Finite Group Databasebeta

← #16822865

Subgroups — #16822865

Order 3712.

1246 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D29C211yesmaximal, characteristic, complemented
2C2×#11745292C211yesmaximal, characteristic, complemented
3C2×#11745301C211yesmaximal, characteristic, complemented
4C2×#11745244C211yesmaximal, characteristic, complemented
5C2×#11745244C211yesmaximal, characteristic, complemented
6C22×#90781C211yesmaximal, characteristic, complemented
7#14271081C211yesmaximal, characteristic, complemented
8#14271079C211yesmaximal, characteristic, complemented
9#14271073C211yesmaximal, characteristic, complemented
10#14271072C211yesmaximal, characteristic, complemented
11#14271041C211yesmaximal, characteristic, complemented
12#14271040C211yesmaximal, characteristic, complemented
13#14271037C211yesmaximal, characteristic, complemented
14#14271018C211yesmaximal, characteristic, complemented
15C29×#386C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C24×D29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C23×C4×C29C2211yescharacteristic, complemented
20C22×C22⋊D29C2211yescharacteristic
21C22×C22⋊D29C2211yescharacteristic
22C22×C22⋊D29C2211yescharacteristic, complemented
23C22×C22⋊D29C2211yescharacteristic, complemented
24C23×Dic29C2211yescharacteristic, complemented
25C2×D4×D29—24no—
26C2×D4×D29—24no—
27C2×D4×D29—24no—
28C22×D116C2211yescharacteristic
29C22×D116C2211yescharacteristic
30C22×D116C2211yescharacteristic, complemented
31C22×D116C2211yescharacteristic, complemented
32C22×C4×D29C2211yescharacteristic
33C2×C22⋊C4×C29C2211yescharacteristic, complemented
34C2×C22⋊C4×C29C2211yescharacteristic, complemented
35C2×C22⋊C4×C29C2211yescharacteristic, complemented
36C2×C22⋊Dic29C2211yescharacteristic, complemented
37#11745301—24no—
38#11745292—24no—
39C2×#90781—24no—
40C2×#90781C2211yescharacteristic
41C2×#90781C2211yescharacteristic
42C2×#90781C2211yescharacteristic
43C2×#90781C2211yescharacteristic, complemented
44C2×#90781C2211yescharacteristic, complemented
45C2×#90781C2211yescharacteristic, complemented
46C2×#90781C2211yescharacteristic, complemented
47C2×#90781C2211yescharacteristic, complemented
48C2×#90781C2211yescharacteristic, complemented
49C2×#90781C2211yescharacteristic, complemented
50C2×#90781C2211yescharacteristic, complemented
51C2×C4⋊Dic29C2211yescharacteristic, complemented
52C2×#90779C2211yescharacteristic, complemented
53#11745244—24no—
54#11745244—24no—
55C29×#95C2211yescharacteristic, complemented
56C29×#95C2211yescharacteristic, complemented
57#11745179C2211yescharacteristic, complemented
58#11745179C2211yescharacteristic, complemented
59C24×C29C2311yescharacteristic
60C24×C29C2311yescharacteristic
61C23×D29—22no—
62C23×D29—22no—
63C23×D29—22no—
64C23×D29—22no—
65C23×D29—22no—
66C23×D29—22no—
67C23×D29—22no—
68C23×D29—22no—
69C23×D29—22no—
70C23×D29—41no—
71C23×D29—41no—
72C23×D29—41no—
73C23×D29—41no—
