Finite Group Databasebeta

← #29752668

Subgroups — #29752668

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#21450241C211yesmaximal, characteristic, complemented
2#21448833C211yesmaximal, characteristic
3#21447224C211yesmaximal, characteristic, complemented
4#21447206C211yesmaximal, characteristic, complemented
5#21447002C211yesmaximal, characteristic
6#21447002C211yesmaximal, characteristic
7#21446578C211yesmaximal, characteristic, complemented
8#21446552C211yesmaximal, characteristic, complemented
9#21446391C211yesmaximal, characteristic, complemented
10#21446391C211yesmaximal, characteristic, complemented
11#21446069C211yesmaximal, characteristic, complemented
12#21446009C211yesmaximal, characteristic, complemented
13#21445906C211yesmaximal, characteristic, complemented
14C4×#14519699C211yesmaximal, characteristic, complemented
15C61×#1923C211yesmaximal, characteristic, complemented
16C2×#14519770—21no—
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519737—21no—
20C22×C4⋊Dic61C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28C2×#14519699C2211yescharacteristic
29#16839702—21no—
30#16839687—21no—
31#16839664C2211yescharacteristic
32#16839660C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839654—21no—
36#16839647—21no—
37#16839639—21no—
38#16839636—21no—
39#16839632C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C22×C4×D61—21no—
63#14519770—44no—
64#14519751—22no—
65#14519751—22no—
66C4×D244—22no—
67C4×D244—41no—
68#14519737—44no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—41no—
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61—21no—
92#14519711—22no—
93#14519711—22no—
94#14519711—22no—
95#14519711—41no—
96#14519699—22no—
97#14519699—22no—
98#14519699—22no—
99#14519699—41no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C2×C22⋊C4×C61D411yescharacteristic
113C2×C22⋊C4×C61D411yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116C4⋊C8×C61—22no—
117C22⋊C8×C61—22no—
118C22⋊C8×C61—41no—
119C4×C8×C61—41no—
120#95×C61D411yescharacteristic
121#95×C61D411yescharacteristic
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×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2411yescharacteristic
136C2×C22⋊D61—24no—
137C2×C22⋊D61—42no—
138C2×C22⋊D61—42no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—42no—
147C22×Dic61—42no—
148C22×Dic61—81no—
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—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61#4112yes—
170C22⋊C4×C61—41no—
171C22⋊C4×C61D814yes—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—21no—
176C22⋊Dic61—42no—
177C22⋊Dic61—42no—
178#11758198—24no—
179#11758198—42no—
180#11758198—42no—
181#11758198—81no—
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—21no—
194C4⋊Dic61—42no—
195C4⋊Dic61—42no—
196C4⋊Dic61—42no—
197C4⋊Dic61#4112yes—
198C4⋊Dic61#4112yes—
199#11758196—42no—
200#11758196—42no—
201#11758196—42no—
202C4×Dic61—42no—
203C4×Dic61—42no—
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—21no—
221C2×C4×C61—21no—
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—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C2×D812yes—
237C2×C4×C61C2×D812yes—
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61H(5,𝔽2)11yescharacteristic
243C2×C4×C612−1+411yescharacteristic
244C22⋊D61—48no—
245C2×Dic61—22no—
246C2×Dic61—22no—
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—
267D244—22no—
268D244—22no—
269D244—41no—
270D244—41no—
271C4×D61—84no—
272C8×C61—22no—
273C8×C61—41no—
274C8×C61—41no—
275C8×C61—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—22no—
299C4×C61—22no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61#52911yescharacteristic
304C4×C61#53911yescharacteristic
305C4×C61#55311yescharacteristic
306C4×C61#55611yescharacteristic
307Dic61—42no—
308Dic61—42no—
309Dic61—81no—
310Dic61—81no—
311Dic61—81no—
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#1923D6111yescharacteristic, complemented
323#1918—611no—
324#1918—611no—
325#1862—611no—
326#1852—611no—
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⋊C4—611no—
343C2×#107—611no—
344C2×#107—611no—
345C2×#107—611no—
346C2×#107—611no—
347C2×C4⋊C8C2×D6111yescharacteristic
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×C22⋊C8C2×D6111yescharacteristic
