Finite Group Databasebeta

← #18011195

Subgroups — #18011195

Order 4736.

800 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 198 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
1#14558600C212yesmaximal, complemented
2#14558513C212yesmaximal, complemented
3#14558512C212yesmaximal, complemented
4D37⋊#99C214yesmaximal, complemented
5C2×#11924594C214yesmaximal, complemented
6C2×#11924581C211yesmaximal, characteristic
7D4×#3866—28no—
8#11924615C2214yescomplemented
9C2×C22⋊#3866C2218yescomplemented
10#11924595C2214yescomplemented
11#11924594C2214yescomplemented
12#11924594C2218yescomplemented
13#11924581—28no—
14C2×#10596962C411yescharacteristic, complemented
15C2×#10596962C2211yescharacteristic
16C2×#10596964C412yescomplemented
17C2×#10596964C411yescharacteristic, complemented
18C2×#10596964C2211yescharacteristic
19C22×C22⋊D37C412yescomplemented
20C22×C22⋊D37C2212yes—
21C2×D4×D37C411yescharacteristic, complemented
22C2×D4×D37C2212yes—
23C2×D4×D37C2211yescharacteristic
24C22×D4×C37C411yescharacteristic, complemented
25C24×C37C2×C412yescomplemented
26C23×D37C2×C412yescomplemented
27C23×D37C2312yes—
28C22×#3866—28no—
29C2×D4×C37—24no—
30C2×D4×C37C2×C411yescharacteristic
31C2×D4×C37C2×C411yescharacteristic, complemented
32C2×D4×C37C2×C412yescomplemented
33C22×C4×C37C2×C411yescharacteristic, complemented
34C2×C22⋊D37—28no—
35C2×C22⋊D37—28no—
36C2×C22⋊D37C2×C412yes—
37C2×C22⋊D37C2×C412yescomplemented
38C2×C22⋊D37C2×C412yescomplemented
39C2×C22⋊D37C2×C411yescharacteristic, complemented
40C2×C22⋊D37C2×C412yescomplemented
41C2×C22⋊D37C2312yes—
42C2×C22⋊D37C2311yescharacteristic
43C22×Dic37C2×C412yescomplemented
44C22×Dic37C2×C412yescomplemented
45#10596964—24no—
46#10596964—28no—
47#10596964—24no—
48D4×D37—28no—
49D4×D37—24no—
50D4×D37D418yes—
51#10596962—24no—
52#10596962—24no—
53C2×D148C2×C411yescharacteristic
54C2×D148C2311yescharacteristic
55C2×C4×D37C2×C411yescharacteristic, complemented
56C2×C4×D37C2×C412yescomplemented
57C2×C4×D37C2311yescharacteristic
58C2×Dic74C2×C411yescharacteristic, complemented
59C2×Dic74C2×C411yescharacteristic, complemented
60C22⋊#3866—28no—
61C22⋊#3866C2318yes—
62C4⋊#3866—24no—
63C4×#3866—24no—
64C23×C37—24no—
65C23×C37—82no—
66C23×C37C22×C412yes—
67C23×C37C22×C411yescharacteristic
68C23×C37C22×C412yes—
69C22×D37—24no—
70C22×D37—82no—
71C22×D37—82no—
72C22×D37C22×C411yescharacteristic
73C22×D37C22×C412yes—
74C22×D37C2×D418yes—
75C22×D37C2411yescharacteristic
76C2×#3866—28no—
77C2×#3866—88no—
78D4×C37—24no—
79D4×C37—22no—
80D4×C37C22⋊C414yes—
81C2×C4×C37—22no—
82C2×C4×C37C22×C411yescharacteristic
83C2×C4×C37C22×C411yescharacteristic
84C22⋊D37—24no—
85C22⋊D37—24no—
86C22⋊D37—24no—
87C22⋊D37—22no—
88C22⋊D37—24no—
89C22⋊D37—22no—
90C22⋊D37C22⋊C418yes—
91C2×Dic37—24no—
92C2×Dic37—24no—
93C2×Dic37C22×C411yescharacteristic
94C2×Dic37C22×C412yes—
95C2×Dic37C22×C411yescharacteristic
96D148—22no—
97D148C22⋊C414yes—
98C4×D37—24no—
99C4×D37—22no—
100C4×D37C2×D414yes—
101Dic74—22no—
102Dic74—22no—
103C22×C37—22no—
104C22×C37—21no—
105C22×C37—42no—
106C22×C37—42no—
107C22×C37—41no—
108C22×C37—84no—
109C22×C37C2×C22⋊C414yes—
110C22×C37C23×C411yescharacteristic
111C2×D37—21no—
112C2×D37—48no—
113C2×D37—42no—
114C2×D37—41no—
115C2×D37—41no—
116C2×D37—84no—
117C2×D37C2×C22⋊C414yes—
118C2×D37C22×D412yes—
119#3866—48no—
120C4×C37—21no—
121C4×C37C2×C22⋊C412yes—
122Dic37—22no—
123Dic37—21no—
124Dic37C2×C22⋊C412yes—
125#2883—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—24no—
128C2×C37—42no—
129C2×C37—41no—
130C2×C37C22×C22⋊C411yescharacteristic
131D37—22no—
132D37—24no—
133D37—41no—
134C2×H(5,𝔽2)—371no—
135#518—372no—
136#410—372no—
137#410—372no—
138C2×#99—374no—
139C2×#99—374no—
