Finite Group Databasebeta

← C2×#23757448 #34109474

Subgroups — C2×#23757448 #34109474

Order 20096.

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×#19097819C211yesmaximal, characteristic, complemented
2C2×#19097799C212yesmaximal, complemented
3C2×#19097760C211yesmaximal, characteristic, complemented
4#23757448C218yesmaximal, direct product factor
5C2×#19097697C212yesmaximal, complemented
6C2×#101×C157C211yesmaximal, characteristic, complemented
7#19097819—22no—
8#19097819—24no—
9#19097819C2214yescomplemented
10C2×#14578955—22no—
11C2×#14578954—22no—
12C2×#14578954C2212yes—
13C2×Q8×D157—22no—
14C22×D628C2211yescharacteristic
15#19097799—24no—
16#19097799C2218yescomplemented
17C2×#14578943—22no—
18C2×D1256—22no—
19#19097760—22no—
20#19097760C2214yescomplemented
21C2×#14578931—22no—
22C2×C4×Dic157C2211yescharacteristic
23#19097697C2218yescomplemented
24C22×Q8×C157C2211yescharacteristic
25C2×M16×C157C2212yes—
26#101×C157C2214yescomplemented
27C23×D157—21no—
28#14578955—28no—
29#14578955—28no—
30#14578954—28no—
31#14578954—28no—
32#14578954—22no—
33#14578954—22no—
34#14578954D414yes—
35#14578954C2314yes—
36C2×Dic314—22no—
37C2×Dic314D412yes—
38Q8×D157—28no—
39Q8×D157—28no—
40C2×D628—22no—
41C2×D628—22no—
42C2×D628—22no—
43C2×D628—21no—
44C2×D628D412yes—
45C2×D628C2312yes—
46C2×C22⋊D157—22no—
47C22×Dic157—21no—
48C2×C4×D157—24no—
49C2×C4×D157—22no—
50#14578943—28no—
51D1256—28no—
52#14578931—28no—
53C4×Dic157—21no—
54C4×Dic157C2312yes—
55C2×Q8×C157—22no—
56C2×Q8×C157—22no—
57C2×Q8×C157D412yes—
58C2×Q8×C157C2312yes—
59C22×C4×C157D412yes—
60C22×C4×C157C2311yescharacteristic
61M16×C157—22no—
62M16×C157C2314yes—
63C2×C8×C157—22no—
64C22×D157—22no—
65C22×D157—22no—
66C22×D157—44no—
67C22×D157—41no—
68C22×D157—41no—
69Dic314—28no—
70Dic314—22no—
71Dic314C2×D414yes—
72D628—28no—
73D628—22no—
74D628—24no—
75D628—42no—
76D628C2×D414yes—
77C22⋊D157—24no—
78C22⋊D157—24no—
79C2×Dic157—22no—
80C2×Dic157—22no—
81C2×Dic157—42no—
82C4×D157—216no—
83C4×D157—24no—
84C4×D157—24no—
85C23×C157C2×D411yescharacteristic
86Q8×C157—24no—
87Q8×C157—24no—
88C2×C4×C157—22no—
89C2×C4×C157—22no—
90C2×C4×C157C2×D412yes—
91C2×C4×C157C2×D412yes—
92C2×C4×C157C2×D414yes—
93C2×C4×C157C2×D411yescharacteristic
94C2×C4×C157C2411yescharacteristic
95C8×C157—24no—
96C22×C157—22no—
97C22×C157#12011yescharacteristic
98C22×C157#12011yescharacteristic
99C22×C157C22×D411yescharacteristic
100C2×D157—24no—
101C2×D157—44no—
102C2×D157—44no—
103C2×D157—42no—
104C2×D157—82no—
105C2×D157—82no—
106C4×C157—24no—
107C4×C157#12012yes—
108C4×C157C22×D412yes—
109Dic157—24no—
110Dic157—42no—
111C2×C157—21no—
112C2×C157—21no—
113C2×C157#45412yescomplemented
114C2×C157C2×#12011yescharacteristic
115D157—44no—
116D157—82no—
117C157C2×#45411yescharacteristic, complemented, Sylow
118C2×#454—1571nomaximal, Sylow
119C2×2−1+4—1571no—
120C2×AGL(1,ℤ/8)—1572no—
121C2×#124—1571no—
