Finite Group Databasebeta

← #34103505

Subgroups — #34103505

Order 20096.

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×D157C211yesmaximal, characteristic, complemented
2C2×#19097746C211yesmaximal, characteristic, complemented
3C2×#19097744C211yesmaximal, characteristic, complemented
4C2×#19097741C211yesmaximal, characteristic, complemented
5C2×#19097741C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
7#23757188C211yesmaximal, characteristic, complemented
8#23757182C211yesmaximal, characteristic, complemented
9#23757181C211yesmaximal, characteristic, complemented
10#23757151C211yesmaximal, characteristic, complemented
11#23757151C211yesmaximal, characteristic, complemented
12#23757149C211yesmaximal, characteristic, complemented
13#23757144C211yesmaximal, characteristic, complemented
14#23757128C211yesmaximal, characteristic, complemented
15#394×C157C211yesmaximal, characteristic, complemented
16C24×D157C2211yescharacteristic
17C24×D157C2211yescharacteristic
18C22×D628C2211yescharacteristic
19C22×D628C2211yescharacteristic
20C22×D628C2211yescharacteristic, complemented
21C22×D628C2211yescharacteristic, complemented
22C22×C22⋊D157C2211yescharacteristic
23C22×C22⋊D157C2211yescharacteristic
24C22×C22⋊D157C2211yescharacteristic, complemented
25C22×C22⋊D157C2211yescharacteristic, complemented
26C2×D4×D157—24no—
27C2×D4×D157—24no—
28C2×D4×D157—24no—
29C22×C4×D157C2211yescharacteristic
30C22×C4×D157C2211yescharacteristic, complemented
31C22×C4×D157C2211yescharacteristic, complemented
32#19097746—24no—
33#19097744—24no—
34#19097741—24no—
35#19097741—24no—
36C2×#14578933C2211yescharacteristic, complemented
37C2×C22⋊Dic157C2211yescharacteristic, complemented
38C2×C22⋊Dic157C2211yescharacteristic, complemented
39C2×#14578931C2211yescharacteristic
40C2×#14578931C2211yescharacteristic
41C2×#14578931C2211yescharacteristic
42C2×#14578931C2211yescharacteristic, complemented
43C2×#14578931C2211yescharacteristic, complemented
44C2×#14578931C2211yescharacteristic, complemented
45C2×#14578931C2211yescharacteristic, complemented
46C2×#14578931C2211yescharacteristic, complemented
47C2×#14578931C2211yescharacteristic, complemented
48C22⋊C4×D157—24no—
49#19097678C2211yescharacteristic, complemented
50#19097678C2211yescharacteristic, complemented
51#19097678C2211yescharacteristic, complemented
52C22×D4×C157C2211yescharacteristic
53C2×C4⋊C4×C157C2211yescharacteristic, complemented
54C2×C22⋊C4×C157C2211yescharacteristic, complemented
55C2×C22⋊C4×C157C2211yescharacteristic, complemented
56C2×C22⋊C4×C157C2211yescharacteristic, complemented
57C2×C22⋊C4×C157C2211yescharacteristic, complemented
58#95×C157C2211yescharacteristic, complemented
59C23×D157—22no—
60C23×D157—22no—
61C23×D157—22no—
62C23×D157—22no—
63C23×D157—22no—
64C23×D157—22no—
65C23×D157—22no—
66C23×D157—22no—
67C23×D157—22no—
68C23×D157—41no—
69C23×D157—41no—
70C23×D157—41no—
71C23×D157—41no—
72C23×D157D414yescomplemented
73C23×D157C2311yescharacteristic
74C23×D157C2311yescharacteristic
75C23×D157C2311yescharacteristic
