Finite Group Databasebeta

← #49130763

Subgroups — #49130763

Order 36224.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583638C211yesmaximal, characteristic, complemented
2C22×#17985377C211yesmaximal, characteristic, complemented
3#31827032C211yesmaximal, characteristic, complemented
4#31826939C211yesmaximal, characteristic, complemented
5#31826679C214yesmaximal, complemented
6#31826659C214yesmaximal, complemented
7#31826493C211yesmaximal, characteristic, complemented
8#31826459C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12#22583638—24no—
13C2×#17985381C2212yescomplemented
14C2×D2264C2212yescomplemented
15C2×#17985377—24no—
16C2×#17985377C2214yes—
17C22×C283⋊C8C2211yescharacteristic
18#22583606C2212yescomplemented
19#22583597C2212yescomplemented
20#22583581—22no—
21#22583579—22no—
22C4×D1132—22no—
23#22583572C2214yescomplemented
24#22583569C2211yescharacteristic
25C22⋊C4×D283—22no—
26Dic283⋊C8C2214yescomplemented
27#22583533C2212yescomplemented
28#22583530C2212yescomplemented
29C22×D4×C283C2211yescharacteristic
30C2×M16×C283C2211yescharacteristic
31#117×C283C2211yescharacteristic
32#102×C283C2214yescomplemented
33C23×D283—21no—
34#17985392—22no—
35#17985392—22no—
36C2×Dic566C2311yescharacteristic
37C2×D1132—21no—
38C2×D1132—22no—
39C2×D1132D414yescomplemented
40C2×D1132C2311yescharacteristic
41C2×D1132C2312yes—
42C2×C22⋊D283—24no—
43C2×C22⋊D283—21no—
44C2×C4×D283—24no—
45C2×C4×D283—21no—
46#17985381—24no—
47D2264—24no—
48#17985377—28no—
49C2×C283⋊C8—22no—
50C2×C283⋊C8C2312yes—
51C4⋊Dic283D412yes—
52C22⋊Dic283—24no—
53C22⋊Dic283D412yes—
54(C2×D283)⋊C4—24no—
55C4×Dic283C2312yes—
56C24×C283—21no—
57C2×D4×C283—22no—
58C2×D4×C283—21no—
59C2×D4×C283—22no—
60C2×D4×C283C2312yes—
61C22×C4×C283C2311yescharacteristic
62M16×C283—22no—
63C2×C8×C283C2312yes—
64C4⋊C4×C283C2312yes—
65C22⋊C4×C283—21no—
66C42×C283—21no—
67C22×D283—22no—
68C22×D283—24no—
69C22×D283—21no—
70C22×D283—82no—
71Dic566—21no—
72Dic566—21no—
73D1132—24no—
74D1132—21no—
75D1132—22no—
76D1132—21no—
77D1132C2×D414yes—
78C22⋊D283—42no—
79C22⋊D283—84no—
80C2×Dic283—21no—
81C2×Dic283C2×D414yes—
82C4×D283—42no—
83C4×D283—84no—
84C283⋊C8—22no—
85C23×C283—22no—
86C23×C283—42no—
87C23×C283—82no—
88C23×C283C2×D411yescharacteristic
89D4×C283—22no—
90D4×C283—22no—
91D4×C283—42no—
92C2×C4×C283—22no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D412yes—
95C2×C4×C283#4112yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C22×C283—22no—
99C22×C283—42no—
100C22×C283—44no—
101C22×C283—84no—
102C22×C283#12112yes—
103C22×C283C22×D411yescharacteristic
104C2×D283—24no—
105C2×D283—44no—
106C2×D283—41no—
107C2×D283—42no—
108C2×D283—84no—
109C4×C283—42no—
110C4×C283#12112yes—
111C4×C283C22×D411yescharacteristic
112C4×C283C2×#4111yescharacteristic
113Dic283—24no—
114Dic283—41no—
115C2×C283—22no—
116C2×C283—82no—
117C2×C283C2×#12111yescharacteristic
118C2×C283#57612yes—
119D283—44no—
120D283—81no—
121C283#304111yescharacteristic, complemented, Sylow