74C23×D29D414yescomplemented
75C23×D29C2311yescharacteristic
76C23×D29C2311yescharacteristic
77C23×D29C2311yescharacteristic
78C23×D29C2311yescharacteristic
79C2×D4×C29—22no—
80C2×D4×C29—22no—
81C2×D4×C29D414yescomplemented
82C22×C4×C29—22no—
83C22×C4×C29—22no—
84C22×C4×C29—41no—
85C22×C4×C29C2311yescharacteristic
86C22×C4×C29C2311yescharacteristic
87C22×C4×C29C2311yescharacteristic
88C22×C4×C29C2311yescharacteristic
89C22×C4×C29C2311yescharacteristic
90C2×C22⋊D29—22no—
91C2×C22⋊D29—22no—
92C2×C22⋊D29—22no—
93C2×C22⋊D29—22no—
94C2×C22⋊D29—22no—
95C2×C22⋊D29—22no—
96C2×C22⋊D29—22no—
97C2×C22⋊D29—22no—
98C2×C22⋊D29—22no—
99C2×C22⋊D29—22no—
100C2×C22⋊D29—41no—
101C2×C22⋊D29D414yescomplemented
102C22×Dic29—22no—
103C22×Dic29—22no—
104C22×Dic29—41no—
105C22×Dic29C2311yescharacteristic
106C22×Dic29C2311yescharacteristic
107C22×Dic29C2311yescharacteristic
108C22×Dic29C2311yescharacteristic
109D4×D29—232no—
110C2×D116—22no—
111C2×D116—22no—
112C2×D116—22no—
113C2×D116—22no—
114C2×D116—22no—
115C2×D116—22no—
116C2×D116—22no—
117C2×D116—22no—
118C2×D116—22no—
119C2×D116—41no—
120C2×D116—41no—
121C2×D116—41no—
122C2×C4×D29—22no—
123C2×C4×D29—22no—
124C2×C4×D29—22no—
125C22⋊C4×C29—22no—
126C22⋊C4×C29—22no—
127C22⋊C4×C29—41no—
128C22⋊Dic29—22no—
129#90781—22no—
130#90781—22no—
131#90781—22no—
132#90781—22no—
133#90781—22no—
134#90781—22no—
135#90781—22no—
136#90781—22no—
137#90781—22no—
138#90781—41no—
139#90781D414yescomplemented
140C4⋊Dic29—22no—
141#90779—22no—
142C23×C29—21no—
143C23×C29—21no—
144C23×C29—21no—
145C23×C29—21no—
146C23×C29—21no—
147C23×C29—21no—
148C23×C29—21no—
149C23×C29—21no—
150C23×C29—21no—
151C23×C29—21no—
152C23×C29C2×D412yes—
153C23×C29C2×D412yes—
154C23×C29C2×D412yes—
155C23×C29C2×D412yes—
156C23×C29C2411yescharacteristic
157C22×D29—21no—
158C22×D29—21no—
159C22×D29—21no—
160C22×D29—21no—
161C22×D29—28no—
162C22×D29—28no—
163C22×D29—21no—
164C22×D29—21no—
165C22×D29—21no—
166C22×D29—21no—
167C22×D29—21no—
168C22×D29—21no—
169C22×D29—21no—
170C22×D29—21no—
171C22×D29—21no—
172C22×D29—21no—
173C22×D29—21no—
174C22×D29—21no—
175C22×D29—28no—
176C22×D29—21no—
177C22×D29—21no—
178C22×D29—21no—
179C22×D29—21no—
180C22×D29—21no—
181C22×D29—21no—
182C22×D29—21no—
183C22×D29—44no—
184C22×D29—44no—
185C22×D29—44no—
186C22×D29—44no—
187C22×D29—44no—
188C22×D29—44no—
189C22×D29—44no—
190C22×D29—44no—
191C22×D29—44no—
192C22×D29—44no—
193C22×D29—44no—
194C22×D29C2×D412yes—
195C22×D29C2×D412yes—
196C22×D29C2×D412yes—
197C22×D29C2×D412yes—
198C22×D29#4112yes—
199D4×C29—28no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—21no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—44no—
214C2×C4×C29C2×D412yes—
215C2×C4×C29C2×D412yescomplemented
216C22⋊D29—28no—
217C22⋊D29—28no—
218C22⋊D29—44no—
219C22⋊D29—44no—
220C2×Dic29—21no—
221C2×Dic29—21no—
222C2×Dic29—21no—
223C2×Dic29—21no—
224C2×Dic29—21no—
225C2×Dic29—21no—
226C2×Dic29—21no—