140C37#288311yescharacteristic, complemented, Sylow
141H(5,𝔽2)—748no—
142C2×#41—371no—
143C2×#41—372no—
144C2×#41—371no—
145C2×#41—371no—
146C2×#41—371no—
147C22×D4—371no—
148C22×D4—372no—
149C22×D4—372no—
150C22×D4—371no—
151C22×D4—372no—
152C22×D4#386611yescharacteristic, complemented
153C4×D4—748no—
154#117—374no—
155C2×C22⋊C4—378no—
156#99—374no—
157#99—378no—
158#99—374no—
159C24—372no—
160C24—372no—
161C24C2×#386612yescomplemented
162#41—744no—
163#41—744no—
164#41—744no—
165#41—748no—
166#41—744no—
167C2×Q8—371no—
168C2×Q8—371no—
169C2×D4—24no—
170C2×D4—372no—
171C2×D4—378no—
172C2×D4—372no—
173C2×D4—371no—
174C2×D4—371no—
175C2×D4—372no—
176C2×D4—372no—
177C2×D4—372no—
178C2×D4—371no—
179C2×D4—371no—
180C2×D4—744no—
181C2×D4—748no—
182C2×D4—748no—
183C2×D4—748no—
184C2×D4C2×#386611yescharacteristic
185C2×D4C2×#386612yescomplemented
186C2×D4C2×#386611yescharacteristic, complemented
187C22×C4—371no—
188C22×C4—372no—
189C22×C4—372no—
190C22×C4—372no—
191C22×C4—371no—
192C22×C4—748no—
193C22×C4C2×#386611yescharacteristic, complemented
194C4⋊C4—744no—
195C22⋊C4—378no—
196C22⋊C4—748no—
197C42—744no—
198C23—24no—
199C23—82no—
200C23—378no—
201C23—371no—
202C23—372no—
203C23—371no—
204C23—2962no—
205C23—2962no—
206C23—744no—
207C23C22×#386612yes—
208C23C22×#386611yescharacteristic
209C23C22×#386612yes—
210Q8—742no—
211Q8—742no—
212D4—24no—
213D4—22no—
214D4—378no—
215D4—374no—
216D4—742no—
217D4—742no—
218D4—742no—
219D4—744no—
220D4—744no—
221D4—744no—
222D4—744no—
223D4C22⋊#386614yes—
224C2×C4—22no—
225C2×C4—371no—
226C2×C4—374no—
227C2×C4—372no—
228C2×C4—371no—
229C2×C4—2968no—
230C2×C4—744no—
231C2×C4—744no—
232C2×C4—744no—
233C2×C4—742no—
234C2×C4—748no—
235C2×C4C22×#386611yescharacteristic
236C2×C4C22×#386611yescharacteristic
237C22—21no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—84no—
243C22—372no—
244C22—374no—
245C22—2964no—
246C22—741no—
247C22—1488no—
248C22—1481no—
249C22—1482no—
250C22—1481no—
251C22C2×C22⋊#386614yes—
252C22C23×#386611yescharacteristic
253C4—21no—
254C4—372no—
255C4—742no—
256C4—741no—
257C4—1488no—
258C4C2×C22⋊#386612yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—42no—
263C2—742no—
264C2—744no—
265C2—1481no—
266C2C22×C22⋊#386611yescharacteristic
subgroupG/H
centerC2C22×C22⋊#3866
commutatorC22×C37C23×C4
FrattiniC22C23×#3866
FittingC22×D4×C37C4
socleC2×C37C22×C22⋊C4
prime radicalC2×#11924581C2
cosocleC22×D37C24
hypercenterC22×D4#3866
hypocenterC37#2883
LCSG ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×D4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558600C2semidirect
2. #14558513C2semidirect
3. #14558512C2semidirect
4. D37⋊#99C2semidirect
5. C2×#11924594C2semidirect
8. #11924615C22semidirect
9. C2×C22⋊#3866C22semidirect
10. #11924595C22semidirect
11. #11924594C22semidirect
12. #11924594C22semidirect
14. C2×#10596962C4semidirect
16. C2×#10596964C4semidirect
17. C2×#10596964C4semidirect
19. C22×C22⋊D37C4semidirect
21. C2×D4×D37C4semidirect
24. C22×D4×C37C4semidirect
25. C24×C37C2×C4semidirect
26. C23×D37C2×C4semidirect
31. C2×D4×C37C2×C4semidirect
32. C2×D4×C37C2×C4semidirect
33. C22×C4×C37C2×C4semidirect
37. C2×C22⋊D37C2×C4semidirect
38. C2×C22⋊D37C2×C4semidirect
39. C2×C22⋊D37C2×C4semidirect
40. C2×C22⋊D37C2×C4semidirect
43. C22×Dic37C2×C4semidirect
44. C22×Dic37C2×C4semidirect
55. C2×C4×D37C2×C4semidirect
56. C2×C4×D37C2×C4semidirect
58. C2×Dic74C2×C4semidirect
59. C2×Dic74C2×C4semidirect
140. C37#2883semidirect
152. C22×D4#3866semidirect
161. C24C2×#3866semidirect
185. C2×D4C2×#3866semidirect
186. C2×D4C2×#3866semidirect
193. C22×C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145586002
#145585132
#145585122
D37⋊#992
C2×#119245942
C2×#119245812
#288337