Finite Group Databasebeta

← #18007731

Subgroups — #18007731

Order 4736.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11924559C211yesmaximal, characteristic, complemented
2#135×D37C211yesmaximal, characteristic, complemented
3#14557975C212yesmaximal, complemented
4#14557974C211yesmaximal, characteristic, complemented
5#14557971C211yesmaximal, characteristic, complemented
6#14557970C212yesmaximal, complemented
7#14557968C211yesmaximal, characteristic, complemented
8#14557966C212yesmaximal, complemented
9#14557964C212yesmaximal, complemented
10M32×D37C211yesmaximal, characteristic, complemented
11C37×#510C211yesmaximal, characteristic, complemented
12C2×#10596966—21no—
13#41×D37—21no—
14#11924559—21no—
15#11924559—21no—
16#11924559C2212yes—
17#11924559C2212yescomplemented
18#11924559C2211yescharacteristic, complemented
19#11924558C2211yescharacteristic
20#11924557—21no—
21#11924556—21no—
22#11924555C2211yescharacteristic, complemented
23Q16×D37C2211yescharacteristic, complemented
24C2×#10596941—21no—
25SD16×D37—21no—
26C2×D296C2211yescharacteristic, complemented
27D8×D37C2211yescharacteristic, complemented
28C2×C8×D37C2211yescharacteristic
29#11924482C2212yescomplemented
30#11924481C2212yescomplemented
31#11924479C2212yescomplemented
32#11924479C2212yescomplemented
33D592C2212yescomplemented
34#11924477C2212yescomplemented
35#11924476C2211yescharacteristic, complemented
36#11924475C2212yescomplemented
37C16×D37C2212yescomplemented
38#135×C37C2211yescharacteristic
39C2×Q16×C37C2211yescharacteristic, complemented
40Q32×C37C2212yescomplemented
41SD32×C37C2212yescomplemented
42M32×C37C2211yescharacteristic, complemented
43#41×C37—21no—
44C2×Q8×C37—21no—
45#10596966—21no—
46#10596966—22no—
47#10596966—22no—
48#10596966—41no—
49#10596966—41no—
50Q8×D37—21no—
51#10596964—21no—
52#10596964—41no—
53D4×D37—21no—
54D4×D37—41no—
55#10596962—21no—
56#10596962—41no—
57C2×D148—21no—
58C2×D148—41no—
59C2×C4×D37—41no—
60C2×C4×D37—41no—
61C2×C4×D37D411yescharacteristic
62Q16×C37—21no—
63Q16×C37C2312yes—
64Q16×C37C2311yescharacteristic
65SD16×C37—21no—
66D8×C37C2311yescharacteristic
67C2×C8×C37C2311yescharacteristic
68#10596942—21no—
69#10596941—21no—
70#10596941—22no—
71#10596941—22no—
72#10596940—21no—
73#10596939—21no—
74C2×#64436D411yescharacteristic
75Dic148C2311yescharacteristic
76D296—21no—
77D296C2312yes—
78D296C2311yescharacteristic
79#10596930—21no—
80C8×D37D411yescharacteristic
81C8×D37D411yescharacteristic
82C8×D37C2311yescharacteristic
83C8×D37C2311yescharacteristic
84C16×C37C2312yes—
85#10596925C2312yes—
86C22×D37—41no—
87C22×D37—41no—
88C22×D37D811yescharacteristic
89Q8×C37—22no—
90Q8×C37—21no—
91Q8×C37—41no—
92D4×C37—21no—
93D4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37—41no—
96C2×C4×C37C2×D411yescharacteristic
97C22⋊D37—41no—
98C22⋊D37—41no—
99C22⋊D37—41no—
100C2×Dic37—41no—
101C2×Dic37D811yescharacteristic
102D148—21no—
103D148—22no—
104D148—42no—
105D148—42no—
106D148—41no—
107D148—41no—
108C4×D37—41no—
109C4×D37—41no—
110C4×D37—41no—
111C4×D37—42no—
112C4×D37—42no—
113C4×D37D811yescharacteristic
114C4×D37D811yescharacteristic
115C4×D37C2×D411yescharacteristic
116C4×D37C2×D411yescharacteristic
117Dic74—21no—
118Dic74—41no—
119C8×C37C2×D411yescharacteristic
120C8×C37C2411yescharacteristic
121#64436C2×D411yescharacteristic
122#64436C2×D411yescharacteristic
123C22×C37—41no—
124C22×C37C2×D811yescharacteristic
125C2×D37—41no—
126C2×D37—42no—
127C2×D37—41no—
128C2×D37—82no—
129C2×D37—82no—
130C2×D37C2×D811yescharacteristic
131C2×D37C2×D811yescharacteristic
132C4×C37—41no—
133C4×C37—42no—
134C4×C37C2×D811yescharacteristic
135C4×C37C22×D411yescharacteristic
136Dic37—41no—
137Dic37C2×D811yescharacteristic
138Dic37C2×D811yescharacteristic
139#3414—371nomaximal, Sylow
140C2×C37—21no—
141C2×C37—81no—
142C2×C37C22×D811yescharacteristic
