Finite Group Databasebeta

← #17997414

Subgroups — #17997414

Order 4736.

1252 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D37C211yesmaximal, characteristic
2C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
3C2×#11924496C211yesmaximal, characteristic, complemented
4C22×#10596938C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D37C211yesmaximal, characteristic, complemented
6#14557433C211yesmaximal, characteristic, complemented
7#14557433C211yesmaximal, characteristic, complemented
8#14557413C211yesmaximal, characteristic, complemented
9#14557411C211yesmaximal, characteristic, complemented
10#14557411C211yesmaximal, characteristic, complemented
11#14557392C211yesmaximal, characteristic, complemented
12#14557388C211yesmaximal, characteristic, complemented
13#14557388C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#386C211yesmaximal, characteristic, complemented
16C24×D37C2211yescharacteristic
17C24×D37C2211yescharacteristic
18C22×D148C2211yescharacteristic
19C22×C22⋊D37C2211yescharacteristic
20C22×C22⋊D37C2211yescharacteristic
21C2×D4×D37—24no—
22C2×D4×D37—24no—
23C2×D4×D37C418yescomplemented
24C23×Dic37C2211yescharacteristic, complemented
25C22×C4×D37C2211yescharacteristic
26C22×C4×D37C2211yescharacteristic, complemented
27C22×C4×D37C2211yescharacteristic, complemented
28C4×C22⋊D37—24no—
29#11924496—24no—
30C2×#10596936C2211yescharacteristic, complemented
31C2×#10596936C2211yescharacteristic, complemented
32C2×C22⋊Dic37C2211yescharacteristic, complemented
33C2×C22⋊Dic37C2211yescharacteristic, complemented
34C2×C22⋊Dic37C2211yescharacteristic, complemented
35C2×#10596938—24no—
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic
38C2×#10596938C2211yescharacteristic
39C2×#10596938C2211yescharacteristic
40C2×#10596938C2211yescharacteristic, complemented
41C2×#10596938C2211yescharacteristic, complemented
42C2×#10596938C2211yescharacteristic, complemented
43C2×#10596938C2211yescharacteristic, complemented
44C2×#10596938C2211yescharacteristic, complemented
45C2×#10596938C2211yescharacteristic, complemented
46C22⋊C4×D37—24no—
47C2×C4×Dic37C2211yescharacteristic, complemented
48C2×C4×Dic37C2211yescharacteristic, complemented
49#11924443C2211yescharacteristic, complemented
50#11924443C2211yescharacteristic, complemented
51C22×D4×C37C2211yescharacteristic
52C23×C4×C37C2211yescharacteristic, complemented
53C2×C22⋊C4×C37C2211yescharacteristic, complemented
54C2×C22⋊C4×C37C2211yescharacteristic, complemented
55C2×C22⋊C4×C37C2211yescharacteristic, complemented
56#95×C37C2211yescharacteristic, complemented
57#95×C37C2211yescharacteristic, complemented
58C24×C37C2311yescharacteristic
59C24×C37C2311yescharacteristic
60C23×D37—22no—
61C23×D37—22no—
62C23×D37—22no—
63C23×D37—22no—
64C23×D37—22no—
65C23×D37—22no—
66C23×D37—22no—
67C23×D37—22no—
68C23×D37—41no—
69C23×D37—41no—
70C23×D37—41no—
71C23×D37—41no—
72C23×D37C2×C414yescomplemented
