Finite Group Databasebeta

← #18003869

Subgroups — #18003869

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×#11924581C211yesmaximal, characteristic
2C2×#11924567C211yesmaximal, characteristic, complemented
3#14558107C211yesmaximal, characteristic, complemented
4#14557692C214yesmaximal, complemented
5#14557682C214yesmaximal, complemented
6#14557538C211yesmaximal, characteristic, complemented
7#14557530C211yesmaximal, characteristic, complemented
8#14557499C211yesmaximal, characteristic, complemented
9C22×SD16×C37C211yesmaximal, characteristic, complemented
10#11924581—24no—
11#11924581—24no—
12C2×#10596962C2211yescharacteristic
13C2×#10596962C2211yescharacteristic
14C2×#10596964—21no—
15C2×#10596964C2212yes—
16C22×C22⋊D37—22no—
17C2×D4×D37—21no—
18C2×D4×D37C2212yes—
19#11924567—24no—
20C2×#10596942C2212yescomplemented
21C2×#10596941C2212yescomplemented
22C2×#10596934C2211yescharacteristic, complemented
23#11924534—21no—
24#11924525—21no—
25#11924519—22no—
26#11924512C2214yescomplemented
27#11924495C2211yescharacteristic, complemented
28#11924461C2212yescomplemented
29#11924458C2212yescomplemented
30#11924457C2214yescomplemented
31#11924448C2214yescomplemented
32C22×Q8×C37C2211yescharacteristic, complemented
33C22×D4×C37C2211yescharacteristic
34C2×SD16×C37—24no—
35C2×SD16×C37C2214yescomplemented
36C22×C8×C37C2211yescharacteristic, complemented
37C24×C37—21no—
38C23×D37—22no—
39C2×Q8×C37—21no—
40C2×Q8×C37—22no—
41C2×Q8×C37—22no—
42C2×Q8×C37C2312yes—
43C2×D4×C37—21no—
44C2×D4×C37—22no—
45C2×D4×C37D414yes—
46C2×D4×C37C2312yes—
47C22×C4×C37—21no—
48C22×C4×C37C2311yescharacteristic
49C2×C22⋊D37—216no—
50C2×C22⋊D37—21no—
51C2×C22⋊D37—22no—
52C2×C22⋊D37—22no—
53C2×C22⋊D37D412yes—
54C22×Dic37—22no—
55#10596964—28no—
56#10596964—24no—
57#10596964—24no—
58D4×D37—28no—
59D4×D37—24no—
60D4×D37—24no—
61#10596962—22no—
62#10596962—22no—
63#10596962—22no—
64#10596962D414yes—
65C2×D148D411yescharacteristic
66C2×D148C2311yescharacteristic
67C2×C4×D37—21no—
68C2×C4×D37C2312yes—
69C2×Dic74D411yescharacteristic
70C2×Dic74C2311yescharacteristic
71SD16×C37—28no—
72C2×C8×C37—22no—
73C2×C8×C37C2312yes—
74C22⋊Dic37—21no—
75#10596942—24no—
76#10596941—24no—
77#10596938—24no—
78C4⋊Dic37C2312yes—
79#10596936—24no—
80C4×Dic37—21no—
81#10596934—22no—
82C2×#64436C2312yes—
83C23×C37—22no—
84C23×C37—24no—
85C23×C37—82no—
86C23×C37C2×D411yescharacteristic
87C22×D37—21no—
88C22×D37—28no—
89C22×D37—84no—
90C22×D37C2×D412yes—
91Q8×C37—22no—
92Q8×C37—22no—
93Q8×C37—42no—
94D4×C37—24no—
95D4×C37—22no—
96D4×C37C2×D414yes—
97C2×C4×C37—22no—
98C2×C4×C37—42no—
99C2×C4×C37C2×D411yescharacteristic
100C2×C4×C37C2×D412yes—
101C2×C4×C37C2×D412yes—
102C2×C4×C37C2411yescharacteristic
103C22⋊D37—28no—
104C22⋊D37—28no—
105C22⋊D37—24no—
106C22⋊D37—24no—
107C2×Dic37—28no—
108C2×Dic37—21no—
109C2×Dic37—22no—
110C2×Dic37C2×D412yes—
111D148—22no—
112D148—21no—
113D148C2×D412yes—
114C4×D37—24no—
115C4×D37—22no—
116C4×D37—22no—
117Dic74—22no—
118Dic74—21no—
119Dic74C2×D412yes—
120C8×C37—22no—
121#64436—22no—
122C22×C37—22no—
123C22×C37—24no—
124C22×C37—44no—
125C22×C37—84no—
126C22×C37#12012yes—
127C22×C37C22×D411yescharacteristic
128C2×D37—22no—
129C2×D37—22no—
130C2×D37—24no—
131C2×D37—42no—
132C2×D37—88no—
133C4×C37—42no—
134C4×C37#12012yes—
135C4×C37C22×D411yescharacteristic
136C4×C37C22×D411yescharacteristic
137Dic37—22no—
138Dic37—22no—
139Dic37—42no—
140#3009—371nomaximal, Sylow
141C2×C37—22no—
142C2×C37—44no—
143C2×C37C2×#12011yescharacteristic
144C2×C37#57712yes—
