Finite Group Databasebeta

← #49098672

Subgroups — #49098672

Order 35968.

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×D281C211yesmaximal, characteristic, complemented
2C2×#22582854C211yesmaximal, characteristic, complemented
3C2×#22582852C211yesmaximal, characteristic, complemented
4C2×#22582849C211yesmaximal, characteristic, complemented
5C2×#22582849C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D281C211yesmaximal, characteristic, complemented
7#31823378C211yesmaximal, characteristic, complemented
8#31823372C211yesmaximal, characteristic, complemented
9#31823371C211yesmaximal, characteristic, complemented
10#31823341C211yesmaximal, characteristic, complemented
11#31823341C211yesmaximal, characteristic, complemented
12#31823339C211yesmaximal, characteristic, complemented
13#31823334C211yesmaximal, characteristic, complemented
14#31823318C211yesmaximal, characteristic, complemented
15#394×C281C211yesmaximal, characteristic, complemented
16C24×D281C2211yescharacteristic
17C24×D281C2211yescharacteristic
18C22×D1124C2211yescharacteristic
19C22×D1124C2211yescharacteristic
20C22×D1124C2211yescharacteristic, complemented
21C22×D1124C2211yescharacteristic, complemented
22C22×C22⋊D281C2211yescharacteristic
23C22×C22⋊D281C2211yescharacteristic
24C22×C22⋊D281C2211yescharacteristic, complemented
25C22×C22⋊D281C2211yescharacteristic, complemented
26C2×D4×D281—24no—
27C2×D4×D281—24no—
28C2×D4×D281—24no—
29C22×C4×D281C2211yescharacteristic
30C22×C4×D281C2211yescharacteristic, complemented
31C22×C4×D281C2211yescharacteristic, complemented
32#22582854—24no—
33#22582852—24no—
34#22582849—24no—
35#22582849—24no—
36C2×#17985117C2211yescharacteristic, complemented
37C2×C22⋊Dic281C2211yescharacteristic, complemented
38C2×C22⋊Dic281C2211yescharacteristic, complemented
39C2×#17985115C2211yescharacteristic
40C2×#17985115C2211yescharacteristic
41C2×#17985115C2211yescharacteristic
42C2×#17985115C2211yescharacteristic, complemented
43C2×#17985115C2211yescharacteristic, complemented
44C2×#17985115C2211yescharacteristic, complemented
45C2×#17985115C2211yescharacteristic, complemented
46C2×#17985115C2211yescharacteristic, complemented
47C2×#17985115C2211yescharacteristic, complemented
48C22⋊C4×D281—24no—
49#22582786C2211yescharacteristic, complemented
50#22582786C2211yescharacteristic, complemented
51#22582786C2211yescharacteristic, complemented
52C22×D4×C281C2211yescharacteristic
53C2×C4⋊C4×C281C2211yescharacteristic, complemented
54C2×C22⋊C4×C281C2211yescharacteristic, complemented
55C2×C22⋊C4×C281C2211yescharacteristic, complemented
56C2×C22⋊C4×C281C2211yescharacteristic, complemented
57C2×C22⋊C4×C281C2211yescharacteristic, complemented
58#95×C281C2211yescharacteristic, complemented
59C23×D281—22no—
60C23×D281—22no—
61C23×D281—22no—
62C23×D281—22no—
63C23×D281—22no—
64C23×D281—22no—
65C23×D281—22no—
66C23×D281—22no—
67C23×D281—22no—
68C23×D281—41no—
69C23×D281—41no—
70C23×D281—41no—
71C23×D281—41no—
72C23×D281D414yescomplemented
73C23×D281C2311yescharacteristic
74C23×D281C2311yescharacteristic
