Finite Group Databasebeta

← #28347034

Subgroups — #28347034

Order 13696.

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

normal subgroups only

This group has 380 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#20293164C212yesmaximal, complemented
2#20293028C211yesmaximal, characteristic, complemented
3#20293012C211yesmaximal, characteristic, complemented
4#20292983C212yesmaximal, complemented
5#20292865C211yesmaximal, characteristic, complemented
6#20292864C211yesmaximal, characteristic
7#20292859C212yesmaximal, complemented
8C4×#13133805C212yesmaximal, complemented
9C4×D856C211yesmaximal, characteristic, complemented
10C4×C8×D107C211yesmaximal, characteristic, complemented
11C4×Q16×C107C211yesmaximal, characteristic, complemented
12C2×#13133805C2212yes—
13C2×D856C2211yescharacteristic
14C2×C8×D107C2211yescharacteristic
15C2×C8×D107C2211yescharacteristic
16#16812104—22no—
17#16812100C2212yes—
18#16812098C2212yes—
19#16812094—22no—
20#16812085C2212yes—
21#16812084C2212yes—
22C4×D428—22no—
23C4×D428C2212yes—
24#16812066—22no—
25C42×D107C2211yescharacteristic
26#16812043C2211yescharacteristic
27#16812040C2212yes—
28#16812033C2212yes—
29#16812031C2212yes—
30#16812029C2212yes—
31C4×C107⋊C8C2211yescharacteristic
32C8×Dic107C2211yescharacteristic
33C8×Dic107C2211yescharacteristic
34C2×Q16×C107C2211yescharacteristic
35C4×Q8×C107C2212yes—
36#107×C107C2211yescharacteristic
37#103×C107C2212yes—
38C4×C8×C107C2211yescharacteristic
39C2×D428—22no—
40C2×D428C2312yes—
41C2×C4×D107—22no—
42C2×C4×D107D411yescharacteristic
43C2×C4×D107D411yescharacteristic
44C2×C4×D107C2311yescharacteristic
45#13133805—24no—
46D856—22no—
47C2×C107⋊C8C2311yescharacteristic
48C2×C107⋊C8C2311yescharacteristic
49C8×D107—22no—
50C8×D107—22no—
51C4⋊Dic107—22no—
52C4⋊Dic107C2312yes—
53Dic107⋊C4—22no—
54Dic107⋊C4—22no—
55(C2×D107)⋊C4—22no—
56(C2×D107)⋊C4—22no—
57(C2×D107)⋊C4—22no—
58(C2×D107)⋊C4—22no—
59(C2×D107)⋊C4—22no—
60C4×Dic107D411yescharacteristic
61C4×Dic107D411yescharacteristic
62C4×Dic107C2311yescharacteristic
63C2×Q8×C107C2312yes—
64Q16×C107—22no—
65C2×C8×C107C2311yescharacteristic
66C2×C8×C107C2311yescharacteristic
67C4⋊C4×C107—22no—
68C4⋊C4×C107C2312yes—
69C42×C107—22no—
70C42×C107C2311yescharacteristic
71C22×D107—22no—
72C22×D107C2×D411yescharacteristic
73Q8×C107—22no—
74Q8×C107—22no—
75C2×C4×C107—22no—
76C2×C4×C107—22no—
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2×D411yescharacteristic
79C2×C4×C107C2411yescharacteristic
80C2×Dic107—22no—
81C2×Dic107C2×D411yescharacteristic
82C2×Dic107C2×D411yescharacteristic
83C2×Dic107C2×D411yescharacteristic
84D428—22no—
85D428—22no—
86D428—44no—
87C4×D107—22no—
88C4×D107—22no—
89C4×D107—21no—
90C4×D107—21no—
91C4×D107—44no—
92C8×C107—21no—
93C8×C107#4112yes—
94C107⋊C8—21no—
95C107⋊C8#4112yes—
96C22×C107C22×D411yescharacteristic
97C2×D107—21no—
98C2×D107—21no—
99C2×D107—42no—
100C2×D107—42no—
101C2×D107—42no—
102C2×D107#13512yes—
103C4×C107—21no—
104C4×C107—42no—
105C4×C107—42no—
106C4×C107#13512yes—
107C4×C107C2×#4111yescharacteristic
108C4×C107C2×#4111yescharacteristic
109Dic107—21no—
110Dic107—21no—
111Dic107—21no—
112Dic107—42no—
113C2×C107#53211yescharacteristic
