Finite Group Databasebeta

← #17993110

Subgroups — #17993110

Order 4736.

346 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 65 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#121×D37C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic, complemented
3#14557380C211yesmaximal, characteristic, complemented
4#14557268C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic, complemented
6#14557266C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×D4×D37—21no—
9C2×D4×D37C411yescharacteristic, complemented
10C22×C4×D37C2211yescharacteristic
11C2×#10596929—21no—
12#11924511C411yescharacteristic, complemented
13#11924510C2211yescharacteristic
14#11924509—21no—
15#11924508—21no—
16#11924507C411yescharacteristic, complemented
17C4⋊C4×D37C411yescharacteristic, complemented
18C2×#10596938—21no—
19C22⋊C4×D37—21no—
20C2×C4×Dic37—21no—
21C22⋊#64436C2211yescharacteristic, complemented
22#11924448—21no—
23#11924443C2211yescharacteristic, complemented
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic, complemented
26#95×C37C2211yescharacteristic, complemented
27C23×D37—21no—
28C23×D37D411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37C2×C411yescharacteristic
31C22×C4×C37—21no—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C22×Dic37—21no—
37C22×Dic37D411yescharacteristic
38D4×D37—42no—
39D4×D37—42no—
40D4×D37—42no—
41C2×D148—21no—
42C2×D148C2×C411yescharacteristic
43C2×C4×D37—21no—
44C2×C4×D37—42no—
45C2×C4×D37C2×C411yescharacteristic
46C2×C4×D37C2×C411yescharacteristic
47C2×C4×D37D411yescharacteristic
48C2×C4×D37D411yescharacteristic
49C2×C8×C37—21no—
50C4⋊C4×C37C2×C411yescharacteristic
51C22⋊C4×C37—21no—
52C22⋊Dic37—21no—
53#10596938—24no—
54#10596938—21no—
55#10596938—21no—
56C4⋊Dic37C2×C411yescharacteristic
57#10596936—21no—
58C4×Dic37—42no—
59C2×#64436—21no—
60#10596929—42no—
61C23×C37—21no—
62C23×C37C2×D411yescharacteristic
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—22no—
66C22×D37—21no—
67C22×D37—41no—
68C22×D37—42no—
69C22×D37—42no—
70C22×D37—42no—
71C22×D37C22⋊C411yescharacteristic
72C22×D37C22⋊C411yescharacteristic
73D4×C37—41no—
74D4×C37—41no—
75D4×C37—41no—
76C2×C4×C37—22no—
77C2×C4×C37—21no—
78C2×C4×C37—41no—
79C2×C4×C37—41no—
80C2×C4×C37—41no—
81C2×C4×C37C22×C411yescharacteristic
82C2×C4×C37C2×D411yescharacteristic
83C22⋊D37—42no—
84C22⋊D37—41no—
85C22⋊D37—41no—
86C22⋊D37—42no—
87C2×Dic37—22no—
88C2×Dic37—22no—
89C2×Dic37—21no—
90C2×Dic37—41no—
91C2×Dic37—41no—
92C2×Dic37C22⋊C411yescharacteristic
93C2×Dic37C22⋊C411yescharacteristic
94D148—41no—
95D148—42no—
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—41no—
99C4×D37—41no—
100C4×D37—42no—
101C8×C37—41no—
102#64436—41no—
103C22×C37—21no—
104C22×C37—21no—
105C22×C37—41no—
106C22×C37—41no—
107C22×C37—41no—
108C22×C37C2×C22⋊C411yescharacteristic
109C22×C37AGL(1,ℤ/8)11yescharacteristic
110C22×C37AGL(1,ℤ/8)11yescharacteristic
111C2×D37—21no—
112C2×D37—21no—
113C2×D37—21no—
114C2×D37—21no—
115C2×D37—21no—
116C2×D37—42no—
117C2×D37—42no—
118C2×D37—41no—
119C2×D37—41no—
120C2×D37—41no—
121C2×D37—84no—
122C2×D37#10412yes—
123C4×C37—21no—
124C4×C37—21no—
125C4×C37—42no—
126C4×C37—41no—
127Dic37—21no—
128Dic37—42no—
129Dic37—41no—
130Dic37#9912yes—
131#1507—371nomaximal, Sylow
132C2×C37—21no—
133C2×C37—21no—
134C2×C37—81no—
135C2×C37C2×#9911yescharacteristic
136C2×C37#41811yescharacteristic
137C2×C37C2×#10411yescharacteristic
