Finite Group Databasebeta

← C2×#31826605 #49130450

Subgroups — C2×#31826605 #49130450

Order 36224.

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×D283C211yesmaximal, characteristic, complemented
2C22×#17985381C211yesmaximal, characteristic, complemented
3C22×#17985379C211yesmaximal, characteristic, complemented
4C2×#22583585C211yesmaximal, characteristic
5#31826605C218yesmaximal, direct product factor
6C2×#22583533C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C2×#103×C283C211yesmaximal, characteristic, complemented
9C22×Dic566—21no—
10C22×Dic566C2211yescharacteristic
11C2×Q8×D283—24no—
12C2×Q8×D283—22no—
13C2×Q8×D283—24no—
14C2×Q8×D283C2214yescomplemented
15C22×D1132—21no—
16C22×D1132C2211yescharacteristic
17C22×C4×D283—21no—
18C22×C4×D283C2211yescharacteristic
19C2×#17985381—24no—
20C2×#17985381C2214yescomplemented
21C2×#17985379—24no—
22C2×#17985379C2214yescomplemented
23C22×C283⋊C8C2211yescharacteristic
24#22583585—22no—
25#22583585C2214yes—
26C2×(C2×D283)⋊C4—21no—
27#22583533C2214yescomplemented
28(C2×D283)⋊C8C2214yescomplemented
29C22×Q8×C283C2211yescharacteristic
30C22×C8×C283C2211yescharacteristic
31C2×C4⋊C4×C283C2211yescharacteristic
32#103×C283C2214yescomplemented
33C23×D283—21no—
34C23×D283D411yescharacteristic
35C2×Dic566—28no—
36C2×Dic566—24no—
37C2×Dic566—21no—
38C2×Dic566—22no—
39C2×Dic566D414yescomplemented
40C2×Dic566C2312yes—
41Q8×D283—216no—
42Q8×D283—28no—
43Q8×D283—28no—
44C2×D1132—24no—
45C2×D1132—22no—
46C2×D1132—22no—
47C2×D1132—21no—
48C2×D1132—44no—
49C2×D1132C2312yes—
50C22×Dic283—21no—
51C22×Dic283D411yescharacteristic
52C2×C4×D283—28no—
53C2×C4×D283—24no—
54C2×C4×D283—22no—
55C2×C4×D283—22no—
56C2×C4×D283D412yes—
57C2×C4×D283C2312yes—
58#17985381—28no—
59#17985379—28no—
60C2×C283⋊C8—22no—
61C2×C283⋊C8C2312yes—
62(C2×D283)⋊C4—24no—
63C2×Q8×C283—22no—
64C2×Q8×C283—21no—
65C2×Q8×C283D414yescomplemented
66C2×Q8×C283C2312yes—
67C22×C4×C283—21no—
68C22×C4×C283—21no—
69C22×C4×C283C2311yescharacteristic
70C2×C8×C283—22no—
71C2×C8×C283C2312yes—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2312yes—
74C22×D283—22no—
75C22×D283—22no—
76C22×D283—22no—
77C22×D283—42no—
78C22×D283—42no—
79C22×D283—42no—
80C22×D283SD1614yescomplemented
81C22×D283C2×D412yes—
82Dic566—216no—
83Dic566—24no—
84Dic566—22no—
85Dic566C2×D414yescomplemented
86D1132—22no—
87D1132—22no—
88D1132—48no—
89D1132—42no—
90C2×Dic283—24no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283C2×D412yes—
94C4×D283—216no—
95C4×D283—24no—
96C4×D283—22no—
97C4×D283—22no—
98C283⋊C8—22no—
99C23×C283C2×D411yescharacteristic
100Q8×C283—24no—
101Q8×C283—22no—
102Q8×C283C2×D414yescomplemented
103C2×C4×C283—24no—
104C2×C4×C283—22no—
105C2×C4×C283—22no—
106C2×C4×C283—42no—
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2×D412yes—
109C2×C4×C283C2×D412yes—
110C2×C4×C283C2411yescharacteristic
111C8×C283—22no—
112C22×C283#12012yes—
113C22×C283C2×SD1612yes—
114C22×C283#13712yes—
115C22×C283C22×D411yescharacteristic
116C2×D283—22no—
117C2×D283—22no—
118C2×D283—28no—
119C2×D283—42no—
120C2×D283—42no—
121C2×D283—42no—
122C2×D283—84no—
123C2×D283C2×SD1614yescomplemented
124C4×C283—24no—
125C4×C283—42no—
126C4×C283#12012yes—
127C4×C283C22×D411yescharacteristic
128C4×C283C22×D411yescharacteristic
129Dic283—24no—
130Dic283—22no—
131C2×C283#44814yescomplemented
132C2×C283C2×#12011yescharacteristic
133C2×C283C22×SD1611yescharacteristic
134C2×C283C2×#13711yescharacteristic
135D283—24no—
136D283—82no—
137C283C2×#44811yescharacteristic, complemented, Sylow
138C2×#448—2831nomaximal, Sylow
139C23×Q8—2831no—
140C22×SD16—2831no—
141C22×SD16—2831no—
142C2×#121—2831no—
