Finite Group Databasebeta

← C2×#30631827 #44559554

Subgroups — C2×#30631827 #44559554

Order 32128.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D251C211yesmaximal, characteristic, complemented
2C22×#16860799C211yesmaximal, characteristic, complemented
3C22×#16860797C211yesmaximal, characteristic, complemented
4C2×#22548690C211yesmaximal, characteristic
5#30631827C218yesmaximal, direct product factor
6C2×#22548638C211yesmaximal, characteristic, complemented
7C2×(C2×D251)⋊C8C211yesmaximal, characteristic, complemented
8C2×#103×C251C211yesmaximal, characteristic, complemented
9C22×Dic502—21no—
10C22×Dic502C2211yescharacteristic
11C2×Q8×D251—24no—
12C2×Q8×D251—22no—
13C2×Q8×D251—24no—
14C2×Q8×D251C2214yescomplemented
15C22×D1004—21no—
16C22×D1004C2211yescharacteristic
17C22×C4×D251—21no—
18C22×C4×D251C2211yescharacteristic
19C2×#16860799—24no—
20C2×#16860799C2214yescomplemented
21C2×#16860797—24no—
22C2×#16860797C2214yescomplemented
23C22×C251⋊C8C2211yescharacteristic
24#22548690—22no—
25#22548690C2214yes—
26C2×(C2×D251)⋊C4—21no—
27#22548638C2214yescomplemented
28(C2×D251)⋊C8C2214yescomplemented
29C22×Q8×C251C2211yescharacteristic
30C22×C8×C251C2211yescharacteristic
31C2×C4⋊C4×C251C2211yescharacteristic
32#103×C251C2214yescomplemented
33C23×D251—21no—
34C23×D251D411yescharacteristic
35C2×Dic502—28no—
36C2×Dic502—24no—
37C2×Dic502—21no—
38C2×Dic502—22no—
39C2×Dic502D414yescomplemented
40C2×Dic502C2312yes—
41Q8×D251—216no—
42Q8×D251—28no—
43Q8×D251—28no—
44C2×D1004—24no—
45C2×D1004—22no—
46C2×D1004—22no—
47C2×D1004—21no—
48C2×D1004—44no—
49C2×D1004C2312yes—
50C22×Dic251—21no—
51C22×Dic251D411yescharacteristic
52C2×C4×D251—28no—
53C2×C4×D251—24no—
54C2×C4×D251—22no—
55C2×C4×D251—22no—
56C2×C4×D251D412yes—
57C2×C4×D251C2312yes—
58#16860799—28no—
59#16860797—28no—
60C2×C251⋊C8—22no—
61C2×C251⋊C8C2312yes—
62(C2×D251)⋊C4—24no—
63C2×Q8×C251—22no—
64C2×Q8×C251—21no—
65C2×Q8×C251D414yescomplemented
66C2×Q8×C251C2312yes—
67C22×C4×C251—21no—
68C22×C4×C251—21no—
69C22×C4×C251C2311yescharacteristic
70C2×C8×C251—22no—
71C2×C8×C251C2312yes—
72C4⋊C4×C251—21no—
73C4⋊C4×C251C2312yes—
74C22×D251—22no—
75C22×D251—22no—
76C22×D251—22no—
77C22×D251—42no—
78C22×D251—42no—
79C22×D251—42no—
80C22×D251SD1614yescomplemented
81C22×D251C2×D412yes—
82Dic502—216no—
83Dic502—24no—
84Dic502—22no—
85Dic502C2×D414yescomplemented
86D1004—22no—
87D1004—22no—
88D1004—48no—
89D1004—42no—
90C2×Dic251—24no—
91C2×Dic251—22no—
92C2×Dic251—22no—
93C2×Dic251C2×D412yes—
94C4×D251—216no—
95C4×D251—24no—
96C4×D251—22no—
97C4×D251—22no—
98C251⋊C8—22no—
99C23×C251C2×D411yescharacteristic
100Q8×C251—24no—
101Q8×C251—22no—
102Q8×C251C2×D414yescomplemented
103C2×C4×C251—24no—
104C2×C4×C251—22no—
105C2×C4×C251—22no—
106C2×C4×C251—42no—
107C2×C4×C251C2×D411yescharacteristic
108C2×C4×C251C2×D412yes—
109C2×C4×C251C2×D412yes—
110C2×C4×C251C2411yescharacteristic
111C8×C251—22no—
112C22×C251#12012yes—
113C22×C251C2×SD1612yes—
114C22×C251#13712yes—
115C22×C251C22×D411yescharacteristic
116C2×D251—22no—
117C2×D251—22no—
118C2×D251—28no—
119C2×D251—42no—
120C2×D251—42no—
121C2×D251—42no—
122C2×D251—84no—
123C2×D251C2×SD1614yescomplemented
124C4×C251—24no—
125C4×C251—42no—
126C4×C251#12012yes—
127C4×C251C22×D411yescharacteristic
128C4×C251C22×D411yescharacteristic
129Dic251—24no—
130Dic251—22no—
131C2×C251#44814yescomplemented
132C2×C251C2×#12011yescharacteristic
133C2×C251C22×SD1611yescharacteristic
134C2×C251C2×#13711yescharacteristic
135D251—24no—
136D251—82no—
137C251C2×#44811yescharacteristic, complemented, Sylow
138C2×#448—2511nomaximal, Sylow
139C23×Q8—2511no—
140C22×SD16—2511no—
141C22×SD16—2511no—
142C2×#121—2511no—
143#448—2518no—
144C2×#103—2511no—
