Finite Group Databasebeta

← #16822310

Subgroups — #16822310

Order 3712.

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×D29C211yesmaximal, characteristic
2C2×C4×C22⋊D29C211yesmaximal, characteristic, complemented
3C2×#11745243C211yesmaximal, characteristic, complemented
4C22×#90781C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
6#14271063C211yesmaximal, characteristic, complemented
7#14271063C211yesmaximal, characteristic, complemented
8#14271043C211yesmaximal, characteristic, complemented
9#14271041C211yesmaximal, characteristic, complemented
10#14271041C211yesmaximal, characteristic, complemented
11#14271022C211yesmaximal, characteristic, complemented
12#14271018C211yesmaximal, characteristic, complemented
13#14271018C211yesmaximal, characteristic, complemented
14#14271010C211yesmaximal, characteristic, complemented
15C29×#386C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C24×D29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C23×C4×C29C2211yescharacteristic, complemented
20C22×C22⋊D29C2211yescharacteristic
21C22×C22⋊D29C2211yescharacteristic
22C23×Dic29C2211yescharacteristic, complemented
23C2×D4×D29—24no—
24C2×D4×D29—24no—
25C2×D4×D29C418yescomplemented
26C22×D116C2211yescharacteristic
27C22×C4×D29C2211yescharacteristic
28C22×C4×D29C2211yescharacteristic, complemented
29C22×C4×D29C2211yescharacteristic, complemented
30C2×C22⋊C4×C29C2211yescharacteristic, complemented
31C2×C22⋊C4×C29C2211yescharacteristic, complemented
32C2×C22⋊C4×C29C2211yescharacteristic, complemented
33C2×C22⋊Dic29C2211yescharacteristic, complemented
34C2×C22⋊Dic29C2211yescharacteristic, complemented
35C2×C22⋊Dic29C2211yescharacteristic, complemented
36C4×C22⋊D29—24no—
37C2×#90781—24no—
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×#90781C2211yescharacteristic
41C2×#90781C2211yescharacteristic
42C2×#90781C2211yescharacteristic, complemented
43C2×#90781C2211yescharacteristic, complemented
44C2×#90781C2211yescharacteristic, complemented
45C2×#90781C2211yescharacteristic, complemented
46C2×#90781C2211yescharacteristic, complemented
47C2×#90781C2211yescharacteristic, complemented
48C2×#90779C2211yescharacteristic, complemented
49C2×#90779C2211yescharacteristic, complemented
50C2×C4×Dic29C2211yescharacteristic, complemented
51C2×C4×Dic29C2211yescharacteristic, complemented
52#11745243—24no—
53C22⋊C4×D29—24no—
54C29×#95C2211yescharacteristic, complemented
55C29×#95C2211yescharacteristic, complemented
56#11745179C2211yescharacteristic, complemented
57#11745179C2211yescharacteristic, complemented
58C24×C29C2311yescharacteristic
59C24×C29C2311yescharacteristic
60C23×D29—22no—
61C23×D29—22no—
62C23×D29—22no—
63C23×D29—22no—
64C23×D29—22no—
65C23×D29—22no—
66C23×D29—22no—
67C23×D29—22no—
68C23×D29—41no—
69C23×D29—41no—
70C23×D29—41no—
71C23×D29—41no—
72C23×D29C2×C414yescomplemented
73C23×D29C2×C414yescomplemented
