Finite Group Databasebeta

← #17995422

Subgroups — #17995422

Order 4736.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#14558079C211yesmaximal, characteristic
2#14557556C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic, complemented
4C2×#11924463C211yesmaximal, characteristic, complemented
5C2×#11924462C211yesmaximal, characteristic, complemented
6C42×Dic37C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924534C411yescharacteristic, complemented
11#11924532C411yescharacteristic, complemented
12#11924525C411yescharacteristic, complemented
13#11924523C411yescharacteristic, complemented
14#11924508—22no—
15C4×C22⋊D37—22no—
16C2×C4×Dic37—22no—
17C2×C4×Dic37C2211yescharacteristic
18C2×C4×Dic37C2211yescharacteristic
19#11924465—22no—
20#11924464—22no—
21#11924463—22no—
22#11924462—22no—
23C2×#41×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26#104×C37—22no—
27#41×C37—21no—
28#41×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31C2×Q8×C37C2×C411yescharacteristic
32C2×D4×C37—21no—
33C2×D4×C37C2×C411yescharacteristic
34C22×C4×C37—21no—
35C22×C4×C37—21no—
36C22×C4×C37C2311yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—22no—
39C22×Dic37—21no—
40C22×Dic37D412yes—
41#10596962—21no—
42#10596962—21no—
43#10596962—21no—
44#10596962—21no—
45C2×D148C2×C411yescharacteristic
46C2×C4×D37—21no—
47C2×Dic74C2×C411yescharacteristic
48M16×C37—21no—
49M16×C37—21no—
50C2×C8×C37—21no—
51C42×C37—21no—
52C42×C37D412yescomplemented
53C22⋊Dic37—22no—
54#10596938—22no—
55#10596936—22no—
56C4×Dic37—28no—
57C4×Dic37—21no—
58C4×Dic37C2×C411yescharacteristic
59C4×Dic37C2×C411yescharacteristic
60C4×Dic37D412yes—
61C4×Dic37D412yescomplemented
62#10596934—21no—
63#10596934—21no—
64C2×#64436—21no—
65C23×C37—21no—
66C23×C37C2×D411yescharacteristic
67C22×D37—21no—
68Q8×C37—21no—
69Q8×C37—21no—
70D4×C37—21no—
71D4×C37—21no—
72D4×C37—41no—
73D4×C37—41no—
74C2×C4×C37—24no—
75C2×C4×C37—22no—
76C2×C4×C37—21no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37C22×C411yescharacteristic
80C2×C4×C37C2×D411yescharacteristic
81C2×C4×C37C2×D411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C2×C4×C37#4111yescharacteristic
84C2×C4×C37#4111yescharacteristic
85C22⋊D37—41no—
86C22⋊D37—41no—
87C22⋊D37—44no—
88C2×Dic37—24no—
89C2×Dic37—22no—
90C2×Dic37—24no—
91C2×Dic37—21no—
92C2×Dic37C22⋊C412yes—
93C2×Dic37C22⋊C412yes—
94D148—21no—
95D148—21no—
96C4×D37—41no—
97C4×D37—41no—
98Dic74—21no—
99Dic74—21no—
100C8×C37—41no—
101#64436—41no—
102C22×C37—22no—
103C22×C37—41no—
104C22×C37—42no—
105C22×C37C2×C22⋊C411yescharacteristic
106C22×C37#12111yescharacteristic
107C22×C37#12111yescharacteristic
108C2×D37—41no—
109C2×D37—42no—
110C4×C37—24no—
111C4×C37—41no—
112C4×C37C4×D411yescharacteristic
113C4×C37C4×D411yescharacteristic
114C4×C37#12411yescharacteristic
115C4×C37#12711yescharacteristic
116Dic37—24no—
117Dic37—22no—
118Dic37—41no—
119Dic37#10414yescomplemented
120#1962—371nomaximal, Sylow
121C2×C37—21no—
122C2×C37—21no—
123C2×C37—81no—
124C2×C37#39011yescharacteristic
125C2×C37C2×#10412yes—
126D37—81no—
127#532—371no—
