Finite Group Databasebeta

← #17997237

Subgroups — #17997237

Order 4736.

540 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924496C211yesmaximal, characteristic
2#14557433C211yesmaximal, characteristic
3#14557433C211yesmaximal, characteristic
4#14557430C211yesmaximal, characteristic, complemented
5#14557428C211yesmaximal, characteristic, complemented
6#14557426C211yesmaximal, characteristic, complemented
7#14557424C211yesmaximal, characteristic, complemented
8#14557422C211yesmaximal, characteristic, complemented
9#14557395C211yesmaximal, characteristic, complemented
10#14557394C211yesmaximal, characteristic, complemented
11#14557391C211yesmaximal, characteristic, complemented
12#14557390C211yesmaximal, characteristic, complemented
13C4×#10596936C211yesmaximal, characteristic, complemented
14#14557378C211yesmaximal, characteristic, complemented
15C37×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C23×Dic37C2211yescharacteristic
18C22×C4×D37C2211yescharacteristic
19#11924496C418yescomplemented
20C2×C4⋊Dic37C2211yescharacteristic
21C2×#10596936C2211yescharacteristic
22C2×#10596936C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×C22⋊Dic37C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45C2×C4⋊C4×C37C2211yescharacteristic
46C2×C22⋊C4×C37C2211yescharacteristic
47C2×C22⋊C4×C37C2211yescharacteristic
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C42×C37C2211yescharacteristic
50#95×C37C2211yescharacteristic
51#95×C37C2211yescharacteristic
52C24×C37C2311yescharacteristic
53C23×D37C2311yescharacteristic
54C22×C4×C37C2311yescharacteristic
55C22×C4×C37C2311yescharacteristic
56C22×C4×C37C2311yescharacteristic
57C22×C4×C37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C2×C22⋊D37—22no—
61C2×C22⋊D37—22no—
62C2×C22⋊D37C2×C414yes—
63C22×Dic37—41no—
64C22×Dic37—41no—
65C22×Dic37C2×C414yes—
66C22×Dic37C2311yescharacteristic
67C22×Dic37C2311yescharacteristic
68C22×Dic37C2311yescharacteristic
69C22×Dic37C2311yescharacteristic
70C22×Dic37C2311yescharacteristic
71C22×Dic37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C2×C4×D37—41no—
74C2×C4×D37—41no—
75C2×C4×D37C2×C414yes—
76C4⋊C4×C37—41no—
77C22⋊C4×C37—41no—
78C22⋊C4×C37—41no—
79C22⋊C4×C37C2×C414yes—
80C42×C37—41no—
81C22⋊Dic37—41no—
82C22⋊Dic37—41no—
83#10596938—41no—
84#10596938—41no—
85#10596938—41no—
86#10596938—41no—
87#10596938C2×C414yes—
88C4⋊Dic37—41no—
89#10596936—22no—
90#10596936—22no—
91#10596936—41no—
92#10596936—41no—
93#10596936C2×C414yes—
94C4×Dic37—22no—
95C4×Dic37—22no—
96C4×Dic37—41no—
97C4×Dic37C2×C414yes—
98C23×C37—21no—
99C23×C37—21no—
100C23×C37—21no—
101C23×C37—21no—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37C22×C412yes—
105C23×C37C2411yescharacteristic
106C22×D37—21no—
107C22×D37—21no—
108C22×D37—21no—
109C22×D37—21no—
110C22×D37—21no—
111C22×D37—21no—
112C22×D37C22×C412yes—
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×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37—21no—
129C2×C4×C37C22×C412yes—
130C2×C4×C37C22×C412yes—
131C22⋊D37—28no—
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×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—44no—
149C2×Dic37C22×C412yes—
150C2×Dic37C22×C412yes—
151C2×Dic37C22×C412yes—
152C2×Dic37#4112yes—
153C2×Dic37#4112yes—
154C4×D37—44no—
155C22×C37—22no—
156C22×C37—22no—
157C22×C37—22no—
158C22×C37—41no—
159C22×C37—41no—
160C22×C37—41no—
161C22×C37—41no—
162C22×C37C23×C411yescharacteristic
163C22×C37C2×#4111yescharacteristic
164C22×C37C2×#4111yescharacteristic
165C22×C37H(5,𝔽2)11yescharacteristic
166C22×C37H(5,𝔽2)11yescharacteristic
167C22×C37H(5,𝔽2)11yescharacteristic
168C22×C372−1+411yescharacteristic
169C2×D37—22no—
170C2×D37—22no—
171C2×D37—22no—
172C2×D37—41no—
173C2×D37—41no—
174C2×D37—41no—
175C2×D37—41no—
176C4×C37—22no—
177C4×C37—22no—
178C4×C37—41no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182Dic37—22no—
183Dic37—22no—
184Dic37—41no—
185Dic37—41no—
186Dic37—41no—
187Dic37—41no—
188Dic37#11714yes—
189#2319—371nomaximal, Sylow
190C2×C37—42no—
191C2×C37C2×#11711yescharacteristic
192C2×C37#51811yescharacteristic
193C2×C37#52011yescharacteristic
194C2×C37#54011yescharacteristic
195C2×C37#54011yescharacteristic
196C2×C37#54211yescharacteristic
