Finite Group Databasebeta

← #49131217

Subgroups — #49131217

Order 36224.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827032C211yesmaximal, characteristic
2#31826945C211yesmaximal, characteristic, complemented
3#31826788C212yesmaximal, complemented
4#31826787C212yesmaximal, complemented
5#31826782C212yesmaximal, complemented
6#31826777C212yesmaximal, complemented
7#31826507C211yesmaximal, characteristic, complemented
8#31826501C211yesmaximal, characteristic, complemented
9C2×#22583531C211yesmaximal, characteristic, complemented
10#31826433C211yesmaximal, characteristic, complemented
11#418×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C22×C283⋊C8C2211yescharacteristic
14#22583606—21no—
15#22583597—21no—
16#22583581C2212yes—
17#22583581C2212yes—
18#22583579—22no—
19C4×Dic566—21no—
20C4×D1132—21no—
21(C22⋊D283)⋊C4—22no—
22#22583569C2211yescharacteristic
23#22583568C2212yescomplemented
24C2×C4⋊Dic283C2211yescharacteristic
25C4⋊C4×D283C2212yescomplemented
26#22583544C2212yescomplemented
27#22583543C2211yescharacteristic, complemented
28#22583543C2211yescharacteristic, complemented
29#22583542C2212yescomplemented
30#22583541C2211yescharacteristic, complemented
31#22583541C2211yescharacteristic, complemented
32#22583531C2212yes—
33#22583531C2212yes—
34(C2×D283)⋊C8C2212yescomplemented
35(C2×D283)⋊C8C2212yescomplemented
36C22×D4×C283C2211yescharacteristic
37C2×M16×C283C2211yescharacteristic
38#117×C283C2211yescharacteristic
39#102×C283C2212yes—
40#102×C283C2212yes—
41#17985392—22no—
42#17985392—22no—
43C2×Dic566D411yescharacteristic
44C2×D1132D411yescharacteristic
45C2×C22⋊D283—22no—
46C2×C22⋊D283—22no—
47C2×C22⋊D283D412yes—
48C22×Dic283—21no—
49C2×C4×D283—22no—
50C2×C4×D283C2312yes—
51C2×C283⋊C8—22no—
52C2×C283⋊C8C2311yescharacteristic
53C2×C283⋊C8C2311yescharacteristic
54C4⋊Dic283—21no—
55C4⋊Dic283C2312yes—
56C4⋊Dic283C2311yescharacteristic
57C4⋊Dic283C2311yescharacteristic
58Dic283⋊C4—22no—
59C22⋊Dic283—22no—
60C22⋊Dic283—22no—
61C22⋊Dic283—21no—
62(C2×D283)⋊C4—22no—
63C4×Dic283—22no—
64C4×Dic283—21no—
65C24×C283—21no—
66C2×D4×C283—21no—
67C2×D4×C283—22no—
68C2×D4×C283—22no—
69C2×D4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71M16×C283—22no—
72C2×C8×C283C2312yes—
73C4⋊C4×C283C2311yescharacteristic
74C4⋊C4×C283C2311yescharacteristic
75C22⋊C4×C283—21no—
76C42×C283—21no—
77C22×D283C2×D412yes—
78Dic566—22no—
79D1132—22no—
80C22⋊D283—24no—
81C22⋊D283—82no—
82C22⋊D283—82no—
83C2×Dic283—22no—
84C2×Dic283—21no—
85C2×Dic283—21no—
86C2×Dic283—81no—
87C2×Dic283C2×D412yes—
88C4×D283—22no—
89C4×D283—22no—
90C4×D283—82no—
91C283⋊C8—21no—
92C283⋊C8—21no—
93C23×C283—22no—
94C23×C283—42no—
95C23×C283—81no—
96C23×C283—81no—
97C23×C283C2×D411yescharacteristic
98D4×C283—22no—
99D4×C283—22no—
100D4×C283—42no—
101C2×C4×C283—21no—
102C2×C4×C283—21no—
103C2×C4×C283C2×D411yescharacteristic
104C2×C4×C283#4112yes—
105C2×C4×C283#4112yes—
106C2×C4×C283C2411yescharacteristic
107C8×C283—22no—
108C22×C283—21no—
109C22×C283—21no—
110C22×C283—42no—
111C22×C283—42no—
112C22×C283—42no—
113C22×C283—84no—
114C22×C283#12312yes—
115C22×C283C22×D411yescharacteristic
116C2×D283—22no—
117C2×D283—22no—
118C2×D283—22no—
119C4×C283—41no—
120C4×C283—41no—
121C4×C283#12312yes—
122C4×C283C2×#4111yescharacteristic
123C4×C283C2×#4111yescharacteristic
124Dic283—22no—
125Dic283—42no—
126Dic283—41no—
127Dic283—41no—
128C2×C283—22no—
129C2×C283—82no—
130C2×C283C2×#12311yescharacteristic
131C2×C283#57611yescharacteristic
132C2×C283#57711yescharacteristic
133D283—42no—