73C23×D37C2×C414yescomplemented
74C23×D37C2311yescharacteristic
75C23×D37C2311yescharacteristic
76C23×D37C2311yescharacteristic
77C2×D4×C37—22no—
78C2×D4×C37—22no—
79C2×D4×C37C2×C414yescomplemented
80C22×C4×C37—22no—
81C22×C4×C37—22no—
82C22×C4×C37—41no—
83C22×C4×C37C2311yescharacteristic
84C22×C4×C37C2311yescharacteristic
85C22×C4×C37C2311yescharacteristic
86C22×C4×C37C2311yescharacteristic
87C22×C4×C37C2311yescharacteristic
88C2×C22⋊D37—22no—
89C2×C22⋊D37—22no—
90C2×C22⋊D37C2×C414yes—
91C2×C22⋊D37C2×C414yescomplemented
92C2×C22⋊D37D414yes—
93C2×C22⋊D37D414yes—
94C22×Dic37—22no—
95C22×Dic37—22no—
96C22×Dic37—41no—
97C22×Dic37C2311yescharacteristic
98C22×Dic37C2311yescharacteristic
99C22×Dic37C2311yescharacteristic
100C22×Dic37C2311yescharacteristic
101C22×Dic37C2311yescharacteristic
102D4×D37—232no—
103C2×D148—22no—
104C2×D148—22no—
105C2×D148C2×C414yescomplemented
106C2×C4×D37—22no—
107C2×C4×D37—22no—
108C2×C4×D37—22no—
109C2×C4×D37—22no—
110C2×C4×D37—22no—
111C2×C4×D37—22no—
112C2×C4×D37—41no—
113C2×C4×D37—41no—
114C2×C4×D37C2×C414yescomplemented
115C22⋊C4×C37—22no—
116C22⋊C4×C37—22no—
117C22⋊C4×C37—41no—
118C22⋊Dic37—22no—
119C22⋊Dic37—22no—
120C22⋊Dic37—41no—
121#10596938—22no—
122#10596938—22no—
123#10596938—22no—
124#10596938—22no—
125#10596938—22no—
126#10596938—22no—
127#10596938—22no—
128#10596938—41no—
129#10596938—41no—
130#10596938D414yescomplemented
131#10596936—22no—
132#10596936—22no—
133C4×Dic37—22no—
134C4×Dic37—22no—
135C23×C37—21no—
136C23×C37—21no—
137C23×C37—21no—
138C23×C37—21no—
139C23×C37—21no—
140C23×C37—21no—
141C23×C37—21no—
142C23×C37—21no—
143C23×C37—21no—
144C23×C37—21no—
145C23×C37C22×C412yes—
146C23×C37C22×C412yes—
147C23×C37C2×D412yes—
148C23×C37C2×D412yes—
149C23×C37C2411yescharacteristic
150C22×D37—21no—
151C22×D37—21no—
152C22×D37—21no—
153C22×D37—21no—
154C22×D37—21no—
155C22×D37—21no—
156C22×D37—21no—
157C22×D37—21no—
158C22×D37—28no—
159C22×D37—21no—
160C22×D37—21no—
161C22×D37—21no—
162C22×D37—21no—
163C22×D37—21no—
164C22×D37—21no—
165C22×D37—28no—
166C22×D37—28no—
167C22×D37—28no—
168C22×D37—44no—
169C22×D37—44no—
170C22×D37—44no—
171C22×D37—44no—
172C22×D37—44no—
173C22×D37—44no—
174C22×D37—44no—
175C22×D37—44no—
176C22×D37—44no—
177C22×D37—44no—
178C22×D37C22×C412yes—
179C22×D37C22×C412yes—
180C22×D37C22×C412yes—
181C22×D37C2×D412yes—
182C22×D37C2×D412yes—
183C22×D37C2×D412yes—
184C22×D37#4112yes—
185D4×C37—28no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—21no—
189C2×C4×C37—21no—
190C2×C4×C37—21no—
191C2×C4×C37—21no—
192C2×C4×C37—21no—
193C2×C4×C37—21no—
194C2×C4×C37—21no—
195C2×C4×C37—21no—
196C2×C4×C37—21no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—44no—
200C2×C4×C37C22×C412yes—
201C2×C4×C37C2×D412yescomplemented
202C22⋊D37—28no—
203C22⋊D37C22⋊C4116yescomplemented
204C2×Dic37—21no—
205C2×Dic37—21no—
206C2×Dic37—21no—
207C2×Dic37—21no—
208C2×Dic37—21no—
209C2×Dic37—21no—
210C2×Dic37—21no—
