Finite Group Databasebeta

← #18005199

Subgroups — #18005199

Order 4736.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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#14558088C211yesmaximal, characteristic, complemented
2#14558062C211yesmaximal, characteristic
3#14557942C211yesmaximal, characteristic, complemented
4#14557901C211yesmaximal, characteristic, complemented
5#14557892C211yesmaximal, characteristic, complemented
6#14557788C212yesmaximal, complemented
7#14557776C212yesmaximal
8Q16×Dic37C212yesmaximal, complemented
9SD16×Dic37C212yesmaximal, complemented
10#14557485C211yesmaximal, characteristic, complemented
11C37×#497C211yesmaximal, characteristic, complemented
12C2×#10596929C2212yes—
13#11924536C2211yescharacteristic
14#11924529—21no—
15#11924528C2211yescharacteristic
16#11924527—21no—
17#11924518—21no—
18#11924516—21no—
19#11924512C2212yes—
20#11924512C2211yescharacteristic
21#11924507C2211yescharacteristic
22Q8×Dic37C2211yescharacteristic
23Q8×Dic37C2212yes—
24#11924501—21no—
25D4×Dic37C2211yescharacteristic
26#11924496—21no—
27#11924494—21no—
28#11924492—21no—
29C42×D37C2211yescharacteristic
30#11924470C2212yes—
31#11924468C2212yes—
32#11924460C2212yes—
33#11924460C2212yes—
34#11924460C2212yes—
35#11924457C2212yes—
36#11924447C2211yescharacteristic
37C8×Dic37C2212yes—
38C2×Q16×C37C2212yes—
39C2×SD16×C37C2212yes—
40C4⋊Q8×C37C2211yescharacteristic
41#124×C37C2211yescharacteristic
42#97×C37C2211yescharacteristic
43C2×Q8×C37C2311yescharacteristic
44C2×Q8×C37C2312yes—
45C2×D4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C22×Dic37—21no—
48C2×C4×D37D411yescharacteristic
49C2×C4×D37D411yescharacteristic
50C2×C4×D37C2311yescharacteristic
51C2×Dic74—21no—
52Q16×C37—24no—
53SD16×C37—24no—
54C2×C8×C37C2312yes—
55C4⋊C4×C37—21no—
56C4⋊C4×C37—21no—
57C22⋊C4×C37—21no—
58C22⋊C4×C37—21no—
59C42×C37C2311yescharacteristic
60C22⋊Dic37—21no—
61C22⋊Dic37—21no—
62#10596938—22no—
63#10596938—21no—
64C4⋊Dic37—21no—
65C4⋊Dic37—22no—
66C4⋊Dic37—21no—
67C4⋊Dic37C2311yescharacteristic
68C4⋊Dic37C2311yescharacteristic
69C4⋊Dic37C2312yes—
70#10596936—21no—
71#10596936—21no—
72#10596936—21no—
73#10596936—22no—
74C4×Dic37—21no—
75C4×Dic37—22no—
76C4×Dic37D411yescharacteristic
77C4×Dic37D411yescharacteristic
78C4×Dic37C2311yescharacteristic
79C2×#64436C2312yes—
80#10596929—24no—
81C23×C37—21no—
82C22×D37C2×D411yescharacteristic
83Q8×C37—22no—
84Q8×C37—22no—
85Q8×C37—22no—
86D4×C37—22no—
87C2×C4×C37—21no—
88C2×C4×C37—22no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37C2411yescharacteristic
92C22⋊D37—42no—
93C2×Dic37—21no—
94C2×Dic37—22no—
95C2×Dic37—21no—
96C2×Dic37—42no—
97C2×Dic37C2×D411yescharacteristic
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C4×D37—22no—
101C4×D37—22no—
102C4×D37—41no—
103Dic74—42no—
104C8×C37#4114yes—
105#64436—22no—
106C22×C37—41no—
107C22×C37—41no—
108C22×C37—41no—
109C22×C37C22×D411yescharacteristic
110C2×D37—21no—
111C2×D37—21no—
112C2×D37—21no—
113C4×C37—21no—
114C4×C37—21no—
115C4×C37—41no—
116C4×C37—42no—
117C4×C37C2×#4112yes—
118Dic37—21no—
119Dic37—21no—
120Dic37—41no—
121Dic37—42no—
122Dic37—41no—
123Dic37#13712yes—
