Finite Group Databasebeta

← #18010740

Subgroups — #18010740

Order 4736.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#14558536C211yesmaximal, characteristic, complemented
2C2×#11924597C212yesmaximal, complemented
3C2×#11924596C212yesmaximal
4C4×#10596957C211yesmaximal, characteristic, complemented
5C2×#11924522C211yesmaximal, characteristic
6C2×#10596957C2212yes—
7C2×#10596957C2212yes—
8#11924603—21no—
9C4⋊#64438—21no—
10#11924597—24no—
11#11924596—24no—
12#11924591—21no—
13C4×#64438—21no—
14C22×Dic74C2211yescharacteristic
15C22×C22⋊D37C2211yescharacteristic
16#11924522—21no—
17#11924522—21no—
18#11924522—21no—
19#11924522—21no—
20C2×C22⋊Dic37C411yescharacteristic
21C2×#10596938C411yescharacteristic
22C2×#10596938C411yescharacteristic
23C2×C4×Dic37C2211yescharacteristic
24C2×C22⋊C4×C37C411yescharacteristic
25C24×C37C2×C411yescharacteristic
26C23×D37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—22no—
32C2×C22⋊D37—22no—
33C22×Dic37C2×C411yescharacteristic
34C22×Dic37C2×C411yescharacteristic
35C22×Dic37C2311yescharacteristic
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—22no—
39C2×Dic74—22no—
40#10596957—22no—
41#10596957—22no—
42#10596957—22no—
43#10596957D414yes—
44C2×#64438—22no—
45C2×#64438—22no—
46C22⋊C4×C37—21no—
47C22⋊C4×C37—21no—
48C22⋊Dic37—21no—
49C22⋊Dic37—21no—
50#10596938—21no—
51#10596938—21no—
52#10596938—21no—
53#10596938—21no—
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C4×Dic37D411yescharacteristic
57C4×Dic37D411yescharacteristic
58C23×C37—21no—
59C23×C37—22no—
60C23×C37—41no—
61C23×C37—41no—
62C23×C37C22×C411yescharacteristic
63C22×D37—21no—
64C22×D37—22no—
65C22×D37—41no—
66C22×D37—41no—
67C2×C4×C37—21no—
68C2×C4×C37—22no—
69C2×C4×C37—41no—
70C2×C4×C37C22⋊C411yescharacteristic
71C2×C4×C37C22⋊C411yescharacteristic
72C22⋊D37—42no—
73C22⋊D37—41no—
74C22⋊D37—41no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37—41no—
78C2×Dic37C22⋊C411yescharacteristic
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C2×D411yescharacteristic
81C2×Dic37C2×D412yes—
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37#4112yes—
84Dic74—42no—
85Dic74—41no—
86Dic74—41no—
87#64438—24no—
88#64438—42no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37—82no—
95C22×C37C2×C22⋊C411yescharacteristic
96C22×C37C4×D412yes—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—41no—
100C2×D37—82no—
101C4×C37—21no—
102C4×C37—21no—
103C4×C37—41no—
104Dic37—21no—
105Dic37—21no—
106Dic37—41no—
107Dic37#12112yes—
108Dic37#12411yescharacteristic
109Dic37#12711yescharacteristic
110#1967—371nomaximal, Sylow
111C2×C37—22no—
112C2×C37—81no—
113C2×C37#39011yescharacteristic
114C2×C37#41311yescharacteristic
115C2×C37#41311yescharacteristic
116D37—81no—
117C2×#124—371no—
118#423—371no—
119C2×#101—372no—
120C2×#100—372no—
121C4×M16—371no—
122C37#196711yescharacteristic, complemented, Sylow
123C22×Q8—371no—
124C22×D4—371no—
125C2×M16—372no—
126C2×M16—372no—
127#124—741no—
128#124—741no—
129#124—741no—
130#124—741no—
131C2×C22⋊C4—371no—
132C2×C22⋊C4—371no—
133C2×C22⋊C4—371no—
134C2×C22⋊C4#386611yescharacteristic
135C2×C42—371no—
136C4⋊C8—741no—
137C4⋊C8—741no—
138#101—744no—
139#100—744no—
140#97—741no—
141C4×C8—741no—
142C24—371no—
143C24C2×#386611yescharacteristic
144C2×Q8—742no—
145C2×Q8—741no—
146C2×Q8—741no—
147C2×Q8—742no—
148C2×D4—742no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4—742no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4C2×#386611yescharacteristic
156C22×C4C2×#386611yescharacteristic
157M16—374no—
158M16—742no—
159M16—742no—
160M16—742no—
161C2×C8—742no—
162C2×C8—742no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C42—371no—
172C42—371no—
173C42—371no—
174C42—371no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—742no—
180C23—741no—
181C23—1481no—
182C23—1481no—
183C23C22×#386611yescharacteristic
184Q8—1482no—
185Q8—1481no—
186Q8—1481no—
187D4—1482no—
188D4—1481no—
189D4—1481no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—371no—
194C2×C4—371no—
195C2×C4—372no—
196C2×C4—372no—
197C2×C4—371no—
198C2×C4—371no—
199C2×C4—741no—
200C2×C4—742no—
201C2×C4—1481no—
202C2×C4C22⋊#386611yescharacteristic
203C2×C4C22⋊#386611yescharacteristic
204C8—744no—
205C8—1482no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—2962no—
213C22—1481no—
214C22—1481no—
215C22—1481no—
216C22C2×C22⋊#386611yescharacteristic
217C22D4×#386612yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—372no—
222C4—371no—
223C4—371no—
224C4—741no—
225C4—741no—
226C4—1481no—
227C2—22no—
228C2—81no—
229C2—2961no—
230C2#1455848511yescharacteristic
231C2#1455851911yescharacteristic
232C2#1455852011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC22×Dic37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37#1967
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558536C2semidirect
2. C2×#11924597C2semidirect
4. C4×#10596957C2semidirect
122. C37#1967semidirect

Maximal subgroups

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

subgroupindex
#145585362
C2×#119245972
C2×#119245962
C4×#105969572
C2×#119245222
#196737