Finite Group Databasebeta

← #49124026

Subgroups — #49124026

Order 36224.

596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C2×#22583584C211yesmaximal, characteristic
2#31826365C212yesmaximal, complemented
3#31826356C212yesmaximal, complemented
4#31826348C212yesmaximal, complemented
5#31826343C212yesmaximal, complemented
6#31826341C212yesmaximal, complemented
7#31826328C211yesmaximal, characteristic, complemented
8C4×(C2×D283)⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C22×C22⋊D283C2212yes—
12C22×C4×D283C2212yes—
13#22583584C418yescomplemented
14C2×C4⋊Dic283C2211yescharacteristic
15C2×Dic283⋊C4C2212yes—
16C2×C22⋊Dic283C2211yescharacteristic
17C2×C22⋊Dic283C2211yescharacteristic
18C2×(C2×D283)⋊C4C2212yes—
19C2×(C2×D283)⋊C4C2212yes—
20C2×(C2×D283)⋊C4C2212yes—
21C2×(C2×D283)⋊C4C2212yes—
22C2×C4×Dic283C2212yes—
23C283⋊#95C2212yes—
24C283⋊#95C2212yes—
25C283⋊#95C2212yes—
26C283⋊#95C2212yes—
27C23×C4×C283C2211yescharacteristic
28C2×C22⋊C4×C283C2212yes—
29C2×C42×C283C2211yescharacteristic
30C2×C42×C283C2211yescharacteristic
31#95×C283C2212yes—
32C23×D283C2312yes—
33C2×D1132—41no—
34C2×D1132—41no—
35C2×D1132C2×C414yes—
36C2×C22⋊D283—42no—
37C2×C22⋊D283—42no—
38C2×C22⋊D283C2×C418yescomplemented
39C22×Dic283C2312yes—
40C22×Dic283C2312yes—
41C22×Dic283C2312yes—
42C2×C4×D283—24no—
43C2×C4×D283—42no—
44C2×C4×D283—42no—
45C4⋊Dic283C2×C414yescomplemented
46Dic283⋊C4—42no—
47C22⋊Dic283—41no—
48C22⋊Dic283—41no—
49(C2×D283)⋊C4—24no—
50(C2×D283)⋊C4—42no—
51(C2×D283)⋊C4—42no—
52(C2×D283)⋊C4C2×C418yescomplemented
53C4×Dic283—42no—
54C24×C283C2311yescharacteristic
55C22×C4×C283—41no—
56C22×C4×C283—41no—
57C22×C4×C283C2×C414yescomplemented
58C22×C4×C283C2312yes—
59C22×C4×C283C2311yescharacteristic
60C22×C4×C283C2311yescharacteristic
61C22×C4×C283C2312yes—
62C22⋊C4×C283—24no—
63C42×C283—41no—
64C42×C283—41no—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283—22no—
68C22×D283—22no—
69C22×D283—22no—
70C22×D283—22no—
71C22×D283C22×C414yes—
72D1132—44no—
73C22⋊D283—48no—
74C2×Dic283—22no—
75C2×Dic283—22no—
76C2×Dic283—22no—
77C2×Dic283—22no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—22no—
81C2×Dic283—22no—
82C2×Dic283C22×C414yes—
83C4×D283—48no—
84C23×C283—22no—
85C23×C283—21no—
86C23×C283—21no—
87C23×C283—22no—
88C23×C283C22×C412yes—
89C23×C283C2411yescharacteristic
90C2×C4×C283—21no—
91C2×C4×C283—21no—
92C2×C4×C283—22no—
93C2×C4×C283—21no—
94C2×C4×C283—21no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
97C2×C4×C283—22no—
98C2×C4×C283—22no—
99C2×C4×C283—44no—
100C2×C4×C283C22×C412yes—
101C2×C4×C283C22×C412yes—
102C2×C4×C283#4114yes—
103C22×C283—22no—
104C22×C283—22no—
105C22×C283—22no—
106C22×C283—42no—
107C22×C283—42no—
108C22×C283C23×C411yescharacteristic
109C22×C283C2×#4112yes—
110C22×C283H(5,𝔽2)11yescharacteristic
111C22×C283H(5,𝔽2)11yescharacteristic
112C22×C283H(5,𝔽2)12yes—
113C2×D283—24no—
114C2×D283—24no—
115C2×D283—24no—
116C2×D283—42no—
117C2×D283—42no—
118C2×D283—42no—
119C2×D283—42no—
120C4×C283—22no—
121C4×C283—22no—
122C4×C283—24no—
123C4×C283—42no—
124Dic283—24no—
125Dic283—42no—
126Dic283—42no—
127C2×C283—42no—
128C2×C283C4×#4111yescharacteristic
129C2×C283#51811yescharacteristic
130C2×C283#51811yescharacteristic
131C2×C283#53812yes—
132C2×C283#54012yes—
133D283—44no—
134C283#233311yescharacteristic, complemented, Sylow