74C23×D29C2311yescharacteristic
75C23×D29C2311yescharacteristic
76C23×D29C2311yescharacteristic
77C2×D4×C29—22no—
78C2×D4×C29—22no—
79C2×D4×C29C2×C414yescomplemented
80C22×C4×C29—22no—
81C22×C4×C29—22no—
82C22×C4×C29—41no—
83C22×C4×C29C2311yescharacteristic
84C22×C4×C29C2311yescharacteristic
85C22×C4×C29C2311yescharacteristic
86C22×C4×C29C2311yescharacteristic
87C22×C4×C29C2311yescharacteristic
88C2×C22⋊D29—22no—
89C2×C22⋊D29—22no—
90C2×C22⋊D29C2×C414yes—
91C2×C22⋊D29C2×C414yescomplemented
92C2×C22⋊D29D414yes—
93C2×C22⋊D29D414yes—
94C22×Dic29—22no—
95C22×Dic29—22no—
96C22×Dic29—41no—
97C22×Dic29C2311yescharacteristic
98C22×Dic29C2311yescharacteristic
99C22×Dic29C2311yescharacteristic
100C22×Dic29C2311yescharacteristic
101C22×Dic29C2311yescharacteristic
102D4×D29—232no—
103C2×D116—22no—
104C2×D116—22no—
105C2×D116C2×C414yescomplemented
106C2×C4×D29—22no—
107C2×C4×D29—22no—
108C2×C4×D29—22no—
109C2×C4×D29—22no—
110C2×C4×D29—22no—
111C2×C4×D29—22no—
112C2×C4×D29—41no—
113C2×C4×D29—41no—
114C2×C4×D29C2×C414yescomplemented
115C22⋊C4×C29—22no—
116C22⋊C4×C29—22no—
117C22⋊C4×C29—41no—
118C22⋊Dic29—22no—
119C22⋊Dic29—22no—
120C22⋊Dic29—41no—
121#90781—22no—
122#90781—22no—
123#90781—22no—
124#90781—22no—
125#90781—22no—
126#90781—22no—
127#90781—22no—
128#90781—41no—
129#90781—41no—
130#90781D414yescomplemented
131#90779—22no—
132#90779—22no—
133C4×Dic29—22no—
134C4×Dic29—22no—
135C23×C29—21no—
136C23×C29—21no—
137C23×C29—21no—
138C23×C29—21no—
139C23×C29—21no—
140C23×C29—21no—
141C23×C29—21no—
142C23×C29—21no—
143C23×C29—21no—
144C23×C29—21no—
145C23×C29C22×C412yes—
146C23×C29C22×C412yes—
147C23×C29C2×D412yes—
148C23×C29C2×D412yes—
149C23×C29C2411yescharacteristic
150C22×D29—21no—
151C22×D29—21no—
152C22×D29—21no—
153C22×D29—21no—
154C22×D29—21no—
155C22×D29—21no—
156C22×D29—21no—
157C22×D29—21no—
158C22×D29—28no—
159C22×D29—21no—
160C22×D29—21no—
161C22×D29—21no—
162C22×D29—21no—
163C22×D29—21no—
164C22×D29—21no—
165C22×D29—28no—
166C22×D29—28no—
167C22×D29—28no—
168C22×D29—44no—
169C22×D29—44no—
170C22×D29—44no—
171C22×D29—44no—
172C22×D29—44no—
173C22×D29—44no—
174C22×D29—44no—
175C22×D29—44no—
176C22×D29—44no—
177C22×D29—44no—
178C22×D29C22×C412yes—
179C22×D29C22×C412yes—
180C22×D29C22×C412yes—
181C22×D29C2×D412yes—
182C22×D29C2×D412yes—
183C22×D29C2×D412yes—
184C22×D29#4112yes—
185D4×C29—28no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—21no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—44no—
200C2×C4×C29C22×C412yes—
201C2×C4×C29C2×D412yescomplemented
202C22⋊D29—28no—
203C22⋊D29C22⋊C4116yescomplemented
204C2×Dic29—21no—
205C2×Dic29—21no—
206C2×Dic29—21no—
207C2×Dic29—21no—
208C2×Dic29—21no—
209C2×Dic29—21no—
210C2×Dic29—21no—
211C2×Dic29—21no—
212C2×Dic29—21no—
213C2×Dic29—21no—
214C2×Dic29—21no—
215C2×Dic29—44no—
216C2×Dic29C22×C412yes—
217C2×Dic29C2×D412yes—
218C2×Dic29C2×D412yes—
