Finite Group Databasebeta

← #18003871

Subgroups — #18003871

Order 4736.

752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924582C211yesmaximal, characteristic
2C2×#11924567C211yesmaximal, characteristic, complemented
3C22×#10596941C211yesmaximal, characteristic, complemented
4#14557693C214yesmaximal, complemented
5#14557683C214yesmaximal, complemented
6#14557537C211yesmaximal, characteristic, complemented
7#14557527C211yesmaximal, characteristic, complemented
8#14557500C211yesmaximal, characteristic, complemented
9C37×#536C211yesmaximal, characteristic, complemented
10#11924582—24no—
11#11924582—24no—
12C2×#10596966—21no—
13C2×#10596962C2212yes—
14C2×#10596962C2211yescharacteristic
15C22×D148C2212yes—
16C22×D148C2211yescharacteristic
17C2×D4×D37—22no—
18C2×D4×D37—21no—
19#11924567—24no—
20C2×#10596942C2212yescomplemented
21C2×#10596941—24no—
22C2×#10596941C2214yescomplemented
23C2×#10596941C2212yescomplemented
24C2×#10596934C2211yescharacteristic, complemented
25C22×#64436C2211yescharacteristic, complemented
26#11924459C2212yescomplemented
27#11924456C2212yescomplemented
28#11924456C2214yescomplemented
29C22⋊#64436C2214yescomplemented
30C2×#41×C37C2211yescharacteristic
31C22×Q8×C37C2211yescharacteristic, complemented
32C4⋊Q8×C37—21no—
33#124×C37—21no—
34#123×C37—22no—
35C22⋊Q8×C37C2214yescomplemented
36#117×C37C2211yescharacteristic, complemented
37C23×D37—22no—
38C23×D37—21no—
39#41×C37—22no—
40#41×C37—22no—
41C2×Q8×C37—21no—
42C2×Q8×C37—22no—
43C2×Q8×C37—22no—
44C2×Q8×C37D411yescharacteristic
45C2×Q8×C37C2312yes—
46C2×D4×C37D412yes—
47C2×D4×C37D411yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37C2312yes—
50C22×C4×C37C2311yescharacteristic
51C2×C22⋊D37—22no—
52C2×C22⋊D37—21no—
53#10596966—28no—
54D4×D37—216no—
55D4×D37—28no—
56#10596962—22no—
57#10596962—24no—
58#10596962—24no—
59#10596962D414yes—
60C2×D148—22no—
61C2×D148—21no—
62C2×D148—22no—
63C2×D148—24no—
64C2×D148—24no—
65C2×D148D414yes—
66C2×D148C2311yescharacteristic
67C2×D148C2312yes—
68C2×C4×D37—22no—
69C2×C4×D37—21no—
70C2×Dic74C2311yescharacteristic
71C4⋊C4×C37—24no—
72C4⋊C4×C37C2312yes—
73C22⋊C4×C37—21no—
74C22⋊C4×C37—24no—
75C42×C37—21no—
76#10596942—24no—
77#10596941—28no—
78#10596941—24no—
79#10596934—22no—
80C2×#64436—22no—
81C2×#64436C2312yes—
82C2×#64436C2312yes—
83C23×C37C2×D412yes—
84C23×C37C2×D411yescharacteristic
85C22×D37—22no—
86C22×D37—21no—
87C22×D37—28no—
88C22×D37—24no—
89C22×D37—82no—
90C22×D37—84no—
91Q8×C37—22no—
92Q8×C37—22no—
93Q8×C37—22no—
94Q8×C37—42no—
95D4×C37—24no—
96D4×C37—22no—
97C2×C4×C37—22no—
98C2×C4×C37—22no—
99C2×C4×C37—22no—
100C2×C4×C37—22no—
101C2×C4×C37—42no—
102C2×C4×C37C2×D412yes—
103C2×C4×C37C2×D412yes—
104C2×C4×C37C2×D412yes—
105C2×C4×C37C2×D411yescharacteristic
106C2×C4×C37C2411yescharacteristic
107C22⋊D37—28no—
108C22⋊D37—24no—
109C2×Dic37—21no—
110D148—28no—
111D148—24no—
112D148—21no—
113D148—22no—
114D148C2×D412yes—
115D148C2×D414yes—
116C4×D37—28no—
117C4×D37—24no—
118Dic74—21no—
119Dic74C2×D412yes—
120#64436—22no—
121#64436—22no—
122C22×C37—22no—
123C22×C37—22no—
124C22×C37—24no—
125C22×C37#12012yes—
126C22×C37C22×D411yescharacteristic
127C2×D37—24no—
128C2×D37—22no—
129C2×D37—44no—
130C2×D37—42no—
131C2×D37—84no—
132C2×D37—88no—
133C4×C37—22no—
134C4×C37—42no—
135C4×C37—42no—
136C4×C37#12012yes—
137C4×C37C22×D411yescharacteristic
138C4×C37C22×D411yescharacteristic
139Dic37—22no—
140#3009—371nomaximal, Sylow
141C2×C37—22no—
142C2×C37—42no—
143C2×C37C2×#12011yescharacteristic
144C2×C37#57712yes—
145D37—44no—
146D37—42no—
147C2×H(5,𝔽2)—371no—
148C2×#137—371no—
149C22×SD16—371no—