124#3172—371nomaximal, Sylow
125C2×C37—81no—
126C2×C37#53211yescharacteristic
127C2×C37C2×#13711yescharacteristic
128C2×C37#57511yescharacteristic
129D37—41no—
130#533—371no—
131#529—371no—
132#501—371no—
133#497D3711yescharacteristic, complemented
134#491—371no—
135#489—371no—
136#470—372no—
137#468—372no—
138C4×Q16—372no—
139C4×SD16—372no—
140C4×M16—371no—
141C37#317211yescharacteristic, complemented, Sylow
142C2×Q16C2×D3712yes—
143C2×SD16C2×D3712yes—
144C2×M16—372no—
145C4⋊Q8—371no—
146C4⋊Q8C2×D3711yescharacteristic
147#126—741no—
148#125—371no—
149#125—741no—
150#124C2×D3711yescharacteristic
151#123—741no—
152C22⋊Q8—371no—
153C22⋊Q8—372no—
154C22⋊Q8—741no—
155#121—371no—
156C4×Q8—371no—
157C4×Q8—372no—
158C4×Q8—741no—
159C4×D4—371no—
160C4×D4—741no—
161#117—741no—
162#117—741no—
163C2×C42—371no—
164#107—372no—
165#106—372no—
166#103—372no—
167#103—372no—
168#103—372no—
169#102—372no—
170#97—371no—
171#97C2×D3711yescharacteristic
172C4×C8—372no—
173C2×Q8—741no—
174C2×Q8C22×D3711yescharacteristic
175C2×Q8C22×D3712yes—
176C2×D4—741no—
177C2×D4C22×D3711yescharacteristic
178C22×C4—371no—
179C22×C4—371no—
180C22×C4—371no—
181C22×C4—741no—
182Q16—24no—
183SD16—24no—
184M16—744no—
185C2×C8—372no—
186C2×C8C22×D3712yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—372no—
190C4⋊C4—371no—
191C4⋊C4—371no—
192C4⋊C4—741no—
193C4⋊C4—742no—
194C4⋊C4—742no—
195C4⋊C4—741no—
196C4⋊C4—741no—
197C4⋊C4—741no—
198C4⋊C4—741no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—742no—
202C22⋊C4—741no—
203C22⋊C4—741no—
204C22⋊C4—741no—
205C42—371no—
206C42—371no—
207C42—371no—
208C42—741no—
209C42—742no—
210C42C22×D3711yescharacteristic
211C23—21no—
212C23—371no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—1482no—
217D4—22no—
218D4—1482no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—371no—
222C2×C4—371no—
223C2×C4—371no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—741no—
227C2×C4—742no—
228C2×C4—741no—
229C2×C4—1481no—
230C2×C4—1482no—
231C2×C4D4×D3711yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4C23×D3711yescharacteristic
234C8—742no—
235C8#1059696414yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—741no—
240C22—741no—
241C22—741no—
242C22C2×D4×D3711yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—372no—
248C4—741no—
249C4—741no—
250C4—1481no—
251C4—1481no—
252C4—1482no—
253C4C2×#1059696412yes—
254C2—81no—
255C2—1481no—
256C2#1455808111yescharacteristic
257C2#137×D3711yescharacteristic
258C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#497C2
socleC22×C37C22×D4
prime radical#11924507C22
hypercenter#497D37
hypocenterC37#3172
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14558088C2semidirect
3. #14557942C2semidirect
4. #14557901C2semidirect
5. #14557892C2semidirect
6. #14557788C2semidirect
8. Q16×Dic37C2semidirect
9. SD16×Dic37C2semidirect
10. #14557485C2semidirect
11. C37×#497C2semidirect
133. #497D37semidirect
141. C37#3172semidirect

Maximal subgroups

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

subgroupindex
#145580882
#145580622
#145579422
#145579012
#145578922
#145577882
#145577762
Q16×Dic372
SD16×Dic372
#145574852
C37×#4972
#317237