197C2×C37#54211yescharacteristic
198D37—42no—
199C2×C4×D4—371no—
200#390—371no—
201#390—371no—
202#389—371no—
203#389—371no—
204#388—371no—
205#388—371no—
206#388—371no—
207#388D3711yescharacteristic, complemented
208#381—371no—
209#381—371no—
210#380—371no—
211#380—371no—
212C4×C4⋊C4—371no—
213#376—371no—
214C37#231911yescharacteristic, complemented, Sylow
215C22×D4—371no—
216C23×C4—371no—
217C23×C4—371no—
218C4×D4—378no—
219C2×C4⋊C4—371no—
220C2×C4⋊C4—371no—
221C2×C4⋊C4—371no—
222C2×C4⋊C4—371no—
223C2×C4⋊C4—371no—
224C2×C4⋊C4—371no—
225C2×C4⋊C4C2×D3711yescharacteristic
226C2×C22⋊C4—371no—
227C2×C22⋊C4—371no—
228C2×C22⋊C4—371no—
229C2×C22⋊C4—371no—
230C2×C22⋊C4—371no—
231C2×C22⋊C4—371no—
232C2×C22⋊C4—371no—
233C2×C22⋊C4C2×D3711yescharacteristic
234C2×C22⋊C4C2×D3711yescharacteristic
235C2×C22⋊C4C2×D3711yescharacteristic
236C2×C42—371no—
237C2×C42—371no—
238C2×C42—371no—
239C2×C42—371no—
240C2×C42C2×D3711yescharacteristic
241#95—371no—
242#95—371no—
243#95—371no—
244#95—371no—
245#95—371no—
246#95—371no—
247#95—371no—
248#95—371no—
249#95C2×D3711yescharacteristic
250#95C2×D3711yescharacteristic
251C24—371no—
252C24C22×D3711yescharacteristic
253C2×D4—374no—
254C2×D4—742no—
255C2×D4—742no—
256C22×C4—371no—
257C22×C4—371no—
258C22×C4—371no—
259C22×C4—374no—
260C22×C4—374no—
261C22×C4—371no—
262C22×C4—371no—
263C22×C4—371no—
264C22×C4—371no—
265C22×C4—1481no—
266C22×C4—1481no—
267C22×C4—1481no—
268C22×C4—1481no—
269C22×C4C22×D3711yescharacteristic
270C22×C4C22×D3711yescharacteristic
271C22×C4C22×D3711yescharacteristic
272C22×C4C22×D3711yescharacteristic
273C22×C4C22×D3711yescharacteristic
274C22×C4C22×D3711yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—374no—
277C4⋊C4—742no—
278C4⋊C4—742no—
279C4⋊C4—1481no—
280C4⋊C4—1481no—
281C4⋊C4—1481no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—374no—
285C22⋊C4—1481no—
286C22⋊C4—1481no—
287C22⋊C4—1481no—
288C22⋊C4—1481no—
289C22⋊C4—1481no—
290C22⋊C4—1481no—
291C22⋊C4C4×D3714yes—
292C42—41no—
293C42—374no—
294C42—742no—
295C42—742no—
296C42—1481no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—372no—
304C23—741no—
305C23—741no—
306C23—741no—
307C23—741no—
308C23—741no—
309C23—741no—
310C23C2×C4×D3712yes—
311C23C23×D3711yescharacteristic
312D4—748no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—372no—
330C2×C4—372no—
331C2×C4—372no—
332C2×C4—372no—
333C2×C4—372no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
345C2×C4—741no—
346C2×C4—741no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—1484no—
351C2×C4—1484no—
352C2×C4C2×C4×D3712yes—
353C2×C4C2×C4×D3712yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—742no—
362C22—742no—
363C22—742no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22—1481no—
368C22C22×C4×D3711yescharacteristic
369C22#41×D3711yescharacteristic
370C22#41×D3711yescharacteristic
371C22#1192458111yescharacteristic
372C22#1192458111yescharacteristic
373C22#1192458211yescharacteristic
374C22#1192458311yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—374no—
382C4—742no—
383C4—742no—
384C4—1481no—
385C4—1481no—
386C4—1481no—
387C4—1481no—
388C2—42no—
389C2—1482no—
390C2#117×D3711yescharacteristic
391C2#1455800511yescharacteristic
392C2#1455801211yescharacteristic
393C2#1455813311yescharacteristic
394C2#1455813511yescharacteristic
395C2#1455814711yescharacteristic
396C2#1455814911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#388C2
socle, cosocleC23×C37C24
prime radicalC22×C22⋊D37C22
hypercenter#388D37
hypocenterC37#2319
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
4. #14557430C2semidirect
5. #14557428C2semidirect
6. #14557426C2semidirect
7. #14557424C2semidirect
8. #14557422C2semidirect
9. #14557395C2semidirect
10. #14557394C2semidirect
11. #14557391C2semidirect
12. #14557390C2semidirect
13. C4×#10596936C2semidirect
14. #14557378C2semidirect
15. C37×#388C2semidirect
19. #11924496C4semidirect
207. #388D37semidirect
214. C37#2319semidirect

Maximal subgroups

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

subgroupindex
C2×#119244962
#145574332
#145574302
#145574282
#145574262
#145574242
#145574222
#145573952
#145573942
#145573912
#145573902
C4×#105969362
#145573782
C37×#3882
#231937