Finite Group Databasebeta

← #17997440

Subgroups — #17997440

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×#11924493C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D37C211yesmaximal, characteristic
3C2×C22⋊C4×D37C211yesmaximal, characteristic
4#14557427C211yesmaximal, characteristic, complemented
5#14557426C211yesmaximal, characteristic, complemented
6#14557421C211yesmaximal, characteristic, complemented
7#14557407C211yesmaximal, characteristic, complemented
8#14557404C211yesmaximal, characteristic, complemented
9#14557395C211yesmaximal, characteristic, complemented
10#14557390C211yesmaximal, characteristic, complemented
11#14557388C211yesmaximal, characteristic
12C4×#10596938C211yesmaximal, characteristic, complemented
13#14557380C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#388C211yesmaximal, characteristic, complemented
16C24×D37C2211yescharacteristic
17C22×C4×D37C2211yescharacteristic
18C22×C4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21#11924493—24no—
22C2×C4⋊Dic37C2211yescharacteristic, complemented
23C2×#10596936C2211yescharacteristic, complemented
24C2×#10596936C2211yescharacteristic, complemented
25C2×C22⋊Dic37C2211yescharacteristic
26C2×C22⋊Dic37C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×#10596938C2211yescharacteristic
29C2×#10596938C2211yescharacteristic
30C2×#10596938C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C22⋊C4×D37—24no—
37C22⋊C4×D37C418yescomplemented
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
47C2×C4⋊C4×C37C2211yescharacteristic, complemented
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C42×C37C2211yescharacteristic, complemented
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×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×Dic37C2311yescharacteristic
71C22×Dic37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C22×Dic37C2311yescharacteristic
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C2×C4×D37—22no—
77C2×C4×D37—22no—
78C2×C4×D37—22no—
79C2×C4×D37—22no—
80C2×C4×D37—22no—
81C2×C4×D37—22no—
82C2×C4×D37—41no—
83C2×C4×D37—41no—
84C2×C4×D37—41no—
85C2×C4×D37—41no—
86C2×C4×D37C2×C414yescomplemented
87C2×C4×D37C2×C414yescomplemented
88C4⋊C4×C37—41no—
89C22⋊C4×C37—22no—
90C22⋊C4×C37—41no—
91C22⋊C4×C37C2×C414yescomplemented
92C42×C37—22no—
93C22⋊Dic37—22no—
94C22⋊Dic37—41no—
95C22⋊Dic37C2×C414yescomplemented
96#10596938—22no—
97#10596938—22no—
98#10596938—22no—
99#10596938—22no—
100#10596938—22no—
101#10596938C2×C414yes—
102#10596938C2×C414yes—
103#10596938D414yes—
104C4⋊Dic37—41no—
105#10596936—22no—
106#10596936—22no—
107C4×Dic37—22no—
108C4×Dic37—41no—
109C4×Dic37—41no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—21no—
116C23×C37C22×C412yes—
117C23×C37C2411yescharacteristic
118C22×D37—21no—
119C22×D37—21no—
120C22×D37—21no—
121C22×D37—21no—
122C22×D37—21no—
123C22×D37—21no—
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—28no—
127C22×D37—28no—
128C22×D37—44no—
129C22×D37—44no—
130C22×D37—44no—
131C22×D37—44no—
132C22×D37—44no—
133C22×D37C22×C412yes—
134C22×D37C22×C412yes—
135C22×D37C2×D412yes—
136C22×D37#4112yes—
137C22×D37#4112yes—
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×C37C22×C412yes—
155C2×C4×C37C22×C412yes—
156C2×C4×C37C2×D412yes—
157C2×Dic37—21no—
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×Dic37C22×C412yes—
173C2×Dic37C22×C412yes—
174C2×Dic37C2×D412yes—
175C4×D37—28no—
176C4×D37—44no—
177C4×D37—44no—
178C4×D37—44no—
179C22×C37—22no—
180C22×C37—22no—
181C22×C37—22no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37—41no—
185C22×C37—41no—
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—22no—
203C2×D37—22no—
204C2×D37—22no—
205C2×D37—416no—
206C2×D37#11714yescomplemented
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—42no—
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—24no—
231C2×#117—371no—
232C22×C22⋊C4—371no—
233C22×C22⋊C4—371no—
234#388—371no—
235#388—371no—
236#388—371no—
237#388D3711yescharacteristic, complemented
238#385—371no—
239#385—371no—
