Finite Group Databasebeta

← #28344584

Subgroups — #28344584

Order 13696.

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

normal subgroups only

This group has 508 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#20292566C211yesmaximal, characteristic, complemented
2#20292554C212yesmaximal, complemented
3#20292543C212yesmaximal, complemented
4#20292543C212yesmaximal, complemented
5#20292536C212yesmaximal, complemented
6#20292535C212yesmaximal, complemented
7#20292528C211yesmaximal, characteristic, complemented
8#20292520C212yesmaximal, complemented
9#394×C107C211yesmaximal, characteristic, complemented
10C22×D428C2211yescharacteristic
11C22×C22⋊D107C2212yes—
12C22×C22⋊D107C2212yes—
13C2×C4⋊Dic107C2212yes—
14C2×C4⋊Dic107C2211yescharacteristic
15C2×C22⋊Dic107C2212yes—
16C2×C22⋊Dic107C2212yes—
17C2×(C2×D107)⋊C4C2212yes—
18C2×(C2×D107)⋊C4C2212yes—
19C2×(C2×D107)⋊C4C2212yes—
20C2×(C2×D107)⋊C4C2212yes—
21C2×C4×Dic107C2211yescharacteristic
22C107⋊#95C2212yes—
23C107⋊#95C2212yes—
24C107⋊#95C2212yes—
25C107⋊#95C2211yescharacteristic
26C22×D4×C107C2211yescharacteristic
27C2×C4⋊C4×C107C2211yescharacteristic
28C2×C22⋊C4×C107C2212yes—
29C2×C22⋊C4×C107C2212yes—
30#95×C107C2211yescharacteristic
31C23×D107C2312yes—
32C2×D428—22no—
33C2×D428—41no—
34C2×D428—41no—
35C2×C22⋊D107—42no—
36C2×C22⋊D107—42no—
37C2×C22⋊D107—42no—
38C2×C22⋊D107—42no—
39C2×C22⋊D107—42no—
40C2×C22⋊D107—42no—
41C22×Dic107C2312yes—
42C22×Dic107C2312yes—
43C22×Dic107C2312yes—
44C4⋊Dic107—42no—
45C4⋊Dic107—41no—
46C22⋊Dic107—42no—
47C22⋊Dic107—42no—
48(C2×D107)⋊C4—42no—
49(C2×D107)⋊C4—42no—
50(C2×D107)⋊C4—42no—
51(C2×D107)⋊C4—42no—
52C4×Dic107—41no—
53C24×C107C2312yes—
54C2×D4×C107—41no—
55C2×D4×C107—42no—
56C22×C4×C107C2312yes—
57C22×C4×C107C2311yescharacteristic
58C22×C4×C107C2311yescharacteristic
59C22×C4×C107C2311yescharacteristic
60C4⋊C4×C107—41no—
61C22⋊C4×C107—24no—
62C22⋊C4×C107—42no—
63C23×C107—22no—
64C23×C107—22no—
65C23×C107—22no—
66C23×C107—22no—
67C23×C107—22no—
68C23×C107—22no—
69C23×C107—22no—
70C23×C107C2411yescharacteristic
71C22×D107—22no—
72C22×D107—22no—
73C22×D107—22no—
74C22×D107—22no—
75C22×D107—22no—
76C22×D107—22no—
77C22×D107—22no—
78D4×C107—44no—
79C2×C4×C107—21no—
80C2×C4×C107—21no—
81C2×C4×C107—22no—
82C2×C4×C107—22no—
83C2×C4×C107—22no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—22no—
87C2×C4×C107—22no—
88C2×C4×C107#4112yes—
89C22⋊D107—48no—
90C22⋊D107—48no—
91C2×Dic107—22no—
92C2×Dic107—22no—
93C2×Dic107—22no—
94C2×Dic107—22no—
95C2×Dic107—22no—
96C2×Dic107—22no—
97C2×Dic107—22no—
98C2×Dic107—22no—
99C2×Dic107—22no—
100D428—44no—
101C22×C107—42no—
102C22×C107—42no—
103C22×C107—42no—
104C22×C107—42no—
105C22×C107—42no—
106C22×C107—42no—
107C22×C107—42no—
108C22×C107C2×#4111yescharacteristic
109C22×C107H(5,𝔽2)11yescharacteristic
110C22×C107H(5,𝔽2)12yes—
111C22×C107H(5,𝔽2)11yescharacteristic
112C22×C107H(5,𝔽2)12yes—
113C2×D107—42no—
114C2×D107—42no—
115C2×D107—42no—
116C2×D107—42no—
117C2×D107—42no—
118C2×D107—42no—
119C2×D107—42no—
120C4×C107—22no—
121C4×C107—42no—
122C4×C107—41no—
123C4×C107—41no—
124Dic107—42no—
125Dic107—42no—
126Dic107—42no—