138D37—22no—
139D37—41no—
140D37—81no—
141C2×#121—371no—
142#407—371no—
143C4×C22⋊C4—371no—
144#327—371no—
145#327—371no—
146#327—371no—
147#327D3711yescharacteristic, complemented
148C37#150711yescharacteristic, complemented, Sylow
149C22×D4—371no—
150C22×D4—741no—
151C23×C4—371no—
152C2×M16—741no—
153#121—371no—
154#121—371no—
155#121—371no—
156#121—741no—
157#121—741no—
158#121C2×D3711yescharacteristic
159C2×C4⋊C4—371no—
160C2×C22⋊C4—741no—
161C2×C22⋊C4—741no—
162C2×C42—741no—
163C22⋊C8—371no—
164C22⋊C8—741no—
165C22⋊C8C2×D3711yescharacteristic, complemented
166#95—371no—
167#95C2×D3711yescharacteristic, complemented
168C24—371no—
169C24—741no—
170C2×D4—21no—
171C2×D4—371no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4—741no—
175C2×D4—741no—
176C2×D4—1482no—
177C2×D4—1482no—
178C2×D4—1482no—
179C2×D4C4×D3711yescharacteristic
180C22×C4—21no—
181C22×C4—371no—
182C22×C4—371no—
183C22×C4—371no—
184C22×C4—371no—
185C22×C4—371no—
186C22×C4—741no—
187C22×C4—741no—
188C22×C4—1482no—
189C22×C4C22×D3711yescharacteristic
190M16—1482no—
191C2×C8—21no—
192C2×C8—741no—
193C4⋊C4—371no—
194C4⋊C4—741no—
195C4⋊C4C4×D3711yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—741no—
198C22⋊C4—744no—
199C22⋊C4—741no—
200C22⋊C4—741no—
201C42—1482no—
202C23—21no—
203C23—371no—
204C23—371no—
205C23—742no—
206C23—741no—
207C23—741no—
208C23—741no—
209C23—1481no—
210C23—1482no—
211C23—1482no—
212C23—1482no—
213C23D4×D3711yescharacteristic
214D4—41no—
215D4—41no—
216D4—41no—
217D4—1481no—
218D4—1482no—
219D4—1482no—
220D4—1482no—
221D4—1481no—
222D4—1481no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—371no—
229C2×C4—371no—
230C2×C4—742no—
231C2×C4—742no—
232C2×C4—742no—
233C2×C4—742no—
234C2×C4—741no—
235C2×C4—1481no—
236C2×C4—1481no—
237C2×C4—1482no—
238C2×C4—1481no—
239C2×C4—1481no—
240C2×C4C2×C4×D3711yescharacteristic
241C2×C4D4×D3711yescharacteristic
242C8—41no—
243C8—1481no—
244C22—21no—
245C22—21no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—372no—
250C22—2964no—
251C22—741no—
252C22—741no—
253C22—741no—
254C22—741no—
255C22—741no—
256C22—1482no—
257C22—1482no—
258C22—1481no—
259C22—1481no—
260C22—1481no—
261C22C22⋊C4×D3711yescharacteristic
262C22#1192456011yescharacteristic
263C22#1192456311yescharacteristic
264C4—21no—
265C4—21no—
266C4—42no—
267C4—41no—
268C4—372no—
269C4—741no—
270C4—1482no—
271C4—1481no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—2961no—
276C2—742no—
277C2—1481no—
278C2#99×D3711yescharacteristic
279C2#1455753611yescharacteristic
280C2#104×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37C2×C22⋊C4
prime radical#121×D37C2
cosocleC22×C4×C37C23
hypercenter#327D37
hypocenterC37#1507
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14557495C2semidirect
3. #14557380C2semidirect
4. #14557268C2semidirect
5. #14557267C2semidirect
6. #14557266C2semidirect
7. C37×#327C2semidirect
9. C2×D4×D37C4semidirect
12. #11924511C4semidirect
16. #11924507C4semidirect
17. C4⋊C4×D37C4semidirect
21. C22⋊#64436C22semidirect
23. #11924443C22semidirect
25. C22⋊C8×C37C22semidirect
26. #95×C37C22semidirect
147. #327D37semidirect
148. C37#1507semidirect
165. C22⋊C8C2×D37semidirect
167. #95C2×D37semidirect

Maximal subgroups

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

subgroupindex
#121×D372
#145574952
#145573802
#145572682
#145572672
#145572662
C37×#3272
#150737