Finite Group Databasebeta

← #29748142

Subgroups — #29748142

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450167C211yesmaximal, characteristic
2#21448828C211yesmaximal, characteristic, complemented
3#21447133C211yesmaximal, characteristic, complemented
4#21446968C211yesmaximal, characteristic, complemented
5#21446820C211yesmaximal, characteristic
6#21446773C211yesmaximal, characteristic, complemented
7#21446503C211yesmaximal, characteristic, complemented
8#21446438C211yesmaximal, characteristic, complemented
9#21446428C211yesmaximal, characteristic, complemented
10#21446413C211yesmaximal, characteristic, complemented
11#21446172C211yesmaximal, characteristic, complemented
12#21446134C211yesmaximal, characteristic
13#21445903C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#2036C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519751C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839691—21no—
29#16839678—21no—
30#16839669C2211yescharacteristic
31#16839663C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839662—21no—
34#16839661—21no—
35#16839661C2211yescharacteristic
36#16839654—21no—
37#16839648—21no—
38#16839637—21no—
39C4⋊C4×Dic61C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C22⋊C4×Dic61—21no—
42C4×C22⋊Dic61C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C2×#11758201—22no—
63C2×#11758201—41no—
64C2×#11758201—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519768—22no—
68#14519768—41no—
69#14519751—22no—
70#14519751—41no—
71Q8×Dic61—22no—
72Q8×Dic61—41no—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—41no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×C22⋊Dic61D411yescharacteristic
84C2×C22⋊Dic61D411yescharacteristic
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519706—41no—
96#14519701—22no—
97#14519699—22no—
98#14519699—41no—
99#14519697—22no—
100C22⋊#92418—41no—
101C8×Dic61—41no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684D411yescharacteristic
108#14519684D411yescharacteristic
109C22×Q8×C61C2311yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121#107×C61—22no—
122#103×C61—22no—
123#103×C61—41no—
124C22⋊C8×C61—41no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C23×D61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61#4112yes—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—42no—
147C2×C22⋊D61—42no—
148C2×C22⋊D61—81no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61—81no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61#4112yes—
178C22⋊C4×C61—24no—
179C22⋊C4×C61—81no—
180C22⋊Dic61—22no—
181C22⋊Dic61—22no—
182#11758201—44no—
183#11758198—42no—
184#11758198—42no—
185#11758198—81no—
186#11758198—81no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—42no—
193C4⋊Dic61—42no—
194C4⋊Dic61—42no—
195C4⋊Dic61—81no—
196C4⋊Dic61#4112yes—
197C4⋊Dic61#4112yes—
198#11758196—42no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—42no—
204C4×Dic61—81no—
205C4×Dic61—81no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61#13512yes—
219C23×C61C22×D411yescharacteristic
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—41no—
226C22×D61—41no—
227Q8×C61—22no—
228Q8×C61—22no—
229Q8×C61—41no—
230Q8×C61—41no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C22⋊D61—84no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—22no—
263C2×Dic61—22no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—84no—
278C2×Dic61#13712yes—
279D244—41no—
280D244—41no—
281D244—41no—
282D244—41no—
283C8×C61—41no—
284C8×C61—41no—
285#92418—41no—
286#92418—41no—
287#26727—611nomaximal, Sylow
288C22×C61—22no—
289C22×C61—22no—
290C22×C61—22no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61#52511yescharacteristic
296C22×C61#54611yescharacteristic
297C22×C61#54611yescharacteristic
298C22×C61C2×#13511yescharacteristic
299C22×C61C2×#13711yescharacteristic
300C22×C61#57611yescharacteristic
301C22×C61#57711yescharacteristic
302C2×D61—81no—
303C2×D61—81no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—81no—
307C2×D61—81no—
308C2×D61—81no—
309C4×C61—42no—
310C4×C61—41no—
311C4×C61—42no—
312C4×C61—81no—
313C4×C61—81no—
314C4×C61#52911yescharacteristic
315C4×C61#53811yescharacteristic
316C4×C61#55511yescharacteristic
317C4×C61#55911yescharacteristic
318Dic61—22no—
319Dic61—41no—
320Dic61—41no—
321Dic61—42no—
322Dic61—41no—
323Dic61—42no—
324Dic61—81no—
325#2490—611no—
326#2360—611no—
327#2055—611no—
328#2036D6111yescharacteristic, complemented
329#2026—611no—
330#2000—611no—
331#1989—611no—
332#1934—611no—
333#1925—611no—
334#1923—611no—
335#1921—611no—
336#1880—611no—
337#1874—611no—
338#1823—611no—
339C4×#103—611no—
340C2×C61—42no—
341C2×C61#245911yescharacteristic
342C2×C61#310811yescharacteristic
343C2×C61#311911yescharacteristic
344C2×C61#329611yescharacteristic
345C2×C61#329711yescharacteristic
346C2×C61#332011yescharacteristic
347C2×C61#333311yescharacteristic
348D61—161no—
349C22×SD16—611no—
350C2×#125—611no—
351C2×C22⋊Q8C2×D6111yescharacteristic
352C2×#121—611no—
353C2×C4×Q8—611no—
354C22×C4⋊C4—611no—
355C2×#107C2×D6111yescharacteristic
356C2×C4⋊C8—611no—
357C2×#103—611no—
358C2×#103C2×D6111yescharacteristic
359C2×#103C2×D6111yescharacteristic
360C2×#102—611no—