145D37—42no—
146D37—42no—
147C2×H(5,𝔽2)—371no—
148C2×#137—371no—
149C22×SD16D3711yescharacteristic, complemented
150#536—371no—
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—371no—
162C2×#41—741no—
163C22×Q8C2×D3711yescharacteristic, complemented
164C22×D4—372no—
165C22×D4—741no—
166C22×D4—742no—
167C22×D4C2×D3711yescharacteristic
168#137—744no—
169C2×Q16—372no—
170C2×SD16—24no—
171C2×SD16—372no—
172C2×SD16C2×D3714yescomplemented
173C2×M16—371no—
174C22×C8C2×D3711yescharacteristic, complemented
175C4⋊Q8—741no—
176#124—741no—
177#123—742no—
178C22⋊Q8—374no—
179#117—371no—
180#103—372no—
181#102—374no—
182#102—372no—
183C22⋊C8—374no—
184C24—21no—
185C24—742no—
186#41—374no—
187#41—744no—
188#41—748no—
189#41—744no—
190#41—742no—
191#41—742no—
192#41—742no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—371no—
197C2×Q8—371no—
198C2×Q8C22×D3712yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—372no—
202C2×D4—371no—
203C2×D4—371no—
204C2×D4—742no—
205C2×D4—744no—
206C2×D4—748no—
207C2×D4—742no—
208C2×D4—7416no—
209C2×D4—741no—
210C2×D4—744no—
211C2×D4C22⋊D3714yes—
212C2×D4C22×D3712yes—
213C22×C4—21no—
214C22×C4—372no—
215C22×C4—742no—
216C22×C4—741no—
217C22×C4C22×D3711yescharacteristic
218Q16—744no—
219SD16—28no—
220SD16—744no—
221M16—742no—
222C2×C8—22no—
223C2×C8—372no—
224C2×C8C22×D3712yes—
225C4⋊C4—372no—
226C4⋊C4—744no—
227C22⋊C4—744no—
228C22⋊C4—741no—
229C42—741no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—372no—
234C23—2964no—
235C23—748no—
236C23—741no—
237C23D4×D3711yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—372no—
242Q8—742no—
243Q8—741no—
244D4—24no—
245D4—22no—
246D4—372no—
247D4—748no—
248D4—748no—
249D4—744no—
250D4—744no—
251D4—742no—
252D4—741no—
253D4C2×C22⋊D3714yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—372no—
257C2×C4—748no—
258C2×C4—741no—
259C2×C4—744no—
260C2×C4—742no—
261C2×C4—742no—
262C2×C4—742no—
263C2×C4D4×D3711yescharacteristic
264C2×C4D4×D3712yes—
265C2×C4C2×C22⋊D3712yes—
266C2×C4C23×D3711yescharacteristic
267C8—22no—
268C8—742no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—2968no—
274C22—742no—
275C22—742no—
276C22—744no—
277C22—1482no—
278C22#1192450412yes—
279C22C2×D4×D3711yescharacteristic
280C4—42no—
281C4—742no—
282C4—742no—
283C4—1482no—
284C4#1192450412yes—
285C4C2×D4×D3711yescharacteristic
286C4C22×C22⋊D3711yescharacteristic
287C2—22no—
288C2—44no—
289C2—1482no—
290C2—1482no—
291C2C2×#1192450411yescharacteristic
292C2#1455833912yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC22×SD16×C37C2
socleC22×C37C22×D4
prime radicalC2×#11924581C2
hypercenterC22×SD16D37
hypocenterC37#3009
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#11924567C2semidirect
3. #14558107C2semidirect
4. #14557692C2semidirect
5. #14557682C2semidirect
6. #14557538C2semidirect
7. #14557530C2semidirect
8. #14557499C2semidirect
9. C22×SD16×C37C2semidirect
20. C2×#10596942C22semidirect
21. C2×#10596941C22semidirect
22. C2×#10596934C22semidirect
26. #11924512C22semidirect
27. #11924495C22semidirect
28. #11924461C22semidirect
29. #11924458C22semidirect
30. #11924457C22semidirect
31. #11924448C22semidirect
32. C22×Q8×C37C22semidirect
35. C2×SD16×C37C22semidirect
36. C22×C8×C37C22semidirect
149. C22×SD16D37semidirect
156. C37#3009semidirect
163. C22×Q8C2×D37semidirect
172. C2×SD16C2×D37semidirect
174. C22×C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245812
C2×#119245672
#145581072
#145576922
#145576822
#145575382
#145575302
#145574992
C22×SD16×C372
#300937