Finite Group Databasebeta

← #18007728

Subgroups — #18007728

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×#11924555C211yesmaximal, characteristic, complemented
2#135×D37C211yesmaximal, characteristic, complemented
3#14557976C211yesmaximal, characteristic, complemented
4#14557973C211yesmaximal, characteristic, complemented
5#14557972C212yesmaximal, complemented
6#14557969C211yesmaximal, characteristic, complemented
7#14557967C212yesmaximal, complemented
8#14557964C212yesmaximal, complemented
9#14557962C212yesmaximal, complemented
10M32×D37C211yesmaximal, characteristic, complemented
11C37×#509C211yesmaximal, characteristic, complemented
12C2×#10596964—21no—
13#41×D37—21no—
14#11924559C2211yescharacteristic, complemented
15#11924558C2211yescharacteristic
16#11924557—21no—
17#11924556—21no—
18#11924555—21no—
19#11924555—21no—
20#11924555C2212yes—
21#11924555C2211yescharacteristic, complemented
22#11924555C2212yescomplemented
23C2×Dic148C2211yescharacteristic, complemented
24Q16×D37C2211yescharacteristic, complemented
25C2×#10596940—21no—
26SD16×D37—21no—
27D8×D37C2211yescharacteristic, complemented
28C2×C8×D37C2211yescharacteristic
29Dic296C2212yescomplemented
30#11924482C2212yescomplemented
31#11924481C2212yescomplemented
32#11924480C2212yescomplemented
33#11924480C2212yescomplemented
34#11924477C2212yescomplemented
35#11924476C2211yescharacteristic, complemented
36#11924475C2212yescomplemented
37C16×D37C2212yescomplemented
38#135×C37C2211yescharacteristic
39C2×D8×C37C2211yescharacteristic, complemented
40SD32×C37C2212yescomplemented
41D16×C37C2212yescomplemented
42M32×C37C2211yescharacteristic, complemented
43#41×C37—21no—
44C2×D4×C37—21no—
45C2×C22⋊D37—41no—
46C22×Dic37—41no—
47#10596966—21no—
48Q8×D37—21no—
49#10596964—22no—
50#10596964—22no—
51#10596964—21no—
52#10596964—41no—
53#10596964—41no—
54#10596964—41no—
55D4×D37—21no—
56D4×D37—41no—
57#10596962—21no—
58#10596962—41no—
59C2×C4×D37—41no—
60C2×C4×D37D411yescharacteristic
61C2×Dic74—21no—
62Q16×C37C2311yescharacteristic
63SD16×C37—21no—
64D8×C37—21no—
65D8×C37C2311yescharacteristic
66D8×C37C2312yes—
67C2×C8×C37C2311yescharacteristic
68#10596942—21no—
69#10596941—21no—
70#10596940—21no—
71#10596940—22no—
72#10596940—22no—
73#10596939—21no—
74C2×#64436D411yescharacteristic
75Dic148—21no—
76Dic148C2311yescharacteristic
77Dic148C2312yes—
78D296C2311yescharacteristic
79#10596930—21no—
80C8×D37D411yescharacteristic
81C8×D37D411yescharacteristic
82C8×D37C2311yescharacteristic
83C8×D37C2311yescharacteristic
84C16×C37C2312yes—
85#10596925C2312yes—
86C23×C37—41no—
87C22×D37—41no—
88C22×D37D811yescharacteristic
89Q8×C37—21no—
90D4×C37—21no—
91D4×C37—22no—
92D4×C37—41no—
93D4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37C2×D411yescharacteristic
96C22⋊D37—41no—
97C22⋊D37—41no—
98C22⋊D37—42no—
99C22⋊D37—42no—
100C22⋊D37—41no—
101C2×Dic37—41no—
102C2×Dic37—41no—
103C2×Dic37—42no—
104C2×Dic37—42no—
105C2×Dic37D811yescharacteristic
106D148—21no—
107D148—41no—
108C4×D37—41no—
109C4×D37—41no—
110C4×D37—41no—
111C4×D37D811yescharacteristic
112C4×D37D811yescharacteristic
113C4×D37C2×D411yescharacteristic
114C4×D37C2×D411yescharacteristic
115Dic74—21no—
116Dic74—22no—
117Dic74—41no—
118Dic74—41no—
119C8×C37C2×D411yescharacteristic
120C8×C37C2411yescharacteristic
121#64436C2×D411yescharacteristic
122#64436C2×D411yescharacteristic
123C22×C37—42no—
124C22×C37—41no—
125C22×C37—82no—
126C22×C37C2×D811yescharacteristic
127C2×D37—41no—
128C2×D37—41no—
129C2×D37—82no—
130C2×D37C2×D811yescharacteristic
131C2×D37C2×D811yescharacteristic
132C4×C37—41no—
133C4×C37C2×D811yescharacteristic
134C4×C37C22×D411yescharacteristic
135Dic37—41no—
136Dic37—42no—
137Dic37C2×D811yescharacteristic
138Dic37C2×D811yescharacteristic
