Finite Group Databasebeta

← C2×#20292535 #28339656

Subgroups — C2×#20292535 #28339656

Order 13696.

1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 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
1C23×C22⋊D107C212yesmaximal, complemented
2C22×C22⋊Dic107C212yesmaximal, complemented
3C22×(C2×D107)⋊C4C211yesmaximal, characteristic, complemented
4#20292535C218yesmaximal, direct product factor
5C2×C107⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C107C211yesmaximal, characteristic, complemented
7C24×D107C2211yescharacteristic
8C22×C22⋊D107—28no—
9C22×C22⋊D107—28no—
10C22×C22⋊D107—28no—
11C22×C22⋊D107C2218yescomplemented
12C23×Dic107C2211yescharacteristic
13C23×Dic107C2212yes—
14C2×C22⋊Dic107—28no—
15C2×C22⋊Dic107C2218yescomplemented
16C2×(C2×D107)⋊C4—24no—
17C2×(C2×D107)⋊C4C2214yescomplemented
18C107⋊#95C2214yescomplemented
19C25×C107C2212yes—
20C22×D4×C107—28no—
21C22×D4×C107—24no—
22C22×D4×C107C2214yescomplemented
23C23×C4×C107C2211yescharacteristic
24C23×D107—22no—
25C23×D107—24no—
26C23×D107—24no—
27C23×D107—22no—
28C23×D107D414yescomplemented
29C23×D107C2312yes—
30C2×C22⋊D107—264no—
31C2×C22⋊D107—216no—
32C2×C22⋊D107—216no—
33C2×C22⋊D107—216no—
34C22×Dic107—24no—
35C22×Dic107—24no—
36C22×Dic107—22no—
37C22×Dic107—24no—
38C22×Dic107D418yescomplemented
39C22×Dic107C2312yes—
40C22×Dic107C2314yes—
41C22⋊Dic107—216no—
42(C2×D107)⋊C4—28no—
43C24×C107—24no—
44C24×C107—24no—
45C24×C107—24no—
46C24×C107—24no—
47C24×C107—24no—
48C24×C107—24no—
49C24×C107D418yescomplemented
50C24×C107C2314yes—
51C24×C107C2311yescharacteristic
52C2×D4×C107—232no—
53C2×D4×C107—216no—
54C2×D4×C107—28no—
55C22×C4×C107—24no—
56C22×C4×C107D414yescomplemented
57C22×C4×C107C2312yes—
58C23×C107—216no—
59C23×C107—216no—
60C23×C107—216no—
61C23×C107—24no—
62C23×C107—24no—
63C23×C107—24no—
64C23×C107—24no—
65C23×C107—24no—
66C23×C107—24no—
67C23×C107—48no—
68C23×C107—48no—
69C23×C107—48no—
70C23×C107—48no—
71C23×C107C2×D412yes—
72C23×C107C2×D414yes—
73C23×C107C2×D414yes—
74C23×C107C2×D412yes—
75C23×C107C2×D418yescomplemented
76C23×C107#4112yes—
77C23×C107C2411yescharacteristic
78C22×D107—216no—
79C22×D107—28no—
80C22×D107—22no—
81C22×D107—24no—
82C22×D107—24no—
83C22×D107—22no—
84C22×D107—44no—
85C22×D107—48no—
86C22×D107—44no—
87C22×D107C2×D414yescomplemented
88D4×C107—232no—
89C2×C4×C107—28no—
90C2×C4×C107—24no—
91C2×C4×C107C2×D414yescomplemented
92C22⋊D107—264no—
93C2×Dic107—216no—
94C2×Dic107—24no—
95C2×Dic107—24no—
96C2×Dic107—22no—
97C2×Dic107—24no—
98C2×Dic107—44no—
99C2×Dic107C2×D418yescomplemented
100C22×C107—28no—
101C22×C107—28no—
102C22×C107—28no—
103C22×C107—44no—
104C22×C107—44no—
105C22×C107—44no—
106C22×C107—44no—
107C22×C107—432no—
108C22×C107#12018yes—
109C22×C107#12014yes—
110C22×C107#12114yes—
111C22×C107#12118yes—
112C22×C107#12714yes—
113C22×C107C22×D411yescharacteristic
114C22×C107C22×D412yes—
115C22×C107C22×D412yes—
116C22×C107C22×D411yescharacteristic
117C22×C107C2×#4111yescharacteristic
118C2×D107—28no—
119C2×D107—24no—
120C2×D107—42no—
121C2×D107—44no—
122C2×D107—42no—
123C2×D107—416no—
124C4×C107—24no—
125Dic107—28no—
126Dic107—42no—
127C2×C107—48no—
128C2×C107#39218yescomplemented
129C2×C107C2×#12012yes—
130C2×C107C2×#12011yescharacteristic
131C2×C107C2×#12111yescharacteristic
132C2×C107C2×#12112yes—
133C2×C107C2×#12711yescharacteristic
134D107—44no—
135C2×#392—1071nomaximal, Sylow
136C107C2×#39211yescharacteristic, complemented, Sylow
137C23×D4—1072no—
138C23×D4D10711yescharacteristic, complemented
139C22×C22⋊C4—1072no—
140C22×C22⋊C4—1071no—
141#392—1078no—
142C2×#95—1071no—