353C2×C22⋊C8C2×D6111yescharacteristic
354C2×C4×C8C2×D6111yescharacteristic
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#380—611no—
368C4×C4⋊C4—611no—
369C4×C4⋊C4—611no—
370C4×C22⋊C4C2×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#336C2×D6111yescharacteristic
380#336C2×D6111yescharacteristic
381C61#2703011yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4C22×D6111yescharacteristic
387C22×C8C22×D6111yescharacteristic
388C22×C8C22×D6111yescharacteristic
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—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1222no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—2441no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4D24411yescharacteristic
419C2×C22⋊C4D24411yescharacteristic
420C2×C42—1221no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423C2×C42C22×D6111yescharacteristic
424#107—1222no—
425#107—1222no—
426#107—1222no—
427#107—2441no—
428C4⋊C8—22no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433C22⋊C8—22no—
434C22⋊C8—41no—
435C4×C8—41no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441#95—1221no—
442#95—1221no—
443#95D24411yescharacteristic
444#95D24411yescharacteristic
445C24—1221no—
446C24C2×D24411yescharacteristic
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—1221no—
463C22×C4—1221no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—4881no—
470C22×C4—4881no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4C2×D24411yescharacteristic
476C22×C4C2×D24411yescharacteristic
477C22×C4C2×D24411yescharacteristic
478C22×C4C2×D24411yescharacteristic
479C22×C4C2×D24411yescharacteristic
480C22×C4C23×D6111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8#1175822412yes—
493C4⋊C4—612no—
494C4⋊C4—612no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
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—2442no—
513C22⋊C4—41no—
514C22⋊C4—1224no—
515C22⋊C4—4881no—
516C22⋊C4—2442no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C22⋊C4D48814yes—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
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—
540C23C2×D48812yes—
541C23C22×D24411yescharacteristic
542D4—1222no—
543D4—1222no—
544D4—2448no—
545D4—2441no—
546D4—2441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—4884no—
567C2×C4—4884no—
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—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4C2×D48812yes—
588C2×C4C2×D48812yes—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4C2×#1175822411yescharacteristic
593C2×C4#1451982211yescharacteristic
594C2×C4#1451982411yescharacteristic
595C8—22no—
596C8—41no—
597C8—41no—
598C8—41no—
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#1684027411yescharacteristic
614C22#1684040711yescharacteristic
615C22#1684041611yescharacteristic
616C22C22×D48811yescharacteristic
617C22#1684056211yescharacteristic
618C22#1684057411yescharacteristic
619C22#1684057911yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—4881no—
626C4—4881no—
627C4—4881no—
628C4—4881no—
629C4—4881no—
630C4—2442no—
631C4—2442no—
632C4#1684029111yescharacteristic
633C4#1684035511yescharacteristic
634C4#1684045511yescharacteristic
635C4#1684047911yescharacteristic
636C2—42no—
637C2—4882no—
638C2#2144985311yescharacteristic
639C2#2145582011yescharacteristic
640C2#2145603511yescharacteristic
641C2#2145763311yescharacteristic
642C2#2145788711yescharacteristic
643C2#2145816711yescharacteristic
644C2#2145838111yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1923C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#1923D61
hypocenterC61#27030
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #21450241C2semidirect
3. #21447224C2semidirect
4. #21447206C2semidirect
7. #21446578C2semidirect
8. #21446552C2semidirect
9. #21446391C2semidirect
10. #21446391C2semidirect
11. #21446069C2semidirect
12. #21446009C2semidirect
13. #21445906C2semidirect
14. C4×#14519699C2semidirect
15. C61×#1923C2semidirect
322. #1923D61semidirect
381. C61#27030semidirect

Maximal subgroups

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

subgroupindex
#214502412
#214488332
#214472242
#214472062
#214470022
#214465782
#214465522
#214463912
#214460692
#214460092
#214459062
C4×#145196992
C61×#19232
#2703061