Finite Group Databasebeta

← #49130110

Subgroups — #49130110

Order 36224.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D283C211yesmaximal, characteristic
2#31826937C212yesmaximal, complemented
3#31826578C211yesmaximal, characteristic, complemented
4#31826577C211yesmaximal, characteristic, complemented
5#31826576C211yesmaximal, characteristic, complemented
6C4×#17985377C212yesmaximal, complemented
7#31826545C212yesmaximal, complemented
8#31826500C211yesmaximal, characteristic, complemented
9#31826468C212yesmaximal, complemented
10#31826422C211yesmaximal, characteristic, complemented
11#442×C283C211yesmaximal, characteristic, complemented
12C2×D4×D283C2212yes—
13C2×D2264C2211yescharacteristic
14C2×#17985377C2212yes—
15D8×D283C418yescomplemented
16C2×#17985375C2211yescharacteristic
17C2×C8×D283C2211yescharacteristic
18C4×D1132C2212yescomplemented
19D4×Dic283C2212yescomplemented
20#22583572C2212yescomplemented
21C4×C22⋊D283—22no—
22(C22⋊D283)⋊C4—22no—
23#22583568C2212yes—
24#22583567C2211yescharacteristic
25C2×(C2×D283)⋊C4—22no—
26C22⋊C4×D283—22no—
27#22583543C2212yescomplemented
28#22583542C2211yescharacteristic, complemented
29#22583532C2212yescomplemented
30#22583531C2212yescomplemented
31#22583530C2212yescomplemented
32#22583520C2211yescharacteristic, complemented
33C4×C283⋊C8C2211yescharacteristic, complemented
34C8×Dic283C2211yescharacteristic, complemented
35C2×D8×C283C2211yescharacteristic
36C4×D4×C283C2212yescomplemented
37#106×C283C2211yescharacteristic, complemented
38#102×C283C2212yescomplemented
39#97×C283C2211yescharacteristic, complemented
40C23×D283—22no—
41C2×D1132C2312yes—
42C2×C22⋊D283—22no—
43D4×D283—24no—
44D4×D283C2×C418yescomplemented
45C22×Dic283—22no—
46C2×C4×D283—22no—
47C2×C4×D283—22no—
48C2×C4×D283C2311yescharacteristic
49D2264C2×C414yescomplemented
50#17985377C2×C418yescomplemented
51#17985375—22no—
52C2×C283⋊C8C2311yescharacteristic
53C2×C283⋊C8C2311yescharacteristic
54C8×D283C2×C414yescomplemented
55C4⋊Dic283C2312yes—
56Dic283⋊C4D412yes—
57C22⋊Dic283—22no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4D412yes—
62C4×Dic283—22no—
63C4×Dic283C2311yescharacteristic
64C2×D4×C283C2312yes—
65C22×C4×C283—22no—
66D8×C283C2×C414yescomplemented
67C2×C8×C283C2311yescharacteristic
68C2×C8×C283C2311yescharacteristic
69C4⋊C4×C283C2312yes—
70C22⋊C4×C283—22no—
71C42×C283C2311yescharacteristic
72C22×D283—22no—
73C22×D283—28no—
74C22×D283—82no—
75C22×D283—82no—
76C22×D283C2×D411yescharacteristic
77D1132—22no—
78D1132C22×C414yes—
79C22⋊D283—28no—
80C2×Dic283—22no—
81C2×Dic283—82no—
82C2×Dic283C2×D412yes—
83C2×Dic283C2×D411yescharacteristic
84C4×D283—82no—
85C4×D283—82no—
86C4×D283C22×C412yes—
87C4×D283#4112yes—
88C283⋊C8—21no—
89C283⋊C8C22×C412yes—
90C23×C283—22no—
91D4×C283—22no—
92D4×C283C22×C414yes—
93C2×C4×C283—22no—
94C2×C4×C283—82no—
95C2×C4×C283C2×D412yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283—21no—
98C8×C283C22×C412yes—
99C22×C283—24no—
100C22×C283—42no—
101C22×C283—42no—
102C22×C283C22×D411yescharacteristic
103C2×D283—22no—
104C2×D283—24no—
105C2×D283—42no—
106C2×D283—42no—
107C2×D283—88no—
108C2×D283C4×D412yes—
109C4×C283—22no—
110C4×C283—42no—
111C4×C283C23×C411yescharacteristic
112C4×C283C2×#4111yescharacteristic
113Dic283—22no—
114Dic283—42no—
115Dic283C4×D412yes—
116C2×C283—44no—
117C2×C283C2×C4×D411yescharacteristic
118C2×C283#57612yes—
119D283—22no—
120D283—44no—
121C283#294811yescharacteristic, complemented, Sylow
122#2948—2831nomaximal, Sylow
123C22×D8—2831no—
124#518—2832no—
125#442—2831no—
126#442—2831no—
127#442—2831no—
128#442D28311yescharacteristic, complemented