227C2×Dic29—21no—
228C2×Dic29—21no—
229C2×Dic29—21no—
230C2×Dic29—44no—
231C2×Dic29C2×D412yes—
232C2×Dic29C2×D412yescomplemented
233D116—28no—
234D116—44no—
235D116—44no—
236D116—44no—
237C4×D29—28no—
238#2410—291nomaximal, Sylow
239C22×C29—22no—
240C22×C29—22no—
241C22×C29—22no—
242C22×C29—22no—
243C22×C29—22no—
244C22×C29—22no—
245C22×C29—22no—
246C22×C29—22no—
247C22×C29—22no—
248C22×C29—41no—
249C22×C29—41no—
250C22×C29—41no—
251C22×C29—41no—
252C22×C29#12014yescomplemented
253C22×C29C22×D411yescharacteristic
254C22×C29C22×D411yescharacteristic
255C22×C29C22×D411yescharacteristic
256C22×C29C22×D411yescharacteristic
257C22×C29C2×#4111yescharacteristic
258C22×C29H(5,𝔽2)11yescharacteristic
259C22×C29H(5,𝔽2)11yescharacteristic
260C2×D29—22no—
261C2×D29—22no—
262C2×D29—22no—
263C2×D29—22no—
264C2×D29—22no—
265C2×D29—22no—
266C2×D29—22no—
267C2×D29—22no—
268C2×D29—22no—
269C2×D29—22no—
270C2×D29—22no—
271C2×D29—22no—
272C2×D29—416no—
273C2×D29—416no—
274C2×D29—41no—
275C2×D29—41no—
276C2×D29—41no—
277C2×D29—41no—
278C2×D29—41no—
279C2×D29—41no—
280C2×D29—41no—
281C2×D29—41no—
282C2×D29—41no—
283C2×D29—41no—
284C2×D29—41no—
285C2×D29—41no—
286C2×D29—41no—
287C2×D29—41no—
288C2×D29—41no—
289C2×D29#12114yescomplemented
290C4×C29—22no—
291C4×C29—22no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295Dic29—22no—
296Dic29—22no—
297Dic29—41no—
298Dic29—41no—
299C23×D4—291no—
300C2×#121—291no—
301C2×#121—291no—
302C2×#120—291no—
303C2×#120—291no—
304C22×C22⋊C4—291no—
305#394—291no—
306#394—291no—
307#392—291no—
308#392—291no—
309#386—291no—
310#386—291no—
311#386D2911yescharacteristic, complemented
312#385—291no—
313#379—291no—
314C2×C29—24no—
315C2×C29—42no—
316C2×C29C2×#12011yescharacteristic
317C2×C29C2×#12111yescharacteristic
318C2×C29#53411yescharacteristic
319C2×C29D4211yescharacteristic
320C2×C29D4211yescharacteristic
321C2×C29#54611yescharacteristic
322C2×C29#54611yescharacteristic
323D29—24no—
324D29—42no—
325D29—42no—
326D29—81no—
327C25—291no—
328C25—291no—
329C22×D4—291no—
330C22×D4—291no—
331C22×D4—291no—
332C22×D4—291no—
333C22×D4—291no—
334C22×D4—291no—
335C22×D4—291no—
336C22×D4—291no—
337C22×D4—584no—
338C22×D4—584no—
339C22×D4—584no—
340C22×D4C2×D2911yescharacteristic
341C23×C4—291no—
342C23×C4—291no—
343C23×C4C2×D2911yescharacteristic, complemented
344#121—584no—
345#121—584no—
346#120—584no—
347#120—584no—
348C2×C4⋊C4—291no—
349C2×C4⋊C4—291no—
350C2×C22⋊C4—291no—
351C2×C22⋊C4—291no—
352C2×C22⋊C4—291no—
353C2×C22⋊C4—291no—
354C2×C22⋊C4—291no—
355C2×C22⋊C4—291no—
356C2×C22⋊C4—291no—
357C2×C22⋊C4—291no—
358C2×C22⋊C4—291no—
359C2×C22⋊C4—291no—
360C2×C22⋊C4—291no—
361C2×C22⋊C4—291no—
362C2×C22⋊C4—584no—
363C2×C22⋊C4C2×D2911yescharacteristic, complemented
364C2×C22⋊C4C2×D2911yescharacteristic, complemented
365C2×C22⋊C4C2×D2911yescharacteristic, complemented
366#95—291no—
367#95—291no—
368#95C2×D2911yescharacteristic, complemented