150#536D3711yescharacteristic, complemented
151#452—374no—
152#450—374no—
153#418—371no—
154#416—371no—
155#408—371no—
156C37#300911yescharacteristic, complemented, Sylow
157H(5,𝔽2)—744no—
158H(5,𝔽2)—744no—
159C2×#41—371no—
160C2×#41—372no—
161C2×#41—741no—
162C2×#41C2×D3711yescharacteristic
163C22×Q8C2×D3711yescharacteristic, complemented
164C22×D4—371no—
165C22×D4—372no—
166C22×D4—742no—
167C22×D4—741no—
168#137—744no—
169C2×Q16—372no—
170C2×SD16—374no—
171C2×SD16—372no—
172C2×SD16—744no—
173C2×M16—371no—
174C22×C8—371no—
175C4⋊Q8—21no—
176#124—21no—
177#123—22no—
178C22⋊Q8C2×D3714yescomplemented
179#117C2×D3711yescharacteristic, complemented
180#103—372no—
181#102—372no—
182#102—374no—
183C22⋊C8—374no—
184C24—742no—
185C24—741no—
186#41—22no—
187#41—22no—
188#41—374no—
189#41—744no—
190#41—744no—
191#41—748no—
192#41—742no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—371no—
197C2×Q8C22⋊D3711yescharacteristic
198C2×Q8C22×D3712yes—
199C2×D4—374no—
200C2×D4—372no—
201C2×D4—371no—
202C2×D4—744no—
203C2×D4—744no—
204C2×D4—7416no—
205C2×D4—748no—
206C2×D4—742no—
207C2×D4—741no—
208C2×D4—742no—
209C2×D4—742no—
210C2×D4—741no—
211C2×D4C22⋊D3712yes—
212C2×D4C22⋊D3711yescharacteristic
213C22×C4—21no—
214C22×C4—742no—
215C22×C4—741no—
216C22×C4C22×D3712yes—
217C22×C4C22×D3711yescharacteristic
218Q16—744no—
219SD16—748no—
220SD16—744no—
221M16—742no—
222C2×C8—372no—
223C2×C8—372no—
224C2×C8—742no—
225C4⋊C4—24no—
226C4⋊C4C22×D3712yes—
227C22⋊C4—21no—
228C22⋊C4—24no—
229C42—21no—
230C23—2962no—
231C23—2964no—
232C23—748no—
233C23—744no—
234C23—742no—
235C23—741no—
236C23C2×C22⋊D3712yes—
237C23C2×C22⋊D3711yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—22no—
241Q8—42no—
242Q8—372no—
243Q8—741no—
244D4—24no—
245D4—22no—
246D4—374no—
247D4—372no—
248D4—748no—
249D4—748no—
250D4—744no—
251D4—744no—
252D4—741no—
253D4—742no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—748no—
260C2×C4—741no—
261C2×C4—744no—
262C2×C4D4×D3712yes—
263C2×C4D4×D3712yes—
264C2×C4C2×C22⋊D3712yes—
265C2×C4C2×C22⋊D3711yescharacteristic
266C2×C4C23×D3711yescharacteristic
267C8—742no—
268C8—742no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—2964no—
273C22—2968no—
274C22—744no—
275C22—742no—
276C22—1484no—
277C22—1482no—
278C22#1192450412yes—
279C22C22×C22⋊D3711yescharacteristic
280C4—22no—
281C4—42no—
282C4—42no—
283C4—742no—
284C4#1192450412yes—
285C4C2×D4×D3711yescharacteristic
286C4C2×D4×D3711yescharacteristic
287C2—22no—
288C2—42no—
289C2—1484no—
290C2—1482no—
291C2C2×#1192450411yescharacteristic
292C2#1455834112yes—
subgroupG/H
centerC22C22×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#536C2
socleC22×C37C22×D4
prime radicalC2×#11924582C2
hypercenter#536D37
hypocenterC37#3009
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C2×#11924567C2semidirect
3. C22×#10596941C2semidirect
4. #14557693C2semidirect
5. #14557683C2semidirect
6. #14557537C2semidirect
7. #14557527C2semidirect
8. #14557500C2semidirect
9. C37×#536C2semidirect
20. C2×#10596942C22semidirect
22. C2×#10596941C22semidirect
23. C2×#10596941C22semidirect
24. C2×#10596934C22semidirect
25. C22×#64436C22semidirect
26. #11924459C22semidirect
27. #11924456C22semidirect
28. #11924456C22semidirect
29. C22⋊#64436C22semidirect
31. C22×Q8×C37C22semidirect
35. C22⋊Q8×C37C22semidirect
36. #117×C37C22semidirect
150. #536D37semidirect
156. C37#3009semidirect
163. C22×Q8C2×D37semidirect
178. C22⋊Q8C2×D37semidirect
179. #117C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245822
C2×#119245672
C22×#105969412
#145576932
#145576832
#145575372
#145575272
#145575002
C37×#5362
#300937