75C23×D281C2311yescharacteristic
76C23×D281C2311yescharacteristic
77C2×D1124—22no—
78C2×D1124—22no—
79C2×D1124—22no—
80C2×D1124—22no—
81C2×D1124—22no—
82C2×D1124—22no—
83C2×D1124—22no—
84C2×D1124—22no—
85C2×D1124—22no—
86C2×D1124—22no—
87C2×D1124—41no—
88C2×D1124D414yescomplemented
89C2×C22⋊D281—22no—
90C2×C22⋊D281—22no—
91C2×C22⋊D281—22no—
92C2×C22⋊D281—22no—
93C2×C22⋊D281—22no—
94C2×C22⋊D281—22no—
95C2×C22⋊D281—22no—
96C2×C22⋊D281—22no—
97C2×C22⋊D281—41no—
98C2×C22⋊D281—41no—
99C2×C22⋊D281—41no—
100C2×C22⋊D281D414yescomplemented
101D4×D281—232no—
102C22×Dic281C2311yescharacteristic
103C22×Dic281C2311yescharacteristic
104C22×Dic281C2311yescharacteristic
105C22×Dic281C2311yescharacteristic
106C2×C4×D281—22no—
107C2×C4×D281—22no—
108C2×C4×D281—22no—
109C2×C4×D281—22no—
110C2×C4×D281—22no—
111C2×C4×D281—22no—
112C2×C4×D281—22no—
113C2×C4×D281—41no—
114C2×C4×D281—41no—
115#17985117—22no—
116C22⋊Dic281—22no—
117C22⋊Dic281—41no—
118#17985115—22no—
119#17985115—22no—
120#17985115—22no—
121#17985115—22no—
122#17985115—22no—
123#17985115—22no—
124#17985115—22no—
125#17985115—41no—
126#17985115D414yescomplemented
127C24×C281C2311yescharacteristic
128C24×C281C2311yescharacteristic
129C2×D4×C281—22no—
130C2×D4×C281—22no—
131C2×D4×C281—22no—
132C22×C4×C281C2311yescharacteristic
133C22×C4×C281C2311yescharacteristic
134C22×C4×C281C2311yescharacteristic
135C22×C4×C281C2311yescharacteristic
136C22×C4×C281C2311yescharacteristic
137C4⋊C4×C281—22no—
138C22⋊C4×C281—22no—
139C22⋊C4×C281—22no—
140C22⋊C4×C281—22no—
141C22⋊C4×C281—22no—
142C22×D281—21no—
143C22×D281—21no—
144C22×D281—21no—
145C22×D281—21no—
146C22×D281—21no—
147C22×D281—21no—
148C22×D281—21no—
149C22×D281—21no—
150C22×D281—28no—
151C22×D281—21no—
152C22×D281—21no—
153C22×D281—21no—
154C22×D281—21no—
155C22×D281—21no—
156C22×D281—21no—
157C22×D281—28no—
158C22×D281—28no—
159C22×D281—21no—
160C22×D281—21no—
161C22×D281—21no—
162C22×D281—21no—
163C22×D281—21no—
164C22×D281—21no—
165C22×D281—21no—
166C22×D281—44no—
167C22×D281—44no—
168C22×D281—44no—
169C22×D281—44no—
170C22×D281—44no—
171C22×D281—44no—
172C22×D281—44no—
173C22×D281—44no—
174C22×D281—44no—
175C22×D281—44no—
176C22×D281—44no—
177C22×D281C2×D412yes—
178C22×D281C2×D412yes—
179C22×D281C2×D412yes—
180C22×D281C2×D412yes—
181C22×D281C2×D412yes—
182C22×D281C2×D412yes—
183C22×D281#4112yes—
184D1124—28no—
185D1124—44no—
186D1124—44no—
187D1124—44no—
188C22⋊D281—28no—
189C22⋊D281—28no—
190C22⋊D281—44no—
191C22⋊D281—44no—
192C2×Dic281—21no—
193C2×Dic281—21no—
194C2×Dic281—21no—
195C2×Dic281—21no—
196C2×Dic281—21no—
197C2×Dic281—21no—
198C2×Dic281—21no—
199C2×Dic281—21no—
200C2×Dic281—21no—
201C2×Dic281—21no—
202C2×Dic281C2×D412yes—
203C2×Dic281C2×D412yescomplemented
204C4×D281—28no—
205C4×D281—44no—
206C4×D281—44no—
207C23×C281—21no—
208C23×C281—21no—
209C23×C281—21no—
210C23×C281—21no—
211C23×C281—21no—
212C23×C281—21no—
213C23×C281—21no—
214C23×C281—21no—
215C23×C281—21no—
216C23×C281—21no—
217C23×C281—21no—
218C23×C281—21no—
219C23×C281C2×D412yes—
220C23×C281C2×D412yes—
221C23×C281C2411yescharacteristic
222D4×C281—28no—
