Finite Group Databasebeta

← #49131186

Subgroups — #49131186

Order 36224.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1#31826976C211yesmaximal, characteristic
2C22×C4⋊Dic283C211yesmaximal, characteristic, complemented
3#31826801C212yesmaximal, complemented
4#31826796C212yesmaximal, complemented
5#31826784C212yesmaximal, complemented
6#31826779C212yesmaximal, complemented
7#31826507C212yesmaximal, complemented
8#31826467C212yesmaximal, complemented
9#407×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C23×Dic283—21no—
12#22583593—21no—
13#22583589C2211yescharacteristic
14#22583589C2211yescharacteristic
15#22583584C2211yescharacteristic
16#22583584C2211yescharacteristic
17#22583579—21no—
18C4×C22⋊D283—21no—
19C4×C22⋊D283—21no—
20#22583569C2211yescharacteristic
21C2×C4⋊Dic283—21no—
22C2×C4⋊Dic283—21no—
23C2×C4⋊Dic283—21no—
24C2×C4⋊Dic283C2212yes—
25C2×C4⋊Dic283C2212yes—
26C2×C4⋊Dic283C2212yes—
27#22583544C2214yescomplemented
28#22583542C2214yescomplemented
29#22583535C2214yescomplemented
30#22583532C2214yescomplemented
31C23×C4×C283C2211yescharacteristic
32C2×M16×C283C2212yes—
33C22⋊C8×C283C2212yes—
34C22⋊C8×C283C2212yes—
35#17985392—24no—
36C2×Dic566C2311yescharacteristic
37C2×D1132C2311yescharacteristic
38C2×C22⋊D283—21no—
39C2×C22⋊D283—21no—
40C2×C22⋊D283—21no—
41C22×Dic283—22no—
42C22×Dic283—22no—
43C22×Dic283—22no—
44C22×Dic283—44no—
45C2×C4×D283—21no—
46C4⋊Dic283—22no—
47C4⋊Dic283—22no—
48C4⋊Dic283—22no—
49C4⋊Dic283C2314yes—
50C4⋊Dic283C2311yescharacteristic
51C4⋊Dic283C2311yescharacteristic
52Dic283⋊C4—21no—
53Dic283⋊C4—21no—
54C22⋊Dic283—21no—
55C22⋊Dic283—21no—
56C22⋊Dic283—21no—
57(C2×D283)⋊C4—21no—
58(C2×D283)⋊C4—21no—
59C4×Dic283—21no—
60C24×C283D411yescharacteristic
61C22×C4×C283—24no—
62C22×C4×C283D411yescharacteristic
63C22×C4×C283D411yescharacteristic
64C22×C4×C283D411yescharacteristic
65C22×C4×C283C2311yescharacteristic
66C22×C4×C283C2311yescharacteristic
67C22×C4×C283C2311yescharacteristic
68M16×C283—24no—
69C2×C8×C283C2314yes—
70C22×D283—21no—
71Dic566—22no—
72D1132—22no—
73C22⋊D283—42no—
74C22⋊D283—42no—
75C22⋊D283—42no—
76C2×Dic283—21no—
77C2×Dic283—21no—
78C2×Dic283—21no—
79C2×Dic283—24no—
80C2×Dic283—44no—
81C2×Dic283—44no—
82C2×Dic283—44no—
83C4×D283—42no—
84C23×C283—22no—
85C23×C283—22no—
86C23×C283—22no—
87C23×C283C2×D411yescharacteristic
88C23×C283C2×D411yescharacteristic
89C23×C283C2×D411yescharacteristic
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283—22no—
93C2×C4×C283—22no—
94C2×C4×C283—22no—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283#4114yes—
99C2×C4×C283C2411yescharacteristic
100C8×C283—24no—
101C22×C283—28no—
102C22×C283—21no—
103C22×C283—21no—
104C22×C283—21no—
105C22×C283—21no—
106C22×C283—21no—
107C22×C283—21no—
108C22×C283#12312yes—
109C22×C283AGL(1,ℤ/8)12yes—
110C22×C283#13712yes—
111C22×C283C22×D411yescharacteristic
112C2×D283—41no—
113C2×D283—41no—
114C2×D283—41no—
115C4×C283—21no—
116C4×C283—21no—
117C4×C283#12312yes—
118C4×C283C2×#4112yes—
119Dic283—41no—
120Dic283—44no—
121Dic283—41no—
122Dic283—41no—
123C2×C283—22no—
124C2×C283—22no—
125C2×C283—22no—
126C2×C283C2×#12311yescharacteristic
127C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C283C2×#13711yescharacteristic
