Finite Group Databasebeta

← #17994560

Subgroups — #17994560

Order 4736.

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

normal subgroups only

This group has 548 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#14557550C212yesmaximal, complemented
2#14557529C212yesmaximal, complemented
3#14557507C211yesmaximal, characteristic, complemented
4#14557500C211yesmaximal, characteristic, complemented
5C37×#585C211yesmaximal, characteristic
6C2×#10596934C2211yescharacteristic, complemented
7C22×#64436C2211yescharacteristic, complemented
8#11924495C2212yescomplemented
9#11924463—24no—
10#11924460—22no—
11#11924457—22no—
12#11924451—22no—
13C22⋊#64436—22no—
142−1+4×C37—22no—
152−1+4×C37C412yescomplemented
16H(5,𝔽2)×C37—22no—
17H(5,𝔽2)×C37—22no—
18H(5,𝔽2)×C37C412yescomplemented
19C2×#41×C37—24no—
20C2×#41×C37—22no—
21C2×#41×C37C2212yes—
22C2×#41×C37C2211yescharacteristic
23#41×C37—24no—
24#41×C37—28no—
25#41×C37—24no—
26#41×C37—24no—
27#41×C37—24no—
28#41×C37—24no—
29#41×C37—22no—
30#41×C37—22no—
31#41×C37—22no—
32#41×C37—22no—
33#41×C37C2×C414yes—
34#41×C37D414yes—
35C2×Q8×C37—22no—
36C2×Q8×C37—24no—
37C2×Q8×C37C2×C411yescharacteristic
38C2×Q8×C37D412yes—
39C2×D4×C37—28no—
40C2×D4×C37—22no—
41C2×D4×C37—24no—
42C2×D4×C37—22no—
43C2×D4×C37—24no—
44C2×D4×C37C2×C411yescharacteristic
45C2×D4×C37D412yes—
46C2×D4×C37D412yes—
47C22×C4×C37—24no—
48C22×C4×C37—22no—
49C22×C4×C37D412yes—
50C22×C4×C37C2311yescharacteristic
51C22⋊Dic37—22no—
52C4⋊Dic37—22no—
53C4×Dic37—22no—
54#10596934—22no—
55C2×#64436—21no—
56C2×#64436—22no—
57C2×#64436—21no—
58C23×C37—24no—
59C23×C37—22no—
60C23×C37C22⋊C412yes—
61C23×C37C2×D411yescharacteristic
62Q8×C37—24no—
63Q8×C37—22no—
64Q8×C37—22no—
65Q8×C37C22⋊C414yes—
66D4×C37—28no—
67D4×C37—24no—
68D4×C37—24no—
69D4×C37—24no—
70D4×C37—24no—
71D4×C37—22no—
72D4×C37—22no—
73D4×C37C22⋊C414yes—
74C2×C4×C37—24no—
75C2×C4×C37—28no—
76C2×C4×C37—22no—
77C2×C4×C37—24no—
78C2×C4×C37—24no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37C22⋊C412yes—
82C2×C4×C37C22×C411yescharacteristic
83C2×C4×C37C2×D412yes—
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2×D411yescharacteristic
86C2×Dic37—42no—
87#64436—41no—
88#64436—41no—
89C22×C37—22no—
90C22×C37—24no—
91C22×C37—41no—
92C22×C37—42no—
93C22×C37—82no—
94C22×C37—84no—
95C22×C37C2×C22⋊C411yescharacteristic
96C22×C37#12012yes—
97C4×C37—24no—
98C4×C37—22no—
99C4×C37C2×C22⋊C412yes—
100C4×C37#12011yescharacteristic
101C4×C37#12011yescharacteristic
102Dic37—82no—
103#1794—371nomaximal, Sylow
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—42no—
107C2×C37—44no—
108C2×C37#37911yescharacteristic
109#585D3711yescharacteristic
110#421—372no—
111#416—372no—
112#410—371no—
113#408—371no—
114C37#179411yescharacteristic, complemented, Sylow
1152−1+4—22no—
1162−1+4Dic3712yescomplemented
117H(5,𝔽2)—22no—
118H(5,𝔽2)—22no—
119H(5,𝔽2)Dic3712yescomplemented
120C2×#41—24no—
121C2×#41—22no—
122C2×#41C2×D3712yes—
123C2×#41C2×D3711yescharacteristic
124C2×M16—371no—
125C22×C8—371no—
126#117—372no—
127#104—744no—
128#103—742no—
129#102—742no—
130#99—742no—
131C22⋊C8—742no—
132#41—24no—
133#41—28no—
134#41—24no—
135#41—24no—
136#41—24no—
137#41—24no—
138#41—22no—
139#41—22no—
140#41—22no—
141#41—22no—
142#41C2×Dic3714yes—
143#41C22⋊D3714yes—
144C2×Q8—22no—
145C2×Q8—24no—
146C2×Q8C2×Dic3711yescharacteristic
147C2×Q8C22⋊D3712yes—
148C2×D4—28no—
149C2×D4—22no—
150C2×D4—24no—
151C2×D4—22no—
152C2×D4—24no—
153C2×D4C2×Dic3711yescharacteristic
154C2×D4C22⋊D3712yes—
155C2×D4C22⋊D3712yes—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4C22⋊D3712yes—
159C22×C4C22×D3711yescharacteristic
160M16—742no—
161C2×C8—741no—
162C2×C8—741no—
163C2×C8—742no—
164C4⋊C4—742no—
165C22⋊C4—742no—
166C42—742no—
167C23—24no—
168C23—22no—
169C23C22⋊Dic3712yes—
170C23C2×C22⋊D3711yescharacteristic
171Q8—24no—
172Q8—22no—
173Q8—22no—
174Q8C22⋊Dic3714yes—
175D4—28no—
176D4—24no—
177D4—24no—
178D4—24no—
179D4—24no—
180D4—22no—
181D4—22no—
182D4C22⋊Dic3714yes—
183C2×C4—24no—
184C2×C4—28no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—1482no—
191C2×C4C22⋊Dic3712yes—
192C2×C4C22×Dic3711yescharacteristic
193C2×C4C2×C22⋊D3712yes—
194C2×C4C2×C22⋊D3712yes—
195C2×C4C2×C22⋊D3711yescharacteristic
196C8—1481no—
197C8—1481no—
198C22—22no—
199C22—24no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—84no—
204C22C2×C22⋊Dic3711yescharacteristic
205C22#1192450512yes—
206C4—24no—
207C4—22no—
208C4—2962no—
209C4C2×C22⋊Dic3712yes—
210C4#1192450511yescharacteristic
211C4#1192450511yescharacteristic
212C2—22no—
213C2—21no—
214C2—42no—
215C2—44no—
216C2#1455738911yescharacteristic
subgroupG/H
centerC4#11924505
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#585C2
socleC2×C37#379
cosocleC22×C4×C37C23
hypercenter#585D37
hypocenterC37#1794
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #14557550C2semidirect
2. #14557529C2semidirect
3. #14557507C2semidirect
4. #14557500C2semidirect
6. C2×#10596934C22semidirect
7. C22×#64436C22semidirect
8. #11924495C22semidirect
15. 2−1+4×C37C4semidirect
18. H(5,𝔽2)×C37C4semidirect
114. C37#1794semidirect
116. 2−1+4Dic37semidirect
119. H(5,𝔽2)Dic37semidirect

Maximal subgroups

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

subgroupindex
#145575502
#145575292
#145575072
#145575002
C37×#5852
#179437