Finite Group Databasebeta

← #16822859

Subgroups — #16822859

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×#11745246C211yesmaximal, characteristic, complemented
3C2×#11745300C211yesmaximal, characteristic, complemented
4C2×#11745299C211yesmaximal, characteristic, complemented
5C2×#11745299C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
7#14271079C211yesmaximal, characteristic, complemented
8#14271077C211yesmaximal, characteristic, complemented
9#14271071C211yesmaximal, characteristic, complemented
10#14271041C211yesmaximal, characteristic, complemented
11#14271039C211yesmaximal, characteristic, complemented
12#14271039C211yesmaximal, characteristic, complemented
13#14271037C211yesmaximal, characteristic, complemented
14#14271018C211yesmaximal, characteristic, complemented
15C29×#392C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C24×D29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C22×D4×C29C2211yescharacteristic, complemented
20C22×D4×C29C2211yescharacteristic, complemented
21C22×C22⋊D29C2211yescharacteristic
22C22×C22⋊D29C2211yescharacteristic
23C22×C22⋊D29C2211yescharacteristic
24C22×C22⋊D29C2211yescharacteristic, complemented
25C22×C22⋊D29C2211yescharacteristic, complemented
26C2×D4×D29—24no—
27C2×D4×D29—24no—
28C2×D4×D29—24no—
29C22×D116C2211yescharacteristic
30C22×C4×D29C2211yescharacteristic
31C22×C4×D29C2211yescharacteristic, complemented
32C22×C4×D29C2211yescharacteristic, complemented
33C2×C22⋊C4×C29C2211yescharacteristic, complemented
34C2×C22⋊C4×C29C2211yescharacteristic, complemented
35C2×C22⋊C4×C29C2211yescharacteristic, complemented
36C2×C22⋊Dic29C2211yescharacteristic, complemented
37C2×C22⋊Dic29C2211yescharacteristic, complemented
38C2×C22⋊Dic29C2211yescharacteristic, complemented
39C2×C22⋊Dic29C2211yescharacteristic, complemented
40C2×C22⋊Dic29C2211yescharacteristic, complemented
41#11745300—24no—
42#11745299—24no—
43#11745299—24no—
44C2×#90781C2211yescharacteristic
45C2×#90781C2211yescharacteristic
46C2×#90781C2211yescharacteristic
47C2×#90781C2211yescharacteristic, complemented
48C2×#90781C2211yescharacteristic, complemented
49C2×#90781C2211yescharacteristic, complemented
50C2×#90781C2211yescharacteristic, complemented
51C2×C4⋊Dic29C2211yescharacteristic, complemented
52C2×#90779C2211yescharacteristic, complemented
53#11745246—24no—
54C22⋊C4×D29—24no—
55C29×#95C2211yescharacteristic, complemented
56#11745179C2211yescharacteristic, complemented
57#11745179C2211yescharacteristic, complemented
58#11745179C2211yescharacteristic, complemented
59C24×C29C2311yescharacteristic
60C24×C29C2311yescharacteristic
61C24×C29C2311yescharacteristic
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—22no—
71C23×D29—41no—
72C23×D29—41no—
73C23×D29—41no—
74C23×D29—41no—
75C23×D29D414yescomplemented
76C23×D29C2311yescharacteristic
77C23×D29C2311yescharacteristic
78C23×D29C2311yescharacteristic
79C2×D4×C29—22no—
80C2×D4×C29—22no—
81C2×D4×C29—22no—
82C2×D4×C29—22no—
83C2×D4×C29—22no—
84C2×D4×C29—22no—
85C2×D4×C29—41no—
86C2×D4×C29—41no—
