Finite Group Databasebeta

← #29724366

Subgroups — #29724366

Order 15616.

754 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450116C211yesmaximal, characteristic
2#21448748C211yesmaximal, characteristic
3#21447388C211yesmaximal, characteristic, complemented
4#21447302C211yesmaximal, characteristic, complemented
5#21447252C211yesmaximal, characteristic, complemented
6#21447242C211yesmaximal, characteristic, complemented
7#21446412C211yesmaximal, characteristic, complemented
8#21446391C211yesmaximal, characteristic, complemented
9#21446020C211yesmaximal, characteristic, complemented
10#21446009C211yesmaximal, characteristic, complemented
11#21445915C211yesmaximal, characteristic, complemented
12#21445910C211yesmaximal, characteristic, complemented
13#21445848C211yesmaximal, characteristic, complemented
14#21445536C211yesmaximal, characteristic, complemented
15C61×#1869C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519711C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23#16839690—21no—
24#16839676—21no—
25#16839660C2211yescharacteristic
26#16839660C2211yescharacteristic
27#16839655—21no—
28#16839650—21no—
29#16839648—21no—
30#16839643—21no—
31#16839642—21no—
32#16839628C2211yescharacteristic
33#16839622C2211yescharacteristic
34#16839622C2211yescharacteristic
35#16839622C2211yescharacteristic
36#16839622C2211yescharacteristic
37#16839622C2211yescharacteristic
38C4×C4⋊Dic61C2211yescharacteristic
39C22⋊C4×Dic61—21no—
40#16839525C2211yescharacteristic
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C23×C8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C23×Dic61—21no—
60#14519736—22no—
61#14519736—22no—
62#14519736—22no—
63#14519736—41no—
64C2×C4⋊Dic61—22no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—41no—
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
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⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87#14519711—22no—
88#14519711—22no—
89#14519711—41no—
90#14519709—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—
101C22×D4×C61D411yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C22×C8×C61—22no—
105C22×C8×C61—22no—
106C22×C8×C61—41no—
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C22⋊C4×C61D411yescharacteristic
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C22⋊C8×C61—22no—
118C22⋊C8×C61—22no—
119C22⋊C8×C61—41no—
120C24×C61C2×D411yescharacteristic
121C24×C61C2×D411yescharacteristic
122C2×D4×C61—22no—
123C2×D4×C61—22no—
124C2×D4×C61—41no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—42no—
151C22×Dic61—42no—
152C22×Dic61—81no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—44no—
165C2×C8×C61#4112yes—
166C4⋊C4×C61—22no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C42×C61—21no—
170C42×C61—21no—
171C22⋊Dic61—42no—
172C22⋊Dic61—42no—
173C22⋊Dic61—42no—
174C22⋊Dic61—42no—
175C22⋊Dic61—81no—
176C22⋊Dic61—81no—
177C22⋊Dic61—81no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—42no—
194C4⋊Dic61#4112yes—
195#11758196—42no—
196#11758196—81no—
197C4×Dic61—42no—
198C4×Dic61—42no—
199C4×Dic61—81no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61#12312yes—
213C23×C61#13512yes—
214C23×C61C22×D411yescharacteristic
215D4×C61—44no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61#12312yes—
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—84no—
267C8×C61—22no—
268C8×C61—41no—
269C8×C61—41no—
270C8×C61—41no—
271#24934—611nomaximal, Sylow
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61C2×#12311yescharacteristic
287C22×C61#54611yescharacteristic
288C22×C61#54711yescharacteristic
289C22×C61C2×#13511yescharacteristic
290C22×C61#57511yescharacteristic
291C22×C61#57611yescharacteristic
292C22×C61#57811yescharacteristic
293C4×C61—22no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61#52911yescharacteristic
298C4×C61#53911yescharacteristic
299C4×C61#55111yescharacteristic
300C4×C61#55211yescharacteristic
301Dic61—42no—
302Dic61—81no—
303Dic61—81no—
304Dic61—81no—
305Dic61—81no—
306Dic61—81no—
307Dic61—81no—
308Dic61—81no—
309#2485—611no—
310#2352—611no—
311#2101—611no—
312#2085—611no—
313#2077—611no—
314#2075—611no—
315#1921—611no—
316#1918—611no—
317#1869D6111yescharacteristic
318#1854—611no—
319#1852—611no—
320#1825—611no—
321#1824—611no—
322#1808—611no—
323#1735—611no—
324C2×C61—42no—
325C2×C61—42no—
326C2×C61#241911yescharacteristic
327C2×C61#309111yescharacteristic
328C2×C61#309811yescharacteristic
329C2×C61#330011yescharacteristic
330C2×C61#331911yescharacteristic
331C2×C61#333911yescharacteristic
332C2×C61#334911yescharacteristic
333C23×C8C2×D6111yescharacteristic
334C2×C4×D4C2×D6111yescharacteristic
335C2×#117—611no—
336C2×#117—611no—
337C22×C4⋊C4—611no—
