Finite Group Databasebeta

← #49134394

Subgroups — #49134394

Order 36224.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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#31826907C212yesmaximal, complemented
3#31826904C212yesmaximal, complemented
4#31826902C212yesmaximal, complemented
5#31826899C212yesmaximal, complemented
6#31826897C211yesmaximal, characteristic, complemented
7#31826895C212yesmaximal, complemented
8C2×#22583549C211yesmaximal, characteristic, complemented
9#508×C283C211yesmaximal, characteristic, complemented
10#41×D283—22no—
11#22583633C2212yes—
12#22583632C2212yescomplemented
13#22583631—22no—
14#22583630—22no—
15#22583629C2212yes—
16Q16×D283C2212yescomplemented
17SD16×D283—22no—
18D8×D283C2212yescomplemented
19C2×C8×D283C2211yescharacteristic
20Dic2264C2211yescharacteristic, complemented
21#22583556C2212yescomplemented
22#22583555C2212yescomplemented
23#22583554C2212yescomplemented
24#22583553C2212yescomplemented
25D4528C2211yescharacteristic, complemented
26#22583551C2212yescomplemented
27#22583549C2212yescomplemented
28#22583549C2212yescomplemented
29C2×C283⋊C16C2211yescharacteristic, complemented
30#135×C283C2212yescomplemented
31Q32×C283C2211yescharacteristic, complemented
32SD32×C283C2212yescomplemented
33D16×C283C2211yescharacteristic, complemented
34C2×C16×C283C2211yescharacteristic, complemented
35#17985393—22no—
36#17985392—22no—
37#17985392—42no—
38#17985391—22no—
39#17985391—42no—
40Q8×D283—22no—
41D4×D283—22no—
42D4×D283—42no—
43C2×C4×D283—42no—
44C2×C4×D283D411yescharacteristic
45Dic1132C2312yes—
46#17985382—22no—
47#17985381—22no—
48#17985380—22no—
49#17985379—22no—
50D2264C2312yes—
51#17985377—22no—
52C2×C283⋊C8D411yescharacteristic
53C8×D283D412yes—
54C8×D283C2312yes—
55C283⋊C16C2312yes—
56#41×C283—22no—
57Q16×C283C2312yes—
58SD16×C283—22no—
59D8×C283C2312yes—
60C2×C8×C283C2311yescharacteristic
61C16×C283C2311yescharacteristic
62C16×C283C2311yescharacteristic
63C22×D283—42no—
64C22×D283D811yescharacteristic
65Dic566—22no—
66Dic566—42no—
67D1132—22no—
68D1132—42no—
69C22⋊D283—42no—
70C22⋊D283—42no—
71C22⋊D283—42no—
72C2×Dic283—42no—
73C2×Dic283D811yescharacteristic
74C4×D283—42no—
75C4×D283—42no—
76C4×D283—42no—
77C4×D283D812yes—
78C4×D283C2×D412yes—
79C283⋊C8C2×D412yes—
80Q8×C283—22no—
81D4×C283—22no—
82D4×C283—42no—
83C2×C4×C283—42no—
84C2×C4×C283C2×D411yescharacteristic
85C8×C283C2×D411yescharacteristic
86C8×C283C2411yescharacteristic
87C22×C283—42no—
88C22×C283C2×D811yescharacteristic
89C2×D283—41no—
90C2×D283—42no—
91C2×D283—84no—
92C2×D283C2×D812yes—
93C4×C283—42no—
94C4×C283C2×D811yescharacteristic
95C4×C283C22×D411yescharacteristic
96Dic283—42no—
97Dic283C2×D812yes—
98C2×C283—21no—
99C2×C283—82no—
100C2×C283C22×D811yescharacteristic
101D283—22no—
102D283—82no—
103C283#341411yescharacteristic, complemented, Sylow
104#3414—2831nomaximal, Sylow
105C2×#135—2832no—
106#510—2832no—
107#510—2832no—
108#509—2832no—
109#509—2832no—
110#508—2832no—
111#508—2831no—
112#508D28311yescharacteristic, complemented
