Finite Group Databasebeta

← #17995411

Subgroups — #17995411

Order 4736.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#11924523C211yesmaximal, characteristic
2C2×#11924461C211yesmaximal, characteristic, complemented
3C2×#11924459C211yesmaximal, characteristic, complemented
4C2×#11924457C211yesmaximal, characteristic
5C2×#11924446C211yesmaximal, characteristic, complemented
6#14557402C211yesmaximal, characteristic, complemented
7C2×#102×C37C211yesmaximal, characteristic
8C22×Dic74C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924523—22no—
11#11924523C414yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936—22no—
14C2×C22⋊Dic37—22no—
15C2×C4×Dic37C2211yescharacteristic
16#11924461—22no—
17#11924459—22no—
18#11924457—22no—
19#11924446—22no—
20C22×D4×C37C2211yescharacteristic
21C22×C8×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23#102×C37—22no—
24C24×C37—21no—
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37C2×C412yes—
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C22×Dic37—21no—
34C22×Dic37—21no—
35C22×Dic37D412yes—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74C2×C412yes—
42C2×C8×C37—21no—
43C2×C8×C37—21no—
44C2×C8×C37D412yes—
45C4⋊C4×C37—21no—
46C4⋊C4×C37—21no—
47C22⋊Dic37—28no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50#10596936—44no—
51C4×Dic37C2×C412yes—
52C4×Dic37D412yes—
53C2×#64436—21no—
54C2×#64436—21no—
55C2×#64436D412yes—
56C23×C37—22no—
57C23×C37—41no—
58C23×C37—41no—
59C23×C37—42no—
60C23×C37—42no—
61C23×C37C2×D411yescharacteristic
62D4×C37—22no—
63D4×C37—22no—
64D4×C37—41no—
65D4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—42no—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37#4111yescharacteristic
73C2×C4×C37#4111yescharacteristic
74C2×Dic37—22no—
75C2×Dic37—22no—
76C2×Dic37—22no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37—42no—
81C2×Dic37C22⋊C414yes—
82Dic74—22no—
83Dic74—22no—
84Dic74—41no—
85Dic74—41no—
86C8×C37—22no—
87#64436—22no—
88C22×C37—42no—
89C22×C37—44no—
90C22×C37—82no—
91C22×C37—81no—
92C22×C37—81no—
93C22×C37C2×C22⋊C411yescharacteristic
94C22×C37#12411yescharacteristic
95C22×C37#12711yescharacteristic
96C22×C37AGL(1,ℤ/8)12yes—
97C22×C37#13712yes—
98C4×C37—81no—
99C4×C37C4×D411yescharacteristic
100C4×C37C4×D411yescharacteristic
101C4×C37#12111yescharacteristic
102C4×C37#12111yescharacteristic
103Dic37—24no—
104Dic37—42no—
105Dic37—81no—
106#1959—371nomaximal, Sylow
107C2×C37—82no—
108C2×C37#39011yescharacteristic
109C2×C37#41712yes—
110C2×C37#48912yes—
111C2×C37#49611yescharacteristic
112C2×C37#49711yescharacteristic
113C2×#124—371no—
114C2×#103—371no—
115C2×#103—371no—
116C2×#102—371no—
117C2×#102D3711yescharacteristic
118C2×#97—371no—
119#384—371no—
120C37#195911yescharacteristic, complemented, Sylow
121C22×Q8—371no—
122C22×D4C2×D3711yescharacteristic
123C22×C8—371no—
124C22×C8C2×D3711yescharacteristic
125#124—374no—
126#124—742no—
127C2×C4⋊C4—371no—
128C2×C4⋊C4—742no—
129C2×C4⋊C4C2×D3711yescharacteristic
130C2×C22⋊C4—742no—
131C2×C42—371no—
132#103—742no—
133#103—742no—
134#102—22no—
135#102—742no—
136#97—742no—
137C24—21no—
138C2×Q8—372no—
139C2×Q8—741no—
140C2×Q8—741no—
141C2×Q8—741no—
142C2×Q8—741no—
143C2×Q8—741no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D3712yes—
150C22×C4—21no—
151C22×C4—372no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4C22×D3711yescharacteristic
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—372no—
158C2×C8—741no—
159C2×C8—741no—
160C2×C8C22⋊D3712yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—1484no—
166C22⋊C4—748no—
167C42—372no—
168C42—372no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D3711yescharacteristic
175Q8—742no—
176Q8—742no—
177Q8—1481no—
178Q8—1481no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—374no—
186C2×C4—742no—
187C2×C4—742no—
188C2×C4—742no—
189C2×C4—1481no—
190C2×C4—1482no—
191C2×C4—1481no—
192C2×C4—1481no—
193C2×C4C2×C4×D3711yescharacteristic
194C2×C4#1059696211yescharacteristic
195C2×C4D4×D3711yescharacteristic
196C2×C4D4×D3711yescharacteristic
197C2×C4#1059696411yescharacteristic
198C2×C4C2×C22⋊D3711yescharacteristic
199C8—22no—
200C8—742no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22C22⋊C4×D3711yescharacteristic
207C22#1192452211yescharacteristic
208C22#1192453211yescharacteristic
209C22#1192456012yes—
210C22#1192456512yes—
211C4—81no—
212C4—2961no—
213C4—744no—
214C4—1482no—
215C4#1192449611yescharacteristic
216C4C4×C22⋊D3711yescharacteristic
217C4#1192450811yescharacteristic
218C4#1192450911yescharacteristic
219C2—82no—
220C2#1455743311yescharacteristic
221C2#1455753112yes—
222C2#1455789112yes—
223C2#1455792111yescharacteristic
224C2#1455792411yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#102×C37C2
socleC23×C37C2×D4
prime radicalC22×D4×C37C22
cosocleC22×C4×C37C23
hypercenterC2×#102D37
hypocenterC37#1959
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#11924461C2semidirect
3. C2×#11924459C2semidirect
5. C2×#11924446C2semidirect
6. #14557402C2semidirect
11. #11924523C4semidirect
120. C37#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#119245232
C2×#119244612
C2×#119244592
C2×#119244572
C2×#119244462
#145574022
C2×#102×C372
#195937