Finite Group Databasebeta

← #49148534

Subgroups — #49148534

Order 36928.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#32914657C211yesmaximal, characteristic, complemented
2#32914657C211yesmaximal, characteristic, complemented
3#32914651C211yesmaximal, characteristic, complemented
4#32914650C211yesmaximal, characteristic, complemented
5#32914646C211yesmaximal, characteristic, complemented
6#32914645C211yesmaximal, characteristic, complemented
7#32914641C211yesmaximal, characteristic, complemented
8#32914636C211yesmaximal, characteristic, complemented
9#32914636C211yesmaximal, characteristic, complemented
10#32914635C211yesmaximal, characteristic, complemented
11#32914633C211yesmaximal, characteristic, complemented
12D4×Dic577C211yesmaximal, characteristic, complemented
13#32914624C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic577C211yesmaximal, characteristic, complemented
15#120×C577C211yesmaximal, characteristic, complemented
16C2×Dic1154C2211yescharacteristic, complemented
17C2×C22⋊D577C2211yescharacteristic
18C2×C22⋊D577C2211yescharacteristic
19C2×C22⋊D577C2211yescharacteristic
20C2×C22⋊D577C2211yescharacteristic, complemented
21C22×Dic577C2211yescharacteristic
22C22×Dic577C2211yescharacteristic
23C22×Dic577C2211yescharacteristic, complemented
24C2×C4×D577C2211yescharacteristic, complemented
25C4⋊Dic577C2211yescharacteristic, complemented
26C4⋊Dic577C2211yescharacteristic, complemented
27#22604397C2211yescharacteristic, complemented
28#22604397C2211yescharacteristic, complemented
29#22604397C2211yescharacteristic, complemented
30#22604397C2211yescharacteristic, complemented
31C22⋊Dic577C2211yescharacteristic
32C22⋊Dic577C2211yescharacteristic
33C22⋊Dic577C2211yescharacteristic
34C22⋊Dic577C2211yescharacteristic
35C22⋊Dic577C2211yescharacteristic
36C22⋊Dic577C2211yescharacteristic
37C22⋊Dic577C2211yescharacteristic
38C22⋊Dic577C2211yescharacteristic, complemented
39C22⋊Dic577C2211yescharacteristic, complemented
40#22604395C2211yescharacteristic, complemented
41#22604395C2211yescharacteristic, complemented
42C4×Dic577C2211yescharacteristic, complemented
43C4×Dic577C2211yescharacteristic, complemented
44C24×C577C2211yescharacteristic
45C2×D4×C577C2211yescharacteristic
46C2×D4×C577C2211yescharacteristic
47C2×D4×C577C2211yescharacteristic
48C22⋊C4×C577C2211yescharacteristic
49C22⋊C4×C577C2211yescharacteristic
50C22⋊C4×C577C2211yescharacteristic
51C22×D577C2311yescharacteristic
52Dic1154—41no—
53C22⋊D577—22no—
54C22⋊D577—41no—
55C22⋊D577—41no—
56C22⋊D577—41no—
57C2×Dic577—41no—
58C2×Dic577—41no—
59C2×Dic577—41no—
60C2×Dic577C2311yescharacteristic
61C2×Dic577C2311yescharacteristic
62C2×Dic577C2311yescharacteristic
63C2×Dic577C2311yescharacteristic
64C2×Dic577C2311yescharacteristic
65C2×Dic577C2311yescharacteristic
66C2×Dic577C2311yescharacteristic
67C4×D577—41no—
68C23×C577—22no—
69C23×C577—41no—
70C23×C577—41no—
71C23×C577C2311yescharacteristic
72C23×C577C2311yescharacteristic
73C23×C577C2311yescharacteristic
74C23×C577C2311yescharacteristic
75D4×C577—22no—
76D4×C577—41no—
77D4×C577—41no—
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×C577—21no—
88C22×C577—21no—
89C22×C577—21no—
90C22×C577—21no—
91C22×C577—21no—
92C22×C577—44no—
93C22×C577#4112yes—
94C22×C577C2411yescharacteristic
95C2×D577—21no—
96C2×D577—21no—
97C2×D577—21no—
98C4×C577—21no—
