Finite Group Databasebeta

← #29740598

Subgroups — #29740598

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21449233C211yesmaximal, characteristic
2#21448750C211yesmaximal, characteristic, complemented
3#21447390C211yesmaximal, characteristic, complemented
4#21447255C211yesmaximal, characteristic, complemented
5#21447235C211yesmaximal, characteristic, complemented
6#21446449C211yesmaximal, characteristic, complemented
7#21446392C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446137C211yesmaximal, characteristic, complemented
11#21446108C211yesmaximal, characteristic, complemented
12#21446015C211yesmaximal, characteristic, complemented
13#21445910C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#2033C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519748C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27#16839678—21no—
28#16839670—21no—
29#16839665—21no—
30#16839665C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839654—21no—
33#16839650—21no—
34#16839649—21no—
35#16839639—21no—
36#16839627C2211yescharacteristic
37#16839622C2211yescharacteristic
38#16839619C2211yescharacteristic
39C4⋊C4×Dic61C2211yescharacteristic
40C22⋊C4×Dic61—21no—
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×C22⋊D61—21no—
60C22×C22⋊D61D411yescharacteristic
61C23×Dic61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—22no—
66C2×C8×D61—41no—
67C2×C8×D61—41no—
68#14519748—22no—
69#14519748—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72#14519735—22no—
73#14519735—22no—
74#14519735—41no—
75#14519735—41no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—41no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×#11758196D411yescharacteristic
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198D411yescharacteristic
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98#14519708—41no—
99#14519698—22no—
100#14519698—41no—
101C22⋊#92418—41no—
102#14519689—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109C22×D4×C61—21no—
110C22×D4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114#121×C61—22no—
115#121×C61—41no—
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#102×C61—41no—
123#102×C61—41no—
124C22⋊C8×C61—41no—
125#95×C61—21no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128C23×D61C2×D411yescharacteristic
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×C61C2411yescharacteristic
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—42no—
153C2×C22⋊D61—81no—
154C2×C22⋊D61—81no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—42no—
160C22×Dic61—42no—
161C22×Dic61—81no—
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61#4112yes—
170C2×C4×D61#4112yes—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61#4112yes—
183C22⋊C4×C61—42no—
184C22⋊C4×C61—42no—
185C22⋊Dic61—22no—
186C22⋊Dic61—42no—
187C22⋊Dic61—42no—
188C22⋊Dic61—81no—
189C22⋊Dic61—81no—
190#11758198—22no—
191#11758198—42no—
192#11758198—42no—
193#11758198—81no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—42no—
202C4⋊Dic61—81no—
203C4⋊Dic61#4112yes—
204#11758196—22no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—42no—
208C4×Dic61—42no—
209C4×Dic61—81no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C8×D61—44no—
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×C61#13512yes—
231C23×C61C22×D411yescharacteristic
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61—21no—
236C22×D61—21no—
237C22×D61—21no—
238C22×D61#12312yes—
239D4×C61—41no—
240D4×C61—41no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—84no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61H(5,𝔽2)11yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C22⋊D61—44no—
267C22⋊D61—84no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—84no—
289C2×Dic61#12312yes—
290C4×D61—22no—
291C4×D61—22no—
292C4×D61—22no—
293C4×D61—22no—
294C8×C61—41no—
295C8×C61—41no—
296#92418—41no—
297#92418—41no—
298#26199—611nomaximal, Sylow
299C22×C61—22no—
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61—41no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—81no—
313C22×C61C2×#12311yescharacteristic
314C22×C61#54611yescharacteristic
315C22×C61#54611yescharacteristic
316C22×C61C2×#13511yescharacteristic
317C22×C61#57511yescharacteristic
318C22×C61#57611yescharacteristic
319C22×C61#57711yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C4×C61—41no—
328C4×C61—42no—
329C4×C61—81no—
330C4×C61—81no—
331C4×C61#52911yescharacteristic
332C4×C61#53811yescharacteristic
333C4×C61#55311yescharacteristic
334C4×C61#55311yescharacteristic
335Dic61—22no—
336Dic61—41no—
337Dic61—41no—
338Dic61—42no—
339Dic61—81no—
340Dic61—81no—
341Dic61—81no—
342#2414—611no—
343#2352—611no—
344#2101—611no—
345#2077—611no—
346#2073—611no—
347#2033D6111yescharacteristic, complemented
348#1926—611no—
349#1918—611no—
350#1893—611no—
351#1875—611no—
352#1874—611no—
353#1869—611no—
354#1854—611no—
355#1824—611no—
356#1735—611no—
357C2×C61—42no—
358C2×C61—161no—
359C2×C61#244411yescharacteristic
360C2×C61#309111yescharacteristic
361C2×C61#309611yescharacteristic
362C2×C61#329711yescharacteristic
363C2×C61#330111yescharacteristic
364C2×C61#331711yescharacteristic
365C2×C61#331911yescharacteristic
366D61—42no—
367C23×C8—611no—
368C2×#121—611no—
369C2×#121C2×D6111yescharacteristic
370C2×C4×D4—611no—
371C2×#117—611no—
372C2×#117—611no—
373C22×C4⋊C4—611no—
374C2×#107C2×D6111yescharacteristic
375C2×#106—611no—
376C2×#102—611no—
377C2×#102—611no—
378C2×#102C2×D6111yescharacteristic