143#448—2838no—
144C2×#103—2831no—
145C2×#103D28311yescharacteristic, complemented
146C2×C22⋊C8—2831no—
147C22×Q8—2834no—
148C22×Q8—2831no—
149C22×Q8—5661no—
150C22×Q8—5662no—
151C22×Q8—5664no—
152C22×Q8—5664no—
153C22×Q8C2×D28311yescharacteristic
154C22×D4—2831no—
155C22×D4—5661no—
156C23×C4—2831no—
157C23×C4—5661no—
158C2×SD16—2834no—
159C2×SD16—2834no—
160C2×SD16—5664no—
161C2×SD16—5664no—
162C22×C8—2831no—
163C22×C8C2×D28311yescharacteristic
164#121—2834no—
165#121—5662no—
166C2×C4⋊C4C2×D28311yescharacteristic
167C2×C22⋊C4—5661no—
168#103—2834no—
169#103C2×D28314yescomplemented
170C22⋊C8—2834no—
171C24—2831no—
172C24—5661no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—2834no—
176C2×Q8—2832no—
177C2×Q8—5664no—
178C2×Q8—5668no—
179C2×Q8—5668no—
180C2×Q8—56616no—
181C2×Q8—5668no—
182C2×Q8—5661no—
183C2×Q8—5662no—
184C2×Q8D113214yescomplemented
185C2×Q8C22×D28312yes—
186C2×D4—2832no—
187C2×D4—5664no—
188C2×D4—5662no—
189C2×D4—5661no—
190C2×D4—5662no—
191C2×D4—11324no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—2831no—
195C22×C4—2832no—
196C22×C4—2832no—
197C22×C4—5664no—
198C22×C4—5668no—
199C22×C4—5661no—
200C22×C4—5662no—
201C22×C4—5662no—
202C22×C4C22×D28311yescharacteristic
203SD16—5668no—
204SD16—5668no—
205C2×C8—22no—
206C2×C8—2832no—
207C2×C8—5662no—
208C2×C8C22×D28312yes—
209C4⋊C4—21no—
210C4⋊C4C22×D28312yes—
211C22⋊C4—5664no—
212C23—2834no—
213C23—2832no—
214C23—5662no—
215C23—5662no—
216C23—5662no—
217C23—11322no—
218C23—11322no—
219C23—11322no—
220C23D4×D28311yescharacteristic
221Q8—24no—
222Q8—22no—
223Q8—2834no—
224Q8—56616no—
225Q8—5664no—
226Q8—5662no—
227Q8C2×D113214yescomplemented
228D4—5662no—
229D4—5662no—
230D4—11328no—
231D4—11322no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—2832no—
237C2×C4—56616no—
238C2×C4—5662no—
239C2×C4—5664no—
240C2×C4—5662no—
241C2×C4—5664no—
242C2×C4—5662no—
243C2×C4—5662no—
244C2×C4D4×D28311yescharacteristic
245C2×C4D4×D28312yes—
246C2×C4C2×D113212yes—
247C2×C4C23×D28311yescharacteristic
248C8—22no—
249C8—5662no—
250C22—2834no—
251C22—5662no—
252C22—5662no—
253C22—5668no—
254C22—11322no—
255C22—11322no—
256C22—11322no—
257C22—22644no—
258C22#2258358012yes—
259C22SD16×D28312yes—
260C22#2258364212yes—
261C22C2×D4×D28311yescharacteristic
262C4—24no—
263C4—42no—
264C4—5662no—
265C4—5664no—
266C4#2258358012yes—
267C4C2×D4×D28311yescharacteristic
268C4C22×D113211yescharacteristic
269C2—5664no—
270C2—22642no—
271C2#3182660514yesdirect product factor
272C2C2×#2258358011yescharacteristic
273C2C2×SD16×D28311yescharacteristic
274C2C2×#2258364211yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583585C2
hypercenterC2×#103D283
hypocenterC283C2×#448
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D283C2semidirect
2. C22×#17985381C2semidirect
3. C22×#17985379C2semidirect
5. #31826605C2direct (N × H)
6. C2×#22583533C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C2×#103×C283C2semidirect
14. C2×Q8×D283C22semidirect
20. C2×#17985381C22semidirect
22. C2×#17985379C22semidirect
27. #22583533C22semidirect
28. (C2×D283)⋊C8C22semidirect
32. #103×C283C22semidirect
39. C2×Dic566D4semidirect
65. C2×Q8×C283D4semidirect
80. C22×D283SD16semidirect
85. Dic566C2×D4semidirect
102. Q8×C283C2×D4semidirect
123. C2×D283C2×SD16semidirect
131. C2×C283#448semidirect
137. C283C2×#448semidirect
145. C2×#103D283semidirect
169. #103C2×D283semidirect
184. C2×Q8D1132semidirect
227. Q8C2×D1132semidirect
271. C2#31826605direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D2832
C22×#179853812
C22×#179853792
C2×#225835852
#318266052
C2×#225835332
C2×(C2×D283)⋊C82
C2×#103×C2832
C2×#448283