Finite Group Databasebeta

← C2×#28409207 #44409072

Subgroups — C2×#28409207 #44409072

Order 29056.

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×#20300336C211yesmaximal, characteristic, complemented
2C2×#20300316C212yesmaximal, complemented
3C2×#20300277C211yesmaximal, characteristic, complemented
4#28409207C218yesmaximal, direct product factor
5C2×#20300214C212yesmaximal, complemented
6C2×#101×C227C211yesmaximal, characteristic, complemented
7#20300336—24no—
8#20300336—22no—
9#20300336C2214yescomplemented
10C2×#16813885—22no—
11C2×#16813884—22no—
12C2×#16813884C2212yes—
13C2×Q8×D227—22no—
14C22×D908C2211yescharacteristic
15#20300316—24no—
16#20300316C2218yescomplemented
17C2×#16813873—22no—
18C2×D1816—22no—
19#20300277—22no—
20#20300277C2214yescomplemented
21C2×(C2×D227)⋊C4—22no—
22C2×C4×Dic227C2211yescharacteristic
23#20300214C2218yescomplemented
24C22×Q8×C227C2211yescharacteristic
25C2×M16×C227C2212yes—
26#101×C227C2214yescomplemented
27C23×D227—21no—
28#16813885—28no—
29#16813885—28no—
30#16813884—28no—
31#16813884—28no—
32#16813884—22no—
33#16813884—22no—
34#16813884D414yes—
35#16813884C2314yes—
36C2×Dic454—22no—
37C2×Dic454D412yes—
38Q8×D227—28no—
39Q8×D227—28no—
40C2×D908—22no—
41C2×D908—22no—
42C2×D908—22no—
43C2×D908—21no—
44C2×D908D412yes—
45C2×D908C2312yes—
46C2×C22⋊D227—22no—
47C22×Dic227—21no—
48C2×C4×D227—24no—
49C2×C4×D227—22no—
50#16813873—28no—
51D1816—28no—
52(C2×D227)⋊C4—28no—
53C4×Dic227—21no—
54C4×Dic227C2312yes—
55C2×Q8×C227—22no—
56C2×Q8×C227—22no—
57C2×Q8×C227D412yes—
58C2×Q8×C227C2312yes—
59C22×C4×C227D412yes—
60C22×C4×C227C2311yescharacteristic
61M16×C227—22no—
62M16×C227C2314yes—
63C2×C8×C227—22no—
64C22×D227—22no—
65C22×D227—22no—
66C22×D227—44no—
67C22×D227—41no—
68C22×D227—41no—
69Dic454—28no—
70Dic454—22no—
71Dic454C2×D414yes—
72D908—28no—
73D908—22no—
74D908—24no—
75D908—42no—
76D908C2×D414yes—
77C22⋊D227—24no—
78C22⋊D227—24no—
79C2×Dic227—22no—
80C2×Dic227—22no—
81C2×Dic227—42no—
82C4×D227—216no—
83C4×D227—24no—
84C4×D227—24no—
85C23×C227C2×D411yescharacteristic
86Q8×C227—24no—
87Q8×C227—24no—
88C2×C4×C227—22no—
89C2×C4×C227—22no—
90C2×C4×C227C2×D414yes—
91C2×C4×C227C2×D411yescharacteristic
92C2×C4×C227C2×D412yes—
93C2×C4×C227C2×D412yes—
94C2×C4×C227C2411yescharacteristic
95C8×C227—24no—
96C22×C227—22no—
97C22×C227#12011yescharacteristic
98C22×C227#12011yescharacteristic
99C22×C227C22×D411yescharacteristic
100C2×D227—24no—
101C2×D227—44no—
102C2×D227—44no—
103C2×D227—42no—
104C2×D227—82no—
105C2×D227—82no—
106C4×C227—24no—
107C4×C227#12012yes—
108C4×C227C22×D412yes—
109Dic227—24no—
110Dic227—42no—
111C2×C227—21no—
112C2×C227—21no—
113C2×C227#45412yescomplemented
114C2×C227C2×#12011yescharacteristic
115D227—44no—
116D227—82no—
117C227C2×#45411yescharacteristic, complemented, Sylow
118C2×#454—2271nomaximal, Sylow
119C2×2−1+4—2271no—
120C2×AGL(1,ℤ/8)—2272no—
121C2×#124—2271no—
122#454—2278no—