129D283—81no—
130C283#309211yescharacteristic, complemented, Sylow
131#3092—2831nomaximal, Sylow
132#525—2831no—
133C22×C4⋊C4—2831no—
134#484—2832no—
135#483—2832no—
136#481—2832no—
137#480—2832no—
138#428—2832no—
139#417—2832no—
140#407D28311yescharacteristic, complemented
141C2×#41—2831no—
142C23×C4—5661no—
143C23×C4C2×D28311yescharacteristic
144C2×M16C2×D28312yes—
145#123—5661no—
146C22⋊Q8—2831no—
147C22⋊Q8—2831no—
148#121—2831no—
149#121—2831no—
150#120—5661no—
151C4×D4—5661no—
152C4×D4—5661no—
153#117—2831no—
154C2×C4⋊C4—2832no—
155C2×C4⋊C4—2832no—
156C2×C4⋊C4—2832no—
157C2×C4⋊C4—5661no—
158C2×C4⋊C4—5661no—
159C2×C4⋊C4—5661no—
160#107—2834no—
161#106—2834no—
162#103—2834no—
163#102—2834no—
164C22⋊C8C2×D28312yes—
165C22⋊C8C2×D28312yes—
166C24D113211yescharacteristic
167#41—5664no—
168C2×Q8—2831no—
169C2×D4—2831no—
170C2×D4—5661no—
171C2×D4—5661no—
172C2×D4—5661no—
173C22×C4—24no—
174C22×C4—5662no—
175C22×C4—5662no—
176C22×C4—5662no—
177C22×C4—5661no—
178C22×C4—11324no—
179C22×C4D113211yescharacteristic
180C22×C4D113211yescharacteristic
181C22×C4D113211yescharacteristic
182C22×C4C22×D28311yescharacteristic
183C22×C4C22×D28311yescharacteristic
184C22×C4C22×D28311yescharacteristic
185M16—24no—
186C2×C8C22×D28314yes—
187C4⋊C4—2834no—
188C4⋊C4—2831no—
189C4⋊C4—2831no—
190C4⋊C4—5661no—
191C4⋊C4—5661no—
192C4⋊C4—5662no—
193C4⋊C4—5662no—
194C4⋊C4—5662no—
195C22⋊C4—5661no—
196C22⋊C4—5661no—
197C22⋊C4—5661no—
198C22⋊C4—5661no—
199C22⋊C4—5661no—
200C42—5661no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—5661no—
205C23C2×D113211yescharacteristic
206C23C2×D113211yescharacteristic
207C23C2×D113211yescharacteristic
208Q8—5662no—
209D4—5662no—
210D4—11322no—
211D4—11322no—
212D4—11322no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—5661no—
219C2×C4—5661no—
220C2×C4—5661no—
221C2×C4—5664no—
222C2×C4—11324no—
223C2×C4—11324no—
224C2×C4—11324no—
225C2×C4—11322no—
226C2×C4C2×D113211yescharacteristic
227C2×C4C2×D113211yescharacteristic
228C2×C4C2×D113211yescharacteristic
229C2×C4#1798539114yes—
230C2×C4C23×D28311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—11321no—
240C22—11321no—
241C22—11321no—
242C22#2258359412yes—
243C22#2258363812yes—
244C22#2258364312yes—
245C22C22×D113211yescharacteristic
246C4—21no—
247C4—21no—
248C4—11321no—
249C4—11324no—
250C4—11321no—
251C4—11321no—
252C4#2258359412yes—
253C4C2×#1798539112yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—22641no—
258C2C2×#2258359411yescharacteristic
259C2C2×#2258363811yescharacteristic
260C2C2×#2258364311yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#407×C283C2
socleC22×C283C22×D4
prime radical#31826976C2
hypercenter#407D283
hypocenterC283#3092
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic283C2semidirect
3. #31826801C2semidirect
4. #31826796C2semidirect
5. #31826784C2semidirect
6. #31826779C2semidirect
7. #31826507C2semidirect
8. #31826467C2semidirect
9. #407×C283C2semidirect
27. #22583544C22semidirect
28. #22583542C22semidirect
29. #22583535C22semidirect
30. #22583532C22semidirect
130. C283#3092semidirect
140. #407D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
C22×C4⋊Dic2832
#318268012
#318267962
#318267842
#318267792
#318265072
#318264672
#407×C2832
#3092283