76C23×D157C2311yescharacteristic
77C2×D628—22no—
78C2×D628—22no—
79C2×D628—22no—
80C2×D628—22no—
81C2×D628—22no—
82C2×D628—22no—
83C2×D628—22no—
84C2×D628—22no—
85C2×D628—22no—
86C2×D628—22no—
87C2×D628—41no—
88C2×D628D414yescomplemented
89C2×C22⋊D157—22no—
90C2×C22⋊D157—22no—
91C2×C22⋊D157—22no—
92C2×C22⋊D157—22no—
93C2×C22⋊D157—22no—
94C2×C22⋊D157—22no—
95C2×C22⋊D157—22no—
96C2×C22⋊D157—22no—
97C2×C22⋊D157—41no—
98C2×C22⋊D157—41no—
99C2×C22⋊D157—41no—
100C2×C22⋊D157D414yescomplemented
101D4×D157—232no—
102C22×Dic157C2311yescharacteristic
103C22×Dic157C2311yescharacteristic
104C22×Dic157C2311yescharacteristic
105C22×Dic157C2311yescharacteristic
106C2×C4×D157—22no—
107C2×C4×D157—22no—
108C2×C4×D157—22no—
109C2×C4×D157—22no—
110C2×C4×D157—22no—
111C2×C4×D157—22no—
112C2×C4×D157—22no—
113C2×C4×D157—41no—
114C2×C4×D157—41no—
115#14578933—22no—
116C22⋊Dic157—22no—
117C22⋊Dic157—41no—
118#14578931—22no—
119#14578931—22no—
120#14578931—22no—
121#14578931—22no—
122#14578931—22no—
123#14578931—22no—
124#14578931—22no—
125#14578931—41no—
126#14578931D414yescomplemented
127C24×C157C2311yescharacteristic
128C24×C157C2311yescharacteristic
129C2×D4×C157—22no—
130C2×D4×C157—22no—
131C2×D4×C157—22no—
132C22×C4×C157C2311yescharacteristic
133C22×C4×C157C2311yescharacteristic
134C22×C4×C157C2311yescharacteristic
135C22×C4×C157C2311yescharacteristic
136C22×C4×C157C2311yescharacteristic
137C4⋊C4×C157—22no—
138C22⋊C4×C157—22no—
139C22⋊C4×C157—22no—
140C22⋊C4×C157—22no—
141C22⋊C4×C157—22no—
142C22×D157—21no—
143C22×D157—21no—
144C22×D157—21no—
145C22×D157—21no—
146C22×D157—21no—
147C22×D157—21no—
148C22×D157—21no—
149C22×D157—21no—
150C22×D157—28no—
151C22×D157—21no—
152C22×D157—21no—
153C22×D157—21no—
154C22×D157—21no—
155C22×D157—21no—
156C22×D157—21no—
157C22×D157—28no—
158C22×D157—28no—
159C22×D157—21no—
160C22×D157—21no—
161C22×D157—21no—
162C22×D157—21no—
163C22×D157—21no—
164C22×D157—21no—
165C22×D157—21no—
166C22×D157—44no—
167C22×D157—44no—
168C22×D157—44no—
169C22×D157—44no—
170C22×D157—44no—
171C22×D157—44no—
172C22×D157—44no—
173C22×D157—44no—
174C22×D157—44no—
175C22×D157—44no—
176C22×D157—44no—
177C22×D157C2×D412yes—
178C22×D157C2×D412yes—
179C22×D157C2×D412yes—
180C22×D157C2×D412yes—
181C22×D157C2×D412yes—
182C22×D157C2×D412yes—
183C22×D157#4112yes—
184D628—28no—
185D628—44no—
186D628—44no—
187D628—44no—
188C22⋊D157—28no—
189C22⋊D157—28no—
190C22⋊D157—44no—
191C22⋊D157—44no—
192C2×Dic157—21no—
193C2×Dic157—21no—
194C2×Dic157—21no—
195C2×Dic157—21no—
196C2×Dic157—21no—
197C2×Dic157—21no—
198C2×Dic157—21no—
199C2×Dic157—21no—
200C2×Dic157—21no—
201C2×Dic157—21no—
202C2×Dic157C2×D412yes—
203C2×Dic157C2×D412yescomplemented
204C4×D157—28no—
205C4×D157—44no—
206C4×D157—44no—
207C23×C157—21no—
208C23×C157—21no—
209C23×C157—21no—
210C23×C157—21no—
211C23×C157—21no—
212C23×C157—21no—
213C23×C157—21no—
214C23×C157—21no—
215C23×C157—21no—
216C23×C157—21no—
217C23×C157—21no—
218C23×C157—21no—
219C23×C157C2×D412yes—
220C23×C157C2×D412yes—
221C23×C157C2411yescharacteristic
222D4×C157—28no—
