Finite Group Databasebeta

← C2×#20292802 #28345799

Subgroups — C2×#20292802 #28345799

Order 13696.

728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#16812157C211yesmaximal, characteristic, complemented
2C2×#16812137C212yesmaximal, complemented
3C2×#16812098C211yesmaximal, characteristic, complemented
4#20292802C218yesmaximal, direct product factor
5C2×#16812035C212yesmaximal, complemented
6C2×#101×C107C211yesmaximal, characteristic, complemented
7#16812157—24no—
8#16812157—22no—
9#16812157C2214yescomplemented
10C2×#13133819—22no—
11C2×#13133818—22no—
12C2×#13133818C2212yes—
13C2×Q8×D107—22no—
14C22×D428C2211yescharacteristic
15#16812137—24no—
16#16812137C2218yescomplemented
17C2×#13133807—22no—
18C2×D856—22no—
19#16812098—22no—
20#16812098C2214yescomplemented
21C2×(C2×D107)⋊C4—22no—
22C2×C4×Dic107C2211yescharacteristic
23#16812035C2218yescomplemented
24C22×Q8×C107C2211yescharacteristic
25C2×M16×C107C2212yes—
26#101×C107C2214yescomplemented
27C23×D107—21no—
28#13133819—28no—
29#13133819—28no—
30#13133818—28no—
31#13133818—28no—
32#13133818—22no—
33#13133818—22no—
34#13133818D414yes—
35#13133818C2314yes—
36C2×Dic214—22no—
37C2×Dic214D412yes—
38Q8×D107—28no—
39Q8×D107—28no—
40C2×D428—22no—
41C2×D428—22no—
42C2×D428—22no—
43C2×D428—21no—
44C2×D428D412yes—
45C2×D428C2312yes—
46C2×C22⋊D107—22no—
47C22×Dic107—21no—
48C2×C4×D107—24no—
49C2×C4×D107—22no—
50#13133807—28no—
51D856—28no—
52(C2×D107)⋊C4—28no—
53C4×Dic107—21no—
54C4×Dic107C2312yes—
55C2×Q8×C107—22no—
56C2×Q8×C107—22no—
57C2×Q8×C107D412yes—
58C2×Q8×C107C2312yes—
59C22×C4×C107D412yes—
60C22×C4×C107C2311yescharacteristic
61M16×C107—22no—
62M16×C107C2314yes—
63C2×C8×C107—22no—
64C23×C107C2×D411yescharacteristic
65C22×D107—22no—
66C22×D107—22no—
67C22×D107—44no—
68C22×D107—41no—
69C22×D107—41no—
70Q8×C107—24no—
71Q8×C107—24no—
72C2×C4×C107—22no—
73C2×C4×C107—22no—
74C2×C4×C107C2×D412yes—
75C2×C4×C107C2×D412yes—
76C2×C4×C107C2×D414yes—
77C2×C4×C107C2×D411yescharacteristic
78C2×C4×C107C2411yescharacteristic
79C22⋊D107—24no—
80C22⋊D107—24no—
81C2×Dic107—22no—
82C2×Dic107—22no—
83C2×Dic107—42no—
84D428—28no—
85D428—22no—
86D428—24no—
87D428—42no—
88D428C2×D414yes—
89C4×D107—216no—
90C4×D107—24no—
91C4×D107—24no—
92Dic214—28no—
93Dic214—22no—
94Dic214C2×D414yes—
95C8×C107—24no—
96C22×C107—22no—
97C22×C107#12011yescharacteristic
98C22×C107#12011yescharacteristic
99C22×C107C22×D411yescharacteristic
100C2×D107—24no—
101C2×D107—44no—
102C2×D107—44no—
103C2×D107—42no—
104C2×D107—82no—
105C2×D107—82no—
106C4×C107—24no—
107C4×C107#12012yes—
108C4×C107C22×D412yes—
109Dic107—24no—
110Dic107—42no—
111C2×C107—21no—
112C2×C107—21no—
113C2×C107#45412yescomplemented
114C2×C107C2×#12011yescharacteristic
115D107—44no—
116D107—82no—
117C2×#454—1071nomaximal, Sylow
118C107C2×#45411yescharacteristic, complemented, Sylow
119C2×2−1+4—1071no—
120C2×AGL(1,ℤ/8)—1072no—