114C2×C107C2×#13511yescharacteristic
115C2×C107C2×#13511yescharacteristic
116D107—22no—
117D107—82no—
118#3168—1071nomaximal, Sylow
119C107#316811yescharacteristic, complemented, Sylow
120#529—1072no—
121#499—1071no—
122#495—1071no—
123#488—1072no—
124#467—1071no—
125#466—1071no—
126#465—1072no—
127C4×Q16D10711yescharacteristic, complemented
128C4×SD16—1072no—
129C4×D8—1071no—
130C2×C4×C8—1071no—
131C2×Q16C2×D10711yescharacteristic
132C2×SD16—1072no—
133C2×D8—1071no—
134C22×C8—1071no—
135C22×C8—1071no—
136#126—2142no—
137#125—1072no—
138#124—1072no—
139#123—2142no—
140C22⋊Q8—1072no—
141#121—1072no—
142C4×Q8C2×D10712yes—
143C4×D4—1072no—
144C4×D4—2142no—
145#117—2142no—
146C2×C42—1071no—
147#107—1071no—
148#107C2×D10711yescharacteristic
149#106—1072no—
150#103—1072no—
151#103C2×D10712yes—
152#102—1072no—
153#102—1072no—
154C4×C8—1071no—
155C4×C8—1071no—
156C4×C8—1071no—
157C4×C8C2×D10711yescharacteristic
158C2×Q8C22×D10712yes—
159C2×D4—1072no—
160C2×D4—2142no—
161C22×C4—1071no—
162C22×C4—1071no—
163C22×C4—1071no—
164C22×C4—2142no—
165Q16—22no—
166SD16—2144no—
167D8—2142no—
168C2×C8—1071no—
169C2×C8—1071no—
170C2×C8—2142no—
171C2×C8—2142no—
172C2×C8C22×D10711yescharacteristic
173C2×C8C22×D10711yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—1072no—
176C4⋊C4—2142no—
177C4⋊C4—2142no—
178C4⋊C4—2142no—
179C4⋊C4C22×D10712yes—
180C22⋊C4—2142no—
181C22⋊C4—2142no—
182C22⋊C4—2142no—
183C22⋊C4—2142no—
184C22⋊C4—2142no—
185C42—22no—
186C42—1071no—
187C42—1071no—
188C42—1071no—
189C42C22×D10711yescharacteristic
190C23—1071no—
191C23—2142no—
192Q8—22no—
193Q8—22no—
194D4—4284no—
195D4—2142no—
196D4—2142no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—1071no—
200C2×C4—1071no—
201C2×C4—1071no—
202C2×C4—4284no—
203C2×C4—2142no—
204C2×C4—2142no—
205C2×C4—2142no—
206C2×C4—2141no—
207C2×C4—2141no—
208C2×C4D4×D10711yescharacteristic
209C2×C4D4×D10711yescharacteristic
210C2×C4C23×D10711yescharacteristic
211C8—21no—
212C8—1072no—
213C8—2141no—
214C8#1313381812yes—
215C22—1072no—
216C22—4282no—
217C22—4282no—
218C22—4282no—
219C22—2141no—
220C22—2141no—
221C22C2×D4×D10711yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—4282no—
226C4—2141no—
227C4—2141no—
228C4—2141no—
229C4#1681213212yes—
230C4#41×D10711yescharacteristic
231C4C2×#1313381811yescharacteristic
232C2—8562no—
233C2—2142no—
234C2#2029317411yescharacteristic
235C2#135×D10711yescharacteristic
236C2C2×#1681213211yescharacteristic
subgroupG/H
centerC2×C4D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×Q16×C107C2
socleC22×C107C22×D4
prime radical#20292864C2
hypercenterC4×Q16D107
hypocenterC107#3168
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #20293164C2semidirect
2. #20293028C2semidirect
3. #20293012C2semidirect
4. #20292983C2semidirect
5. #20292865C2semidirect
7. #20292859C2semidirect
8. C4×#13133805C2semidirect
9. C4×D856C2semidirect
10. C4×C8×D107C2semidirect
11. C4×Q16×C107C2semidirect
119. C107#3168semidirect
127. C4×Q16D107semidirect

Maximal subgroups

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

subgroupindex
#202931642
#202930282
#202930122
#202929832
#202928652
#202928642
#202928592
C4×#131338052
C4×D8562
C4×C8×D1072
C4×Q16×C1072
#3168107