Finite Group Databasebeta

← #29748190

Subgroups — #29748190

Order 15616.

824 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448855C211yesmaximal, characteristic, complemented
2#21447129C211yesmaximal, characteristic, complemented
3#21447001C211yesmaximal, characteristic, complemented
4#21446962C211yesmaximal, characteristic, complemented
5#21446815C211yesmaximal, characteristic
6#21446777C211yesmaximal, characteristic, complemented
7#21446505C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic, complemented
9#21446427C211yesmaximal, characteristic, complemented
10#21446411C211yesmaximal, characteristic, complemented
11#21446170C211yesmaximal, characteristic, complemented
12#21446142C211yesmaximal, characteristic, complemented
13#21445911C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2490C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C4×#92418C2211yescharacteristic
31#16839664C2211yescharacteristic
32#16839662—21no—
33#16839660C2211yescharacteristic
34#16839651—21no—
35#16839638—21no—
36C4×C4⋊Dic61C2211yescharacteristic
37#16839609—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#125×C61C2211yescharacteristic
49C2×#121×C61C2211yescharacteristic
50C61×#397—21no—
51C61×#394—21no—
52C61×#390—21no—
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C22×C4×D61—21no—
62C2×#11758199—22no—
63C2×#11758199—41no—
64C2×#11758199—41no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519751—22no—
70#14519751—22no—
71C4×D244—22no—
72C4×D244—41no—
73#14519736—22no—
74#14519736—41no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86#14519710—22no—
87C4⋊#92418—41no—
88#14519698—22no—
89#14519698—22no—
90#14519698—41no—
91#14519697—22no—
92#14519697—22no—
93#14519697—41no—
94C22⋊#92418—41no—
95C22⋊#92418—41no—
96C4×#92418—41no—
97#14519684—21no—
98#14519684—21no—
99C22×D4×C61—21no—
100C22×D4×C61C2311yescharacteristic
101C23×C4×C61C2311yescharacteristic
102#125×C61—22no—
103#125×C61—41no—
104#121×C61—22no—
105#121×C61—41no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C23×D61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—42no—
136C2×D4×C61—42no—
137C2×D4×C61—81no—
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×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—24no—
154C2×C22⋊D61—81no—
155C2×C22⋊D61—81no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244#4112yes—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61—81no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—42no—
174C4⋊C4×C61—42no—
175C4⋊C4×C61#4112yes—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—42no—
179C22⋊C4×C61—42no—
180C22⋊C4×C61—81no—
181C22⋊C4×C61—81no—
182C22⋊C4×C61—81no—
183C22⋊C4×C61—81no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—81no—
189C22⋊Dic61—42no—
190#11758199—44no—
191#11758198—24no—
192#11758198—42no—
193#11758198—42no—
194#11758198—81no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61#4112yes—
200C4⋊Dic61#4112yes—
201#11758196—81no—
202C4×Dic61—42no—
203C4×Dic61—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231C22×D61—22no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—84no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—22no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61#13512yes—
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61H(5,𝔽2)11yescharacteristic
276C2×C4×C61H(5,𝔽2)11yescharacteristic
277C22⋊D61—84no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287D244—22no—
288D244—22no—
289D244—41no—
290D244—41no—
291C4×D61—84no—
292#92418—41no—
293#92418—41no—
294#92418—41no—
295#92418—41no—
296#26730—611nomaximal, Sylow
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61#52511yescharacteristic
312C22×C61#54611yescharacteristic
313C22×C61#54611yescharacteristic
314C22×C61C2×#13511yescharacteristic
315C22×C61#57511yescharacteristic
316C22×C61#57611yescharacteristic
317C22×C61#57611yescharacteristic
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—81no—
322C2×D61—81no—
323C2×D61—81no—
324C2×D61—81no—
325C4×C61—22no—
326C4×C61—41no—
327C4×C61—41no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—42no—
331C4×C61—81no—
332C4×C61—81no—
333C4×C61#52911yescharacteristic
334C4×C61#53811yescharacteristic
335C4×C61#55511yescharacteristic
336C4×C61#55911yescharacteristic
337Dic61—42no—
338Dic61—42no—
339Dic61—81no—
340#2490D6111yescharacteristic, complemented
341#2363—611no—
342#2054—611no—
343#2033—611no—
344#2025—611no—
345#1999—611no—
346#1989—611no—
347#1934—611no—
348#1925—611no—
349#1923—611no—
350#1921—611no—
351#1879—611no—
352#1875—611no—
353#1825—611no—
354C4×#102—611no—
355C2×C61—81no—
356C2×C61—161no—
357C2×C61#245911yescharacteristic
358C2×C61#310211yescharacteristic
359C2×C61#312211yescharacteristic
360C2×C61#329711yescharacteristic
361C2×C61#330511yescharacteristic
362C2×C61#330911yescharacteristic
363C2×C61#332211yescharacteristic
364D61—82no—
365C22×D8—611no—
366C2×#125C2×D6111yescharacteristic
367C2×#121—611no—
368C2×#121C2×D6111yescharacteristic
369C2×C4×D4—611no—
370C2×#117—611no—
371C2×#107—611no—
372C2×C4⋊C8—611no—
373C2×#102—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102—611no—
377C2×#102—611no—
378C2×#102—611no—
379C2×C22⋊C8—611no—
380C2×C22⋊C8—611no—
381C2×C4×C8—611no—