135#2333—2831nomaximal, Sylow
136C2×#121—2831no—
137#390—2832no—
138#388—2832no—
139#387—2832no—
140#386—2832no—
141#386—2832no—
142#381—2831no—
143C4×C22⋊C4—2832no—
144C4×C22⋊C4D28311yescharacteristic, complemented
145C22×D4—2832no—
146C22×D4—2831no—
147C23×C4—2832no—
148C23×C4C2×D28311yescharacteristic
149#121—2838no—
150C2×C4⋊C4—2831no—
151C2×C4⋊C4—2832no—
152C2×C22⋊C4—2832no—
153C2×C22⋊C4—2832no—
154C2×C22⋊C4—2831no—
155C2×C22⋊C4—2831no—
156C2×C22⋊C4—2832no—
157C2×C22⋊C4—2832no—
158C2×C22⋊C4C2×D28312yes—
159C2×C42—2832no—
160C2×C42C2×D28311yescharacteristic
161C2×C42C2×D28311yescharacteristic
162#95—2832no—
163#95—2832no—
164#95—2832no—
165#95—2832no—
166#95C2×D28312yes—
167C24—2832no—
168C24C22×D28311yescharacteristic
169C2×D4—2838no—
170C2×D4—2834no—
171C2×D4—11321no—
172C2×D4—11321no—
173C2×D4—11322no—
174C2×D4—11322no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—2832no—
178C22×C4—2832no—
179C22×C4—2832no—
180C22×C4—5664no—
181C22×C4—11322no—
182C22×C4—11322no—
183C22×C4C4×D28314yescomplemented
184C22×C4C22×D28312yes—
185C22×C4C22×D28311yescharacteristic
186C22×C4C22×D28311yescharacteristic
187C22×C4C22×D28312yes—
188C4⋊C4—2834no—
189C4⋊C4—11322no—
190C22⋊C4—24no—
191C22⋊C4—2838no—
192C22⋊C4—5664no—
193C22⋊C4—11322no—
194C22⋊C4—11322no—
195C22⋊C4—11321no—
196C22⋊C4—11321no—
197C42—41no—
198C42—41no—
199C42—11322no—
200C23—22no—
201C23—21no—
202C23—21no—
203C23—22no—
204C23—2834no—
205C23—5662no—
206C23—5662no—
207C23—5662no—
208C23—5662no—
209C23—5662no—
210C23—5662no—
211C23C2×C4×D28312yes—
212C23C23×D28311yescharacteristic
213D4—11324no—
214D4—11328no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—44no—
225C2×C4—2834no—
226C2×C4—5662no—
227C2×C4—5662no—
228C2×C4—5662no—
229C2×C4—5662no—
230C2×C4—5662no—
231C2×C4—5662no—
232C2×C4—5662no—
233C2×C4—5662no—
234C2×C4—11328no—
235C2×C4C2×C4×D28312yes—
236C2×C4C2×C4×D28312yes—
237C2×C4#1798539214yes—
238C22—22no—
239C22—22no—
240C22—22no—
241C22—42no—
242C22—42no—
243C22—5664no—
244C22—5664no—
245C22—5664no—
246C22—11322no—
247C22—11322no—
248C22—11322no—
249C22—11322no—
250C22C22×C4×D28311yescharacteristic
251C22C2×#1798539212yes—
252C22#2258365511yescharacteristic
253C22#2258365511yescharacteristic
254C22#2258365612yes—
255C4—24no—
256C4—22no—
257C4—22no—
258C4—42no—
259C4—5664no—
260C4—11322no—
261C4—11322no—
262C2—42no—
263C2—11324no—
264C2C4×#1798539211yescharacteristic
265C2#3182693811yescharacteristic
266C2#3182693911yescharacteristic
267C2#3182704812yes—
268C2#3182706612yes—
subgroupG/H
center, FrattiniC23C23×D283
commutatorC22×C283C23×C4
FittingC4×C22⋊C4×C283C2
socle, cosocleC23×C283C24
prime radicalC2×#22583584C2
hypercenterC4×C22⋊C4D283
hypocenterC283#2333
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #31826365C2semidirect
3. #31826356C2semidirect
4. #31826348C2semidirect
5. #31826343C2semidirect
6. #31826341C2semidirect
7. #31826328C2semidirect
8. C4×(C2×D283)⋊C4C2semidirect
9. C4×C22⋊C4×C283C2semidirect
13. #22583584C4semidirect
38. C2×C22⋊D283C2×C4semidirect
45. C4⋊Dic283C2×C4semidirect
52. (C2×D283)⋊C4C2×C4semidirect
57. C22×C4×C283C2×C4semidirect
134. C283#2333semidirect
144. C4×C22⋊C4D283semidirect
183. C22×C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225835842
#318263652
#318263562
#318263482
#318263432
#318263412
#318263282
C4×(C2×D283)⋊C42
C4×C22⋊C4×C2832
#2333283