—
88C22×C107—22no—
89C22×C107C22×D411yescharacteristic
90C2×D107—24no—
91C2×D107—42no—
92C2×D107—42no—
93C2×D107—42no—
94C2×D107—42no—
95C2×D107—42no—
96C2×D107—84no—
97C4×C107—21no—
98C4×C107—22no—
99C4×C107—22no—
100C4×C107C2×#4112yes—
101Dic107—42no—
102Dic107—42no—
103C2×C107—41no—
104C2×C107#52511yescharacteristic
105C2×C107#57612yes—
106D107—44no—
107D107—82no—
108#3122—1071nomaximal, Sylow
109C107#312211yescharacteristic, complemented, Sylow
110#540—1071no—
111#518—1071no—
112#482—1072no—
113#478—1072no—
114#459—1072no—
115#447—1072no—
116#442—1072no—
117C4×D8—1072no—
118#433D10711yescharacteristic, complemented
119C22×D4—1071no—
120C2×D8—1072no—
121C2×D8—1072no—
122#127—1071no—
123#125—1071no—
124#123—2142no—
125#121—1072no—
126#121—2142no—
127C4×D4—1072no—
128C4×D4—1072no—
129C4×D4—1072no—
130C4×D4—2142no—
131#117—1071no—
132#117C2×D10711yescharacteristic
133C2×C22⋊C4—2142no—
134#107—1072no—
135#106—1072no—
136C4⋊C8C2×D10712yescomplemented
137#102—1072no—
138#102—1072no—
139#102—1072no—
140#102—1072no—
141C22⋊C8C2×D10712yes—
142#97C2×D10711yescharacteristic, complemented
143C4×C8C2×D10711yescharacteristic, complemented
144C24—2141no—
145C2×D4—1072no—
146C2×D4—1072no—
147C2×D4—2144no—
148C2×D4—2142no—
149C2×D4—2142no—
150C2×D4—2141no—
151C22×C4—2142no—
152C22×C4—2142no—
153C22×C4—2142no—
154C22×C4C22×D10711yescharacteristic
155D8—2144no—
156D8—2144no—
157C2×C8C22×D10712yes—
158C2×C8C22×D10712yes—
159C4⋊C4—1072no—
160C4⋊C4—1072no—
161C4⋊C4—2142no—
162C4⋊C4D42812yes—
163C22⋊C4—2141no—
164C22⋊C4—2142no—
165C22⋊C4—2142no—
166C22⋊C4—2142no—
167C22⋊C4—2142no—
168C22⋊C4D42812yes—
169C42—2141no—
170C42C22×D10711yescharacteristic
171C42C22×D10711yescharacteristic
172C23—8562no—
173C23—2144no—
174C23—2142no—
175C23—2142no—
176C23C2×D42811yescharacteristic
177D4—8562no—
178D4—8562no—
179D4—1074no—
180D4—2144no—
181D4—2142no—
182D4—2142no—
183D4—2142no—
184C2×C4—22no—
185C2×C4—8562no—
186C2×C4—8562no—
187C2×C4—8562no—
188C2×C4—2142no—
189C2×C4—2142no—
190C2×C4C2×D42811yescharacteristic
191C2×C4C2×D42812yes—
192C2×C4C2×D42812yes—
193C2×C4C23×D10711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—8564no—
199C22—4282no—
200C22—4282no—
201C22—4282no—
202C22—4282no—
203C22—4282no—
204C22—2144no—
205C22C22×D42811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—4282no—
210C4—4282no—
211C4#41×D10712yes—
212C2—41no—
213C2—8562no—
214C2—4284no—
215C2#2029313911yescharacteristic
216C2#2029343212yes—
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#433×C107C2
socleC22×C107C22×D4
hypercenter#433D107
hypocenterC107#3122
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20293232C2semidirect
2. #20293101C2semidirect
3. #20292952C2semidirect
4. #20292928C2semidirect
5. #20292823C2semidirect
6. #20292763C2semidirect
7. #20292740C2semidirect
8. C4×D856C2semidirect
9. #433×C107C2semidirect
13. #16812106C22semidirect
14. #16812101C22semidirect
20. C4×D428C22semidirect
24. #16812043C22semidirect
25. #16812041C22semidirect
28. #16812031C22semidirect
29. #16812031C22semidirect
31. C4⋊C8×C107C22semidirect
33. #97×C107C22semidirect
34. C4×C8×C107C22semidirect
109. C107#3122semidirect
118. #433D107semidirect
136. C4⋊C8C2×D107semidirect
142. #97C2×D107semidirect
143. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202932322
#202931012
#202929522
#202929282
#202928232
#202927632
#202927402
C4×D8562
#433×C1072
#3122107