211C2×Dic37—21no—
212C2×Dic37—21no—
213C2×Dic37—21no—
214C2×Dic37—21no—
215C2×Dic37—44no—
216C2×Dic37C22×C412yes—
217C2×Dic37C2×D412yes—
218C2×Dic37C2×D412yes—
219C2×Dic37C2×D412yescomplemented
220D148—28no—
221C4×D37—28no—
222C4×D37—44no—
223C4×D37—44no—
224C22×C37—22no—
225C22×C37—22no—
226C22×C37—22no—
227C22×C37—22no—
228C22×C37—22no—
229C22×C37—22no—
230C22×C37—22no—
231C22×C37—22no—
232C22×C37—22no—
233C22×C37—41no—
234C22×C37—41no—
235C22×C37—41no—
236C22×C37—41no—
237C22×C37C2×C22⋊C414yescomplemented
238C22×C37C23×C411yescharacteristic
239C22×C37C22×D411yescharacteristic
240C22×C37C22×D411yescharacteristic
241C22×C37C22×D411yescharacteristic
242C22×C37C2×#4111yescharacteristic
243C22×C37H(5,𝔽2)11yescharacteristic
244C22×C37H(5,𝔽2)11yescharacteristic
245C2×D37—22no—
246C2×D37—22no—
247C2×D37—22no—
248C2×D37—22no—
249C2×D37—22no—
250C2×D37—22no—
251C2×D37—22no—
252C2×D37—22no—
253C2×D37—22no—
254C2×D37—22no—
255C2×D37—22no—
256C2×D37—22no—
257C2×D37—22no—
258C2×D37—22no—
259C2×D37—22no—
260C2×D37—416no—
261C2×D37—416no—
262C2×D37—41no—
263C2×D37—41no—
264C2×D37—41no—
265C2×D37—41no—
266C2×D37C2×C22⋊C414yescomplemented
267C2×D37C4×D414yescomplemented
268C4×C37—22no—
269C4×C37—22no—
270C4×C37—41no—
271C4×C37—41no—
272C4×C37—41no—
273Dic37—22no—
274Dic37—41no—
275Dic37—41no—
276Dic37—41no—
277Dic37C2×C22⋊C414yescomplemented
278D4×C22⋊C4—371nomaximal, Sylow
279C2×C37—24no—
280C2×C37—42no—
281C2×C37C22×C22⋊C411yescharacteristic
282C2×C37C2×C4×D411yescharacteristic
283C2×C37#51811yescharacteristic
284C2×C37D4211yescharacteristic
285C2×C37D4211yescharacteristic
286C2×C37#54611yescharacteristic
287C2×C37#54611yescharacteristic
288D37—24no—
289D37—24no—
290D37—42no—
291C23×D4—371no—
292C2×C4×D4—371no—
293C2×C4×D4—371no—
294C22×C22⋊C4—371no—
295C22×C22⋊C4—371no—
296#390—371no—
297#390—371no—
298#386—371no—
299#386—371no—
300#386—371no—
301#386D3711yescharacteristic, complemented
302#380—371no—
303#379—371no—
304#379—371no—
305C4×C22⋊C4—371no—
306C37D4×C22⋊C411yescharacteristic, complemented, Sylow
307C25—371no—
308C25—371no—
309C22×D4—371no—
310C22×D4—371no—
311C22×D4—378no—
312C22×D4—371no—
313C22×D4—744no—
314C22×D4—744no—
315C22×D4C2×D3711yescharacteristic
316C23×C4—371no—
317C23×C4—371no—
318C23×C4—371no—
319C23×C4—371no—
320C23×C4C2×D3711yescharacteristic, complemented
321C4×D4—744no—
322C4×D4—744no—
323C2×C4⋊C4—371no—
324C2×C4⋊C4—371no—
325C2×C22⋊C4—371no—
326C2×C22⋊C4—371no—
327C2×C22⋊C4—371no—
328C2×C22⋊C4—371no—
329C2×C22⋊C4—371no—
330C2×C22⋊C4—371no—
331C2×C22⋊C4—371no—
332C2×C22⋊C4—371no—
333C2×C22⋊C4—371no—
334C2×C22⋊C4—371no—
335C2×C22⋊C4—371no—
336C2×C22⋊C4—371no—
337C2×C22⋊C4—371no—
338C2×C22⋊C4—744no—
339C2×C22⋊C4—744no—
340C2×C22⋊C4C2×D3711yescharacteristic, complemented
341C2×C22⋊C4C2×D3711yescharacteristic, complemented
342C2×C22⋊C4C2×D3711yescharacteristic, complemented
343C2×C42—371no—
344C2×C42—371no—
345#95—371no—
346#95—371no—
