Finite Group Databasebeta

← #16822861

Subgroups — #16822861

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×#11745257C211yesmaximal, characteristic, complemented
3C2×#11745246C211yesmaximal, characteristic, complemented
4C2×#11745244C211yesmaximal, characteristic, complemented
5C2×#11745244C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D29C211yesmaximal, characteristic, complemented
7#14271078C211yesmaximal, characteristic, complemented
8#14271072C211yesmaximal, characteristic, complemented
9#14271071C211yesmaximal, characteristic, complemented
10#14271041C211yesmaximal, characteristic, complemented
11#14271041C211yesmaximal, characteristic, complemented
12#14271039C211yesmaximal, characteristic, complemented
13#14271034C211yesmaximal, characteristic, complemented
14#14271018C211yesmaximal, characteristic, complemented
15C29×#394C211yesmaximal, characteristic, complemented
16C24×D29C2211yescharacteristic
17C24×D29C2211yescharacteristic
18C22×D4×C29C2211yescharacteristic
19C22×C22⋊D29C2211yescharacteristic
20C22×C22⋊D29C2211yescharacteristic
21C22×C22⋊D29C2211yescharacteristic, complemented
22C22×C22⋊D29C2211yescharacteristic, complemented
23C2×D4×D29—24no—
24C2×D4×D29—24no—
25C2×D4×D29—24no—
26C22×D116C2211yescharacteristic
27C22×D116C2211yescharacteristic
28C22×D116C2211yescharacteristic, complemented
29C22×D116C2211yescharacteristic, complemented
30C22×C4×D29C2211yescharacteristic
31C22×C4×D29C2211yescharacteristic, complemented
32C22×C4×D29C2211yescharacteristic, complemented
33C2×C4⋊C4×C29C2211yescharacteristic, complemented
34C2×C22⋊C4×C29C2211yescharacteristic, complemented
35C2×C22⋊C4×C29C2211yescharacteristic, complemented
36C2×C22⋊C4×C29C2211yescharacteristic, complemented
37C2×C22⋊C4×C29C2211yescharacteristic, complemented
38C2×C22⋊Dic29C2211yescharacteristic, complemented
39C2×C22⋊Dic29C2211yescharacteristic, complemented
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×#90779C2211yescharacteristic, complemented
50#11745257—24no—
51#11745246—24no—
52#11745244—24no—
53#11745244—24no—
54C22⋊C4×D29—24no—
55C29×#95C2211yescharacteristic, complemented
56#11745179C2211yescharacteristic, 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×C29—22no—
82C22×C4×C29C2311yescharacteristic
83C22×C4×C29C2311yescharacteristic
84C22×C4×C29C2311yescharacteristic
85C22×C4×C29C2311yescharacteristic
86C22×C4×C29C2311yescharacteristic
87C2×C22⋊D29—22no—
88C2×C22⋊D29—22no—
89C2×C22⋊D29—22no—
90C2×C22⋊D29—22no—
91C2×C22⋊D29—22no—
92C2×C22⋊D29—22no—
93C2×C22⋊D29—22no—
94C2×C22⋊D29—22no—
95C2×C22⋊D29—41no—
96C2×C22⋊D29—41no—
97C2×C22⋊D29—41no—
98C2×C22⋊D29D414yescomplemented
99C22×Dic29C2311yescharacteristic
100C22×Dic29C2311yescharacteristic
101C22×Dic29C2311yescharacteristic
102C22×Dic29C2311yescharacteristic
103D4×D29—232no—
104C2×D116—22no—
105C2×D116—22no—
106C2×D116—22no—
107C2×D116—22no—
108C2×D116—22no—
109C2×D116—22no—
110C2×D116—22no—
111C2×D116—22no—
112C2×D116—22no—
113C2×D116—22no—
114C2×D116—41no—
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—
125C4⋊C4×C29—22no—
126C22⋊C4×C29—22no—
127C22⋊C4×C29—22no—
128C22⋊C4×C29—22no—
129C22⋊C4×C29—22no—
130C22⋊Dic29—22no—
131C22⋊Dic29—41no—
132#90781—22no—
133#90781—22no—
134#90781—22no—
135#90781—22no—
136#90781—22no—
137#90781—22no—
138#90781—22no—
139#90781—41no—
140#90781D414yescomplemented
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×C29C2×D412yes—
155C23×C29C2×D412yes—
156C23×C29C2411yescharacteristic
157C22×D29—21no—
158C22×D29—21no—
159C22×D29—21no—
160C22×D29—21no—
161C22×D29—21no—
162C22×D29—21no—
163C22×D29—21no—
164C22×D29—21no—
165C22×D29—28no—
166C22×D29—21no—
167C22×D29—21no—
168C22×D29—21no—
169C22×D29—21no—
170C22×D29—21no—
171C22×D29—21no—
172C22×D29—28no—
173C22×D29—28no—
174C22×D29—21no—
175C22×D29—21no—
176C22×D29—21no—
177C22×D29—21no—
178C22×D29—21no—
179C22×D29—21no—
180C22×D29—21no—
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—
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×C29C2×D412yes—
214C2×C4×C29C2×D412yescomplemented
215C22⋊D29—28no—
216C22⋊D29—28no—
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×Dic29C2×D412yes—
230C2×Dic29C2×D412yescomplemented
231D116—28no—
232D116—44no—
233D116—44no—
234D116—44no—
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×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—22no—
273C2×D29—22no—
274C2×D29—22no—
275C2×D29—416no—
276C2×D29—416no—
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#12014yescomplemented
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#394D2911yescharacteristic, complemented
307#392—291no—
308#392—291no—
309#386—291no—
310#386—291no—
311#386—291no—
312#385—291no—
313#379—291no—
314C2×C29—42no—
