Finite Group Databasebeta

← #18010435

Subgroups — #18010435

Order 4736.

592 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 104 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×#11924599C214yesmaximal, complemented
2D37⋊(C22⋊C8)C211yesmaximal, characteristic
3#14558475C211yesmaximal, characteristic
4C22×Q8×D37C211yesmaximal, characteristic
5C2×D37⋊C8C2212yes—
6C2×C4⋊#3866C2212yes—
7C2×C22⋊#3866—21no—
8#11924599—28no—
9#11924593—21no—
10C22⋊#64438—21no—
11(C2×#3866)⋊C4—21no—
12C22×Dic74—21no—
13C22×Dic74C411yescharacteristic, complemented
14C2×Q8×D37—28no—
15C2×Q8×D37—21no—
16C2×Q8×D37—21no—
17C2×Q8×D37C412yescomplemented
18C2×Q8×D37C2212yes—
19C22×C4×D37—21no—
20C22×C4×D37C2211yescharacteristic
21C22×Q8×C37C411yescharacteristic, complemented
22C23×D37D411yescharacteristic
23C22×#3866—22no—
24C2×Q8×C37—24no—
25C2×Q8×C37—21no—
26C2×Q8×C37C2×C412yes—
27C22×C4×C37—21no—
28C22×C4×C37C2×C411yescharacteristic
29C22×Dic37—21no—
30C22×Dic37D411yescharacteristic
31Q8×D37—28no—
32Q8×D37—28no—
33Q8×D37—24no—
34Q8×D37—24no—
35Q8×D37—24no—
36Q8×D37D418yes—
37C2×C4×D37—28no—
38C2×C4×D37—22no—
39C2×C4×D37—22no—
40C2×C4×D37—24no—
41C2×C4×D37C2×C411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C4×D37D411yescharacteristic
44C2×C4×D37C2311yescharacteristic
45C2×Dic74—28no—
46C2×Dic74—21no—
47C2×Dic74—22no—
48C2×Dic74—22no—
49C2×Dic74—24no—
50C2×Dic74C2×C412yes—
51C22⋊#3866—42no—
52C2×#64438—22no—
53C4⋊#3866—24no—
54D37⋊C8—24no—
55C23×C37C22⋊C411yescharacteristic
56C22×D37—22no—
57C22×D37—22no—
58C22×D37C22⋊C411yescharacteristic
59C22×D37SD1612yes—
60C22×D37Q1612yes—
61C22×D37C2×D411yescharacteristic
62C2×#3866—42no—
63C2×#3866—42no—
64C2×#3866—42no—
65Q8×C37—24no—
66Q8×C37—22no—
67Q8×C37C22⋊C414yescomplemented
68C2×C4×C37—24no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C22×C411yescharacteristic
73C2×Dic37—24no—
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37C22⋊C411yescharacteristic
77C2×Dic37C2×D411yescharacteristic
78C4×D37—28no—
79C4×D37—28no—
80C4×D37—22no—
81C4×D37—22no—
82C4×D37—22no—
83C4×D37C2×D414yes—
84Dic74—28no—
85Dic74—24no—
86Dic74—22no—
87Dic74—28no—
88Dic74C22⋊C414yescomplemented
89#64438—42no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37#10312yescomplemented
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—24no—
97C2×D37—24no—
98C2×D37#10312yescomplemented
99C2×D37#12012yes—
100C2×D37C2×SD1611yescharacteristic
101C2×D37C2×Q1611yescharacteristic
102C2×D37#13712yes—
103#3866—82no—
104C4×C37—24no—
105C4×C37—21no—
106C4×C37C2×C22⋊C412yes—
107Dic37—21no—
108Dic37—24no—
109Dic37#12012yes—
110#1787—371nomaximal, Sylow
111C2×C37—22no—
112C2×C37#37911yescharacteristic
113C2×C37C2×#10311yescharacteristic