382#397—21no—
383#394—21no—
384#390—21no—
385#390—611no—
386#390—1221no—
387#390C2×D6111yescharacteristic
388#390C2×D6111yescharacteristic
389#389—611no—
390#388—21no—
391#388—1221no—
392#386—1221no—
393#380C2×D6111yescharacteristic
394C4×C4⋊C4—611no—
395C4×C4⋊C4C2×D6111yescharacteristic
396C4×C22⋊C4—1221no—
397C4×C22⋊C4C2×D6111yescharacteristic
398#340—611no—
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#340—611no—
404#340—611no—
405#340—611no—
406#336—611no—
407#336—611no—
408C61#2673011yescharacteristic, complemented, Sylow
409C22×D4—21no—
410C22×D4—611no—
411C22×D4—1221no—
412C22×D4C22×D6111yescharacteristic
413C23×C4—1221no—
414C23×C4C22×D6111yescharacteristic
415C2×D8—1222no—
416C2×D8—2441no—
417C2×D8—2441no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—611no—
422#125—22no—
423#125—41no—
424#121—22no—
425#121—41no—
426#121—1222no—
427#121—1222no—
428C4×D4—1222no—
429C4×D4—2441no—
430#117—1222no—
431#117—2441no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4C22×D6111yescharacteristic
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C4⋊C4C22×D6111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4C22⋊D6111yescharacteristic
453C2×C22⋊C4C22⋊D6111yescharacteristic
454C2×C42—21no—
455C2×C42—1221no—
456C2×C42—1221no—
457C2×C42C22×D6111yescharacteristic
458C2×C42C22×D6111yescharacteristic
459#107—1222no—
460C4⋊C8—2441no—
461#102—1222no—
462#102—1222no—
463#102—1222no—
464#102—1222no—
465#102—2441no—
466#102—2441no—
467C22⋊C8—2441no—
468C22⋊C8—2441no—
469C4×C8—2441no—
470#95—21no—
471#95—21no—
472#95—1221no—
473#95—1221no—
474#95C22⋊D6111yescharacteristic
475#95C22⋊D6111yescharacteristic
476C24—21no—
477C24—1221no—
478C24C2×C22⋊D6111yescharacteristic
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4—612no—
489C2×D4—1224no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4—1221no—
494C2×D4—1221no—
495C2×D4—4881no—
496C2×D4—4881no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—4881no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4C2×C22⋊D6111yescharacteristic
513C22×C4C2×C22⋊D6111yescharacteristic
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C2×C22⋊D6111yescharacteristic
517C22×C4C23×D6111yescharacteristic
518D8—2444no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—612no—
539C4⋊C4—612no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—4881no—
545C4⋊C4#1175822412yes—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—1224no—
555C22⋊C4—4881no—
556C22⋊C4—2442no—
557C22⋊C4—2442no—
558C22⋊C4—2442no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—81no—
564C42—4881no—
565C42—2442no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—1222no—
581C23—2441no—
582C23—2441no—
583C23—2441no—
584C23—2441no—
585C23—2441no—
586C23—2441no—
587C23C22×C22⋊D6111yescharacteristic
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593D4—1222no—
594D4—1222no—
595D4—4884no—
596D4—2441no—
597D4—2441no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—4884no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4#1451979712yes—
636C2×C4#41×D6111yescharacteristic
637C2×C4#41×D6111yescharacteristic
638C2×C4#41×D6111yescharacteristic
639C2×C4C2×#1175822411yescharacteristic
640C2×C4#1451982211yescharacteristic
641C2×C4#1451982311yescharacteristic
642C8—2441no—
643C8—2441no—
644C8—2441no—
645C8—2441no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—4881no—
661C22—4881no—
662C22—4881no—
663C22—4881no—
664C22—2442no—
665C22—2442no—
666C22—2442no—
667C22#1684026911yescharacteristic
668C22#1684040011yescharacteristic
669C22#1684040611yescharacteristic
670C22C2×#1451979711yescharacteristic
671C22#1684056011yescharacteristic
672C22#1684056511yescharacteristic
673C22#1684056511yescharacteristic
674C4—22no—
675C4—41no—
676C4—41no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4—4881no—
683C4—2442no—
684C4—2442no—
685C4#1684029111yescharacteristic
686C4#1684034611yescharacteristic
687C4#1684047411yescharacteristic
688C4#1684049411yescharacteristic
689C2—81no—
690C2—161no—
691C2—4882no—
692C2#2144975211yescharacteristic
693C2#2145583111yescharacteristic
694C2#2145605711yescharacteristic
695C2#2145766311yescharacteristic
696C2#2145776911yescharacteristic
697C2#2145781911yescharacteristic
698C2#2145802011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2490C2
socleC23×C61C22×D4
prime radical#21446815C2
hypercenter#2490D61
hypocenterC61#26730
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2490

Complements

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

NH ≅ G/Ntype
1. #21448855C2semidirect
2. #21447129C2semidirect
3. #21447001C2semidirect
4. #21446962C2semidirect
6. #21446777C2semidirect
7. #21446505C2semidirect
8. #21446436C2semidirect
9. #21446427C2semidirect
10. #21446411C2semidirect
11. #21446170C2semidirect
12. #21446142C2semidirect
13. #21445911C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2490C2semidirect
340. #2490D61semidirect
408. C61#26730semidirect

Maximal subgroups

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

subgroupindex
#214488552
#214471292
#214470012
#214469622
#214468152
#214467772
#214465052
#214464362
#214464272
#214464112
#214461702
#214461422
#214459112
C4×#145196972
C61×#24902
#2673061