Finite Group Databasebeta

← #508×D37 #18007710

Subgroups — #508×D37 #18007710

Order 4736.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#135×D37C212yesmaximal, complemented
2#14557966C211yesmaximal, characteristic, complemented
3#14557965C211yesmaximal, characteristic, complemented
4#14557964C212yesmaximal, complemented
5#14557963C212yesmaximal, complemented
6#14557962C211yesmaximal, characteristic, complemented
7Q32×D37C211yesmaximal, characteristic, complemented
8SD32×D37C212yesmaximal, complemented
9D16×D37C211yesmaximal, characteristic, complemented
10C2×C16×D37C211yesmaximal, characteristic, complemented
11C37×#508C211yesmaximal, characteristic, complemented
12#41×D37—22no—
13#11924559C2212yescomplemented
14#11924558C2212yescomplemented
15#11924557—22no—
16#11924556—22no—
17#11924555C2212yescomplemented
18Q16×D37C2212yes—
19SD16×D37—22no—
20D8×D37C2212yes—
21C2×C8×D37C2211yescharacteristic
22Dic296C2211yescharacteristic, complemented
23#11924482C2212yescomplemented
24#11924481C2212yescomplemented
25#11924480C2212yescomplemented
26#11924479C2212yescomplemented
27D592C2211yescharacteristic, complemented
28#11924477C2212yescomplemented
29C2×#10596925C2211yescharacteristic, complemented
30C16×D37C2211yescharacteristic
31C16×D37C2211yescharacteristic
32C16×D37C2211yescharacteristic, complemented
33C16×D37C2211yescharacteristic, complemented
34#135×C37C2212yescomplemented
35Q32×C37C2211yescharacteristic, complemented
36SD32×C37C2212yescomplemented
37D16×C37C2211yescharacteristic, complemented
38C2×C16×C37C2211yescharacteristic, complemented
39#41×C37—22no—
40#10596966—22no—
41Q8×D37—22no—
42#10596964—22no—
43#10596964—42no—
44D4×D37—22no—
45D4×D37—42no—
46#10596962—22no—
47#10596962—42no—
48C2×C4×D37—42no—
49C2×C4×D37D411yescharacteristic
50Q16×C37C2312yes—
51SD16×C37—22no—
52D8×C37C2312yes—
53C2×C8×C37C2311yescharacteristic
54#10596942—22no—
55#10596941—22no—
56#10596940—22no—
57#10596939—22no—
58C2×#64436D411yescharacteristic
59Dic148C2312yes—
60D296C2312yes—
61#10596930—22no—
62C8×D37D411yescharacteristic
63C8×D37D411yescharacteristic
64C8×D37C2311yescharacteristic
65C8×D37C2311yescharacteristic
66C16×C37C2311yescharacteristic
67C16×C37C2311yescharacteristic
68#10596925C2311yescharacteristic
69#10596925C2311yescharacteristic
70C22×D37—42no—
71C22×D37D811yescharacteristic
72Q8×C37—22no—
73D4×C37—22no—
74D4×C37—42no—
75C2×C4×C37—42no—
76C2×C4×C37C2×D411yescharacteristic
77C22⋊D37—42no—
78C22⋊D37—42no—
79C22⋊D37—42no—
80C2×Dic37—42no—
81C2×Dic37D811yescharacteristic
82D148—22no—
83D148—42no—
84C4×D37—42no—
85C4×D37—42no—
86C4×D37—42no—
87C4×D37D811yescharacteristic
88C4×D37D811yescharacteristic
89C4×D37C2×D411yescharacteristic
90C4×D37C2×D411yescharacteristic
91Dic74—22no—
92Dic74—42no—
93C8×C37C2×D411yescharacteristic
94C8×C37C2411yescharacteristic
95#64436C2×D411yescharacteristic
96#64436C2×D411yescharacteristic
97C22×C37—42no—
98C22×C37C2×D811yescharacteristic
99C2×D37—22no—
100C2×D37—42no—
101C2×D37—84no—
102C2×D37C2×D811yescharacteristic
103C2×D37C2×D811yescharacteristic
104C4×C37—42no—
105C4×C37C2×D811yescharacteristic
106C4×C37C22×D411yescharacteristic
107Dic37—42no—
108Dic37C2×D811yescharacteristic
109Dic37C2×D811yescharacteristic
110C2×#508—371nomaximal, Sylow
111C2×C37—21no—
112C2×C37—82no—
113C2×C37C22×D811yescharacteristic
114D37—21no—
115D37—82no—
116D37#50812yesdirect product factor
117C2×#135—372no—
118#508—372no—
119#508—371no—
120#508—372no—
