Finite Group Databasebeta

← #28344290

Subgroups — #28344290

Order 13696.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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#20292566C211yesmaximal, characteristic, complemented
2#20292549C212yesmaximal, complemented
3#20292544C211yesmaximal, characteristic
4#20292544C212yesmaximal
5#20292518C212yesmaximal, complemented
6#20292517C212yesmaximal, complemented
7#20292517C212yesmaximal, complemented
8#20292508C212yesmaximal, complemented
9#384×C107C211yesmaximal, characteristic, complemented
10C22×D428C2211yescharacteristic
11C2×C4⋊Dic107C2211yescharacteristic
12C2×Dic107⋊C4C2212yes—
13C2×(C2×D107)⋊C4C2212yes—
14C2×(C2×D107)⋊C4C2212yes—
15C2×(C2×D107)⋊C4C2212yes—
16C2×(C2×D107)⋊C4C2212yes—
17C2×(C2×D107)⋊C4C2212yes—
18C2×(C2×D107)⋊C4C2212yes—
19C2×C4×Dic107C2212yes—
20C107⋊#95C2211yescharacteristic
21C107⋊#95C2212yes—
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2211yescharacteristic
25C107⋊#95C2212yes—
26C2×C4⋊C4×C107C2212yes—
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C4⋊C4×C107C2212yes—
29C2×C4⋊C4×C107C2211yescharacteristic
30C2×C42×C107C2211yescharacteristic
31C23×D107C2312yes—
32C2×D428—41no—
33C2×D428—42no—
34C22×Dic107C2312yes—
35C22×Dic107C2312yes—
36C22×Dic107C2312yes—
37C4⋊Dic107—41no—
38Dic107⋊C4—24no—
39(C2×D107)⋊C4—24no—
40(C2×D107)⋊C4—24no—
41(C2×D107)⋊C4—24no—
42(C2×D107)⋊C4—42no—
43(C2×D107)⋊C4—42no—
44(C2×D107)⋊C4—42no—
45C4×Dic107—42no—
46C22×C4×C107C2312yes—
47C22×C4×C107C2311yescharacteristic
48C22×C4×C107C2311yescharacteristic
49C22×C4×C107C2312yes—
50C22×C4×C107C2311yescharacteristic
51C4⋊C4×C107—42no—
52C4⋊C4×C107—41no—
53C4⋊C4×C107—42no—
54C4⋊C4×C107—41no—
55C42×C107—22no—
56C23×C107C2411yescharacteristic
57C22×D107—22no—
58C22×D107—22no—
59C22×D107—22no—
60C22×D107—22no—
61C22×D107—22no—
62C22×D107—22no—
63C22×D107—22no—
64C2×C4×C107—22no—
65C2×C4×C107—21no—
66C2×C4×C107—22no—
67C2×C4×C107—21no—
68C2×C4×C107—22no—
69C2×C4×C107—22no—
70C2×C4×C107—22no—
71C2×C4×C107—22no—
72C2×C4×C107—21no—
73C2×C4×C107—21no—
74C2×C4×C107—22no—
75C2×C4×C107#4112yes—
76C2×C4×C107#4114yes—
77C2×Dic107—22no—
78C2×Dic107—22no—
79C2×Dic107—22no—
80C2×Dic107—22no—
81C2×Dic107—22no—
82C2×Dic107—22no—
83C2×Dic107—22no—
84C2×Dic107—22no—
85C2×Dic107—22no—
86D428—44no—
87C22×C107C2×#4111yescharacteristic
88C22×C107C2×#4112yes—
89C22×C107H(5,𝔽2)11yescharacteristic
90C22×C107H(5,𝔽2)12yes—
91C22×C1072−1+411yescharacteristic
92C2×D107—42no—
93C2×D107—42no—
94C2×D107—42no—
95C2×D107—42no—
96C2×D107—42no—
97C2×D107—42no—
98C2×D107—42no—
99C4×C107—22no—
100C4×C107—24no—
101C4×C107—41no—
102C4×C107—42no—
103C4×C107—41no—
104Dic107—42no—
105Dic107—42no—
106Dic107—42no—
107C2×C107#53911yescharacteristic
108C2×C107#54212yes—
109C2×C107#55312yes—
