Finite Group Databasebeta

← #18005310

Subgroups — #18005310

Order 4736.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#14558090C211yesmaximal, characteristic, complemented
2#14557936C211yesmaximal, characteristic, complemented
3#14557905C211yesmaximal, characteristic, complemented
4#14557885C211yesmaximal, characteristic, complemented
5#14557879C211yesmaximal, characteristic, complemented
6#14557777C214yesmaximal, complemented
7#14557633C214yesmaximal, complemented
8C4×#10596934C211yesmaximal, characteristic, complemented
9C37×#532C211yesmaximal, characteristic
10C2×#10596940C2214yes—
11C2×#10596934C2212yes—
12#11924536C2211yescharacteristic
13#11924536C2211yescharacteristic
14#11924528—21no—
15#11924515—21no—
16#11924515C2212yes—
17C4×Dic74—21no—
18C4×Dic74C2212yes—
19#11924495—21no—
20#11924469C2214yes—
21#11924459C2214yes—
22#11924457C2214yes—
23#11924447C2212yes—
24C4×#64436C2211yescharacteristic
25C4×#64436C2211yescharacteristic
26C2×#41×C37—21no—
27C4⋊Q8×C37C2211yescharacteristic
28#127×C37C2211yescharacteristic
29#124×C37—21no—
30#121×C37—21no—
31#121×C37C2212yes—
32C4×D4×C37—21no—
33C4×D4×C37C2212yes—
34C2×C42×C37C2211yescharacteristic
35#41×C37—44no—
36C2×Q8×C37—21no—
37C2×D4×C37—22no—
38C2×D4×C37—21no—
39C2×D4×C37—21no—
40C2×D4×C37C2312yes—
41C22×C4×C37—22no—
42C22×C4×C37D411yescharacteristic
43C22×C4×C37D411yescharacteristic
44C22×C4×C37C2311yescharacteristic
45C2×Dic74—21no—
46C2×Dic74C2312yes—
47C4⋊C4×C37—21no—
48C4⋊C4×C37C2312yes—
49C22⋊C4×C37—22no—
50C22⋊C4×C37—22no—
51C42×C37D411yescharacteristic
52C42×C37D411yescharacteristic
53C42×C37C2311yescharacteristic
54C42×C37C2311yescharacteristic
55C22⋊Dic37—22no—
56#10596940—28no—
57C4⋊Dic37—21no—
58C4⋊Dic37—21no—
59C4⋊Dic37—21no—
60C4⋊Dic37C2312yes—
61#10596936—22no—
62#10596936—22no—
63C4×Dic37—22no—
64#10596934—24no—
65C2×#64436C2312yes—
66C2×#64436C2312yes—
67C23×C37—22no—
68C23×C37C2×D411yescharacteristic
69Q8×C37—42no—
70D4×C37—24no—
71D4×C37—44no—
72D4×C37—42no—
73D4×C37—42no—
74C2×C4×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—22no—
78C2×C4×C37—44no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2411yescharacteristic
85C2×Dic37—22no—
86C2×Dic37—22no—
87Dic74—24no—
88Dic74—42no—
89#64436—22no—
90#64436#4114yescomplemented
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—21no—
94C22×C37—42no—
95C22×C37—42no—
96C22×C37—42no—
97C22×C37C22×D411yescharacteristic
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—21no—
101C4×C37—42no—
102C4×C37AGL(1,ℤ/8)12yes—
103C4×C37#13712yes—
104C4×C37C2×#4112yes—
105Dic37—42no—
106Dic37—42no—
107#3182—371nomaximal, Sylow
108C2×C37—41no—
109C2×C37—82no—
110C2×C37#53211yescharacteristic
111C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C37C2×#13711yescharacteristic
113#533—371no—
114#532D3711yescharacteristic
115#500—371no—
116#492—371no—
117#487—371no—
118#486—371no—
119#468—374no—
120#440—374no—
121C4×M16—371no—
122C37#318211yescharacteristic, complemented, Sylow
123C2×#41—21no—
124C2×SD16—374no—
125C2×M16—372no—
126C4⋊Q8—371no—
127C4⋊Q8—371no—
128C4⋊Q8C2×D3711yescharacteristic
129#127C2×D3711yescharacteristic
130#125—741no—
131#124—21no—
132C22⋊Q8—372no—
133C22⋊Q8—741no—
134#121—21no—
135#121C2×D3712yes—
136C4×Q8—372no—
137C4×Q8—741no—
138C4×D4—21no—
139C4×D4C2×D3712yes—
140#117—741no—
141C2×C42C2×D3711yescharacteristic
142#107—374no—
143#103—374no—
144#102—374no—
145#97—372no—
146C4×C8—371no—
147C4×C8—371no—
148#41—44no—
149C2×Q8—21no—
150C2×Q8—372no—
151C2×Q8—741no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4C22×D3712yes—
156C22×C4—22no—
157C22×C4C22⋊D3711yescharacteristic
158C22×C4C22⋊D3711yescharacteristic
159C22×C4C22×D3711yescharacteristic
160SD16—748no—
161M16—744no—
162C2×C8—372no—
163C2×C8—372no—
164C4⋊C4—21no—
165C4⋊C4—372no—
166C4⋊C4—742no—
167C4⋊C4—742no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4C22×D3712yes—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—742no—
175C42—742no—
176C42C22⋊D3711yescharacteristic
177C42C22⋊D3711yescharacteristic
178C42C22×D3711yescharacteristic
179C42C22×D3711yescharacteristic
180C23—22no—
181C23C2×C22⋊D3711yescharacteristic
182Q8—42no—
183Q8—744no—
184Q8—1482no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4C2×C22⋊D3711yescharacteristic
197C2×C4C2×C22⋊D3711yescharacteristic
198C2×C4C2×C22⋊D3711yescharacteristic
199C2×C4C2×C22⋊D3711yescharacteristic
200C2×C4C2×C22⋊D3711yescharacteristic
201C2×C4C23×D3711yescharacteristic
202C8—374no—
203C8—742no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C22×C22⋊D3711yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—1482no—
216C4—1482no—
217C4#1192456212yes—
218C4#1192456612yes—
219C4#41×D3712yes—
220C2—41no—
221C2—82no—
222C2#1455807911yescharacteristic
223C2C2×#1192456211yescharacteristic
224C2C2×#1192456611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC37×#532C2
socleC22×C37C22×D4
hypercenter#532D37
hypocenterC37#3182
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14558090C2semidirect
2. #14557936C2semidirect
3. #14557905C2semidirect
4. #14557885C2semidirect
5. #14557879C2semidirect
6. #14557777C2semidirect
7. #14557633C2semidirect
8. C4×#10596934C2semidirect
90. #64436#41semidirect
122. C37#3182semidirect

Maximal subgroups

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

subgroupindex
#145580902
#145579362
#145579052
#145578852
#145578792
#145577772
#145576332
C4×#105969342
C37×#5322
#318237