223C2×C4×C281—21no—
224C2×C4×C281—21no—
225C2×C4×C281—21no—
226C2×C4×C281—21no—
227C2×C4×C281—21no—
228C2×C4×C281—21no—
229C2×C4×C281—21no—
230C2×C4×C281—21no—
231C2×C4×C281—21no—
232C2×C4×C281—21no—
233C2×C4×C281—21no—
234C2×C4×C281—21no—
235C2×C4×C281—21no—
236C2×C4×C281C2×D412yes—
237C2×C4×C281C2×D412yescomplemented
238C22×C281—22no—
239C22×C281—22no—
240C22×C281—22no—
241C22×C281—22no—
242C22×C281—22no—
243C22×C281—22no—
244C22×C281—41no—
245C22×C281—41no—
246C22×C281—41no—
247C22×C281—41no—
248C22×C281—41no—
249C22×C281—41no—
250C22×C281—41no—
251C22×C281—41no—
252C22×C281C22×D411yescharacteristic
253C22×C281C22×D411yescharacteristic
254C22×C281C22×D411yescharacteristic
255C22×C281C22×D411yescharacteristic
256C22×C281C2×#4111yescharacteristic
257C22×C281H(5,𝔽2)11yescharacteristic
258C22×C281H(5,𝔽2)11yescharacteristic
259C2×D281—22no—
260C2×D281—22no—
261C2×D281—22no—
262C2×D281—22no—
263C2×D281—22no—
264C2×D281—22no—
265C2×D281—22no—
266C2×D281—22no—
267C2×D281—22no—
268C2×D281—22no—
269C2×D281—22no—
270C2×D281—22no—
271C2×D281—22no—
272C2×D281—22no—
273C2×D281—22no—
274C2×D281—416no—
275C2×D281—416no—
276C2×D281—41no—
277C2×D281—41no—
278C2×D281—41no—
279C2×D281—41no—
280C2×D281—41no—
281C2×D281—41no—
282C2×D281—41no—
283C2×D281—41no—
284C2×D281—41no—
285C2×D281—41no—
286C2×D281—41no—
287C2×D281#12014yescomplemented
288C2×D281#12114yescomplemented
289C4×C281—22no—
290C4×C281—22no—
291C4×C281—41no—
292C4×C281—41no—
293C4×C281—41no—
294Dic281—22no—
295Dic281—22no—
296Dic281—41no—
297Dic281—41no—
298C2×C281—42no—
299C2×C281—42no—
300C2×C281C2×#12011yescharacteristic
301C2×C281C2×#12111yescharacteristic
302C2×C281#53411yescharacteristic
303C2×C281D4211yescharacteristic
304C2×C281D4211yescharacteristic
305C2×C281#54611yescharacteristic
306C2×C281#54611yescharacteristic
307D281—24no—
308D281—24no—
309D281—42no—
310D281—81no—
311C281#241011yescharacteristic, complemented, Sylow
312#2410—2811nomaximal, Sylow
313C23×D4—2811no—
314C2×#121—2811no—
315C2×#121—2811no—
316C2×#120—2811no—
317C2×#120—2811no—
318C22×C22⋊C4—2811no—
319#394—2811no—
320#394D28111yescharacteristic, complemented
321#392—2811no—
322#392—2811no—
323#386—2811no—
324#386—2811no—
325#386—2811no—
326#385—2811no—
327#379—2811no—
328C25—2811no—
329C25—2811no—
330C22×D4—2811no—
331C22×D4—2811no—
332C22×D4—2811no—
333C22×D4—2811no—
334C22×D4—2811no—
335C22×D4—2811no—
336C22×D4—2811no—
337C22×D4—2811no—
338C22×D4—5624no—
339C22×D4—5624no—
340C22×D4—5624no—
341C22×D4C2×D28111yescharacteristic
342C23×C4—2811no—
343C23×C4—2811no—
344C23×C4—2811no—
345#121—5624no—
346#121—5624no—
347#120—5624no—
348#120—5624no—
349C2×C4⋊C4—2811no—
350C2×C4⋊C4C2×D28111yescharacteristic, complemented
351C2×C22⋊C4—2811no—
352C2×C22⋊C4—2811no—
353C2×C22⋊C4—2811no—
354C2×C22⋊C4—2811no—
355C2×C22⋊C4—2811no—
356C2×C22⋊C4—2811no—
357C2×C22⋊C4—2811no—
358C2×C22⋊C4—2811no—
359C2×C22⋊C4—2811no—
360C2×C22⋊C4—2811no—
361C2×C22⋊C4—2811no—
362C2×C22⋊C4—5624no—
363C2×C22⋊C4C2×D28111yescharacteristic, complemented
364C2×C22⋊C4C2×D28111yescharacteristic, complemented
