Finite Group Databasebeta

← #508×D283 #49134375

Subgroups — #508×D283 #49134375

Order 36224.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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#135×D283C212yesmaximal, complemented
2#31826898C211yesmaximal, characteristic, complemented
3#31826897C211yesmaximal, characteristic, complemented
4#31826896C212yesmaximal, complemented
5#31826895C212yesmaximal, complemented
6#31826894C211yesmaximal, characteristic, complemented
7Q32×D283C211yesmaximal, characteristic, complemented
8SD32×D283C212yesmaximal, complemented
9D16×D283C211yesmaximal, characteristic, complemented
10C2×C16×D283C211yesmaximal, characteristic, complemented
11#508×C283C211yesmaximal, characteristic, complemented
12#41×D283—22no—
13#22583633C2212yescomplemented
14#22583632C2212yescomplemented
15#22583631—22no—
16#22583630—22no—
17#22583629C2212yescomplemented
18Q16×D283C2212yes—
19SD16×D283—22no—
20D8×D283C2212yes—
21C2×C8×D283C2211yescharacteristic
22Dic2264C2211yescharacteristic, complemented
23#22583556C2212yescomplemented
24#22583555C2212yescomplemented
25#22583554C2212yescomplemented
26#22583553C2212yescomplemented
27D4528C2211yescharacteristic, complemented
28#22583551C2212yescomplemented
29C2×C283⋊C16C2211yescharacteristic, complemented
30C16×D283C2211yescharacteristic
31C16×D283C2211yescharacteristic
32C16×D283C2211yescharacteristic, complemented
33C16×D283C2211yescharacteristic, complemented
34#135×C283C2212yescomplemented
35Q32×C283C2211yescharacteristic, complemented
36SD32×C283C2212yescomplemented
37D16×C283C2211yescharacteristic, complemented
38C2×C16×C283C2211yescharacteristic, complemented
39#17985393—22no—
40#17985392—22no—
41#17985392—42no—
42#17985391—22no—
43#17985391—42no—
44Q8×D283—22no—
45D4×D283—22no—
46D4×D283—42no—
47C2×C4×D283—42no—
48C2×C4×D283D411yescharacteristic
49Dic1132C2312yes—
50#17985382—22no—
51#17985381—22no—
52#17985380—22no—
53#17985379—22no—
54D2264C2312yes—
55#17985377—22no—
56C2×C283⋊C8D411yescharacteristic
57C8×D283D411yescharacteristic
58C8×D283D411yescharacteristic
59C8×D283C2311yescharacteristic
60C8×D283C2311yescharacteristic
61C283⋊C16C2311yescharacteristic
62C283⋊C16C2311yescharacteristic
63#41×C283—22no—
64Q16×C283C2312yes—
65SD16×C283—22no—
66D8×C283C2312yes—
67C2×C8×C283C2311yescharacteristic
68C16×C283C2311yescharacteristic
69C16×C283C2311yescharacteristic
70C22×D283—42no—
71C22×D283D811yescharacteristic
72Dic566—22no—
73Dic566—42no—
74D1132—22no—
75D1132—42no—
76C22⋊D283—42no—
77C22⋊D283—42no—
78C22⋊D283—42no—
79C2×Dic283—42no—
80C2×Dic283D811yescharacteristic
81C4×D283—42no—
82C4×D283—42no—
83C4×D283—42no—
84C4×D283D811yescharacteristic
85C4×D283D811yescharacteristic
86C4×D283C2×D411yescharacteristic
87C4×D283C2×D411yescharacteristic
88C283⋊C8C2×D411yescharacteristic
89C283⋊C8C2×D411yescharacteristic
90Q8×C283—22no—
91D4×C283—22no—
92D4×C283—42no—
93C2×C4×C283—42no—
94C2×C4×C283C2×D411yescharacteristic
95C8×C283C2×D411yescharacteristic
96C8×C283C2411yescharacteristic
97C22×C283—42no—
98C22×C283C2×D811yescharacteristic
99C2×D283—22no—
100C2×D283—42no—
101C2×D283—84no—
102C2×D283C2×D811yescharacteristic
103C2×D283C2×D811yescharacteristic
104C4×C283—42no—
105C4×C283C2×D811yescharacteristic
106C4×C283C22×D411yescharacteristic
107Dic283—42no—
108Dic283C2×D811yescharacteristic
109Dic283C2×D811yescharacteristic
110C2×C283—21no—
111C2×C283—82no—
112C2×C283C22×D811yescharacteristic
113D283—21no—
114D283—82no—
115D283#50812yesdirect product factor
116C283C2×#50811yescharacteristic, complemented, Sylow
117C2×#508—2831nomaximal, Sylow