143C25—1071no—
144C25C2×D10712yes—
145C22×D4—28no—
146C22×D4—24no—
147C22×D4—1078no—
148C22×D4—2148no—
149C22×D4—2148no—
150C22×D4—2148no—
151C22×D4C2×D10714yescomplemented
152C23×C4—1072no—
153C23×C4—1071no—
154C23×C4C2×D10711yescharacteristic
155C2×C22⋊C4—1078no—
156C2×C22⋊C4—1074no—
157C2×C22⋊C4—2148no—
158C2×C22⋊C4—2144no—
159#95—1074no—
160C24—24no—
161C24—24no—
162C24—24no—
163C24—24no—
164C24—24no—
165C24—24no—
166C24—1074no—
167C24—1072no—
168C24—2144no—
169C24—2142no—
170C24—2144no—
171C24—2142no—
172C24C22⋊D10718yescomplemented
173C24C22×D10714yes—
174C24C22×D10711yescharacteristic
175C2×D4—232no—
176C2×D4—216no—
177C2×D4—28no—
178C2×D4—21416no—
179C2×D4—21416no—
180C2×D4—21464no—
181C2×D4—21416no—
182C22×C4—24no—
183C22×C4—1078no—
184C22×C4—1074no—
185C22×C4—1072no—
186C22×C4—2144no—
187C22×C4—2142no—
188C22×C4—2144no—
189C22×C4—2144no—
190C22×C4C22⋊D10714yescomplemented
191C22×C4C22×D10712yes—
192C22⋊C4—21416no—
193C22⋊C4—2148no—
194C23—216no—
195C23—216no—
196C23—216no—
197C23—24no—
198C23—24no—
199C23—24no—
200C23—24no—
201C23—24no—
202C23—24no—
203C23—48no—
204C23—48no—
205C23—48no—
206C23—48no—
207C23—1074no—
208C23—4284no—
209C23—4288no—
210C23—4284no—
211C23—21416no—
212C23—2148no—
213C23—2144no—
214C23—2142no—
215C23—2144no—
216C23—2142no—
217C23D4×D10712yes—
218C23D4×D10714yes—
219C23C2×C22⋊D10714yes—
220C23C2×C22⋊D10712yes—
221C23C2×C22⋊D10718yescomplemented
222C23#1313381712yes—
223C23C23×D10711yescharacteristic
224D4—232no—
225D4—21464no—
226C2×C4—28no—
227C2×C4—24no—
228C2×C4—1078no—
229C2×C4—4284no—
230C2×C4—2144no—
231C2×C4—2142no—
232C2×C4—21416no—
233C2×C4—2144no—
234C2×C4—2144no—
235C2×C4C2×C22⋊D10714yescomplemented
236C22—28no—
237C22—28no—
238C22—28no—
239C22—44no—
240C22—432no—
241C22—44no—
242C22—44no—
243C22—44no—
244C22—4282no—
245C22—42816no—
246C22—4282no—
247C22—4284no—
248C22—2148no—
249C22—2144no—
250C22#1681207718yes—
251C22#1681207814yes—
252C22#1681208014yes—
253C22#1681208118yes—
254C22#1681210514yes—
255C22C2×D4×D10712yes—
256C22C2×D4×D10711yescharacteristic
257C22C22×C22⋊D10711yescharacteristic
258C22C22×C22⋊D10712yes—
259C22C2×#1313381711yescharacteristic
260C4—24no—
261C4—4282no—
262C4—2148no—
263C2—48no—
264C2—4284no—
265C2#2029253518yesdirect product factor
266C2C2×#1681207712yes—
267C2C2×#1681207811yescharacteristic
268C2C2×#1681208011yescharacteristic
269C2C2×#1681208112yes—
270C2C2×#1681210511yescharacteristic
subgroupG/H
centerC24C22×D107
commutator, cosocleC23×C107C24
FrattiniC23C23×D107
FittingC23×D4×C107C2
socleC24×C107C23
hypercenterC23×D4D107
hypocenterC107C2×#392
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D107C2semidirect
2. C22×C22⋊Dic107C2semidirect
3. C22×(C2×D107)⋊C4C2semidirect
4. #20292535C2direct (N × H)
5. C2×C107⋊#95C2semidirect
6. C23×D4×C107C2semidirect
11. C22×C22⋊D107C22semidirect
15. C2×C22⋊Dic107C22semidirect
17. C2×(C2×D107)⋊C4C22semidirect
18. C107⋊#95C22semidirect
22. C22×D4×C107C22semidirect
28. C23×D107D4semidirect
38. C22×Dic107D4semidirect
49. C24×C107D4semidirect
56. C22×C4×C107D4semidirect
75. C23×C107C2×D4semidirect
87. C22×D107C2×D4semidirect
91. C2×C4×C107C2×D4semidirect
99. C2×Dic107C2×D4semidirect
128. C2×C107#392semidirect
136. C107C2×#392semidirect
138. C23×D4D107semidirect
151. C22×D4C2×D107semidirect
172. C24C22⋊D107semidirect
190. C22×C4C22⋊D107semidirect
221. C23C2×C22⋊D107semidirect
235. C2×C4C2×C22⋊D107semidirect
265. C2#20292535direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1072
C22×C22⋊Dic1072
C22×(C2×D107)⋊C42
#202925352
C2×C107⋊#952
C23×D4×C1072
C2×#392107