Finite Group Databasebeta

← C2×#31826614 #49130441

Subgroups — C2×#31826614 #49130441

Order 36224.

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

normal subgroups only

This group has 996 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×D4×D283C211yesmaximal, characteristic
2C22×#17985379C211yesmaximal, characteristic, complemented
3C2×#22583586C211yesmaximal, characteristic, complemented
4#31826614C218yesmaximal, direct product factor
5C2×#22583532C211yesmaximal, characteristic, complemented
6C2×#22583531C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C283C211yesmaximal, characteristic, complemented
9C24×D283—21no—
10C22×D1132C2211yescharacteristic
11C22×C22⋊D283—21no—
12C2×D4×D283—24no—
13C2×D4×D283—22no—
14C2×D4×D283—24no—
15C2×D4×D283C2214yes—
16C22×C4×D283C2211yescharacteristic
17C2×#17985379—24no—
18C2×#17985379C2214yescomplemented
19C22×C283⋊C8C2211yescharacteristic, complemented
20#22583586—22no—
21#22583586C2214yescomplemented
22C2×C4⋊Dic283C2211yescharacteristic, complemented
23C2×Dic283⋊C4—21no—
24C2×(C2×D283)⋊C4—21no—
25#22583532C2214yescomplemented
26#22583531C2214yescomplemented
27(C2×D283)⋊C8C2214yescomplemented
28C22×Q8×C283C2211yescharacteristic, complemented
29C22×D4×C283C2211yescharacteristic
30C2×SD16×C283—24no—
31C2×SD16×C283C2214yescomplemented
32C22×C8×C283C2211yescharacteristic, complemented
33C23×D283—28no—
34C23×D283—24no—
35C23×D283—21no—
36C23×D283—44no—
37C23×D283—44no—
38C23×D283D411yescharacteristic
39C2×D1132—21no—
40C2×D1132—22no—
41C2×D1132D414yes—
42C2×D1132C2312yes—
43C2×C22⋊D283—28no—
44C2×C22⋊D283—24no—
45D4×D283—216no—
46D4×D283—28no—
47D4×D283—28no—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C2×C4×D283—22no—
51C2×C4×D283—22no—
52C2×C4×D283D412yes—
53C2×C4×D283C2312yes—
54#17985379—28no—
55C2×C283⋊C8—22no—
56C2×C283⋊C8C2312yescomplemented
57C4⋊Dic283—21no—
58C4⋊Dic283C2312yescomplemented
59Dic283⋊C4—24no—
60(C2×D283)⋊C4—24no—
61C24×C283—21no—
62C2×Q8×C283—21no—
63C2×Q8×C283—22no—
64C2×Q8×C283—22no—
65C2×Q8×C283C2312yescomplemented
66C2×D4×C283—21no—
67C2×D4×C283—22no—
68C2×D4×C283D414yes—
69C2×D4×C283C2312yes—
70C22×C4×C283—21no—
71C22×C4×C283C2311yescharacteristic
72SD16×C283—28no—
73C2×C8×C283—22no—
74C2×C8×C283C2312yescomplemented
75C22×D283—22no—
76C22×D283—22no—
77C22×D283—216no—
78C22×D283—24no—
79C22×D283—22no—
80C22×D283—48no—
81C22×D283—432no—
82C22×D283—42no—
83C22×D283—42no—
84C22×D283—48no—
85C22×D283SD1614yescomplemented
86C22×D283C2×D412yes—
87D1132—24no—
88D1132—22no—
89D1132C2×D414yes—
90C22⋊D283—216no—
91C2×Dic283—22no—
92C2×Dic283—22no—
93C2×Dic283—42no—
94C2×Dic283C2×D412yes—
95C4×D283—24no—
96C4×D283—22no—
97C4×D283—22no—
98C283⋊C8—22no—
99C23×C283—24no—
100C23×C283—22no—
101C23×C283—42no—
102C23×C283—42no—
103C23×C283C2×D411yescharacteristic
104Q8×C283—22no—
105Q8×C283—22no—
106Q8×C283—42no—
107D4×C283—24no—
108D4×C283—22no—
109D4×C283C2×D414yes—
110C2×C4×C283—22no—
111C2×C4×C283—42no—
112C2×C4×C283C2×D411yescharacteristic
113C2×C4×C283C2×D412yes—
114C2×C4×C283C2×D412yes—
115C2×C4×C283C2411yescharacteristic
116C8×C283—22no—
117C22×C283—24no—
118C22×C283—42no—
119C22×C283—42no—
120C22×C283—48no—
121C22×C283#12012yes—
122C22×C283C2×SD1612yes—
123C22×C283AGL(1,ℤ/8)12yes—
124C22×C283C22×D411yescharacteristic
125C2×D283—22no—
126C2×D283—22no—
127C2×D283—28no—
128C2×D283—24no—
129C2×D283—432no—
130C2×D283—42no—
131C2×D283—42no—
132C2×D283—48no—
133C2×D283C2×SD1614yescomplemented
134C4×C283—42no—
135C4×C283#12012yes—
136C4×C283C22×D411yescharacteristic
137C4×C283C22×D411yescharacteristic
138Dic283—22no—
139Dic283—42no—
140C2×C283—44no—
141C2×C283#45014yescomplemented
142C2×C283C2×#12011yescharacteristic
143C2×C283C22×SD1611yescharacteristic
144C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
145D283—24no—
146D283—44no—
147C283C2×#45011yescharacteristic, complemented, Sylow
148C2×#450—2831nomaximal, Sylow
149C23×D4—2831no—
150C22×SD16—2831no—
151C22×SD16D28311yescharacteristic, complemented
