Finite Group Databasebeta

← #14558207

Subgroups — #14558207

Order 2368.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#11924531C211yesmaximal, characteristic, complemented
2#11924530C211yesmaximal, characteristic, complemented
3#11924524C211yesmaximal, characteristic, complemented
4#11924521C211yesmaximal, characteristic, complemented
5#11924521C211yesmaximal, characteristic, complemented
6#11924519C211yesmaximal, characteristic, complemented
7#11924514C211yesmaximal, characteristic, complemented
8#11924513C211yesmaximal, characteristic, complemented
9#11924506C211yesmaximal, characteristic
10C4×D148C211yesmaximal, characteristic, complemented
11#11924496C211yesmaximal, characteristic, complemented
12#11924493C211yesmaximal, characteristic, complemented
13C2×#10596938C211yesmaximal, characteristic, complemented
14C22⋊C4×D37C211yesmaximal, characteristic, complemented
15#117×C37C211yesmaximal, characteristic, complemented
16C23×D37C2211yescharacteristic
17C22×C4×C37C2211yescharacteristic
18C2×C22⋊D37C2211yescharacteristic
19C22×Dic37C2211yescharacteristic
20C2×D148C2211yescharacteristic
21C2×D148C2211yescharacteristic
22C2×C4×D37C2211yescharacteristic
23C2×C4×D37C2211yescharacteristic
24C2×C4×D37C2211yescharacteristic, complemented
25C2×Dic74C2211yescharacteristic, complemented
26C4⋊C4×C37C2211yescharacteristic, complemented
27C4⋊C4×C37C2211yescharacteristic, complemented
28C22⋊C4×C37C2211yescharacteristic
29C22⋊C4×C37C2211yescharacteristic
30C42×C37C2211yescharacteristic, complemented
31C42×C37C2211yescharacteristic, complemented
32C22⋊Dic37C2211yescharacteristic
33#10596938C2211yescharacteristic
34#10596938C2211yescharacteristic
35#10596938C2211yescharacteristic
36#10596938C2211yescharacteristic
37#10596938C2211yescharacteristic
38#10596938C2211yescharacteristic
39#10596938C2211yescharacteristic
40#10596938C2211yescharacteristic
41#10596938C2211yescharacteristic, complemented
42#10596938C2211yescharacteristic, complemented
43#10596938C2211yescharacteristic, complemented
44C4⋊Dic37C2211yescharacteristic, complemented
45#10596936C2211yescharacteristic, complemented
46#10596936C2211yescharacteristic, complemented
47#10596936C2211yescharacteristic, complemented
48#10596936C2211yescharacteristic, complemented
49#10596936C2211yescharacteristic, complemented
50C4×Dic37C2211yescharacteristic, complemented
51C23×C37C2311yescharacteristic
52C22×D37—22no—
53C22×D37—22no—
54C22×D37—41no—
55C22×D37C2311yescharacteristic
56C22×D37C2311yescharacteristic
57C22×D37C2311yescharacteristic
58C2×C4×C37—22no—
59C2×C4×C37C2311yescharacteristic
60C2×C4×C37C2311yescharacteristic
61C2×C4×C37C2311yescharacteristic
62C2×C4×C37C2311yescharacteristic
63C2×C4×C37C2311yescharacteristic
64C2×C4×C37C2311yescharacteristic
65C22⋊D37—22no—
66C2×Dic37—41no—
67C2×Dic37C2311yescharacteristic
68C2×Dic37C2311yescharacteristic
69C2×Dic37C2311yescharacteristic
70C2×Dic37C2311yescharacteristic
71C2×Dic37C2311yescharacteristic
72D148—22no—
73D148—41no—
74C4×D37—22no—
75C4×D37—41no—
76C4×D37—41no—
77Dic74—41no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37#4112yes—
81C22×C37C2411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—21no—
89C2×D37—21no—
90C2×D37—44no—
91C2×D37#4112yes—
92C4×C37—21no—
93C4×C37—21no—
94C4×C37—21no—
95C4×C37—21no—
96C4×C37—21no—
97C4×C37—21no—
98Dic37—21no—
99Dic37—21no—
100Dic37—21no—
101Dic37—21no—
102Dic37—21no—
103C2×C37—22no—
104C2×C37C2×#4111yescharacteristic
105C2×C37C2×#4111yescharacteristic