379C2×#102C2×D6111yescharacteristic
380C2×C22⋊C8—611no—
381C2×C22⋊C8—611no—
382C2×C22⋊C8C2×D6111yescharacteristic
383#394—1221no—
384#392—1221no—
385#390—611no—
386#390—1221no—
387#389—611no—
388#388—1221no—
389#388—1221no—
390#387—1221no—
391#386—1221no—
392#382—611no—
393#380—611no—
394#380—611no—
395#380C2×D6111yescharacteristic
396C4×C4⋊C4—611no—
397C4×C22⋊C4—1221no—
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#340—611no—
407#340C2×D6111yescharacteristic
408#336—611no—
409#336—611no—
410C61#2619911yescharacteristic, complemented, Sylow
411C22×D4—21no—
412C22×D4—611no—
413C22×D4—1221no—
414C22×D4C22×D6111yescharacteristic
415C23×C4—611no—
416C23×C4—1221no—
417C23×C4C22×D6111yescharacteristic
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—1222no—
421C22×C8—2441no—
422C22×C8—2441no—
423C22×C8C22×D6111yescharacteristic
424C22×C8C22×D6111yescharacteristic
425#121—22no—
426#121—41no—
427#121—1222no—
428#121—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431#117—1222no—
432#117—1222no—
433#117—2441no—
434#117—2441no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—611no—
440C2×C4⋊C4—1222no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—2441no—
444C2×C4⋊C4C22×D6111yescharacteristic
445C2×C4⋊C4C22×D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—611no—
450C2×C22⋊C4—611no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C42—611no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42—1221no—
462#107—22no—
463#106—2441no—
464#102—41no—
465#102—41no—
466#102—1222no—
467#102—2441no—
468C22⋊C8—41no—
469C22⋊C8—1222no—
470C22⋊C8—2441no—
471#95—21no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476#95—1221no—
477#95—1221no—
478C24—21no—
479C24—611no—
480C24D4×D6111yescharacteristic
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—81no—
490C2×D4—1222no—
491C2×D4—1222no—
492C2×D4—4881no—
493C2×D4—4881no—
494C2×D4—2441no—
495C2×D4—2442no—
496C22×C4—21no—
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—611no—
506C22×C4—612no—
507C22×C4—612no—
508C22×C4—611no—
509C22×C4—611no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—4881no—
519C22×C4—2442no—
520C22×C4—2442no—
521C22×C4D4×D6111yescharacteristic
522C22×C4C23×D6111yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—2444no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—612no—
542C4⋊C4—1222no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—4881no—
551C4⋊C4—2442no—
552C4⋊C4#1175822412yes—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—1222no—
556C22⋊C4—1222no—
557C22⋊C4—4881no—
558C22⋊C4—4881no—
559C22⋊C4—4881no—
560C22⋊C4—2442no—
561C22⋊C4—2442no—
562C22⋊C4—2442no—
563C22⋊C4—2442no—
564C42—1221no—
565C42—1221no—
566C42—4881no—
567C42—2442no—
568C42—2442no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—612no—
583C23—1221no—
584C23—1221no—
585C23—1221no—
586C23—1221no—
587C23—1221no—
588C23—1221no—
589C23#1451979612yes—
590C23C2×D4×D6111yescharacteristic
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—84no—
596D4—4884no—
597D4—2444no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—612no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1222no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1222no—
621C2×C4—1221no—
622C2×C4—1221no—
623C2×C4—1221no—
624C2×C4—1221no—
625C2×C4—1221no—
626C2×C4—1221no—
627C2×C4—1222no—
628C2×C4—4884no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4#41×D6111yescharacteristic
641C2×C4#41×D6111yescharacteristic
642C2×C4#41×D6111yescharacteristic
643C2×C4C2×#1175822411yescharacteristic
644C2×C4#1451982211yescharacteristic
645C2×C4#1451982211yescharacteristic
646C8—41no—
647C8—41no—
648C8—2441no—
649C8—2441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—1222no—
665C22—1222no—
666C22—1222no—
667C22—2441no—
668C22—2441no—
669C22—2441no—
670C22—2441no—
671C22#123×D6111yescharacteristic
672C22#1684039911yescharacteristic
673C22#1684040111yescharacteristic
674C22C2×#1451979611yescharacteristic
675C22#1684056111yescharacteristic
676C22#1684056611yescharacteristic
677C22#1684056911yescharacteristic
678C4—42no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4—1222no—
683C4—4881no—
684C4—4881no—
685C4—4881no—
686C4—2442no—
687C4—2441no—
688C4—2441no—
689C4#1684029111yescharacteristic
690C4#1684034411yescharacteristic
691C4#1684045711yescharacteristic
692C4#1684045911yescharacteristic
693C2—42no—
694C2—161no—
695C2—2442no—
696C2#2144956211yescharacteristic
697C2#2145572711yescharacteristic
698C2#2145577211yescharacteristic
699C2#2145767311yescharacteristic
700C2#2145772711yescharacteristic
701C2#2145793811yescharacteristic
702C2#2145797011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2033C2
socleC23×C61C22×D4
prime radical#21449233C2
hypercenter#2033D61
hypocenterC61#26199
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
2. #21448750C2semidirect
3. #21447390C2semidirect
4. #21447255C2semidirect
5. #21447235C2semidirect
6. #21446449C2semidirect
7. #21446392C2semidirect
8. #21446244C2semidirect
9. #21446138C2semidirect
10. #21446137C2semidirect
11. #21446108C2semidirect
12. #21446015C2semidirect
13. #21445910C2semidirect
14. #21445534C2semidirect
15. C61×#2033C2semidirect
347. #2033D61semidirect
410. C61#26199semidirect

Maximal subgroups

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

subgroupindex
#214492332
#214487502
#214473902
#214472552
#214472352
#214464492
#214463922
#214462442
#214461382
#214461372
#214461082
#214460152
#214459102
#214455342
C61×#20332
#2619961