Finite Group Databasebeta

← #18005117

Subgroups — #18005117

Order 4736.

348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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#14558089C211yesmaximal, characteristic
2#14558088C211yesmaximal, characteristic
3#14557943C211yesmaximal, characteristic, complemented
4#14557942C211yesmaximal, characteristic, complemented
5#14557941C212yesmaximal, complemented
6#14557940C212yesmaximal, complemented
7#14557939C211yesmaximal, characteristic, complemented
8#14557570C212yesmaximal
9#14557568C212yesmaximal
10#97×D37C211yesmaximal, characteristic
11C37×#501C211yesmaximal, characteristic, complemented
12C2×C8×D37C2212yes—
13#11924536C2211yescharacteristic
14#11924535C2211yescharacteristic
15#11924535C2211yescharacteristic
16#11924528C2211yescharacteristic
17#11924527C2212yes—
18#11924516—21no—
19#11924514—21no—
20#11924514—21no—
21#11924512—21no—
22Q8×Dic37—21no—
23#11924501—21no—
24#11924501—21no—
25#11924501—21no—
26#11924494C2211yescharacteristic
27#11924494C2212yes—
28#11924494C2211yescharacteristic
29C42×D37C2211yescharacteristic
30#11924470C2212yes—
31#11924469C2212yes—
32#11924469C2212yes—
33#11924468C2212yes—
34#11924467C2212yes—
35#11924467C2212yes—
36#11924447C2211yescharacteristic
37#11924446C2212yes—
38C4⋊Q8×C37C2211yescharacteristic
39#125×C37C2211yescharacteristic
40#107×C37C2212yes—
41#106×C37C2212yes—
42#97×C37C2211yescharacteristic
43C2×Q8×C37—21no—
44C2×C4×D37D411yescharacteristic
45C2×C4×D37D411yescharacteristic
46C2×C4×D37C2311yescharacteristic
47C2×Dic74—21no—
48C2×Dic74—21no—
49C2×Dic74—21no—
50C2×C8×C37C2312yes—
51C4⋊C4×C37—21no—
52C4⋊C4×C37—21no—
53C4⋊C4×C37—21no—
54C4⋊C4×C37C2312yes—
55C4⋊C4×C37C2311yescharacteristic
56C4⋊C4×C37C2311yescharacteristic
57C42×C37C2311yescharacteristic
58#10596938—22no—
59#10596938—21no—
60#10596938—21no—
61C4⋊Dic37—21no—
62C4⋊Dic37—22no—
63C4⋊Dic37C2312yes—
64C4⋊Dic37C2311yescharacteristic
65C4⋊Dic37C2311yescharacteristic
66#10596936—21no—
67#10596936—21no—
68#10596936—22no—
69#10596936—21no—
70#10596936—21no—
71C4×Dic37—21no—
72C4×Dic37—21no—
73C4×Dic37—22no—
74C4×Dic37D411yescharacteristic
75C4×Dic37D411yescharacteristic
76C4×Dic37C2311yescharacteristic
77C2×#64436C2312yes—
78C8×D37Q818yescomplemented
79C22×D37C2×D411yescharacteristic
80Q8×C37—42no—
81C2×C4×C37—22no—
82C2×C4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37C2411yescharacteristic
87C2×Dic37—21no—
88C2×Dic37—21no—
89C2×Dic37—22no—
90C2×Dic37C2×D411yescharacteristic
91C2×Dic37C2×D411yescharacteristic
92C2×Dic37C2×D411yescharacteristic
93C4×D37—41no—
94C4×D37—41no—
95C4×D37C2×Q814yes—
96Dic74—42no—
97Dic74—42no—
98Dic74—42no—
99C8×C37C2×Q814yes—
100#64436C2×Q814yes—
101C22×C37C22×D411yescharacteristic
102C2×D37—21no—
103C2×D37—21no—
104C2×D37C4⋊Q812yes—
105C4×C37—21no—
106C4×C37—21no—
107C4×C37—41no—
108C4×C37—41no—
109C4×C37—42no—
110C4×C37C22×Q812yes—
111Dic37—21no—
112Dic37—21no—
113Dic37—41no—
114Dic37—41no—
115Dic37—42no—