99C4×C577—21no—
100C4×C577—21no—
101Dic577—21no—
102Dic577—21no—
103Dic577—21no—
104Dic577—21no—
105Dic577—21no—
106Dic577—21no—
107Dic577—21no—
108C2×C577—22no—
109C2×C577—41no—
110C2×C577—41no—
111C2×C577—41no—
112C2×C577C2×#4111yescharacteristic
113C2×C577H(5,𝔽2)11yescharacteristic
114C2×C577H(5,𝔽2)11yescharacteristic
115D577—41no—
116C577#53811yescharacteristic, complemented, Sylow
117#538—5771nomaximal, Sylow
118#126—5771no—
119#126—5771no—
120#124—5771no—
121#124—5771no—
122#123—5771no—
123#123—5771no—
124C22⋊Q8—5771no—
125#121—5771no—
126#121—5771no—
127#121—5771no—
128#120—5771no—
129#120D57711yescharacteristic, complemented
130C4×D4—5771no—
131C4×D4—5771no—
132C2×C22⋊C4—5771no—
133C24C2×D57711yescharacteristic
134C2×Q8—5771no—
135C2×D4—5771no—
136C2×D4—5771no—
137C2×D4—5771no—
138C2×D4—5771no—
139C2×D4C2×D57711yescharacteristic
140C2×D4C2×D57711yescharacteristic
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⋊C4—5771no—
163C22⋊C4C2×D57711yescharacteristic
164C22⋊C4C2×D57711yescharacteristic
165C22⋊C4C2×D57711yescharacteristic
166C42—5771no—
167C42—5771no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—5771no—
172C23C22×D57711yescharacteristic
173C23C22×D57711yescharacteristic
174C23C22×D57711yescharacteristic
175C23C22×D57711yescharacteristic
176Q8—23081no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—23081no—
181D4—23081no—
182D4—23081no—
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×C4—5771no—
194C2×C4—5771no—
195C2×C4C22×D57711yescharacteristic
196C2×C4C22×D57711yescharacteristic
197C2×C4C22×D57711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—11541no—
211C22—11541no—
212C22—11541no—
213C22#2260441712yes—
214C22C23×D57711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—11541no—
219C4—11541no—
220C4—11541no—
221C4—11541no—
222C4—11541no—
223C4—11541no—
224C4—11541no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—23081no—
230C2C2×#2260441711yescharacteristic
231C2#3291470911yescharacteristic
232C2#3291470911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D577
commutator, socle, cosocleC22×C577C24
Fitting#120×C577C2
hypercenter#120D577
hypocenterC577#538
LCSG ▷ C22×C577 ▷ C577
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #32914657C2semidirect
2. #32914657C2semidirect
3. #32914651C2semidirect
4. #32914650C2semidirect
5. #32914646C2semidirect
6. #32914645C2semidirect
7. #32914641C2semidirect
8. #32914636C2semidirect
9. #32914636C2semidirect
10. #32914635C2semidirect
11. #32914633C2semidirect
12. D4×Dic577C2semidirect
13. #32914624C2semidirect
14. C2×C22⋊Dic577C2semidirect
15. #120×C577C2semidirect
16. C2×Dic1154C22semidirect
20. C2×C22⋊D577C22semidirect
23. C22×Dic577C22semidirect
24. C2×C4×D577C22semidirect
25. C4⋊Dic577C22semidirect
26. C4⋊Dic577C22semidirect
27. #22604397C22semidirect
28. #22604397C22semidirect
29. #22604397C22semidirect
30. #22604397C22semidirect
38. C22⋊Dic577C22semidirect
39. C22⋊Dic577C22semidirect
40. #22604395C22semidirect
41. #22604395C22semidirect
42. C4×Dic577C22semidirect
43. C4×Dic577C22semidirect
116. C577#538semidirect
129. #120D577semidirect

Maximal subgroups

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

subgroupindex
#329146572
#329146512
#329146502
#329146462
#329146452
#329146412
#329146362
#329146352
#329146332
D4×Dic5772
#329146242
C2×C22⋊Dic5772
#120×C5772
#538577