Finite Group Databasebeta

← #17997684

Subgroups — #17997684

Order 4736.

496 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C2×#11924534C211yesmaximal, characteristic
2#14557440C211yesmaximal, characteristic
3#14557437C212yesmaximal
4#14557430C212yesmaximal
5#14557428C212yesmaximal
6C4×#10596936C212yesmaximal
7#14557384C212yesmaximal
8#14557384C212yesmaximal
9C37×#391C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924534C418yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936C2212yes—
14C2×#10596936C2212yes—
15C2×#10596936C2212yes—
16C2×#10596936C2212yes—
17C2×#10596936C2212yes—
18C2×C4×Dic37C2212yes—
19C2×C4×Dic37C2212yes—
20C2×C4×Dic37C2211yescharacteristic
21C2×C4×Dic37C2212yes—
22C2×C4×Dic37C2211yescharacteristic
23#11924443C2212yes—
24#11924443C2212yes—
25#11924443C2212yes—
26#11924443C2212yes—
27C22×Q8×C37C2211yescharacteristic
28C2×C4⋊C4×C37C2211yescharacteristic
29C2×C42×C37C2211yescharacteristic
30#95×C37C2212yes—
31#95×C37C2212yes—
32C2×Q8×C37—41no—
33C2×Q8×C37—41no—
34C2×Q8×C37C2×C414yes—
35C22×C4×C37C2312yes—
36C22×C4×C37C2311yescharacteristic
37C22×C4×C37C2311yescharacteristic
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C2312yes—
40C22×Dic37C2312yes—
41C22×Dic37C2312yes—
42C22×Dic37C2312yes—
43C22×Dic37C2312yes—
44C2×Dic74—41no—
45C2×Dic74—41no—
46C2×Dic74C2×C414yes—
47C4⋊C4×C37—41no—
48C42×C37—41no—
49C4⋊Dic37—41no—
50#10596936—24no—
51#10596936—42no—
52#10596936C2×C418yes—
53#10596936C2×C418yes—
54#10596936Q818yescomplemented
55C4×Dic37—24no—
56C4×Dic37—24no—
57C4×Dic37—41no—
58C4×Dic37—42no—
59C4×Dic37C2×C414yes—
60C23×C37C2411yescharacteristic
61Q8×C37—44no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37C22×C412yes—
74C2×C4×C37C22×C412yes—
75C2×C4×C37C22×C412yes—
76C2×C4×C37C2×Q814yes—
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—22no—
83C2×Dic37—22no—
84C2×Dic37C22×C414yes—
85C2×Dic37C22×C414yes—
86C2×Dic37C2×Q814yes—
87C2×Dic37C2×Q814yes—
88C2×Dic37#4114yes—
89Dic74—44no—
90C22×C37C23×C411yescharacteristic
91C22×C37C22×Q812yes—
92C22×C37C2×#4112yes—
93C22×C37H(5,𝔽2)11yescharacteristic
94C22×C37H(5,𝔽2)11yescharacteristic
95C4×C37—22no—
96C4×C37—22no—
97C4×C37—22no—
98C4×C37—24no—
99C4×C37—42no—
100Dic37—24no—
101Dic37—24no—
102Dic37—42no—
103Dic37C4×Q818yes—
104#2369—371nomaximal, Sylow
105C2×C37C2×C4×Q812yes—
106C2×C37#51811yescharacteristic
107C2×C37#55412yes—
108C2×C37#55511yescharacteristic
109C2×C37Q8211yescharacteristic
110C2×C4⋊Q8—371no—
111#391—371no—
112#391—372no—
113#391D3711yescharacteristic
114#389—372no—
115#389—372no—
116C4×C4⋊C4—372no—
117C4×C4⋊C4—372no—
118C4×C4⋊C4—372no—
119C37#236911yescharacteristic, complemented, Sylow
120C22×Q8—371no—
121C22×Q8C2×D3711yescharacteristic
122C4⋊Q8—378no—
123C2×C4⋊C4—372no—
124C2×C4⋊C4—372no—
125C2×C4⋊C4—372no—
126C2×C4⋊C4—372no—
127C2×C4⋊C4—372no—
128C2×C4⋊C4—371no—
129C2×C4⋊C4C2×D3711yescharacteristic
130C2×C42—371no—
131C2×C42—372no—
132C2×C42—372no—
133C2×C42—371no—
134C2×C42—372no—
135C2×C42C2×D3711yescharacteristic
136#95—372no—
137#95—372no—
138#95—372no—
139#95—372no—
140#95C2×D3712yes—
141#95C2×D3712yes—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—374no—
145C2×Q8—1481no—
146C2×Q8—1481no—
147C2×Q8C4×D3714yes—
148C22×C4—372no—
149C22×C4—372no—
150C22×C4—372no—
151C22×C4—372no—
152C22×C4C22×D3712yes—
153C22×C4C22×D3711yescharacteristic
154C22×C4C22×D3711yescharacteristic
155C22×C4C22×D3711yescharacteristic
156C22×C4C22×D3712yes—
157C4⋊C4—41no—
158C4⋊C4—378no—
159C4⋊C4—378no—
160C4⋊C4—378no—
161C4⋊C4—744no—
162C4⋊C4—1482no—
163C4⋊C4—1481no—
164C42—41no—
165C42—374no—
166C42—744no—
167C42—744no—
168C42—1482no—
169C42—1481no—
170C23C23×D3711yescharacteristic
171Q8—44no—
172Q8—1484no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—374no—
185C2×C4—374no—
186C2×C4—374no—
187C2×C4—374no—
188C2×C4—374no—
189C2×C4—742no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4C2×C4×D3712yes—
197C2×C4C2×C4×D3712yes—
198C2×C4C2×C4×D3712yes—
199C2×C4Q8×D3714yes—
200C22C22×C4×D3711yescharacteristic
201C22C2×Q8×D3712yes—
202C22#41×D3712yes—
203C22#1192458111yescharacteristic
204C22#1192458111yescharacteristic
205C4—24no—
206C4—22no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—378no—
211C4—744no—
212C4—744no—
213C4—1482no—
214C2C4×Q8×D3712yes—
215C2#1455800611yescharacteristic
216C2#1455823712yes—
217C2#1455824511yescharacteristic
218C2#1455826311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#391C2
socle, prime radical, cosocleC23×C37C24
hypercenter#391D37
hypocenterC37#2369
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #11924534C4semidirect
54. #10596936Q8semidirect
119. C37#2369semidirect

Maximal subgroups

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

subgroupindex
C2×#119245342
#145574402
#145574372
#145574302
#145574282
C4×#105969362
#145573842
C37×#3912
#236937