87C2×D4×C29—41no—
88C22×C4×C29C2311yescharacteristic
89C22×C4×C29C2311yescharacteristic
90C22×C4×C29C2311yescharacteristic
91C22×C4×C29C2311yescharacteristic
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—22no—
101C2×C22⋊D29—22no—
102C2×C22⋊D29—22no—
103C2×C22⋊D29—22no—
104C2×C22⋊D29—22no—
105C2×C22⋊D29—41no—
106C2×C22⋊D29D414yescomplemented
107C22×Dic29C2311yescharacteristic
108C22×Dic29C2311yescharacteristic
109C22×Dic29C2311yescharacteristic
110C22×Dic29C2311yescharacteristic
111C22×Dic29C2311yescharacteristic
112D4×D29—232no—
113C2×D116—22no—
114C2×D116—22no—
115C2×D116D414yescomplemented
116C2×C4×D29—22no—
117C2×C4×D29—22no—
118C2×C4×D29—22no—
119C2×C4×D29—22no—
120C2×C4×D29—22no—
121C2×C4×D29—22no—
122C2×C4×D29—22no—
123C2×C4×D29—41no—
124C2×C4×D29—41no—
125C22⋊C4×C29—22no—
126C22⋊C4×C29—22no—
127C22⋊C4×C29—41no—
128C22⋊Dic29—22no—
129C22⋊Dic29—22no—
130C22⋊Dic29—22no—
131C22⋊Dic29—22no—
132C22⋊Dic29—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×C29—21no—
153C23×C29—21no—
154C23×C29—21no—
155C23×C29—21no—
156C23×C29—21no—
157C23×C29—21no—
158C23×C29—21no—
159C23×C29—21no—
160C23×C29—21no—
161C23×C29C2×D412yes—
162C23×C29C2×D412yes—
163C23×C29C2411yescharacteristic
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—28no—
173C22×D29—21no—
174C22×D29—21no—
175C22×D29—21no—
176C22×D29—21no—
177C22×D29—21no—
178C22×D29—21no—
179C22×D29—28no—
180C22×D29—28no—
181C22×D29—44no—
182C22×D29—44no—
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×D29C2×D412yes—
193C22×D29C2×D412yes—
194C22×D29C2×D412yes—
195C22×D29C2×D412yes—
196C22×D29C2×D412yes—
197C22×D29C2×D412yes—
198C22×D29#4112yes—
199D4×C29—28no—
200D4×C29—44no—
201D4×C29—44no—
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×C29C2×D412yes—
213C2×C4×C29C2×D412yescomplemented
214C22⋊D29—28no—
215C22⋊D29—28no—
216C22⋊D29—44no—
217C22⋊D29—44no—
218C22⋊D29—44no—
219C2×Dic29—21no—
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—21no—
231C2×Dic29—21no—
232C2×Dic29C2×D412yes—
233C2×Dic29C2×D412yescomplemented
234D116—28no—
235C4×D29—28no—
236C4×D29—44no—
237C4×D29—44no—
238#2410—291nomaximal, Sylow
239C22×C29—22no—
240C22×C29—22no—
241C22×C29—22no—
242C22×C29—22no—
243C22×C29—22no—
244C22×C29—22no—
245C22×C29—41no—
246C22×C29—41no—
247C22×C29—41no—
248C22×C29—41no—
249C22×C29—41no—
250C22×C29—41no—
251C22×C29—41no—
252C22×C29—41no—
253C22×C29—41no—
254C22×C29—41no—
255C22×C29—41no—
256C22×C29—41no—
257C22×C29—41no—
258C22×C29—41no—
259C22×C29—41no—
260C22×C29C22×D411yescharacteristic
261C22×C29C22×D411yescharacteristic
262C22×C29C22×D411yescharacteristic
263C22×C29C22×D411yescharacteristic
264C22×C29C2×#4111yescharacteristic
265C22×C29H(5,𝔽2)11yescharacteristic
266C22×C29H(5,𝔽2)11yescharacteristic
267C2×D29—22no—
268C2×D29—22no—
269C2×D29—22no—
270C2×D29—22no—
271C2×D29—22no—
272C2×D29—22no—
273C2×D29—22no—
274C2×D29—22no—
275C2×D29—22no—
276C2×D29—22no—
277C2×D29—22no—
278C2×D29—22no—
279C2×D29—22no—
280C2×D29—22no—
281C2×D29—22no—
282C2×D29—416no—
283C2×D29—416no—
284C2×D29—41no—