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×C4—371no—
252#117—744no—
253C2×C4⋊C4—371no—
254C2×C4⋊C4—371no—
255C2×C4⋊C4—371no—
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—744no—
270C2×C22⋊C4C2×D3711yescharacteristic
271C2×C22⋊C4C2×D3711yescharacteristic
272C2×C22⋊C4C2×D3711yescharacteristic
273C2×C42—371no—
274C2×C42—371no—
275C2×C42—371no—
276C2×C42C2×D3711yescharacteristic, complemented
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—371no—
296C22×C4—371no—
297C22×C4—371no—
298C22×C4—374no—
299C22×C4—374no—
300C22×C4—371no—
301C22×C4—371no—
302C22×C4—371no—
303C22×C4—742no—
304C22×C4—742no—
305C22×C4—742no—
306C22×C4—742no—
307C22×C4—742no—
308C22×C4—742no—
309C22×C4—1481no—
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—41no—
320C4⋊C4—742no—
321C4⋊C4—742no—
322C4⋊C4—1481no—
323C22⋊C4—22no—
324C22⋊C4—41no—
325C22⋊C4—374no—
326C22⋊C4—374no—
327C22⋊C4—374no—
328C22⋊C4—374no—
329C22⋊C4—742no—
330C22⋊C4—742no—
331C22⋊C4—742no—
332C22⋊C4—742no—
333C22⋊C4—742no—
334C22⋊C4—742no—
335C22⋊C4—1481no—
336C22⋊C4C4×D3714yescomplemented
337C42—22no—
338C42—742no—
339C42—1481no—
340C42—1481no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—372no—
348C23—372no—
349C23—372no—
350C23—372no—
351C23—372no—
352C23—372no—
353C23—748no—
354C23—748no—
355C23—741no—
356C23—741no—
357C23—741no—
358C23—741no—
359C23—741no—
360C23—741no—
361C23—741no—
362C23—741no—
363C23—1484no—
364C23—1484no—
365C23—1484no—
366C23—1484no—
367C23—1484no—
368C23C2×C4×D3712yes—
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—372no—
386C2×C4—372no—
387C2×C4—372no—
388C2×C4—748no—
389C2×C4—741no—
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—1484no—
405C2×C4—1484no—
406C2×C4—1484no—
407C2×C4C2×C4×D3712yes—
408C2×C4C2×C4×D3712yes—
409C2×C4D4×D3712yes—
410C22—22no—
411C22—22no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—374no—
418C22—374no—
419C22—742no—
420C22—742no—
421C22—742no—
422C22—742no—
423C22—742no—
424C22—742no—
425C22—742no—
426C22—742no—
427C22—742no—
428C22—742no—
429C22—742no—
430C22—742no—
431C22—14816no—
432C22C22×C4×D3711yescharacteristic
433C22C2×D4×D3711yescharacteristic
434C22#41×D3711yescharacteristic
435C22#41×D3711yescharacteristic
436C22#41×D3711yescharacteristic
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—42no—
452C2—744no—
453C2—744no—
454C2#117×D3711yescharacteristic
455C2C4×D4×D3711yescharacteristic
456C2#1455800511yescharacteristic
457C2#1455817511yescharacteristic
458C2#1455818011yescharacteristic
459C2#1455820811yescharacteristic
460C2#1455821311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#388C2
socle, cosocleC23×C37C24
prime radicalC24×D37C22
hypercenter#388D37
hypocenterC37#2342
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#11924493C2semidirect
4. #14557427C2semidirect
5. #14557426C2semidirect
6. #14557421C2semidirect
7. #14557407C2semidirect
8. #14557404C2semidirect
9. #14557395C2semidirect
10. #14557390C2semidirect
12. C4×#10596938C2semidirect
13. #14557380C2semidirect
14. #14557380C2semidirect
15. C37×#388C2semidirect
22. C2×C4⋊Dic37C22semidirect
23. C2×#10596936C22semidirect
24. C2×#10596936C22semidirect
37. C22⋊C4×D37C4semidirect
38. C2×C4×Dic37C22semidirect
39. C2×C4×Dic37C22semidirect
40. C2×C4×Dic37C22semidirect
41. #11924443C22semidirect
42. #11924443C22semidirect
43. #11924443C22semidirect
44. #11924443C22semidirect
45. #11924443C22semidirect
46. #11924443C22semidirect
47. C2×C4⋊C4×C37C22semidirect
51. C2×C42×C37C22semidirect
52. #95×C37C22semidirect
53. #95×C37C22semidirect
86. C2×C4×D37C2×C4semidirect
87. C2×C4×D37C2×C4semidirect
91. C22⋊C4×C37C2×C4semidirect
95. C22⋊Dic37C2×C4semidirect
206. C2×D37#117semidirect
237. #388D37semidirect
246. C37#2342semidirect
256. C2×C4⋊C4C2×D37semidirect
276. C2×C42C2×D37semidirect
283. #95C2×D37semidirect
284. #95C2×D37semidirect
336. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119244932
C2×C22⋊C4×D372
#145574272
#145574262
#145574212
#145574072
#145574042
#145573952
#145573902
#145573882
C4×#105969382
#145573802
C37×#3882
#234237