Finite Group Databasebeta

← C2×#30631936 #44559956

Subgroups — C2×#30631936 #44559956

Order 32128.

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

normal subgroups only

This group has 544 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×#16860797C211yesmaximal, characteristic, complemented
2C22×#16860793C211yesmaximal, characteristic, complemented
3C2×#22548691C211yesmaximal, characteristic, complemented
4C2×#22548690C211yesmaximal, characteristic
5#30631936C218yesmaximal, direct product factor
6C2×#22548648C211yesmaximal, characteristic, complemented
7C2×#22548637C211yesmaximal, characteristic, complemented
8C2×#103×C251C211yesmaximal, characteristic, complemented
9C22×D1004—21no—
10C22×D1004C2211yescharacteristic
11C22×C4×D251C2211yescharacteristic
12C2×#16860797—24no—
13C2×#16860797C2214yescomplemented
14C2×#16860793—24no—
15C2×#16860793C2214yescomplemented
16C22×C251⋊C8C2211yescharacteristic
17#22548691—22no—
18#22548691C2214yescomplemented
19#22548690—22no—
20#22548690C2214yes—
21C2×C4⋊Dic251C2211yescharacteristic
22C2×Dic251⋊C4—21no—
23C2×(C2×D251)⋊C4—21no—
24C2×(C2×D251)⋊C4—21no—
25#22548648C2214yescomplemented
26#22548637C2214yescomplemented
27C22×Q8×C251C2211yescharacteristic
28C22×C8×C251C2211yescharacteristic
29C2×C4⋊C4×C251C2211yescharacteristic
30#103×C251C2214yescomplemented
31C23×D251—21no—
32C23×D251D411yescharacteristic
33C2×D1004—24no—
34C2×D1004—22no—
35C2×D1004—21no—
36C2×D1004—22no—
37C2×D1004—44no—
38C2×D1004C2312yes—
39C22×Dic251—21no—
40C22×Dic251D411yescharacteristic
41C2×C4×D251—22no—
42C2×C4×D251—22no—
43C2×C4×D251D412yes—
44C2×C4×D251C2312yes—
45#16860797—28no—
46#16860793—28no—
47C2×C251⋊C8D414yescomplemented
48C2×C251⋊C8C2312yes—
49C4⋊Dic251—21no—
50C4⋊Dic251C2312yes—
51Dic251⋊C4—24no—
52(C2×D251)⋊C4—24no—
53(C2×D251)⋊C4—24no—
54C2×Q8×C251—21no—
55C2×Q8×C251—22no—
56C2×Q8×C251—22no—
57C2×Q8×C251C2312yes—
58C22×C4×C251—21no—
59C22×C4×C251—21no—
60C22×C4×C251C2311yescharacteristic
61C2×C8×C251—22no—
62C2×C8×C251C2312yes—
63C4⋊C4×C251—21no—
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—
73D1004—22no—
74D1004—22no—
75D1004—48no—
76D1004—42no—
77C2×Dic251—22no—
78C2×Dic251—22no—
79C2×Dic251—42no—
80C2×Dic251C2×D412yes—
81C4×D251—24no—
82C4×D251—22no—
83C4×D251—22no—
84C251⋊C8C2×D414yescomplemented
85C23×C251C2×D411yescharacteristic
86Q8×C251—22no—
87Q8×C251—22no—
88Q8×C251—42no—
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×C251—22no—
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×#107—2511no—
131C2×#103D25111yescharacteristic, complemented
132C2×#102—2511no—
133C22×Q8C2×D25111yescharacteristic
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⋊C4—2511no—
149C2×C4⋊C4C2×D25111yescharacteristic
150C2×C22⋊C4—5021no—
151C2×C22⋊C4—5021no—
152#107—2514no—
153#103C2×D25114yescomplemented
154#102—2514no—
155C24—5021no—
156C24—2511no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D25112yes—
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—22no—
179C2×C8—2514no—
180C2×C8—2512no—
181C2×C8C22×D25112yes—
182C4⋊C4—21no—
183C4⋊C4—5024no—
184C4⋊C4—5021no—
185C4⋊C4—2512no—
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—22no—
199Q8—22no—
200Q8—42no—
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×D25112yes—
217C2×C4D4×D25111yescharacteristic
218C2×C4#1686081012yes—
219C2×C4C23×D25111yescharacteristic
220C8—22no—
221C8—2514no—
222C22—20084no—
223C22—10042no—
224C22—10042no—
225C22—10042no—
226C22—10044no—
227C22—5022no—
228C22—5022no—
229C22—5022no—
230C22#2254868812yes—
231C22#2254874212yes—
232C22#2254874712yes—
233C22C2×D4×D25111yescharacteristic
234C4—42no—
235C4—42no—
236C4—10042no—
237C4—5022no—
238C4#2254868812yes—
239C4C2×D4×D25111yescharacteristic
240C4C2×#1686081011yescharacteristic
241C2—20082no—
242C2—10042no—
243C2#3063193614yesdirect product factor
244C2C2×#2254868811yescharacteristic
245C2C2×#2254874211yescharacteristic
246C2C2×#2254874711yescharacteristic
subgroupG/H
centerC23D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC2×#103×C251C2
socleC23×C251C2×D4
prime radicalC2×#22548690C2
hypercenterC2×#103D251
hypocenterC251C2×#468
LCSG ▷ C2×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
1. C22×#16860797C2semidirect
2. C22×#16860793C2semidirect
3. C2×#22548691C2semidirect
5. #30631936C2direct (N × H)
6. C2×#22548648C2semidirect
7. C2×#22548637C2semidirect
8. C2×#103×C251C2semidirect
13. C2×#16860797C22semidirect
15. C2×#16860793C22semidirect
18. #22548691C22semidirect
25. #22548648C22semidirect
26. #22548637C22semidirect
30. #103×C251C22semidirect
47. C2×C251⋊C8D4semidirect
84. C251⋊C8C2×D4semidirect
117. C2×C251#468semidirect
123. C251C2×#468semidirect
131. C2×#103D251semidirect
153. #103C2×D251semidirect
243. C2#30631936direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168607972
C22×#168607932
C2×#225486912
C2×#225486902
#306319362
C2×#225486482
C2×#225486372
C2×#103×C2512
C2×#468251