Finite Group Databasebeta

← #17995135

Subgroups — #17995135

Order 4736.

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

normal subgroups only

This group has 380 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#14558092C211yesmaximal, characteristic
2#14558006C211yesmaximal, characteristic, complemented
3C2×#11924451C211yesmaximal, characteristic, complemented
4C2×#11924450C211yesmaximal, characteristic, complemented
5#14557300C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C2×#99×C37C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9#11924519C412yescomplemented
10#11924517—21no—
11#11924508—22no—
12#11924505C412yescomplemented
13#11924504—21no—
14C4×C22⋊D37—22no—
15#11924496—22no—
16#11924492—21no—
17C2×C22⋊Dic37C2211yescharacteristic
18C2×C22⋊Dic37C2211yescharacteristic
19C2×C22⋊Dic37C2211yescharacteristic
20C22⋊C4×D37—21no—
21#11924451—22no—
22#11924450—22no—
23C22×D4×C37C2211yescharacteristic
24C2×C22⋊C4×C37C2211yescharacteristic
25C2×C22⋊C4×C37C2211yescharacteristic
26#99×C37—22no—
27C24×C37C2×C411yescharacteristic, complemented
28C24×C37C2311yescharacteristic
29C23×D37D411yescharacteristic
30C2×D4×C37—21no—
31C2×D4×C37—21no—
32C2×D4×C37—21no—
33C2×D4×C37—21no—
34C2×D4×C37—21no—
35C2×D4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37—21no—
38C22×C4×C37C2×C411yescharacteristic, complemented
39C2×C22⋊D37—21no—
40C2×C22⋊D37—21no—
41C2×C22⋊D37—21no—
42C2×C22⋊D37—21no—
43C2×C22⋊D37—22no—
44C2×C22⋊D37C2×C412yes—
45C2×C22⋊D37D412yes—
46C22×Dic37—21no—
47C22×Dic37—21no—
48C22×Dic37—21no—
49C22×Dic37D411yescharacteristic
50C2×C4×D37—22no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C22⋊C4×C37—21no—
54C22⋊C4×C37D412yescomplemented
55C22⋊Dic37—21no—
56C22⋊Dic37—21no—
57C22⋊Dic37—22no—
58C22⋊Dic37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37C2×C412yescomplemented
61C22⋊Dic37D412yescomplemented
62#10596938—22no—
63#10596938—22no—
64#10596936—22no—
65#10596936—22no—
66C4×Dic37—22no—
67C23×C37—21no—
68C23×C37—21no—
69C23×C37—21no—
70C23×C37—81no—
71C23×C37—81no—
72C23×C37C22×C411yescharacteristic
73C23×C37C2×D411yescharacteristic
74C23×C37C2×D411yescharacteristic
75C23×C37C2×D411yescharacteristic
76C23×C37C2×D411yescharacteristic
77C23×C37#4111yescharacteristic
78C23×C37#4111yescharacteristic
79C22×D37—21no—
80C22×D37—21no—
81C22×D37—81no—
82C22×D37C22⋊C412yes—
83D4×C37—41no—
84D4×C37—41no—
85D4×C37—41no—
86D4×C37—41no—
87C2×C4×C37—21no—
88C2×C4×C37—21no—
89C2×C4×C37—21no—
90C2×C4×C37—22no—
91C2×C4×C37—41no—
92C2×C4×C37—81no—
93C2×C4×C37—81no—
94C22⋊D37—22no—
95C22⋊D37—22no—
96C22⋊D37—22no—
97C22⋊D37—22no—
98C22⋊D37—82no—
99C2×Dic37—21no—
100C2×Dic37—21no—
101C2×Dic37—22no—
102C2×Dic37—22no—
103C2×Dic37—41no—
104C2×Dic37—81no—
105C2×Dic37—81no—
106C2×Dic37—81no—
107C2×Dic37C22⋊C412yes—
108C4×D37—82no—
109C22×C37—41no—
110C22×C37—41no—
111C22×C37—41no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37—41no—
115C22×C37—41no—
116C22×C37—42no—
117C22×C37—41no—
118C22×C37—81no—
119C22×C37—81no—
120C22×C37C2×C22⋊C411yescharacteristic
121C22×C37C4×D411yescharacteristic
122C22×C37C4×D411yescharacteristic
123C22×C37#12011yescharacteristic
124C22×C37#12111yescharacteristic
125C22×C37#12111yescharacteristic
126C22×C37#12311yescharacteristic
127C2×D37—22no—
128C2×D37—42no—
129C2×D37—42no—
130C2×D37—81no—
131C4×C37—42no—
132C4×C37—41no—
133C4×C37—81no—
134Dic37—22no—
135Dic37—42no—
136Dic37—42no—
137Dic37—81no—
138#1913—371nomaximal, Sylow
139C2×C37—21no—
140C2×C37—21no—
141C2×C37—21no—
142C2×C37—21no—
143C2×C37—21no—
