Finite Group Databasebeta

← #17995097

Subgroups — #17995097

Order 4736.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#14558331C211yesmaximal, characteristic
2#14557550C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic, complemented
4#14557506C211yesmaximal, characteristic, complemented
5#14557303C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C4×#41×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567—21no—
10#11924566C412yescomplemented
11#11924562—21no—
12#11924561C412yescomplemented
13#11924556—22no—
14C2×#10596934C2211yescharacteristic
15C2×#10596934C2211yescharacteristic
16#11924495C2211yescharacteristic
17#11924464—21no—
18#11924464—21no—
19#11924463—22no—
20#11924450—22no—
21C2×#41×C37C2211yescharacteristic
22C4×Q8×C37—21no—
23C4×D4×C37—21no—
24C4×D4×C37—22no—
25#117×C37—21no—
26#117×C37C2211yescharacteristic
27C2×C42×C37—21no—
28C2×C42×C37C2211yescharacteristic
29#41×C37—21no—
30#41×C37—21no—
31#41×C37C2×C412yes—
32#41×C37D412yes—
33C2×Q8×C37D411yescharacteristic
34C2×D4×C37—21no—
35C2×D4×C37D411yescharacteristic
36C22×C4×C37—21no—
37C22×C4×C37—22no—
38C22×C4×C37—21no—
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—21no—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45C2×D148C2×C411yescharacteristic, complemented
46C2×C4×D37—21no—
47C2×Dic74C2×C411yescharacteristic, complemented
48C4⋊C4×C37—22no—
49C4⋊C4×C37—21no—
50C22⋊C4×C37—22no—
51C22⋊C4×C37D412yes—
52C42×C37—22no—
53C42×C37—21no—
54C42×C37—21no—
55C42×C37D411yescharacteristic
56C42×C37D411yescharacteristic
57C22⋊Dic37—21no—
58#10596942—22no—
59#10596941—22no—
60#10596940—22no—
61#10596939—22no—
62C4⋊Dic37—21no—
63C4×Dic37—21no—
64#10596934—21no—
65#10596934—21no—
66#10596934—21no—
67#10596934C2×C412yescomplemented
68C2×#64436—21no—
69C2×#64436—21no—
70C23×C37—21no—
71C23×C37C2×D411yescharacteristic
72C22×D37—21no—
73Q8×C37—21no—
74Q8×C37C22⋊C412yes—
75D4×C37—22no—
76D4×C37—22no—
77D4×C37—21no—
78D4×C37C22⋊C412yes—
79C2×C4×C37—21no—
80C2×C4×C37—21no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—22no—
84C2×C4×C37—21no—
85C2×C4×C37—42no—
86C2×C4×C37—44no—
87C2×C4×C37C22×C411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2×D411yescharacteristic
91C2×C4×C37#4111yescharacteristic
92C2×C4×C37#4111yescharacteristic
93C22⋊D37—41no—
94C22⋊D37—41no—
95C2×Dic37—21no—
96C2×Dic37—41no—
97D148—21no—
98D148—21no—
99C4×D37—41no—
100C4×D37—41no—
101Dic74—21no—
102Dic74—21no—
103#64436—22no—
104#64436—41no—
105C22×C37—22no—
106C22×C37—41no—
107C22×C37—42no—
108C22×C37C4×D411yescharacteristic
109C22×C37#12011yescharacteristic
110C22×C37#12111yescharacteristic
111C2×D37—41no—
112C2×D37—81no—
113C4×C37—22no—
114C4×C37—22no—
115C4×C37—42no—
116C4×C37—41no—
117C4×C37C2×C22⋊C411yescharacteristic
118C4×C37C4×D411yescharacteristic
119C4×C37#12111yescharacteristic
120C4×C37#12311yescharacteristic
121Dic37—41no—
122Dic37—81no—
123#1906—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—42no—
128C2×C37#38611yescharacteristic
129D37—81no—
130#575—371no—
131C4×#41D3711yescharacteristic, complemented
132#421—371no—
133C2×#104—371no—
134#410—371no—
135#344—371no—
136#339—371no—
137C37#190611yescharacteristic, complemented, Sylow
138C2×#41—371no—
139C2×#41C2×D3711yescharacteristic
140#137—372no—
141#137—741no—
142AGL(1,ℤ/8)—372no—
143AGL(1,ℤ/8)—741no—
144#135—742no—
145C2×M16—371no—
146C2×M16—371no—
147C4×Q8—21no—
148C4×D4—21no—
149C4×D4—22no—
150#117—21no—
151#117—371no—
152#117C2×D3711yescharacteristic
153C2×C42—21no—
154C2×C42C2×D3711yescharacteristic
155#104—742no—
156#104—741no—
157#104—741no—
158#99—742no—
159#41—21no—
160#41—21no—
161#41—741no—
162#41—741no—
163#41—741no—
164#41—741no—
165#41C4×D3712yes—
166#41D14812yes—
167C2×Q8—371no—
168C2×Q8C22⋊D3711yescharacteristic
169C2×D4—21no—
170C2×D4—371no—
171C2×D4—741no—
172C2×D4C22⋊D3711yescharacteristic
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178Q16—742no—
179SD16—742no—
180SD16—742no—
181D8—742no—
182M16—372no—
183M16—741no—
184M16—741no—
185M16—741no—
186C2×C8—741no—
187C2×C8—741no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—741no—
191C22⋊C4—22no—
192C22⋊C4—741no—
193C22⋊C4C22⋊D3712yes—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—741no—
198C42C22⋊D3711yescharacteristic
199C42C22⋊D3711yescharacteristic
200C23—21no—
201C23—741no—
202C23C2×C22⋊D3711yescharacteristic
203Q8—21no—
204Q8—741no—
205Q8—741no—
206Q8#1059693812yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—741no—
211D4—741no—
212D4—1481no—
213D4—1481no—
214D4#1059693812yes—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—741no—
224C2×C4—1481no—
225C2×C4—1481no—
226C2×C4—1481no—
227C2×C4C2×C4×D3711yescharacteristic
228C2×C4C2×D14811yescharacteristic
229C2×C4#1059696211yescharacteristic
230C2×C4#1059696211yescharacteristic
231C2×C4C2×C22⋊D3711yescharacteristic
232C2×C4C2×C22⋊D3711yescharacteristic
233C8—742no—
234C8—1481no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—2961no—
239C22—1481no—
240C22C4×C22⋊D3711yescharacteristic
241C22#1192450511yescharacteristic
242C22#1192451011yescharacteristic
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—2961no—
248C4—1481no—
249C4C2×#1059693811yescharacteristic
250C4C4×C22⋊D3711yescharacteristic
251C4#1192451011yescharacteristic
252C4#1192451911yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—42no—
257C2—2961no—
258C2#1455741211yescharacteristic
subgroupG/H
centerC4#11924510
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC4×#41×C37C2
socleC2×C37#386
prime radical#14558331C2
cosocleC22×C4×C37C23
hypercenterC4×#41D37
hypocenterC37#1906
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #14557550C2semidirect
3. C2×#11924464C2semidirect
4. #14557506C2semidirect
5. #14557303C2semidirect
6. #14557293C2semidirect
7. C4×#41×C37C2semidirect
10. #11924566C4semidirect
12. #11924561C4semidirect
45. C2×D148C2×C4semidirect
47. C2×Dic74C2×C4semidirect
67. #10596934C2×C4semidirect
131. C4×#41D37semidirect
137. C37#1906semidirect

Maximal subgroups

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

subgroupindex
#145583312
#145575502
C2×#119244642
#145575062
#145573032
#145572932
C4×#41×C372
#190637