118C2×#135—2832no—
119#508—2832no—
120#508—2831no—
121#508—2832no—
122#508—2831no—
123#508—2831no—
124#508D28311yescharacteristic, direct product factor
125C2×Q32—2831no—
126C2×SD32—2832no—
127C2×D16—2831no—
128C22×C16—2831no—
129C2×#41—5662no—
130#135—2832no—
131#135—2832no—
132#135—2832no—
133#135—5662no—
134#135—5662no—
135#135C2×D28312yescomplemented
136C2×Q16—2832no—
137C2×SD16—5662no—
138C2×D8—2832no—
139C22×C8—2831no—
140Q32—2832no—
141Q32—2831no—
142Q32C2×D28311yescharacteristic, complemented
143SD32—2832no—
144SD32—2832no—
145SD32—2832no—
146SD32C2×D28312yescomplemented
147D16—2832no—
148D16—2831no—
149D16C2×D28311yescharacteristic, complemented
150C2×C16—2831no—
151C2×C16—2831no—
152C2×C16—2831no—
153C2×C16—2831no—
154C2×C16—2831no—
155C2×C16C2×D28311yescharacteristic, complemented
156#41—22no—
157#41—5662no—
158#41—5662no—
159#41—5662no—
160#41—11322no—
161#41—11322no—
162C2×Q8—5662no—
163C2×D4—5662no—
164C2×D4—11322no—
165C22×C4—2831no—
166C22×C4—11322no—
167Q16—2832no—
168Q16—5662no—
169Q16C22×D28312yes—
170SD16—22no—
171SD16—5662no—
172SD16—5662no—
173SD16—5662no—
174D8—2832no—
175D8—5662no—
176D8C22×D28312yes—
177C2×C8—2831no—
178C2×C8—2831no—
179C2×C8—2831no—
180C2×C8—2831no—
181C2×C8—2831no—
182C2×C8C22×D28311yescharacteristic
183C16—2831no—
184C16—2831no—
185C16C22×D28311yescharacteristic
186C16C22×D28311yescharacteristic
187C23—2831no—
188C23—11322no—
189Q8—22no—
190Q8—5662no—
191Q8—11322no—
192D4—22no—
193D4—42no—
194D4—5662no—
195D4—11322no—
196D4—11322no—
197D4—11322no—
198D4—11322no—
199C2×C4—42no—
200C2×C4—2831no—
201C2×C4—2831no—
202C2×C4—2831no—
203C2×C4—2831no—
204C2×C4—2831no—
205C2×C4—11322no—
206C2×C4—11322no—
207C2×C4—11322no—
208C2×C4—11322no—
209C2×C4D4×D28311yescharacteristic
210C8—2831no—
211C8—2831no—
212C8D4×D28311yescharacteristic
213C8C23×D28311yescharacteristic
214C22—42no—
215C22—2831no—
216C22—2831no—
217C22—5662no—
218C22—11322no—
219C22—22644no—
220C22D8×D28311yescharacteristic
221C4—42no—
222C4—2831no—
223C4—2831no—
224C4—11322no—
225C4D8×D28311yescharacteristic
226C4C2×D4×D28311yescharacteristic
227C2—21no—
228C2—82no—
229C2—2832no—
230C2—5661no—
231C2—22642no—
232C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC4D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#508×C283C2
socleC2×C283C22×D8
hypercenter#508D283
hypocenterC283C2×#508
LCSG ▷ C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D283C2semidirect
2. #31826898C2semidirect
3. #31826897C2semidirect
4. #31826896C2semidirect
5. #31826895C2semidirect
6. #31826894C2semidirect
7. Q32×D283C2semidirect
8. SD32×D283C2semidirect
9. D16×D283C2semidirect
10. C2×C16×D283C2semidirect
11. #508×C283C2semidirect
13. #22583633C22semidirect
14. #22583632C22semidirect
17. #22583629C22semidirect
22. Dic2264C22semidirect
23. #22583556C22semidirect
24. #22583555C22semidirect
25. #22583554C22semidirect
26. #22583553C22semidirect
27. D4528C22semidirect
28. #22583551C22semidirect
29. C2×C283⋊C16C22semidirect
32. C16×D283C22semidirect
33. C16×D283C22semidirect
34. #135×C283C22semidirect
35. Q32×C283C22semidirect
36. SD32×C283C22semidirect
37. D16×C283C22semidirect
38. C2×C16×C283C22semidirect
115. D283#508direct (N × H)
116. C283C2×#508semidirect
124. #508D283direct (N × H)
135. #135C2×D283semidirect
142. Q32C2×D283semidirect
146. SD32C2×D283semidirect
149. D16C2×D283semidirect
155. C2×C16C2×D283semidirect

Maximal subgroups

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

subgroupindex
#135×D2832
#318268982
#318268972
#318268962
#318268952
#318268942
Q32×D2832
SD32×D2832
D16×D2832
C2×C16×D2832
#508×C2832
C2×#508283