Finite Group Databasebeta

← #17995627

Subgroups — #17995627

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×#11924569C211yesmaximal, characteristic, complemented
2#14558100C211yesmaximal, characteristic
3C2×#11924523C211yesmaximal, characteristic, complemented
4C2×#11924462C211yesmaximal, characteristic, complemented
5#14557543C211yesmaximal, characteristic, complemented
6#14557294C211yesmaximal, characteristic, complemented
7C2×#100×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×Dic74C2211yescharacteristic
10#11924569—22no—
11#11924569—22no—
12C2×Dic148—21no—
13C2×#10596930—21no—
14#11924532—21no—
15#11924523—21no—
16#11924523—22no—
17#11924523—22no—
18#11924507—22no—
19#11924505—22no—
20#11924495C2211yescharacteristic
21C2×C22⋊Dic37—22no—
22C2×C4×Dic37C2211yescharacteristic
23#11924462—22no—
24#11924461—22no—
25C22×D4×C37C2211yescharacteristic
26C2×M16×C37C2211yescharacteristic
27C2×M16×C37C2211yescharacteristic
28#100×C37—22no—
29C24×C37D412yes—
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—24no—
39C22×Dic37—21no—
40C22×Dic37—21no—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45C2×D148D411yescharacteristic
46C2×C4×D37—21no—
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×Dic74—21no—
51C2×Dic74—21no—
52C2×Dic74D411yescharacteristic
53C2×Dic74D412yescomplemented
54M16×C37—21no—
55M16×C37—21no—
56M16×C37—21no—
57M16×C37D412yescomplemented
58C2×C8×C37—21no—
59C2×C8×C37—21no—
60C22⋊Dic37—28no—
61C22⋊Dic37—24no—
62C22⋊Dic37—21no—
63C4⋊Dic37D412yes—
64C4×Dic37—21no—
65C4×Dic37—21no—
66C4×Dic37D412yescomplemented
67Dic148—24no—
68#10596930—24no—
69C23×C37—22no—
70C23×C37—22no—
71C23×C37—22no—
72C23×C37—44no—
73C23×C37C2×D411yescharacteristic
74C22×D37—21no—
75D4×C37—41no—
76D4×C37—41no—
77D4×C37—41no—
78D4×C37—41no—
79C2×C4×C37C2×D411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C22⋊D37—41no—
86C22⋊D37—41no—
87C22⋊D37—84no—
88C2×Dic37—22no—
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—21no—
92C2×Dic37—42no—
93C2×Dic37—41no—
94C2×Dic37—41no—
95D148—21no—
96D148—21no—
97C4×D37—41no—
98C4×D37—41no—
99Dic74—22no—
100Dic74—21no—
101Dic74—22no—
102Dic74—21no—
103Dic74—41no—
104Dic74—41no—
105C8×C37—22no—
106C8×C37—41no—
107C22×C37—22no—
108C22×C37—44no—
109C22×C37—42no—
110C22×C37—44no—
111C22×C37—82no—
112C22×C37#12011yescharacteristic
113C22×C37#12011yescharacteristic
114C22×C37#12111yescharacteristic
115C2×D37—41no—
116C2×D37—42no—
117C4×C37#12011yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12111yescharacteristic
120C4×C37#12711yescharacteristic
121Dic37—42no—
122Dic37—42no—
123Dic37—41no—
124Dic37—42no—
125#2004—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37—82no—
129C2×C37#39211yescharacteristic
130C2×C37#45512yes—
131D37—81no—
132C2×#137—371no—
133#535—371no—
134C2×#124—371no—
135C2×#104—371no—
136#419—371no—
137C2×#100D3711yescharacteristic, complemented
138#339—371no—
139C37#200411yescharacteristic, complemented, Sylow
140C2×#41—371no—
141C22×Q8—371no—
142C22×D4C2×D3711yescharacteristic
143#137—742no—
144#137—742no—
145C2×Q16—741no—
146C2×SD16—741no—
147C2×M16C2×D3711yescharacteristic
148C2×M16C2×D3711yescharacteristic
149#127—741no—
150#124—742no—
151#124—742no—
152#124—741no—
153#121—742no—
154#120—742no—
155#117—371no—
156C2×C22⋊C4—742no—
157C2×C42—371no—
158#104—742no—
159#103—742no—
160#100—22no—
161C24D14812yes—
162#41—741no—
163#41—741no—
164#41—741no—
165#41—741no—
166C2×Q8—371no—
167C2×Q8—372no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×Q8—741no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—371no—
180C2×D4—744no—
181C2×D4—741no—
182C22×C4—741no—
183C22×C4—741no—
184C22×C4—741no—
185C22×C4C22×D3711yescharacteristic
186Q16—744no—
187SD16—744no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D3712yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—372no—
195C22⋊C4—748no—
196C22⋊C4—744no—
197C22⋊C4—741no—
198C42—372no—
199C42—741no—
200C42—741no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—741no—
206C23C2×D14811yescharacteristic
207Q8—742no—
208Q8—741no—
209Q8—742no—
210Q8—741no—
211Q8—1481no—
212Q8—1481no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—2964no—
218D4—741no—
219D4—741no—
220D4—1481no—
221D4—1481no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—742no—
225C2×C4—741no—
226C2×C4—1482no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4—1481no—
230C2×C4—1481no—
231C2×C4#1059696211yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4D4×D3711yescharacteristic
234C2×C4D4×D3711yescharacteristic
235C2×C4D4×D3711yescharacteristic
236C2×C4C2×C22⋊D3711yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—1481no—
245C22—1482no—
246C22#1192450611yescharacteristic
247C22#1192450611yescharacteristic
248C22#1192451011yescharacteristic
249C4—1482no—
250C4—1481no—
251C4—1482no—
252C4—1482no—
253C4#1192450411yescharacteristic
254C4#1192450911yescharacteristic
255C4#1192450911yescharacteristic
256C4#1192453211yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—2961no—
261C2#1455744211yescharacteristic
262C2#1455771312yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#100×C37C2
socleC22×C37#120
prime radical#14558100C2
hypercenterC2×#100D37
hypocenterC37#2004
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#11924569C2semidirect
3. C2×#11924523C2semidirect
4. C2×#11924462C2semidirect
5. #14557543C2semidirect
6. #14557294C2semidirect
7. C2×#100×C37C2semidirect
53. C2×Dic74D4semidirect
57. M16×C37D4semidirect
66. C4×Dic37D4semidirect
137. C2×#100D37semidirect
139. C37#2004semidirect
191. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245692
#145581002
C2×#119245232
C2×#119244622
#145575432
#145572942
C2×#100×C372
#200437