285C2×D29—41no—
286C2×D29—41no—
287C2×D29—41no—
288C2×D29#12014yescomplemented
289C2×D29#12114yescomplemented
290C4×C29—22no—
291C4×C29—22no—
292C4×C29—41no—
293C4×C29—41no—
294Dic29—22no—
295Dic29—22no—
296Dic29—41no—
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#392D2911yescharacteristic, complemented
309#386—291no—
310#386—291no—
311#386—291no—
312#385—291no—
313#379—291no—
314C2×C29—42no—
315C2×C29—42no—
316C2×C29—81no—
317C2×C29C2×#12011yescharacteristic
318C2×C29C2×#12111yescharacteristic
319C2×C29#53411yescharacteristic
320C2×C29D4211yescharacteristic
321C2×C29D4211yescharacteristic
322C2×C29#54611yescharacteristic
323C2×C29#54611yescharacteristic
324D29—24no—
325D29—24no—
326D29—42no—
327C25—291no—
328C25—291no—
329C22×D4—291no—
330C22×D4—291no—
331C22×D4—291no—
332C22×D4—291no—
333C22×D4—291no—
334C22×D4—291no—
335C22×D4—584no—
336C22×D4—584no—
337C22×D4—584no—
338C22×D4C2×D2911yescharacteristic
339C22×D4C2×D2911yescharacteristic, complemented
340C22×D4C2×D2911yescharacteristic, complemented
341C23×C4—291no—
342C23×C4—291no—
343C23×C4—291no—
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#95—291no—
369#95C2×D2911yescharacteristic, complemented
370C29#241011yescharacteristic, complemented, Sylow
371C24—291no—
372C24—291no—
373C24—291no—
374C24—294no—
375C24—582no—
376C24—582no—
377C24—582no—
378C24—582no—
379C24—582no—
380C24—582no—
381C24—582no—
382C24—582no—
383C24—582no—
384C24—1161no—
385C24—1161no—
386C24—1161no—
387C24—1161no—
388C24C22×D2911yescharacteristic
389C24C22×D2911yescharacteristic
390C24C22×D2911yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—294no—
401C2×D4—294no—
402C2×D4—582no—
403C2×D4—582no—
404C2×D4—582no—
405C2×D4—582no—
406C2×D4—5832no—
407C2×D4—582no—
408C2×D4—582no—
409C2×D4—582no—
410C2×D4—582no—
411C2×D4—582no—
412C2×D4—582no—
413C2×D4—582no—
414C2×D4—582no—
415C2×D4—582no—
416C2×D4—582no—
417C2×D4—582no—
418C2×D4—1161no—
419C22×C4—291no—
420C22×C4—291no—
421C22×C4—291no—
422C22×C4—291no—
423C22×C4—291no—
424C22×C4—582no—
425C22×C4—582no—
426C22×C4—582no—
427C22×C4—582no—
428C22×C4—582no—
429C22×C4—582no—
430C22×C4—582no—
431C22×C4—1161no—
432C22×C4—1161no—
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—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—292no—
474C23—292no—
475C23—292no—
476C23—292no—
477C23—292no—
478C23—292no—
479C23—292no—
480C23—588no—
481C23—588no—
482C23—588no—
483C23—581no—
484C23—581no—
485C23—581no—
486C23—581no—
487C23—581no—
488C23—581no—
489C23—581no—
490C23—581no—
491C23—581no—
492C23—581no—
493C23—581no—
494C23—581no—
495C23—581no—
496C23—581no—
497C23—1164no—
498C23—1164no—
499C23—1164no—
500C23—1164no—
501C23—1164no—
502C23—1164no—
503C23—1164no—
504C23—1164no—
505C23—1164no—
506C23—1164no—
507C23—1164no—
508C23D4×D2912yes—
509C23D4×D2912yes—
510C23C23×D2911yescharacteristic
511D4—28no—
512D4—44no—
513D4—44no—
514D4—588no—
515D4—588no—
516D4—588no—
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—292no—
531C2×C4—292no—
532C2×C4—588no—
533C2×C4—581no—
534C2×C4—581no—
