Finite Group Databasebeta

← #17997886

Subgroups — #17997886

Order 4736.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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×Q8×Dic37C211yesmaximal, characteristic
2C2×#11924501C211yesmaximal, characteristic
3#14557466C212yesmaximal
4#14557465C211yesmaximal, characteristic
5#14557463C211yesmaximal, characteristic
6#14557454C212yesmaximal
7#14557452C211yesmaximal, characteristic
8C4⋊C4×Dic37C212yesmaximal
9#14557384C212yesmaximal
10#14557378C211yesmaximal, characteristic
11C37×#395C211yesmaximal, characteristic
12C22×Dic74C2211yescharacteristic
13Q8×Dic37—24no—
14#11924501—24no—
15C2×C4⋊Dic37C2212yes—
16C2×C4⋊Dic37C2212yes—
17C2×C4⋊Dic37C2211yescharacteristic
18C2×#10596936C2211yescharacteristic
19C2×#10596936C2212yes—
20C2×#10596936C2212yes—
21C2×#10596936C2211yescharacteristic
22C2×C4×Dic37C2211yescharacteristic
23C2×C4×Dic37C2211yescharacteristic
24C2×C4×Dic37C2212yes—
25C2×C4×Dic37C2211yescharacteristic
26C2×C4×Dic37C2212yes—
27#11924443C2212yes—
28#11924443C2211yescharacteristic
29#11924443C2212yes—
30#11924443C2212yes—
31#11924443C2212yes—
32C22×Q8×C37C2211yescharacteristic
33C2×C4⋊C4×C37C2211yescharacteristic
34C2×C4⋊C4×C37C2212yes—
35#95×C37C2212yes—
36#95×C37C2211yescharacteristic
37C2×Q8×C37—22no—
38C2×Q8×C37—24no—
39C22×C4×C37C2311yescharacteristic
40C22×C4×C37C2311yescharacteristic
41C22×C4×C37C2312yes—
42C22×C4×C37C2311yescharacteristic
43C22×C4×C37C2312yes—
44C22×Dic37C2311yescharacteristic
45C22×Dic37C2312yes—
46C22×Dic37C2311yescharacteristic
47C22×Dic37C2312yes—
48C22×Dic37C2311yescharacteristic
49C22×Dic37C2311yescharacteristic
50C2×Dic74—22no—
51C2×Dic74—22no—
52C2×Dic74—22no—
53C4⋊C4×C37—22no—
54C4⋊C4×C37—24no—
55C4⋊Dic37—22no—
56C4⋊Dic37—24no—
57C4⋊Dic37—24no—
58#10596936—22no—
59#10596936—24no—
60#10596936—24no—
61#10596936—22no—
62C4×Dic37—22no—
63C4×Dic37—22no—
64C4×Dic37—24no—
65C4×Dic37D414yes—
66C4×Dic37Q818yescomplemented
67C23×C37C2411yescharacteristic
68Q8×C37—28no—
69C2×C4×C37—22no—
70C2×C4×C37—21no—
71C2×C4×C37—22no—
72C2×C4×C37—22no—
73C2×C4×C37—21no—
74C2×C4×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37—21no—
77C2×C4×C37—22no—
78C2×C4×C37C2×D412yes—
79C2×C4×C37C2×Q814yes—
80C2×C4×C37#4114yes—
81C2×C4×C37#4112yes—
82C2×Dic37—21no—
83C2×Dic37—22no—
84C2×Dic37—22no—
85C2×Dic37—21no—
86C2×Dic37—21no—
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—22no—
92C2×Dic37—22no—
93C2×Dic37C2×D412yes—
94C2×Dic37C2×D412yes—
95C2×Dic37C2×Q814yes—
96C2×Dic37C2×Q814yes—
97C2×Dic37#4112yes—
98Dic74—28no—
99C22×C37C22×D411yescharacteristic
100C22×C37C22×Q812yes—
101C22×C37C2×#4111yescharacteristic
102C22×C37C2×#4112yes—
103C22×C37C2×#4111yescharacteristic
104C4×C37—22no—
105C4×C37—22no—
106C4×C37—24no—
107C4×C37—24no—
108C4×C37—41no—
109Dic37—22no—
110Dic37—22no—
111Dic37—24no—
112Dic37—41no—
