Finite Group Databasebeta

← #29779624

Subgroups — #29779624

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451644C211yesmaximal, characteristic
2#21448405C211yesmaximal, characteristic
3#21447240C211yesmaximal, characteristic, complemented
4#21447240C211yesmaximal, characteristic, complemented
5#21446958C211yesmaximal, characteristic, complemented
6#21446958C211yesmaximal, characteristic, complemented
7#21446511C211yesmaximal, characteristic, complemented
8#21446506C211yesmaximal, characteristic, complemented
9#21446497C211yesmaximal, characteristic, complemented
10#21446492C211yesmaximal, characteristic, complemented
11#21445915C211yesmaximal, characteristic
12#21445911C211yesmaximal, characteristic
13#21445754C211yesmaximal, characteristic
14#21445587C211yesmaximal, characteristic
15C61×#1787C211yesmaximal, characteristic
16C2×#14519776C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519701C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519687C2211yescharacteristic
25C2×C8×Dic61C2211yescharacteristic
26#16839704—21no—
27#16839698—21no—
28#16839683—21no—
29#16839674—21no—
30#16839669—21no—
31#16839669—21no—
32#16839669C2211yescharacteristic
33#16839669C2211yescharacteristic
34#16839669C2211yescharacteristic
35#16839669C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839658C2211yescharacteristic
38#16839627C2211yescharacteristic
39#16839625—21no—
40#16839625—21no—
41#16839622C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C23×Q8×C61C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C22×Dic122—21no—
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519776—41no—
63#14519776—41no—
64#14519736—22no—
65#14519736—22no—
66#14519736—41no—
67#14519736—41no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61D411yescharacteristic
70C2×C4⋊Dic61D411yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61D411yescharacteristic
80C2×C22⋊Dic61D411yescharacteristic
81C2×C4×Dic61—21no—
82C2×C4×Dic61C2311yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84#14519701—22no—
85#14519701—22no—
86#14519701—41no—
87#14519701—41no—
88C22⋊#92418—22no—
89#14519687—41no—
90C8×Dic61—41no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104C22×Q8×C61—22no—
105C22×Q8×C61—22no—
106C22×Q8×C61—21no—
107C22×Q8×C61—22no—
108C22×Q8×C61—22no—
109C22×Q8×C61—41no—
110C22×Q8×C61—41no—
111C22×Q8×C61C2311yescharacteristic
112C22×Q8×C61C2311yescharacteristic
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120#103×C61—22no—
121#103×C61—22no—
122#103×C61—41no—
123#103×C61—41no—
124C22⋊C8×C61—22no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C2×Q8×C61—24no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—44no—
139C2×Q8×C61—44no—
140C2×Q8×C61—44no—
141C2×Q8×C61—44no—
142C2×Q8×C61—42no—
143C2×Q8×C61—42no—
144C2×Q8×C61#4112yes—
145C2×Q8×C61#4112yes—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—24no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4112yes—
159C22×C4×C61#4112yes—
160C22×C4×C61C2411yescharacteristic
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C2×D411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C2×Dic122—42no—
170C2×Dic122—81no—
171C2×Dic122—81no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C22⋊C4×C61—81no—
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185C22⋊Dic61—42no—
186C22⋊Dic61—81no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—41no—
196C4⋊Dic61—41no—
197C4⋊Dic61—81no—
198#11758196—42no—
199#11758196—81no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—42no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61#12412yes—
218C23×C61C22×D411yescharacteristic
219Q8×C61—22no—
220Q8×C61—22no—
221Q8×C61—22no—
222Q8×C61—22no—
223Q8×C61—48no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—41no—
227Q8×C61—41no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—48no—
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#12412yes—
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278Dic122—84no—
279C8×C61—41no—
280C8×C61—41no—
281#92418—41no—
282#92418—41no—
283#29118—611nomaximal, Sylow
284C22×C61—22no—
285C22×C61—22no—
286C22×C61—22no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61#52511yescharacteristic
292C22×C61C2×#12411yescharacteristic
293C22×C61#53411yescharacteristic
294C22×C61#57711yescharacteristic
295C22×C61#57711yescharacteristic
296C22×C61#57811yescharacteristic
297C22×C61#57811yescharacteristic
298C4×C61—22no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#55111yescharacteristic
304C4×C61#55111yescharacteristic
305C4×C61#55111yescharacteristic
306C4×C61#55111yescharacteristic
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314Dic61—81no—
315#2628—611no—
316#2310—611no—
317#2074—611no—
318#2074—611no—
319#2024—611no—
320#2024—611no—
321#1935—611no—