338C2×#107—611no—
339C2×#107—611no—
340C2×#107—611no—
341C2×#106—611no—
342C2×C22⋊C8C2×D6111yescharacteristic
343C2×C22⋊C8C2×D6111yescharacteristic
344C2×C22⋊C8C2×D6111yescharacteristic
345#397—1221no—
346#394—1221no—
347#389—611no—
348#389—611no—
349#388—1221no—
350#388—1221no—
351#387—1221no—
352#387—1221no—
353#386—1221no—
354#382—611no—
355#380—611no—
356#380—611no—
357#380—611no—
358#380—611no—
359#380—611no—
360C4×C4⋊C4—611no—
361C4×C22⋊C4—1221no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#336C2×D6111yescharacteristic
375#336C2×D6111yescharacteristic
376C61#2493411yescharacteristic, complemented, Sylow
377C22×D4D24411yescharacteristic
378C23×C4—1221no—
379C23×C4C22×D6111yescharacteristic
380C23×C4C22×D6111yescharacteristic
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—41no—
384C22×C8C22×D6111yescharacteristic
385C22×C8C22×D6111yescharacteristic
386C22×C8C22×D6111yescharacteristic
387C22×C8C22×D6111yescharacteristic
388C4×D4—22no—
389C4×D4—22no—
390#117—1222no—
391#117—1222no—
392#117—1222no—
393#117—2441no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—1222no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—2441no—
407C2×C4⋊C4D24411yescharacteristic
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4D24411yescharacteristic
416C2×C22⋊C4D24411yescharacteristic
417C2×C42—1221no—
418C2×C42—1221no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421#107—1222no—
422#107—1222no—
423#107—2441no—
424#106—2441no—
425C22⋊C8—22no—
426C22⋊C8—22no—
427C22⋊C8—41no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435#95—1221no—
436#95—1221no—
437#95—1221no—
438C24C2×D24411yescharacteristic
439C24C2×D24411yescharacteristic
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—41no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—4881no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4C2×D24411yescharacteristic
465C22×C4C2×D24411yescharacteristic
466C22×C4C2×D24411yescharacteristic
467C22×C4C2×D24411yescharacteristic
468C22×C4#1175822412yes—
469C22×C4#1175822412yes—
470C22×C4C23×D6111yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—44no—
483C2×C8#1175822412yes—
484C4⋊C4—22no—
485C4⋊C4—612no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—4881no—
502C4⋊C4—2442no—
503C4⋊C4—2442no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—4881no—
507C22⋊C4—4881no—
508C22⋊C4—4881no—
509C22⋊C4—2442no—
510C22⋊C4—2442no—
511C22⋊C4—2442no—
512C22⋊C4—2442no—
513C42—21no—
514C42—21no—
515C42—4881no—
516C42—2442no—
517C42—2442no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#1451976112yes—
531C23#1451979912yes—
532C23C22×D24411yescharacteristic
533D4—44no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—1222no—
554C2×C4—4884no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4#1451976112yes—
579C2×C4#41×D6111yescharacteristic
580C2×C4C2×#1175822411yescharacteristic
581C2×C4C2×#1175822411yescharacteristic
582C2×C4C2×#1175822411yescharacteristic
583C2×C4#1451982211yescharacteristic
584C2×C4#1451982411yescharacteristic
585C8—22no—
586C8—41no—
587C8—41no—
588C8—41no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22C2×#1451976111yescharacteristic
604C22#1684040711yescharacteristic
605C22#1684041611yescharacteristic
606C22C2×#1451979911yescharacteristic
607C22#1684056211yescharacteristic
608C22#1684056711yescharacteristic
609C22#1684057911yescharacteristic
610C4—22no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—4881no—
615C4—4881no—
616C4—4881no—
617C4—4881no—
618C4—4881no—
619C4—4881no—
620C4—4881no—
621C4—2442no—
622C4#1684029311yescharacteristic
623C4#1684035711yescharacteristic
624C4#1684044311yescharacteristic
625C4#1684044911yescharacteristic
626C2—42no—
627C2—42no—
628C2#2144929411yescharacteristic
629C2#2145573411yescharacteristic
630C2#2145579911yescharacteristic
631C2#2145770811yescharacteristic
632C2#2145797711yescharacteristic
633C2#2145822211yescharacteristic
634C2#2145835111yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1869C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#1869D61
hypocenterC61#24934
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. #21447388C2semidirect
4. #21447302C2semidirect
5. #21447252C2semidirect
6. #21447242C2semidirect
7. #21446412C2semidirect
8. #21446391C2semidirect
9. #21446020C2semidirect
10. #21446009C2semidirect
11. #21445915C2semidirect
12. #21445910C2semidirect
13. #21445848C2semidirect
14. #21445536C2semidirect
376. C61#24934semidirect

Maximal subgroups

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

subgroupindex
#214501162
#214487482
#214473882
#214473022
#214472522
#214472422
#214464122
#214463912
#214460202
#214460092
#214459152
#214459102
#214458482
#214455362
C61×#18692
#2493461