128#423—371no—
129C2×#104—371no—
130C2×#104—371no—
131C2×#104—371no—
132C2×#104D3711yescharacteristic, complemented
133C43—371no—
134C37#196211yescharacteristic, complemented, Sylow
135C2×#41—371no—
136C2×#41C2×D3711yescharacteristic
137C2×M16—371no—
138C2×M16C2×D3711yescharacteristic
139C4⋊Q8—371no—
140#127—371no—
141#124—371no—
142#124—371no—
143#121—742no—
144C4×D4—742no—
145C2×C42—371no—
146C2×C42—371no—
147C2×C42—742no—
148C2×C42C2×D3711yescharacteristic
149C4⋊C8—742no—
150#104—22no—
151#104—742no—
152#104—742no—
153#104—742no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—741no—
159#41—741no—
160#41—741no—
161#41—741no—
162C2×Q8—371no—
163C2×Q8C4×D3711yescharacteristic
164C2×D4—21no—
165C2×D4—371no—
166C2×D4—742no—
167C2×D4—741no—
168C2×D4C4×D3711yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—372no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4C22×D3711yescharacteristic
175M16—21no—
176M16—21no—
177M16—741no—
178M16—741no—
179C2×C8—21no—
180C2×C8—741no—
181C4⋊C4—742no—
182C22⋊C4—742no—
183C22⋊C4—742no—
184C42—21no—
185C42—371no—
186C42—371no—
187C42—372no—
188C42—372no—
189C42—748no—
190C42—741no—
191C42C22⋊D3712yescomplemented
192C23—21no—
193C23—741no—
194C23D4×D3711yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—741no—
198Q8—741no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—741no—
204D4—741no—
205D4—1484no—
206D4—1481no—
207D4—1481no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—372no—
214C2×C4—372no—
215C2×C4—744no—
216C2×C4—744no—
217C2×C4—742no—
218C2×C4—741no—
219C2×C4—1481no—
220C2×C4—1481no—
221C2×C4C2×C4×D3711yescharacteristic
222C2×C4#1059696211yescharacteristic
223C2×C4D4×D3711yescharacteristic
224C2×C4D4×D3711yescharacteristic
225C2×C4#1059696411yescharacteristic
226C2×C4C2×C22⋊D3711yescharacteristic
227C8—41no—
228C8—1481no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—1482no—
233C22—1481no—
234C22C22⋊C4×D3711yescharacteristic
235C22#1192450811yescharacteristic
236C22#1192450911yescharacteristic
237C4—24no—
238C4—41no—
239C4—374no—
240C4—744no—
241C4—742no—
242C4—1481no—
243C4#1192449611yescharacteristic
244C4C4×C22⋊D3711yescharacteristic
245C4#1192452211yescharacteristic
246C4#1192453211yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—2961no—
251C2#1455743311yescharacteristic
252C2#104×D3712yes—
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37C2×C22⋊C4
prime radical#14558079C2
cosocleC22×C4×C37C23
hypercenterC2×#104D37
hypocenterC37#1962
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #14557556C2semidirect
3. C2×#11924464C2semidirect
4. C2×#11924463C2semidirect
5. C2×#11924462C2semidirect
6. C42×Dic37C2semidirect
7. C2×#104×C37C2semidirect
10. #11924534C4semidirect
11. #11924532C4semidirect
12. #11924525C4semidirect
13. #11924523C4semidirect
52. C42×C37D4semidirect
61. C4×Dic37D4semidirect
119. Dic37#104semidirect
132. C2×#104D37semidirect
134. C37#1962semidirect
191. C42C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580792
#145575562
C2×#119244642
C2×#119244632
C2×#119244622
C42×Dic372
C2×#104×C372
#196237