Finite Group Databasebeta

← #17997873

Subgroups — #17997873

Order 4736.

528 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924501C211yesmaximal, characteristic, complemented
2C2×#11924494C211yesmaximal, characteristic
3#14557475C211yesmaximal, characteristic, complemented
4#14557468C211yesmaximal, characteristic
5#14557466C211yesmaximal, characteristic, complemented
6#14557455C211yesmaximal, characteristic
7#14557455C211yesmaximal, characteristic
8#14557454C211yesmaximal, characteristic, complemented
9#14557446C211yesmaximal, characteristic
10C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
12#14557384C211yesmaximal, characteristic, complemented
13#14557380C211yesmaximal, characteristic
14#14557380C211yesmaximal, characteristic
15C37×#398C211yesmaximal, characteristic, complemented
16C22×Dic74C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18#11924501—24no—
19#11924494—24no—
20C2×C4⋊Dic37C2211yescharacteristic
21C2×C4⋊Dic37C2211yescharacteristic
22C2×C4⋊Dic37C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×#10596938C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37C2×C4×Dic37C2211yescharacteristic
38C2×C4×Dic37C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46C2×C4⋊C4×C37C2211yescharacteristic
47C2×C4⋊C4×C37C2211yescharacteristic
48C2×C4⋊C4×C37C2211yescharacteristic
49C2×C4⋊C4×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53C23×D37C2311yescharacteristic
54C22×C4×C37C2311yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×Dic37C2311yescharacteristic
62C22×Dic37C2311yescharacteristic
63C22×Dic37C2311yescharacteristic
64C22×Dic37C2311yescharacteristic
65C22×Dic37C2311yescharacteristic
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C2×C4×D37—22no—
69C2×C4×D37—22no—
70C2×C4×D37Q814yescomplemented
71C2×Dic74—22no—
72C2×Dic74—22no—
73C2×Dic74—22no—
74C4⋊C4×C37—22no—
75C4⋊C4×C37—22no—
76C4⋊C4×C37—22no—
77C4⋊C4×C37—22no—
78#10596938—22no—
79#10596938—22no—
80#10596938—22no—
81#10596938—22no—
82#10596938—22no—
83#10596938—22no—
84C4⋊Dic37—22no—
85C4⋊Dic37—22no—
86C4⋊Dic37—22no—
87#10596936—22no—
88#10596936—22no—
89#10596936—22no—
90#10596936—22no—
91C4×Dic37—22no—
92C4×Dic37—22no—
93C4×Dic37—22no—
94C4×Dic37—22no—
95C4×Dic37—22no—
96C4×Dic37D414yes—
97C23×C37C2411yescharacteristic
98C22×D37—21no—
99C22×D37—21no—
100C22×D37—21no—
101C22×D37—21no—
102C22×D37—21no—
103C22×D37—21no—
104C22×D37C2×Q812yes—
105C2×C4×C37—21no—
106C2×C4×C37—21no—
107C2×C4×C37—21no—
108C2×C4×C37—21no—
109C2×C4×C37—21no—
110C2×C4×C37—21no—
111C2×C4×C37—21no—
112C2×C4×C37—21no—
113C2×C4×C37—21no—
114C2×C4×C37—21no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37C2×D412yes—
123C2×C4×C37C2×Q812yes—
124C2×C4×C37#4112yes—
125C2×C4×C37#4112yes—
126C2×Dic37—21no—
127C2×Dic37—21no—
128C2×Dic37—21no—
129C2×Dic37—21no—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—21no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37C2×D412yes—
142C2×Dic37C2×D412yes—
143C2×Dic37C2×Q812yes—
144C2×Dic37#4112yes—
145C2×Dic37#4112yes—
146C2×Dic37#4112yes—
147C4×D37—28no—
148Dic74—28no—
149C22×C37C22×D411yescharacteristic
150C22×C37C22×Q811yescharacteristic
151C22×C37C2×#4111yescharacteristic
152C22×C37C2×#4111yescharacteristic
153C22×C37C2×#4111yescharacteristic
154C22×C37C2×#4111yescharacteristic
155C22×C37C2×#4111yescharacteristic
156C2×D37—22no—
157C2×D37—22no—
158C2×D37—22no—
159C2×D37—41no—
160C2×D37—41no—
161C2×D37—41no—
162C2×D37—41no—
163C4×C37—22no—
164C4×C37—22no—
165C4×C37—22no—
166C4×C37—22no—
167C4×C37—41no—
168C4×C37—41no—
169C4×C37—41no—
170Dic37—22no—
171Dic37—22no—
172Dic37—22no—
173Dic37—41no—
174Dic37—41no—
175Dic37—41no—
176Dic37C22⋊Q814yes—
177#2396—371nomaximal, Sylow
178C2×C37C2×C22⋊Q811yescharacteristic
179C2×C37#52511yescharacteristic
180C2×C37#52911yescharacteristic
181C2×C37#52911yescharacteristic
182C2×C37#53211yescharacteristic
183C2×C37#53311yescharacteristic
184C2×C37#53311yescharacteristic
185D37—42no—
