Finite Group Databasebeta

← C2×#30631934 #44559954

Subgroups — C2×#30631934 #44559954

Order 32128.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16860799C211yesmaximal, characteristic, complemented
2C22×#16860793C211yesmaximal, characteristic, complemented
3C2×#22548695C211yesmaximal, characteristic, complemented
4C2×#22548690C211yesmaximal, characteristic
5#30631934C218yesmaximal, direct product factor
6C2×#22548638C211yesmaximal, characteristic, complemented
7C2×#22548635C211yesmaximal, characteristic, complemented
8C2×#107×C251C211yesmaximal, characteristic, complemented
9C22×Dic502C2211yescharacteristic
10C22×D1004—21no—
11C22×D1004C2211yescharacteristic
12C22×C4×D251C2211yescharacteristic
13C2×#16860799—24no—
14C2×#16860799C2214yescomplemented
15C2×#16860793—24no—
16C2×#16860793C2214yescomplemented
17C22×C251⋊C8C2211yescharacteristic
18#22548695—22no—
19#22548695C2214yescomplemented
20#22548690—22no—
21#22548690C2214yes—
22C2×C4⋊Dic251—21no—
23C2×(C2×D251)⋊C4—21no—
24C2×(C2×D251)⋊C4—21no—
25#22548638C2214yescomplemented
26#22548635C2214yescomplemented
27C22×C8×C251C2211yescharacteristic
28C2×C4⋊C4×C251C2211yescharacteristic
29C2×C4⋊C4×C251C2211yescharacteristic
30#107×C251C2214yescomplemented
31C23×D251—21no—
32C23×D251D411yescharacteristic
33C2×Dic502—21no—
34C2×Dic502—22no—
35C2×Dic502—22no—
36C2×Dic502C2312yes—
37C2×D1004—24no—
38C2×D1004—22no—
39C2×D1004—21no—
40C2×D1004—22no—
41C2×D1004—44no—
42C2×D1004C2312yes—
43C22×Dic251—21no—
44C22×Dic251D411yescharacteristic
45C2×C4×D251—22no—
46C2×C4×D251—22no—
47C2×C4×D251D412yes—
48C2×C4×D251C2312yes—
49#16860799—28no—
50#16860793—28no—
51C2×C251⋊C8—22no—
52C2×C251⋊C8C2312yes—
53C4⋊Dic251—24no—
54(C2×D251)⋊C4—24no—
55(C2×D251)⋊C4—24no—
56C22×C4×C251—21no—
57C22×C4×C251—21no—
58C22×C4×C251C2311yescharacteristic
59C2×C8×C251D414yescomplemented
60C2×C8×C251C2312yes—
61C4⋊C4×C251—21no—
62C4⋊C4×C251—21no—
63C4⋊C4×C251C2312yes—
64C4⋊C4×C251C2312yes—
65C22×D251—22no—
66C22×D251—22no—
67C22×D251—22no—
68C22×D251—22no—
69C22×D251—42no—
70C22×D251—42no—
71C22×D251—42no—
72C22×D251C2×D412yes—
73Dic502—22no—
74Dic502—22no—
75Dic502—42no—
76D1004—22no—
77D1004—22no—
78D1004—48no—
79D1004—42no—
80C2×Dic251—22no—
81C2×Dic251—22no—
82C2×Dic251—42no—
83C2×Dic251C2×D412yes—
84C4×D251—24no—
85C4×D251—22no—
86C4×D251—22no—
87C251⋊C8—22no—
88C23×C251C2×D411yescharacteristic
89C2×C4×C251—22no—
90C2×C4×C251—22no—
91C2×C4×C251—42no—
92C2×C4×C251—42no—
93C2×C4×C251C2×D411yescharacteristic
94C2×C4×C251C2×D412yes—
95C2×C4×C251#4112yes—
96C2×C4×C251C2411yescharacteristic
97C8×C251C2×D414yescomplemented
98C22×C251#12112yes—
99C22×C251AGL(1,ℤ/8)12yes—
100C22×C251#13712yes—
101C22×C251C22×D411yescharacteristic
102C2×D251—22no—
103C2×D251—22no—
104C2×D251—22no—
105C2×D251—44no—
106C2×D251—42no—
107C2×D251—42no—
108C2×D251—42no—
109C2×D251—84no—
110C4×C251—42no—
111C4×C251—42no—
112C4×C251#12112yes—
113C4×C251C22×D411yescharacteristic
114C4×C251C2×#4111yescharacteristic
115Dic251—22no—
116Dic251—42no—
117C2×C251#46814yescomplemented
118C2×C251C2×#12111yescharacteristic
119C2×C251C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C251C2×#13711yescharacteristic
121D251—42no—
122D251—82no—
123C251C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2511nomaximal, Sylow
125C22×SD16—2511no—
126C22×M16—2511no—
127C2×C22⋊Q8—2511no—
128C2×#121—2511no—
129#468—2518no—
