Finite Group Databasebeta

← #28344628

Subgroups — #28344628

Order 13696.

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

normal subgroups only

This group has 416 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#20292568C212yesmaximal, complemented
2#20292556C212yesmaximal, complemented
3#20292547C211yesmaximal, characteristic, complemented
4#20292545C212yesmaximal
5#20292544C211yesmaximal, characteristic
6#20292540C212yesmaximal, complemented
7#20292538C212yesmaximal, complemented
8#20292518C212yesmaximal, complemented
9#391×C107C211yesmaximal, characteristic, complemented
10C22×Dic214C2211yescharacteristic
11C22×D428C2211yescharacteristic
12C2×Dic107⋊C4C2212yes—
13C2×Dic107⋊C4C2212yes—
14C2×(C2×D107)⋊C4C2212yes—
15C2×(C2×D107)⋊C4C2212yes—
16C2×(C2×D107)⋊C4C2212yes—
17C2×(C2×D107)⋊C4C2212yes—
18C2×(C2×D107)⋊C4C2212yes—
19C2×(C2×D107)⋊C4C2212yes—
20C107⋊#95C2212yes—
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2211yescharacteristic
26C22×Q8×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C42×C107C2211yescharacteristic
29#95×C107C2212yes—
30#95×C107C2212yes—
31C23×D107C2312yes—
32C2×Dic214—41no—
33C2×Dic214—42no—
34C2×D428—41no—
35C2×D428—42no—
36C22×Dic107C2312yes—
37C22×Dic107C2312yes—
38C22×Dic107C2312yes—
39Dic107⋊C4—42no—
40Dic107⋊C4—42no—
41(C2×D107)⋊C4—24no—
42(C2×D107)⋊C4—42no—
43(C2×D107)⋊C4—42no—
44(C2×D107)⋊C4—42no—
45(C2×D107)⋊C4—42no—
46(C2×D107)⋊C4—42no—
47C2×Q8×C107—22no—
48C2×Q8×C107—41no—
49C2×Q8×C107—41no—
50C22×C4×C107C2312yes—
51C22×C4×C107C2311yescharacteristic
52C22×C4×C107C2312yes—
53C22×C4×C107C2311yescharacteristic
54C22×C4×C107C2311yescharacteristic
55C4⋊C4×C107—41no—
56C42×C107—41no—
57C23×C107C2411yescharacteristic
58C22×D107—22no—
59C22×D107—22no—
60C22×D107—22no—
61C22×D107—22no—
62C22×D107—22no—
63C22×D107—22no—
64C22×D107—22no—
65Q8×C107—44no—
66C2×C4×C107—21no—
67C2×C4×C107—21no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—21no—
71C2×C4×C107—21no—
72C2×C4×C107—22no—
73C2×C4×C107—22no—
74C2×C4×C107—22no—
75C2×C4×C107—22no—
76C2×C4×C107—22no—
77C2×C4×C107—22no—
78C2×C4×C107#4112yes—
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—22no—
82C2×Dic107—22no—
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—22no—
86C2×Dic107—22no—
87C2×Dic107—22no—
88D428—44no—
89Dic214—44no—
90C22×C107C2×#4111yescharacteristic
91C22×C107H(5,𝔽2)11yescharacteristic
92C22×C107H(5,𝔽2)11yescharacteristic
93C22×C107H(5,𝔽2)12yes—
94C22×C1072−1+412yes—
95C2×D107—42no—
96C2×D107—42no—
97C2×D107—42no—
98C2×D107—42no—
99C2×D107—42no—
100C2×D107—42no—
101C2×D107—42no—
102C4×C107—22no—
103C4×C107—42no—
104C4×C107—41no—
105C4×C107—41no—
106C4×C107—42no—
107Dic107—42no—
108Dic107—42no—
109Dic107—42no—
110C2×C107#53811yescharacteristic
111C2×C107#54212yes—
112C2×C107H(3,𝔽4)11yescharacteristic
113C2×C107#56212yes—
114C2×C107#56311yescharacteristic
115D107—82no—
116#2832—1071nomaximal, Sylow
117C107#283211yescharacteristic, complemented, Sylow
118#400—1072no—
119#397—1072no—
120#395—1071no—
121#394—1071no—
122#394—1072no—
123#393—1072no—
124#393—1072no—
125#391D10711yescharacteristic, complemented
126#388—1072no—
127C22×Q8—1071no—
128C22×Q8C2×D10711yescharacteristic
129C22×D4—1071no—
130C2×C4⋊C4—1072no—
131C2×C4⋊C4—1072no—
132C2×C4⋊C4C2×D10711yescharacteristic
133C2×C22⋊C4—1072no—
134C2×C22⋊C4—1072no—
135C2×C22⋊C4—1072no—
136C2×C22⋊C4—1072no—
137C2×C22⋊C4—1072no—
138C2×C22⋊C4—1072no—
139C2×C42C2×D10711yescharacteristic
140#95—1072no—
141#95—1072no—
142#95—1072no—
143#95—1072no—
144#95—1071no—
145#95—1071no—
146#95C2×D10712yes—
147#95C2×D10712yes—
148C24—1072no—
149C2×Q8—22no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—4281no—
153C2×Q8—4282no—
154C2×D4—4281no—
155C2×D4—4282no—
156C22×C4—1072no—
157C22×C4—1072no—
158C22×C4—1072no—
159C22×C4C22×D10712yes—
160C22×C4C22×D10712yes—
161C22×C4C22×D10711yescharacteristic
162C22×C4C22×D10711yescharacteristic
163C22×C4C22×D10711yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—4282no—
166C4⋊C4—4282no—
167C22⋊C4—4282no—
168C22⋊C4—4282no—
169C22⋊C4—4282no—
170C22⋊C4—4282no—
171C22⋊C4—4282no—
172C22⋊C4—2144no—
173C42—41no—
174C23—2142no—
175C23—2142no—
176C23—2142no—
177C23—2142no—
178C23—2142no—
179C23—2142no—
180C23—2142no—
181C23C23×D10711yescharacteristic
182Q8—44no—
183Q8—4284no—
184D4—4284no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—2142no—
198C2×C4—2142no—
199C2×C4—2142no—
200C2×C4—2142no—
201C2×C4—2142no—
202C2×C4—2142no—
203C2×C4—2142no—
204C2×C4—2142no—
205C2×C4—2142no—
206C2×C4#1313381812yes—
207C22—4282no—
208C22—4282no—
209C22—4282no—
210C22—4282no—
211C22—4282no—
212C22—4282no—
213C22—4282no—
214C22C2×#1313381811yescharacteristic
215C22#1681215411yescharacteristic
216C22#1681215411yescharacteristic
217C22#1681215512yes—
218C22#1681215712yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—4282no—
225C4—4282no—
226C4—4282no—
227C2—8562no—
228C2#2029321511yescharacteristic
229C2#2029324912yes—
230C2#2029336911yescharacteristic
231C2#2029337312yes—
232C2#2029337611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#391×C107C2
prime radicalC22×D428C22
hypercenter#391D107
hypocenterC107#2832
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. #20292568C2semidirect
2. #20292556C2semidirect
3. #20292547C2semidirect
6. #20292540C2semidirect
7. #20292538C2semidirect
8. #20292518C2semidirect
9. #391×C107C2semidirect
117. C107#2832semidirect
125. #391D107semidirect

Maximal subgroups

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

subgroupindex
#202925682
#202925562
#202925472
#202925452
#202925442
#202925402
#202925382
#202925182
#391×C1072
#2832107