Finite Group Databasebeta

← #17997443

Subgroups — #17997443

Order 4736.

792 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924494C211yesmaximal, characteristic, complemented
2C22×#10596938C211yesmaximal, characteristic
3C2×C22⋊C4×D37C211yesmaximal, characteristic
4#14557425C211yesmaximal, characteristic, complemented
5#14557425C211yesmaximal, characteristic, complemented
6#14557423C211yesmaximal, characteristic, complemented
7#14557423C211yesmaximal, characteristic, complemented
8#14557408C211yesmaximal, characteristic, complemented
9#14557395C211yesmaximal, characteristic, complemented
10#14557390C211yesmaximal, characteristic, complemented
11#14557388C211yesmaximal, characteristic
12C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic37C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#385C211yesmaximal, characteristic, complemented
16C24×D37C2211yescharacteristic
17C23×Dic37C2211yescharacteristic
18C22×C4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20#11924494—24no—
21C2×C4⋊Dic37C2211yescharacteristic, complemented
22C2×C4⋊Dic37C2211yescharacteristic, complemented
23C2×C22⋊Dic37C2211yescharacteristic
24C2×C22⋊Dic37C2211yescharacteristic
25C2×#10596938—24no—
26C2×#10596938C2211yescharacteristic
27C2×#10596938C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C22⋊C4×D37C418yescomplemented
37C2×C4×Dic37C2211yescharacteristic, complemented
38C2×C4×Dic37C2211yescharacteristic, complemented
39C2×C4×Dic37C2211yescharacteristic, complemented
40C2×C4×Dic37C2211yescharacteristic, complemented
41#11924443C2211yescharacteristic, complemented
42#11924443C2211yescharacteristic, complemented
43#11924443C2211yescharacteristic, complemented
44#11924443C2211yescharacteristic, complemented
45#11924443C2211yescharacteristic, complemented
46#11924443C2211yescharacteristic, complemented
47C23×C4×C37C2211yescharacteristic
48C2×C4⋊C4×C37C2211yescharacteristic, complemented
49C2×C4⋊C4×C37C2211yescharacteristic, complemented
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic, complemented
53#95×C37C2211yescharacteristic, complemented
54C24×C37C2311yescharacteristic
55C23×D37—22no—
56C23×D37—22no—
57C23×D37—22no—
58C23×D37—22no—
59C23×D37—41no—
60C23×D37—41no—
61C23×D37C2×C414yes—
62C23×D37C2311yescharacteristic
63C23×D37C2311yescharacteristic
64C22×C4×C37—22no—
65C22×C4×C37—22no—
66C22×C4×C37—41no—
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C22×C4×C37C2311yescharacteristic
72C22×C4×C37C2311yescharacteristic
73C22×Dic37—22no—
74C22×Dic37—22no—
75C22×Dic37—41no—
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C22×Dic37C2311yescharacteristic
82C2×C4×D37—22no—
83C2×C4×D37—22no—
84C2×C4×D37—41no—
85C2×C4×D37—41no—
86C2×C4×D37C2×C414yescomplemented
87C2×C4×D37C2×C414yescomplemented
88C4⋊C4×C37—22no—
89C4⋊C4×C37—41no—
90C22⋊C4×C37—22no—
91C22⋊C4×C37C2×C414yes—
92C22⋊Dic37—22no—
93C22⋊Dic37C2×C414yes—
94#10596938—22no—
95#10596938—22no—
96#10596938—22no—
97#10596938—22no—
98#10596938—22no—
99#10596938—41no—
100#10596938—41no—
101#10596938C2×C414yescomplemented
102#10596938C2×C414yescomplemented
103#10596938D414yes—
104C4⋊Dic37—22no—
105C4⋊Dic37—41no—
106C4×Dic37—22no—
107C4×Dic37—22no—
108C4×Dic37—41no—
109C4×Dic37—41no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37C22×C412yes—
115C23×C37#4112yes—
116C23×C37#4112yes—
117C23×C37C2411yescharacteristic
118C22×D37—21no—
119C22×D37—21no—
120C22×D37—21no—
121C22×D37—21no—
122C22×D37—28no—
123C22×D37—21no—
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—28no—
130C22×D37—44no—
131C22×D37—44no—
132C22×D37—44no—
133C22×D37—44no—
134C22×D37—44no—
135C22×D37C22×C412yes—
136C22×D37C22×C412yes—
137C22×D37C2×D412yes—