365C2×C22⋊C4C2×D28111yescharacteristic, complemented
366C2×C22⋊C4C2×D28111yescharacteristic, complemented
367#95—2811no—
368#95—2811no—
369#95—2811no—
370#95C2×D28111yescharacteristic, complemented
371C24—2811no—
372C24—2811no—
373C24—2811no—
374C24—2814no—
375C24—2811no—
376C24—5622no—
377C24—5622no—
378C24—5622no—
379C24—5622no—
380C24—5622no—
381C24—5622no—
382C24—5622no—
383C24—5622no—
384C24—5622no—
385C24—11241no—
386C24—11241no—
387C24—11241no—
388C24—11241no—
389C24C22×D28111yescharacteristic
390C24C22×D28111yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—2814no—
395C2×D4—2814no—
396C2×D4—5622no—
397C2×D4—5622no—
398C2×D4—5622no—
399C2×D4—5622no—
400C2×D4—5622no—
401C2×D4—5622no—
402C2×D4—5622no—
403C2×D4—5622no—
404C2×D4—5622no—
405C2×D4—5622no—
406C2×D4—5622no—
407C2×D4—56232no—
408C2×D4—5622no—
409C2×D4—5622no—
410C2×D4—5622no—
411C2×D4—5622no—
412C2×D4—5622no—
413C2×D4—5622no—
414C2×D4—5622no—
415C2×D4—11241no—
416C2×D4—11241no—
417C2×D4—11241no—
418C2×D4—11241no—
419C22×C4—2811no—
420C22×C4—2811no—
421C22×C4—2811no—
422C22×C4—2811no—
423C22×C4—5622no—
424C22×C4—5622no—
425C22×C4—5622no—
426C22×C4—5622no—
427C22×C4—5622no—
428C22×C4—5622no—
429C22×C4—5622no—
430C22×C4—11241no—
431C22×C4—11241no—
432C22×C4C22×D28111yescharacteristic
433C22×C4C22×D28111yescharacteristic
434C22×C4C22×D28111yescharacteristic
435C22×C4C22×D28111yescharacteristic
436C22×C4C22×D28111yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—5622no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—2814no—
444C22⋊C4—5622no—
445C22⋊C4—5622no—
446C22⋊C4—5622no—
447C22⋊C4—5622no—
448C22⋊C4—5622no—
449C22⋊C4—5622no—
450C22⋊C4—5622no—
451C22⋊C4—5622no—
452C22⋊C4—11241no—
453C22⋊C4—11241no—
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—2812no—
467C23—2812no—
468C23—2812no—
469C23—2812no—
470C23—2812no—
471C23—2812no—
472C23—2812no—
473C23—5628no—
474C23—5628no—
475C23—5628no—
476C23—5621no—
477C23—5621no—
478C23—5621no—
479C23—5621no—
480C23—5621no—
481C23—5621no—
482C23—5621no—
483C23—5621no—
484C23—5621no—
485C23—5621no—
486C23—5621no—
487C23—5621no—
488C23—5621no—
489C23—5621no—
490C23—5621no—
491C23—5621no—
492C23—5621no—
493C23—5621no—
494C23—5621no—
495C23—5621no—
496C23—5621no—
497C23—11244no—
498C23—11244no—
499C23—11244no—
500C23—11244no—
501C23—11244no—
502C23—11244no—
503C23—11244no—
504C23—11244no—
505C23—11244no—
506C23—11244no—
507C23—11244no—
508C23D4×D28112yes—
509C23D4×D28112yes—
510C23C23×D28111yescharacteristic
511D4—28no—
512D4—5628no—
513D4—5628no—
514D4—5628no—
515D4—11244no—
516D4—11244no—
517D4—11244no—
518D4—11244no—
519D4—11244no—
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—2812no—
534C2×C4—2812no—
535C2×C4—5628no—
536C2×C4—5621no—
537C2×C4—5621no—
538C2×C4—5621no—
539C2×C4—5621no—
540C2×C4—5621no—
541C2×C4—5621no—
542C2×C4—5621no—
543C2×C4—5621no—
544C2×C4—5621no—
545C2×C4—5621no—
546C2×C4—11244no—
547C2×C4—11244no—
548C2×C4D4×D28112yes—
549C2×C4D4×D28112yescomplemented
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—2814no—
565C22—2814no—
566C22—5622no—
567C22—5622no—
