Finite Group Databasebeta

← #49148533

Subgroups — #49148533

Order 36928.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#32914658C211yesmaximal, characteristic, complemented
2#32914657C211yesmaximal, characteristic, complemented
3#32914653C211yesmaximal, characteristic, complemented
4#32914648C211yesmaximal, characteristic, complemented
5#32914646C211yesmaximal, characteristic, complemented
6#32914640C211yesmaximal, characteristic, complemented
7#32914637C211yesmaximal, characteristic, complemented
8#32914637C211yesmaximal, characteristic, complemented
9#32914636C211yesmaximal, characteristic, complemented
10#32914634C211yesmaximal, characteristic, complemented
11#32914632C211yesmaximal, characteristic, complemented
12C4×D2308C211yesmaximal, characteristic, complemented
13#32914624C211yesmaximal, characteristic, complemented
14C22⋊C4×D577C211yesmaximal, characteristic, complemented
15#124×C577C211yesmaximal, characteristic, complemented
16C23×D577C2211yescharacteristic
17C2×D2308C2211yescharacteristic
18C2×D2308C2211yescharacteristic
19C2×C22⋊D577C2211yescharacteristic
20C2×C22⋊D577C2211yescharacteristic
21C2×C22⋊D577C2211yescharacteristic
22C2×C22⋊D577C2211yescharacteristic, complemented
23C22×Dic577C2211yescharacteristic, complemented
24C2×C4×D577C2211yescharacteristic
25C2×C4×D577C2211yescharacteristic
26C2×C4×D577C2211yescharacteristic, complemented
27C4⋊Dic577C2211yescharacteristic, complemented
28C4⋊Dic577C2211yescharacteristic, complemented
29#22604397C2211yescharacteristic, complemented
30#22604397C2211yescharacteristic, complemented
31#22604397C2211yescharacteristic, complemented
32#22604397C2211yescharacteristic, complemented
33C22⋊Dic577C2211yescharacteristic
34C22⋊Dic577C2211yescharacteristic
35#22604395C2211yescharacteristic
36#22604395C2211yescharacteristic
37#22604395C2211yescharacteristic
38#22604395C2211yescharacteristic
39#22604395C2211yescharacteristic
40#22604395C2211yescharacteristic
41#22604395C2211yescharacteristic, complemented
42#22604395C2211yescharacteristic, complemented
43C4×Dic577C2211yescharacteristic, complemented
44C2×Q8×C577C2211yescharacteristic, complemented
45C2×D4×C577C2211yescharacteristic
46C22⋊C4×C577C2211yescharacteristic
47C22⋊C4×C577C2211yescharacteristic
48C22⋊C4×C577C2211yescharacteristic, complemented
49C22⋊C4×C577C2211yescharacteristic, complemented
50C42×C577C2211yescharacteristic, complemented
51C22×D577—22no—
52C22×D577—41no—
53C22×D577—41no—
54C22×D577C2311yescharacteristic
55C22×D577C2311yescharacteristic
56C22×D577C2311yescharacteristic
57D2308—22no—
58D2308—41no—
59C22⋊D577—22no—
60C22⋊D577—41no—
61C22⋊D577—41no—
62C22⋊D577—41no—
63C2×Dic577—41no—
64C2×Dic577C2311yescharacteristic
65C2×Dic577C2311yescharacteristic
66C2×Dic577C2311yescharacteristic
67C2×Dic577C2311yescharacteristic
68C2×Dic577C2311yescharacteristic
69C4×D577—41no—
70C4×D577—41no—
71C4×D577—41no—
72C23×C577C2311yescharacteristic
73C23×C577C2311yescharacteristic
74Q8×C577—41no—
75D4×C577—41no—
76C2×C4×C577C2311yescharacteristic
77C2×C4×C577C2311yescharacteristic
78C2×C4×C577C2311yescharacteristic
79C2×C4×C577C2311yescharacteristic
80C2×C4×C577C2311yescharacteristic
81C22×C577—21no—
82C22×C577—21no—
83C22×C577—21no—
84C22×C577—21no—
85C22×C577—21no—
86C22×C577—21no—
87C22×C577C2411yescharacteristic
88C2×D577—21no—
89C2×D577—21no—
90C2×D577—21no—
91C2×D577—21no—
92C2×D577—21no—
93C2×D577—21no—
94C2×D577—21no—
95C2×D577—21no—
96C2×D577—44no—
97C2×D577#4112yes—
98C4×C577—21no—
99C4×C577—21no—
100C4×C577—21no—
101C4×C577—21no—
102C4×C577—21no—
103Dic577—21no—
104Dic577—21no—
105Dic577—21no—
106Dic577—21no—
107Dic577—21no—
108C2×C577—41no—
109C2×C577—41no—
110C2×C577C2×#4111yescharacteristic
111C2×C577H(5,𝔽2)11yescharacteristic