110C2×C107#55511yescharacteristic
111C2×C107#56011yescharacteristic
112D107—82no—
113#2795—1071nomaximal, Sylow
114C107#279511yescharacteristic, complemented, Sylow
115#400—1071no—
116#396—1072no—
117#394—1071no—
118#394—1072no—
119#388—1072no—
120#388—1072no—
121#388—1072no—
122#387—1072no—
123#384D10711yescharacteristic, complemented
124C22×D4—1071no—
125C2×C4⋊C4—1071no—
126C2×C4⋊C4—1072no—
127C2×C4⋊C4C2×D10712yes—
128C2×C4⋊C4C2×D10711yescharacteristic
129C2×C4⋊C4C2×D10712yes—
130C2×C4⋊C4C2×D10711yescharacteristic
131C2×C22⋊C4—1072no—
132C2×C22⋊C4—1072no—
133C2×C22⋊C4—1072no—
134C2×C22⋊C4—1072no—
135C2×C22⋊C4—1072no—
136C2×C22⋊C4—1072no—
137C2×C42—1072no—
138C2×C42C2×D10711yescharacteristic
139#95—1071no—
140#95—1072no—
141#95—1072no—
142#95—1072no—
143#95—1071no—
144#95—1072no—
145C24—1072no—
146C2×D4—4281no—
147C2×D4—4282no—
148C22×C4—1072no—
149C22×C4—1072no—
150C22×C4—1072no—
151C22×C4C22×D10711yescharacteristic
152C22×C4C22×D10712yes—
153C22×C4C22×D10711yescharacteristic
154C22×C4C22×D10711yescharacteristic
155C22×C4C22×D10712yes—
156C4⋊C4—42no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—41no—
160C4⋊C4—4281no—
161C4⋊C4—2144no—
162C22⋊C4—4282no—
163C22⋊C4—4282no—
164C22⋊C4—4282no—
165C22⋊C4—2144no—
166C22⋊C4—2144no—
167C22⋊C4—2144no—
168C42—22no—
169C42—4282no—
170C23—2142no—
171C23—2142no—
172C23—2142no—
173C23—2142no—
174C23—2142no—
175C23—2142no—
176C23—2142no—
177C23C23×D10711yescharacteristic
178D4—4284no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—2142no—
191C2×C4—2142no—
192C2×C4—2142no—
193C2×C4—2142no—
194C2×C4—2142no—
195C2×C4—2142no—
196C2×C4—2142no—
197C2×C4—2142no—
198C2×C4—2142no—
199C2×C4#1313381812yes—
200C2×C4#1313381914yes—
201C22—4282no—
202C22—4282no—
203C22—4282no—
204C22—4282no—
205C22—4282no—
206C22—4282no—
207C22—4282no—
208C22C2×#1313381811yescharacteristic
209C22C2×#1313381912yes—
210C22#1681215411yescharacteristic
211C22#1681215412yes—
212C22#1681215711yescharacteristic
213C4—22no—
214C4—24no—
215C4—41no—
216C4—42no—
217C4—41no—
218C4—4282no—
219C4—4282no—
220C4—4282no—
221C2—8562no—
222C2#2029322411yescharacteristic
223C2#2029325112yes—
224C2#2029332512yes—
225C2#2029334311yescharacteristic
226C2#2029336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#384×C107C2
prime radicalC22×D428C22
hypercenter#384D107
hypocenterC107#2795
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #20292566C2semidirect
2. #20292549C2semidirect
5. #20292518C2semidirect
6. #20292517C2semidirect
7. #20292517C2semidirect
8. #20292508C2semidirect
9. #384×C107C2semidirect
114. C107#2795semidirect
123. #384D107semidirect

Maximal subgroups

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

subgroupindex
#202925662
#202925492
#202925442
#202925182
#202925172
#202925082
#384×C1072
#2795107