Finite Group Databasebeta

← #49131184

Subgroups — #49131184

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
2#31826800C212yesmaximal, complemented
3#31826795C212yesmaximal, complemented
4#31826783C212yesmaximal, complemented
5#31826778C212yesmaximal, complemented
6#31826505C212yesmaximal, complemented
7#31826464C212yesmaximal, complemented
8#31826429C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C2×#17985376C2212yes—
12#22583593—21no—
13#22583589C2211yescharacteristic
14#22583589C2211yescharacteristic
15#22583584C2211yescharacteristic
16#22583584C2211yescharacteristic
17#22583579—21no—
18C4×C22⋊D283—21no—
19C4×C22⋊D283—21no—
20#22583569C2211yescharacteristic
21#22583543C2214yescomplemented
22#22583541C2214yescomplemented
23#22583533C2214yescomplemented
24#22583530C2214yescomplemented
25C22⋊(C283⋊C8)C2212yes—
26C22⋊(C283⋊C8)C2212yes—
27C23×C4×C283—21no—
28C23×C4×C283C2211yescharacteristic
29C2×C4⋊C4×C283—21no—
30C2×C4⋊C4×C283—21no—
31C2×C4⋊C4×C283—21no—
32C2×C4⋊C4×C283C2212yes—
33C2×C4⋊C4×C283C2212yes—
34C2×C4⋊C4×C283C2212yes—
35#17985392—24no—
36C2×Dic566C2311yescharacteristic
37C2×D1132C2311yescharacteristic
38C2×C22⋊D283—21no—
39C2×C22⋊D283—21no—
40C2×C22⋊D283—21no—
41C2×C4×D283—21no—
42#17985376—24no—
43C2×C283⋊C8C2314yes—
44C4⋊Dic283C2311yescharacteristic
45C4⋊Dic283C2311yescharacteristic
46Dic283⋊C4—21no—
47Dic283⋊C4—21no—
48C22⋊Dic283—21no—
49C22⋊Dic283—21no—
50C22⋊Dic283—21no—
51(C2×D283)⋊C4—21no—
52(C2×D283)⋊C4—21no—
53C4×Dic283—21no—
54C24×C283D411yescharacteristic
55C22×C4×C283—24no—
56C22×C4×C283—22no—
57C22×C4×C283—22no—
58C22×C4×C283—22no—
59C22×C4×C283—44no—
60C22×C4×C283D411yescharacteristic
61C22×C4×C283D411yescharacteristic
62C22×C4×C283D411yescharacteristic
63C22×C4×C283C2311yescharacteristic
64C22×C4×C283C2311yescharacteristic
65C22×C4×C283C2311yescharacteristic
66C4⋊C4×C283—22no—
67C4⋊C4×C283—22no—
68C4⋊C4×C283—22no—
69C4⋊C4×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—
79C4×D283—42no—
80C283⋊C8—24no—
81C23×C283—22no—
82C23×C283—22no—
83C23×C283—22no—
84C23×C283C2×D411yescharacteristic
85C23×C283C2×D411yescharacteristic
86C23×C283C2×D411yescharacteristic
87C2×C4×C283—22no—
88C2×C4×C283—22no—
89C2×C4×C283—22no—
90C2×C4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283—24no—
93C2×C4×C283—44no—
94C2×C4×C283—44no—
95C2×C4×C283—44no—
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283#4114yes—
100C2×C4×C283C2411yescharacteristic
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—44no—
118C4×C283#12312yes—
119C4×C283C2×#4112yes—
120Dic283—41no—
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⋊C4D28311yescharacteristic, complemented
134#484—2832no—
135#483—2832no—
136#481—2832no—
137#480—2832no—
138#428—2832no—
139#417—2832no—
140#407—2831no—
141C2×#41—2831no—
142C23×C4—21no—
143C23×C4C2×D28311yescharacteristic
144C2×M16—2832no—
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—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D28312yes—
158C2×C4⋊C4C2×D28312yes—
159C2×C4⋊C4C2×D28312yes—
160#107—2834no—
161#106—2834no—
162#103—2834no—
163#102—2834no—
164C22⋊C8—2832no—
165C22⋊C8—2832no—
166C24C22⋊D28311yescharacteristic
167#41—5664no—
168C2×Q8—2831no—
169C2×D4—2831no—
170C2×D4—5661no—
171C2×D4—5661no—
172C2×D4—5661no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—5661no—
179C22×C4C22⋊D28311yescharacteristic
180C22×C4C22⋊D28311yescharacteristic
181C22×C4C22⋊D28311yescharacteristic
182C22×C4C22×D28311yescharacteristic
183C22×C4C22×D28311yescharacteristic
184C22×C4C22×D28311yescharacteristic
185M16—5664no—
186C2×C8—2834no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—2831no—
191C4⋊C4—2831no—
192C4⋊C4—5661no—
193C4⋊C4—5661no—
194C4⋊C4C22×D28314yes—
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×C22⋊D28311yescharacteristic
206C23C2×C22⋊D28311yescharacteristic
207C23C2×C22⋊D28311yescharacteristic
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—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—5661no—
223C2×C4—5661no—
224C2×C4—5661no—
225C2×C4—11322no—
226C2×C4C2×C22⋊D28311yescharacteristic
227C2×C4C2×C22⋊D28311yescharacteristic
228C2×C4C2×C22⋊D28311yescharacteristic
229C2×C4#1798539214yes—
230C2×C4C23×D28311yescharacteristic
231C8—5664no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—11321no—
240C22—11321no—
241C22—11321no—
242C22#2258359312yes—
243C22#2258363612yes—
244C22#2258364112yes—
245C22C22×C22⋊D28311yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—11321no—
250C4—11321no—
251C4—11321no—
252C4#2258359312yes—
253C4C2×#1798539212yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—22641no—
258C2C2×#2258359311yescharacteristic
259C2C2×#2258363611yescharacteristic
260C2C2×#2258364111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×C4⋊C4×C283C2
socleC22×C283C22×D4
prime radical#31826976C2
hypercenterC22×C4⋊C4D283
hypocenterC283#3092
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #31826800C2semidirect
3. #31826795C2semidirect
4. #31826783C2semidirect
5. #31826778C2semidirect
6. #31826505C2semidirect
7. #31826464C2semidirect
8. #31826429C2semidirect
9. C22×C4⋊C4×C283C2semidirect
21. #22583543C22semidirect
22. #22583541C22semidirect
23. #22583533C22semidirect
24. #22583530C22semidirect
130. C283#3092semidirect
133. C22×C4⋊C4D283semidirect

Maximal subgroups

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

subgroupindex
#318269762
#318268002
#318267952
#318267832
#318267782
#318265052
#318264642
#318264292
C22×C4⋊C4×C2832
#3092283