112C2×C577H(5,𝔽2)11yescharacteristic
113D577—22no—
114D577—41no—
115D577—41no—
116C577#53811yescharacteristic, complemented, Sylow
117#538—5771nomaximal, Sylow
118#126—5771no—
119#126—5771no—
120#124—5771no—
121#124D57711yescharacteristic, complemented
122#123—5771no—
123#123—5771no—
124C22⋊Q8—5771no—
125#121—5771no—
126#121—5771no—
127#121—5771no—
128#120—5771no—
129#120—5771no—
130C4×D4—5771no—
131C4×D4—5771no—
132C2×C22⋊C4—5771no—
133C24—5771no—
134C2×Q8C2×D57711yescharacteristic, complemented
135C2×D4—5771no—
136C2×D4—5771no—
137C2×D4—5771no—
138C2×D4—5771no—
139C2×D4—5771no—
140C2×D4—5771no—
141C2×D4C2×D57711yescharacteristic
142C22×C4—5771no—
143C22×C4—5771no—
144C22×C4—5771no—
145C22×C4—5771no—
146C4⋊C4—5771no—
147C4⋊C4—5771no—
148C4⋊C4—5771no—
149C4⋊C4—5771no—
150C4⋊C4—5771no—
151C4⋊C4—5771no—
152C22⋊C4—5771no—
153C22⋊C4—5771no—
154C22⋊C4—5771no—
155C22⋊C4—5771no—
156C22⋊C4—5771no—
157C22⋊C4—5771no—
158C22⋊C4—5771no—
159C22⋊C4—5771no—
160C22⋊C4—5771no—
161C22⋊C4—5771no—
162C22⋊C4C2×D57711yescharacteristic
163C22⋊C4C2×D57711yescharacteristic
164C22⋊C4C2×D57711yescharacteristic, complemented
165C22⋊C4C2×D57711yescharacteristic, complemented
166C42—5771no—
167C42C2×D57711yescharacteristic, complemented
168C23—23081no—
169C23—23081no—
170C23—5771no—
171C23—5771no—
172C23—5771no—
173C23—11542no—
174C23C22×D57711yescharacteristic
175C23C22×D57711yescharacteristic
176Q8—41no—
177D4—41no—
178D4—23081no—
179D4—23081no—
180D4—23081no—
181D4—23081no—
182D4—11542no—
183D4—11542no—
184C2×C4—23081no—
185C2×C4—23081no—
186C2×C4—23081no—
187C2×C4—23081no—
188C2×C4—5771no—
189C2×C4—5771no—
190C2×C4—5771no—
191C2×C4—5771no—
192C2×C4—5771no—
193C2×C4C22×D57711yescharacteristic
194C2×C4C22×D57711yescharacteristic
195C2×C4C22×D57711yescharacteristic
196C2×C4C22×D57711yescharacteristic
197C2×C4C22×D57711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—23084no—
205C22—5772no—
206C22—11541no—
207C22—11541no—
208C22—11541no—
209C22—11541no—
210C22—11541no—
211C22—11541no—
212C22—11541no—
213C22—11541no—
214C22C23×D57711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—11541no—
221C4—11541no—
222C4—11541no—
223C4—11541no—
224C4—11541no—
225C2—41no—
226C2—41no—
227C2—23081no—
228C2—23081no—
229C2—11542no—
230C2#41×D57711yescharacteristic
231C2#3291470911yescharacteristic
232C2#3291471011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#124×C577C2
hypercenter#124D577
hypocenterC577#538
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #32914658C2semidirect
2. #32914657C2semidirect
3. #32914653C2semidirect
4. #32914648C2semidirect
5. #32914646C2semidirect
6. #32914640C2semidirect
7. #32914637C2semidirect
8. #32914637C2semidirect
9. #32914636C2semidirect
10. #32914634C2semidirect
11. #32914632C2semidirect
12. C4×D2308C2semidirect
13. #32914624C2semidirect
14. C22⋊C4×D577C2semidirect
15. #124×C577C2semidirect
22. C2×C22⋊D577C22semidirect
23. C22×Dic577C22semidirect
26. C2×C4×D577C22semidirect
27. C4⋊Dic577C22semidirect
28. C4⋊Dic577C22semidirect
29. #22604397C22semidirect
30. #22604397C22semidirect
31. #22604397C22semidirect
32. #22604397C22semidirect
41. #22604395C22semidirect
42. #22604395C22semidirect
43. C4×Dic577C22semidirect
44. C2×Q8×C577C22semidirect
48. C22⋊C4×C577C22semidirect
49. C22⋊C4×C577C22semidirect
50. C42×C577C22semidirect
116. C577#538semidirect
121. #124D577semidirect
134. C2×Q8C2×D577semidirect
164. C22⋊C4C2×D577semidirect
165. C22⋊C4C2×D577semidirect
167. C42C2×D577semidirect

Maximal subgroups

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

subgroupindex
#329146582
#329146572
#329146532
#329146482
#329146462
#329146402
#329146372
#329146362
#329146342
#329146322
C4×D23082
#329146242
C22⋊C4×D5772
#124×C5772
#538577