186C2×C4×Q8—371no—
187C2×#117—371no—
188#400—371no—
189#399—371no—
190#398—371no—
191#398D3711yescharacteristic, complemented
192#396—371no—
193#396—371no—
194#395—371no—
195#393—371no—
196C4×C4⋊C4—371no—
197C4×C4⋊C4—371no—
198C4×C4⋊C4—371no—
199C4×C22⋊C4—371no—
200C4×C22⋊C4—371no—
201C37#239611yescharacteristic, complemented, Sylow
202C22×Q8—371no—
203C23×C4—371no—
204C4×Q8—744no—
205#117—744no—
206C2×C4⋊C4—371no—
207C2×C4⋊C4—371no—
208C2×C4⋊C4—371no—
209C2×C4⋊C4—371no—
210C2×C4⋊C4—371no—
211C2×C4⋊C4—371no—
212C2×C4⋊C4—371no—
213C2×C4⋊C4C2×D3711yescharacteristic
214C2×C4⋊C4C2×D3711yescharacteristic
215C2×C4⋊C4C2×D3711yescharacteristic
216C2×C4⋊C4C2×D3711yescharacteristic
217C2×C22⋊C4—371no—
218C2×C22⋊C4—371no—
219C2×C22⋊C4—371no—
220C2×C22⋊C4—371no—
221C2×C22⋊C4—371no—
222C2×C22⋊C4—371no—
223C2×C42—371no—
224C2×C42—371no—
225C2×C42—371no—
226C2×C42—371no—
227C2×C42—371no—
228C2×C42—371no—
229#95—371no—
230#95—371no—
231#95—371no—
232#95—371no—
233#95—371no—
234#95—371no—
235#95—371no—
236#95C2×D3711yescharacteristic
237#95C2×D3711yescharacteristic
238#95C2×D3711yescharacteristic
239C24—371no—
240C2×Q8—742no—
241C2×Q8—742no—
242C2×Q8—742no—
243C22×C4—371no—
244C22×C4—371no—
245C22×C4—371no—
246C22×C4—371no—
247C22×C4—374no—
248C22×C4—371no—
249C22×C4—371no—
250C22×C4—371no—
251C22×C4—742no—
252C22×C4—742no—
253C22×C4C22×D3711yescharacteristic
254C22×C4C22×D3711yescharacteristic
255C22×C4C22×D3711yescharacteristic
256C22×C4C22×D3711yescharacteristic
257C22×C4C22×D3711yescharacteristic
258C22×C4C22×D3711yescharacteristic
259C22×C4C22×D3711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—742no—
265C4⋊C4—742no—
266C4⋊C4—742no—
267C4⋊C4—742no—
268C4⋊C4—742no—
269C4⋊C4—742no—
270C4⋊C4—742no—
271C22⋊C4—742no—
272C22⋊C4—742no—
273C22⋊C4—742no—
274C22⋊C4—742no—
275C22⋊C4—742no—
276C22⋊C4—742no—
277C42—374no—
278C42—742no—
279C42—742no—
280C42—742no—
281C42—742no—
282C42—742no—
283C23—372no—
284C23—741no—
285C23—741no—
286C23—741no—
287C23—741no—
288C23—741no—
289C23—741no—
290C23C23×D3711yescharacteristic
291Q8—748no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—372no—
310C2×C4—372no—
311C2×C4—372no—
312C2×C4—372no—
313C2×C4—372no—
314C2×C4—372no—
315C2×C4—748no—
316C2×C4—741no—
317C2×C4—741no—
318C2×C4—741no—
319C2×C4—741no—
320C2×C4—741no—
321C2×C4—741no—
322C2×C4—741no—
323C2×C4—741no—
324C2×C4—741no—
325C2×C4—741no—
326C2×C4—741no—
327C2×C4—741no—
328C2×C4—741no—
329C2×C4—741no—
330C2×C4—741no—
331C2×C4D4×D3712yes—
332C2×C4#1059696412yes—
333C2×C4Q8×D3712yes—
334C2×C4#1059696612yes—
335C22—742no—
336C22—742no—
337C22—742no—
338C22—1481no—
339C22—1481no—
340C22—1481no—
341C22—1481no—
342C22C2×D4×D3711yescharacteristic
343C22C2×Q8×D3711yescharacteristic
344C22#41×D3711yescharacteristic
345C22#41×D3711yescharacteristic
346C22#41×D3711yescharacteristic
347C22C2×#1059696411yescharacteristic
348C22C2×#1059696611yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—374no—
357C4—742no—
358C4—742no—
359C4—742no—
360C4—1481no—
361C4—1481no—
362C4—1481no—
363C2—1482no—
364C2C22⋊Q8×D3711yescharacteristic
365C2#1455804611yescharacteristic
366C2#1455806011yescharacteristic
367C2#1455806811yescharacteristic
368C2#1455807811yescharacteristic
369C2#1455808811yescharacteristic
370C2#1455808911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#398C2
prime radicalC23×D37C23
hypercenter#398D37
hypocenterC37#2396
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#11924501C2semidirect
3. #14557475C2semidirect
5. #14557466C2semidirect
8. #14557454C2semidirect
10. C4⋊C4×Dic37C2semidirect
11. C4⋊C4×Dic37C2semidirect
12. #14557384C2semidirect
15. C37×#398C2semidirect
70. C2×C4×D37Q8semidirect
191. #398D37semidirect
201. C37#2396semidirect

Maximal subgroups

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

subgroupindex
C2×#119245012
C2×#119244942
#145574752
#145574682
#145574662
#145574552
#145574542
#145574462
C4⋊C4×Dic372
#145573842
#145573802
C37×#3982
#239637