Finite Group Databasebeta

← #49130764

Subgroups — #49130764

Order 36224.

526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583636C211yesmaximal, characteristic, complemented
2C22×#17985377C211yesmaximal, characteristic, complemented
3#31827034C211yesmaximal, characteristic, complemented
4#31826680C214yesmaximal, complemented
5#31826660C214yesmaximal, complemented
6#31826492C211yesmaximal, characteristic, complemented
7#31826469C211yesmaximal, characteristic, complemented
8#31826459C211yesmaximal, characteristic, complemented
9#518×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12#22583636—24no—
13C2×#17985380C2212yescomplemented
14C2×#17985377—24no—
15C2×#17985377C2214yes—
16C2×#17985377C2212yescomplemented
17C2×#17985376C2211yescharacteristic
18C22×C283⋊C8C2211yescharacteristic
19#22583607C2212yescomplemented
20#22583598C2212yescomplemented
21#22583585—22no—
22#22583580—22no—
23C4⋊(C283⋊C8)C2214yescomplemented
24#22583533C2212yescomplemented
25#22583530C2212yescomplemented
26#22583530C2214yescomplemented
27C22×D4×C283C2211yescharacteristic
28C4×D4×C283—22no—
29C4×D4×C283C2214yescomplemented
30#117×C283C2211yescharacteristic
31#117×C283C2211yescharacteristic
32C2×C22⋊C4×C283—22no—
33C23×D283—21no—
34#17985392—22no—
35#17985392—22no—
36C2×Dic566C2311yescharacteristic
37C2×D1132—22no—
38C2×D1132—21no—
39C2×D1132—24no—
40C2×D1132—22no—
41C2×D1132C2312yes—
42C2×D1132C2311yescharacteristic
43C2×C22⋊D283—21no—
44C2×C4×D283—21no—
45#17985380—24no—
46#17985377—28no—
47#17985377—24no—
48#17985376—22no—
49C2×C283⋊C8—22no—
50C2×C283⋊C8C2312yes—
51C2×C283⋊C8C2312yes—
52(C2×D283)⋊C4—24no—
53C24×C283—21no—
54C2×D4×C283—21no—
55C2×D4×C283—22no—
56C2×D4×C283D414yescomplemented
57C2×D4×C283C2312yes—
58C22×C4×C283—24no—
59C22×C4×C283C2311yescharacteristic
60C4⋊C4×C283D412yes—
61C4⋊C4×C283C2312yes—
62C22⋊C4×C283—21no—
63C22⋊C4×C283—24no—
64C22⋊C4×C283D412yes—
65C42×C283—21no—
66C42×C283C2312yes—
67C22×D283—22no—
68C22×D283—21no—
69C22×D283—42no—
70C22×D283—82no—
71Dic566—21no—
72Dic566—21no—
73D1132—22no—
74D1132—21no—
75D1132—22no—
76D1132—21no—
77D1132—42no—
78D1132—84no—
79C22⋊D283—42no—
80C2×Dic283—21no—
81C4×D283—42no—
82C283⋊C8—22no—
83C283⋊C8—22no—
84C23×C283—22no—
85C23×C283—24no—
86C23×C283—82no—
87C23×C283C2×D411yescharacteristic
88D4×C283—24no—
89D4×C283—22no—
90D4×C283C2×D414yes—
91C2×C4×C283—22no—
92C2×C4×C283—84no—
93C2×C4×C283C2×D414yes—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D412yes—
96C2×C4×C283#4112yes—
97C2×C4×C283C2411yescharacteristic
98C22×C283—22no—
99C22×C283—24no—
100C22×C283—44no—
101C22×C283—84no—
102C22×C283#12112yes—
103C22×C283C22×D411yescharacteristic
104C2×D283—41no—
105C2×D283—42no—
106C2×D283—42no—
107C2×D283—44no—
108C2×D283—84no—
109C4×C283—24no—
110C4×C283—42no—
111C4×C283#12112yes—
112C4×C283C22×D411yescharacteristic
113C4×C283C2×#4111yescharacteristic
114Dic283—41no—
115C2×C283—22no—
116C2×C283—44no—
117C2×C283C2×#12111yescharacteristic
118C2×C283#57612yes—
119D283—81no—
120D283—82no—
121C283#304111yescharacteristic, complemented, Sylow
122#3041—2831nomaximal, Sylow
123C2×AGL(1,ℤ/8)—2831no—
124C22×D8—2831no—
125#535—2831no—
