Finite Group Databasebeta

← #18004173

Subgroups — #18004173

Order 4736.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C22×C8×D37C211yesmaximal, characteristic, complemented
2#14558040C212yesmaximal, complemented
3#14557771C212yesmaximal, complemented
4#14557766C212yesmaximal, complemented
5#14557759C214yesmaximal, complemented
6#14557571C211yesmaximal, characteristic, complemented
7#14557529C212yesmaximal, complemented
8C2×#135×C37C211yesmaximal, characteristic, complemented
9C22×C4×D37C2211yescharacteristic
10C22×#64436C2211yescharacteristic
11C2×C8×D37—24no—
12C2×C8×D37C2212yes—
13C2×C8×D37C2212yes—
14#11924517—22no—
15#11924512C2214yes—
16#11924507C2214yes—
17#11924504—22no—
18C4×C22⋊D37—24no—
19#11924495C2212yes—
20#11924470C2212yescomplemented
21#11924468C2212yescomplemented
22#11924460C2214yescomplemented
23#11924457C2214yescomplemented
24C2×#41×C37C2212yes—
25#135×C37—24no—
26C2×Q16×C37C2211yescharacteristic, complemented
27C2×SD16×C37C2212yescomplemented
28C2×D8×C37C2211yescharacteristic, complemented
29C22×C8×C37C2211yescharacteristic
30C23×D37D411yescharacteristic
31#41×C37—24no—
32#41×C37—24no—
33C2×Q8×C37C2312yes—
34C2×D4×C37—22no—
35C2×D4×C37C2312yes—
36C22×C4×C37—22no—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—24no—
39C22×Dic37D411yescharacteristic
40C2×C4×D37—22no—
41C2×C4×D37—22no—
42C2×C4×D37D412yes—
43C2×C4×D37C2312yes—
44Q16×C37—22no—
45SD16×C37—24no—
46D8×C37—22no—
47C2×C8×C37D414yescomplemented
48C2×C8×C37C2311yescharacteristic
49C2×C8×C37C2311yescharacteristic
50C22⋊Dic37—22no—
51C22⋊Dic37—24no—
52#10596938—24no—
53C4⋊Dic37C2314yes—
54#10596936—24no—
55C4×Dic37—22no—
56C2×#64436—22no—
57C2×#64436C2312yes—
58C8×D37—24no—
59C8×D37—24no—
60C23×C37—22no—
61C23×C37C2×D411yescharacteristic
62C22×D37—22no—
63C22×D37—24no—
64C22×D37C2×D412yes—
65Q8×C37—22no—
66Q8×C37—22no—
67D4×C37—22no—
68D4×C37—22no—
69D4×C37—44no—
70C2×C4×C37—22no—
71C2×C4×C37—44no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D412yes—
74C2×C4×C37#4112yes—
75C2×C4×C37C2411yescharacteristic
76C22⋊D37—48no—
77C2×Dic37—22no—
78C2×Dic37—24no—
79C2×Dic37C2×D412yes—
80C4×D37—24no—
81C4×D37—22no—
82C4×D37—22no—
83C8×C37C2×D412yes—
84C8×C37C2×D412yes—
85#64436—22no—
86C22×C37—22no—
87C22×C37—42no—
88C22×C37—44no—
89C22×C37#12112yes—
90C22×C37C22×D411yescharacteristic
91C2×D37—28no—
92C2×D37—22no—
93C2×D37—22no—
94C2×D37#13514yescomplemented
95C4×C37—42no—
96C4×C37#12112yes—
97C4×C37C22×D411yescharacteristic
98C4×C37C2×#4111yescharacteristic
99Dic37—22no—
100Dic37—44no—
101#3050—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37—82no—
104C2×C37C2×#12111yescharacteristic
105C2×C37C2×#13512yes—
106D37—24no—
107C2×#135D3711yescharacteristic, complemented
108C23×C8—371no—
109#525—372no—
110#467—372no—
111#466—372no—
112#465—374no—
