Finite Group Databasebeta

← #18004840

Subgroups — #18004840

Order 4736.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#14558138C211yesmaximal, characteristic, complemented
2#14558007C211yesmaximal, characteristic, complemented
3#14557858C212yesmaximal, complemented
4#14557834C212yesmaximal, complemented
5#14557729C212yesmaximal, complemented
6#14557669C212yesmaximal, complemented
7#14557646C212yesmaximal, complemented
8C4×D296C212yesmaximal, complemented
9C37×#433C211yesmaximal, characteristic, complemented
10C22×D148C2211yescharacteristic
11C2×D296C2212yes—
12C2×D296C2212yes—
13#11924533C2211yescharacteristic, complemented
14#11924528C2211yescharacteristic, complemented
15#11924521—22no—
16#11924510C2212yes—
17#11924509—22no—
18C4×D148C2212yes—
19C4×D148C2212yes—
20C4×D148C2212yescomplemented
21#11924498—22no—
22#11924495C2211yescharacteristic
23C22⋊C4×D37—22no—
24#11924470C2212yescomplemented
25#11924468C2212yescomplemented
26#11924458C2212yes—
27#11924458C2212yes—
28#11924458C2212yescomplemented
29#11924458C2212yescomplemented
30#117×C37C2211yescharacteristic
31C4⋊C8×C37C2212yescomplemented
32C22⋊C8×C37C2212yes—
33#97×C37C2211yescharacteristic, complemented
34C4×C8×C37C2211yescharacteristic, complemented
35C23×D37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—22no—
38C2×D148—21no—
39C2×D148—24no—
40C2×D148—22no—
41C2×D148C2312yes—
42C2×D148C2312yes—
43C2×C4×D37—22no—
44C2×C4×D37—22no—
45C2×C4×D37—22no—
46C2×C8×C37C2312yes—
47C2×C8×C37C2312yes—
48C4⋊C4×C37D412yes—
49C22⋊C4×C37D412yes—
50C42×C37C2311yescharacteristic
51C42×C37C2311yescharacteristic
52C22⋊Dic37—21no—
53#10596938—22no—
54#10596938—22no—
55#10596938—22no—
56#10596938—22no—
57C4⋊Dic37C2312yes—
58C4⋊Dic37C2312yes—
59#10596936—22no—
60C4×Dic37—21no—
61D296—24no—
62D296—24no—
63C23×C37C2×D411yescharacteristic
64C22×D37—22no—
65C22×D37—24no—
66C22×D37—22no—
67C22×D37—82no—
68C2×C4×C37—22no—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D412yes—
71C2×C4×C37C2×D412yes—
72C2×C4×C37C2411yescharacteristic
73C22⋊D37—82no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76D148—24no—
77D148—22no—
78D148—22no—
79D148—22no—
80D148—82no—
81D148#4114yes—
82C4×D37—82no—
83C4×D37—82no—
84C4×D37—82no—
85C8×C37—22no—
86C8×C37—22no—
87C22×C37—21no—
88C22×C37—22no—
89C22×C37C22×D411yescharacteristic
90C2×D37—24no—
91C2×D37—42no—
92C2×D37—42no—
93C2×D37—42no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—84no—
97C4×C37—21no—
98C4×C37—22no—
99C4×C37—22no—
100C4×C37C2×#4112yes—
101Dic37—42no—
102Dic37—42no—
103#3122—371nomaximal, Sylow
104C2×C37—41no—
105C2×C37#52511yescharacteristic
106C2×C37#57612yes—
107D37—44no—
108D37—82no—
109#540—371no—
110#518—371no—
111#482—372no—
112#478—372no—
113#459—372no—
114#447—372no—
115#442—372no—
116C4×D8—372no—
117#433D3711yescharacteristic, complemented
118C37#312211yescharacteristic, complemented, Sylow
119C22×D4—371no—
120C2×D8—372no—
121C2×D8—372no—
122#127—371no—
123#125—371no—
124#123—742no—
125#121—372no—
126#121—742no—
127C4×D4—372no—
128C4×D4—372no—
129C4×D4—372no—
130C4×D4—742no—
131#117—371no—
132#117C2×D3711yescharacteristic
133C2×C22⋊C4—742no—
134#107—372no—
135#106—372no—
136C4⋊C8C2×D3712yescomplemented
137#102—372no—
138#102—372no—
139#102—372no—
140#102—372no—
141C22⋊C8C2×D3712yes—
142#97C2×D3711yescharacteristic, complemented
143C4×C8C2×D3711yescharacteristic, complemented
144C24—741no—
145C2×D4—372no—
146C2×D4—372no—
147C2×D4—744no—
148C2×D4—742no—
149C2×D4—742no—
150C2×D4—741no—
151C22×C4—742no—
152C22×C4—742no—
153C22×C4—742no—
154C22×C4C22×D3711yescharacteristic
155D8—744no—
156D8—744no—
157C2×C8C22×D3712yes—
158C2×C8C22×D3712yes—
159C4⋊C4—372no—
160C4⋊C4—372no—
161C4⋊C4—742no—
162C4⋊C4D14812yes—
163C22⋊C4—741no—
164C22⋊C4—742no—
165C22⋊C4—742no—
166C22⋊C4—742no—
167C22⋊C4—742no—
168C22⋊C4D14812yes—
169C42—741no—
170C42C22×D3711yescharacteristic
171C42C22×D3711yescharacteristic
172C23—2962no—
173C23—744no—
174C23—742no—
175C23—742no—
176C23C2×D14811yescharacteristic
177D4—374no—
178D4—2962no—
179D4—2962no—
180D4—744no—
181D4—742no—
182D4—742no—
183D4—742no—
184C2×C4—22no—
185C2×C4—2962no—
186C2×C4—2962no—
187C2×C4—2962no—
188C2×C4—742no—
189C2×C4—742no—
190C2×C4C2×D14811yescharacteristic
191C2×C4C2×D14812yes—
192C2×C4C2×D14812yes—
193C2×C4C23×D3711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—2964no—
199C22—744no—
200C22—1482no—
201C22—1482no—
202C22—1482no—
203C22—1482no—
204C22—1482no—
205C22C22×D14811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—1482no—
210C4—1482no—
211C4#41×D3712yes—
212C2—41no—
213C2—2962no—
214C2—1484no—
215C2#1455804511yescharacteristic
216C2#1455833812yes—
subgroupG/H
centerC22C22×D148
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#433C2
socleC22×C37C22×D4
hypercenter#433D37
hypocenterC37#3122
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14558138C2semidirect
2. #14558007C2semidirect
3. #14557858C2semidirect
4. #14557834C2semidirect
5. #14557729C2semidirect
6. #14557669C2semidirect
7. #14557646C2semidirect
8. C4×D296C2semidirect
9. C37×#433C2semidirect
13. #11924533C22semidirect
14. #11924528C22semidirect
20. C4×D148C22semidirect
24. #11924470C22semidirect
25. #11924468C22semidirect
28. #11924458C22semidirect
29. #11924458C22semidirect
31. C4⋊C8×C37C22semidirect
33. #97×C37C22semidirect
34. C4×C8×C37C22semidirect
117. #433D37semidirect
118. C37#3122semidirect
136. C4⋊C8C2×D37semidirect
142. #97C2×D37semidirect
143. C4×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145581382
#145580072
#145578582
#145578342
#145577292
#145576692
#145576462
C4×D2962
C37×#4332
#312237