Finite Group Databasebeta

← C2×#30631687 #44558876

Subgroups — C2×#30631687 #44558876

Order 32128.

816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×#16860811C211yesmaximal, characteristic
2C22×#16860793C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D251C211yesmaximal, characteristic, complemented
4#30631687C218yesmaximal, direct product factor
5C2×#22548639C211yesmaximal, characteristic, complemented
6C2×#22548637C211yesmaximal, characteristic, complemented
7C2×#22548635C211yesmaximal, characteristic, complemented
8C2×#103×C251C211yesmaximal, characteristic, complemented
9C2×#16860811—24no—
10C2×#16860811—22no—
11C2×#16860811C418yescomplemented
12C2×#16860811C2214yes—
13C22×D1004—21no—
14C22×D1004C2211yescharacteristic
15C22×C4×D251—21no—
16C22×C4×D251—21no—
17C22×C4×D251C2211yescharacteristic
18C2×#16860793—24no—
19C2×#16860793C2214yescomplemented
20C22×C251⋊C8C2211yescharacteristic
21C2×C4⋊Dic251C2211yescharacteristic
22C2×Dic251⋊C4—21no—
23C4⋊C4×D251—22no—
24C4⋊C4×D251C2214yescomplemented
25#22548639C2214yescomplemented
26#22548637C2214yescomplemented
27#22548635C2214yescomplemented
28C22×Q8×C251C2211yescharacteristic
29C22×C8×C251C2211yescharacteristic
30C2×C4⋊C4×C251C2211yescharacteristic
31#103×C251C2214yescomplemented
32C23×D251—21no—
33C23×D251D411yescharacteristic
34#16860811—216no—
35#16860811—28no—
36#16860811C2×C4116yescomplemented
37C2×D1004—28no—
38C2×D1004—24no—
39C2×D1004—21no—
40C2×D1004—22no—
41C2×D1004C2×C414yescomplemented
42C2×D1004C2312yes—
43C22×Dic251—21no—
44C22×Dic251D411yescharacteristic
45C2×C4×D251—28no—
46C2×C4×D251—24no—
47C2×C4×D251—24no—
48C2×C4×D251—44no—
49C2×C4×D251C2×C414yes—
50C2×C4×D251D412yes—
51C2×C4×D251D414yes—
52C2×C4×D251C2312yes—
53#16860793—28no—
54C2×C251⋊C8—22no—
55C2×C251⋊C8C2312yes—
56C4⋊Dic251—21no—
57C4⋊Dic251C2312yes—
58Dic251⋊C4—24no—
59C2×Q8×C251—22no—
60C2×Q8×C251—21no—
61C2×Q8×C251C2×C414yescomplemented
62C2×Q8×C251C2312yes—
63C22×C4×C251—21no—
64C22×C4×C251—21no—
65C22×C4×C251C2311yescharacteristic
66C2×C8×C251—22no—
67C2×C8×C251C2312yes—
68C4⋊C4×C251—21no—
69C4⋊C4×C251C2312yes—
70C22×D251—22no—
71C22×D251—22no—
72C22×D251—24no—
73C22×D251—22no—
74C22×D251—42no—
75C22×D251—42no—
76C22×D251C22⋊C414yes—
77C22×D251C2×D412yes—
78D1004—216no—
79D1004—24no—
80D1004—22no—
81D1004C22×C414yescomplemented
82C2×Dic251—22no—
83C2×Dic251—42no—
84C2×Dic251C22⋊C414yes—
85C2×Dic251C2×D412yes—
86C4×D251—216no—
87C4×D251—48no—
88C4×D251C22⋊C418yes—
89C4×D251C22×C414yes—
90C4×D251C2×D414yes—
91C251⋊C8—22no—
92C23×C251C2×D411yescharacteristic
93Q8×C251—24no—
94Q8×C251—22no—
95Q8×C251C22×C414yescomplemented
96C2×C4×C251—24no—
97C2×C4×C251—22no—
98C2×C4×C251—22no—
99C2×C4×C251—42no—
100C2×C4×C251C22×C412yes—
101C2×C4×C251C2×D411yescharacteristic
102C2×C4×C251C2×D412yes—
103C2×C4×C251C2411yescharacteristic
104C8×C251—22no—
105C22×C251C2×C22⋊C412yes—
106C22×C251AGL(1,ℤ/8)12yes—
107C22×C251#13712yes—
108C22×C251C22×D411yescharacteristic
109C2×D251—22no—
110C2×D251—22no—
111C2×D251—28no—
112C2×D251—24no—
113C2×D251—42no—
114C2×D251—42no—
115C2×D251—48no—
116C2×D251C2×C22⋊C414yes—
117C4×C251—24no—
118C4×C251—42no—
119C4×C251C2×C22⋊C412yes—
120C4×C251C23×C411yescharacteristic
121C4×C251C22×D411yescharacteristic
122Dic251—42no—
123Dic251C2×C22⋊C414yes—
124C2×C251#41714yescomplemented
125C2×C251C22×C22⋊C411yescharacteristic
126C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C251C2×#13711yescharacteristic
128D251—24no—
129D251—44no—
130C251C2×#41711yescharacteristic, complemented, Sylow
131C2×#417—2511nomaximal, Sylow
132C22×#41—2511no—
133C22×M16—2511no—
134C22×C4⋊C4—2511no—
135#417—2518no—
