Finite Group Databasebeta

← C2×#31826624 #49130467

Subgroups — C2×#31826624 #49130467

Order 36224.

760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17985391C211yesmaximal, characteristic
2C22×#17985382C211yesmaximal, characteristic, complemented
3C2×#22583586C211yesmaximal, characteristic, complemented
4#31826624C218yesmaximal, direct product factor
5C2×#22583535C211yesmaximal, characteristic, complemented
6C2×#22583531C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C283C211yesmaximal, characteristic, complemented
9C2×#17985391—24no—
10C2×#17985391—22no—
11C2×#17985391—24no—
12C2×#17985391C2214yes—
13C22×Dic566C2211yescharacteristic
14C22×C22⋊D283—21no—
15C23×Dic283—21no—
16C22×C4×D283C2211yescharacteristic
17C2×#17985382—24no—
18C2×#17985382C2214yescomplemented
19C22×C283⋊C8C2211yescharacteristic
20#22583586—22no—
21#22583586C2214yescomplemented
22C2×C4⋊Dic283C2211yescharacteristic
23C2×Dic283⋊C4—21no—
24C2×(C2×D283)⋊C4—21no—
25#22583535C2214yescomplemented
26#22583531C2214yescomplemented
27(C2×D283)⋊C8C2214yescomplemented
28C22×Q8×C283C2211yescharacteristic
29C22×D4×C283C2211yescharacteristic
30C2×SD16×C283—24no—
31C2×SD16×C283C2214yescomplemented
32C22×C8×C283C2211yescharacteristic
33C23×D283D411yescharacteristic
34#17985391—216no—
35#17985391—28no—
36#17985391—28no—
37C2×Dic566—21no—
38C2×Dic566—22no—
39C2×Dic566D414yes—
40C2×Dic566C2312yes—
41C2×C22⋊D283—28no—
42C2×C22⋊D283—24no—
43C22×Dic283—28no—
44C22×Dic283—24no—
45C22×Dic283—21no—
46C22×Dic283—21no—
47C22×Dic283D411yescharacteristic
48C2×C4×D283—22no—
49C2×C4×D283—22no—
50C2×C4×D283D412yes—
51C2×C4×D283C2312yes—
52#17985382—28no—
53C2×C283⋊C8—22no—
54C2×C283⋊C8C2312yes—
55C4⋊Dic283—21no—
56C4⋊Dic283C2312yes—
57Dic283⋊C4—24no—
58(C2×D283)⋊C4—24no—
59C24×C283—21no—
60C2×Q8×C283—21no—
61C2×Q8×C283—22no—
62C2×Q8×C283—22no—
63C2×Q8×C283C2312yes—
64C2×D4×C283—21no—
65C2×D4×C283—22no—
66C2×D4×C283D414yes—
67C2×D4×C283C2312yes—
68C22×C4×C283—21no—
69C22×C4×C283C2311yescharacteristic
70SD16×C283—28no—
71C2×C8×C283—22no—
72C2×C8×C283C2312yes—
73C22×D283—22no—
74C22×D283—22no—
75C22×D283—22no—
76C22×D283C2×D412yes—
77Dic566—24no—
78Dic566—22no—
79Dic566C2×D414yes—
80C22⋊D283—216no—
81C2×Dic283—216no—
82C2×Dic283—22no—
83C2×Dic283—24no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C2×Dic283—42no—
87C2×Dic283C2×D412yes—
88C4×D283—24no—
89C4×D283—22no—
90C4×D283—22no—
91C283⋊C8—22no—
92C23×C283—24no—
93C23×C283—22no—
94C23×C283—42no—
95C23×C283—42no—
96C23×C283C2×D411yescharacteristic
97Q8×C283—22no—
98Q8×C283—22no—
99Q8×C283—42no—
100D4×C283—24no—
101D4×C283—22no—
102D4×C283C2×D414yes—
103C2×C4×C283—22no—
104C2×C4×C283—42no—
105C2×C4×C283C2×D411yescharacteristic
106C2×C4×C283C2×D412yes—
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2411yescharacteristic
109C8×C283—22no—
110C22×C283—24no—
111C22×C283—42no—
112C22×C283—42no—
113C22×C283—48no—
114C22×C283#12012yes—
115C22×C283#13512yes—
116C22×C283#13712yes—
117C22×C283C22×D411yescharacteristic
118C2×D283—22no—
119C2×D283—22no—
120C2×D283—22no—
121C2×D283—44no—
122C4×C283—42no—
123C4×C283#12012yes—
124C4×C283C22×D411yescharacteristic
125C4×C283C22×D411yescharacteristic
126Dic283—22no—
127Dic283—24no—
128Dic283—42no—
129C2×C283—44no—
130C2×C283#45214yescomplemented
131C2×C283C2×#12011yescharacteristic
132C2×C283C2×#13511yescharacteristic
133C2×C283C2×#13711yescharacteristic
134D283—42no—
135C283C2×#45211yescharacteristic, complemented, Sylow
136C2×#452—2831nomaximal, Sylow
