Finite Group Databasebeta

← #28346808

Subgroups — #28346808

Order 13696.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#20293183C211yesmaximal, characteristic, complemented
2#20293178C211yesmaximal, characteristic
3#20292995C211yesmaximal, characteristic, complemented
4#20292993C211yesmaximal, characteristic, complemented
5#20292992C211yesmaximal, characteristic, complemented
6#20292988C214yesmaximal, complemented
7#20292622C214yesmaximal, complemented
8#97×D107C211yesmaximal, characteristic, complemented
9#491×C107C211yesmaximal, characteristic, complemented
10C2×#13133819C2212yes—
11C2×C8×D107C2212yes—
12#16812108C2212yes—
13#16812106C2211yescharacteristic
14#16812101C2211yescharacteristic
15#16812098C2212yes—
16#16812087—22no—
17#16812084—22no—
18#16812074—22no—
19#16812071—22no—
20#16812067C2212yes—
21C42×D107C2211yescharacteristic
22#16812033C2214yes—
23#16812031C2214yes—
24#16812029C2214yes—
25#16812020C2211yescharacteristic
26#16812019C2212yes—
27C4⋊Q8×C107C2211yescharacteristic
28#125×C107C2211yescharacteristic
29#103×C107C2214yes—
30#97×C107C2211yescharacteristic
31#13133819—28no—
32C2×Dic214—22no—
33C2×D428—22no—
34C2×D428—22no—
35C2×D428C2312yes—
36C2×C4×D107—22no—
37C2×C4×D107D412yes—
38C2×C4×D107C2311yescharacteristic
39C2×C107⋊C8C2312yes—
40C8×D107—24no—
41C4⋊Dic107C2312yes—
42Dic107⋊C4—22no—
43Dic107⋊C4—22no—
44(C2×D107)⋊C4—22no—
45(C2×D107)⋊C4—24no—
46C4×Dic107—22no—
47C4×Dic107D412yes—
48C4×Dic107C2311yescharacteristic
49C2×Q8×C107C2312yes—
50C2×C8×C107C2312yes—
51C4⋊C4×C107—22no—
52C4⋊C4×C107—22no—
53C4⋊C4×C107C2312yes—
54C42×C107C2311yescharacteristic
55C22×D107—22no—
56C22×D107C2×D411yescharacteristic
57Q8×C107—24no—
58C2×C4×C107—22no—
59C2×C4×C107—22no—
60C2×C4×C107C2×D412yes—
61C2×C4×C107C2411yescharacteristic
62C2×Dic107—22no—
63C2×Dic107C2×D412yes—
64C2×Dic107C2×D411yescharacteristic
65D428—24no—
66D428—44no—
67D428—44no—
68C4×D107—42no—
69C4×D107—44no—
70C4×D107#4114yes—
71Dic214—44no—
72C8×C107—22no—
73C107⋊C8—22no—
74C22×C107C22×D411yescharacteristic
75C2×D107—22no—
76C2×D107—42no—
77C2×D107—44no—
78C2×D107#12412yes—
79C4×C107—22no—
80C4×C107—42no—
81C4×C107—42no—
82C4×C107C2×#4112yes—
83Dic107—22no—
84Dic107—42no—
85Dic107#12412yes—
86C2×C107C2×#12411yescharacteristic
87C2×C107#57512yes—
88D107—22no—
89D107—82no—
90#3135—1071nomaximal, Sylow
91C107#313511yescharacteristic, complemented, Sylow
92#533—1071no—
93#532—1071no—
94#491—1071no—
95#491D10711yescharacteristic, complemented
96#490—1071no—
97#490—1071no—
98#489—1074no—
99#416—1074no—
100C2×#97—1071no—
101C2×#41—1072no—
102C22×C8—1072no—
103C4⋊Q8—1072no—
104C4⋊Q8C2×D10711yescharacteristic
105#127—1071no—
106#125—1071no—
107#125C2×D10711yescharacteristic
108#124—1072no—
109C22⋊Q8—2142no—
110#121—2142no—
111C4×Q8—2142no—
112C4×D4—2142no—
113#117—1072no—
114C2×C42—1071no—
115#103—1074no—
116#103C2×D10714yes—
117#102—1074no—
118#102—1074no—
119#97—1072no—
120#97—1071no—
121#97C2×D10711yescharacteristic
122#41—2148no—
123C2×Q8—2142no—
124C2×Q8C22×D10712yes—
125C2×D4—1072no—
126C2×D4—2142no—
127C2×D4—2142no—
128C22×C4—1071no—
129C22×C4—1072no—
130C22×C4—2142no—
131C2×C8—1072no—
132C2×C8—2144no—
133C2×C8C22×D10712yes—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—1072no—
137C4⋊C4—2142no—
138C4⋊C4—2142no—
139C4⋊C4C22×D10712yes—
140C22⋊C4—2144no—
141C22⋊C4—2142no—
142C42—1072no—
143C42—1071no—
144C42—2142no—
145C42C22×D10711yescharacteristic
146C23—1071no—
147C23—2142no—
148Q8—24no—
149Q8—4284no—
150D4—4284no—
151D4—4284no—
152D4—2144no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—1071no—
156C2×C4—1074no—
157C2×C4—1072no—
158C2×C4—4282no—
159C2×C4—4284no—
160C2×C4—2142no—
161C2×C4D4×D10712yes—
162C2×C4C23×D10711yescharacteristic
163C8—22no—
164C8—2142no—
165C22—1072no—
166C22—4282no—
167C22—4284no—
168C22—2142no—
169C22C2×D4×D10711yescharacteristic
170C4—22no—
171C4—42no—
172C4—42no—
173C4—1072no—
174C4—4282no—
175C4—2142no—
176C4#41×D10712yes—
177C2—8562no—
178C2—2142no—
179C2#124×D10711yescharacteristic
180C2#2029342612yes—
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#491×C107C2
socleC22×C107C22×D4
prime radical#20293178C2
hypercenter#491D107
hypocenterC107#3135
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #20293183C2semidirect
3. #20292995C2semidirect
4. #20292993C2semidirect
5. #20292992C2semidirect
6. #20292988C2semidirect
7. #20292622C2semidirect
8. #97×D107C2semidirect
9. #491×C107C2semidirect
91. C107#3135semidirect
95. #491D107semidirect

Maximal subgroups

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

subgroupindex
#202931832
#202931782
#202929952
#202929932
#202929922
#202929882
#202926222
#97×D1072
#491×C1072
#3135107