122#3041—2831nomaximal, Sylow
123C2×AGL(1,ℤ/8)—2831no—
124C22×D8—2831no—
125#535—2831no—
126#518—2831no—
127#463—2834no—
128#459—2834no—
129#424—2831no—
130#418D28311yescharacteristic, complemented
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×M16C2×D28311yescharacteristic
141C22×C8—2831no—
142#127—2832no—
143#124—2832no—
144#121—5662no—
145#120—5662no—
146C4×D4—2834no—
147C4×D4—5662no—
148#117—2831no—
149#117C2×D28311yescharacteristic
150C2×C22⋊C4—5662no—
151C4⋊C8—2834no—
152#103—2832no—
153#102—2832no—
154#102C2×D28314yescomplemented
155C24—21no—
156C24—5661no—
157#41—5662no—
158#41—5662no—
159C2×Q8—2831no—
160C2×D4—22no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—2834no—
164C2×D4—2832no—
165C2×D4—2831no—
166C2×D4—5664no—
167C2×D4—5661no—
168C2×D4—5661no—
169C2×D4—5662no—
170C2×D4C22×D28312yes—
171C22×C4—5664no—
172C22×C4—5661no—
173C22×C4C22×D28311yescharacteristic
174SD16—5664no—
175D8—5664no—
176D8—5668no—
177M16—22no—
178C2×C8—2832no—
179C2×C8—5662no—
180C2×C8C22×D28312yes—
181C4⋊C4—2832no—
182C4⋊C4C22×D28312yes—
183C22⋊C4—21no—
184C22⋊C4—2832no—
185C22⋊C4—5664no—
186C22⋊C4—5664no—
187C42—21no—
188C42—2832no—
189C23—22no—
190C23—42no—
191C23—82no—
192C23—5662no—
193C23—5664no—
194C23—5661no—
195C23—22642no—
196C23D4×D28311yescharacteristic
197Q8—5661no—
198Q8—5661no—
199D4—22no—
200D4—22no—
201D4—42no—
202D4—2834no—
203D4—5664no—
204D4—5661no—
205D4—5662no—
206D4—5661no—
207D4—11322no—
208D4—22644no—
209C2×C4—22no—
210C2×C4—2834no—
211C2×C4—5661no—
212C2×C4—11322no—
213C2×C4—22644no—
214C2×C4D4×D28311yescharacteristic
215C2×C4D4×D28312yes—
216C2×C4#1798539212yes—
217C2×C4C23×D28311yescharacteristic
218C8—22no—
219C8—5662no—
220C22—22no—
221C22—42no—
222C22—44no—
223C22—84no—
224C22—5664no—
225C22—11324no—
226C22—11321no—
227C22—11322no—
228C22—22644no—
229C22#2258358312yes—
230C22C2×D4×D28311yescharacteristic
231C4—42no—
232C4—5664no—
233C4—11321no—
234C4#2258358312yes—
235C4C2×D4×D28311yescharacteristic
236C4C2×#1798539211yescharacteristic
237C2—22no—
238C2—82no—
239C2—11324no—
240C2—22641no—
241C2C2×#2258358311yescharacteristic
242C2#3182726912yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
hypercenter#418D283
hypocenterC283#3041
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
1. C2×#22583638C2semidirect
2. C22×#17985377C2semidirect
3. #31827032C2semidirect
4. #31826939C2semidirect
5. #31826679C2semidirect
6. #31826659C2semidirect
7. #31826493C2semidirect
8. #31826459C2semidirect
9. #418×C283C2semidirect
13. C2×#17985381C22semidirect
14. C2×D2264C22semidirect
18. #22583606C22semidirect
19. #22583597C22semidirect
23. #22583572C22semidirect
26. Dic283⋊C8C22semidirect
27. #22583533C22semidirect
28. #22583530C22semidirect
32. #102×C283C22semidirect
39. C2×D1132D4semidirect
121. C283#3041semidirect
130. #418D283semidirect
154. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
C22×#179853772
#318270322
#318269392
#318266792
#318266592
#318264932
#318264592
#418×C2832
#3041283