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—24no—
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×C4—291no—
344#121—584no—
345#121—584no—
346#120—584no—
347#120—584no—
348C2×C4⋊C4—291no—
349C2×C4⋊C4C2×D2911yescharacteristic, complemented
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—584no—
362C2×C22⋊C4C2×D2911yescharacteristic, complemented
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—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—22no—
394C2×D4—294no—
395C2×D4—294no—
396C2×D4—582no—
397C2×D4—582no—
398C2×D4—582no—
399C2×D4—582no—
400C2×D4—582no—
401C2×D4—582no—
402C2×D4—582no—
403C2×D4—582no—
404C2×D4—582no—
405C2×D4—582no—
406C2×D4—582no—
407C2×D4—5832no—
408C2×D4—582no—
409C2×D4—582no—
410C2×D4—582no—
411C2×D4—582no—
412C2×D4—582no—
413C2×D4—582no—
414C2×D4—582no—
415C2×D4—1161no—
416C2×D4—1161no—
417C2×D4—1161no—
418C2×D4—1161no—
419C22×C4—291no—
420C22×C4—291no—
421C22×C4—291no—
422C22×C4—291no—
423C22×C4—582no—
424C22×C4—582no—
425C22×C4—582no—
426C22×C4—582no—
427C22×C4—582no—
428C22×C4—582no—
429C22×C4—582no—
430C22×C4—1161no—
431C22×C4—1161no—
432C22×C4C22×D2911yescharacteristic
433C22×C4C22×D2911yescharacteristic
434C22×C4C22×D2911yescharacteristic
435C22×C4C22×D2911yescharacteristic
436C22×C4C22×D2911yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—582no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—294no—
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—1161no—
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—292no—
467C23—292no—
468C23—292no—
469C23—292no—
470C23—292no—
471C23—292no—
472C23—292no—
473C23—588no—
474C23—588no—
475C23—588no—
476C23—581no—
477C23—581no—
478C23—581no—
479C23—581no—
480C23—581no—
481C23—581no—
482C23—581no—
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—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—292no—
534C2×C4—292no—
535C2×C4—588no—
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—294no—
565C22—294no—
566C22—582no—
567C22—582no—
568C22—582no—
569C22—582no—
570C22—582no—
571C22—582no—
572C22—582no—
573C22—582no—
574C22—582no—
575C22—582no—
576C22—582no—
577C22—582no—
578C22—582no—
579C22—582no—
580C22—582no—
581C22—11616no—
582C22—11616no—
583C22—1161no—
584C22—1161no—
585C22—1161no—
586C22—1161no—
587C22—1161no—
588C22—1161no—
589C22—1161no—
590C22—1161no—
591C22—1161no—
592C22—1161no—
593C22—1161no—
594C22C2×D4×D2911yescharacteristic
595C22C2×D4×D2911yescharacteristic
596C22C2×D4×D2911yescharacteristic
597C22C2×D4×D2911yescharacteristic
598C22#41×D2911yescharacteristic
599C22#1174536411yescharacteristic
600C22#1174536411yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—582no—
607C4—582no—
608C4—1161no—
609C4—1161no—
610C2—42no—
611C2—42no—
612C2—584no—
613C2—584no—
614C2—1162no—
615C2—2321no—
616C2#120×D2911yescharacteristic
617C2#121×D2911yescharacteristic
618C2#1427172411yescharacteristic
619C2#1427179711yescharacteristic
620C2#1427179711yescharacteristic
621C2#1427180511yescharacteristic
622C2#1427180611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#394C2
hypercenter#394D29
hypocenterC29#2410
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×#11745257C2semidirect
3. C2×#11745246C2semidirect
4. C2×#11745244C2semidirect
5. C2×#11745244C2semidirect
6. C2×C22⋊C4×D29C2semidirect
7. #14271078C2semidirect
8. #14271072C2semidirect
9. #14271071C2semidirect
10. #14271041C2semidirect
11. #14271041C2semidirect
12. #14271039C2semidirect
13. #14271034C2semidirect
14. #14271018C2semidirect
15. C29×#394C2semidirect
21. C22×C22⋊D29C22semidirect
22. C22×C22⋊D29C22semidirect
28. C22×D116C22semidirect
29. C22×D116C22semidirect
31. C22×C4×D29C22semidirect
32. C22×C4×D29C22semidirect
33. C2×C4⋊C4×C29C22semidirect
34. C2×C22⋊C4×C29C22semidirect
35. C2×C22⋊C4×C29C22semidirect
36. C2×C22⋊C4×C29C22semidirect
37. C2×C22⋊C4×C29C22semidirect
38. C2×C22⋊Dic29C22semidirect
39. C2×C22⋊Dic29C22semidirect
43. C2×#90781C22semidirect
44. C2×#90781C22semidirect
45. C2×#90781C22semidirect
46. C2×#90781C22semidirect
47. C2×#90781C22semidirect
48. C2×#90781C22semidirect
49. C2×#90779C22semidirect
55. C29×#95C22semidirect
56. #11745179C22semidirect
57. #11745179C22semidirect
58. #11745179C22semidirect
74. C23×D29D4semidirect
98. C2×C22⋊D29D4semidirect
115. C2×D116D4semidirect
140. #90781D4semidirect
214. C2×C4×C29C2×D4semidirect
230. C2×Dic29C2×D4semidirect
288. C2×D29#120semidirect
289. C2×D29#121semidirect
306. #394D29semidirect
349. C2×C4⋊C4C2×D29semidirect
362. C2×C22⋊C4C2×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×#117452572
C2×#117452462
C2×#117452442
C2×C22⋊C4×D292
#142710782
#142710722
#142710712
#142710412
#142710392
#142710342
#142710182
C29×#3942
#241029