Finite Group Databasebeta

← #18005345

Subgroups — #18005345

Order 4736.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#11924507C211yesmaximal, characteristic, complemented
2#121×D37C211yesmaximal, characteristic, complemented
3#14557847C211yesmaximal, characteristic, complemented
4#14557845C212yesmaximal, complemented
5#14557844C211yesmaximal, characteristic, complemented
6#14557768C212yesmaximal, complemented
7#14557766C212yesmaximal, complemented
8#14557667C211yesmaximal, characteristic, complemented
9#14557665C212yesmaximal, complemented
10C22⋊C8×D37C211yesmaximal, characteristic, complemented
11C37×#447C211yesmaximal, characteristic, complemented
12C22×C22⋊D37—21no—
13C2×D4×D37—21no—
14C2×D4×D37C2211yescharacteristic, complemented
15C22×C4×D37C2211yescharacteristic
16C2×#10596939C2212yescomplemented
17C2×C8×D37C2212yescomplemented
18#11924511C2211yescharacteristic, complemented
19#11924510C2211yescharacteristic
20#11924509—21no—
21#11924508—21no—
22#11924507—21no—
23#11924507—21no—
24#11924507C2212yes—
25#11924507C2211yescharacteristic, complemented
26#11924507C2212yescomplemented
27C2×C4⋊Dic37C2211yescharacteristic, complemented
28C4⋊C4×D37C2211yescharacteristic, complemented
29C2×C22⋊Dic37—21no—
30C22⋊C4×D37—21no—
31#11924470C2212yescomplemented
32#11924469C2212yescomplemented
33#11924458C2212yescomplemented
34#11924457C2212yescomplemented
35#11924457C2212yescomplemented
36C22⋊#64436C2211yescharacteristic, complemented
37#11924448C2212yescomplemented
38C22×D4×C37C2211yescharacteristic, complemented
39C2×D8×C37C2212yescomplemented
40#121×C37C2211yescharacteristic
41#102×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic, complemented
43C24×C37—21no—
44C23×D37—21no—
45C23×D37D411yescharacteristic
46C2×D4×C37—21no—
47C2×D4×C37—21no—
48C2×D4×C37—42no—
49C2×D4×C37C2312yes—
50C2×D4×C37C2311yescharacteristic
51C22×C4×C37C2311yescharacteristic
52C2×C22⋊D37—21no—
53C2×C22⋊D37—22no—
54C2×C22⋊D37—22no—
55C2×C22⋊D37—21no—
56C2×C22⋊D37—21no—
57C2×C22⋊D37—44no—
58C22×Dic37—21no—
59C22×Dic37D411yescharacteristic
60D4×D37—42no—
61D4×D37—44no—
62C2×D148—21no—
63C2×D148C2311yescharacteristic
64C2×C4×D37—21no—
65C2×C4×D37—42no—
66C2×C4×D37D411yescharacteristic
67C2×C4×D37D411yescharacteristic
68C2×C4×D37C2311yescharacteristic
69C2×C4×D37C2311yescharacteristic
70D8×C37—42no—
71C2×C8×C37C2312yes—
72C4⋊C4×C37C2311yescharacteristic
73C22⋊C4×C37—21no—
74C22⋊Dic37—21no—
75C22⋊Dic37—22no—
76C22⋊Dic37—22no—
77#10596939—42no—
78#10596938—21no—
79#10596938—21no—
80C4⋊Dic37—21no—
81C4⋊Dic37C2311yescharacteristic
82C4⋊Dic37C2312yes—
83#10596936—21no—
84C2×#64436C2312yes—
85C8×D37—42no—
86C23×C37—22no—
87C23×C37—21no—
88C23×C37—42no—
89C23×C37—42no—
90C23×C37—42no—
91C23×C37C2×D411yescharacteristic
92C22×D37—21no—
93C22×D37—41no—
94C22×D37—41no—
95C22×D37—42no—