219C2×Dic29C2×D412yescomplemented
220D116—28no—
221C4×D29—28no—
222C4×D29—44no—
223C4×D29—44no—
224D4×C22⋊C4—291nomaximal, Sylow
225C22×C29—22no—
226C22×C29—22no—
227C22×C29—22no—
228C22×C29—22no—
229C22×C29—22no—
230C22×C29—22no—
231C22×C29—22no—
232C22×C29—22no—
233C22×C29—22no—
234C22×C29—41no—
235C22×C29—41no—
236C22×C29—41no—
237C22×C29—41no—
238C22×C29C2×C22⋊C414yescomplemented
239C22×C29C23×C411yescharacteristic
240C22×C29C22×D411yescharacteristic
241C22×C29C22×D411yescharacteristic
242C22×C29C22×D411yescharacteristic
243C22×C29C2×#4111yescharacteristic
244C22×C29H(5,𝔽2)11yescharacteristic
245C22×C29H(5,𝔽2)11yescharacteristic
246C2×D29—22no—
247C2×D29—22no—
248C2×D29—22no—
249C2×D29—22no—
250C2×D29—22no—
251C2×D29—22no—
252C2×D29—22no—
253C2×D29—22no—
254C2×D29—22no—
255C2×D29—22no—
256C2×D29—22no—
257C2×D29—22no—
258C2×D29—22no—
259C2×D29—22no—
260C2×D29—22no—
261C2×D29—416no—
262C2×D29—416no—
263C2×D29—41no—
264C2×D29—41no—
265C2×D29—41no—
266C2×D29—41no—
267C2×D29C2×C22⋊C414yescomplemented
268C2×D29C4×D414yescomplemented
269C4×C29—22no—
270C4×C29—22no—
271C4×C29—41no—
272C4×C29—41no—
273C4×C29—41no—
274Dic29—22no—
275Dic29—41no—
276Dic29—41no—
277Dic29—41no—
278Dic29C2×C22⋊C414yescomplemented
279C23×D4—291no—
280C2×C4×D4—291no—
281C2×C4×D4—291no—
282C22×C22⋊C4—291no—
283C22×C22⋊C4—291no—
284#390—291no—
285#390—291no—
286#386—291no—
287#386—291no—
288#386—291no—
289#386D2911yescharacteristic, complemented
290#380—291no—
291#379—291no—
292#379—291no—
293C4×C22⋊C4—291no—
294C2×C29—24no—
295C2×C29—42no—
296C2×C29C22×C22⋊C411yescharacteristic
297C2×C29C2×C4×D411yescharacteristic
298C2×C29#51811yescharacteristic
299C2×C29D4211yescharacteristic
300C2×C29D4211yescharacteristic
301C2×C29#54611yescharacteristic
302C2×C29#54611yescharacteristic
303D29—24no—
304D29—24no—
305D29—42no—
306C25—291no—
307C25—291no—
308C22×D4—291no—
309C22×D4—291no—
310C22×D4—298no—
311C22×D4—291no—
312C22×D4—584no—
313C22×D4—584no—
314C22×D4C2×D2911yescharacteristic
315C23×C4—291no—
316C23×C4—291no—
317C23×C4—291no—
318C23×C4—291no—
319C23×C4C2×D2911yescharacteristic, complemented
320C4×D4—584no—
321C4×D4—584no—
322C2×C4⋊C4—291no—
323C2×C4⋊C4—291no—
324C2×C22⋊C4—291no—
325C2×C22⋊C4—291no—
326C2×C22⋊C4—291no—
327C2×C22⋊C4—291no—
328C2×C22⋊C4—291no—
329C2×C22⋊C4—291no—
330C2×C22⋊C4—291no—
331C2×C22⋊C4—291no—
332C2×C22⋊C4—291no—
333C2×C22⋊C4—291no—
334C2×C22⋊C4—291no—
335C2×C22⋊C4—291no—
336C2×C22⋊C4—291no—
337C2×C22⋊C4—584no—
338C2×C22⋊C4—584no—
339C2×C22⋊C4C2×D2911yescharacteristic, complemented
340C2×C22⋊C4C2×D2911yescharacteristic, complemented
341C2×C22⋊C4C2×D2911yescharacteristic, complemented
342C2×C42—291no—
343C2×C42—291no—
344#95—291no—
345#95—291no—
346#95C2×D2911yescharacteristic, complemented
347#95C2×D2911yescharacteristic, complemented
348C29D4×C22⋊C411yescharacteristic, complemented, Sylow
349C24—291no—
350C24—291no—