347#95C2×D3711yescharacteristic, complemented
348#95C2×D3711yescharacteristic, complemented
349C24—371no—
350C24—371no—
351C24—371no—
352C24—374no—
353C24—374no—
354C24—742no—
355C24—742no—
356C24—742no—
357C24—742no—
358C24—742no—
359C24—742no—
360C24—742no—
361C24—742no—
362C24—1481no—
363C24—1481no—
364C24—1481no—
365C24—1481no—
366C24C22×D3711yescharacteristic
367C24C22×D3711yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—374no—
371C2×D4—374no—
372C2×D4—374no—
373C2×D4—374no—
374C2×D4—374no—
375C2×D4—742no—
376C2×D4—742no—
377C2×D4—742no—
378C2×D4—742no—
379C2×D4—7432no—
380C2×D4C4×D3714yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—371no—
385C22×C4—371no—
386C22×C4—374no—
387C22×C4—371no—
388C22×C4—371no—
389C22×C4—371no—
390C22×C4—742no—
391C22×C4—742no—
392C22×C4—742no—
393C22×C4—742no—
394C22×C4—742no—
395C22×C4—742no—
396C22×C4—742no—
397C22×C4—742no—
398C22×C4—1481no—
399C22×C4—1481no—
400C22×C4—1481no—
401C22×C4C22×D3711yescharacteristic
402C22×C4C22×D3711yescharacteristic
403C22×C4C22×D3711yescharacteristic
404C22×C4C22×D3711yescharacteristic
405C22×C4C22×D3711yescharacteristic
406C4⋊C4—742no—
407C4⋊C4—742no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—374no—
412C22⋊C4—742no—
413C22⋊C4—742no—
414C22⋊C4—742no—
415C22⋊C4—742no—
416C22⋊C4—742no—
417C22⋊C4—742no—
418C22⋊C4—742no—
419C22⋊C4—742no—
420C22⋊C4—742no—
421C22⋊C4—1481no—
422C22⋊C4—1481no—
423C22⋊C4—1481no—
424C42—742no—
425C42—742no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—372no—
437C23—372no—
438C23—372no—
439C23—372no—
440C23—372no—
441C23—372no—
442C23—372no—
443C23—748no—
444C23—748no—
445C23—748no—
446C23—741no—
447C23—741no—
448C23—741no—
449C23—741no—
450C23—741no—
451C23—741no—
452C23—741no—
453C23—741no—
454C23—748no—
455C23—741no—
456C23—741no—
457C23—741no—
458C23—741no—
459C23—741no—
460C23—741no—
461C23—1484no—
462C23—1484no—
463C23—1484no—
464C23—1484no—
465C23—1484no—
466C23—1484no—
467C23—1484no—
468C23—1484no—
469C23—1484no—
470C23—1484no—
471C23C2×C4×D3712yes—
472C23C2×C4×D3712yes—
473C23D4×D3712yes—
474C23D4×D3712yes—
475C23C23×D3711yescharacteristic
476D4—28no—
477D4—3716no—
478D4—748no—
479D4—748no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—44no—
494C2×C4—372no—
495C2×C4—372no—
496C2×C4—372no—
497C2×C4—372no—
498C2×C4—748no—
499C2×C4—741no—
500C2×C4—741no—
501C2×C4—741no—
502C2×C4—741no—
503C2×C4—741no—
504C2×C4—741no—
505C2×C4—741no—
506C2×C4—741no—
507C2×C4—741no—
508C2×C4—741no—
509C2×C4—741no—
510C2×C4—1484no—
511C2×C4—1484no—
512C2×C4—1484no—
513C2×C4C2×C4×D3712yes—
514C2×C4D4×D3712yescomplemented
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—374no—
529C22—374no—
530C22—742no—
531C22—742no—
532C22—742no—
533C22—742no—
534C22—742no—
535C22—742no—
536C22—742no—
537C22—742no—
538C22—742no—
539C22—742no—
540C22—742no—
541C22—742no—
542C22—742no—
543C22—742no—
544C22—742no—
545C22—14816no—
546C22—14816no—
547C22—1481no—