145C2×#103D25111yescharacteristic, complemented
146C2×C22⋊C8—2511no—
147C22×Q8—5021no—
148C22×Q8—5024no—
149C22×Q8—5024no—
150C22×Q8—5022no—
151C22×Q8—2514no—
152C22×Q8—2511no—
153C22×Q8C2×D25111yescharacteristic
154C22×D4—5021no—
155C22×D4—2511no—
156C23×C4—5021no—
157C23×C4—2511no—
158C2×SD16—5024no—
159C2×SD16—5024no—
160C2×SD16—2514no—
161C2×SD16—2514no—
162C22×C8—2511no—
163C22×C8C2×D25111yescharacteristic
164#121—5022no—
165#121—2514no—
166C2×C4⋊C4C2×D25111yescharacteristic
167C2×C22⋊C4—5021no—
168#103—2514no—
169#103C2×D25114yescomplemented
170C22⋊C8—2514no—
171C24—5021no—
172C24—2511no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—5028no—
176C2×Q8—5024no—
177C2×Q8—50216no—
178C2×Q8—5028no—
179C2×Q8—5028no—
180C2×Q8—5021no—
181C2×Q8—5022no—
182C2×Q8—2514no—
183C2×Q8—2512no—
184C2×Q8D100414yescomplemented
185C2×Q8C22×D25112yes—
186C2×D4—10044no—
187C2×D4—5024no—
188C2×D4—5021no—
189C2×D4—5022no—
190C2×D4—5022no—
191C2×D4—2512no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—5028no—
195C22×C4—5024no—
196C22×C4—5021no—
197C22×C4—5022no—
198C22×C4—5022no—
199C22×C4—2511no—
200C22×C4—2512no—
201C22×C4—2512no—
202C22×C4C22×D25111yescharacteristic
203SD16—5028no—
204SD16—5028no—
205C2×C8—22no—
206C2×C8—5022no—
207C2×C8—2512no—
208C2×C8C22×D25112yes—
209C4⋊C4—21no—
210C4⋊C4C22×D25112yes—
211C22⋊C4—5024no—
212C23—10042no—
213C23—10042no—
214C23—10042no—
215C23—5022no—
216C23—5022no—
217C23—5022no—
218C23—2512no—
219C23—2514no—
220C23D4×D25111yescharacteristic
221Q8—22no—
222Q8—24no—
223Q8—50216no—
224Q8—5022no—
225Q8—5024no—
226Q8—2514no—
227Q8C2×D100414yescomplemented
228D4—10048no—
229D4—10042no—
230D4—5022no—
231D4—5022no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—50216no—
237C2×C4—5022no—
238C2×C4—5024no—
239C2×C4—5022no—
240C2×C4—5022no—
241C2×C4—5022no—
242C2×C4—5024no—
243C2×C4—2512no—
244C2×C4D4×D25112yes—
245C2×C4D4×D25111yescharacteristic
246C2×C4C2×D100412yes—
247C2×C4C23×D25111yescharacteristic
248C8—22no—
249C8—5022no—
250C22—20084no—
251C22—10042no—
252C22—10042no—
253C22—10042no—
254C22—5022no—
255C22—5028no—
256C22—5022no—
257C22—2514no—
258C22#2254868512yes—
259C22SD16×D25112yes—
260C22#2254874712yes—
261C22C2×D4×D25111yescharacteristic
262C4—24no—
263C4—42no—
264C4—5024no—
265C4—5022no—
266C4#2254868512yes—
267C4C2×D4×D25111yescharacteristic
268C4C22×D100411yescharacteristic
269C2—20082no—
270C2—5024no—
271C2#3063182714yesdirect product factor
272C2C2×#2254868511yescharacteristic
273C2C2×SD16×D25111yescharacteristic
274C2C2×#2254874711yescharacteristic
subgroupG/H
centerC23D4×D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
FittingC2×#103×C251C2
socleC23×C251C2×D4
prime radicalC2×#22548690C2
hypercenterC2×#103D251
hypocenterC251C2×#448
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×Q8×D251C2semidirect
2. C22×#16860799C2semidirect
3. C22×#16860797C2semidirect
5. #30631827C2direct (N × H)
6. C2×#22548638C2semidirect
7. C2×(C2×D251)⋊C8C2semidirect
8. C2×#103×C251C2semidirect
14. C2×Q8×D251C22semidirect
20. C2×#16860799C22semidirect
22. C2×#16860797C22semidirect
27. #22548638C22semidirect
28. (C2×D251)⋊C8C22semidirect
32. #103×C251C22semidirect
39. C2×Dic502D4semidirect
65. C2×Q8×C251D4semidirect
80. C22×D251SD16semidirect
85. Dic502C2×D4semidirect
102. Q8×C251C2×D4semidirect
123. C2×D251C2×SD16semidirect
131. C2×C251#448semidirect
137. C251C2×#448semidirect
145. C2×#103D251semidirect
169. #103C2×D251semidirect
184. C2×Q8D1004semidirect
227. Q8C2×D1004semidirect
271. C2#30631827direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D2512
C22×#168607992
C22×#168607972
C2×#225486902
#306318272
C2×#225486382
C2×(C2×D251)⋊C82
C2×#103×C2512
C2×#448251