130C2×#107D25111yescharacteristic, complemented
131C2×#103—2511no—
132C2×#102—2511no—
133C22×Q8—2511no—
134C22×D4—5021no—
135C22×D4—2511no—
136C23×C4—2511no—
137C2×SD16—5024no—
138C2×SD16—2514no—
139C2×M16—5024no—
140C2×M16—2514no—
141C22×C8—2511no—
142C22×C8C2×D25111yescharacteristic
143C22⋊Q8—5022no—
144C22⋊Q8—2514no—
145#121—5022no—
146#121—2514no—
147C2×C4⋊C4—5021no—
148C2×C4⋊C4C2×D25111yescharacteristic
149C2×C4⋊C4C2×D25111yescharacteristic
150C2×C22⋊C4—5021no—
151C2×C22⋊C4—5021no—
152#107C2×D25114yescomplemented
153#103—2514no—
154#102—2514no—
155C24—5021no—
156C24—2511no—
157C2×Q8—5022no—
158C2×Q8—5022no—
159C2×Q8—5021no—
160C2×Q8—2512no—
161C2×D4—10044no—
162C2×D4—5024no—
163C2×D4—5021no—
164C2×D4—5022no—
165C2×D4—5022no—
166C2×D4—2512no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—5021no—
170C22×C4—5022no—
171C22×C4—5022no—
172C22×C4—2511no—
173C22×C4—2512no—
174C22×C4—2512no—
175C22×C4C22×D25111yescharacteristic
176SD16—5028no—
177M16—5028no—
178C2×C8—5022no—
179C2×C8—2512no—
180C2×C8D100414yescomplemented
181C2×C8C22×D25112yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—5024no—
185C4⋊C4C22×D25112yes—
186C4⋊C4C22×D25112yes—
187C22⋊C4—5024no—
188C22⋊C4—5024no—
189C23—10042no—
190C23—10042no—
191C23—10042no—
192C23—5022no—
193C23—5022no—
194C23—5022no—
195C23—5022no—
196C23—2512no—
197C23D4×D25111yescharacteristic
198Q8—10042no—
199Q8—5022no—
200Q8—5022no—
201D4—10048no—
202D4—10042no—
203D4—5022no—
204D4—5022no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—10042no—
210C2×C4—5022no—
211C2×C4—5022no—
212C2×C4—5022no—
213C2×C4—5022no—
214C2×C4—5024no—
215C2×C4—2512no—
216C2×C4D4×D25111yescharacteristic
217C2×C4C2×D100412yes—
218C2×C4#1686081112yes—
219C2×C4C23×D25111yescharacteristic
220C8—5022no—
221C8C2×D100414yescomplemented
222C22—20084no—
223C22—10042no—
224C22—10042no—
225C22—10042no—
226C22—10044no—
227C22—5022no—
228C22—5022no—
229C22—5022no—
230C22#2254869012yes—
231C22#2254873912yes—
232C22#2254874712yes—
233C22C2×D4×D25111yescharacteristic
234C4—42no—
235C4—42no—
236C4—10042no—
237C4—5022no—
238C4#2254869012yes—
239C4C22×D100411yescharacteristic
240C4C2×#1686081111yescharacteristic
241C2—20082no—
242C2—10042no—
243C2#3063193414yesdirect product factor
244C2C2×#2254869011yescharacteristic
245C2C2×#2254873911yescharacteristic
246C2C2×#2254874711yescharacteristic
subgroupG/H
centerC23D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC2×#107×C251C2
socleC23×C251C2×D4
prime radicalC2×#22548690C2
hypercenterC2×#107D251
hypocenterC251C2×#468
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#16860799C2semidirect
2. C22×#16860793C2semidirect
3. C2×#22548695C2semidirect
5. #30631934C2direct (N × H)
6. C2×#22548638C2semidirect
7. C2×#22548635C2semidirect
8. C2×#107×C251C2semidirect
14. C2×#16860799C22semidirect
16. C2×#16860793C22semidirect
19. #22548695C22semidirect
25. #22548638C22semidirect
26. #22548635C22semidirect
30. #107×C251C22semidirect
59. C2×C8×C251D4semidirect
97. C8×C251C2×D4semidirect
117. C2×C251#468semidirect
123. C251C2×#468semidirect
130. C2×#107D251semidirect
152. #107C2×D251semidirect
180. C2×C8D1004semidirect
221. C8C2×D1004semidirect
243. C2#30631934direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168607992
C22×#168607932
C2×#225486952
C2×#225486902
#306319342
C2×#225486382
C2×#225486352
C2×#107×C2512
C2×#468251