123C2×#104—2272no—
124C2×#101D22711yescharacteristic, complemented
1252−1+4—4544no—
1262−1+4—4542no—
1272−1+4—2274no—
128C2×#41—4542no—
129C2×#41—4542no—
130C2×#41—2272no—
131C22×Q8—4542no—
132C22×Q8C2×D22711yescharacteristic
133C22×D4—2271no—
134AGL(1,ℤ/8)—4544no—
135AGL(1,ℤ/8)—2278no—
136C2×SD16—4542no—
137C2×D8—4542no—
138C2×M16C2×D22712yes—
139#124—4542no—
140#124—2274no—
141C2×C22⋊C4—4542no—
142C2×C42—2271no—
143#104—2278no—
144#101C2×D22714yescomplemented
145C24—4541no—
146#41—4548no—
147#41—4548no—
148#41—4548no—
149#41—4542no—
150#41—4548no—
151#41—4542no—
152#41—2274no—
153#41—2274no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—4542no—
157C2×Q8—4548no—
158C2×Q8—4548no—
159C2×Q8—2272no—
160C2×Q8D90812yes—
161C2×Q8C22×D22712yes—
162C2×D4—4542no—
163C2×D4—4542no—
164C2×D4—4542no—
165C2×D4—4542no—
166C2×D4—4541no—
167C2×D4—2272no—
168C2×D4—2272no—
169C22×C4—4544no—
170C22×C4—4541no—
171C22×C4—4542no—
172C22×C4D90812yes—
173C22×C4C22×D22711yescharacteristic
174SD16—4548no—
175D8—4548no—
176M16—22no—
177M16C22×D22714yes—
178C2×C8—22no—
179C22⋊C4—4548no—
180C42—4541no—
181C42—2272no—
182C23—9084no—
183C23—9081no—
184C23—9081no—
185C23—4542no—
186C23—4542no—
187C23C2×D90811yescharacteristic
188Q8—24no—
189Q8—24no—
190Q8—4548no—
191Q8—4542no—
192Q8—2274no—
193D4—9082no—
194D4—4548no—
195D4—4544no—
196D4—4544no—
197D4—4544no—
198D4—4542no—
199D4—2274no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—9082no—
203C2×C4—45416no—
204C2×C4—4542no—
205C2×C4—4542no—
206C2×C4—4544no—
207C2×C4—4544no—
208C2×C4D4×D22712yes—
209C2×C4D4×D22712yes—
210C2×C4C2×D90814yes—
211C2×C4C2×D90811yescharacteristic
212C2×C4C23×D22711yescharacteristic
213C8—24no—
214C22—22no—
215C22—18162no—
216C22—18162no—
217C22—9084no—
218C22—9082no—
219C22—9084no—
220C22—4544no—
221C22#2030025811yescharacteristic
222C22#2030025811yescharacteristic
223C22C22×D90811yescharacteristic
224C4—24no—
225C4—9082no—
226C4—4544no—
227C4#2030025812yes—
228C4C2×D4×D22712yes—
229C2—21no—
230C2—21no—
231C2—18162no—
232C2—9084no—
233C2#2840920712yesdirect product factor
234C2C2×#2030025811yescharacteristic
subgroupG/H
centerC22#20300258
commutator, cosocleC2×C4×C227C24
FrattiniC2×C4C23×D227
FittingC2×#101×C227C2
socleC22×C227#120
hypercenterC2×#101D227
hypocenterC227C2×#454
LCSG ▷ C2×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#20300336C2semidirect
2. C2×#20300316C2semidirect
3. C2×#20300277C2semidirect
4. #28409207C2direct (N × H)
5. C2×#20300214C2semidirect
6. C2×#101×C227C2semidirect
9. #20300336C22semidirect
16. #20300316C22semidirect
20. #20300277C22semidirect
23. #20300214C22semidirect
26. #101×C227C22semidirect
113. C2×C227#454semidirect
117. C227C2×#454semidirect
124. C2×#101D227semidirect
144. #101C2×D227semidirect
233. C2#28409207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#203003362
C2×#203003162
C2×#203002772
#284092072
C2×#203002142
C2×#101×C2272
C2×#454227