Finite Group Databasebeta

← #17989176

Subgroups — #17989176

Order 4672.

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#14556586C211yesmaximal, characteristic, complemented
2#14556579C211yesmaximal, characteristic, complemented
3#14556577C211yesmaximal, characteristic, complemented
4#14556576C211yesmaximal, characteristic, complemented
5#14556573C211yesmaximal, characteristic, complemented
6#14556569C211yesmaximal, characteristic, complemented
7#14556566C211yesmaximal, characteristic, complemented
8#14556566C211yesmaximal, characteristic, complemented
9#14556564C211yesmaximal, characteristic, complemented
10#14556561C211yesmaximal, characteristic, complemented
11#14556561C211yesmaximal, characteristic, complemented
12C4×D292C211yesmaximal, characteristic, complemented
13#14556553C211yesmaximal, characteristic, complemented
14C22⋊C4×D73C211yesmaximal, characteristic, complemented
15#126×C73C211yesmaximal, characteristic, complemented
16C23×D73C2211yescharacteristic
17C2×Dic146C2211yescharacteristic, complemented
18C2×D292C2211yescharacteristic
19C2×D292C2211yescharacteristic
20C2×D292C2211yescharacteristic
21C2×D292C2211yescharacteristic
22C2×D292C2211yescharacteristic, complemented
23C2×C22⋊D73C2211yescharacteristic
24C2×C22⋊D73C2211yescharacteristic
25C2×C4×D73C2211yescharacteristic
26C2×C4×D73C2211yescharacteristic
27C2×C4×D73C2211yescharacteristic, complemented
28C2×C4×D73C2211yescharacteristic, complemented
29C4⋊Dic73C2211yescharacteristic, complemented
30#11924007C2211yescharacteristic, complemented
31#11924007C2211yescharacteristic, complemented
32C22⋊Dic73C2211yescharacteristic
33#11924005C2211yescharacteristic
34#11924005C2211yescharacteristic
35#11924005C2211yescharacteristic
36#11924005C2211yescharacteristic
37#11924005C2211yescharacteristic
38#11924005C2211yescharacteristic
39#11924005C2211yescharacteristic, complemented
40#11924005C2211yescharacteristic, complemented
41#11924005C2211yescharacteristic, complemented
42#11924005C2211yescharacteristic, complemented
43C4×Dic73C2211yescharacteristic, complemented
44C4⋊C4×C73C2211yescharacteristic, complemented
45C4⋊C4×C73C2211yescharacteristic, complemented
46C4⋊C4×C73C2211yescharacteristic, complemented
47C22⋊C4×C73C2211yescharacteristic
48C22⋊C4×C73C2211yescharacteristic
49C22⋊C4×C73C2211yescharacteristic
50C42×C73C2211yescharacteristic, complemented
51C23×C73C2311yescharacteristic
52C22×D73—22no—
53C22×D73—41no—
54C22×D73—41no—
55C22×D73C2311yescharacteristic
56C22×D73C2311yescharacteristic
57C22×D73C2311yescharacteristic
58C22×D73C2311yescharacteristic
59C2×C4×C73C2311yescharacteristic
60C2×C4×C73C2311yescharacteristic
61C2×C4×C73C2311yescharacteristic
62C2×C4×C73C2311yescharacteristic
63C2×C4×C73C2311yescharacteristic
64C2×C4×C73C2311yescharacteristic
65C22⋊D73—41no—
66C22⋊D73—41no—
67C2×Dic73C2311yescharacteristic
68C2×Dic73C2311yescharacteristic
69C2×Dic73C2311yescharacteristic
70C2×Dic73C2311yescharacteristic
71D292—22no—
72D292—22no—
73D292—41no—
74D292—41no—
75D292—41no—
76C4×D73—41no—
77C4×D73—41no—
78C4×D73—41no—
79C4×D73—41no—
80Dic146—41no—
81C22×C73—21no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73C2411yescharacteristic
85C2×D73—21no—
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—44no—
97C2×D73#4112yes—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—21no—
104Dic73—21no—
105Dic73—21no—
106Dic73—21no—
107Dic73—21no—
108C2×C73—41no—
109C2×C73C2×#4111yescharacteristic
110C2×C73H(5,𝔽2)11yescharacteristic
111C2×C73H(5,𝔽2)11yescharacteristic
112D73—22no—
113D73—41no—
114D73—41no—
115D73—41no—
