Finite Group Databasebeta

← #34103503

Subgroups — #34103503

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×#19097744C211yesmaximal, characteristic, complemented
3C2×#19097742C211yesmaximal, characteristic, complemented
4C2×#19097739C211yesmaximal, characteristic, complemented
5C2×#19097739C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D157C211yesmaximal, characteristic, complemented
7#23757189C211yesmaximal, characteristic, complemented
8#23757187C211yesmaximal, characteristic, complemented
9#23757181C211yesmaximal, characteristic, complemented
10#23757151C211yesmaximal, characteristic, complemented
11#23757149C211yesmaximal, characteristic, complemented
12#23757149C211yesmaximal, characteristic, complemented
13#23757147C211yesmaximal, characteristic, complemented
14#23757128C211yesmaximal, characteristic, complemented
15#392×C157C211yesmaximal, characteristic, complemented
16C24×D157C2211yescharacteristic
17C24×D157C2211yescharacteristic
18C22×D628C2211yescharacteristic
19C22×C22⋊D157C2211yescharacteristic
20C22×C22⋊D157C2211yescharacteristic
21C22×C22⋊D157C2211yescharacteristic
22C22×C22⋊D157C2211yescharacteristic, complemented
23C22×C22⋊D157C2211yescharacteristic, complemented
24C2×D4×D157—24no—
25C2×D4×D157—24no—
26C2×D4×D157—24no—
27C22×C4×D157C2211yescharacteristic
28C22×C4×D157C2211yescharacteristic, complemented
29C22×C4×D157C2211yescharacteristic, complemented
30#19097744—24no—
31#19097742—24no—
32#19097739—24no—
33#19097739—24no—
34C2×C4⋊Dic157C2211yescharacteristic, complemented
35C2×#14578933C2211yescharacteristic, complemented
36C2×C22⋊Dic157C2211yescharacteristic, complemented
37C2×C22⋊Dic157C2211yescharacteristic, complemented
38C2×C22⋊Dic157C2211yescharacteristic, complemented
39C2×C22⋊Dic157C2211yescharacteristic, complemented
40C2×C22⋊Dic157C2211yescharacteristic, complemented
41C2×#14578931C2211yescharacteristic
42C2×#14578931C2211yescharacteristic
43C2×#14578931C2211yescharacteristic
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
53C22×D4×C157C2211yescharacteristic, complemented
54C22×D4×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
76C2×D628—22no—
77C2×D628—22no—
78C2×D628D414yescomplemented
79C2×C22⋊D157—22no—
80C2×C22⋊D157—22no—
81C2×C22⋊D157—22no—
82C2×C22⋊D157—22no—
83C2×C22⋊D157—22no—
84C2×C22⋊D157—22no—
85C2×C22⋊D157—22no—
86C2×C22⋊D157—22no—
87C2×C22⋊D157—22no—
88C2×C22⋊D157—22no—
89C2×C22⋊D157—22no—
90C2×C22⋊D157—22no—
91C2×C22⋊D157—22no—
92C2×C22⋊D157—41no—
93C2×C22⋊D157D414yescomplemented
94D4×D157—232no—
95C22×Dic157C2311yescharacteristic
96C22×Dic157C2311yescharacteristic
97C22×Dic157C2311yescharacteristic
98C22×Dic157C2311yescharacteristic
99C22×Dic157C2311yescharacteristic
100C2×C4×D157—22no—
101C2×C4×D157—22no—
102C2×C4×D157—22no—
103C2×C4×D157—22no—
104C2×C4×D157—22no—
105C2×C4×D157—22no—
106C2×C4×D157—22no—
107C2×C4×D157—41no—
108C2×C4×D157—41no—
109C4⋊Dic157—22no—
110#14578933—22no—
111C22⋊Dic157—22no—
112C22⋊Dic157—22no—
113C22⋊Dic157—22no—
114C22⋊Dic157—22no—
115C22⋊Dic157—22no—
116#14578931—22no—
117#14578931—22no—
118#14578931—22no—
119#14578931—22no—
120#14578931—22no—
121#14578931—41no—
122#14578931D414yescomplemented
123C24×C157C2311yescharacteristic
124C24×C157C2311yescharacteristic
125C24×C157C2311yescharacteristic
126C2×D4×C157—22no—
127C2×D4×C157—22no—
128C2×D4×C157—22no—
129C2×D4×C157—22no—
130C2×D4×C157—22no—
131C2×D4×C157—22no—
132C2×D4×C157—41no—
133C2×D4×C157—41no—
