Finite Group Databasebeta

← #18004994

Subgroups — #18004994

Order 4736.

392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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
2C2×#11924527C211yesmaximal, characteristic, complemented
3#14557900C212yesmaximal, complemented
4#14557896C212yesmaximal, complemented
5#14557889C212yesmaximal, complemented
6#14557886C212yesmaximal, complemented
7#14557535C211yesmaximal, characteristic, complemented
8#14557534C211yesmaximal, characteristic, complemented
9#14557532C211yesmaximal, characteristic, complemented
10M16×Dic37C211yesmaximal, characteristic, complemented
11C37×#417C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C2×#10596934C2211yescharacteristic
14#11924534C2211yescharacteristic
15#11924532C2211yescharacteristic
16#11924527—21no—
17#11924527—21no—
18#11924527C2212yes—
19#11924527C2212yes—
20#11924525C2211yescharacteristic
21#11924523C2211yescharacteristic
22#11924508—21no—
23#11924508—21no—
24C4×C22⋊D37—21no—
25C4×C22⋊D37—21no—
26C2×C4⋊Dic37—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596936—21no—
29C2×C4×Dic37C2211yescharacteristic
30#11924461C2212yes—
31#11924460C2212yes—
32#11924459C2212yes—
33#11924458C2212yes—
34#11924457C2212yes—
35#11924456C2212yes—
36#11924446C2212yes—
37C8×Dic37C2212yes—
38C2×#41×C37C2211yescharacteristic
39C2×M16×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41#103×C37C2212yes—
42#102×C37C2212yes—
43#41×C37—22no—
44#41×C37—22no—
45C2×Q8×C37C2311yescharacteristic
46C2×D4×C37—21no—
47C2×D4×C37C2311yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37—21no—
50C22×C4×C37C2311yescharacteristic
51C2×C22⋊D37—21no—
52C2×C22⋊D37—21no—
53C2×C22⋊D37—21no—
54C22×Dic37—21no—
55C22×Dic37D411yescharacteristic
56C22×Dic37D411yescharacteristic
57#10596962—22no—
58#10596962—22no—
59C2×D148C2311yescharacteristic
60C2×C4×D37—21no—
61C2×Dic74C2311yescharacteristic
62M16×C37—22no—
63C2×C8×C37C2312yes—
64C4⋊C4×C37—21no—
65C4⋊C4×C37C2312yes—
66C22⋊Dic37—21no—
67C22⋊Dic37—21no—
68#10596938—21no—
69#10596938—21no—
70C4⋊Dic37—21no—
71C4⋊Dic37—22no—
72C4⋊Dic37—22no—
73C4⋊Dic37C2312yes—
74#10596936—22no—
75#10596936—22no—
76#10596936—21no—
77#10596936—21no—
78C4×Dic37D411yescharacteristic
79C4×Dic37D411yescharacteristic
80C4×Dic37C2311yescharacteristic
81C4×Dic37C2311yescharacteristic
82#10596934—22no—
83C2×#64436C2312yes—
84C23×C37—21no—
85C23×C37C2×D411yescharacteristic
86C22×D37—21no—
87Q8×C37—21no—
88Q8×C37—21no—
89D4×C37—21no—
90D4×C37—21no—
91D4×C37—42no—
92C2×C4×C37—22no—
93C2×C4×C37—21no—
94C2×C4×C37—42no—
95C2×C4×C37—42no—
96C2×C4×C37C2×D411yescharacteristic
97C2×C4×C37#4112yes—
98C2×C4×C37#4112yes—
99C2×C4×C37C2411yescharacteristic
100C22⋊D37—42no—
101C22⋊D37—42no—
102C22⋊D37—42no—
103C2×Dic37—22no—
104C2×Dic37—21no—
105C2×Dic37—41no—
106C2×Dic37—41no—
107C2×Dic37—42no—
108C2×Dic37C2×D411yescharacteristic
109C2×Dic37C2×D411yescharacteristic
110C2×Dic37C2×D411yescharacteristic
111C2×Dic37C2×D411yescharacteristic
112D148—21no—
113D148—21no—
114C4×D37—42no—
115Dic74—21no—
116Dic74—21no—
117C8×C37—22no—
118#64436—22no—
119C22×C37—21no—
120C22×C37—21no—
121C22×C37—41no—
122C22×C37—41no—
123C22×C37—41no—
124C22×C37#12412yes—
125C22×C37C22×D411yescharacteristic
126C2×D37—41no—
127C2×D37—41no—
128C2×D37—41no—
129C4×C37—41no—
130C4×C37—42no—
131C4×C37#12412yes—
132C4×C37C2×#4111yescharacteristic
133C4×C37C2×#4111yescharacteristic
134Dic37—21no—
135Dic37—21no—
136Dic37—21no—
137Dic37—21no—
138Dic37—41no—