138C22×D37#4112yes—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
152C2×C4×C37—21no—
153C2×C4×C37—21no—
154C2×C4×C37—44no—
155C2×C4×C37C22×C412yes—
156C2×C4×C37C22×C412yes—
157C2×C4×C37C2×D412yes—
158C2×Dic37—21no—
159C2×Dic37—21no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—21no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37—21no—
169C2×Dic37—21no—
170C2×Dic37—21no—
171C2×Dic37—21no—
172C2×Dic37—21no—
173C2×Dic37—44no—
174C2×Dic37C22×C412yes—
175C2×Dic37C22×C412yes—
176C2×Dic37C2×D412yes—
177C4×D37—28no—
178C4×D37—44no—
179C22×C37—22no—
180C22×C37—22no—
181C22×C37—22no—
182C22×C37—22no—
183C22×C37—22no—
184C22×C37—22no—
185C22×C37#11714yescomplemented
186C22×C37C23×C411yescharacteristic
187C22×C37C22×D411yescharacteristic
188C22×C37C2×#4111yescharacteristic
189C22×C37C2×#4111yescharacteristic
190C22×C37C2×#4111yescharacteristic
191C22×C37H(5,𝔽2)11yescharacteristic
192C22×C37H(5,𝔽2)11yescharacteristic
193C2×D37—22no—
194C2×D37—22no—
195C2×D37—22no—
196C2×D37—22no—
197C2×D37—22no—
198C2×D37—22no—
199C2×D37—22no—
200C2×D37—22no—
201C2×D37—22no—
202C2×D37—416no—
203C2×D37—41no—
204C2×D37—41no—
205C2×D37—41no—
206C2×D37—41no—
207C2×D37C4×D414yes—
208C4×C37—22no—
209C4×C37—22no—
210C4×C37—22no—
211C4×C37—41no—
212C4×C37—41no—
213C4×C37—41no—
214Dic37—22no—
215Dic37—22no—
216Dic37—22no—
217Dic37—41no—
218Dic37—41no—
219Dic37—41no—
220#2342—371nomaximal, Sylow
221C2×C37—24no—
222C2×C37C2×#11711yescharacteristic
223C2×C37C2×C4×D411yescharacteristic
224C2×C37#51811yescharacteristic
225C2×C37#54611yescharacteristic
226C2×C37#54611yescharacteristic
227C2×C37#55111yescharacteristic
228C2×C37#55111yescharacteristic
229D37—24no—
230D37—42no—
231C2×#117—371no—
232C22×C22⋊C4—371no—
233C22×C22⋊C4—371no—
234#388—371no—
235#388—371no—
236#388—371no—
237#388—371no—
238#385—371no—
239#385D3711yescharacteristic, complemented
240#381—371no—
241#380—371no—
242#379—371no—
243C4×C22⋊C4—371no—
244C4×C22⋊C4—371no—
245C4×C22⋊C4—371no—
246C37#234211yescharacteristic, complemented, Sylow
247C25—371no—
248C23×C4—371no—
249C23×C4—371no—
250C23×C4—371no—
251C23×C4C2×D3711yescharacteristic
252#117—744no—
253C2×C4⋊C4—371no—
254C2×C4⋊C4—371no—
255C2×C4⋊C4C2×D3711yescharacteristic, complemented
256C2×C4⋊C4C2×D3711yescharacteristic, complemented
257C2×C22⋊C4—371no—
258C2×C22⋊C4—371no—
259C2×C22⋊C4—371no—
260C2×C22⋊C4—371no—
261C2×C22⋊C4—378no—
262C2×C22⋊C4—371no—
263C2×C22⋊C4—371no—
264C2×C22⋊C4—371no—
265C2×C22⋊C4—371no—
266C2×C22⋊C4—371no—
267C2×C22⋊C4—371no—
268C2×C22⋊C4—371no—
269C2×C22⋊C4—371no—
270C2×C22⋊C4—744no—
271C2×C22⋊C4C2×D3711yescharacteristic
272C2×C22⋊C4C2×D3711yescharacteristic
273C2×C42—371no—
274C2×C42—371no—
275C2×C42—371no—
276C2×C42—371no—
277#95—371no—
278#95—371no—
279#95—371no—
280#95—371no—
281#95—371no—
282#95—371no—
283#95C2×D3711yescharacteristic, complemented
284#95C2×D3711yescharacteristic, complemented
285C24—371no—
286C24—371no—
287C24—374no—
288C24—742no—
289C24—742no—
290C24—742no—
291C24—742no—
292C24—1481no—
293C24—1481no—
294C24C22×D3711yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—41no—
298C22×C4—371no—
299C22×C4—371no—
300C22×C4—371no—
301C22×C4—374no—
302C22×C4—374no—
303C22×C4—371no—
304C22×C4—371no—
305C22×C4—371no—
306C22×C4—742no—
307C22×C4—742no—
308C22×C4—742no—
309C22×C4—742no—
310C22×C4—1481no—
311C22×C4—1481no—
312C22×C4—1481no—
313C22×C4C22×D3711yescharacteristic
314C22×C4C22×D3711yescharacteristic
315C22×C4C22×D3711yescharacteristic
316C22×C4C22×D3711yescharacteristic
317C22×C4C22×D3711yescharacteristic
318C22×C4C22×D3711yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—41no—
321C4⋊C4—742no—
322C4⋊C4—1481no—
323C22⋊C4—22no—
324C22⋊C4—374no—
325C22⋊C4—374no—
326C22⋊C4—374no—