134C2×D4×C157—41no—
135C22×C4×C157C2311yescharacteristic
136C22×C4×C157C2311yescharacteristic
137C22×C4×C157C2311yescharacteristic
138C22×C4×C157C2311yescharacteristic
139C22⋊C4×C157—22no—
140C22⋊C4×C157—22no—
141C22⋊C4×C157—41no—
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—44no—
160C22×D157—44no—
161C22×D157—44no—
162C22×D157—44no—
163C22×D157—44no—
164C22×D157—44no—
165C22×D157—44no—
166C22×D157—44no—
167C22×D157—44no—
168C22×D157—44no—
169C22×D157—44no—
170C22×D157C2×D412yes—
171C22×D157C2×D412yes—
172C22×D157C2×D412yes—
173C22×D157C2×D412yes—
174C22×D157C2×D412yes—
175C22×D157C2×D412yes—
176C22×D157#4112yes—
177D628—28no—
178C22⋊D157—28no—
179C22⋊D157—28no—
180C22⋊D157—44no—
181C22⋊D157—44no—
182C22⋊D157—44no—
183C2×Dic157—21no—
184C2×Dic157—21no—
185C2×Dic157—21no—
186C2×Dic157—21no—
187C2×Dic157—21no—
188C2×Dic157—21no—
189C2×Dic157—21no—
190C2×Dic157—21no—
191C2×Dic157—21no—
192C2×Dic157—21no—
193C2×Dic157—21no—
194C2×Dic157—21no—
195C2×Dic157—21no—
196C2×Dic157C2×D412yes—
197C2×Dic157C2×D412yescomplemented
198C4×D157—28no—
199C4×D157—44no—
200C4×D157—44no—
201C23×C157—21no—
202C23×C157—21no—
203C23×C157—21no—
204C23×C157—21no—
205C23×C157—21no—
206C23×C157—21no—
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×C157—21no—
220C23×C157C2×D412yes—
221C23×C157C2×D412yes—
222C23×C157C2411yescharacteristic
223D4×C157—28no—
224D4×C157—44no—
225D4×C157—44no—
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×C157—41no—
253C22×C157—41no—
254C22×C157—41no—
255C22×C157—41no—
256C22×C157—41no—
257C22×C157—41no—
258C22×C157—41no—
259C22×C157C22×D411yescharacteristic
260C22×C157C22×D411yescharacteristic
261C22×C157C22×D411yescharacteristic
262C22×C157C22×D411yescharacteristic
263C22×C157C2×#4111yescharacteristic
264C22×C157H(5,𝔽2)11yescharacteristic
265C22×C157H(5,𝔽2)11yescharacteristic
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—22no—
275C2×D157—22no—
276C2×D157—22no—
277C2×D157—22no—
278C2×D157—22no—
279C2×D157—22no—
280C2×D157—22no—
281C2×D157—416no—
282C2×D157—416no—
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—
293Dic157—22no—
294Dic157—22no—
295Dic157—41no—
296Dic157—41no—
297Dic157—41no—
298C2×C157—42no—
299C2×C157—42no—
300C2×C157—81no—
301C2×C157C2×#12011yescharacteristic
302C2×C157C2×#12111yescharacteristic
303C2×C157#53411yescharacteristic
304C2×C157D4211yescharacteristic
305C2×C157D4211yescharacteristic
306C2×C157#54611yescharacteristic
307C2×C157#54611yescharacteristic
308D157—24no—
309D157—24no—
310D157—42no—
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#394—1571no—
321#392—1571no—
322#392D15711yescharacteristic, complemented
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×D4C2×D15711yescharacteristic
340C22×D4C2×D15711yescharacteristic, complemented
341C22×D4C2×D15711yescharacteristic, complemented
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⋊C4—1571no—
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⋊C4—1571no—
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—1574no—
386C24—1571no—
387C24—1571no—
388C24C22×D15711yescharacteristic
389C24C22×D15711yescharacteristic
390C24C22×D15711yescharacteristic
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—3142no—
401C2×D4—3142no—
402C2×D4—31432no—
403C2×D4—3142no—
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—3142no—
414C2×D4—3142no—
415C2×D4—3142no—
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×C4—1571no—