96C22×D37—42no—
97C22×D37—42no—
98C22×D37D814yescomplemented
99C22×D37C2×D411yescharacteristic
100C22×D37C2×D411yescharacteristic
101D4×C37—22no—
102D4×C37—22no—
103D4×C37—22no—
104D4×C37—42no—
105D4×C37—42no—
106C2×C4×C37—22no—
107C2×C4×C37—21no—
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37C2411yescharacteristic
110C22⋊D37—42no—
111C22⋊D37—42no—
112C22⋊D37—42no—
113C22⋊D37—44no—
114C22⋊D37—44no—
115C2×Dic37—21no—
116C2×Dic37—22no—
117C2×Dic37—41no—
118C2×Dic37—42no—
119C2×Dic37C2×D411yescharacteristic
120C2×Dic37C2×D411yescharacteristic
121D148—22no—
122D148—42no—
123C4×D37—22no—
124C4×D37—22no—
125C4×D37—41no—
126C4×D37—41no—
127C4×D37—42no—
128C8×C37—22no—
129#64436—22no—
130C22×C37—21no—
131C22×C37—21no—
132C22×C37—41no—
133C22×C37—42no—
134C22×C37—42no—
135C22×C37—41no—
136C22×C37—41no—
137C22×C37—42no—
138C22×C37—84no—
139C22×C37C2×D812yes—
140C22×C37C22×D411yescharacteristic
141C2×D37—21no—
142C2×D37—21no—
143C2×D37—21no—
144C2×D37—21no—
145C2×D37—44no—
146C2×D37—41no—
147C2×D37—41no—
148C2×D37—41no—
149C2×D37—84no—
150C2×D37C2×D812yes—
151C2×D37C2×D812yes—
152C4×C37—21no—
153C4×C37—41no—
154C4×C37H(5,𝔽2)12yes—
155Dic37—21no—
156Dic37—21no—
157Dic37—41no—
158Dic37—42no—
159#3186—371nomaximal, Sylow
160C2×C37—22no—
161C2×C37—81no—
162C2×C37—82no—
163C2×C37#53411yescharacteristic
164C2×C37C22×D811yescharacteristic
165C2×C37#57511yescharacteristic
166D37—22no—
167D37—22no—
168D37—81no—
169C2×#121—371no—
170C2×#121—371no—
171#480—371no—
172#480—372no—
173#480—371no—
174#466—372no—
175#466—372no—
176#447—371no—
177#447—372no—
178#447D3711yescharacteristic, complemented
179C2×C22⋊C8—371no—
180C37#318611yescharacteristic, complemented, Sylow
181C22×D4—371no—
182C22×D4—741no—
183C22×D4—741no—
184C22×D4C2×D3711yescharacteristic, complemented
185C23×C4—371no—
186C2×D8—372no—
187C2×D8C2×D3712yescomplemented
188C22×C8—372no—
189#121—372no—
190#121—371no—
191#121—372no—
192#121—371no—
193#121—371no—
194#121—741no—
195#121—741no—
196#121—741no—
197#121—741no—
198#121C2×D3711yescharacteristic
199C2×C4⋊C4—371no—
200C2×C4⋊C4—371no—
201C2×C22⋊C4—741no—
202C2×C22⋊C4—741no—
203#107—372no—
204#107—372no—
205#102—372no—
206#102—372no—
207#102—372no—
208#102C2×D3712yescomplemented
209C22⋊C8—371no—
210C22⋊C8—372no—
211C22⋊C8C2×D3711yescharacteristic, complemented
212C24—21no—
213C24—371no—
214C24—741no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—42no—
218C2×D4—371no—
219C2×D4—741no—
220C2×D4—741no—
221C2×D4—741no—
222C2×D4—742no—
223C2×D4—742no—
224C2×D4—741no—
225C2×D4—1482no—
226C2×D4—1484no—
227C2×D4—1484no—
228C2×D4C22×D3711yescharacteristic
229C2×D4C22×D3712yes—
230C22×C4—371no—
231C22×C4—371no—
232C22×C4—371no—
233C22×C4—371no—
234C22×C4—371no—
235C22×C4—741no—
236C22×C4—741no—
237C22×C4—1482no—
238C22×C4C22×D3711yescharacteristic
239D8—42no—