127C2×C107—82no—
128C2×C107#53811yescharacteristic
129C2×C107#54012yes—
130C2×C107#56011yescharacteristic
131C2×C107#56012yes—
132C2×C107H(3,𝔽4)11yescharacteristic
133D107—82no—
134#2828—1071nomaximal, Sylow
135C107#282811yescharacteristic, complemented, Sylow
136#400—1071no—
137#397—1072no—
138#394—1072no—
139#394—1072no—
140#394D10711yescharacteristic, complemented
141#392—1072no—
142#392—1072no—
143#390—1071no—
144#388—1072no—
145C22×D4—1072no—
146C22×D4—1072no—
147C22×D4—1071no—
148C22×D4C2×D10711yescharacteristic
149C2×C4⋊C4—1072no—
150C2×C4⋊C4—1071no—
151C2×C4⋊C4C2×D10711yescharacteristic
152C2×C22⋊C4—1072no—
153C2×C22⋊C4—1072no—
154C2×C22⋊C4—1072no—
155C2×C22⋊C4—1072no—
156C2×C22⋊C4—1072no—
157C2×C22⋊C4—1072no—
158C2×C22⋊C4C2×D10712yes—
159C2×C22⋊C4C2×D10712yes—
160C2×C42—1071no—
161#95—1072no—
162#95—1072no—
163#95—1072no—
164#95—1071no—
165#95C2×D10711yescharacteristic
166C24—1072no—
167C24C22×D10712yes—
168C2×D4—42no—
169C2×D4—41no—
170C2×D4—4281no—
171C2×D4—4281no—
172C2×D4—4282no—
173C2×D4—4282no—
174C2×D4—4282no—
175C2×D4—4282no—
176C2×D4—4282no—
177C2×D4—4282no—
178C2×D4—2142no—
179C22×C4—1072no—
180C22×C4—1072no—
181C22×C4—1072no—
182C22×C4C22×D10711yescharacteristic
183C22×C4C22×D10712yes—
184C22×C4C22×D10711yescharacteristic
185C22×C4C22×D10711yescharacteristic
186C4⋊C4—41no—
187C4⋊C4—4281no—
188C4⋊C4—4282no—
189C22⋊C4—24no—
190C22⋊C4—42no—
191C22⋊C4—4282no—
192C22⋊C4—4282no—
193C22⋊C4—4282no—
194C22⋊C4—4282no—
195C22⋊C4—4282no—
196C22⋊C4—4282no—
197C42—4281no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—2142no—
206C23—2142no—
207C23—2142no—
208C23—2142no—
209C23—2142no—
210C23—2142no—
211C23—2142no—
212C23C23×D10711yescharacteristic
213D4—44no—
214D4—4284no—
215D4—4288no—
216D4—4288no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—2142no—
227C2×C4—2142no—
228C2×C4—2142no—
229C2×C4—2142no—
230C2×C4—2142no—
231C2×C4—2142no—
232C2×C4—2142no—
233C2×C4—2142no—
234C2×C4—2142no—
235C2×C4#1313381712yes—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—4282no—
244C22—4282no—
245C22—4282no—
246C22—4282no—
247C22—4282no—
248C22—4282no—
249C22—4282no—
250C22C2×#1313381711yescharacteristic
251C22#1681215411yescharacteristic
252C22#1681215412yes—
253C22#1681215511yescharacteristic
254C22#1681215512yes—
255C4—22no—
256C4—42no—
257C4—41no—
258C4—41no—
259C4—4282no—
260C4—4282no—
261C4—4282no—
262C2—82no—
263C2—8562no—
264C2#2029321411yescharacteristic
265C2#2029323012yes—
266C2#2029336611yescharacteristic
267C2#2029336712yes—
268C2#2029336911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#394×C107C2
hypercenter#394D107
hypocenterC107#2828
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #20292566C2semidirect
2. #20292554C2semidirect
3. #20292543C2semidirect
4. #20292543C2semidirect
5. #20292536C2semidirect
6. #20292535C2semidirect
7. #20292528C2semidirect
8. #20292520C2semidirect
9. #394×C107C2semidirect
135. C107#2828semidirect
140. #394D107semidirect

Maximal subgroups

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

subgroupindex
#202925662
#202925542
#202925432
#202925362
#202925352
#202925282
#202925202
#394×C1072
#2828107