433C22×C4C22×D15711yescharacteristic
434C22×C4C22×D15711yescharacteristic
435C22×C4C22×D15711yescharacteristic
436C22×C4C22×D15711yescharacteristic
437C4⋊C4—3142no—
438C4⋊C4—3142no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—41no—
442C22⋊C4—3142no—
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—3142no—
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—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—3148no—
474C23—3148no—
475C23—3148no—
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—44no—
513D4—44no—
514D4—3148no—
515D4—3148no—
516D4—3148no—
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—3148no—
531C2×C4—3141no—
532C2×C4—3141no—
533C2×C4—3141no—
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—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—3142no—
572C22—3142no—
573C22—3142no—
574C22—3142no—
575C22—3142no—
576C22—3142no—
577C22—3142no—
578C22—3142no—
579C22—3142no—
580C22—3142no—
581C22—3142no—
582C22—3142no—
583C22—3142no—
584C22—3142no—
585C22—3142no—
586C22—62816no—
587C22—62816no—
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#1909781611yescharacteristic
600C22#1909781611yescharacteristic
601C4—22no—
602C4—22no—
603C4—41no—
604C4—41no—
605C4—3142no—
606C4—3142no—
607C4—6281no—
608C4—6281no—
609C4—6281no—
610C2—42no—
611C2—42no—
612C2—81no—
613C2—3144no—
614C2—3144no—
615C2—6282no—
616C2#120×D15711yescharacteristic
617C2#121×D15711yescharacteristic
618C2#2375783311yescharacteristic
619C2#2375790511yescharacteristic
620C2#2375790811yescharacteristic
621C2#2375791211yescharacteristic
622C2#2375792011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D157
commutator, socle, cosocleC23×C157C24
Fitting#392×C157C2
hypercenter#392D157
hypocenterC157#2410
LCSG ▷ C23×C157 ▷ C157
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D157C2semidirect
2. C2×#19097744C2semidirect
3. C2×#19097742C2semidirect
4. C2×#19097739C2semidirect
5. C2×#19097739C2semidirect
6. C2×C22⋊C4×D157C2semidirect
7. #23757189C2semidirect
8. #23757187C2semidirect
9. #23757181C2semidirect
10. #23757151C2semidirect
11. #23757149C2semidirect
12. #23757149C2semidirect
13. #23757147C2semidirect
14. #23757128C2semidirect
15. #392×C157C2semidirect
22. C22×C22⋊D157C22semidirect
23. C22×C22⋊D157C22semidirect
28. C22×C4×D157C22semidirect
29. C22×C4×D157C22semidirect
34. C2×C4⋊Dic157C22semidirect
35. C2×#14578933C22semidirect
36. C2×C22⋊Dic157C22semidirect
37. C2×C22⋊Dic157C22semidirect
38. C2×C22⋊Dic157C22semidirect
39. C2×C22⋊Dic157C22semidirect
40. C2×C22⋊Dic157C22semidirect
44. C2×#14578931C22semidirect
45. C2×#14578931C22semidirect
46. C2×#14578931C22semidirect
47. C2×#14578931C22semidirect
49. #19097678C22semidirect
50. #19097678C22semidirect
51. #19097678C22semidirect
53. C22×D4×C157C22semidirect
54. C22×D4×C157C22semidirect
55. C2×C22⋊C4×C157C22semidirect
56. C2×C22⋊C4×C157C22semidirect
57. C2×C22⋊C4×C157C22semidirect
58. #95×C157C22semidirect
72. C23×D157D4semidirect
78. C2×D628D4semidirect
93. C2×C22⋊D157D4semidirect
122. #14578931D4semidirect
197. C2×Dic157C2×D4semidirect
237. C2×C4×C157C2×D4semidirect
287. C2×D157#120semidirect
288. C2×D157#121semidirect
311. C157#2410semidirect
322. #392D157semidirect
340. C22×D4C2×D157semidirect
341. C22×D4C2×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×#190977442
C2×#190977422
C2×#190977392
C2×C22⋊C4×D1572
#237571892
#237571872
#237571812
#237571512
#237571492
#237571472
#237571282
#392×C1572
#2410157