Finite Group Databasebeta

← C2×#30631939 #44559960

Subgroups — C2×#30631939 #44559960

Order 32128.

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

normal subgroups only

This group has 596 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
1C22×#16860795C211yesmaximal, characteristic, complemented
2C22×#16860793C211yesmaximal, characteristic, complemented
3C2×#22548690C211yesmaximal, characteristic, complemented
4C2×#22548686C211yesmaximal, characteristic, complemented
5#30631939C218yesmaximal, direct product factor
6C2×#22548646C211yesmaximal, characteristic, complemented
7C2×#22548637C211yesmaximal, characteristic, complemented
8C2×#102×C251C211yesmaximal, characteristic, complemented
9C22×D1004—21no—
10C22×D1004C2211yescharacteristic
11C22×C22⋊D251—21no—
12C22×C4×D251C2211yescharacteristic
13C2×#16860795—24no—
14C2×#16860795C2214yescomplemented
15C2×#16860793—24no—
16C2×#16860793C2214yescomplemented
17C22×C251⋊C8C2211yescharacteristic
18#22548690—22no—
19#22548690C2214yescomplemented
20#22548686—22no—
21#22548686C2214yescomplemented
22C2×C4⋊Dic251C2211yescharacteristic
23C2×C22⋊Dic251—21no—
24C2×(C2×D251)⋊C4—21no—
25#22548646C2214yescomplemented
26#22548637C2214yescomplemented
27C22×D4×C251C2211yescharacteristic
28C22×C8×C251C2211yescharacteristic
29C2×C4⋊C4×C251C2211yescharacteristic
30#102×C251C2214yescomplemented
31C23×D251—21no—
32C23×D251D411yescharacteristic
33C2×D1004—24no—
34C2×D1004—22no—
35C2×D1004—21no—
36C2×D1004—22no—
37C2×D1004—44no—
38C2×D1004C2312yes—
39C2×C22⋊D251—24no—
40C2×C22⋊D251—44no—
41C22×Dic251—21no—
42C22×Dic251D411yescharacteristic
43C2×C4×D251—22no—
44C2×C4×D251—22no—
45C2×C4×D251D412yes—
46C2×C4×D251C2312yes—
47#16860795—28no—
48#16860793—28no—
49C2×C251⋊C8D414yescomplemented
50C2×C251⋊C8C2312yes—
51C4⋊Dic251—21no—
52C4⋊Dic251C2312yes—
53C22⋊Dic251—24no—
54(C2×D251)⋊C4—24no—
55C24×C251—21no—
56C2×D4×C251—22no—
57C2×D4×C251—21no—
58C2×D4×C251—22no—
59C2×D4×C251C2312yes—
60C22×C4×C251—21no—
61C22×C4×C251C2311yescharacteristic
62C2×C8×C251—22no—
63C2×C8×C251C2312yes—
64C4⋊C4×C251—21no—
65C4⋊C4×C251C2312yes—
66C22×D251—22no—
67C22×D251—22no—
68C22×D251—22no—
69C22×D251—22no—
70C22×D251—42no—
71C22×D251—42no—
72C22×D251—42no—
73C22×D251C2×D412yes—
74D1004—22no—
75D1004—22no—
76D1004—48no—
77D1004—42no—
78C22⋊D251—48no—
79C2×Dic251—22no—
80C2×Dic251—22no—
81C2×Dic251—42no—
82C2×Dic251C2×D412yes—
83C4×D251—24no—
84C4×D251—22no—
85C4×D251—22no—
86C251⋊C8C2×D414yescomplemented
87C23×C251—22no—
88C23×C251—42no—
89C23×C251—42no—
90C23×C251—42no—
91C23×C251C2×D411yescharacteristic
92D4×C251—22no—
93D4×C251—22no—
94D4×C251—42no—
95C2×C4×C251—22no—
96C2×C4×C251—42no—
97C2×C4×C251C2×D411yescharacteristic
98C2×C4×C251C2×D412yes—
99C2×C4×C251#4112yes—
100C2×C4×C251C2411yescharacteristic
101C8×C251—22no—
102C22×C251—42no—
103C22×C251—42no—
104C22×C251—42no—
105C22×C251—84no—
106C22×C251#12112yes—
107C22×C251AGL(1,ℤ/8)12yes—
108C22×C251AGL(1,ℤ/8)12yes—
109C22×C251C22×D411yescharacteristic
110C2×D251—22no—
111C2×D251—22no—
112C2×D251—22no—
113C2×D251—44no—
114C2×D251—42no—
115C2×D251—42no—
116C2×D251—42no—
117C2×D251—84no—
118C4×C251—42no—
119C4×C251#12112yes—
120C4×C251C22×D411yescharacteristic
121C4×C251C2×#4111yescharacteristic
122Dic251—22no—
123Dic251—42no—
124C2×C251—82no—
125C2×C251#46914yescomplemented
126C2×C251C2×#12111yescharacteristic
127C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
129D251—42no—
130D251—82no—
131C251C2×#46911yescharacteristic, complemented, Sylow