327C22⋊C4—374no—
328C22⋊C4—742no—
329C22⋊C4—742no—
330C22⋊C4—742no—
331C22⋊C4—742no—
332C22⋊C4—742no—
333C22⋊C4—742no—
334C22⋊C4—1481no—
335C22⋊C4—1481no—
336C22⋊C4C4×D3714yes—
337C42—742no—
338C42—742no—
339C42—1481no—
340C42—1481no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—372no—
346C23—372no—
347C23—372no—
348C23—372no—
349C23—748no—
350C23—741no—
351C23—741no—
352C23—741no—
353C23—741no—
354C23—748no—
355C23—741no—
356C23—741no—
357C23—741no—
358C23—741no—
359C23—741no—
360C23—741no—
361C23—1484no—
362C23—1484no—
363C23—1484no—
364C23—1484no—
365C23—1484no—
366C23C2×C4×D3712yes—
367C23#1059696412yes—
368C23#1059696612yes—
369C23C23×D3711yescharacteristic
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—44no—
386C2×C4—372no—
387C2×C4—372no—
388C2×C4—372no—
389C2×C4—748no—
390C2×C4—741no—
391C2×C4—741no—
392C2×C4—741no—
393C2×C4—741no—
394C2×C4—741no—
395C2×C4—741no—
396C2×C4—741no—
397C2×C4—741no—
398C2×C4—741no—
399C2×C4—741no—
400C2×C4—741no—
401C2×C4—741no—
402C2×C4—741no—
403C2×C4—741no—
404C2×C4—741no—
405C2×C4—1484no—
406C2×C4—1484no—
407C2×C4C2×C4×D3712yes—
408C2×C4C2×C4×D3712yes—
409C2×C4D4×D3712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—374no—
417C22—742no—
418C22—742no—
419C22—742no—
420C22—742no—
421C22—742no—
422C22—742no—
423C22—742no—
424C22—742no—
425C22—742no—
426C22—14816no—
427C22—1481no—
428C22—1481no—
429C22—1481no—
430C22—1481no—
431C22#1192449414yescomplemented
432C22C22×C4×D3711yescharacteristic
433C22C2×D4×D3711yescharacteristic
434C22#41×D3711yescharacteristic
435C22C2×#1059696411yescharacteristic
436C22C2×#1059696611yescharacteristic
437C22#1192458111yescharacteristic
438C22#1192458211yescharacteristic
439C4—22no—
440C4—22no—
441C4—22no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—742no—
446C4—742no—
447C4—742no—
448C4—1481no—
449C4—1481no—
450C4—1481no—
451C2—24no—
452C2—744no—
453C2—1482no—
454C2C2×#1192449411yescharacteristic
455C2C4×D4×D3711yescharacteristic
456C2#1455800511yescharacteristic
457C2#1455817011yescharacteristic
458C2#1455817411yescharacteristic
459C2#1455820611yescharacteristic
460C2#1455821011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#385C2
socle, cosocleC23×C37C24
prime radicalC24×D37C22
hypercenter#385D37
hypocenterC37#2342
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#11924494C2semidirect
4. #14557425C2semidirect
5. #14557425C2semidirect
6. #14557423C2semidirect
7. #14557423C2semidirect
8. #14557408C2semidirect
9. #14557395C2semidirect
10. #14557390C2semidirect
12. C22⋊C4×Dic37C2semidirect
13. C4×C22⋊Dic37C2semidirect
14. #14557380C2semidirect
15. C37×#385C2semidirect
21. C2×C4⋊Dic37C22semidirect
22. C2×C4⋊Dic37C22semidirect
36. C22⋊C4×D37C4semidirect
37. C2×C4×Dic37C22semidirect
38. C2×C4×Dic37C22semidirect
39. C2×C4×Dic37C22semidirect
40. C2×C4×Dic37C22semidirect
41. #11924443C22semidirect
42. #11924443C22semidirect
43. #11924443C22semidirect
44. #11924443C22semidirect
45. #11924443C22semidirect
46. #11924443C22semidirect
48. C2×C4⋊C4×C37C22semidirect
49. C2×C4⋊C4×C37C22semidirect
52. #95×C37C22semidirect
53. #95×C37C22semidirect
86. C2×C4×D37C2×C4semidirect
87. C2×C4×D37C2×C4semidirect
101. #10596938C2×C4semidirect
102. #10596938C2×C4semidirect
185. C22×C37#117semidirect
239. #385D37semidirect
246. C37#2342semidirect
255. C2×C4⋊C4C2×D37semidirect
256. C2×C4⋊C4C2×D37semidirect
283. #95C2×D37semidirect
284. #95C2×D37semidirect
431. C22#11924494semidirect

Maximal subgroups

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

subgroupindex
C2×#119244942
C22×#105969382
C2×C22⋊C4×D372
#145574252
#145574232
#145574082
#145573952
#145573902
#145573882
C22⋊C4×Dic372
C4×C22⋊Dic372
#145573802
C37×#3852
#234237