Finite Group Databasebeta

← #18004201

Subgroups — #18004201

Order 4736.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10596929C211yesmaximal, characteristic, complemented
2#14558040C212yesmaximal, complemented
3#14557788C212yesmaximal, complemented
4#14557783C212yesmaximal, complemented
5#14557776C214yesmaximal, complemented
6#14557571C211yesmaximal, characteristic, complemented
7#14557529C212yesmaximal, complemented
8C2×#135×C37C211yesmaximal, characteristic, complemented
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—24no—
11C2×#10596929C2212yes—
12C2×#10596929C2212yes—
13C22×#64436C2211yescharacteristic
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—
58#10596929—24no—
59#10596929—24no—
60C23×C37—22no—
61C23×C37C2×D411yescharacteristic
62C22×D37—22no—
63C22×D37—42no—
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—22no—
92C2×D37—24no—
93C2×D37—44no—
94C4×C37—42no—
95C4×C37#12112yes—
96C4×C37C22×D411yescharacteristic
97C4×C37C2×#4111yescharacteristic
98Dic37—22no—
99Dic37—44no—
100#3054—371nomaximal, Sylow
101C2×C37—22no—
102C2×C37—82no—
103C2×C37C2×#12111yescharacteristic
104C2×C37#57512yes—
105D37—42no—
106C2×#135D3711yescharacteristic, complemented
107C22×M16—371no—
108#525—372no—
109#470—372no—
110#469—372no—
111#468—374no—
112#427—371no—
113#416—372no—
114C37#305411yescharacteristic, complemented, Sylow
115C2×#41C2×D3712yes—
116C23×C4—371no—
117#135—24no—
118C2×Q16C2×D3711yescharacteristic, complemented
119C2×SD16C2×D3712yescomplemented
120C2×D8C2×D3711yescharacteristic, complemented
121C2×M16—372no—
122C2×M16—372no—
123C2×M16—744no—
124C22×C8—371no—
125C22×C8C2×D3711yescharacteristic
126#123—742no—
127C22⋊Q8—374no—
128#121—374no—
129#120—742no—
130C4×D4—744no—
131#117—372no—
132#107—372no—
133#106—372no—
134#103—374no—
135#102—374no—
136C24—371no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D3712yes—
140C2×D4—22no—
141C2×D4—744no—
142C2×D4C22×D3712yes—
143C22×C4—22no—
144C22×C4—371no—
145C22×C4—372no—
146C22×C4—372no—
147C22×C4—742no—
148C22×C4—742no—
149C22×C4C22×D3711yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—744no—
154M16—744no—
155C2×C8—372no—
156C2×C8—742no—
157C2×C8C22⋊D3714yescomplemented
158C2×C8C22×D3711yescharacteristic
159C2×C8C22×D3711yescharacteristic
160C4⋊C4—374no—
161C4⋊C4—744no—
162C22⋊C4—744no—
163C22⋊C4—744no—
164C22⋊C4—742no—
165C42—742no—
166C23—22no—
167C23—372no—
168C23—742no—
169C23—1482no—
170C23D4×D3711yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—1488no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—372no—
180C2×C4—742no—
181C2×C4—744no—
182C2×C4—742no—
183C2×C4—742no—
184C2×C4—744no—
185C2×C4D4×D3711yescharacteristic
186C2×C4#1059696412yes—
187C2×C4C2×C22⋊D3712yes—
188C2×C4C23×D3711yescharacteristic
189C8—742no—
190C8C2×C22⋊D3712yes—
191C8C2×C22⋊D3712yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—742no—
196C22—744no—
197C22—1484no—
198C22#1192450712yes—
199C22C2×D4×D3711yescharacteristic
200C4—42no—
201C4—742no—
202C4—1484no—
203C4#1192450712yes—
204C4C22×C22⋊D3711yescharacteristic
205C4C2×#1059696411yescharacteristic
206C2—22no—
207C2—82no—
208C2—1482no—
209C2C2×#1192450711yescharacteristic
210C2#1455833012yes—
subgroupG/H
centerC2×C4D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#135×C37C2
socleC22×C37C22×D4
hypercenterC2×#135D37
hypocenterC37#3054
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×#10596929C2semidirect
2. #14558040C2semidirect
3. #14557788C2semidirect
4. #14557783C2semidirect
5. #14557776C2semidirect
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
106. C2×#135D37semidirect
114. C37#3054semidirect
118. C2×Q16C2×D37semidirect
119. C2×SD16C2×D37semidirect
120. C2×D8C2×D37semidirect
157. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C22×#105969292
#145580402
#145577882
#145577832
#145577762
#145575712
#145575292
C2×#135×C372
#305437