113Dic37—42no—
114Dic37C4⋊Q814yes—
115#2399—371nomaximal, Sylow
116C2×C37#52511yescharacteristic
117C2×C37#52511yescharacteristic
118C2×C37C2×C4⋊Q811yescharacteristic
119C2×C37#53312yes—
120C2×C37#53312yes—
121C2×C4×Q8—371no—
122C2×C4×Q8—371no—
123#398—371no—
124#398—372no—
125#398—371no—
126#395—371no—
127#395—372no—
128#395D3711yescharacteristic
129C4×C4⋊C4—372no—
130C4×C4⋊C4—372no—
131#376—371no—
132C37#239911yescharacteristic, complemented, Sylow
133C22×Q8—371no—
134C22×Q8C2×D3711yescharacteristic
135C4×Q8—744no—
136C4×Q8—744no—
137C2×C4⋊C4—371no—
138C2×C4⋊C4—371no—
139C2×C4⋊C4—372no—
140C2×C4⋊C4—371no—
141C2×C4⋊C4—372no—
142C2×C4⋊C4—372no—
143C2×C4⋊C4—372no—
144C2×C4⋊C4C2×D3711yescharacteristic
145C2×C4⋊C4C2×D3712yes—
146C2×C42—371no—
147C2×C42—372no—
148C2×C42—371no—
149C2×C42—372no—
150C2×C42—371no—
151#95—371no—
152#95—372no—
153#95—372no—
154#95—372no—
155#95—372no—
156#95C2×D3711yescharacteristic
157#95C2×D3712yes—
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—742no—
161C2×Q8—742no—
162C2×Q8—742no—
163C22×C4—371no—
164C22×C4—372no—
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—372no—
168C22×C4—371no—
169C22×C4C22×D3711yescharacteristic
170C22×C4C22×D3711yescharacteristic
171C22×C4C22×D3712yes—
172C22×C4C22×D3712yes—
173C22×C4C22×D3711yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—742no—
177C4⋊C4—744no—
178C4⋊C4—744no—
179C4⋊C4—742no—
180C4⋊C4—742no—
181C4⋊C4—744no—
182C4⋊C4—744no—
183C42—374no—
184C42—378no—
185C42—742no—
186C42—744no—
187C42—742no—
188C23C23×D3711yescharacteristic
189Q8—28no—
190Q8—748no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—372no—
201C2×C4—374no—
202C2×C4—372no—
203C2×C4—374no—
204C2×C4—372no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—742no—
208C2×C4—742no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—741no—
212C2×C4—742no—
213C2×C4—742no—
214C2×C4—742no—
215C2×C4—742no—
216C2×C4D4×D3712yes—
217C2×C4#1059696414yes—
218C2×C4Q8×D3714yes—
219C2×C4#1059696612yes—
220C22C2×D4×D3711yescharacteristic
221C22C2×Q8×D3712yes—
222C22#41×D3711yescharacteristic
223C22C2×#1059696412yes—
224C22C2×#1059696611yescharacteristic
225C4—22no—
226C4—24no—
227C4—22no—
228C4—24no—
229C4—41no—
230C4—374no—
231C4—742no—
232C4—742no—
233C4—744no—
234C4—1481no—
235C4—1482no—
236C2#1455803911yescharacteristic
237C2#1455804611yescharacteristic
238C2C4⋊Q8×D3711yescharacteristic
239C2#1455808512yes—
240C2#1455808812yes—
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, prime radical, cosocleC23×C37C24
FittingC37×#395C2
hypercenter#395D37
hypocenterC37#2399
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
66. C4×Dic37Q8semidirect
132. C37#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic372
C2×#119245012
#145574662
#145574652
#145574632
#145574542
#145574522
C4⋊C4×Dic372
#145573842
#145573782
C37×#3952
#239937