113#427—371no—
114#416—372no—
115C37#305011yescharacteristic, complemented, Sylow
116C2×#41C2×D3712yes—
117C23×C4—371no—
118#135—24no—
119C2×Q16C2×D3711yescharacteristic, complemented
120C2×SD16C2×D3712yescomplemented
121C2×D8C2×D3711yescharacteristic, complemented
122C22×C8—371no—
123C22×C8—372no—
124C22×C8—372no—
125C22×C8—744no—
126C22×C8C2×D3711yescharacteristic
127#123—742no—
128C22⋊Q8—374no—
129#121—374no—
130#120—742no—
131C4×D4—744no—
132#117—372no—
133#107—372no—
134#106—372no—
135#103—374no—
136#102—374no—
137C24—371no—
138#41—24no—
139#41—24no—
140C2×Q8C22×D3712yes—
141C2×D4—22no—
142C2×D4—744no—
143C2×D4C22×D3712yes—
144C22×C4—22no—
145C22×C4—371no—
146C22×C4—372no—
147C22×C4—372no—
148C22×C4—742no—
149C22×C4—742no—
150C22×C4C22×D3711yescharacteristic
151Q16—22no—
152SD16—24no—
153D8—22no—
154C2×C8—372no—
155C2×C8—742no—
156C2×C8—744no—
157C2×C8—744no—
158C2×C8C22⋊D3714yescomplemented
159C2×C8C22×D3711yescharacteristic
160C2×C8C22×D3711yescharacteristic
161C4⋊C4—374no—
162C4⋊C4—744no—
163C22⋊C4—744no—
164C22⋊C4—744no—
165C22⋊C4—742no—
166C42—742no—
167C23—22no—
168C23—372no—
169C23—744no—
170C23—742no—
171C23D4×D3711yescharacteristic
172Q8—22no—
173Q8—22no—
174D4—22no—
175D4—22no—
176D4—44no—
177D4—1488no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—372no—
181C2×C4—742no—
182C2×C4—744no—
183C2×C4—742no—
184C2×C4—742no—
185C2×C4—744no—
186C2×C4D4×D3711yescharacteristic
187C2×C4#1059696412yes—
188C2×C4C2×C22⋊D3712yes—
189C2×C4C23×D3711yescharacteristic
190C8—742no—
191C8C2×C22⋊D3712yes—
192C8C2×C22⋊D3712yes—
193C22—22no—
194C22—42no—
195C22—44no—
196C22—374no—
197C22—748no—
198C22—742no—
199C22—742no—
200C22#1192450712yes—
201C22C2×D4×D3711yescharacteristic
202C4—42no—
203C4—742no—
204C4—1484no—
205C4#1192450712yes—
206C4C22×C22⋊D3711yescharacteristic
207C4C2×#1059696411yescharacteristic
208C2—22no—
209C2—82no—
210C2—744no—
211C2C2×#1192450711yescharacteristic
212C2#135×D3712yes—
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3050
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×C8×D37C2semidirect
2. #14558040C2semidirect
3. #14557771C2semidirect
4. #14557766C2semidirect
5. #14557759C2semidirect
6. #14557571C2semidirect
7. #14557529C2semidirect
8. C2×#135×C37C2semidirect
20. #11924470C22semidirect
21. #11924468C22semidirect
22. #11924460C22semidirect
23. #11924457C22semidirect
26. C2×Q16×C37C22semidirect
27. C2×SD16×C37C22semidirect
28. C2×D8×C37C22semidirect
47. C2×C8×C37D4semidirect
94. C2×D37#135semidirect
107. C2×#135D37semidirect
115. C37#3050semidirect
119. C2×Q16C2×D37semidirect
120. C2×SD16C2×D37semidirect
121. C2×D8C2×D37semidirect
158. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C22×C8×D372
#145580402
#145577712
#145577662
#145577592
#145575712
#145575292
C2×#135×C372
#305037