143D37—21no—
144D37—21no—
145D37—82no—
146D37—81no—
147C2×#135—371no—
148C2×#135—371no—
149#510—371no—
150#510—372no—
151#510D3711yescharacteristic, complemented
152#509—371no—
153#509—372no—
154#509—371no—
155#508—372no—
156#508—372no—
157C2×M32—371no—
158C37#341411yescharacteristic, complemented, Sylow
159C2×#41—741no—
160C2×#41—741no—
161#135—372no—
162#135—371no—
163#135—372no—
164#135—371no—
165#135—371no—
166#135—741no—
167#135—741no—
168#135—741no—
169#135—741no—
170#135C2×D3711yescharacteristic
171C2×Q16—371no—
172C2×Q16C2×D3711yescharacteristic, complemented
173C2×SD16—741no—
174C2×SD16—741no—
175C2×D8—371no—
176C2×D8—371no—
177C22×C8—371no—
178Q32—372no—
179Q32C2×D3712yescomplemented
180SD32—372no—
181SD32—372no—
182SD32—372no—
183SD32C2×D3712yescomplemented
184D16—372no—
185D16—372no—
186M32—371no—
187M32—372no—
188M32C2×D3711yescharacteristic, complemented
189C2×C16—372no—
190#41—21no—
191#41—741no—
192#41—742no—
193#41—741no—
194#41—742no—
195#41—741no—
196#41—1481no—
197#41—1481no—
198#41—1481no—
199#41—1481no—
200C2×Q8—21no—
201C2×Q8—741no—
202C2×D4—741no—
203C2×D4—741no—
204C2×D4—1481no—
205C2×D4—1481no—
206C22×C4—371no—
207C22×C4—1481no—
208C22×C4—1481no—
209Q16—21no—
210Q16—371no—
211Q16—741no—
212Q16C22×D3711yescharacteristic
213Q16C22×D3712yes—
214SD16—21no—
215SD16—741no—
216SD16—742no—
217SD16—741no—
218SD16—742no—
219SD16—741no—
220D8—372no—
221D8—371no—
222D8—741no—
223D8—741no—
224D8C22×D3711yescharacteristic
225C2×C8—371no—
226C2×C8—371no—
227C2×C8—371no—
228C2×C8—371no—
229C2×C8—371no—
230C2×C8C22×D3711yescharacteristic
231C16—372no—
232C16C22×D3712yes—
233C23—371no—
234C23—1481no—
235C23—1481no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—741no—
240Q8—1481no—
241D4—21no—
242D4—41no—
243D4—741no—
244D4—742no—
245D4—1481no—
246D4—1482no—
247D4—1482no—
248D4—1481no—
249D4—1481no—
250D4—1481no—
251D4—1481no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—371no—
255C2×C4—371no—
256C2×C4—371no—
257C2×C4—371no—
258C2×C4—371no—
259C2×C4—1481no—
260C2×C4—1482no—
261C2×C4—1482no—
262C2×C4—1481no—
263C2×C4—1481no—
264C2×C4—1481no—
265C2×C4D4×D3711yescharacteristic
266C8—371no—
267C8—371no—
268C8D4×D3711yescharacteristic
269C8C23×D3711yescharacteristic
270C22—41no—
271C22—371no—
272C22—371no—
273C22—2962no—
274C22—2962no—
275C22—1481no—
276C22—1482no—
277C22—1481no—
278C22D8×D3711yescharacteristic
279C4—41no—
280C4—42no—
281C4—371no—
282C4—371no—
283C4—1481no—
284C4D8×D3711yescharacteristic
285C4C2×D4×D3711yescharacteristic
286C2—21no—
287C2—81no—
288C2—2962no—
289C2—2961no—
290C2—741no—
291C2—741no—
292C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#510C2
socleC2×C37C22×D8
hypercenter#510D37
hypocenterC37#3414
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#11924559C2semidirect
2. #135×D37C2semidirect
3. #14557975C2semidirect
4. #14557974C2semidirect
5. #14557971C2semidirect
6. #14557970C2semidirect
7. #14557968C2semidirect
8. #14557966C2semidirect
9. #14557964C2semidirect
10. M32×D37C2semidirect
11. C37×#510C2semidirect
17. #11924559C22semidirect
18. #11924559C22semidirect
22. #11924555C22semidirect
23. Q16×D37C22semidirect
26. C2×D296C22semidirect
27. D8×D37C22semidirect
29. #11924482C22semidirect
30. #11924481C22semidirect
31. #11924479C22semidirect
32. #11924479C22semidirect
33. D592C22semidirect
34. #11924477C22semidirect
35. #11924476C22semidirect
36. #11924475C22semidirect
37. C16×D37C22semidirect
39. C2×Q16×C37C22semidirect
40. Q32×C37C22semidirect
41. SD32×C37C22semidirect
42. M32×C37C22semidirect
151. #510D37semidirect
158. C37#3414semidirect
172. C2×Q16C2×D37semidirect
179. Q32C2×D37semidirect
183. SD32C2×D37semidirect
188. M32C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245592
#135×D372
#145579752
#145579742
#145579712
#145579702
#145579682
#145579662
#145579642
M32×D372
C37×#5102
#341437