369#95C2×D2911yescharacteristic, complemented
370C29#241011yescharacteristic, complemented, Sylow
371C24—291no—
372C24—291no—
373C24—291no—
374C24—294no—
375C24—291no—
376C24—582no—
377C24—582no—
378C24—582no—
379C24—582no—
380C24—582no—
381C24—582no—
382C24—582no—
383C24—582no—
384C24—582no—
385C24—1161no—
386C24—1161no—
387C24—1161no—
388C24—1161no—
389C24C22×D2911yescharacteristic
390C24C22×D2911yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—294no—
394C2×D4—582no—
395C2×D4—582no—
396C2×D4—582no—
397C2×D4—582no—
398C2×D4—582no—
399C2×D4—582no—
400C2×D4—582no—
401C2×D4—582no—
402C2×D4—582no—
403C2×D4—5832no—
404C2×D4—582no—
405C2×D4—582no—
406C2×D4—582no—
407C2×D4—582no—
408C2×D4—582no—
409C2×D4—582no—
410C2×D4—582no—
411C2×D4—582no—
412C2×D4—582no—
413C2×D4—582no—
414C2×D4—1161no—
415C2×D4—1161no—
416C2×D4—1161no—
417C2×D4—1161no—
418C2×D4D11614yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—41no—
422C22×C4—291no—
423C22×C4—291no—
424C22×C4—291no—
425C22×C4—291no—
426C22×C4—582no—
427C22×C4—582no—
428C22×C4—582no—
429C22×C4—582no—
430C22×C4—582no—
431C22×C4—1161no—
432C22×C4C22×D2911yescharacteristic
433C22×C4C22×D2911yescharacteristic
434C22×C4C22×D2911yescharacteristic
435C22×C4C22×D2911yescharacteristic
436C22×C4C22×D2911yescharacteristic
437C4⋊C4—582no—
438C4⋊C4—582no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—294no—
443C22⋊C4—582no—
444C22⋊C4—582no—
445C22⋊C4—582no—
446C22⋊C4—582no—
447C22⋊C4—582no—
448C22⋊C4—582no—
449C22⋊C4—582no—
450C22⋊C4—582no—
451C22⋊C4—582no—
452C22⋊C4—582no—
453C22⋊C4—1161no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—292no—
465C23—292no—
466C23—292no—
467C23—292no—
468C23—292no—
469C23—588no—
470C23—588no—
471C23—581no—
472C23—581no—
473C23—581no—
474C23—581no—
475C23—581no—
476C23—581no—
477C23—581no—
478C23—581no—
479C23—581no—
480C23—581no—
481C23—581no—
482C23—581no—
483C23—581no—
484C23—581no—
485C23—581no—
486C23—581no—
487C23—588no—
488C23—581no—
489C23—581no—
490C23—581no—
491C23—581no—
492C23—581no—
493C23—581no—
494C23—581no—
495C23—1164no—
496C23—1164no—
497C23—1164no—
498C23—1164no—
499C23—1164no—
500C23—1164no—
501C23—1164no—
502C23—1164no—
503C23—1164no—
504C23—1164no—
505C23—1164no—
506C23C2×D11612yes—
507C23C2×D11612yes—
508C23D4×D2912yes—
509C23D4×D2912yes—
510C23C23×D2911yescharacteristic
511D4—28no—
512D4—588no—
513D4—588no—
514D4—588no—
515D4—1164no—
516D4—1164no—
517D4—1164no—
518D4—1164no—
519D4—1164no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—44no—
534C2×C4—292no—
535C2×C4—292no—
536C2×C4—588no—
537C2×C4—581no—
538C2×C4—581no—
539C2×C4—581no—
540C2×C4—581no—
541C2×C4—581no—
542C2×C4—581no—
543C2×C4—581no—
544C2×C4—581no—
545C2×C4—581no—
546C2×C4—581no—
547C2×C4—1164no—
548C2×C4C2×D11612yes—
549C2×C4D4×D2912yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—294no—
564C22—582no—
565C22—582no—
566C22—582no—
567C22—582no—
568C22—582no—
569C22—582no—