535C2×C4—581no—
536C2×C4—581no—
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—1164no—
547C2×C4—1164no—
548C2×C4D4×D2912yes—
549C2×C4D4×D2912yescomplemented
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—294no—
572C22—294no—
573C22—582no—
574C22—582no—
575C22—582no—
576C22—582no—
577C22—582no—
578C22—582no—
579C22—582no—
580C22—582no—
581C22—582no—
582C22—582no—
583C22—582no—
584C22—582no—
585C22—582no—
586C22—582no—
587C22—582no—
588C22—11616no—
589C22—11616no—
590C22—1161no—
591C22—1161no—
592C22—1161no—
593C22—1161no—
594C22C2×D4×D2911yescharacteristic
595C22C2×D4×D2911yescharacteristic
596C22C2×D4×D2911yescharacteristic
597C22C2×D4×D2911yescharacteristic
598C22#1174535911yescharacteristic
599C22#1174535911yescharacteristic
600C22#41×D2911yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—582no—
606C4—582no—
607C4—1161no—
608C4—1161no—
609C4—1161no—
610C2—42no—
611C2—42no—
612C2—81no—
613C2—584no—
614C2—584no—
615C2—1162no—
616C2#120×D2911yescharacteristic
617C2#121×D2911yescharacteristic
618C2#1427172311yescharacteristic
619C2#1427179511yescharacteristic
620C2#1427179811yescharacteristic
621C2#1427180211yescharacteristic
622C2#1427181011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#392C2
hypercenter#392D29
hypocenterC29#2410
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×#11745246C2semidirect
3. C2×#11745300C2semidirect
4. C2×#11745299C2semidirect
5. C2×#11745299C2semidirect
6. C2×C22⋊C4×D29C2semidirect
7. #14271079C2semidirect
8. #14271077C2semidirect
9. #14271071C2semidirect
10. #14271041C2semidirect
11. #14271039C2semidirect
12. #14271039C2semidirect
13. #14271037C2semidirect
14. #14271018C2semidirect
15. C29×#392C2semidirect
19. C22×D4×C29C22semidirect
20. C22×D4×C29C22semidirect
24. C22×C22⋊D29C22semidirect
25. C22×C22⋊D29C22semidirect
31. C22×C4×D29C22semidirect
32. C22×C4×D29C22semidirect
33. C2×C22⋊C4×C29C22semidirect
34. C2×C22⋊C4×C29C22semidirect
35. C2×C22⋊C4×C29C22semidirect
36. C2×C22⋊Dic29C22semidirect
37. C2×C22⋊Dic29C22semidirect
38. C2×C22⋊Dic29C22semidirect
39. C2×C22⋊Dic29C22semidirect
40. C2×C22⋊Dic29C22semidirect
47. C2×#90781C22semidirect
48. C2×#90781C22semidirect
49. C2×#90781C22semidirect
50. C2×#90781C22semidirect
51. C2×C4⋊Dic29C22semidirect
52. C2×#90779C22semidirect
55. C29×#95C22semidirect
56. #11745179C22semidirect
57. #11745179C22semidirect
58. #11745179C22semidirect
75. C23×D29D4semidirect
106. C2×C22⋊D29D4semidirect
115. C2×D116D4semidirect
139. #90781D4semidirect
213. C2×C4×C29C2×D4semidirect
233. C2×Dic29C2×D4semidirect
288. C2×D29#120semidirect
289. C2×D29#121semidirect
308. #392D29semidirect
339. C22×D4C2×D29semidirect
340. C22×D4C2×D29semidirect
363. C2×C22⋊C4C2×D29semidirect
364. C2×C22⋊C4C2×D29semidirect
365. C2×C22⋊C4C2×D29semidirect
369. #95C2×D29semidirect
370. C29#2410semidirect
549. C2×C4D4×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×#117452462
C2×#117453002
C2×#117452992
C2×C22⋊C4×D292
#142710792
#142710772
#142710712
#142710412
#142710392
#142710372
#142710182
C29×#3922
#241029