121C2×#124—1071no—
122#454—1078no—
123C2×#104—1072no—
124C2×#101D10711yescharacteristic, complemented
1252−1+4—1074no—
1262−1+4—2144no—
1272−1+4—2142no—
128C2×#41—1072no—
129C2×#41—2142no—
130C2×#41—2142no—
131C22×Q8—2142no—
132C22×Q8C2×D10711yescharacteristic
133C22×D4—1071no—
134AGL(1,ℤ/8)—1078no—
135AGL(1,ℤ/8)—2144no—
136C2×SD16—2142no—
137C2×D8—2142no—
138C2×M16C2×D10712yes—
139#124—1074no—
140#124—2142no—
141C2×C22⋊C4—2142no—
142C2×C42—1071no—
143#104—1078no—
144#101C2×D10714yescomplemented
145C24—2141no—
146#41—1074no—
147#41—1074no—
148#41—2148no—
149#41—2148no—
150#41—2148no—
151#41—2142no—
152#41—2142no—
153#41—2148no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—1072no—
157C2×Q8—2142no—
158C2×Q8—2148no—
159C2×Q8—2148no—
160C2×Q8D42812yes—
161C2×Q8C22×D10712yes—
162C2×D4—1072no—
163C2×D4—1072no—
164C2×D4—2142no—
165C2×D4—2142no—
166C2×D4—2142no—
167C2×D4—2142no—
168C2×D4—2141no—
169C22×C4—2144no—
170C22×C4—2141no—
171C22×C4—2142no—
172C22×C4D42812yes—
173C22×C4C22×D10711yescharacteristic
174SD16—2148no—
175D8—2148no—
176M16—22no—
177M16C22×D10714yes—
178C2×C8—22no—
179C22⋊C4—2148no—
180C42—1072no—
181C42—2141no—
182C23—4284no—
183C23—4281no—
184C23—4281no—
185C23—2142no—
186C23—2142no—
187C23C2×D42811yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—1074no—
191Q8—2148no—
192Q8—2142no—
193D4—1074no—
194D4—4282no—
195D4—2148no—
196D4—2144no—
197D4—2144no—
198D4—2142no—
199D4—2144no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—4282no—
203C2×C4—21416no—
204C2×C4—2142no—
205C2×C4—2142no—
206C2×C4—2144no—
207C2×C4—2144no—
208C2×C4D4×D10712yes—
209C2×C4D4×D10712yes—
210C2×C4C2×D42814yes—
211C2×C4C2×D42811yescharacteristic
212C2×C4C23×D10711yescharacteristic
213C8—24no—
214C22—22no—
215C22—8562no—
216C22—8562no—
217C22—4284no—
218C22—4282no—
219C22—4284no—
220C22—2144no—
221C22#1681207911yescharacteristic
222C22#1681207911yescharacteristic
223C22C22×D42811yescharacteristic
224C4—24no—
225C4—4282no—
226C4—2144no—
227C4#1681207912yes—
228C4C2×D4×D10712yes—
229C2—21no—
230C2—21no—
231C2—8562no—
232C2—4284no—
233C2#2029280212yesdirect product factor
234C2C2×#1681207911yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#101×C107C2
socleC22×C107#120
hypercenterC2×#101D107
hypocenterC107C2×#454
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#16812157C2semidirect
2. C2×#16812137C2semidirect
3. C2×#16812098C2semidirect
4. #20292802C2direct (N × H)
5. C2×#16812035C2semidirect
6. C2×#101×C107C2semidirect
9. #16812157C22semidirect
16. #16812137C22semidirect
20. #16812098C22semidirect
23. #16812035C22semidirect
26. #101×C107C22semidirect
113. C2×C107#454semidirect
118. C107C2×#454semidirect
124. C2×#101D107semidirect
144. #101C2×D107semidirect
233. C2#20292802direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168121572
C2×#168121372
C2×#168120982
#202928022
C2×#168120352
C2×#101×C1072
C2×#454107