Finite Group Databasebeta

← #495×D107 #28346878

Subgroups — #495×D107 #28346878

Order 13696.

592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×Q16×D107C211yesmaximal, characteristic, complemented
2C2×SD16×D107C212yesmaximal, complemented
3C2×D8×D107C211yesmaximal, characteristic
4#124×D107C212yesmaximal, complemented
5#20293012C211yesmaximal, characteristic, complemented
6#20293011C211yesmaximal, characteristic, complemented
7#20293010C211yesmaximal, characteristic, complemented
8#20293009C212yesmaximal, complemented
9#20293008C212yesmaximal, complemented
10C4×C8×D107C211yesmaximal, characteristic, complemented
11#495×C107C211yesmaximal, characteristic, complemented
12C2×Q8×D107C2212yes—
13C2×D4×D107C2212yes—
14C2×Dic428C2211yescharacteristic, complemented
15C2×#13133808C2212yescomplemented
16Q16×D107—24no—
17C2×#13133807C2212yescomplemented
18C2×#13133806C2212yescomplemented
19C2×#13133805C2212yescomplemented
20SD16×D107—28no—
21C2×D856C2211yescharacteristic
22C2×#13133803C2212yes—
23D8×D107—24no—
24C2×C8×D107C2211yescharacteristic
25C2×C8×D107C2211yescharacteristic
26#16812098C2212yescomplemented
27#16812097C2212yescomplemented
28#16812096C2212yescomplemented
29#16812095—24no—
30C22⋊C4×D107—24no—
31C42×D107C2211yescharacteristic
32C4×C107⋊C8C2211yescharacteristic, complemented
33C8×Dic107C2211yescharacteristic, complemented
34C8×Dic107C2211yescharacteristic, complemented
35C2×Q16×C107C2211yescharacteristic, complemented
36C2×SD16×C107C2212yescomplemented
37C2×D8×C107C2211yescharacteristic
38#124×C107C2212yescomplemented
39C4×C8×C107C2211yescharacteristic, complemented
40C23×D107—22no—
41C2×Dic214—22no—
42C2×Dic214C2312yes—
43Q8×D107—24no—
44Q8×D107—24no—
45C2×D428C2312yes—
46C2×C22⋊D107—22no—
47D4×D107—24no—
48D4×D107—24no—
49C2×C4×D107—22no—
50C2×C4×D107D412yes—
51C2×C4×D107C2311yescharacteristic
52Dic428—22no—
53#13133808—24no—
54#13133807—24no—
55#13133806—24no—
56#13133805—24no—
57D856—22no—
58#13133803—24no—
59C2×C107⋊C8C2311yescharacteristic
60C2×C107⋊C8C2311yescharacteristic
61C8×D107D414yes—
62C8×D107D414yes—
63C22⋊Dic107—24no—
64(C2×D107)⋊C4—24no—
65(C2×D107)⋊C4—24no—
66C4×Dic107D412yes—
67C4×Dic107C2311yescharacteristic
68C2×Q8×C107C2312yes—
69C2×D4×C107C2312yes—
70Q16×C107—22no—
71SD16×C107—24no—
72D8×C107—22no—
73C2×C8×C107C2311yescharacteristic
74C2×C8×C107C2311yescharacteristic
75C22⋊C4×C107—24no—
76C42×C107C2311yescharacteristic
77C23×C107—22no—
78C22×D107—22no—
79C22×D107—44no—
80C22×D107—48no—
81C22×D107C2×D411yescharacteristic
82Q8×C107—22no—
83Q8×C107—22no—
84D4×C107—22no—
85D4×C107—22no—
86C2×C4×C107—22no—
87C2×C4×C107C2×D412yes—
88C2×C4×C107C2411yescharacteristic
89C22⋊D107—44no—
90C2×Dic107—22no—
91C2×Dic107C2×D412yes—
92C2×Dic107C2×D411yescharacteristic
93D428—22no—
94D428—22no—
95C4×D107—24no—
96C4×D107—44no—
97C4×D107C2×D412yes—
98C4×D107C2×D412yes—
99Dic214—22no—
100Dic214—22no—
101Dic214—44no—
102C8×C107C2×D412yes—
103C8×C107C2×D412yes—
104C107⋊C8C2×D412yes—
105C107⋊C8C2×D412yes—
106C22×C107—42no—
107C22×C107—44no—
108C22×C107C22×D411yescharacteristic
109C2×D107—42no—
110C2×D107—44no—
111C2×D107—88no—
112C2×D107#12712yes—
113C2×D107#13514yes—
114C4×C107—22no—
115C4×C107—42no—
116C4×C107C22×D411yescharacteristic
117C4×C107C22×D411yescharacteristic
118Dic107—22no—
119Dic107—42no—
120Dic107#12712yes—
121C2×C107—82no—
122C2×C107C2×#12711yescharacteristic
123C2×C107C2×#13512yes—
124D107—82no—
125D107#49514yesdirect product factor
126C2×#495—1071nomaximal, Sylow
127C107C2×#49511yescharacteristic, complemented, Sylow
128C22×Q16—1071no—
129C22×SD16—1072no—
