Finite Group Databasebeta

← #17997349

Subgroups — #17997349

Order 4736.

484 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 177 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×#11924515C211yesmaximal, characteristic
2#14557437C212yesmaximal, complemented
3#14557427C212yesmaximal
4#14557421C212yesmaximal
5#14557416C212yesmaximal, complemented
6#14557415C212yesmaximal, complemented
7#14557384C212yesmaximal, complemented
8C4×C22⋊Dic37C211yesmaximal, characteristic
9C37×#381C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924515C418yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936C2212yes—
14C2×#10596936C2212yes—
15C2×#10596936C2212yes—
16C2×C22⋊Dic37C2212yes—
17C2×C22⋊Dic37C2212yes—
18C2×C4×Dic37C2212yes—
19C2×C4×Dic37C2211yescharacteristic
20C2×C4×Dic37C2211yescharacteristic
21C2×C4×Dic37C2212yes—
22#11924443C2212yes—
23#11924443C2212yes—
24#11924443C2212yes—
25#11924443C2212yes—
26#11924443C2212yes—
27C23×C4×C37C2211yescharacteristic
28C2×C22⋊C4×C37C2211yescharacteristic
29C2×C22⋊C4×C37C2211yescharacteristic
30#95×C37C2212yes—
31#95×C37C2212yes—
32C24×C37C2311yescharacteristic
33C22×C4×C37—41no—
34C22×C4×C37—41no—
35C22×C4×C37C2×C414yes—
36C22×C4×C37C2312yes—
37C22×C4×C37C2312yes—
38C22×C4×C37C2311yescharacteristic
39C22×C4×C37C2311yescharacteristic
40C22×Dic37C2312yes—
41C22×Dic37C2312yes—
42C22×Dic37C2312yes—
43C22×Dic37C2312yes—
44C2×Dic74—41no—
45C2×Dic74—41no—
46C2×Dic74C2×C414yes—
47C22⋊C4×C37—41no—
48C22⋊C4×C37—41no—
49C22⋊Dic37—24no—
50C22⋊Dic37C2×C418yes—
51C4⋊Dic37C2×C414yes—
52#10596936—24no—
53#10596936—42no—
54#10596936C2×C418yes—
55C4×Dic37—24no—
56C4×Dic37—41no—
57C4×Dic37—42no—
58C4×Dic37—41no—
59C23×C37—22no—
60C23×C37—21no—
61C23×C37—21no—
62C23×C37—22no—
63C23×C37C22×C412yes—
64C23×C37C2411yescharacteristic
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—44no—
76C2×C4×C37C22×C412yes—
77C2×C4×C37C22×C412yes—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—22no—
83C2×Dic37—22no—
84C2×Dic37—22no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37C22×C414yes—
88C2×Dic37C22×C414yes—
89C2×Dic37#4114yes—
90Dic74—44no—
91C22×C37—22no—
92C22×C37—22no—
93C22×C37—22no—
94C22×C37—42no—
95C22×C37—42no—
96C22×C37C23×C411yescharacteristic
97C22×C37C2×#4112yes—
98C22×C37H(5,𝔽2)11yescharacteristic
99C22×C37H(5,𝔽2)11yescharacteristic
100C22×C372−1+412yes—
101C4×C37—22no—
102C4×C37—22no—
103C4×C37—42no—
104C4×C37—42no—
105Dic37—24no—
106Dic37—24no—
107Dic37—24no—
108Dic37—42no—
109#2332—371nomaximal, Sylow
110C2×C37—42no—
111C2×C37C4×#4111yescharacteristic
112C2×C37#51811yescharacteristic
113C2×C37#51911yescharacteristic
114C2×C37#53912yes—
115C2×C37#54212yes—
116C2×C22⋊Q8—371no—
117#391—372no—
118#388—372no—
119#388—372no—
120#387—372no—
121#387—372no—
122#381D3711yescharacteristic
123C4×C4⋊C4—372no—
124C4×C22⋊C4—371no—
125C37#233211yescharacteristic, complemented, Sylow
126C22×Q8—371no—
127C23×C4C2×D3711yescharacteristic
128C22⋊Q8—378no—
129C2×C4⋊C4—372no—
130C2×C4⋊C4—371no—
131C2×C4⋊C4—372no—
132C2×C4⋊C4—372no—
133C2×C22⋊C4—372no—
134C2×C22⋊C4—372no—
135C2×C22⋊C4C2×D3711yescharacteristic
136C2×C22⋊C4C2×D3711yescharacteristic
137C2×C42—372no—
138C2×C42—371no—
139C2×C42—371no—
140C2×C42—372no—
141#95—372no—
142#95—372no—
143#95—372no—
144#95—372no—
145#95—372no—
146#95C2×D3712yes—
147#95C2×D3712yes—
148C24C22×D3711yescharacteristic
149C2×Q8—374no—
150C2×Q8—1481no—
151C2×Q8—1481no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—372no—
155C22×C4—372no—
156C22×C4—372no—
157C22×C4—372no—
158C22×C4C4×D3714yes—
159C22×C4C22×D3712yes—
160C22×C4C22×D3712yes—
161C22×C4C22×D3711yescharacteristic
162C22×C4C22×D3711yescharacteristic
163C4⋊C4—378no—
164C4⋊C4—374no—
165C4⋊C4—744no—
166C4⋊C4—1482no—
167C22⋊C4—41no—
168C22⋊C4—41no—
169C22⋊C4—378no—
170C22⋊C4—744no—
171C42—744no—
172C42—1481no—
173C42—1481no—
174C42—1482no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D3712yes—
180C23C23×D3711yescharacteristic
181Q8—1484no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—44no—
193C2×C4—374no—
194C2×C4—374no—
195C2×C4—374no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—742no—
199C2×C4—742no—
200C2×C4—742no—
201C2×C4—742no—
202C2×C4—742no—
203C2×C4—742no—
204C2×C4—742no—
205C2×C4C2×C4×D3712yes—
206C2×C4C2×C4×D3712yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D3711yescharacteristic
213C22#41×D3712yes—
214C22#1192458111yescharacteristic
215C22#1192458111yescharacteristic
216C22#1192458312yes—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—42no—
221C4—744no—
222C4—744no—
223C4—744no—
224C4—1482no—
225C2—42no—
226C2#1455800111yescharacteristic
227C2#1455800611yescharacteristic
228C2#1455801011yescharacteristic
229C2#1455812612yes—
230C2#1455815112yes—
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#381C2
socle, cosocleC23×C37C24
prime radicalC24×C37C23
hypercenter#381D37
hypocenterC37#2332
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #14557437C2semidirect
5. #14557416C2semidirect
6. #14557415C2semidirect
7. #14557384C2semidirect
11. #11924515C4semidirect
125. C37#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
#145574372
#145574272
#145574212
#145574162
#145574152
#145573842
C4×C22⋊Dic372
C37×#3812
#233237