Finite Group Databasebeta

← #17995100

Subgroups — #17995100

Order 4736.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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
2C4×#10596962C211yesmaximal, characteristic, complemented
3#14557549C211yesmaximal, characteristic, complemented
4#14557507C211yesmaximal, characteristic, complemented
5#14557304C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9#11924567C412yescomplemented
10#11924566—21no—
11#11924562C412yescomplemented
12#11924561—21no—
13#11924556—22no—
14C2×#10596934C2211yescharacteristic
15C4×Dic74—21no—
16C4×D148—21no—
17C4×C22⋊D37—22no—
18#11924495C2211yescharacteristic
19#11924495C2211yescharacteristic
20#11924493—21no—
21C42×D37—21no—
22#11924462—22no—
23#11924451—22no—
24C2×#41×C37C2211yescharacteristic
25C2×M16×C37C2211yescharacteristic
26C2×C42×C37C2211yescharacteristic
27#104×C37—21no—
28#104×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31#41×C37—21no—
32#41×C37—21no—
33C2×Q8×C37C2×C411yescharacteristic, complemented
34C2×D4×C37—21no—
35C2×D4×C37C2×C411yescharacteristic, complemented
36C22×C4×C37—21no—
37C22×C4×C37—21no—
38C22×C4×C37C2311yescharacteristic
39C2×C22⋊D37—21no—
40#10596962—21no—
41#10596962—21no—
42#10596962C2×C412yes—
43#10596962D412yes—
44C2×D148D411yescharacteristic
45C2×C4×D37—21no—
46C2×C4×D37—22no—
47C2×Dic74D411yescharacteristic
48M16×C37—21no—
49M16×C37—21no—
50C2×C8×C37—21no—
51C42×C37—21no—
52C42×C37D411yescharacteristic
53C42×C37D411yescharacteristic
54C22⋊Dic37—21no—
55C22⋊Dic37D412yes—
56#10596942—22no—
57#10596941—22no—
58#10596940—22no—
59#10596939—22no—
60#10596938—22no—
61C4⋊Dic37—21no—
62C4⋊Dic37—21no—
63#10596936—22no—
64C4×Dic37—22no—
65C4×Dic37—21no—
66C4×Dic37—21no—
67#10596934—21no—
68#10596934C2×C412yescomplemented
69C2×#64436—21no—
70C23×C37—21no—
71C23×C37C2×D411yescharacteristic
72C22×D37—21no—
73Q8×C37—21no—
74Q8×C37—21no—
75D4×C37—21no—
76D4×C37—21no—
77D4×C37—41no—
78D4×C37—41no—
79C2×C4×C37—21no—
80C2×C4×C37—21no—
81C2×C4×C37—21no—
82C2×C4×C37—42no—
83C2×C4×C37—41no—
84C2×C4×C37—41no—
85C2×C4×C37C22×C411yescharacteristic
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37C2×D411yescharacteristic
88C2×C4×C37C2×D411yescharacteristic
89C2×C4×C37#4111yescharacteristic
90C2×C4×C37#4111yescharacteristic
91C22⋊D37—22no—
92C22⋊D37—22no—
93C2×Dic37—21no—
94C2×Dic37—22no—
95C2×Dic37—41no—
96D148—21no—
97D148C22⋊C412yes—
98C4×D37—22no—
99C4×D37—22no—
100C4×D37—44no—
101Dic74—21no—
102Dic74C22⋊C412yes—
103C8×C37—41no—
104#64436—22no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37—81no—
108C22×C37C4×D411yescharacteristic
109C22×C37#12011yescharacteristic
110C22×C37#12111yescharacteristic
111C2×D37—22no—
112C2×D37—42no—
113C4×C37—22no—
114C4×C37—41no—
115C4×C37—41no—
116C4×C37C2×C22⋊C411yescharacteristic
117C4×C37C4×D411yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12311yescharacteristic
120Dic37—22no—
121Dic37—42no—
122Dic37—81no—
123#1906—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37—21no—
127C2×C37—81no—
128C2×C37#38611yescharacteristic
129D37—42no—
130#575—371no—
131C4×#41—371no—
132#421—371no—
133C2×#104D3711yescharacteristic, complemented
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×M16C2×D3711yescharacteristic
147C4×Q8—741no—
148C4×D4—741no—
149C4×D4—742no—
150#117—371no—
151#117—371no—
152#117—741no—
153C2×C42—741no—
154C2×C42C2×D3711yescharacteristic
155#104—21no—
156#104—21no—
157#104—742no—
158#99—742no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—372no—
164#41—372no—
165#41—741no—
166#41—741no—
167C2×Q8—371no—
168C2×Q8C4×D3711yescharacteristic, complemented
169C2×D4—21no—
170C2×D4—371no—
171C2×D4—741no—
172C2×D4C4×D3711yescharacteristic, complemented
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—742no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178Q16—742no—
179SD16—742no—
180SD16—742no—
181D8—742no—
182M16—21no—
183M16—21no—
184M16—372no—
185M16—741no—
186C2×C8—21no—
187C2×C8—741no—
188C4⋊C4—742no—
189C4⋊C4—741no—
190C4⋊C4—741no—
191C22⋊C4—372no—
192C22⋊C4—742no—
193C22⋊C4—741no—
194C42—21no—
195C42—742no—
196C42—741no—
197C42—741no—
198C42C22⋊D3711yescharacteristic
199C42C22⋊D3711yescharacteristic
200C23—21no—
201C23—741no—
202C23D4×D3711yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—372no—
206Q8—741no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—372no—
212D4—742no—
213D4—742no—
214D4—741no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—741no—
222C2×C4—742no—
223C2×C4—742no—
224C2×C4—742no—
225C2×C4—1484no—
226C2×C4—1481no—
227C2×C4C2×C4×D3711yescharacteristic
228C2×C4#1059696211yescharacteristic
229C2×C4D4×D3711yescharacteristic
230C2×C4D4×D3711yescharacteristic
231C2×C4#1059696411yescharacteristic
232C2×C4C2×C22⋊D3711yescharacteristic
233C8—41no—
234C8—742no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—742no—
239C22—1482no—
240C22#1192449611yescharacteristic
241C22#1192450411yescharacteristic
242C22#1192450911yescharacteristic
243C4—22no—
244C4—41no—
245C4—41no—
246C4—2961no—
247C4—742no—
248C4—1482no—
249C4C22⋊C4×D3711yescharacteristic
250C4C4×C22⋊D3711yescharacteristic
251C4#1192450711yescharacteristic
252C4#1192451811yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—81no—
257C2—1482no—
258C2#1455740911yescharacteristic
subgroupG/H
centerC4#11924507
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC2×C37#386
prime radical#14558331C2
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1906
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C4×#10596962C2semidirect
3. #14557549C2semidirect
4. #14557507C2semidirect
5. #14557304C2semidirect
6. #14557293C2semidirect
7. C2×#104×C37C2semidirect
9. #11924567C4semidirect
11. #11924562C4semidirect
33. C2×Q8×C37C2×C4semidirect
35. C2×D4×C37C2×C4semidirect
68. #10596934C2×C4semidirect
133. C2×#104D37semidirect
137. C37#1906semidirect
168. C2×Q8C4×D37semidirect
172. C2×D4C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145583312
C4×#105969622
#145575492
#145575072
#145573042
#145572932
C2×#104×C372
#190637