129C4×D8—2832no—
130C4×D8—2832no—
131#427—2831no—
132#418—2832no—
133#405—2831no—
134C22×D4—2832no—
135C2×D8—2832no—
136C2×D8—2838no—
137C2×D8—2831no—
138C2×D8C2×D28311yescharacteristic
139C2×M16—2831no—
140C22×C8—2831no—
141C4×D4—2832no—
142C4×D4—2832no—
143C4×D4—2832no—
144C4×D4—5662no—
145C4×D4—5662no—
146C4×D4C2×D28312yescomplemented
147#117—2831no—
148#117—2832no—
149C2×C22⋊C4—5662no—
150C2×C22⋊C4—5662no—
151#107—2832no—
152#106—2831no—
153#106C2×D28311yescharacteristic, complemented
154#102—2832no—
155#102—2832no—
156#102—2832no—
157#102C2×D28312yescomplemented
158#97—2831no—
159#97C2×D28311yescharacteristic, complemented
160C4×C8—2831no—
161C4×C8—2831no—
162C24—5662no—
163C2×D4—2838no—
164C2×D4—2832no—
165C2×D4—5664no—
166C2×D4—5662no—
167C2×D4C22×D28312yes—
168C22×C4—22no—
169C22×C4—2831no—
170C22×C4—5662no—
171C22×C4—5662no—
172C22×C4—5662no—
173D8—2838no—
174D8—2834no—
175D8C4×D28314yescomplemented
176M16—5662no—
177C2×C8—2831no—
178C2×C8—2834no—
179C2×C8—2831no—
180C2×C8C22×D28311yescharacteristic
181C2×C8C22×D28311yescharacteristic
182C4⋊C4—2832no—
183C4⋊C4—2832no—
184C4⋊C4C22×D28312yes—
185C22⋊C4—22no—
186C22⋊C4—2832no—
187C22⋊C4—5662no—
188C22⋊C4—5662no—
189C22⋊C4—5662no—
190C22⋊C4—5662no—
191C42—2831no—
192C42—5662no—
193C42C22×D28311yescharacteristic
194C23—22no—
195C23—2831no—
196C23—5668no—
197C23—5662no—
198C23—22642no—
199C23—22642no—
200D4—22no—
201D4—2834no—
202D4—5668no—
203D4—5662no—
204D4C2×C4×D28314yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—2831no—
208C2×C4—2832no—
209C2×C4—2832no—
210C2×C4—2832no—
211C2×C4—5662no—
212C2×C4—22642no—
213C2×C4—22642no—
214C2×C4—22642no—
215C2×C4D4×D28312yes—
216C2×C4C23×D28311yescharacteristic
217C8—21no—
218C8—2832no—
219C8—5661no—
220C8C2×C4×D28312yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—2832no—
225C22—5662no—
226C22—5664no—
227C22—11322no—
228C22—11322no—
229C22—22648no—
230C22C2×D4×D28311yescharacteristic
231C4—22no—
232C4—42no—
233C4—2832no—
234C4—5662no—
235C4—11322no—
236C4C22×C4×D28311yescharacteristic
237C4#41×D28311yescharacteristic
238C2—44no—
239C2—5662no—
240C2—11324no—
241C2C4×D4×D28311yescharacteristic
242C2#3182726912yes—
subgroupG/H
centerC22C2×D4×D283
commutatorC4×C283C23×C4
FrattiniC2×C4C23×D283
Fitting#442×C283C2
socleC22×C283C22×D4
prime radicalC2×D8×D283C2
cosocleC2×C4×C283C24
hypercenter#442D283
hypocenterC283#2948
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #31826937C2semidirect
3. #31826578C2semidirect
4. #31826577C2semidirect
5. #31826576C2semidirect
6. C4×#17985377C2semidirect
7. #31826545C2semidirect
8. #31826500C2semidirect
9. #31826468C2semidirect
10. #31826422C2semidirect
11. #442×C283C2semidirect
15. D8×D283C4semidirect
18. C4×D1132C22semidirect
19. D4×Dic283C22semidirect
20. #22583572C22semidirect
27. #22583543C22semidirect
28. #22583542C22semidirect
29. #22583532C22semidirect
30. #22583531C22semidirect
31. #22583530C22semidirect
32. #22583520C22semidirect
33. C4×C283⋊C8C22semidirect
34. C8×Dic283C22semidirect
36. C4×D4×C283C22semidirect
37. #106×C283C22semidirect
38. #102×C283C22semidirect
39. #97×C283C22semidirect
44. D4×D283C2×C4semidirect
49. D2264C2×C4semidirect
50. #17985377C2×C4semidirect
54. C8×D283C2×C4semidirect
66. D8×C283C2×C4semidirect
121. C283#2948semidirect
128. #442D283semidirect
146. C4×D4C2×D283semidirect
153. #106C2×D283semidirect
157. #102C2×D283semidirect
159. #97C2×D283semidirect
175. D8C4×D283semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D2832
#318269372
#318265782
#318265772
#318265762
C4×#179853772
#318265452
#318265002
#318264682
#318264222
#442×C2832
#2948283