136C2×#103—2511no—
137C2×#103D25111yescharacteristic, complemented
138C2×#102—2511no—
139C2×#102—2511no—
140C2×#41—5022no—
141C2×#41—5024no—
142C2×#41—2518no—
143C2×#41—2514no—
144C22×Q8C2×D25111yescharacteristic
145C22×D4—5021no—
146C22×D4—2511no—
147C23×C4—5021no—
148C23×C4—5021no—
149C23×C4—2511no—
150C2×M16—5024no—
151C2×M16—2514no—
152C22×C8—2511no—
153C22×C8C2×D25111yescharacteristic
154C2×C4⋊C4—5022no—
155C2×C4⋊C4—5021no—
156C2×C4⋊C4—2511no—
157C2×C4⋊C4—2514no—
158C2×C4⋊C4C2×D25111yescharacteristic
159#103—2514no—
160#103C2×D25114yescomplemented
161#102—2514no—
162#102—2514no—
163C24—5021no—
164C24—2511no—
165#41—5028no—
166#41—50216no—
167#41—25116no—
168C2×Q8—21no—
169C2×Q8—22no—
170C2×Q8C4×D25114yescomplemented
171C2×Q8C22×D25112yes—
172C2×D4—5024no—
173C2×D4—5028no—
174C2×D4—5022no—
175C2×D4—5021no—
176C2×D4—2514no—
177C2×D4—2512no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—10044no—
181C22×C4—5024no—
182C22×C4—5024no—
183C22×C4—5028no—
184C22×C4—5021no—
185C22×C4—2511no—
186C22×C4—2514no—
187C22×C4—2512no—
188C22×C4—2514no—
189C22×C4—2512no—
190C22×C4C22×D25111yescharacteristic
191M16—5028no—
192C2×C8—22no—
193C2×C8—5022no—
194C2×C8—2512no—
195C2×C8C22×D25112yes—
196C4⋊C4—21no—
197C4⋊C4—5024no—
198C4⋊C4—5021no—
199C4⋊C4—2512no—
200C4⋊C4C22×D25112yes—
201C23—10042no—
202C23—10042no—
203C23—5022no—
204C23—5024no—
205C23—5022no—
206C23—5022no—
207C23—2512no—
208C23—2514no—
209C23D4×D25111yescharacteristic
210Q8—22no—
211Q8—24no—
212Q8C2×C4×D25114yescomplemented
213D4—50216no—
214D4—5022no—
215D4—5024no—
216D4—2514no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—10048no—
222C2×C4—10042no—
223C2×C4—50216no—
224C2×C4—5022no—
225C2×C4—2512no—
226C2×C4—2514no—
227C2×C4—2514no—
228C2×C4—2514no—
229C2×C4—2518no—
230C2×C4C2×C4×D25112yes—
231C2×C4D4×D25112yes—
232C2×C4D4×D25111yescharacteristic
233C2×C4C23×D25111yescharacteristic
234C8—22no—
235C8—5022no—
236C22—10048no—
237C22—10042no—
238C22—10042no—
239C22—5024no—
240C22—5028no—
241C22—5022no—
242C22—5022no—
243C22—2514no—
244C22C22⋊C4×D25112yes—
245C22#2254874212yes—
246C22#2254874712yes—
247C22C2×D4×D25111yescharacteristic
248C4—24no—
249C4—42no—
250C4—10042no—
251C4—2514no—
252C4C22⋊C4×D25112yes—
253C4C22×C4×D25111yescharacteristic
254C4C2×D4×D25111yescharacteristic
255C2—10044no—
256C2—5024no—
257C2#3063168714yesdirect product factor
258C2C2×C22⋊C4×D25111yescharacteristic
259C2C2×#2254874211yescharacteristic
260C2C2×#2254874711yescharacteristic
subgroupG/H
centerC23D4×D251
commutatorC4×C251C23×C4
FrattiniC2×C4C23×D251
FittingC2×#103×C251C2
socleC23×C251C2×D4
prime radicalC22×#16860811C2
cosocleC2×C4×C251C24
hypercenterC2×#103D251
hypocenterC251C2×#417
LCSG ▷ C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C22×#16860793C2semidirect
3. C2×C4⋊C4×D251C2semidirect
4. #30631687C2direct (N × H)
5. C2×#22548639C2semidirect
6. C2×#22548637C2semidirect
7. C2×#22548635C2semidirect
8. C2×#103×C251C2semidirect
11. C2×#16860811C4semidirect
19. C2×#16860793C22semidirect
24. C4⋊C4×D251C22semidirect
25. #22548639C22semidirect
26. #22548637C22semidirect
27. #22548635C22semidirect
31. #103×C251C22semidirect
36. #16860811C2×C4semidirect
41. C2×D1004C2×C4semidirect
61. C2×Q8×C251C2×C4semidirect
81. D1004C22×C4semidirect
95. Q8×C251C22×C4semidirect
124. C2×C251#417semidirect
130. C251C2×#417semidirect
137. C2×#103D251semidirect
160. #103C2×D251semidirect
170. C2×Q8C4×D251semidirect
212. Q8C2×C4×D251semidirect
257. C2#30631687direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168608112
C22×#168607932
C2×C4⋊C4×D2512
#306316872
C2×#225486392
C2×#225486372
C2×#225486352
C2×#103×C2512
C2×#417251