114C2×C37#41911yescharacteristic
115D37—22no—
116D37#44812yes—
117D37#45112yes—
118C23×Q8—371no—
119C2×#103—374no—
120C2×C22⋊C8—371no—
121#380—371no—
122C37#178711yescharacteristic, complemented, Sylow
123C22×Q8—372no—
124C22×Q8—372no—
125C22×Q8—371no—
126C22×Q8—741no—
127C22×Q8—741no—
128C22×Q8—741no—
129C22×Q8—748no—
130C22×Q8#386611yescharacteristic, complemented
131C23×C4—371no—
132C23×C4—741no—
133C22×C8—372no—
134C2×C4⋊C4—372no—
135C2×C22⋊C4—741no—
136#103—748no—
137C22⋊C8—741no—
138C22⋊C8—741no—
139#95—741no—
140C24—371no—
141C2×Q8—24no—
142C2×Q8—21no—
143C2×Q8—378no—
144C2×Q8—372no—
145C2×Q8—742no—
146C2×Q8—742no—
147C2×Q8—744no—
148C2×Q8—748no—
149C2×Q8—744no—
150C2×Q8—744no—
151C2×Q8—748no—
152C2×Q8—748no—
153C2×Q8—744no—
154C2×Q8—741no—
155C2×Q8C2×#386612yes—
156C22×C4—21no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—744no—
163C22×C4—742no—
164C22×C4—742no—
165C22×C4—748no—
166C22×C4—741no—
167C22×C4—742no—
168C22×C4C2×#386611yescharacteristic
169C2×C8—744no—
170C2×C8—742no—
171C4⋊C4—744no—
172C22⋊C4—1482no—
173C23—371no—
174C23—372no—
175C23—372no—
176C23—371no—
177C23—742no—
178C23—742no—
179C23C22⋊#386611yescharacteristic
180Q8—24no—
181Q8—22no—
182Q8—374no—
183Q8—748no—
184Q8—748no—
185Q8—744no—
186Q8—742no—
187Q8C22⋊#386614yescomplemented
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—371no—
192C2×C4—374no—
193C2×C4—371no—
194C2×C4—742no—
195C2×C4—742no—
196C2×C4—748no—
197C2×C4—748no—
198C2×C4—742no—
199C2×C4—744no—
200C2×C4—742no—
201C2×C4—742no—
202C2×C4—1482no—
203C2×C4—1482no—
204C2×C4—1482no—
205C2×C4C22⋊#386611yescharacteristic
206C2×C4C22×#386611yescharacteristic
207C8—1482no—
208C22—21no—
209C22—21no—
210C22—372no—
211C22—371no—
212C22—371no—
213C22—372no—
214C22—372no—
215C22—744no—
216C22—744no—
217C22—741no—
218C22—741no—
219C22#1192459912yescomplemented
220C22C2×C22⋊#386611yescharacteristic
221C4—24no—
222C4—21no—
223C4—372no—
224C4—2962no—
225C4—741no—
226C4—744no—
227C4C2×C22⋊#386612yes—
228C2—22no—
229C2—372no—
230C2—372no—
231C2—742no—
232C2#1455847411yescharacteristic
233C2C2×#1192459911yescharacteristic
234C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37D4
cosocleC2×C4×D37C23
hypercenterC22×Q8#3866
hypocenterC37#1787
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11924599C2semidirect
13. C22×Dic74C4semidirect
17. C2×Q8×D37C4semidirect
21. C22×Q8×C37C4semidirect
67. Q8×C37C22⋊C4semidirect
88. Dic74C22⋊C4semidirect
92. C22×C37#103semidirect
98. C2×D37#103semidirect
122. C37#1787semidirect
130. C22×Q8#3866semidirect
187. Q8C22⋊#3866semidirect
219. C22#11924599semidirect

Maximal subgroups

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

subgroupindex
C2×#119245992
D37⋊(C22⋊C8)2
#145584752
C22×Q8×D372
#178737