Finite Group Databasebeta

← #18010736

Subgroups — #18010736

Order 4736.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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×#11924595C214yesmaximal, complemented
2#14558475C211yesmaximal, characteristic, complemented
3C4×C22⋊#3866C211yesmaximal, characteristic, complemented
4C2×#11924511C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6C2×C22⋊#3866C2212yes—
7C2×C22⋊#3866C2212yes—
8C2×C4×#3866—21no—
9#11924595—28no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4—21no—
12C22×D148C411yescharacteristic, complemented
13C22×D148C2212yes—
14C22×C4×D37C2211yescharacteristic
15#11924511—21no—
16#11924511—21no—
17#11924511—21no—
18#11924511—21no—
19C2×#10596938C412yescomplemented
20C2×C4⋊C4×C37C411yescharacteristic, complemented
21C23×D37C2×C412yes—
22C23×D37C2311yescharacteristic
23C22×#3866—22no—
24C22×#3866—22no—
25C22×C4×C37C2×C412yes—
26C22×C4×C37C2×C411yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C2×D148—22no—
29C2×D148—22no—
30C2×D148—24no—
31C2×D148—24no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148—42no—
35C2×C4×D37—42no—
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C22⋊#3866—22no—
41C22⋊#3866—24no—
42C22⋊#3866D414yescomplemented
43C4⋊#3866—42no—
44C4×#3866—42no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37—21no—
47#10596938—22no—
48#10596938—22no—
49C23×C37C22×C411yescharacteristic
50C22×D37—22no—
51C22×D37—24no—
52C22×D37—41no—
53C22×D37—41no—
54C22×D37—42no—
55C22×D37—42no—
56C22×D37C2×D411yescharacteristic
57C22×D37C2×D411yescharacteristic
58C22×D37C2×D412yes—
59C22×D37#4112yes—
60C2×#3866—24no—
61C2×#3866—42no—
62C2×#3866—42no—
63C2×#3866—42no—
64C2×#3866—42no—
65C2×#3866—42no—
66C2×C4×C37—22no—
67C2×C4×C37—22no—
68C2×C4×C37—24no—
69C2×C4×C37C22⋊C411yescharacteristic
70C2×C4×C37C22⋊C411yescharacteristic
71C2×Dic37—41no—
72C2×Dic37C22⋊C411yescharacteristic
73C2×Dic37C22⋊C411yescharacteristic
74D148—42no—
75D148—44no—
76D148—42no—
77D148—42no—
78D148—42no—
79C4×D37—22no—
80C4×D37—22no—
81C4×D37—41no—
82C4×D37—41no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37C2×C22⋊C411yescharacteristic
86C22×C37C4×D412yes—
87C2×D37—21no—
88C2×D37—21no—
89C2×D37—21no—
90C2×D37—21no—
91C2×D37—42no—
92C2×D37—42no—
93C2×D37—42no—
94C2×D37—42no—
95C2×D37—42no—
96C2×D37—84no—
97C2×D37#12112yes—
98C2×D37#12411yescharacteristic
99C2×D37#12711yescharacteristic
100#3866—44no—
101#3866—82no—
102C4×C37—21no—
103C4×C37—42no—
104C4×C37#9912yescomplemented
105Dic37—21no—
106Dic37—21no—
107#1964—371nomaximal, Sylow
108C2×C37—22no—
109C2×C37#39011yescharacteristic
110C2×C37C2×#9911yescharacteristic
111C2×C37#41011yescharacteristic
112D37—22no—
113D37—21no—
114D37—21no—
115D37—82no—
116C2×#121—371no—
117C2×#99—374no—
118#380—371no—
119C4×C22⋊C4—371no—
120C37#196411yescharacteristic, complemented, Sylow
121C22×D4—372no—
122C22×D4—371no—
123C23×C4—371no—
124#121—741no—
125#121—741no—
126#121—741no—
127#121—741no—
128C2×C4⋊C4—741no—
129C2×C4⋊C4#386611yescharacteristic, complemented
130C2×C22⋊C4—372no—
131C2×C22⋊C4—372no—
132C2×C22⋊C4—372no—
133C2×C42—741no—
134#99—748no—
135#95—741no—
136#95—741no—
137C24—371no—
138C24—372no—
139C2×D4—744no—
140C2×D4—742no—
141C2×D4—742no—
142C2×D4—744no—
143C2×D4—741no—
144C2×D4—741no—
145C2×D4—1482no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4—742no—
152C22×C4—742no—
153C22×C4—1482no—
154C22×C4C2×#386612yes—
155C22×C4C2×#386611yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—1482no—
159C22⋊C4—374no—
160C22⋊C4—742no—
161C22⋊C4—742no—
162C22⋊C4—742no—
163C22⋊C4—744no—
164C42—1482no—
165C23—371no—
166C23—371no—
167C23—372no—
168C23—372no—
169C23—744no—
170C23—742no—
171C23—1482no—
172C23—1482no—
173C23—1481no—
174C23—1481no—
175C23C22×#386611yescharacteristic
176D4—1482no—
177D4—1484no—
178D4—1482no—
179D4—1482no—
180D4—1482no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—371no—
185C2×C4—371no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—744no—
189C2×C4—1481no—
190C2×C4—1481no—
191C2×C4—1482no—
192C2×C4—1482no—
193C2×C4—1482no—
194C2×C4—1481no—
195C2×C4—1482no—
196C2×C4—1482no—
197C2×C4C22⋊#386611yescharacteristic
198C2×C4C22⋊#386611yescharacteristic
199C22—21no—
200C22—21no—
201C22—372no—
202C22—371no—
203C22—371no—
204C22—2964no—
205C22—741no—
206C22—741no—
207C22—741no—
208C22—741no—
209C22—1482no—
210C22—1482no—
211C22—1482no—
212C22—1482no—
213C22—1482no—
214C22C2×C22⋊#386611yescharacteristic
215C22D4×#386612yes—
216C4—21no—
217C4—42no—
218C4—2962no—
219C4—741no—
220C4—741no—
221C4—1484no—
222C4#1192459512yescomplemented
223C2—22no—
224C2—2962no—
225C2—741no—
226C2—742no—
227C2—741no—
228C2#1455848511yescharacteristic
229C2C2×#1192459511yescharacteristic
230C2#1455851411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924511C2
cosocleC23×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1964
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924595C2semidirect
2. #14558475C2semidirect
3. C4×C22⋊#3866C2semidirect
12. C22×D148C4semidirect
19. C2×#10596938C4semidirect
20. C2×C4⋊C4×C37C4semidirect
42. C22⋊#3866D4semidirect
104. C4×C37#99semidirect
120. C37#1964semidirect
129. C2×C4⋊C4#3866semidirect
222. C4#11924595semidirect

Maximal subgroups

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

subgroupindex
C2×#119245952
#145584752
C4×C22⋊#38662
C2×#119245112
#196437