152C2×C22⋊Q8—2831no—
153#450—2838no—
154C2×#102—2831no—
155C2×#102—2831no—
156C2×C22⋊C8—2831no—
157C25—5661no—
158C22×Q8C2×D28311yescharacteristic, complemented
159C22×D4—2834no—
160C22×D4—2831no—
161C22×D4—5662no—
162C22×D4—5661no—
163C22×D4—5664no—
164C22×D4—5664no—
165C22×D4C2×D28311yescharacteristic
166C23×C4—2831no—
167C2×SD16—24no—
168C2×SD16—2834no—
169C2×SD16—5664no—
170C2×SD16C2×D28314yescomplemented
171C22×C8—2831no—
172C22×C8C2×D28311yescharacteristic, complemented
173C22⋊Q8—2834no—
174C22⋊Q8—5662no—
175C2×C4⋊C4—2831no—
176C2×C4⋊C4—5661no—
177C2×C22⋊C4—5661no—
178#102—2834no—
179#102—2834no—
180C22⋊C8—2834no—
181C24—21no—
182C24—2831no—
183C24—5664no—
184C24—5668no—
185C24—5661no—
186C24—11324no—
187C24—11324no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D28312yescomplemented
192C2×D4—21no—
193C2×D4—22no—
194C2×D4—2834no—
195C2×D4—2832no—
196C2×D4—5664no—
197C2×D4—5668no—
198C2×D4—56616no—
199C2×D4—5668no—
200C2×D4—5668no—
201C2×D4—5661no—
202C2×D4—5662no—
203C2×D4C22⋊D28314yes—
204C2×D4C22×D28312yes—
205C22×C4—21no—
206C22×C4—2831no—
207C22×C4—2832no—
208C22×C4—2832no—
209C22×C4—5662no—
210C22×C4—5662no—
211C22×C4—5661no—
212C22×C4C22×D28311yescharacteristic
213SD16—28no—
214SD16—5668no—
215C2×C8—22no—
216C2×C8—2832no—
217C2×C8—5662no—
218C2×C8C22×D28312yescomplemented
219C4⋊C4—2832no—
220C4⋊C4—5664no—
221C4⋊C4—5661no—
222C22⋊C4—5664no—
223C23—24no—
224C23—22no—
225C23—42no—
226C23—42no—
227C23—2834no—
228C23—2832no—
229C23—56616no—
230C23—5662no—
231C23—5662no—
232C23—5664no—
233C23—5662no—
234C23—11328no—
235C23—11328no—
236C23—113232no—
237C23—11322no—
238C23—11322no—
239C23D4×D28311yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—24no—
244D4—22no—
245D4—2834no—
246D4—56616no—
247D4—5664no—
248D4—5662no—
249D4C2×C22⋊D28314yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—2832no—
253C2×C4—5662no—
254C2×C4—5664no—
255C2×C4—5662no—
256C2×C4—5662no—
257C2×C4—5662no—
258C2×C4—11322no—
259C2×C4D4×D28311yescharacteristic
260C2×C4D4×D28312yes—
261C2×C4C2×C22⋊D28312yes—
262C2×C4C23×D28311yescharacteristic
263C8—22no—
264C8—5662no—
265C22—24no—
266C22—42no—
267C22—42no—
268C22—48no—
269C22—2834no—
270C22—5662no—
271C22—5662no—
272C22—5668no—
273C22—5664no—
274C22—113232no—
275C22—11322no—
276C22—11322no—
277C22—11328no—
278C22#2258357812yes—
279C22SD16×D28312yes—
280C22#2258363712yes—
281C22C2×D4×D28311yescharacteristic
282C4—42no—
283C4—5662no—
284C4—11322no—
285C4#2258357812yes—
286C4C2×D4×D28311yescharacteristic
287C4C22×C22⋊D28311yescharacteristic
288C2—44no—
289C2—5664no—
290C2—11324no—
291C2#3182661414yesdirect product factor
292C2C2×#2258357811yescharacteristic
293C2C2×SD16×D28311yescharacteristic
294C2C2×#2258363711yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC23×C283C2×D4
prime radicalC22×D4×D283C2
hypercenterC22×SD16D283
hypocenterC283C2×#450
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×#17985379C2semidirect
3. C2×#22583586C2semidirect
4. #31826614C2direct (N × H)
5. C2×#22583532C2semidirect
6. C2×#22583531C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C22×SD16×C283C2semidirect
18. C2×#17985379C22semidirect
19. C22×C283⋊C8C22semidirect
21. #22583586C22semidirect
22. C2×C4⋊Dic283C22semidirect
25. #22583532C22semidirect
26. #22583531C22semidirect
27. (C2×D283)⋊C8C22semidirect
28. C22×Q8×C283C22semidirect
31. C2×SD16×C283C22semidirect
32. C22×C8×C283C22semidirect
56. C2×C283⋊C8C23semidirect
58. C4⋊Dic283C23semidirect
65. C2×Q8×C283C23semidirect
74. C2×C8×C283C23semidirect
85. C22×D283SD16semidirect
133. C2×D283C2×SD16semidirect
141. C2×C283#450semidirect
147. C283C2×#450semidirect
151. C22×SD16D283semidirect
158. C22×Q8C2×D283semidirect
170. C2×SD16C2×D283semidirect
172. C22×C8C2×D283semidirect
191. C2×Q8C22×D283semidirect
218. C2×C8C22×D283semidirect
291. C2#31826614direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2832
C22×#179853792
C2×#225835862
#318266142
C2×#225835322
C2×#225835312
C2×(C2×D283)⋊C82
C22×SD16×C2832
C2×#450283