113C2×M32—2831no—
114C2×#41—5662no—
115#135—2832no—
116#135—2832no—
117#135—2832no—
118#135—5662no—
119#135—5662no—
120#135C2×D28312yescomplemented
121C2×Q16—2832no—
122C2×SD16—5662no—
123C2×D8—2832no—
124C22×C8—2831no—
125Q32—2832no—
126Q32—2831no—
127Q32C2×D28311yescharacteristic, complemented
128SD32—2832no—
129SD32—2832no—
130SD32—2832no—
131SD32C2×D28312yescomplemented
132D16—2832no—
133D16—2831no—
134D16C2×D28311yescharacteristic, complemented
135M32—2832no—
136M32—2832no—
137C2×C16—2831no—
138C2×C16C2×D28311yescharacteristic, complemented
139#41—22no—
140#41—5662no—
141#41—5662no—
142#41—5662no—
143#41—11322no—
144#41—11322no—
145C2×Q8—5662no—
146C2×D4—5662no—
147C2×D4—11322no—
148C22×C4—2831no—
149C22×C4—11322no—
150Q16—2832no—
151Q16—5662no—
152Q16C22×D28312yes—
153SD16—22no—
154SD16—5662no—
155SD16—5662no—
156SD16—5662no—
157D8—2832no—
158D8—5662no—
159D8C22×D28312yes—
160C2×C8—2831no—
161C2×C8—2832no—
162C2×C8—2832no—
163C2×C8C22×D28311yescharacteristic
164C16—2832no—
165C16C22×D28311yescharacteristic
166C16C22×D28311yescharacteristic
167C23—2831no—
168C23—11322no—
169Q8—22no—
170Q8—5662no—
171Q8—11322no—
172D4—22no—
173D4—42no—
174D4—5662no—
175D4—11322no—
176D4—11322no—
177D4—11322no—
178D4—11322no—
179C2×C4—42no—
180C2×C4—2831no—
181C2×C4—2832no—
182C2×C4—2832no—
183C2×C4—11322no—
184C2×C4—11322no—
185C2×C4—11322no—
186C2×C4—11322no—
187C2×C4D4×D28311yescharacteristic
188C8—2832no—
189C8D4×D28311yescharacteristic
190C8C23×D28311yescharacteristic
191C22—42no—
192C22—2832no—
193C22—11321no—
194C22—11322no—
195C22—22644no—
196C22D8×D28311yescharacteristic
197C4—42no—
198C4—2832no—
199C4—11322no—
200C4D8×D28311yescharacteristic
201C4C2×D4×D28311yescharacteristic
202C2—21no—
203C2—82no—
204C2—5662no—
205C2—22642no—
206C2C2×D8×D28311yescharacteristic
subgroupG/H
centerC4D8×D283
commutator, cosocleC8×C283C24
FrattiniC8C23×D283
Fitting#508×C283C2
socleC2×C283C22×D8
hypercenter#508D283
hypocenterC283#3414
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. #31826907C2semidirect
3. #31826904C2semidirect
4. #31826902C2semidirect
5. #31826899C2semidirect
6. #31826897C2semidirect
7. #31826895C2semidirect
8. C2×#22583549C2semidirect
9. #508×C283C2semidirect
12. #22583632C22semidirect
16. Q16×D283C22semidirect
18. D8×D283C22semidirect
20. Dic2264C22semidirect
21. #22583556C22semidirect
22. #22583555C22semidirect
23. #22583554C22semidirect
24. #22583553C22semidirect
25. D4528C22semidirect
26. #22583551C22semidirect
27. #22583549C22semidirect
28. #22583549C22semidirect
29. C2×C283⋊C16C22semidirect
30. #135×C283C22semidirect
31. Q32×C283C22semidirect
32. SD32×C283C22semidirect
33. D16×C283C22semidirect
34. C2×C16×C283C22semidirect
103. C283#3414semidirect
112. #508D283semidirect
120. #135C2×D283semidirect
127. Q32C2×D283semidirect
131. SD32C2×D283semidirect
134. D16C2×D283semidirect
138. 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
#318269072
#318269042
#318269022
#318268992
#318268972
#318268952
C2×#225835492
#508×C2832
#3414283