223C2×C4×C157—21no—
224C2×C4×C157—21no—
225C2×C4×C157—21no—
226C2×C4×C157—21no—
227C2×C4×C157—21no—
228C2×C4×C157—21no—
229C2×C4×C157—21no—
230C2×C4×C157—21no—
231C2×C4×C157—21no—
232C2×C4×C157—21no—
233C2×C4×C157—21no—
234C2×C4×C157—21no—
235C2×C4×C157—21no—
236C2×C4×C157C2×D412yes—
237C2×C4×C157C2×D412yescomplemented
238C22×C157—22no—
239C22×C157—22no—
240C22×C157—22no—
241C22×C157—22no—
242C22×C157—22no—
243C22×C157—22no—
244C22×C157—41no—
245C22×C157—41no—
246C22×C157—41no—
247C22×C157—41no—
248C22×C157—41no—
249C22×C157—41no—
250C22×C157—41no—
251C22×C157—41no—
252C22×C157C22×D411yescharacteristic
253C22×C157C22×D411yescharacteristic
254C22×C157C22×D411yescharacteristic
255C22×C157C22×D411yescharacteristic
256C22×C157C2×#4111yescharacteristic
257C22×C157H(5,𝔽2)11yescharacteristic
258C22×C157H(5,𝔽2)11yescharacteristic
259C2×D157—22no—
260C2×D157—22no—
261C2×D157—22no—
262C2×D157—22no—
263C2×D157—22no—
264C2×D157—22no—
265C2×D157—22no—
266C2×D157—22no—
267C2×D157—22no—
268C2×D157—22no—
269C2×D157—22no—
270C2×D157—22no—
271C2×D157—22no—
272C2×D157—22no—
273C2×D157—22no—
274C2×D157—416no—
275C2×D157—416no—
276C2×D157—41no—
277C2×D157—41no—
278C2×D157—41no—
279C2×D157—41no—
280C2×D157—41no—
281C2×D157—41no—
282C2×D157—41no—
283C2×D157—41no—
284C2×D157—41no—
285C2×D157—41no—
286C2×D157—41no—
287C2×D157#12014yescomplemented
288C2×D157#12114yescomplemented
289C4×C157—22no—
290C4×C157—22no—
291C4×C157—41no—
292C4×C157—41no—
293C4×C157—41no—
294Dic157—22no—
295Dic157—22no—
296Dic157—41no—
297Dic157—41no—
298C2×C157—42no—
299C2×C157—42no—
300C2×C157C2×#12011yescharacteristic
301C2×C157C2×#12111yescharacteristic
302C2×C157#53411yescharacteristic
303C2×C157D4211yescharacteristic
304C2×C157D4211yescharacteristic
305C2×C157#54611yescharacteristic
306C2×C157#54611yescharacteristic
307D157—24no—
308D157—24no—
309D157—42no—
310D157—81no—
311C157#241011yescharacteristic, complemented, Sylow
312#2410—1571nomaximal, Sylow
313C23×D4—1571no—
314C2×#121—1571no—
315C2×#121—1571no—
316C2×#120—1571no—
317C2×#120—1571no—
318C22×C22⋊C4—1571no—
319#394—1571no—
320#394D15711yescharacteristic, complemented
321#392—1571no—
322#392—1571no—
323#386—1571no—
324#386—1571no—
325#386—1571no—
326#385—1571no—
327#379—1571no—
328C25—1571no—
329C25—1571no—
330C22×D4—3144no—
331C22×D4—3144no—
332C22×D4—3144no—
333C22×D4—1571no—
334C22×D4—1571no—
335C22×D4—1571no—
336C22×D4—1571no—
337C22×D4—1571no—
338C22×D4—1571no—
339C22×D4—1571no—
340C22×D4—1571no—
341C22×D4C2×D15711yescharacteristic
342C23×C4—1571no—
343C23×C4—1571no—
344C23×C4—1571no—
345#121—3144no—
346#121—3144no—
347#120—3144no—
348#120—3144no—
349C2×C4⋊C4—1571no—
350C2×C4⋊C4C2×D15711yescharacteristic, complemented
351C2×C22⋊C4—3144no—
352C2×C22⋊C4—1571no—
353C2×C22⋊C4—1571no—
354C2×C22⋊C4—1571no—
355C2×C22⋊C4—1571no—
356C2×C22⋊C4—1571no—
357C2×C22⋊C4—1571no—
358C2×C22⋊C4—1571no—
359C2×C22⋊C4—1571no—
360C2×C22⋊C4—1571no—
361C2×C22⋊C4—1571no—
362C2×C22⋊C4—1571no—
363C2×C22⋊C4C2×D15711yescharacteristic, complemented
364C2×C22⋊C4C2×D15711yescharacteristic, complemented