130C22×D8—1071no—
131C2×#124—1072no—
132#495—1071no—
133#495—1072no—
134#495—1071no—
135#495—1072no—
136#495—1071no—
137#495D10711yescharacteristic, direct product factor
138C2×C4×C8—1071no—
139C22×Q8—1072no—
140C22×D4—1072no—
141C2×Q16—1072no—
142C2×Q16—1071no—
143C2×Q16—2144no—
144C2×Q16C2×D10711yescharacteristic, complemented
145C2×SD16—1072no—
146C2×SD16—1072no—
147C2×SD16—1072no—
148C2×SD16—2148no—
149C2×SD16C2×D10712yescomplemented
150C2×D8—1072no—
151C2×D8—1071no—
152C2×D8—2144no—
153C2×D8C2×D10711yescharacteristic
154C22×C8—1071no—
155C22×C8—1071no—
156#124—1072no—
157#124—1072no—
158#124—1072no—
159#124—2144no—
160#124C2×D10712yescomplemented
161C2×C22⋊C4—2144no—
162C2×C42—1071no—
163C4×C8—1071no—
164C4×C8—1071no—
165C4×C8—1071no—
166C4×C8C2×D10711yescharacteristic, complemented
167C24—2142no—
168C2×Q8—1072no—
169C2×Q8—2142no—
170C2×Q8—2144no—
171C2×Q8—2144no—
172C2×Q8C22×D10712yes—
173C2×D4—1072no—
174C2×D4—2144no—
175C2×D4—2144no—
176C2×D4—2142no—
177C2×D4C22×D10712yes—
178C22×C4—1071no—
179C22×C4—1072no—
180C22×C4—2142no—
181Q16—22no—
182Q16—2144no—
183Q16—2142no—
184SD16—24no—
185SD16—2144no—
186SD16—2144no—
187SD16—2144no—
188D8—22no—
189D8—2144no—
190D8—2142no—
191C2×C8—1071no—
192C2×C8—1071no—
193C2×C8—1074no—
194C2×C8—1074no—
195C2×C8C22×D10711yescharacteristic
196C2×C8C22×D10711yescharacteristic
197C22⋊C4—24no—
198C22⋊C4—2144no—
199C22⋊C4—2144no—
200C22⋊C4—2144no—
201C42—1072no—
202C42—1071no—
203C42C22×D10711yescharacteristic
204C23—22no—
205C23—1071no—
206C23—4284no—
207C23—4288no—
208C23—2142no—
209Q8—22no—
210Q8—22no—
211Q8—4284no—
212Q8—2142no—
213Q8—2142no—
214D4—22no—
215D4—22no—
216D4—4284no—
217D4—2142no—
218D4—2142no—
219C2×C4—22no—
220C2×C4—1071no—
221C2×C4—1072no—
222C2×C4—1072no—
223C2×C4—1072no—
224C2×C4—4284no—
225C2×C4—2144no—
226C2×C4—2142no—
227C2×C4D4×D10712yes—
228C2×C4C23×D10711yescharacteristic
229C8—1072no—
230C8—1072no—
231C8D4×D10712yes—
232C8D4×D10712yes—
233C22—44no—
234C22—42no—
235C22—8568no—
236C22—1074no—
237C22—1072no—
238C22—4284no—
239C22—4282no—
240C22C2×D4×D10711yescharacteristic
241C4—22no—
242C4—42no—
243C4—1072no—
244C4—4282no—
245C4—2142no—
246C4C2×D4×D10711yescharacteristic
247C4C2×D4×D10711yescharacteristic
248C2—82no—
249C2—8562no—
250C2—1074no—
251C2#127×D10711yescharacteristic
252C2#135×D10712yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#495×C107C2
socleC22×C107C22×D4
prime radicalC2×D8×D107C2
hypercenter#495D107
hypocenterC107C2×#495
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D107C2semidirect
2. C2×SD16×D107C2semidirect
4. #124×D107C2semidirect
5. #20293012C2semidirect
6. #20293011C2semidirect
7. #20293010C2semidirect
8. #20293009C2semidirect
9. #20293008C2semidirect
10. C4×C8×D107C2semidirect
11. #495×C107C2semidirect
14. C2×Dic428C22semidirect
15. C2×#13133808C22semidirect
17. C2×#13133807C22semidirect
18. C2×#13133806C22semidirect
19. C2×#13133805C22semidirect
26. #16812098C22semidirect
27. #16812097C22semidirect
28. #16812096C22semidirect
32. C4×C107⋊C8C22semidirect
33. C8×Dic107C22semidirect
34. C8×Dic107C22semidirect
35. C2×Q16×C107C22semidirect
36. C2×SD16×C107C22semidirect
38. #124×C107C22semidirect
39. C4×C8×C107C22semidirect
125. D107#495direct (N × H)
127. C107C2×#495semidirect
137. #495D107direct (N × H)
144. C2×Q16C2×D107semidirect
149. C2×SD16C2×D107semidirect
160. #124C2×D107semidirect
166. C4×C8C2×D107semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1072
C2×SD16×D1072
C2×D8×D1072
#124×D1072
#202930122
#202930112
#202930102
#202930092
#202930082
C4×C8×D1072
#495×C1072
C2×#495107