134C283#309611yescharacteristic, complemented, Sylow
135#3096—2831nomaximal, Sylow
136#535—2831no—
137#520—2831no—
138#482—2832no—
139#482—2832no—
140#481—2832no—
141#480—2832no—
142#428—2831no—
143#427—2831no—
144#418D28311yescharacteristic, complemented
145C2×#102—2831no—
146#408—2831no—
147C2×#41—2831no—
148C22×D4C2×D28311yescharacteristic
149C2×M16C2×D28311yescharacteristic
150C22×C8—2831no—
151#127—5661no—
152#124—5661no—
153#121—2832no—
154#121—2832no—
155#120—5662no—
156C4×Q8—5661no—
157C4×D4—5661no—
158C4×D4—5662no—
159#117—2831no—
160#117—2832no—
161#117C2×D28311yescharacteristic
162C2×C4⋊C4—2831no—
163C2×C4⋊C4—2832no—
164#107—2832no—
165#107—2831no—
166#107—2831no—
167#106—2832no—
168#106—2831no—
169#106—2831no—
170#102—2832no—
171#102—2832no—
172#102C2×D28312yes—
173#102C2×D28312yes—
174C22⋊C8—2832no—
175C22⋊C8—2832no—
176C24—21no—
177#41—5662no—
178#41—5662no—
179C2×Q8—2831no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—22no—
183C2×D4—2832no—
184C2×D4—2831no—
185C2×D4—5662no—
186C2×D4—5662no—
187C2×D4C22×D28312yes—
188C22×C4—2832no—
189C22×C4—5662no—
190C22×C4—5661no—
191C22×C4C22×D28311yescharacteristic
192M16—22no—
193C2×C8—2831no—
194C2×C8—2831no—
195C2×C8—5662no—
196C2×C8C22×D28312yes—
197C4⋊C4—2832no—
198C4⋊C4—2831no—
199C4⋊C4—2831no—
200C4⋊C4—5662no—
201C4⋊C4—5661no—
202C4⋊C4C22×D28311yescharacteristic
203C4⋊C4C22×D28311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—5662no—
206C22⋊C4—5662no—
207C22⋊C4—5662no—
208C22⋊C4—5661no—
209C42—21no—
210C42—5662no—
211C42—5661no—
212C23—22no—
213C23—42no—
214C23—81no—
215C23—81no—
216C23—2832no—
217C23D4×D28311yescharacteristic
218Q8—5662no—
219D4—22no—
220D4—22no—
221D4—42no—
222D4—5664no—
223D4—5662no—
224D4—22642no—
225D4—22642no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—2832no—
229C2×C4—5662no—
230C2×C4—5662no—
231C2×C4—5661no—
232C2×C4—5661no—
233C2×C4—5662no—
234C2×C4—22642no—
235C2×C4—22641no—
236C2×C4D4×D28311yescharacteristic
237C2×C4#1798539112yes—
238C2×C4#1798539212yes—
239C2×C4C23×D28311yescharacteristic
240C8—22no—
241C8—5661no—
242C8—5661no—
243C22—21no—
244C22—21no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—84no—
249C22—5662no—
250C22—5662no—
251C22—5662no—
252C22#2258359212yes—
253C22C2×D4×D28311yescharacteristic
254C4—41no—
255C4—41no—
256C4—5662no—
257C4—11322no—
258C4—11321no—
259C4—11321no—
260C4#2258359212yes—
261C4C2×#1798539111yescharacteristic
262C4C2×#1798539211yescharacteristic
263C2—22no—
264C2—82no—
265C2—11322no—
266C2C2×#2258359211yescharacteristic
267C2#3182726911yescharacteristic
268C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
prime radical#31827032C2
hypercenter#418D283
hypocenterC283#3096
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #31826945C2semidirect
3. #31826788C2semidirect
4. #31826787C2semidirect
5. #31826782C2semidirect
6. #31826777C2semidirect
7. #31826507C2semidirect
8. #31826501C2semidirect
9. C2×#22583531C2semidirect
10. #31826433C2semidirect
11. #418×C283C2semidirect
23. #22583568C22semidirect
25. C4⋊C4×D283C22semidirect
26. #22583544C22semidirect
27. #22583543C22semidirect
28. #22583543C22semidirect
29. #22583542C22semidirect
30. #22583541C22semidirect
31. #22583541C22semidirect
34. (C2×D283)⋊C8C22semidirect
35. (C2×D283)⋊C8C22semidirect
134. C283#3096semidirect
144. #418D283semidirect

Maximal subgroups

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

subgroupindex
#318270322
#318269452
#318267882
#318267872
#318267822
#318267772
#318265072
#318265012
C2×#225835312
#318264332
#418×C2832
#3096283