Finite Group Databasebeta

← #17997764

Subgroups — #17997764

Order 4736.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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#14557430C212yesmaximal, complemented
4#14557427C212yesmaximal
5#14557421C212yesmaximal
6#14557420C212yesmaximal, complemented
7#14557418C212yesmaximal, complemented
8#14557393C211yesmaximal, characteristic
9C37×#381C211yesmaximal, characteristic
10C22×Dic74C2211yescharacteristic
11#11924515C418yescomplemented
12C2×C4⋊Dic37C2212yes—
13C2×C4⋊Dic37C2211yescharacteristic
14C2×#10596936C2212yes—
15C2×#10596936C2212yes—
16C2×#10596936C2212yes—
17C2×C22⋊Dic37C2211yescharacteristic
18C2×C22⋊Dic37C2211yescharacteristic
19C2×C22⋊Dic37C2212yes—
20C2×C4×Dic37C2212yes—
21C2×C4×Dic37C2212yes—
22#11924443C2212yes—
23#11924443C2212yes—
24#11924443C2212yes—
25#11924443C2212yes—
26#11924443C2212yes—
27C23×C4×C37C2211yescharacteristic
28C2×C22⋊C4×C37C2212yes—
29#95×C37C2212yes—
30#95×C37C2211yescharacteristic
31#95×C37C2211yescharacteristic
32C24×C37C2311yescharacteristic
33C22×C4×C37—42no—
34C22×C4×C37C2×C414yes—
35C22×C4×C37C2312yes—
36C22×C4×C37C2312yes—
37C22×C4×C37C2311yescharacteristic
38C22×C4×C37C2311yescharacteristic
39C22×Dic37C2312yes—
40C22×Dic37C2312yes—
41C22×Dic37C2312yes—
42C22×Dic37C2312yes—
43C2×Dic74—42no—
44C2×Dic74C2×C414yes—
45C22⋊C4×C37—42no—
46C22⋊Dic37—41no—
47C22⋊Dic37—41no—
48C22⋊Dic37C2×C418yes—
49C4⋊Dic37—42no—
50C4⋊Dic37C2×C414yes—
51#10596936—42no—
52#10596936—42no—
53#10596936C2×C418yes—
54C4×Dic37—42no—
55C4×Dic37—42no—
56C23×C37—21no—
57C23×C37—22no—
58C23×C37—22no—
59C23×C37—21no—
60C23×C37C22×C412yes—
61C23×C37C2411yescharacteristic
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37—22no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37—44no—
71C2×C4×C37C22×C412yes—
72C2×C4×C37C22×C412yes—
73C2×Dic37—22no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—22no—
82C2×Dic37—22no—
83C2×Dic37C22×C414yes—
84C2×Dic37C22×C414yes—
85Dic74—44no—
86C22×C37—22no—
87C22×C37—22no—
88C22×C37—22no—
89C22×C37—42no—
90C22×C37—42no—
91C22×C37C23×C411yescharacteristic
92C22×C37H(5,𝔽2)12yes—
93C22×C37H(5,𝔽2)11yescharacteristic
94C22×C372−1+412yes—
95C22×C372−1+411yescharacteristic
96C4×C37—22no—
97C4×C37—22no—
98C4×C37—42no—
99C4×C37—42no—
100Dic37—24no—
101Dic37—24no—
102Dic37—42no—
103Dic37—42no—
104#2378—371nomaximal, Sylow
105C2×C37—42no—
106C2×C37#51811yescharacteristic
107C2×C37#51911yescharacteristic
108C2×C37#52011yescharacteristic
109C2×C37#56212yes—
110C2×C37#56312yes—
111C2×C22⋊Q8—371no—
112#391—372no—
113#389—372no—
114#388—372no—
115#388—372no—
116#387—372no—
117#387—372no—
118#381D3711yescharacteristic
119#380—371no—
120C37#237811yescharacteristic, complemented, Sylow
121C22×Q8—371no—
122C23×C4C2×D3711yescharacteristic
123C22⋊Q8—378no—
124C2×C4⋊C4—372no—
125C2×C4⋊C4—371no—
126C2×C4⋊C4—372no—
127C2×C4⋊C4—372no—
128C2×C4⋊C4—372no—
129C2×C22⋊C4—372no—
130C2×C22⋊C4—371no—
131C2×C22⋊C4—371no—
132C2×C22⋊C4C2×D3712yes—
133C2×C42—372no—
134C2×C42—372no—
135#95—372no—
136#95—372no—
137#95—372no—
138#95—372no—
139#95—372no—
140#95C2×D3711yescharacteristic
141#95C2×D3712yes—
142#95C2×D3711yescharacteristic
143C24C22×D3711yescharacteristic
144C2×Q8—374no—
145C2×Q8—1482no—
146C22×C4—42no—
147C22×C4—372no—
148C22×C4—372no—
149C22×C4—372no—
150C22×C4—372no—
151C22×C4C4×D3714yes—
152C22×C4C22×D3712yes—
153C22×C4C22×D3712yes—
154C22×C4C22×D3711yescharacteristic
155C22×C4C22×D3711yescharacteristic
156C4⋊C4—378no—
157C4⋊C4—374no—
158C4⋊C4—1482no—
159C4⋊C4—1482no—
160C4⋊C4—1482no—
161C22⋊C4—42no—
162C22⋊C4—378no—
163C22⋊C4—1481no—
164C22⋊C4—1481no—
165C42—1482no—
166C42—1482no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23—21no—
171C23C2×C4×D3712yes—
172C23C23×D3711yescharacteristic
173Q8—1484no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—374no—
184C2×C4—374no—
185C2×C4—742no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—742no—
189C2×C4—742no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4—742no—
194C2×C4—742no—
195C2×C4C2×C4×D3712yes—
196C2×C4C2×C4×D3712yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D3711yescharacteristic
203C22#1192458112yes—
204C22#1192458211yescharacteristic
205C22#1192458312yes—
206C22#1192458311yescharacteristic
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—744no—
212C4—744no—
213C4—1482no—
214C4—1482no—
215C2—42no—
216C2#1455800611yescharacteristic
217C2#1455801011yescharacteristic
218C2#1455801311yescharacteristic
219C2#1455828012yes—
220C2#1455828612yes—
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#381C2
socle, cosocleC23×C37C24
prime radicalC24×C37C23
hypercenter#381D37
hypocenterC37#2378
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #14557437C2semidirect
3. #14557430C2semidirect
6. #14557420C2semidirect
7. #14557418C2semidirect
11. #11924515C4semidirect
120. C37#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#119245152
#145574372
#145574302
#145574272
#145574212
#145574202
#145574182
#145573932
C37×#3812
#237837