240D8—1482no—
241C2×C8—372no—
242C2×C8—1482no—
243C2×C8C22×D3712yes—
244C4⋊C4—371no—
245C4⋊C4—372no—
246C4⋊C4—741no—
247C4⋊C4—741no—
248C4⋊C4C22×D3711yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—741no—
251C22⋊C4—741no—
252C22⋊C4—742no—
253C22⋊C4—742no—
254C22⋊C4—741no—
255C23—21no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—371no—
261C23—371no—
262C23—374no—
263C23—741no—
264C23—1481no—
265C23—1481no—
266C23—1482no—
267C23—1482no—
268C23—1482no—
269C23D4×D3711yescharacteristic
270D4—22no—
271D4—22no—
272D4—22no—
273D4—42no—
274D4—42no—
275D4—742no—
276D4—1482no—
277D4—1482no—
278D4—1482no—
279D4—1484no—
280D4—1484no—
281D4—1482no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—371no—
285C2×C4—371no—
286C2×C4—742no—
287C2×C4—742no—
288C2×C4—742no—
289C2×C4—741no—
290C2×C4—1481no—
291C2×C4—1481no—
292C2×C4—1482no—
293C2×C4—1481no—
294C2×C4—1482no—
295C2×C4D4×D3711yescharacteristic
296C2×C4C23×D3711yescharacteristic
297C8—22no—
298C8—742no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—84no—
308C22—372no—
309C22—372no—
310C22—2964no—
311C22—741no—
312C22—741no—
313C22—741no—
314C22—741no—
315C22—1484no—
316C22—1481no—
317C22—1481no—
318C22—1481no—
319C22D8×D3712yes—
320C22C2×D4×D3711yescharacteristic
321C4—21no—
322C4—41no—
323C4—741no—
324C4—741no—
325C4—1481no—
326C4—1482no—
327C4#1192458112yes—
328C2—22no—
329C2—82no—
330C2—81no—
331C2—2961no—
332C2—742no—
333C2—742no—
334C2#1455809311yescharacteristic
335C2C2×D8×D3711yescharacteristic
336C2#1455832911yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#447C2
socleC22×C37C22×D4
hypercenter#447D37
hypocenterC37#3186
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#11924507C2semidirect
2. #121×D37C2semidirect
3. #14557847C2semidirect
4. #14557845C2semidirect
5. #14557844C2semidirect
6. #14557768C2semidirect
7. #14557766C2semidirect
8. #14557667C2semidirect
9. #14557665C2semidirect
10. C22⋊C8×D37C2semidirect
11. C37×#447C2semidirect
14. C2×D4×D37C22semidirect
16. C2×#10596939C22semidirect
17. C2×C8×D37C22semidirect
18. #11924511C22semidirect
25. #11924507C22semidirect
26. #11924507C22semidirect
27. C2×C4⋊Dic37C22semidirect
28. C4⋊C4×D37C22semidirect
31. #11924470C22semidirect
32. #11924469C22semidirect
33. #11924458C22semidirect
34. #11924457C22semidirect
35. #11924457C22semidirect
36. C22⋊#64436C22semidirect
37. #11924448C22semidirect
38. C22×D4×C37C22semidirect
39. C2×D8×C37C22semidirect
41. #102×C37C22semidirect
42. C22⋊C8×C37C22semidirect
98. C22×D37D8semidirect
178. #447D37semidirect
180. C37#3186semidirect
184. C22×D4C2×D37semidirect
187. C2×D8C2×D37semidirect
208. #102C2×D37semidirect
211. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245072
#121×D372
#145578472
#145578452
#145578442
#145577682
#145577662
#145576672
#145576652
C22⋊C8×D372
C37×#4472
#318637