570C22—582no—
571C22—582no—
572C22—582no—
573C22—582no—
574C22—582no—
575C22—582no—
576C22—11616no—
577C22—11616no—
578C22—1161no—
579C22—1161no—
580C22—1161no—
581C22—1161no—
582C22—1161no—
583C22—1161no—
584C22—1161no—
585C22—1161no—
586C22—1161no—
587C22—1161no—
588C22—1161no—
589C22—1161no—
590C22—1161no—
591C22—1161no—
592C22—1161no—
593C22#1174524414yescomplemented
594C22C22×D11611yescharacteristic
595C22C2×D4×D2911yescharacteristic
596C22C2×D4×D2911yescharacteristic
597C22C2×D4×D2911yescharacteristic
598C22#1174535911yescharacteristic
599C22#41×D2911yescharacteristic
600C22#1174536411yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—582no—
607C4—582no—
608C4—1161no—
609C4—1161no—
610C2—24no—
611C2—42no—
612C2—584no—
613C2—1162no—
614C2—1162no—
615C2—2321no—
616C2C2×#1174524411yescharacteristic
617C2#121×D2911yescharacteristic
618C2#1427172111yescharacteristic
619C2#1427179511yescharacteristic
620C2D4×D11611yescharacteristic
621C2#1427180511yescharacteristic
622C2#1427180811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#386C2
hypercenter#386D29
hypocenterC29#2410
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×#11745292C2semidirect
3. C2×#11745301C2semidirect
4. C2×#11745244C2semidirect
5. C2×#11745244C2semidirect
6. C22×#90781C2semidirect
7. #14271081C2semidirect
8. #14271079C2semidirect
9. #14271073C2semidirect
10. #14271072C2semidirect
11. #14271041C2semidirect
12. #14271040C2semidirect
13. #14271037C2semidirect
14. #14271018C2semidirect
15. C29×#386C2semidirect
19. C23×C4×C29C22semidirect
22. C22×C22⋊D29C22semidirect
23. C22×C22⋊D29C22semidirect
24. C23×Dic29C22semidirect
30. C22×D116C22semidirect
31. C22×D116C22semidirect
33. C2×C22⋊C4×C29C22semidirect
34. C2×C22⋊C4×C29C22semidirect
35. C2×C22⋊C4×C29C22semidirect
36. C2×C22⋊Dic29C22semidirect
43. C2×#90781C22semidirect
44. C2×#90781C22semidirect
45. C2×#90781C22semidirect
46. C2×#90781C22semidirect
47. C2×#90781C22semidirect
48. C2×#90781C22semidirect
49. C2×#90781C22semidirect
50. C2×#90781C22semidirect
51. C2×C4⋊Dic29C22semidirect
52. C2×#90779C22semidirect
55. C29×#95C22semidirect
56. C29×#95C22semidirect
57. #11745179C22semidirect
58. #11745179C22semidirect
74. C23×D29D4semidirect
81. C2×D4×C29D4semidirect
101. C2×C22⋊D29D4semidirect
139. #90781D4semidirect
215. C2×C4×C29C2×D4semidirect
232. C2×Dic29C2×D4semidirect
252. C22×C29#120semidirect
289. C2×D29#121semidirect
311. #386D29semidirect
343. C23×C4C2×D29semidirect
363. C2×C22⋊C4C2×D29semidirect
364. C2×C22⋊C4C2×D29semidirect
365. C2×C22⋊C4C2×D29semidirect
368. #95C2×D29semidirect
369. #95C2×D29semidirect
370. C29#2410semidirect
418. C2×D4D116semidirect
549. C2×C4D4×D29semidirect
593. C22#11745244semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D292
C2×#117452922
C2×#117453012
C2×#117452442
C22×#907812
#142710812
#142710792
#142710732
#142710722
#142710412
#142710402
#142710372
#142710182
C29×#3862
#241029