144C2×C37—21no—
145C2×C37—21no—
146C2×C37—81no—
147C2×C37#38611yescharacteristic
148D37—42no—
149#534—371no—
150#518—371no—
151C2×#99—371no—
152C2×#99—371no—
153C2×#99D3711yescharacteristic, complemented
154#342—371no—
155#342—371no—
156C37#191311yescharacteristic, complemented, Sylow
157C22×D4—371no—
158C22×D4C2×D3711yescharacteristic
159#123—372no—
160#123—741no—
161#121—742no—
162#120—372no—
163#120—741no—
164C4×D4—742no—
165C4×D4—742no—
166#117—741no—
167C2×C22⋊C4—371no—
168C2×C22⋊C4—371no—
169C2×C22⋊C4—371no—
170C2×C22⋊C4—741no—
171C2×C22⋊C4C2×D3711yescharacteristic
172C2×C22⋊C4C2×D3711yescharacteristic
173#99—22no—
174#99—742no—
175#99—742no—
176C24—371no—
177C24C4×D3711yescharacteristic, complemented
178C24C22×D3711yescharacteristic
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—372no—
186C2×D4—372no—
187C2×D4—742no—
188C2×D4—741no—
189C2×D4—741no—
190C2×D4—741no—
191C2×D4—741no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—371no—
195C22×C4—742no—
196C22×C4—741no—
197C22×C4—741no—
198C22×C4—741no—
199C22×C4C4×D3711yescharacteristic, complemented
200C4⋊C4—742no—
201C4⋊C4—742no—
202C22⋊C4—21no—
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—372no—
206C22⋊C4—372no—
207C22⋊C4—742no—
208C22⋊C4—742no—
209C22⋊C4—742no—
210C22⋊C4—741no—
211C22⋊C4—741no—
212C22⋊C4—741no—
213C22⋊C4—741no—
214C22⋊C4C22⋊D3712yescomplemented
215C42—742no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—81no—
220C23—81no—
221C23—372no—
222C23—2961no—
223C23—741no—
224C23—741no—
225C23C2×C4×D3711yescharacteristic
226C23#1059696211yescharacteristic
227C23D4×D3711yescharacteristic
228C23D4×D3711yescharacteristic
229C23D4×D3711yescharacteristic
230C23#1059696411yescharacteristic
231C23C2×C22⋊D3711yescharacteristic
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—2962no—
237D4—742no—
238D4—742no—
239D4—742no—
240D4—742no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—372no—
249C2×C4—2962no—
250C2×C4—2961no—
251C2×C4—2961no—
252C2×C4—2961no—
253C2×C4—741no—
254C2×C4—741no—
255C2×C4—742no—
256C2×C4—742no—
257C2×C4—1481no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—81no—
268C22—81no—
269C22—2961no—
270C22—742no—
271C22—1482no—
272C22—1482no—
273C22C22⋊C4×D3711yescharacteristic
274C22#1192449611yescharacteristic
275C22C4×C22⋊D3711yescharacteristic
276C22#1192450411yescharacteristic
277C22#1192450711yescharacteristic
278C22#1192450911yescharacteristic
279C22#1192451811yescharacteristic
280C4—42no—
281C4—41no—
282C4—81no—
283C4—2961no—
284C4—742no—
285C4—1482no—
286C4—1482no—
287C2—21no—
288C2—21no—
289C2—21no—
290C2—21no—
291C2—21no—
292C2—21no—
293C2—21no—
294C2—81no—
295C2—1482no—
296C2#1455740911yescharacteristic
subgroupG/H
centerC2#14557409
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC2×#99×C37C2
socleC2×C37#386
prime radical#14558092C2
cosocleC24×C37C23
hypercenterC2×#99D37
hypocenterC37#1913
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #14558006C2semidirect
3. C2×#11924451C2semidirect
4. C2×#11924450C2semidirect
5. #14557300C2semidirect
6. #14557299C2semidirect
7. C2×#99×C37C2semidirect
9. #11924519C4semidirect
12. #11924505C4semidirect
27. C24×C37C2×C4semidirect
38. C22×C4×C37C2×C4semidirect
54. C22⋊C4×C37D4semidirect
60. C22⋊Dic37C2×C4semidirect
61. C22⋊Dic37D4semidirect
153. C2×#99D37semidirect
156. C37#1913semidirect
177. C24C4×D37semidirect
199. C22×C4C4×D37semidirect
214. C22⋊C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580922
#145580062
C2×#119244512
C2×#119244502
#145573002
#145572992
C2×#99×C372
#191337