116Dic37C4⋊Q812yes—
117#3162—371nomaximal, Sylow
118C2×C37C2×C4⋊Q811yescharacteristic
119C2×C37#57511yescharacteristic
120C2×C37#57511yescharacteristic
121D37—22no—
122#533—371no—
123#533—371no—
124#501—371no—
125#501—371no—
126#501—372no—
127#501—372no—
128#501—371no—
129#501D3711yescharacteristic, complemented
130#427—372no—
131#427—372no—
132C2×#97—371no—
133C37#316211yescharacteristic, complemented, Sylow
134C22×C8—372no—
135C4⋊Q8—371no—
136C4⋊Q8—371no—
137C4⋊Q8—371no—
138C4⋊Q8C2×D3711yescharacteristic
139#125—372no—
140#125—371no—
141#125C2×D3711yescharacteristic
142C22⋊Q8—741no—
143C22⋊Q8—741no—
144C22⋊Q8—741no—
145C22⋊Q8—741no—
146C4×Q8—741no—
147C4×Q8—741no—
148C4×Q8—741no—
149C4×Q8—741no—
150#117—371no—
151#117—372no—
152#117—371no—
153C2×C42—371no—
154#107—372no—
155#107—372no—
156#107—372no—
157#107C2×D3712yes—
158#106—372no—
159#106—372no—
160#106—372no—
161#106C2×D3712yes—
162#97—372no—
163#97—371no—
164#97C2×D3711yescharacteristic
165C2×Q8—21no—
166C2×Q8—741no—
167C2×Q8—741no—
168C2×Q8—741no—
169C22×C4—371no—
170C22×C4—371no—
171C22×C4—371no—
172C2×C8—372no—
173C2×C8—378no—
174C2×C8C22×D3712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—372no—
179C4⋊C4—371no—
180C4⋊C4—371no—
181C4⋊C4—742no—
182C4⋊C4—741no—
183C4⋊C4—741no—
184C4⋊C4—742no—
185C4⋊C4—741no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C4⋊C4C22×D3711yescharacteristic
189C4⋊C4C22×D3712yes—
190C4⋊C4C22×D3711yescharacteristic
191C22⋊C4—741no—
192C22⋊C4—741no—
193C22⋊C4—742no—
194C42—371no—
195C42—371no—
196C42—371no—
197C42—741no—
198C42—741no—
199C42—742no—
200C42C22×D3711yescharacteristic
201C23—371no—
202Q8—42no—
203Q8—1482no—
204Q8—1482no—
205Q8—1482no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—371no—
210C2×C4—374no—
211C2×C4—371no—
212C2×C4—371no—
213C2×C4—741no—
214C2×C4—742no—
215C2×C4—741no—
216C2×C4—1481no—
217C2×C4—1481no—
218C2×C4D4×D3711yescharacteristic
219C2×C4D4×D3711yescharacteristic
220C2×C4C23×D3711yescharacteristic
221C8—374no—
222C8Q8×D3714yes—
223C22—372no—
224C22—741no—
225C22—741no—
226C22C2×D4×D3711yescharacteristic
227C4—21no—
228C4—21no—
229C4—42no—
230C4—41no—
231C4—41no—
232C4—372no—
233C4—741no—
234C4—741no—
235C4—1481no—
236C4—1482no—
237C4—1481no—
238C4C2×Q8×D3712yes—
239C2—742no—
240C2C4⋊Q8×D3711yescharacteristic
241C2#1455832911yescharacteristic
242C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#501C2
socleC22×C37C22×D4
prime radicalC22×D37C2×D4
hypercenter#501D37
hypocenterC37#3162
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #14557943C2semidirect
4. #14557942C2semidirect
5. #14557941C2semidirect
6. #14557940C2semidirect
7. #14557939C2semidirect
11. C37×#501C2semidirect
78. C8×D37Q8semidirect
129. #501D37semidirect
133. C37#3162semidirect

Maximal subgroups

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

subgroupindex
#145580892
#145580882
#145579432
#145579422
#145579412
#145579402
#145579392
#145575702
#145575682
#97×D372
C37×#5012
#316237