Finite Group Databasebeta

← #29752667

Subgroups — #29752667

Order 15616.

812 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#21450243C211yesmaximal, characteristic, complemented
2#21448835C211yesmaximal, characteristic
3#21447226C211yesmaximal, characteristic, complemented
4#21447202C211yesmaximal, characteristic, complemented
5#21447002C211yesmaximal, characteristic
6#21447001C211yesmaximal, characteristic
7#21446576C211yesmaximal, characteristic, complemented
8#21446550C211yesmaximal, characteristic, complemented
9#21446428C211yesmaximal, characteristic, complemented
10#21446392C211yesmaximal, characteristic, complemented
11#21446388C211yesmaximal, characteristic, complemented
12#21446063C211yesmaximal, characteristic, complemented
13#21445905C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic, complemented
16C2×#14519770—21no—
17C2×#14519751C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×C4×C22⋊D61—21no—
20C2×#14519711C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839704—21no—
30#16839690—21no—
31#16839663C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839658C2211yescharacteristic
34#16839658C2211yescharacteristic
35#16839652—21no—
36#16839644—21no—
37#16839641—21no—
38#16839633—21no—
39#16839631C2211yescharacteristic
40#16839622C2211yescharacteristic
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×C22⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C22×C4×D61—21no—
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519770—44no—
65#14519751—22no—
66#14519751—22no—
67#14519739—22no—
68#14519739—41no—
69C4×C22⋊D61—44no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61D411yescharacteristic
80C2×C22⋊Dic61D411yescharacteristic
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61C2311yescharacteristic
88C2×C4×Dic61C2311yescharacteristic
89#14519711—22no—
90#14519710—22no—
91#14519706—22no—
92#14519699—22no—
93#14519699—22no—
94#14519697—22no—
95#14519697—41no—
96C22⋊#92418—41no—
97C8×Dic61—41no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684D411yescharacteristic
105#14519684D411yescharacteristic
106C23×C4×C61—21no—
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118#107×C61—22no—
119#107×C61—41no—
120C22⋊C8×C61—22no—
121#95×C61—21no—
122C24×C61C2×D411yescharacteristic
123C23×D61—21no—
124C22×C4×C61—21no—
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—42no—
135C22×C4×C61—42no—
136C22×C4×C61—81no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C2×C22⋊D61—24no—
140C2×C22⋊D61—42no—
141C2×C22⋊D61—42no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244#4112yes—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61#4112yes—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—42no—
172C4⋊C4×C61#4112yes—
173C22⋊C4×C61—42no—
174C22⋊Dic61—41no—
175C22⋊Dic61—42no—
176C22⋊Dic61D814yes—
177#11758198—24no—
178#11758198—42no—
179#11758198—42no—
180#11758198—81no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—42no—
187C4⋊Dic61#4112yes—
188#11758196—42no—
189#11758196—42no—
190#11758196—42no—
191#11758196—42no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—42no—
197C4×Dic61—42no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61C2×D812yes—
211C23×C61C22×D411yescharacteristic
212C22×D61—22no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C2×C4×C61—21no—
220C2×C4×C61—22no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—84no—
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61H(5,𝔽2)11yescharacteristic
244C2×C4×C612−1+411yescharacteristic
245C22⋊D61—48no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—22no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
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×Dic61C2×D812yes—
266C2×Dic61C2×D812yes—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272C8×C61—22no—
273C8×C61—41no—
274#92418—41no—
275#92418—41no—
276#27030—611nomaximal, Sylow
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61#52511yescharacteristic
285C22×C61#54611yescharacteristic
286C22×C61#54711yescharacteristic
287C22×C61C22×D811yescharacteristic
288C22×C61#57511yescharacteristic
289C22×C61#57711yescharacteristic
290C22×C61#57811yescharacteristic
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—42no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C4×C61—41no—
299C4×C61—42no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61#52911yescharacteristic
304C4×C61#53911yescharacteristic
305C4×C61#55311yescharacteristic
306C4×C61#55611yescharacteristic
307Dic61—22no—
308Dic61—22no—
309Dic61—41no—
310Dic61—42no—
311Dic61—41no—
312Dic61—81no—
313Dic61—81no—
314#2496—611no—
315#2361—611no—
316#2071—611no—
317#2067—611no—
318#2033—611no—
319#2033—611no—
320#1947—611no—
321#1942—611no—
322#1923—611no—
323#1918—611no—
324#1918—611no—
325#1862—611no—
326#1852D6111yescharacteristic, complemented