116C73#53811yescharacteristic, complemented, Sylow
117#538—731nomaximal, Sylow
118#126—731no—
119#126D7311yescharacteristic, complemented
120#124—731no—
121#124—731no—
122#123—731no—
123#123—731no—
124C22⋊Q8—731no—
125#121—731no—
126#121—731no—
127#121—731no—
128#120—731no—
129#120—731no—
130C4×D4—731no—
131C4×D4—731no—
132C2×C22⋊C4—731no—
133C24—731no—
134C2×Q8—731no—
135C2×D4—731no—
136C2×D4—731no—
137C2×D4—731no—
138C2×D4—731no—
139C2×D4—731no—
140C2×D4—731no—
141C2×D4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C4⋊C4—731no—
147C4⋊C4—731no—
148C4⋊C4—731no—
149C4⋊C4C2×D7311yescharacteristic, complemented
150C4⋊C4C2×D7311yescharacteristic, complemented
151C4⋊C4C2×D7311yescharacteristic, complemented
152C22⋊C4—731no—
153C22⋊C4—731no—
154C22⋊C4—731no—
155C22⋊C4—731no—
156C22⋊C4—731no—
157C22⋊C4—731no—
158C22⋊C4—731no—
159C22⋊C4—731no—
160C22⋊C4—731no—
161C22⋊C4—731no—
162C22⋊C4—731no—
163C22⋊C4C2×D7311yescharacteristic
164C22⋊C4C2×D7311yescharacteristic
165C22⋊C4C2×D7311yescharacteristic
166C42—731no—
167C42C2×D7311yescharacteristic, complemented
168C23—2921no—
169C23—2921no—
170C23—731no—
171C23—731no—
172C23—731no—
173C23—731no—
174C23—1462no—
175C23C22×D7311yescharacteristic
176Q8—2921no—
177D4—2921no—
178D4—2921no—
179D4—2921no—
180D4—2921no—
181D4—2921no—
182D4—1462no—
183D4—1462no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—2921no—
187C2×C4—2921no—
188C2×C4—731no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4C22×D7311yescharacteristic
193C2×C4C22×D7311yescharacteristic
194C2×C4C22×D7311yescharacteristic
195C2×C4C22×D7311yescharacteristic
196C2×C4C22×D7311yescharacteristic
197C2×C4C22×D7311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—2924no—
202C22—732no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22—1461no—
207C22—1461no—
208C22—1461no—
209C22—1461no—
210C22—1461no—
211C22—1461no—
212C22—1461no—
213C22—1461no—
214C22C23×D7311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—1461no—
222C4—1461no—
223C4—1461no—
224C4—1461no—
225C2—41no—
226C2—2921no—
227C2—2921no—
228C2—2921no—
229C2—1462no—
230C2#41×D7311yescharacteristic
231C2#1455663711yescharacteristic
232C2#1455663711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D73
commutator, socle, cosocleC22×C73C24
Fitting#126×C73C2
hypercenter#126D73
hypocenterC73#538
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #14556586C2semidirect
2. #14556579C2semidirect
3. #14556577C2semidirect
4. #14556576C2semidirect
5. #14556573C2semidirect
6. #14556569C2semidirect
7. #14556566C2semidirect
8. #14556566C2semidirect
9. #14556564C2semidirect
10. #14556561C2semidirect
11. #14556561C2semidirect
12. C4×D292C2semidirect
13. #14556553C2semidirect
14. C22⋊C4×D73C2semidirect
15. #126×C73C2semidirect
17. C2×Dic146C22semidirect
22. C2×D292C22semidirect
27. C2×C4×D73C22semidirect
28. C2×C4×D73C22semidirect
29. C4⋊Dic73C22semidirect
30. #11924007C22semidirect
31. #11924007C22semidirect
39. #11924005C22semidirect
40. #11924005C22semidirect
41. #11924005C22semidirect
42. #11924005C22semidirect
43. C4×Dic73C22semidirect
44. C4⋊C4×C73C22semidirect
45. C4⋊C4×C73C22semidirect
46. C4⋊C4×C73C22semidirect
50. C42×C73C22semidirect
116. C73#538semidirect
119. #126D73semidirect
149. C4⋊C4C2×D73semidirect
150. C4⋊C4C2×D73semidirect
151. C4⋊C4C2×D73semidirect
167. C42C2×D73semidirect

Maximal subgroups

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

subgroupindex
#145565862
#145565792
#145565772
#145565762
#145565732
#145565692
#145565662
#145565642
#145565612
C4×D2922
#145565532
C22⋊C4×D732
#126×C732
#53873