122#454—1578no—
123C2×#104—1572no—
124C2×#101D15711yescharacteristic, complemented
1252−1+4—3144no—
1262−1+4—3142no—
1272−1+4—1574no—
128C2×#41—3142no—
129C2×#41—3142no—
130C2×#41—1572no—
131C22×Q8—3142no—
132C22×Q8C2×D15711yescharacteristic
133C22×D4—1571no—
134AGL(1,ℤ/8)—3144no—
135AGL(1,ℤ/8)—1578no—
136C2×SD16—3142no—
137C2×D8—3142no—
138C2×M16C2×D15712yes—
139#124—3142no—
140#124—1574no—
141C2×C22⋊C4—3142no—
142C2×C42—1571no—
143#104—1578no—
144#101C2×D15714yescomplemented
145C24—3141no—
146#41—3148no—
147#41—3148no—
148#41—3148no—
149#41—3142no—
150#41—3148no—
151#41—3142no—
152#41—1574no—
153#41—1574no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—3142no—
157C2×Q8—3148no—
158C2×Q8—3148no—
159C2×Q8—1572no—
160C2×Q8D62812yes—
161C2×Q8C22×D15712yes—
162C2×D4—3142no—
163C2×D4—3142no—
164C2×D4—3142no—
165C2×D4—3142no—
166C2×D4—3141no—
167C2×D4—1572no—
168C2×D4—1572no—
169C22×C4—3144no—
170C22×C4—3142no—
171C22×C4—3141no—
172C22×C4D62812yes—
173C22×C4C22×D15711yescharacteristic
174SD16—3148no—
175D8—3148no—
176M16—22no—
177M16C22×D15714yes—
178C2×C8—22no—
179C22⋊C4—3148no—
180C42—3141no—
181C42—1572no—
182C23—3142no—
183C23—3142no—
184C23—6284no—
185C23—6281no—
186C23—6281no—
187C23C2×D62811yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—3148no—
191Q8—3142no—
192Q8—1574no—
193D4—3148no—
194D4—3144no—
195D4—3144no—
196D4—3142no—
197D4—3144no—
198D4—6282no—
199D4—1574no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—31416no—
203C2×C4—3142no—
204C2×C4—3144no—
205C2×C4—3144no—
206C2×C4—3142no—
207C2×C4—6282no—
208C2×C4D4×D15712yes—
209C2×C4D4×D15712yes—
210C2×C4C2×D62814yes—
211C2×C4C2×D62811yescharacteristic
212C2×C4C23×D15711yescharacteristic
213C8—24no—
214C22—22no—
215C22—3144no—
216C22—6284no—
217C22—6284no—
218C22—6282no—
219C22—12562no—
220C22—12562no—
221C22#1909774111yescharacteristic
222C22#1909774111yescharacteristic
223C22C22×D62811yescharacteristic
224C4—24no—
225C4—3144no—
226C4—6282no—
227C4#1909774112yes—
228C4C2×D4×D15712yes—
229C2—21no—
230C2—21no—
231C2—6284no—
232C2—12562no—
233C2#2375744812yesdirect product factor
234C2C2×#1909774111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC2×#101×C157C2
socleC22×C157#120
hypercenterC2×#101D157
hypocenterC157C2×#454
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#19097819C2semidirect
2. C2×#19097799C2semidirect
3. C2×#19097760C2semidirect
4. #23757448C2direct (N × H)
5. C2×#19097697C2semidirect
6. C2×#101×C157C2semidirect
9. #19097819C22semidirect
16. #19097799C22semidirect
20. #19097760C22semidirect
23. #19097697C22semidirect
26. #101×C157C22semidirect
113. C2×C157#454semidirect
117. C157C2×#454semidirect
124. C2×#101D157semidirect
144. #101C2×D157semidirect
233. C2#23757448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190978192
C2×#190977992
C2×#190977602
#237574482
C2×#190976972
C2×#101×C1572
C2×#454157