361C2×#102—611no—
362C2×#102—611no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8C2×D6111yescharacteristic
365C2×C4×C8—611no—
366#397—1221no—
367#394—1221no—
368#391—611no—
369#390—611no—
370#390—611no—
371#390—1221no—
372#389—611no—
373#389—1221no—
374#388—1221no—
375#387—1221no—
376#385—1221no—
377#380C2×D6111yescharacteristic
378C4×C4⋊C4—611no—
379C4×C4⋊C4—611no—
380C4×C22⋊C4—611no—
381C4×C22⋊C4—1221no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340—611no—
388#340—611no—
389#340C2×D6111yescharacteristic
390#336—611no—
391#336—611no—
392C61#2672711yescharacteristic, complemented, Sylow
393C22×Q8C22×D6111yescharacteristic
394C22×D4—611no—
395C22×D4—1221no—
396C23×C4—1221no—
397C23×C4C22×D6111yescharacteristic
398C2×SD16—1222no—
399C2×SD16—2441no—
400C2×SD16—2441no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8C22×D6111yescharacteristic
404C22×C8C22×D6111yescharacteristic
405#125—1222no—
406#125—2441no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—1222no—
410#121—2441no—
411C4×Q8—1222no—
412C4×Q8—2441no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—1222no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1221no—
420C2×C4⋊C4—1221no—
421C2×C4⋊C4—1221no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—2441no—
424C2×C4⋊C4C22×D6111yescharacteristic
425C2×C4⋊C4C22×D6111yescharacteristic
426C2×C4⋊C4C22×D6111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441#107—22no—
442C4⋊C8—2441no—
443#103—22no—
444#103—41no—
445#103—1222no—
446#102—1222no—
447#102—1222no—
448#102—2441no—
449C22⋊C8—41no—
450C22⋊C8—2441no—
451C4×C8—2441no—
452#95—21no—
453#95—611no—
454#95—611no—
455#95—1221no—
456#95—1221no—
457#95—1221no—
458#95—1221no—
459#95—1221no—
460C24—1221no—
461C24D4×D6111yescharacteristic
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#1175822412yes—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—4881no—
475C2×D4—2442no—
476C2×D4—2442no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—4881no—
495C22×C4—2442no—
496C22×C4—2442no—
497C22×C4D4×D6111yescharacteristic
498C22×C4C23×D6111yescharacteristic
499SD16—2444no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—612no—
519C4⋊C4—612no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1221no—
524C4⋊C4—4881no—
525C4⋊C4—2442no—
526C4⋊C4—2442no—
527C4⋊C4—2442no—
528C4⋊C4—2442no—
529C4⋊C4#1175822412yes—
530C22⋊C4—24no—
531C22⋊C4—81no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—4881no—
535C22⋊C4—4881no—
536C22⋊C4—4881no—
537C22⋊C4—2442no—
538C22⋊C4—2442no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—4881no—
544C42—4881no—
545C42—2442no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—2441no—
553C23—2441no—
554C23—2441no—
555C23—2441no—
556C23—2441no—
557C23—2441no—
558C23—2441no—
559C23#1451980012yes—
560C23C2×D4×D6111yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—41no—
564Q8—41no—
565D4—4884no—
566D4—2441no—
567D4—2441no—
568D4—2441no—
569D4—2441no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—612no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1222no—
601C2×C4—1221no—
602C2×C4—1222no—
603C2×C4—4884no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4#41×D6111yescharacteristic
612C2×C4#41×D6111yescharacteristic
613C2×C4C2×#1175822411yescharacteristic
614C2×C4C2×#1175822411yescharacteristic
615C2×C4#1451982211yescharacteristic
616C2×C4#1451982311yescharacteristic
617C8—41no—
618C8—41no—
619C8—2441no—
620C8—2441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—4881no—
629C22—4881no—
630C22—4881no—
631C22—4881no—
632C22—4881no—
633C22—4881no—
634C22—4881no—
635C22#1684026811yescharacteristic
636C22#1684040111yescharacteristic
637C22#1684040411yescharacteristic
638C22C2×#1451980011yescharacteristic
639C22#137×D6111yescharacteristic
640C22#1684056611yescharacteristic
641C22#1684056911yescharacteristic
642C4—41no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—1222no—
648C4—4881no—
649C4—2441no—
650C4—2442no—
651C4—2441no—
652C4—2441no—
653C4—2442no—
654C4#1684028911yescharacteristic
655C4#1684034911yescharacteristic
656C4#1684047611yescharacteristic
657C4#1684049411yescharacteristic
658C2—42no—
659C2—9761no—
660C2#2144974911yescharacteristic
661C2#2145590011yescharacteristic
662C2#2145601911yescharacteristic
663C2#2145766011yescharacteristic
664C2#2145766711yescharacteristic
665C2#2145799311yescharacteristic
666C2#2145815211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2036C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2036D61
hypocenterC61#26727
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. #21448828C2semidirect
3. #21447133C2semidirect
4. #21446968C2semidirect
6. #21446773C2semidirect
7. #21446503C2semidirect
8. #21446438C2semidirect
9. #21446428C2semidirect
10. #21446413C2semidirect
11. #21446172C2semidirect
13. #21445903C2semidirect
14. #103×Dic61C2semidirect
15. C61×#2036C2semidirect
328. #2036D61semidirect
392. C61#26727semidirect

Maximal subgroups

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

subgroupindex
#214501672
#214488282
#214471332
#214469682
#214468202
#214467732
#214465032
#214464382
#214464282
#214464132
#214461722
#214461342
#214459032
#103×Dic612
C61×#20362
#2672761