548C22—1481no—
549C22—1481no—
550C22—1481no—
551C22C22⋊C4×D3714yescomplemented
552C22C22×C4×D3711yescharacteristic
553C22C2×D4×D3711yescharacteristic
554C22C2×D4×D3711yescharacteristic
555C22C2×D4×D3711yescharacteristic
556C22#41×D3711yescharacteristic
557C22#1192458111yescharacteristic
558C22#1192458211yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—374no—
565C4—742no—
566C4—1481no—
567C4—1481no—
568C4—1481no—
569C2—24no—
570C2—42no—
571C2—744no—
572C2—744no—
573C2—1482no—
574C2C2×C22⋊C4×D3711yescharacteristic
575C2C4×D4×D3711yescharacteristic
576C2#1455800511yescharacteristic
577C2#1455816511yescharacteristic
578C2#1455816711yescharacteristic
579C2#1455817211yescharacteristic
580C2#1455817511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#386C2
socle, cosocleC23×C37C24
prime radicalC22×D4×D37C2
hypercenter#386D37
hypocenterC37D4×C22⋊C4
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D37C2semidirect
3. C2×#11924496C2semidirect
4. C22×#10596938C2semidirect
5. C2×C22⋊C4×D37C2semidirect
6. #14557433C2semidirect
7. #14557433C2semidirect
8. #14557413C2semidirect
9. #14557411C2semidirect
10. #14557411C2semidirect
11. #14557392C2semidirect
12. #14557388C2semidirect
13. #14557388C2semidirect
14. #14557380C2semidirect
15. C37×#386C2semidirect
23. C2×D4×D37C4semidirect
24. C23×Dic37C22semidirect
26. C22×C4×D37C22semidirect
27. C22×C4×D37C22semidirect
30. C2×#10596936C22semidirect
31. C2×#10596936C22semidirect
32. C2×C22⋊Dic37C22semidirect
33. C2×C22⋊Dic37C22semidirect
34. C2×C22⋊Dic37C22semidirect
40. C2×#10596938C22semidirect
41. C2×#10596938C22semidirect
42. C2×#10596938C22semidirect
43. C2×#10596938C22semidirect
44. C2×#10596938C22semidirect
45. C2×#10596938C22semidirect
47. C2×C4×Dic37C22semidirect
48. C2×C4×Dic37C22semidirect
49. #11924443C22semidirect
50. #11924443C22semidirect
52. C23×C4×C37C22semidirect
53. C2×C22⋊C4×C37C22semidirect
54. C2×C22⋊C4×C37C22semidirect
55. C2×C22⋊C4×C37C22semidirect
56. #95×C37C22semidirect
57. #95×C37C22semidirect
72. C23×D37C2×C4semidirect
73. C23×D37C2×C4semidirect
79. C2×D4×C37C2×C4semidirect
91. C2×C22⋊D37C2×C4semidirect
105. C2×D148C2×C4semidirect
114. C2×C4×D37C2×C4semidirect
130. #10596938D4semidirect
201. C2×C4×C37C2×D4semidirect
203. C22⋊D37C22⋊C4semidirect
219. C2×Dic37C2×D4semidirect
237. C22×C37C2×C22⋊C4semidirect
266. C2×D37C2×C22⋊C4semidirect
267. C2×D37C4×D4semidirect
277. Dic37C2×C22⋊C4semidirect
301. #386D37semidirect
306. C37D4×C22⋊C4semidirect
320. C23×C4C2×D37semidirect
340. C2×C22⋊C4C2×D37semidirect
341. C2×C22⋊C4C2×D37semidirect
342. C2×C22⋊C4C2×D37semidirect
347. #95C2×D37semidirect
348. #95C2×D37semidirect
380. C2×D4C4×D37semidirect
514. C2×C4D4×D37semidirect
551. C22C22⋊C4×D37semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D372
C2×C4×C22⋊D372
C2×#119244962
C22×#105969382
C2×C22⋊C4×D372
#145574332
#145574132
#145574112
#145573922
#145573882
#145573802
C37×#3862
D4×C22⋊C437