365C2×C22⋊C4C2×D15711yescharacteristic, complemented
366C2×C22⋊C4C2×D15711yescharacteristic, complemented
367#95—1571no—
368#95—1571no—
369#95—1571no—
370#95C2×D15711yescharacteristic, complemented
371C24—3142no—
372C24—3142no—
373C24—3142no—
374C24—3142no—
375C24—3142no—
376C24—3142no—
377C24—3142no—
378C24—3142no—
379C24—3142no—
380C24—6281no—
381C24—6281no—
382C24—6281no—
383C24—6281no—
384C24—1571no—
385C24—1571no—
386C24—1574no—
387C24—1571no—
388C24—1571no—
389C24C22×D15711yescharacteristic
390C24C22×D15711yescharacteristic
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—3142no—
395C2×D4—3142no—
396C2×D4—3142no—
397C2×D4—3142no—
398C2×D4—3142no—
399C2×D4—3142no—
400C2×D4—3142no—
401C2×D4—3142no—
402C2×D4—3142no—
403C2×D4—31432no—
404C2×D4—3142no—
405C2×D4—3142no—
406C2×D4—3142no—
407C2×D4—3142no—
408C2×D4—3142no—
409C2×D4—3142no—
410C2×D4—3142no—
411C2×D4—3142no—
412C2×D4—3142no—
413C2×D4—6281no—
414C2×D4—6281no—
415C2×D4—6281no—
416C2×D4—6281no—
417C2×D4—1574no—
418C2×D4—1574no—
419C22×C4—3142no—
420C22×C4—3142no—
421C22×C4—3142no—
422C22×C4—3142no—
423C22×C4—3142no—
424C22×C4—3142no—
425C22×C4—3142no—
426C22×C4—6281no—
427C22×C4—6281no—
428C22×C4—1571no—
429C22×C4—1571no—
430C22×C4—1571no—
431C22×C4—1571no—
432C22×C4C22×D15711yescharacteristic
433C22×C4C22×D15711yescharacteristic
434C22×C4C22×D15711yescharacteristic
435C22×C4C22×D15711yescharacteristic
436C22×C4C22×D15711yescharacteristic
437C4⋊C4—22no—
438C4⋊C4—3142no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—3142no—
444C22⋊C4—3142no—
445C22⋊C4—3142no—
446C22⋊C4—3142no—
447C22⋊C4—3142no—
448C22⋊C4—3142no—
449C22⋊C4—3142no—
450C22⋊C4—3142no—
451C22⋊C4—6281no—
452C22⋊C4—6281no—
453C22⋊C4—1574no—
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—3148no—
467C23—3148no—
468C23—3148no—
469C23—3141no—
470C23—3141no—
471C23—3141no—
472C23—3141no—
473C23—3141no—
474C23—3141no—
475C23—3141no—
476C23—3141no—
477C23—3141no—
478C23—3141no—
479C23—3141no—
480C23—3141no—
481C23—3141no—
482C23—3141no—
483C23—3141no—
484C23—3141no—
485C23—3141no—
486C23—3141no—
487C23—3141no—
488C23—3141no—
489C23—3141no—
490C23—6284no—
491C23—6284no—
492C23—6284no—
493C23—6284no—
494C23—6284no—
495C23—6284no—
496C23—6284no—
497C23—6284no—
498C23—6284no—
499C23—6284no—
500C23—6284no—
501C23—1572no—
502C23—1572no—
503C23—1572no—
504C23—1572no—
505C23—1572no—
506C23—1572no—
507C23—1572no—
508C23D4×D15712yes—
509C23D4×D15712yes—
510C23C23×D15711yescharacteristic
511D4—28no—
512D4—3148no—
513D4—3148no—
514D4—3148no—
515D4—6284no—
516D4—6284no—
517D4—6284no—
518D4—6284no—
519D4—6284no—
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—3148no—
534C2×C4—3141no—
535C2×C4—3141no—
536C2×C4—3141no—
537C2×C4—3141no—
538C2×C4—3141no—
539C2×C4—3141no—
540C2×C4—3141no—
541C2×C4—3141no—
542C2×C4—3141no—
543C2×C4—3141no—
544C2×C4—6284no—
545C2×C4—6284no—
546C2×C4—1572no—
547C2×C4—1572no—
548C2×C4D4×D15712yes—
549C2×C4D4×D15712yescomplemented
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—3142no—
565C22—3142no—
566C22—3142no—