351C24—291no—
352C24—294no—
353C24—294no—
354C24—582no—
355C24—582no—
356C24—582no—
357C24—582no—
358C24—582no—
359C24—582no—
360C24—582no—
361C24—582no—
362C24—1161no—
363C24—1161no—
364C24—1161no—
365C24—1161no—
366C24C22×D2911yescharacteristic
367C24C22×D2911yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—294no—
371C2×D4—294no—
372C2×D4—294no—
373C2×D4—294no—
374C2×D4—294no—
375C2×D4—582no—
376C2×D4—582no—
377C2×D4—582no—
378C2×D4—582no—
379C2×D4—5832no—
380C2×D4C4×D2914yescomplemented
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4—291no—
385C22×C4—291no—
386C22×C4—294no—
387C22×C4—291no—
388C22×C4—291no—
389C22×C4—291no—
390C22×C4—582no—
391C22×C4—582no—
392C22×C4—582no—
393C22×C4—582no—
394C22×C4—582no—
395C22×C4—582no—
396C22×C4—582no—
397C22×C4—582no—
398C22×C4—1161no—
399C22×C4—1161no—
400C22×C4—1161no—
401C22×C4C22×D2911yescharacteristic
402C22×C4C22×D2911yescharacteristic
403C22×C4C22×D2911yescharacteristic
404C22×C4C22×D2911yescharacteristic
405C22×C4C22×D2911yescharacteristic
406C4⋊C4—582no—
407C4⋊C4—582no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—41no—
411C22⋊C4—294no—
412C22⋊C4—582no—
413C22⋊C4—582no—
414C22⋊C4—582no—
415C22⋊C4—582no—
416C22⋊C4—582no—
417C22⋊C4—582no—
418C22⋊C4—582no—
419C22⋊C4—582no—
420C22⋊C4—582no—
421C22⋊C4—1161no—
422C22⋊C4—1161no—
423C22⋊C4—1161no—
424C42—582no—
425C42—582no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—292no—
437C23—292no—
438C23—292no—
439C23—292no—
440C23—292no—
441C23—292no—
442C23—292no—
443C23—588no—
444C23—588no—
445C23—588no—
446C23—581no—
447C23—581no—
448C23—581no—
449C23—581no—
450C23—581no—
451C23—581no—
452C23—581no—
453C23—581no—
454C23—581no—
455C23—581no—
456C23—581no—
457C23—581no—
458C23—581no—
459C23—581no—
460C23—588no—
461C23—1164no—
462C23—1164no—
463C23—1164no—
464C23—1164no—
465C23—1164no—
466C23—1164no—
467C23—1164no—
468C23—1164no—
469C23—1164no—
470C23—1164no—
471C23C2×C4×D2912yes—
472C23C2×C4×D2912yes—
473C23D4×D2912yes—
474C23D4×D2912yes—
475C23C23×D2911yescharacteristic
476D4—28no—
477D4—2916no—
478D4—588no—
479D4—588no—
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—292no—
495C2×C4—292no—
496C2×C4—292no—
497C2×C4—292no—
498C2×C4—588no—
499C2×C4—581no—
500C2×C4—581no—
501C2×C4—581no—
502C2×C4—581no—
503C2×C4—581no—
504C2×C4—581no—
505C2×C4—581no—
506C2×C4—581no—
507C2×C4—581no—
508C2×C4—581no—
509C2×C4—581no—
510C2×C4—1164no—
511C2×C4—1164no—
512C2×C4—1164no—
513C2×C4C2×C4×D2912yes—
514C2×C4D4×D2912yescomplemented
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—294no—
529C22—294no—
530C22—582no—
531C22—582no—
532C22—582no—
533C22—582no—
534C22—582no—
535C22—582no—
536C22—582no—
537C22—582no—
538C22—582no—
539C22—582no—
540C22—582no—
541C22—582no—
542C22—582no—
543C22—582no—
544C22—582no—
545C22—11616no—
546C22—11616no—
547C22—1161no—
548C22—1161no—
549C22—1161no—
550C22—1161no—