322#1935—611no—
323#1933—611no—
324#1933—611no—
325#1825—611no—
326#1825—611no—
327#1787—611no—
328#1787D6111yescharacteristic
329#1750—611no—
330C2×C61—42no—
331C2×C61#256111yescharacteristic
332C2×C61#312111yescharacteristic
333C2×C61#312111yescharacteristic
334C2×C61#313711yescharacteristic
335C2×C61#313711yescharacteristic
336C2×C61#320011yescharacteristic
337C2×C61#320211yescharacteristic
338C23×Q8C2×D6111yescharacteristic
339C2×C4⋊Q8—611no—
340C2×#117—611no—
341C2×#117—611no—
342C2×#103—611no—
343C2×#103—611no—
344C2×#103—611no—
345C2×#103—611no—
346C2×#103C2×D6111yescharacteristic
347C2×#103C2×D6111yescharacteristic
348C2×#103C2×D6111yescharacteristic
349C2×#103C2×D6111yescharacteristic
350C2×C22⋊C8—611no—
351C2×C22⋊C8C2×D6111yescharacteristic
352C2×#97—611no—
353C2×C4×C8—611no—
354#400—1221no—
355#399—1221no—
356#395—1221no—
357#393—1221no—
358#391—611no—
359#391—611no—
360#391—611no—
361#391—611no—
362#391—1221no—
363#391—1221no—
364#389—611no—
365#389—611no—
366#382—611no—
367#381—1221no—
368#381—1221no—
369#380—611no—
370#380C2×D6111yescharacteristic
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#336—611no—
380#336—611no—
381C61#2911811yescharacteristic, complemented, Sylow
382C22×Q8—22no—
383C22×Q8—22no—
384C22×Q8—21no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—41no—
388C22×Q8—41no—
389C22×Q8—1221no—
390C22×Q8C22×D6111yescharacteristic
391C22×Q8C22×D6111yescharacteristic
392C23×C4—21no—
393C23×C4C22×D6111yescharacteristic
394C22×C8—611no—
395C22×C8—611no—
396C22×C8C22×D6111yescharacteristic
397C22×C8C22×D6111yescharacteristic
398C4⋊Q8—2441no—
399C4⋊Q8—2441no—
400#117—1222no—
401#117—1222no—
402#117—2441no—
403#117—2441no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1221no—
423#103—22no—
424#103—22no—
425#103—41no—
426#103—41no—
427#103—1222no—
428#103—1222no—
429#103—2441no—
430#103—2441no—
431C22⋊C8—22no—
432C22⋊C8—1222no—
433#97—2441no—
434C4×C8—2441no—
435#95—21no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449C24D4×D6111yescharacteristic
450C2×Q8—24no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—4881no—
468C2×Q8—4881no—
469C2×Q8—2442no—
470C2×Q8#1175822412yes—
471C2×Q8#1175822412yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4#1175822212yes—
492C22×C4D4×D6111yescharacteristic
493C22×C4#1175822412yes—
494C22×C4C23×D6111yescharacteristic
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—4881no—
520C4⋊C4—4881no—
521C4⋊C4—2441no—
522C4⋊C4—2441no—
523C4⋊C4—2442no—
524C22⋊C4—81no—
525C22⋊C4—4881no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C22⋊C4—2442no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42—2442no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23#1451976312yes—
541C23C2×D4×D6111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—22no—
546Q8—48no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—4884no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—48no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4#1451976312yes—
596C2×C4C2×#1175822411yescharacteristic
597C2×C4C2×#1175822411yescharacteristic
598C2×C4C2×#1175822411yescharacteristic
599C2×C4C2×#1175822211yescharacteristic
600C2×C4#1451982211yescharacteristic
601C2×C4#1451982211yescharacteristic
602C8—41no—
603C8—41no—
604C8—2441no—
605C8—2441no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22#1684026811yescharacteristic
614C22C2×#1451976311yescharacteristic
615C22#1684032211yescharacteristic
616C22#1684056811yescharacteristic
617C22#1684057111yescharacteristic
618C22#1684057511yescharacteristic
619C22#1684057811yescharacteristic
620C4—22no—
621C4—42no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—4881no—
626C4—4881no—
627C4—4881no—
628C4—4881no—
629C4—2441no—
630C4—2441no—
631C4—2441no—
632C4—2441no—
633C4#1684043811yescharacteristic
634C4#1684043811yescharacteristic
635C4#1684044311yescharacteristic
636C4#1684044311yescharacteristic
637C2—42no—
638C2#2145097411yescharacteristic
639C2#2145604111yescharacteristic
640C2#2145604911yescharacteristic
641C2#2145618011yescharacteristic
642C2#2145618211yescharacteristic
643C2#2145668911yescharacteristic
644C2#2145671211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1787C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1787D61
hypocenterC61#29118
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. #21447240C2semidirect
4. #21447240C2semidirect
5. #21446958C2semidirect
6. #21446958C2semidirect
7. #21446511C2semidirect
8. #21446506C2semidirect
9. #21446497C2semidirect
10. #21446492C2semidirect
381. C61#29118semidirect

Maximal subgroups

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

subgroupindex
#214516442
#214484052
#214472402
#214469582
#214465112
#214465062
#214464972
#214464922
#214459152
#214459112
#214457542
#214455872
C61×#17872
#2911861