567C22—3142no—
568C22—3142no—
569C22—3142no—
570C22—3142no—
571C22—3142no—
572C22—3142no—
573C22—3142no—
574C22—3142no—
575C22—3142no—
576C22—3142no—
577C22—3142no—
578C22—3142no—
579C22—62816no—
580C22—62816no—
581C22—6281no—
582C22—6281no—
583C22—6281no—
584C22—6281no—
585C22—6281no—
586C22—6281no—
587C22—6281no—
588C22—6281no—
589C22—6281no—
590C22—6281no—
591C22—6281no—
592C22—1574no—
593C22—1574no—
594C22C2×D4×D15711yescharacteristic
595C22C2×D4×D15711yescharacteristic
596C22C2×D4×D15711yescharacteristic
597C22C2×D4×D15711yescharacteristic
598C22#41×D15711yescharacteristic
599C22#1909781711yescharacteristic
600C22#1909781711yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—3142no—
607C4—3142no—
608C4—6281no—
609C4—6281no—
610C2—42no—
611C2—42no—
612C2—3144no—
613C2—3144no—
614C2—6282no—
615C2—12561no—
616C2#120×D15711yescharacteristic
617C2#121×D15711yescharacteristic
618C2#2375783411yescharacteristic
619C2#2375790711yescharacteristic
620C2#2375790711yescharacteristic
621C2#2375791511yescharacteristic
622C2#2375791611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutator, socle, cosocleC23×C157C24
Fitting#394×C157C2
hypercenter#394D157
hypocenterC157#2410
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D157C2semidirect
2. C2×#19097746C2semidirect
3. C2×#19097744C2semidirect
4. C2×#19097741C2semidirect
5. C2×#19097741C2semidirect
6. C2×C22⋊C4×D157C2semidirect
7. #23757188C2semidirect
8. #23757182C2semidirect
9. #23757181C2semidirect
10. #23757151C2semidirect
11. #23757151C2semidirect
12. #23757149C2semidirect
13. #23757144C2semidirect
14. #23757128C2semidirect
15. #394×C157C2semidirect
20. C22×D628C22semidirect
21. C22×D628C22semidirect
24. C22×C22⋊D157C22semidirect
25. C22×C22⋊D157C22semidirect
30. C22×C4×D157C22semidirect
31. C22×C4×D157C22semidirect
36. C2×#14578933C22semidirect
37. C2×C22⋊Dic157C22semidirect
38. C2×C22⋊Dic157C22semidirect
42. C2×#14578931C22semidirect
43. C2×#14578931C22semidirect
44. C2×#14578931C22semidirect
45. C2×#14578931C22semidirect
46. C2×#14578931C22semidirect
47. C2×#14578931C22semidirect
49. #19097678C22semidirect
50. #19097678C22semidirect
51. #19097678C22semidirect
53. C2×C4⋊C4×C157C22semidirect
54. C2×C22⋊C4×C157C22semidirect
55. C2×C22⋊C4×C157C22semidirect
56. C2×C22⋊C4×C157C22semidirect
57. C2×C22⋊C4×C157C22semidirect
58. #95×C157C22semidirect
72. C23×D157D4semidirect
88. C2×D628D4semidirect
100. C2×C22⋊D157D4semidirect
126. #14578931D4semidirect
203. C2×Dic157C2×D4semidirect
237. C2×C4×C157C2×D4semidirect
287. C2×D157#120semidirect
288. C2×D157#121semidirect
311. C157#2410semidirect
320. #394D157semidirect
350. C2×C4⋊C4C2×D157semidirect
363. C2×C22⋊C4C2×D157semidirect
364. C2×C22⋊C4C2×D157semidirect
365. C2×C22⋊C4C2×D157semidirect
366. C2×C22⋊C4C2×D157semidirect
370. #95C2×D157semidirect
549. C2×C4D4×D157semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1572
C2×#190977462
C2×#190977442
C2×#190977412
C2×C22⋊C4×D1572
#237571882
#237571822
#237571812
#237571512
#237571492
#237571442
#237571282
#394×C1572
#2410157