551C22C22⋊C4×D2914yescomplemented
552C22C22×C4×D2911yescharacteristic
553C22C2×D4×D2911yescharacteristic
554C22C2×D4×D2911yescharacteristic
555C22C2×D4×D2911yescharacteristic
556C22#1174535911yescharacteristic
557C22#41×D2911yescharacteristic
558C22#1174536411yescharacteristic
559C4—22no—
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—294no—
565C4—582no—
566C4—1161no—
567C4—1161no—
568C4—1161no—
569C2—24no—
570C2—42no—
571C2—584no—
572C2—584no—
573C2—1162no—
574C2C2×C22⋊C4×D2911yescharacteristic
575C2C4×D4×D2911yescharacteristic
576C2#1427163511yescharacteristic
577C2#1427179511yescharacteristic
578C2#1427179711yescharacteristic
579C2#1427180211yescharacteristic
580C2#1427180511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#386C2
socle, cosocleC23×C29C24
prime radicalC22×D4×D29C2
hypercenter#386D29
hypocenterC29D4×C22⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D29C2semidirect
3. C2×#11745243C2semidirect
4. C22×#90781C2semidirect
5. C2×C22⋊C4×D29C2semidirect
6. #14271063C2semidirect
7. #14271063C2semidirect
8. #14271043C2semidirect
9. #14271041C2semidirect
10. #14271041C2semidirect
11. #14271022C2semidirect
12. #14271018C2semidirect
13. #14271018C2semidirect
14. #14271010C2semidirect
15. C29×#386C2semidirect
19. C23×C4×C29C22semidirect
22. C23×Dic29C22semidirect
25. C2×D4×D29C4semidirect
28. C22×C4×D29C22semidirect
29. C22×C4×D29C22semidirect
30. C2×C22⋊C4×C29C22semidirect
31. C2×C22⋊C4×C29C22semidirect
32. C2×C22⋊C4×C29C22semidirect
33. C2×C22⋊Dic29C22semidirect
34. C2×C22⋊Dic29C22semidirect
35. C2×C22⋊Dic29C22semidirect
42. C2×#90781C22semidirect
43. C2×#90781C22semidirect
44. C2×#90781C22semidirect
45. C2×#90781C22semidirect
46. C2×#90781C22semidirect
47. C2×#90781C22semidirect
48. C2×#90779C22semidirect
49. C2×#90779C22semidirect
50. C2×C4×Dic29C22semidirect
51. C2×C4×Dic29C22semidirect
54. C29×#95C22semidirect
55. C29×#95C22semidirect
56. #11745179C22semidirect
57. #11745179C22semidirect
72. C23×D29C2×C4semidirect
73. C23×D29C2×C4semidirect
79. C2×D4×C29C2×C4semidirect
91. C2×C22⋊D29C2×C4semidirect
105. C2×D116C2×C4semidirect
114. C2×C4×D29C2×C4semidirect
130. #90781D4semidirect
201. C2×C4×C29C2×D4semidirect
203. C22⋊D29C22⋊C4semidirect
219. C2×Dic29C2×D4semidirect
238. C22×C29C2×C22⋊C4semidirect
267. C2×D29C2×C22⋊C4semidirect
268. C2×D29C4×D4semidirect
278. Dic29C2×C22⋊C4semidirect
289. #386D29semidirect
319. C23×C4C2×D29semidirect
339. C2×C22⋊C4C2×D29semidirect
340. C2×C22⋊C4C2×D29semidirect
341. C2×C22⋊C4C2×D29semidirect
346. #95C2×D29semidirect
347. #95C2×D29semidirect
348. C29D4×C22⋊C4semidirect
380. C2×D4C4×D29semidirect
514. C2×C4D4×D29semidirect
551. C22C22⋊C4×D29semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D292
C2×C4×C22⋊D292
C2×#117452432
C22×#907812
C2×C22⋊C4×D292
#142710632
#142710432
#142710412
#142710222
#142710182
#142710102
C29×#3862
D4×C22⋊C429