106C2×C37H(5,𝔽2)11yescharacteristic
107D37—22no—
108D37—41no—
109D37—41no—
110#551—371nomaximal, Sylow
111C37#55111yescharacteristic, complemented, Sylow
112#126—371no—
113#126—371no—
114#124—371no—
115#123—371no—
116#123—371no—
117#123—371no—
118C22⋊Q8—371no—
119C22⋊Q8—371no—
120#120—371no—
121C4×D4—371no—
122C4×D4—371no—
123#117—371no—
124#117D3711yescharacteristic, complemented
125C2×C22⋊C4—371no—
126C2×C22⋊C4—371no—
127C24—371no—
128C2×Q8—371no—
129C2×D4—371no—
130C2×D4—371no—
131C2×D4—371no—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4—371no—
136C22×C4C2×D3711yescharacteristic
137C4⋊C4—371no—
138C4⋊C4—371no—
139C4⋊C4—371no—
140C4⋊C4—371no—
141C4⋊C4—371no—
142C4⋊C4—371no—
143C4⋊C4C2×D3711yescharacteristic, complemented
144C4⋊C4C2×D3711yescharacteristic, complemented
145C22⋊C4—371no—
146C22⋊C4—371no—
147C22⋊C4—371no—
148C22⋊C4—371no—
149C22⋊C4—371no—
150C22⋊C4—371no—
151C22⋊C4—371no—
152C22⋊C4—371no—
153C22⋊C4—371no—
154C22⋊C4—371no—
155C22⋊C4—371no—
156C22⋊C4—371no—
157C22⋊C4C2×D3711yescharacteristic
158C22⋊C4C2×D3711yescharacteristic
159C42—371no—
160C42C2×D3711yescharacteristic, complemented
161C42C2×D3711yescharacteristic, complemented
162C23—371no—
163C23—371no—
164C23—371no—
165C23—742no—
166C23—742no—
167C23—1481no—
168C23C22×D3711yescharacteristic
169Q8—1481no—
170D4—742no—
171D4—742no—
172D4—1481no—
173C2×C4—22no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—742no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4—1481no—
183C2×C4C22×D3711yescharacteristic
184C2×C4C22×D3711yescharacteristic
185C2×C4C22×D3711yescharacteristic
186C2×C4C22×D3711yescharacteristic
187C2×C4C22×D3711yescharacteristic
188C2×C4C22×D3711yescharacteristic
189C22—21no—
190C22—21no—
191C22—372no—
192C22—741no—
193C22—741no—
194C22—741no—
195C22—741no—
196C22—741no—
197C22—741no—
198C22—741no—
199C22—741no—
200C22—1484no—
201C22#1059696212yes—
202C22C23×D3711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—741no—
210C4—741no—
211C4—741no—
212C4—741no—
213C4—741no—
214C2—22no—
215C2—742no—
216C2—1481no—
217C2—1481no—
218C2#41×D3711yescharacteristic
219C2C2×#1059696211yescharacteristic
220C2#1192458211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
Fitting#117×C37C2
prime radical#11924506C2
hypercenter#117D37
hypocenterC37#551
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11924531C2semidirect
2. #11924530C2semidirect
3. #11924524C2semidirect
4. #11924521C2semidirect
5. #11924521C2semidirect
6. #11924519C2semidirect
7. #11924514C2semidirect
8. #11924513C2semidirect
10. C4×D148C2semidirect
11. #11924496C2semidirect
12. #11924493C2semidirect
13. C2×#10596938C2semidirect
14. C22⋊C4×D37C2semidirect
15. #117×C37C2semidirect
24. C2×C4×D37C22semidirect
25. C2×Dic74C22semidirect
26. C4⋊C4×C37C22semidirect
27. C4⋊C4×C37C22semidirect
30. C42×C37C22semidirect
31. C42×C37C22semidirect
41. #10596938C22semidirect
42. #10596938C22semidirect
43. #10596938C22semidirect
44. C4⋊Dic37C22semidirect
45. #10596936C22semidirect
46. #10596936C22semidirect
47. #10596936C22semidirect
48. #10596936C22semidirect
49. #10596936C22semidirect
50. C4×Dic37C22semidirect
111. C37#551semidirect
124. #117D37semidirect
143. C4⋊C4C2×D37semidirect
144. C4⋊C4C2×D37semidirect
160. C42C2×D37semidirect
161. C42C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245312
#119245302
#119245242
#119245212
#119245192
#119245142
#119245132
#119245062
C4×D1482
#119244962
#119244932
C2×#105969382
C22⋊C4×D372
#117×C372
#55137