121#508—371no—
122#508—371no—
123#508D3711yescharacteristic, direct product factor
124C2×Q32—371no—
125C2×SD32—372no—
126C2×D16—371no—
127C22×C16—371no—
128C37C2×#50811yescharacteristic, complemented, Sylow
129C2×#41—742no—
130#135—372no—
131#135—372no—
132#135—372no—
133#135—742no—
134#135—742no—
135#135C2×D3712yescomplemented
136C2×Q16—372no—
137C2×SD16—742no—
138C2×D8—372no—
139C22×C8—371no—
140Q32—372no—
141Q32—371no—
142Q32C2×D3711yescharacteristic, complemented
143SD32—372no—
144SD32—372no—
145SD32—372no—
146SD32C2×D3712yescomplemented
147D16—372no—
148D16—371no—
149D16C2×D3711yescharacteristic, complemented
150C2×C16—371no—
151C2×C16—371no—
152C2×C16—371no—
153C2×C16—371no—
154C2×C16—371no—
155C2×C16C2×D3711yescharacteristic, complemented
156#41—22no—
157#41—742no—
158#41—742no—
159#41—742no—
160#41—1482no—
161#41—1482no—
162C2×Q8—742no—
163C2×D4—742no—
164C2×D4—1482no—
165C22×C4—371no—
166C22×C4—1482no—
167Q16—372no—
168Q16—742no—
169Q16C22×D3712yes—
170SD16—22no—
171SD16—742no—
172SD16—742no—
173SD16—742no—
174D8—372no—
175D8—742no—
176D8C22×D3712yes—
177C2×C8—371no—
178C2×C8—371no—
179C2×C8—371no—
180C2×C8—371no—
181C2×C8—371no—
182C2×C8C22×D3711yescharacteristic
183C16—371no—
184C16—371no—
185C16C22×D3711yescharacteristic
186C16C22×D3711yescharacteristic
187C23—371no—
188C23—1482no—
189Q8—22no—
190Q8—742no—
191Q8—1482no—
192D4—22no—
193D4—42no—
194D4—742no—
195D4—1482no—
196D4—1482no—
197D4—1482no—
198D4—1482no—
199C2×C4—42no—
200C2×C4—371no—
201C2×C4—371no—
202C2×C4—371no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—1482no—
206C2×C4—1482no—
207C2×C4—1482no—
208C2×C4—1482no—
209C2×C4D4×D3711yescharacteristic
210C8—371no—
211C8—371no—
212C8D4×D3711yescharacteristic
213C8C23×D3711yescharacteristic
214C22—42no—
215C22—371no—
216C22—371no—
217C22—2964no—
218C22—742no—
219C22—1482no—
220C22D8×D3711yescharacteristic
221C4—42no—
222C4—371no—
223C4—371no—
224C4—1482no—
225C4D8×D3711yescharacteristic
226C4C2×D4×D3711yescharacteristic
227C2—21no—
228C2—82no—
229C2—372no—
230C2—2962no—
231C2—741no—
232C2C2×D8×D3711yescharacteristic
subgroupG/H
centerC4D8×D37
commutator, cosocleC8×C37C24
FrattiniC8C23×D37
FittingC37×#508C2
socleC2×C37C22×D8
hypercenter#508D37
hypocenterC37C2×#508
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #135×D37C2semidirect
2. #14557966C2semidirect
3. #14557965C2semidirect
4. #14557964C2semidirect
5. #14557963C2semidirect
6. #14557962C2semidirect
7. Q32×D37C2semidirect
8. SD32×D37C2semidirect
9. D16×D37C2semidirect
10. C2×C16×D37C2semidirect
11. C37×#508C2semidirect
13. #11924559C22semidirect
14. #11924558C22semidirect
17. #11924555C22semidirect
22. Dic296C22semidirect
23. #11924482C22semidirect
24. #11924481C22semidirect
25. #11924480C22semidirect
26. #11924479C22semidirect
27. D592C22semidirect
28. #11924477C22semidirect
29. C2×#10596925C22semidirect
32. C16×D37C22semidirect
33. C16×D37C22semidirect
34. #135×C37C22semidirect
35. Q32×C37C22semidirect
36. SD32×C37C22semidirect
37. D16×C37C22semidirect
38. C2×C16×C37C22semidirect
116. D37#508direct (N × H)
123. #508D37direct (N × H)
128. C37C2×#508semidirect
135. #135C2×D37semidirect
142. Q32C2×D37semidirect
146. SD32C2×D37semidirect
149. D16C2×D37semidirect
155. C2×C16C2×D37semidirect

Maximal subgroups

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

subgroupindex
#135×D372
#145579662
#145579652
#145579642
#145579632
#145579622
Q32×D372
SD32×D372
D16×D372
C2×C16×D372
C37×#5082
C2×#50837