Finite Group Databasebeta

← #17994875

Subgroups — #17994875

Order 4736.

374 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 83 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#14558006C211yesmaximal, characteristic
2C2×#11924450C211yesmaximal, characteristic
3#14557412C211yesmaximal, characteristic
4#14557406C211yesmaximal, characteristic, complemented
5#14557300C211yesmaximal, characteristic, complemented
6#14557299C211yesmaximal, characteristic, complemented
7C37×#385C211yesmaximal, characteristic, complemented
8C22×C22⋊D37C2211yescharacteristic
9C4×C22⋊D37—21no—
10C4×C22⋊D37—21no—
11#11924496—21no—
12#11924496—21no—
13#11924492—21no—
14C2×#10596936—21no—
15C2×C22⋊Dic37C2211yescharacteristic
16C2×C22⋊Dic37C2211yescharacteristic
17C2×C22⋊Dic37C2211yescharacteristic
18C2×#10596938—21no—
19C22⋊C4×D37—21no—
20#11924450C414yescomplemented
21#11924443—21no—
22#11924443—21no—
23C23×C4×C37C2211yescharacteristic
24C2×C4⋊C4×C37—21no—
25C2×C22⋊C4×C37C2211yescharacteristic
26C2×C22⋊C4×C37C2211yescharacteristic
27#95×C37—21no—
28C24×C37C2311yescharacteristic
29C23×D37D411yescharacteristic
30C22×C4×C37—21no—
31C22×C4×C37—21no—
32C22×C4×C37—21no—
33C22×C4×C37—21no—
34C22×C4×C37—42no—
35C22×C4×C37D411yescharacteristic
36C22×C4×C37D411yescharacteristic
37C2×C22⋊D37—21no—
38C2×C22⋊D37—21no—
39C2×C22⋊D37—21no—
40C2×C22⋊D37—21no—
41C2×C22⋊D37C2×C412yes—
42C2×C22⋊D37Q812yes—
43C22×Dic37—21no—
44C22×Dic37—21no—
45C22×Dic37D411yescharacteristic
46C22×Dic37D411yescharacteristic
47C22×Dic37D411yescharacteristic
48C2×C4×D37—21no—
49C2×C4×D37—21no—
50C4⋊C4×C37—42no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37—21no—
53C22⋊C4×C37—21no—
54C22⋊C4×C37C2×C412yescomplemented
55C22⋊Dic37—21no—
56C22⋊Dic37—21no—
57C22⋊Dic37—21no—
58C22⋊Dic37—21no—
59C22⋊Dic37—21no—
60C22⋊Dic37C2×C412yescomplemented
61#10596938—21no—
62#10596938—21no—
63#10596938—42no—
64#10596936—21no—
65#10596936—21no—
66#10596936—42no—
67C4×Dic37—21no—
68C4×Dic37—21no—
69C23×C37—41no—
70C23×C37—41no—
71C23×C37C22×C411yescharacteristic
72C23×C37C2×D411yescharacteristic
73C23×C37C2×D411yescharacteristic
74C23×C37C2×D411yescharacteristic
75C23×C37C2×Q811yescharacteristic
76C23×C37#4111yescharacteristic
77C23×C37#4111yescharacteristic
78C22×D37—21no—
79C22×D37—21no—
80C22×D37—41no—
81C22×D37—41no—
82C22×D37C4⋊C412yescomplemented
83C2×C4×C37—22no—
84C2×C4×C37—22no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—21no—
88C2×C4×C37—21no—
89C2×C4×C37—41no—
90C2×C4×C37—41no—
91C2×C4×C37—41no—
92C2×C4×C37—41no—
93C2×C4×C37—41no—
94C2×C4×C37—41no—
95C2×C4×C37—41no—
96C2×C4×C37—41no—
97C22⋊D37—22no—
98C22⋊D37—22no—
99C22⋊D37—22no—
100C22⋊D37—22no—
101C2×Dic37—21no—
102C2×Dic37—21no—
103C2×Dic37—22no—
104C2×Dic37—21no—
105C2×Dic37—21no—
106C2×Dic37—41no—
107C2×Dic37—41no—
108C2×Dic37—41no—
109C2×Dic37—41no—
110C2×Dic37—41no—
111C2×Dic37—41no—
112C2×Dic37—41no—
113C2×Dic37C4⋊C412yescomplemented
114C4×D37—81no—
115C4×D37—81no—
116C22×C37—21no—
117C22×C37—21no—
118C22×C37—21no—
119C22×C37—21no—
120C22×C37—21no—
121C22×C37—21no—
122C22×C37—41no—
123C22×C37—41no—
124C22×C37—41no—
125C22×C37—41no—
126C22×C37C2×C4⋊C411yescharacteristic
127C22×C37C4×D411yescharacteristic
128C22×C37C4×D411yescharacteristic
129C22×C37#12011yescharacteristic
130C22×C37C22⋊Q811yescharacteristic
131C22×C37C22⋊Q811yescharacteristic
132C22×C37#12311yescharacteristic
133C2×D37—22no—
134C2×D37—41no—
135C2×D37—41no—
136C2×D37—42no—
137C2×D37—81no—
138C4×C37—42no—
139C4×C37—41no—
140C4×C37—42no—
141C4×C37—41no—
142Dic37—22no—
143Dic37—42no—
144Dic37—41no—
145Dic37—41no—
