Finite Group Databasebeta

← #29752666

Subgroups — #29752666

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#21448833C211yesmaximal, characteristic
2#21447223C211yesmaximal, characteristic, complemented
3#21447204C211yesmaximal, characteristic, complemented
4#21447001C211yesmaximal, characteristic
5#21447001C211yesmaximal, characteristic
6#21446575C211yesmaximal, characteristic, complemented
7#21446549C211yesmaximal, characteristic, complemented
8#21446427C211yesmaximal, characteristic, complemented
9#21446390C211yesmaximal, characteristic, complemented
10#21446387C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445903C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2496C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519737—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839660C2211yescharacteristic
34#16839654—21no—
35#16839639—21no—
36#16839636—21no—
37C4×C4⋊Dic61C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×#126×C61—21no—
49C61×#400—21no—
50C61×#397—21no—
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#387—21no—
54C61×#384C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#380C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C22×C4×D61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67#14519751—22no—
68#14519751—22no—
69C4×D244—22no—
70C4×D244—41no—
71#14519737—44no—
72C2×C4⋊Dic61—22no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—41no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×C4×Dic61—21no—
84#14519710—22no—
85#14519710—22no—
86#14519710—22no—
87#14519710—41no—
88C4⋊#92418—22no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519697—41no—
93C22⋊#92418—22no—
94C22⋊#92418—41no—
95C4×#92418—41no—
96#14519684—21no—
97#14519684—21no—
98C23×C4×C61C2311yescharacteristic
99#126×C61—44no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61—21no—
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61—21no—
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×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—24no—
141C2×C22⋊D61—42no—
142C2×C22⋊D61—42no—
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—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61—42no—
169C4⋊C4×C61—42no—
170C22⋊C4×C61—41no—
171C22⋊C4×C61—42no—
172C22⋊C4×C61—42no—
173C22⋊C4×C61D814yes—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—42no—
179#11758198—24no—
180#11758198—42no—
181#11758198—42no—
182#11758198—81no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—42no—
188C4⋊Dic61#4112yes—
189C4⋊Dic61#4112yes—
190#11758196—42no—
191C4×Dic61—42no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418#4112yes—
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×C61—41no—
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—41no—
248C2×C4×C61C2×D812yes—
249C2×C4×C61C2×D812yes—
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C612−1+411yescharacteristic
256C22⋊D61—48no—
257C2×Dic61—22no—
258C2×Dic61—22no—
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—
272#92418—22no—
273#92418—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—22no—
299C4×C61—22no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61#52911yescharacteristic
308C4×C61#53911yescharacteristic
309C4×C61#55311yescharacteristic
310C4×C61#55611yescharacteristic
311Dic61—42no—
312Dic61—42no—
313Dic61—81no—
314#2496D6111yescharacteristic, complemented
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#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—21no—
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⋊C8—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×C22⋊C8—611no—
353C2×C22⋊C8—611no—
354C2×C4×C8—611no—
355#400—21no—
356#397—21no—
357#390—611no—
358#389—611no—
359#389C2×D6111yescharacteristic
360#389C2×D6111yescharacteristic
361#388—1221no—
362#387—21no—
363#386—1221no—
364#385—1221no—
365#384C2×D6111yescharacteristic
366#380C2×D6111yescharacteristic
367#380C2×D6111yescharacteristic
368C4×C4⋊C4—611no—
369C4×C4⋊C4C2×D6111yescharacteristic
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#336—611no—
380#336—611no—
381C61#2703011yescharacteristic, complemented, Sylow
382C22×D4—611no—
383C22×D4—1221no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4C22×D6111yescharacteristic
387C22×C8—611no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8—611no—
391#126—44no—
392#121—1222no—
393#121—1222no—
394C4×D4—1222no—
395C4×D4—2441no—
396C4×D4—2444no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
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—2441no—
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4C22⋊D6111yescharacteristic
419C2×C22⋊C4C22⋊D6111yescharacteristic
420C2×C42—21no—
421C2×C42—1221no—
422C2×C42C22×D6111yescharacteristic
423C2×C42C22×D6111yescharacteristic
424#107—1222no—
425#107—1222no—
426#107—1222no—
427#107—2441no—
428C4⋊C8—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433C22⋊C8—1222no—
434C22⋊C8—2441no—
435C4×C8—2441no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—1221no—
442#95—1221no—
443#95C22⋊D6111yescharacteristic
444#95C22⋊D6111yescharacteristic
445C24—1221no—
446C24C2×C22⋊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—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×C22⋊D6111yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C23×D6111yescharacteristic
481C2×C8—612no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—612no—
506C4⋊C4—612no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—1224no—
517C22⋊C4—4881no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C22⋊C4#1175819914yes—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
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×#1175819912yes—
541C23C22×C22⋊D6111yescharacteristic
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—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—4884no—
579C2×C4—4884no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4C2×#1175819912yes—
588C2×C4C2×#1175819912yes—
589C2×C4#41×D6111yescharacteristic
590C2×C4#41×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#1451982311yescharacteristic
594C2×C4#1451982411yescharacteristic
595C8—1222no—
596C8—2441no—
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#1684026911yescharacteristic
614C22#1684040011yescharacteristic
615C22#1684041111yescharacteristic
616C22C22×#1175819911yescharacteristic
617C22#1684056011yescharacteristic
618C22#1684057011yescharacteristic
619C22#1684057711yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—4881no—
630C4—2442no—
631C4—2442no—
632C4#1684029511yescharacteristic
633C4#1684035311yescharacteristic
634C4#1684046311yescharacteristic
635C4#1684047911yescharacteristic
636C2—42no—
637C2—4882no—
638C2#2144985111yescharacteristic
639C2#2145581511yescharacteristic
640C2#2145602711yescharacteristic
641C2#2145762611yescharacteristic
642C2#2145787911yescharacteristic
643C2#2145816211yescharacteristic
644C2#2145837911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2496C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2496D61
hypocenterC61#27030
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2496

Complements

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

NH ≅ G/Ntype
2. #21447223C2semidirect
3. #21447204C2semidirect
6. #21446575C2semidirect
7. #21446549C2semidirect
8. #21446427C2semidirect
9. #21446390C2semidirect
10. #21446387C2semidirect
11. #21446065C2semidirect
12. #21446006C2semidirect
13. #21445903C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2496C2semidirect
314. #2496D61semidirect
381. C61#27030semidirect

Maximal subgroups

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

subgroupindex
#214488332
#214472232
#214472042
#214470012
#214465752
#214465492
#214464272
#214463902
#214463872
#214460652
#214460062
#214459032
C4×#145196972
C61×#24962
#2703061