Finite Group Databasebeta

← #29752711

Subgroups — #29752711

Order 15616.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448833C211yesmaximal, characteristic
2#21447233C211yesmaximal, characteristic, complemented
3#21447204C211yesmaximal, characteristic, complemented
4#21447008C211yesmaximal, characteristic
5#21447001C211yesmaximal, characteristic
6#21446585C211yesmaximal, characteristic, complemented
7#21446549C211yesmaximal, characteristic, complemented
8#21446427C211yesmaximal, characteristic, complemented
9#21446408C211yesmaximal, characteristic, complemented
10#21446397C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446006C211yesmaximal, characteristic, complemented
13#21445907C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2494C211yesmaximal, characteristic, complemented
16C2×#14519751C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×#14519737—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
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
48C61×#401—21no—
49C61×#397—21no—
50C61×#389C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#387—21no—
54C61×#382C2211yescharacteristic
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—41no—
87#14519708—22no—
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
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61D411yescharacteristic
108C2×C22⋊C4×C61D411yescharacteristic
109C2×C42×C61—21no—
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61—21no—
119#95×C61D411yescharacteristic
120#95×C61D411yescharacteristic
121C24×C61C2×D411yescharacteristic
122C23×D61—21no—
123C22×C4×C61—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×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
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×Dic61—42no—
146C22×Dic61—42no—
147C22×Dic61—81no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244#4112yes—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—81no—
157C4⋊C4×C61—21no—
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—42no—
166C4⋊C4×C61—81no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—81no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—21no—
174C42×C61—21no—
175C42×C61—81no—
176#11758198—24no—
177#11758198—42no—
178#11758198—42no—
179#11758198—81no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—42no—
185C4⋊Dic61#4112yes—
186C4⋊Dic61#4112yes—
187#11758196—42no—
188C4×Dic61—42no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
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#4112yes—
201C23×C61—21no—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61#13512yes—
208C23×C61C22×D411yescharacteristic
209C22×D61—22no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213C22×D61—41no—
214C22×D61—41no—
215C22×D61—41no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
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—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—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×C61AGL(1,ℤ/8)12yes—
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61H(5,𝔽2)11yescharacteristic
252C2×C4×C612−1+411yescharacteristic
253C22⋊D61—48no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—84no—
264D244—22no—
265D244—22no—
266D244—41no—
267D244—41no—
268C4×D61—84no—
269#92418—22no—
270#92418—41no—
271#92418—41no—
272#92418—41no—
273#27033—611nomaximal, Sylow
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61#52511yescharacteristic
282C22×C61#54611yescharacteristic
283C22×C61#54711yescharacteristic
284C22×C61C2×#13511yescharacteristic
285C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C61#57611yescharacteristic
287C22×C61#57811yescharacteristic
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—81no—
295C4×C61—22no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61—81no—
304C4×C61#52911yescharacteristic
305C4×C61#53911yescharacteristic
306C4×C61#55311yescharacteristic
307C4×C61#55611yescharacteristic
308Dic61—42no—
309Dic61—42no—
310Dic61—81no—
311#2494D6111yescharacteristic, complemented
312#2361—611no—
313#2073—611no—
314#2067—611no—
315#2034—611no—
316#2033—611no—
317#1949—611no—
318#1942—611no—
319#1923—611no—
320#1921—611no—
321#1919—611no—
322#1862—611no—
323#1852—611no—
324#1824—611no—
325C4×#102—611no—
326C2×C61—42no—
327C2×C61#246611yescharacteristic
328C2×C61#310511yescharacteristic
329C2×C61#312411yescharacteristic
330C2×C61#330011yescharacteristic
331C2×C61#331811yescharacteristic
332C2×C61#333911yescharacteristic
333C2×C61#335311yescharacteristic
334D61—82no—
335C2×#121—611no—
336C2×C4×D4—611no—
337C2×C4×D4—1221no—
338C22×C4⋊C4—611no—
339C2×#107—611no—
340C2×#107—611no—
341C2×#107—611no—
342C2×#106—611no—
343C2×C4⋊C8—611no—
344C2×#102—611no—
345C2×#102—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×C22⋊C8—611no—
349C2×C22⋊C8—611no—
350C2×C4×C8—611no—
351#401—21no—
352#397—21no—
353#390—611no—
354#389—611no—
355#389C2×D6111yescharacteristic
356#389C2×D6111yescharacteristic
357#388—21no—
358#388—1221no—
359#387—21no—