327#1823—611no—
328C4×#102—611no—
329C2×C61—42no—
330C2×C61#246611yescharacteristic
331C2×C61#310011yescharacteristic
332C2×C61#312011yescharacteristic
333C2×C61#329411yescharacteristic
334C2×C61#331311yescharacteristic
335C2×C61#333411yescharacteristic
336C2×C61#335111yescharacteristic
337D61—82no—
338C2×#126—1221no—
339C2×#121—611no—
340C2×C4×D4—611no—
341C2×C4×D4—1221no—
342C22×C4⋊C4C2×D6111yescharacteristic
343C2×#107—611no—
344C2×#107—611no—
345C2×#107C2×D6111yescharacteristic
346C2×#107C2×D6111yescharacteristic
347C2×C4⋊C8—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8C2×D6111yescharacteristic
354C2×C4×C8—611no—
355#400—1221no—
356#397—1221no—
357#390—611no—
358#389—611no—
359#389—611no—
360#389—611no—
361#388—1221no—
362#387—1221no—
363#386—1221no—
364#385—1221no—
365#384—611no—
366#380—611no—
367#380C2×D6111yescharacteristic
368C4×C4⋊C4—611no—
369C4×C4⋊C4—611no—
370C4×C22⋊C4—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340C2×D6111yescharacteristic
378#340C2×D6111yescharacteristic
379#336—611no—
380#336—611no—
381C61#2703011yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C23×C4—21no—
385C23×C4—1221no—
386C23×C4C22×D6111yescharacteristic
387C22×C8—611no—
388C22×C8—611no—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391#126—2444no—
392#121—1222no—
393#121—1222no—
394C4×D4—1222no—
395C4×D4—2441no—
396C4×D4—2444no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—611no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1221no—
423C2×C42—1221no—
424#107—22no—
425#107—41no—
426#107—1222no—
427#107—1222no—
428C4⋊C8—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433C22⋊C8—22no—
434C22⋊C8—2441no—
435C4×C8—2441no—
436#95—21no—
437#95—611no—
438#95—611no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95—1221no—
444#95—1221no—
445C24—1221no—
446C24D4×D6111yescharacteristic
447C2×D4—612no—
448C2×D4—1224no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—2442no—
455C2×D4—2442no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—2442no—
478C22×C4—2442no—
479C22×C4D4×D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8#1175822212yes—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—612no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—2442no—
508C4⋊C4—2442no—
509C4⋊C4—2442no—
510C4⋊C4—2442no—
511C4⋊C4—2442no—
512C4⋊C4#1175822412yes—
513C22⋊C4—42no—
514C22⋊C4—614no—
515C22⋊C4—1224no—
516C22⋊C4—4881no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2441no—
520C22⋊C4—2442no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C42—1221no—
525C42—2442no—
526C42—2442no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—1222no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23D8×D6112yes—
541C23C2×D4×D6111yescharacteristic
542D4—1222no—
543D4—1222no—
544D4—2448no—
545D4—2441no—
546D4—2441no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1222no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—4884no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4C2×#1175822411yescharacteristic
592C2×C4C2×#1175822211yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982511yescharacteristic
595C8—22no—
596C8—41no—
597C8—2441no—
598C8—2441no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22#1684027011yescharacteristic
614C22#1684039911yescharacteristic
615C22#1684041311yescharacteristic
616C22C2×D8×D6111yescharacteristic
617C22#1684056111yescharacteristic
618C22#1684057211yescharacteristic
619C22#1684057511yescharacteristic
620C4—41no—
621C4—42no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—1222no—
626C4—1222no—
627C4—4881no—
628C4—4881no—
629C4—2442no—
630C4—2441no—
631C4—2441no—
632C4#1684029411yescharacteristic
633C4#1684035811yescharacteristic
634C4#1684046111yescharacteristic
635C4#1684048311yescharacteristic
636C2—42no—
637C2—4882no—
638C2#2144985211yescharacteristic
639C2#2145581611yescharacteristic
640C2#2145602811yescharacteristic
641C2#2145762511yescharacteristic
642C2#2145787811yescharacteristic
643C2#2145816411yescharacteristic
644C2#2145838011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1852C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#1852D61
hypocenterC61#27030
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
1. #21450243C2semidirect
3. #21447226C2semidirect
4. #21447202C2semidirect
7. #21446576C2semidirect
8. #21446550C2semidirect
9. #21446428C2semidirect
10. #21446392C2semidirect
11. #21446388C2semidirect
12. #21446063C2semidirect
13. #21445905C2semidirect
14. #21445633C2semidirect
15. C61×#1852C2semidirect
326. #1852D61semidirect
381. C61#27030semidirect

Maximal subgroups

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

subgroupindex
#214502432
#214488352
#214472262
#214472022
#214470022
#214470012
#214465762
#214465502
#214464282
#214463922
#214463882
#214460632
#214459052
#214456332
C61×#18522
#2703061