137C22×#41—2831no—
138C22×Q16—2831no—
139C22×SD16D28311yescharacteristic, complemented
140C2×C22⋊Q8—2831no—
141#452—2838no—
142C2×#103—2831no—
143C2×#102—2831no—
144C2×C22⋊C8—2831no—
145C2×#41—2834no—
146C2×#41—5662no—
147C2×#41—5664no—
148C2×#41—5664no—
149C22×Q8—2831no—
150C22×Q8C2×D28311yescharacteristic
151C22×D4—5661no—
152C22×D4C2×D28311yescharacteristic
153C23×C4—2831no—
154C23×C4—5661no—
155C2×Q16—2834no—
156C2×Q16—5664no—
157C2×SD16—24no—
158C2×SD16C2×D28314yescomplemented
159C22×C8—2831no—
160C22×C8C2×D28311yescharacteristic
161C22⋊Q8—2834no—
162C22⋊Q8—5662no—
163C2×C4⋊C4—2831no—
164C2×C4⋊C4—5661no—
165C2×C22⋊C4—5661no—
166#103—2834no—
167#102—2834no—
168C22⋊C8—2834no—
169C24—21no—
170C24—2831no—
171#41—5668no—
172#41—56616no—
173#41—5668no—
174C2×Q8—21no—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—2834no—
178C2×Q8—2832no—
179C2×Q8—5661no—
180C2×Q8—5662no—
181C2×Q8C22×D28312yes—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—5664no—
185C2×D4—5668no—
186C2×D4C22⋊D28314yes—
187C2×D4C22×D28312yes—
188C22×C4—21no—
189C22×C4—2831no—
190C22×C4—2832no—
191C22×C4—2832no—
192C22×C4—5664no—
193C22×C4—5668no—
194C22×C4—5661no—
195C22×C4—5662no—
196C22×C4—5662no—
197C22×C4—5661no—
198C22×C4C22×D28311yescharacteristic
199Q16—5668no—
200SD16—28no—
201C2×C8—22no—
202C2×C8—2832no—
203C2×C8—5662no—
204C2×C8C22×D28312yes—
205C4⋊C4—2832no—
206C4⋊C4—5664no—
207C4⋊C4—5661no—
208C22⋊C4—5664no—
209C23—24no—
210C23—22no—
211C23—42no—
212C23—42no—
213C23—2832no—
214C23—5662no—
215C23—5662no—
216C23—5662no—
217C23D4×D28311yescharacteristic
218Q8—22no—
219Q8—22no—
220Q8—42no—
221Q8—2834no—
222Q8—5664no—
223Q8—5662no—
224D4—24no—
225D4—22no—
226D4—56616no—
227D4C2×C22⋊D28314yes—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—2832no—
231C2×C4—56616no—
232C2×C4—5662no—
233C2×C4—5664no—
234C2×C4—5662no—
235C2×C4—5664no—
236C2×C4—5662no—
237C2×C4—5662no—
238C2×C4—5662no—
239C2×C4—11322no—
240C2×C4D4×D28311yescharacteristic
241C2×C4D4×D28312yes—
242C2×C4C2×C22⋊D28312yes—
243C2×C4C23×D28311yescharacteristic
244C8—22no—
245C8—5662no—
246C22—24no—
247C22—42no—
248C22—42no—
249C22—48no—
250C22—5662no—
251C22—5662no—
252C22—5662no—
253C22—11324no—
254C22#2258357812yes—
255C22#2258363112yes—
256C22#2258363912yes—
257C22C2×D4×D28311yescharacteristic
258C4—42no—
259C4—5662no—
260C4—5664no—
261C4—11322no—
262C4#2258357812yes—
263C4C2×D4×D28311yescharacteristic
264C4C22×C22⋊D28311yescharacteristic
265C2—44no—
266C2—11322no—
267C2#3182662414yesdirect product factor
268C2C2×#2258357811yescharacteristic
269C2C2×#2258363111yescharacteristic
270C2C2×#2258363911yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC23×C283C2×D4
prime radicalC22×#17985391C2
hypercenterC22×SD16D283
hypocenterC283C2×#452
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#17985382C2semidirect
3. C2×#22583586C2semidirect
4. #31826624C2direct (N × H)
5. C2×#22583535C2semidirect
6. C2×#22583531C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C22×SD16×C283C2semidirect
18. C2×#17985382C22semidirect
21. #22583586C22semidirect
25. #22583535C22semidirect
26. #22583531C22semidirect
27. (C2×D283)⋊C8C22semidirect
31. C2×SD16×C283C22semidirect
130. C2×C283#452semidirect
135. C283C2×#452semidirect
139. C22×SD16D283semidirect
158. C2×SD16C2×D283semidirect
267. C2#31826624direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853912
C22×#179853822
C2×#225835862
#318266242
C2×#225835352
C2×#225835312
C2×(C2×D283)⋊C82
C22×SD16×C2832
C2×#452283