Finite Group Databasebeta

← #17995409

Subgroups — #17995409

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×#11924525C211yesmaximal, characteristic
2C2×#11924460C211yesmaximal, characteristic, complemented
3C2×#11924458C211yesmaximal, characteristic
4C2×#11924456C211yesmaximal, characteristic
5C2×#11924446C211yesmaximal, characteristic, complemented
6#14557402C211yesmaximal, characteristic, complemented
7C2×#103×C37C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C22×#64436C2211yescharacteristic
10#11924525—22no—
11#11924525C414yescomplemented
12C2×C4⋊Dic37C2211yescharacteristic
13C2×#10596936—22no—
14C2×#10596938—22no—
15C2×C4×Dic37C2211yescharacteristic
16#11924460—22no—
17#11924458—22no—
18#11924456—22no—
19#11924446—22no—
20C22×Q8×C37C2211yescharacteristic
21C22×C8×C37C2211yescharacteristic
22C2×C4⋊C4×C37C2211yescharacteristic
23#103×C37—22no—
24C23×D37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37—21no—
29C2×Q8×C37—21no—
30C2×Q8×C37C2×C412yes—
31C22×C4×C37—21no—
32C22×C4×C37—21no—
33C22×C4×C37C2311yescharacteristic
34C22×Dic37—21no—
35C22×Dic37D412yes—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148C2×C412yes—
42C2×C8×C37—21no—
43C2×C8×C37—21no—
44C2×C8×C37D412yes—
45C4⋊C4×C37—21no—
46C4⋊C4×C37—21no—
47#10596938—28no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50#10596936—44no—
51C4×Dic37C2×C412yes—
52C4×Dic37D412yes—
53C2×#64436—21no—
54C2×#64436—21no—
55C2×#64436D412yes—
56C23×C37C2×D411yescharacteristic
57C22×D37—22no—
58C22×D37—41no—
59C22×D37—41no—
60C22×D37—42no—
61C22×D37—42no—
62Q8×C37—22no—
63Q8×C37—22no—
64Q8×C37—41no—
65Q8×C37—41no—
66C2×C4×C37—22no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—42no—
71C2×C4×C37C22×C411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37#4111yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C2×Dic37—22no—
78C2×Dic37—22no—
79C2×Dic37—41no—
80C2×Dic37—42no—
81C2×Dic37C22⋊C414yes—
82D148—22no—
83D148—22no—
84D148—41no—
85D148—41no—
86C8×C37—22no—
87#64436—22no—
88C22×C37C2×C22⋊C411yescharacteristic
89C22×C37#12411yescharacteristic
90C22×C37#12711yescharacteristic
91C22×C37AGL(1,ℤ/8)12yes—
92C22×C37#13712yes—
93C2×D37—42no—
94C2×D37—44no—
95C2×D37—82no—
96C2×D37—81no—
97C2×D37—81no—
98C4×C37—42no—
99C4×C37—81no—
100C4×C37C4×D411yescharacteristic
101C4×C37C4×D411yescharacteristic
102C4×C37#12111yescharacteristic
103C4×C37#12111yescharacteristic
104Dic37—24no—
105Dic37—81no—
106#1959—371nomaximal, Sylow
107C2×C37#39011yescharacteristic
108C2×C37#41712yes—
109C2×C37#48912yes—
110C2×C37#49611yescharacteristic
111C2×C37#49711yescharacteristic
112D37—82no—
113C2×#124—371no—
114C2×#103—371no—
115C2×#103D3711yescharacteristic, complemented
116C2×#102—371no—
117C2×#102—371no—
118C2×#97—371no—
119#384—371no—
120C37#195911yescharacteristic, complemented, Sylow
121C22×Q8C2×D3711yescharacteristic
122C22×D4—371no—
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—22no—
133#103—742no—
134#102—742no—
135#102—742no—
136#97—742no—
137C24—741no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8C4×D3712yes—
144C2×D4—372no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4—741no—
148C2×D4—741no—
149C2×D4—741no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—372no—
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—742no—
170C23—1481no—
171C23—1481no—
172C23—1482no—
173C23—1482no—
174C23D4×D3711yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—41no—
178Q8—41no—
179D4—742no—
180D4—742no—
181D4—1481no—
182D4—1481no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—374no—
189C2×C4—742no—
190C2×C4—742no—
191C2×C4—1481no—
192C2×C4—1482no—
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—2962no—
202C22—2961no—
203C22—2961no—
204C22—1484no—
205C22—1482no—
206C22C22⋊C4×D3711yescharacteristic
207C22#1192452211yescharacteristic
208C22#1192453211yescharacteristic
209C22#1192456312yes—
210C22#1192456812yes—
211C4—42no—
212C4—81no—
213C4—2961no—
214C4—744no—
215C4#1192449611yescharacteristic
216C4C4×C22⋊D3711yescharacteristic
217C4#1192450811yescharacteristic
218C4#1192450911yescharacteristic
219C2—2962no—
220C2#1455743311yescharacteristic
221C2#1455753312yes—
222C2#1455789412yes—
223C2#1455791911yescharacteristic
224C2#1455792611yescharacteristic
subgroupG/H
centerC23D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#103×C37C2
socleC23×C37C2×D4
prime radicalC22×D148C22
cosocleC22×C4×C37C23
hypercenterC2×#103D37
hypocenterC37#1959
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×#11924460C2semidirect
5. C2×#11924446C2semidirect
6. #14557402C2semidirect
7. C2×#103×C37C2semidirect
11. #11924525C4semidirect
115. C2×#103D37semidirect
120. C37#1959semidirect

Maximal subgroups

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

subgroupindex
C2×#119245252
C2×#119244602
C2×#119244582
C2×#119244562
C2×#119244462
#145574022
C2×#103×C372
#195937