146Dic37—81no—
147#1867—371nomaximal, Sylow
148C2×C37—21no—
149C2×C37—21no—
150C2×C37—21no—
151C2×C37—21no—
152C2×C37—21no—
153C2×C37—21no—
154C2×C37#38511yescharacteristic
155C2×C37B(4,𝔽2)11yescharacteristic
156C2×C37#45811yescharacteristic
157D37—42no—
158#518—371no—
159C2×#99—371no—
160#386—371no—
161#385—371no—
162#385D3711yescharacteristic, complemented
163#342—371no—
164#342—371no—
165C37#186711yescharacteristic, complemented, Sylow
166C22×D4—371no—
167C23×C4C2×D3711yescharacteristic
168C4×D4—741no—
169C4×D4—741no—
170C4×D4—741no—
171C4×D4—741no—
172#117—741no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—741no—
175C2×C22⋊C4—371no—
176C2×C22⋊C4—371no—
177C2×C22⋊C4—371no—
178C2×C22⋊C4—741no—
179C2×C22⋊C4—741no—
180C2×C22⋊C4C2×D3711yescharacteristic
181C2×C22⋊C4C2×D3711yescharacteristic
182#99—374no—
183#95—21no—
184#95—741no—
185#95—741no—
186C24—371no—
187C24C22×D3711yescharacteristic
188C2×D4—372no—
189C2×D4—372no—
190C2×D4—741no—
191C2×D4—741no—
192C2×D4—741no—
193C2×D4—741no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—42no—
199C22×C4—371no—
200C22×C4—371no—
201C22×C4—371no—
202C22×C4—741no—
203C22×C4—741no—
204C22×C4—741no—
205C22×C4—741no—
206C22×C4C22⋊D3711yescharacteristic
207C22×C4C22⋊D3711yescharacteristic
208C4⋊C4—42no—
209C4⋊C4—741no—
210C4⋊C4—741no—
211C4⋊C4—1482no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—372no—
216C22⋊C4—741no—
217C22⋊C4—741no—
218C22⋊C4—741no—
219C22⋊C4—741no—
220C22⋊C4—741no—
221C22⋊C4—741no—
222C22⋊C4—741no—
223C22⋊C4—1482no—
224C22⋊C4C4×D3712yescomplemented
225C42—741no—
226C42—741no—
227C23—41no—
228C23—41no—
229C23—372no—
230C23—741no—
231C23—741no—
232C23—1481no—
233C23—1481no—
234C23C2×C4×D3711yescharacteristic
235C23#1059696211yescharacteristic
236C23D4×D3711yescharacteristic
237C23D4×D3711yescharacteristic
238C23Q8×D3711yescharacteristic
239C23#1059696611yescharacteristic
240C23C2×C22⋊D3711yescharacteristic
241D4—742no—
242D4—742no—
243D4—742no—
244D4—742no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—372no—
260C2×C4—2961no—
261C2×C4—2961no—
262C2×C4—741no—
263C2×C4—741no—
264C2×C4—742no—
265C2×C4—741no—
266C2×C4—741no—
267C2×C4—1481no—
268C2×C4—1481no—
269C2×C4—1481no—
270C2×C4—1481no—
271C2×C4—1481no—
272C2×C4—1481no—
273C2×C4—1481no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—2961no—
285C22—742no—
286C22—1482no—
287C22—1481no—
288C22—1481no—
289C22C4⋊C4×D3711yescharacteristic
290C22C4×C22⋊D3711yescharacteristic
291C22#1192449811yescharacteristic
292C22#1192450411yescharacteristic
293C22#1192451211yescharacteristic
294C22#1192451411yescharacteristic
295C22#1192452111yescharacteristic
296C4—42no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—2961no—
301C4—742no—
302C4—1482no—
303C4—1481no—
304C4—1481no—
305C2—21no—
306C2—21no—
307C2—21no—
308C2—21no—
309C2—21no—
310C2—21no—
311C2—1482no—
312C2#1455740411yescharacteristic
313C2#1455771911yescharacteristic
314C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#385C2
socleC22×C37#120
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#385D37
hypocenterC37#1867
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #14557406C2semidirect
5. #14557300C2semidirect
6. #14557299C2semidirect
7. C37×#385C2semidirect
20. #11924450C4semidirect
54. C22⋊C4×C37C2×C4semidirect
60. C22⋊Dic37C2×C4semidirect
82. C22×D37C4⋊C4semidirect
113. C2×Dic37C4⋊C4semidirect
162. #385D37semidirect
165. C37#1867semidirect
224. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
#145580062
C2×#119244502
#145574122
#145574062
#145573002
#145572992
C37×#3852
#186737