126#518D28311yescharacteristic, complemented
127#463—2834no—
128#459—2834no—
129#424—2831no—
130#418—2831no—
131#416—2831no—
132C2×#41—2831no—
133C22×D4—2831no—
134C22×D4C2×D28311yescharacteristic
135AGL(1,ℤ/8)—5664no—
136C2×SD16—2832no—
137C2×D8—2834no—
138C2×D8—2832no—
139C2×D8—5664no—
140C2×M16—2831no—
141C22×C8—2831no—
142#127—2832no—
143#124—2832no—
144#121—5662no—
145#120—5662no—
146C4×D4—22no—
147C4×D4C2×D28314yescomplemented
148#117C2×D28311yescharacteristic
149#117C2×D28311yescharacteristic
150C2×C22⋊C4—22no—
151C4⋊C8—2834no—
152#103—2832no—
153#102—2832no—
154#102—2834no—
155C24—21no—
156C24—5661no—
157#41—5662no—
158#41—5662no—
159C2×Q8—2831no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—2832no—
163C2×D4—2831no—
164C2×D4—5661no—
165C2×D4—5661no—
166C2×D4—5664no—
167C2×D4—5662no—
168C2×D4—5662no—
169C2×D4D113214yescomplemented
170C2×D4C22×D28312yes—
171C22×C4—24no—
172C22×C4—5661no—
173C22×C4C22×D28311yescharacteristic
174SD16—5664no—
175D8—5668no—
176D8—5664no—
177M16—5662no—
178C2×C8—2832no—
179C2×C8—2832no—
180C2×C8—5662no—
181C4⋊C4C22⋊D28312yes—
182C4⋊C4C22×D28312yes—
183C22⋊C4—21no—
184C22⋊C4—24no—
185C22⋊C4—5664no—
186C22⋊C4C22⋊D28312yes—
187C42—21no—
188C42C22×D28312yes—
189C23—22no—
190C23—24no—
191C23—82no—
192C23—5662no—
193C23—5661no—
194C23—11322no—
195C23—22642no—
196C23C2×C22⋊D28311yescharacteristic
197Q8—5661no—
198Q8—5661no—
199D4—24no—
200D4—22no—
201D4—5662no—
202D4—5661no—
203D4—5662no—
204D4—5661no—
205D4—11322no—
206D4—11322no—
207D4—22644no—
208D4C2×D113214yes—
209C2×C4—22no—
210C2×C4—84no—
211C2×C4—5661no—
212C2×C4—11322no—
213C2×C4C2×C22⋊D28314yes—
214C2×C4C2×C22⋊D28311yescharacteristic
215C2×C4C2×D113212yes—
216C2×C4#1798539212yes—
217C2×C4C23×D28311yescharacteristic
218C8—5662no—
219C8—5662no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—84no—
224C22—11321no—
225C22—11322no—
226C22—11322no—
227C22—11324no—
228C22—22644no—
229C22#2258358412yes—
230C22C22×C22⋊D28311yescharacteristic
231C4—24no—
232C4—42no—
233C4—11321no—
234C4#2258358412yes—
235C4C22×D113211yescharacteristic
236C4C2×#1798539211yescharacteristic
237C2—22no—
238C2—44no—
239C2—22642no—
240C2—22641no—
241C2C2×#2258358411yescharacteristic
242C2#3182726812yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#518×C283C2
socleC22×C283C22×D4
hypercenter#518D283
hypocenterC283#3041
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C2×#22583636C2semidirect
2. C22×#17985377C2semidirect
3. #31827034C2semidirect
4. #31826680C2semidirect
5. #31826660C2semidirect
6. #31826492C2semidirect
7. #31826469C2semidirect
8. #31826459C2semidirect
9. #518×C283C2semidirect
13. C2×#17985380C22semidirect
16. C2×#17985377C22semidirect
19. #22583607C22semidirect
20. #22583598C22semidirect
23. C4⋊(C283⋊C8)C22semidirect
24. #22583533C22semidirect
25. #22583530C22semidirect
26. #22583530C22semidirect
29. C4×D4×C283C22semidirect
56. C2×D4×C283D4semidirect
121. C283#3041semidirect
126. #518D283semidirect
147. C4×D4C2×D283semidirect
169. C2×D4D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836362
C22×#179853772
#318270342
#318266802
#318266602
#318264922
#318264692
#318264592
#518×C2832
#3041283