Finite Group Databasebeta

← #17995624

Subgroups — #17995624

Order 4736.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11924566C211yesmaximal, characteristic, complemented
2#14558097C211yesmaximal, characteristic
3C2×#11924524C211yesmaximal, characteristic, complemented
4#14557543C211yesmaximal, characteristic, complemented
5C2×#11924452C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C22×D148C2211yescharacteristic
10#11924566—22no—
11#11924566—22no—
12C2×#10596942—21no—
13C2×#10596940—21no—
14C2×#10596934C2211yescharacteristic
15#11924532—21no—
16#11924525—21no—
17#11924524—22no—
18#11924524—22no—
19#11924510—22no—
20#11924504—22no—
21#11924495C2211yescharacteristic
22C2×#10596938—22no—
23#11924461—22no—
24#11924452—22no—
25C2×#41×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×C42×C37C2211yescharacteristic
28#104×C37—22no—
29C23×D37D412yes—
30#41×C37—21no—
31#41×C37—21no—
32#41×C37—21no—
33#41×C37—21no—
34C2×Q8×C37D411yescharacteristic
35C2×D4×C37—21no—
36C2×D4×C37D411yescharacteristic
37C22×C4×C37—21no—
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—24no—
41C22×Dic37—21no—
42C2×D148—21no—
43C2×D148—21no—
44C2×D148—21no—
45C2×D148—21no—
46C2×D148—21no—
47C2×D148—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74—21no—
52C2×Dic74—21no—
53C2×Dic74D412yescomplemented
54M16×C37—21no—
55M16×C37—21no—
56C2×C8×C37—21no—
57C42×C37—21no—
58C42×C37D412yescomplemented
59C22⋊Dic37—21no—
60#10596942—24no—
61#10596940—24no—
62#10596938—28no—
63#10596938—24no—
64C4⋊Dic37D412yes—
65C4×Dic37—21no—
66#10596934—21no—
67#10596934D412yescomplemented
68C2×#64436—21no—
69C23×C37—21no—
70C23×C37C2×D411yescharacteristic
71C22×D37—22no—
72C22×D37—22no—
73C22×D37—22no—
74C22×D37—44no—
75Q8×C37—21no—
76Q8×C37—21no—
77D4×C37—21no—
78D4×C37—21no—
79D4×C37—41no—
80D4×C37—41no—
81C2×C4×C37—22no—
82C2×C4×C37—21no—
83C2×C4×C37—42no—
84C2×C4×C37—41no—
85C2×C4×C37—41no—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37#4111yescharacteristic
92C22⋊D37—84no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—41no—
96C2×Dic37—41no—
97D148—41no—
98D148—41no—
99D148—41no—
100D148—41no—
101Dic74—22no—
102Dic74—22no—
103Dic74—41no—
104Dic74—41no—
105C8×C37—41no—
106#64436—22no—
107C22×C37—22no—
108C22×C37—41no—
109C22×C37—42no—
110C22×C37#12011yescharacteristic
111C22×C37#12011yescharacteristic
112C22×C37#12111yescharacteristic
113C2×D37—44no—
114C2×D37—42no—
115C2×D37—44no—
116C2×D37—82no—
117C4×C37—42no—
118C4×C37—41no—
119C4×C37#12011yescharacteristic
120C4×C37#12111yescharacteristic
121C4×C37#12111yescharacteristic
122C4×C37#12711yescharacteristic
123Dic37—42no—
124Dic37—42no—
125#2004—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—81no—
129C2×C37#39211yescharacteristic
130C2×C37#45512yes—
131D37—82no—
132C2×#137—371no—
133#535—371no—
134C2×#124—371no—
135C2×#104D3711yescharacteristic, complemented
136#419—371no—
137C2×#100—371no—
138#339—371no—
139C37#200411yescharacteristic, complemented, Sylow
140C2×#41C2×D3711yescharacteristic
141C22×Q8—371no—
142C22×D4—371no—
143#137—742no—
144#137—742no—
145C2×Q16—741no—
146C2×SD16—741no—
147C2×M16—371no—
148C2×M16C2×D3711yescharacteristic
149#127—741no—
150#124—742no—
151#124—741no—
152#124—742no—
153#121—742no—
154#120—742no—
155#117—371no—
156C2×C22⋊C4—742no—
157C2×C42C2×D3711yescharacteristic
158#104—22no—
159#103—742no—
160#100—742no—
161C24—372no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—372no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×Q8D14811yescharacteristic
173C2×D4—21no—
174C2×D4—744no—
175C2×D4—741no—
176C2×D4—741no—
177C2×D4—741no—
178C2×D4—741no—
179C2×D4—741no—
180C2×D4—741no—
181C2×D4D14811yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—741no—
185C22×C4C22×D3711yescharacteristic
186Q16—744no—
187SD16—744no—
188M16—21no—
189M16—21no—
190M16—372no—
191M16—741no—
192C2×C8—21no—
193C2×C8—741no—
194C4⋊C4—372no—
195C22⋊C4—748no—
196C22⋊C4—744no—
197C22⋊C4—741no—
198C42—21no—
199C42—741no—
200C42C22⋊D3712yescomplemented
201C23—21no—
202C23—742no—
203C23—742no—
204C23—742no—
205C23—1484no—
206C23D4×D3711yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—742no—
210Q8—742no—
211Q8—1481no—
212Q8—1481no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—2964no—
218D4—1481no—
219D4—1481no—
220D4—1481no—
221D4—1481no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—742no—
228C2×C4—742no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4C2×D14811yescharacteristic
232C2×C4#1059696211yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4D4×D3711yescharacteristic
235C2×C4D4×D3711yescharacteristic
236C2×C4C2×C22⋊D3711yescharacteristic
237C8—41no—
238C8—742no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—2962no—
243C22—1484no—
244C22—1482no—
245C22—1484no—
246C22#1192450411yescharacteristic
247C22#1192450611yescharacteristic
248C22#1192450911yescharacteristic
249C4—42no—
250C4—41no—
251C4—1482no—
252C4—1482no—
253C4#1192450611yescharacteristic
254C4#1192450911yescharacteristic
255C4#1192451011yescharacteristic
256C4#1192453211yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—2962no—
261C2#1455744211yescharacteristic
262C2#1455771212yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
prime radical#14558097C2
hypercenterC2×#104D37
hypocenterC37#2004
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#11924566C2semidirect
3. C2×#11924524C2semidirect
4. #14557543C2semidirect
5. C2×#11924452C2semidirect
6. #14557293C2semidirect
7. C2×#104×C37C2semidirect
53. C2×Dic74D4semidirect
58. C42×C37D4semidirect
67. #10596934D4semidirect
135. C2×#104D37semidirect
139. C37#2004semidirect
200. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245662
#145580972
C2×#119245242
#145575432
C2×#119244522
#145572932
C2×#104×C372
#200437