132C2×#469—2511nomaximal, Sylow
133C22×D8—2511no—
134C22×M16—2511no—
135C2×#121—2511no—
136C2×#121—2511no—
137#469—2518no—
138C2×#106—2511no—
139C2×#102—2511no—
140C2×#102D25111yescharacteristic, complemented
141C22×D4—5021no—
142C22×D4—5021no—
143C22×D4—2511no—
144C22×D4C2×D25111yescharacteristic
145C23×C4—2511no—
146C2×D8—5024no—
147C2×D8—2514no—
148C2×M16—5024no—
149C2×M16—2514no—
150C22×C8—2511no—
151C22×C8C2×D25111yescharacteristic
152#121—5022no—
153#121—5022no—
154#121—2514no—
155#121—2514no—
156C2×C4⋊C4—2511no—
157C2×C4⋊C4C2×D25111yescharacteristic
158C2×C22⋊C4—5021no—
159C2×C22⋊C4—5021no—
160#106—2514no—
161#102—2514no—
162#102C2×D25114yescomplemented
163C24—21no—
164C24—5021no—
165C24—2511no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—10044no—
170C2×D4—10044no—
171C2×D4—5024no—
172C2×D4—5024no—
173C2×D4—5021no—
174C2×D4—5022no—
175C2×D4—5022no—
176C2×D4—2512no—
177C2×D4C22×D25112yes—
178C22×C4—21no—
179C22×C4—5021no—
180C22×C4—5022no—
181C22×C4—5022no—
182C22×C4—2511no—
183C22×C4—2512no—
184C22×C4—2512no—
185C22×C4C22×D25111yescharacteristic
186D8—5028no—
187M16—5028no—
188C2×C8—22no—
189C2×C8—2514no—
190C2×C8—2512no—
191C2×C8C22×D25112yes—
192C4⋊C4—21no—
193C4⋊C4—5021no—
194C4⋊C4—2512no—
195C4⋊C4C22×D25112yes—
196C22⋊C4—5024no—
197C22⋊C4—5024no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—10042no—
203C23—10042no—
204C23—10042no—
205C23—5022no—
206C23—5022no—
207C23—5022no—
208C23—5022no—
209C23—2512no—
210C23D4×D25111yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—10048no—
215D4—10048no—
216D4—10042no—
217D4—5022no—
218D4—5022no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—10042no—
222C2×C4—5022no—
223C2×C4—5022no—
224C2×C4—5022no—
225C2×C4—5022no—
226C2×C4—5024no—
227C2×C4—2512no—
228C2×C4D4×D25112yes—
229C2×C4D4×D25111yescharacteristic
230C2×C4#1686081012yes—
231C2×C4C23×D25111yescharacteristic
232C8—22no—
233C8—2514no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—20084no—
239C22—10042no—
240C22—10042no—
241C22—10042no—
242C22—10044no—
243C22—5022no—
244C22—5022no—
245C22—5022no—
246C22#2254868812yes—
247C22#2254873912yes—
248C22#2254874212yes—
249C22C2×D4×D25111yescharacteristic
250C4—42no—
251C4—10042no—
252C4—5022no—
253C4#2254868812yes—
254C4C2×D4×D25111yescharacteristic
255C4C2×#1686081011yescharacteristic
256C2—82no—
257C2—20082no—
258C2—10042no—
259C2#3063193914yesdirect product factor
260C2C2×#2254868811yescharacteristic
261C2C2×#2254873911yescharacteristic
262C2C2×#2254874211yescharacteristic
subgroupG/H
centerC23D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC2×#102×C251C2
socleC23×C251C2×D4
hypercenterC2×#102D251
hypocenterC251C2×#469
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#16860795C2semidirect
2. C22×#16860793C2semidirect
3. C2×#22548690C2semidirect
4. C2×#22548686C2semidirect
5. #30631939C2direct (N × H)
6. C2×#22548646C2semidirect
7. C2×#22548637C2semidirect
8. C2×#102×C251C2semidirect
14. C2×#16860795C22semidirect
16. C2×#16860793C22semidirect
19. #22548690C22semidirect
21. #22548686C22semidirect
25. #22548646C22semidirect
26. #22548637C22semidirect
30. #102×C251C22semidirect
49. C2×C251⋊C8D4semidirect
86. C251⋊C8C2×D4semidirect
125. C2×C251#469semidirect
131. C251C2×#469semidirect
140. C2×#102D251semidirect
162. #102C2×D251semidirect
259. C2#30631939direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168607952
C22×#168607932
C2×#225486902
C2×#225486862
#306319392
C2×#225486462
C2×#225486372
C2×#102×C2512
C2×#469251