139#3414—371nomaximal, Sylow
140C2×C37—21no—
141C2×C37—81no—
142C2×C37—82no—
143C2×C37C22×D811yescharacteristic
144D37—21no—
145D37—21no—
146D37—81no—
147C2×#135—371no—
148C2×#135—371no—
149#510—371no—
150#510—372no—
151#510—371no—
152#509—371no—
153#509—372no—
154#509D3711yescharacteristic, complemented
155#508—372no—
156#508—372no—
157C2×M32—371no—
158C37#341411yescharacteristic, complemented, Sylow
159C2×#41—741no—
160C2×#41—741no—
161#135—371no—
162#135—372no—
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×Q16—371no—
173C2×SD16—741no—
174C2×SD16—741no—
175C2×D8—371no—
176C2×D8C2×D3711yescharacteristic, complemented
177C22×C8—371no—
178Q32—372no—
179Q32—372no—
180SD32—372no—
181SD32—372no—
182SD32—372no—
183SD32C2×D3712yescomplemented
184D16—372no—
185D16C2×D3712yescomplemented
186M32—371no—
187M32—372no—
188M32C2×D3711yescharacteristic, complemented
189C2×C16—372no—
190#41—21no—
191#41—742no—
192#41—742no—
193#41—741no—
194#41—741no—
195#41—741no—
196#41—1481no—
197#41—1481no—
198#41—1481no—
199#41—1481no—
200C2×Q8—741no—
201C2×Q8—741no—
202C2×D4—21no—
203C2×D4—741no—
204C2×D4—1481no—
205C2×D4—1481no—
206C22×C4—371no—
207C22×C4—1481no—
208C22×C4—1481no—
209Q16—371no—
210Q16—372no—
211Q16—741no—
212Q16—741no—
213Q16C22×D3711yescharacteristic
214SD16—21no—
215SD16—742no—
216SD16—742no—
217SD16—741no—
218SD16—741no—
219SD16—741no—
220D8—21no—
221D8—371no—
222D8—741no—
223D8C22×D3712yes—
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—41no—
234C23—371no—
235C23—1481no—
236Q8—21no—
237Q8—742no—
238Q8—741no—
239Q8—1481no—
240Q8—1481no—
241D4—22no—
242D4—21no—
243D4—41no—
244D4—41no—
245D4—741no—
246D4—1481no—
247D4—1481no—
248D4—1481no—
249D4—1482no—
250D4—1482no—
251D4—1481no—
252C2×C4—41no—
253C2×C4—371no—
254C2×C4—371no—
255C2×C4—371no—
256C2×C4—371no—
257C2×C4—371no—
258C2×C4—1481no—
259C2×C4—1481no—
260C2×C4—1481no—
261C2×C4—1482no—
262C2×C4—1482no—
263C2×C4—1481no—
264C2×C4—1481no—
265C2×C4D4×D3711yescharacteristic
266C8—371no—
267C8—371no—
268C8D4×D3711yescharacteristic
269C8C23×D3711yescharacteristic
270C22—41no—
271C22—42no—
272C22—82no—
273C22—371no—
274C22—371no—
275C22—2962no—
276C22—1481no—
277C22—1481no—
278C22D8×D3711yescharacteristic
279C4—41no—
280C4—371no—
281C4—371no—
282C4—1481no—
283C4—1482no—
284C4D8×D3711yescharacteristic
285C4C2×D4×D3711yescharacteristic
286C2—21no—
287C2—82no—
288C2—81no—
289C2—2961no—
290C2—741no—
291C2—741no—
292C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC2C2×D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#509C2
socleC2×C37C22×D8
hypercenter#509D37
hypocenterC37#3414
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. C2×#11924555C2semidirect
2. #135×D37C2semidirect
3. #14557976C2semidirect
4. #14557973C2semidirect
5. #14557972C2semidirect
6. #14557969C2semidirect
7. #14557967C2semidirect
8. #14557964C2semidirect
9. #14557962C2semidirect
10. M32×D37C2semidirect
11. C37×#509C2semidirect
14. #11924559C22semidirect
21. #11924555C22semidirect
22. #11924555C22semidirect
23. C2×Dic148C22semidirect
24. Q16×D37C22semidirect
27. D8×D37C22semidirect
29. Dic296C22semidirect
30. #11924482C22semidirect
31. #11924481C22semidirect
32. #11924480C22semidirect
33. #11924480C22semidirect
34. #11924477C22semidirect
35. #11924476C22semidirect
36. #11924475C22semidirect
37. C16×D37C22semidirect
39. C2×D8×C37C22semidirect
40. SD32×C37C22semidirect
41. D16×C37C22semidirect
42. M32×C37C22semidirect
154. #509D37semidirect
158. C37#3414semidirect
176. C2×D8C2×D37semidirect
183. SD32C2×D37semidirect
185. D16C2×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×#119245552
#135×D372
#145579762
#145579732
#145579722
#145579692
#145579672
#145579642
#145579622
M32×D372
C37×#5092
#341437