568C22—5622no—
569C22—5622no—
570C22—5622no—
571C22—5622no—
572C22—5622no—
573C22—5622no—
574C22—5622no—
575C22—5622no—
576C22—5622no—
577C22—5622no—
578C22—5622no—
579C22—5622no—
580C22—5622no—
581C22—112416no—
582C22—112416no—
583C22—11241no—
584C22—11241no—
585C22—11241no—
586C22—11241no—
587C22—11241no—
588C22—11241no—
589C22—11241no—
590C22—11241no—
591C22—11241no—
592C22—11241no—
593C22—11241no—
594C22C2×D4×D28111yescharacteristic
595C22C2×D4×D28111yescharacteristic
596C22C2×D4×D28111yescharacteristic
597C22C2×D4×D28111yescharacteristic
598C22#41×D28111yescharacteristic
599C22#2258292511yescharacteristic
600C22#2258292511yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—5622no—
607C4—5622no—
608C4—11241no—
609C4—11241no—
610C2—42no—
611C2—42no—
612C2—5624no—
613C2—5624no—
614C2—11242no—
615C2—22481no—
616C2#120×D28111yescharacteristic
617C2#121×D28111yescharacteristic
618C2#3182402411yescharacteristic
619C2#3182409711yescharacteristic
620C2#3182409711yescharacteristic
621C2#3182410511yescharacteristic
622C2#3182410611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D281
commutator, socle, cosocleC23×C281C24
Fitting#394×C281C2
hypercenter#394D281
hypocenterC281#2410
LCSG ▷ C23×C281 ▷ C281
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D281C2semidirect
2. C2×#22582854C2semidirect
3. C2×#22582852C2semidirect
4. C2×#22582849C2semidirect
5. C2×#22582849C2semidirect
6. C2×C22⋊C4×D281C2semidirect
7. #31823378C2semidirect
8. #31823372C2semidirect
9. #31823371C2semidirect
10. #31823341C2semidirect
11. #31823341C2semidirect
12. #31823339C2semidirect
13. #31823334C2semidirect
14. #31823318C2semidirect
15. #394×C281C2semidirect
20. C22×D1124C22semidirect
21. C22×D1124C22semidirect
24. C22×C22⋊D281C22semidirect
25. C22×C22⋊D281C22semidirect
30. C22×C4×D281C22semidirect
31. C22×C4×D281C22semidirect
36. C2×#17985117C22semidirect
37. C2×C22⋊Dic281C22semidirect
38. C2×C22⋊Dic281C22semidirect
42. C2×#17985115C22semidirect
43. C2×#17985115C22semidirect
44. C2×#17985115C22semidirect
45. C2×#17985115C22semidirect
46. C2×#17985115C22semidirect
47. C2×#17985115C22semidirect
49. #22582786C22semidirect
50. #22582786C22semidirect
51. #22582786C22semidirect
53. C2×C4⋊C4×C281C22semidirect
54. C2×C22⋊C4×C281C22semidirect
55. C2×C22⋊C4×C281C22semidirect
56. C2×C22⋊C4×C281C22semidirect
57. C2×C22⋊C4×C281C22semidirect
58. #95×C281C22semidirect
72. C23×D281D4semidirect
88. C2×D1124D4semidirect
100. C2×C22⋊D281D4semidirect
126. #17985115D4semidirect
203. C2×Dic281C2×D4semidirect
237. C2×C4×C281C2×D4semidirect
287. C2×D281#120semidirect
288. C2×D281#121semidirect
311. C281#2410semidirect
320. #394D281semidirect
350. C2×C4⋊C4C2×D281semidirect
363. C2×C22⋊C4C2×D281semidirect
364. C2×C22⋊C4C2×D281semidirect
365. C2×C22⋊C4C2×D281semidirect
366. C2×C22⋊C4C2×D281semidirect
370. #95C2×D281semidirect
549. C2×C4D4×D281semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2812
C2×#225828542
C2×#225828522
C2×#225828492
C2×C22⋊C4×D2812
#318233782
#318233722
#318233712
#318233412
#318233392
#318233342
#318233182
#394×C2812
#2410281