139Dic37—42no—
140#3142—371nomaximal, Sylow
141C2×C37—22no—
142C2×C37—81no—
143C2×C37C2×#12411yescharacteristic
144C2×C37#57511yescharacteristic
145C2×C37#57511yescharacteristic
146D37—81no—
147#532—371no—
148C2×#125—371no—
149#491—372no—
150#490—372no—
151#488—372no—
152#488—372no—
153#417—371no—
154#417—371no—
155#417—371no—
156#417D3711yescharacteristic, complemented
157C4×M16—371no—
158C37#314211yescharacteristic, complemented, Sylow
159C2×#41—371no—
160C2×#41C2×D3711yescharacteristic
161C2×M16—371no—
162C2×M16C2×D3711yescharacteristic
163C4⋊Q8—371no—
164#127—371no—
165#125—372no—
166#125—372no—
167#125—741no—
168#125—741no—
169#124—371no—
170#124—371no—
171#121—741no—
172#121—741no—
173C4×D4—741no—
174C4×D4—741no—
175C2×C4⋊C4—371no—
176C2×C4⋊C4—741no—
177C2×C4⋊C4—741no—
178C2×C4⋊C4C2×D3711yescharacteristic
179C2×C42—371no—
180#103—372no—
181#103—372no—
182#103—372no—
183#103C2×D3712yes—
184#102—372no—
185#102—372no—
186#102—372no—
187#102C2×D3712yes—
188#97—372no—
189C4×C8—372no—
190#41—22no—
191#41—22no—
192#41—742no—
193#41—742no—
194C2×Q8—371no—
195C2×Q8C22×D3711yescharacteristic
196C2×D4—21no—
197C2×D4—371no—
198C2×D4—741no—
199C2×D4—741no—
200C2×D4—741no—
201C2×D4C22×D3711yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—371no—
205C22×C4—371no—
206C22×C4—741no—
207C22×C4—741no—
208C22×C4C22×D3711yescharacteristic
209M16—22no—
210M16—742no—
211C2×C8—372no—
212C2×C8C22×D3712yes—
213C4⋊C4—21no—
214C4⋊C4—372no—
215C4⋊C4—742no—
216C4⋊C4—742no—
217C4⋊C4—741no—
218C4⋊C4—741no—
219C4⋊C4—742no—
220C4⋊C4—742no—
221C4⋊C4—741no—
222C4⋊C4C22×D3712yes—
223C22⋊C4—741no—
224C22⋊C4—741no—
225C22⋊C4—741no—
226C22⋊C4—741no—
227C42—371no—
228C42—371no—
229C42—371no—
230C42—371no—
231C23—21no—
232C23—741no—
233C23D4×D3711yescharacteristic
234Q8—21no—
235Q8—21no—
236Q8—741no—
237Q8—741no—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—741no—
242D4—741no—
243D4—1482no—
244D4—1482no—
245D4—1482no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—371no—
251C2×C4—371no—
252C2×C4—371no—
253C2×C4—371no—
254C2×C4—741no—
255C2×C4—742no—
256C2×C4—1481no—
257C2×C4—1481no—
258C2×C4—1482no—
259C2×C4—1482no—
260C2×C4#1059696212yes—
261C2×C4D4×D3711yescharacteristic
262C2×C4#1059696412yes—
263C2×C4C23×D3711yescharacteristic
264C8—22no—
265C8—742no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—1481no—
272C22—1481no—
273C22—1481no—
274C22#1192452212yes—
275C22C2×D4×D3711yescharacteristic
276C4—41no—
277C4—42no—
278C4—741no—
279C4—741no—
280C4—741no—
281C4—741no—
282C4—1481no—
283C4—1482no—
284C4#1192452212yes—
285C4C2×#1059696411yescharacteristic
286C4C2×#1059696211yescharacteristic
287C2—22no—
288C2—81no—
289C2—2961no—
290C2C2×#1192452211yescharacteristic
291C2#1455832911yescharacteristic
292C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#417C2
socleC22×C37C22×D4
prime radical#14558079C2
hypercenter#417D37
hypocenterC37#3142
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#11924527C2semidirect
3. #14557900C2semidirect
4. #14557896C2semidirect
5. #14557889C2semidirect
6. #14557886C2semidirect
7. #14557535C2semidirect
8. #14557534C2semidirect
9. #14557532C2semidirect
10. M16×Dic37C2semidirect
11. C37×#417C2semidirect
156. #417D37semidirect
158. C37#3142semidirect

Maximal subgroups

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

subgroupindex
#145580792
C2×#119245272
#145579002
#145578962
#145578892
#145578862
#145575352
#145575342
#145575322
M16×Dic372
C37×#4172
#314237