360#386—1221no—
361#385—1221no—
362#382C2×D6111yescharacteristic
363#380C2×D6111yescharacteristic
364#380C2×D6111yescharacteristic
365C4×C4⋊C4—611no—
366C4×C4⋊C4C2×D6111yescharacteristic
367C4×C22⋊C4C2×D6111yescharacteristic
368#340—611no—
369#340—611no—
370#340—611no—
371#340—611no—
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#336—611no—
377#336—611no—
378C61#2703311yescharacteristic, complemented, Sylow
379C22×D4—611no—
380C22×D4—1221no—
381C23×C4—1221no—
382C23×C4—1221no—
383C23×C4C22×D6111yescharacteristic
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388#121—1222no—
389#121—1222no—
390C4×D4—1222no—
391C4×D4—2441no—
392C4×D4—2444no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—1222no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—2441no—
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C4⋊C4C22×D6111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4C22⋊D6111yescharacteristic
413C2×C22⋊C4C22⋊D6111yescharacteristic
414C2×C42—21no—
415C2×C42—1221no—
416C2×C42C22×D6111yescharacteristic
417C2×C42C22×D6111yescharacteristic
418#107—1222no—
419#107—1222no—
420#107—2441no—
421#106—1222no—
422C4⋊C8—1222no—
423#102—1222no—
424#102—1222no—
425#102—1222no—
426#102—2441no—
427C22⋊C8—1222no—
428C22⋊C8—2441no—
429C4×C8—2441no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—1221no—
438#95—1221no—
439#95C22⋊D6111yescharacteristic
440#95C22⋊D6111yescharacteristic
441C24—1221no—
442C24C2×C22⋊D6111yescharacteristic
443C2×D4—612no—
444C2×D4—1224no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—2442no—
451C2×D4—2442no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
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—4881no—
466C22×C4—4881no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4—2442no—
471C22×C4C2×C22⋊D6111yescharacteristic
472C22×C4C2×C22⋊D6111yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C2×C22⋊D6111yescharacteristic
476C22×C4C23×D6111yescharacteristic
477C2×C8—612no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—612no—
500C4⋊C4—612no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—2442no—
506C4⋊C4—2442no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—1224no—
512C22⋊C4—4881no—
513C22⋊C4—2442no—
514C22⋊C4—2442no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—81no—
520C42—2442no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—1222no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23—2441no—
532C23—2441no—
533C23—2441no—
534C23#1451979712yes—
535C23C22×C22⋊D6111yescharacteristic
536D4—1222no—
537D4—1222no—
538D4—2448no—
539D4—2441no—
540D4—2441no—
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—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
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—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—1222no—
572C2×C4—1222no—
573C2×C4—4884no—
574C2×C4—4884no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4#1451980212yes—
583C2×C4#41×D6111yescharacteristic
584C2×C4#41×D6111yescharacteristic
585C2×C4#41×D6111yescharacteristic
586C2×C4#41×D6111yescharacteristic
587C2×C4#1451982311yescharacteristic
588C2×C4#1451982411yescharacteristic
589C8—1222no—
590C8—2441no—
591C8—2441no—
592C8—2441no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—4881no—
601C22—4881no—
602C22—4881no—
603C22—4881no—
604C22—2442no—
605C22—2442no—
606C22—2442no—
607C22#1684026911yescharacteristic
608C22#1684040011yescharacteristic
609C22#1684041111yescharacteristic
610C22C2×#1451979711yescharacteristic
611C22C2×#1451980211yescharacteristic
612C22#1684056511yescharacteristic
613C22#1684057711yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—4881no—
624C4—2442no—
625C4—2442no—
626C4#1684029511yescharacteristic
627C4#1684035311yescharacteristic
628C4#1684046311yescharacteristic
629C4#1684047911yescharacteristic
630C2—42no—
631C2—4882no—
632C2#2144985111yescharacteristic
633C2#2145586211yescharacteristic
634C2#2145607511yescharacteristic
635C2#2145770011yescharacteristic
636C2#2145795411yescharacteristic
637C2#2145821511yescharacteristic
638C2#2145839711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2494C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2494D61
hypocenterC61#27033
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2494

Complements

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

NH ≅ G/Ntype
2. #21447233C2semidirect
3. #21447204C2semidirect
6. #21446585C2semidirect
7. #21446549C2semidirect
8. #21446427C2semidirect
9. #21446408C2semidirect
10. #21446397C2semidirect
11. #21446065C2semidirect
12. #21446006C2semidirect
13. #21445907C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2494C2semidirect
311. #2494D61semidirect
378. C61#27033semidirect

Maximal subgroups

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

subgroupindex
#214488332
#214472332
#214472042
#214470082
#214470012
#214465852
#214465492
#214464272
#214464082
#214463972
#214460652
#214460062
#214459072
C4×#145196972
C61×#24942
#2703361