Finite Group Databasebeta

← #29748565

Subgroups — #29748565

Order 15616.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448883C211yesmaximal, characteristic
2#21447233C211yesmaximal, characteristic, complemented
3#21447190C211yesmaximal, characteristic, complemented
4#21447053C211yesmaximal, characteristic
5#21447053C211yesmaximal, characteristic
6#21446501C211yesmaximal, characteristic, complemented
7#21446446C211yesmaximal, characteristic, complemented
8#21446408C211yesmaximal, characteristic, complemented
9#21446394C211yesmaximal, characteristic, complemented
10#21446378C211yesmaximal, characteristic, complemented
11#21446065C211yesmaximal, characteristic, complemented
12#21446065C211yesmaximal, characteristic, complemented
13#21445826C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#2509C211yesmaximal, characteristic, complemented
16C2×#14519774C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519739—21no—
20C2×#14519710C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519697C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×C4×#92418C2211yescharacteristic
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839663—21no—
35#16839640—21no—
36#16839640—21no—
37C4×C4⋊Dic61C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#400—21no—
49C61×#400—21no—
50C61×#389—21no—
51C61×#389C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#387—21no—
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244—21no—
60C22×D244—21no—
61C22×D244C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519774—22no—
70#14519774—22no—
71C4×D244—22no—
72C4×D244—22no—
73C4×D244—41no—
74C4×D244—41no—
75#14519739—44no—
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85#14519710—22no—
86#14519708—22no—
87C4⋊#92418—41no—
88#14519697—22no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519697—22no—
93#14519697—22no—
94#14519697—41no—
95#14519697—41no—
96C4×#92418—41no—
97#14519684—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C4⋊C4×C61D411yescharacteristic
104C2×C4⋊C4×C61C2311yescharacteristic
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C42×C61—21no—
109C2×C42×C61C2311yescharacteristic
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
121C23×D61—21no—
122C23×D61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—24no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—24no—
148C2×D244—42no—
149C2×D244—42no—
150C2×D244—81no—
151C2×D244—81no—
152C2×D244#4112yes—
153C2×D244#4112yes—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61—42no—
158C2×C4×D61—81no—
159C2×C4×D61—81no—
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—42no—
170C4⋊C4×C61—42no—
171C4⋊C4×C61—81no—
172C4⋊C4×C61—81no—
173C4⋊C4×C61#4112yes—
174C42×C61—21no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—81no—
181#11758198—42no—
182#11758198—42no—
183#11758198—42no—
184#11758198—42no—
185#11758198—81no—
186#11758198—81no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61#4112yes—
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—21no—
204C23×C61C22×D411yescharacteristic
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
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—22no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
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#13512yes—
248C2×C4×C61AGL(1,ℤ/8)12yes—
249C2×C4×C61C2×#4111yescharacteristic
250C2×C4×C61C2×#4111yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61H(5,𝔽2)11yescharacteristic
254C2×C4×C612−1+411yescharacteristic
255C2×Dic61—22no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261D244—22no—
262D244—22no—
263D244—22no—
264D244—22no—
265D244—48no—
266D244—41no—
267D244—41no—
268D244—41no—
269D244—41no—
270D244—84no—
271C4×D61—84no—
272C4×D61—84no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#26755—611nomaximal, Sylow
278C22×C61#52511yescharacteristic
279C22×C61#54611yescharacteristic
280C22×C61#54811yescharacteristic
281C22×C61C2×#13511yescharacteristic
282C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C61#57611yescharacteristic
284C22×C61#57711yescharacteristic
285C2×D61—42no—
286C2×D61—42no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—42no—
290C2×D61—42no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C4×C61—22no—
300C4×C61—22no—
301C4×C61—42no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61#52911yescharacteristic
310C4×C61#53911yescharacteristic
311C4×C61#55211yescharacteristic
312C4×C61#55311yescharacteristic
313Dic61—42no—
314Dic61—81no—
315#2509D6111yescharacteristic, complemented
316#2366—611no—
317#2073—611no—
318#2065—611no—
319#2041—611no—
320#2041—611no—
321#1934—611no—
322#1926—611no—
323#1921—611no—
324#1919—611no—
325#1916—611no—
326#1862—611no—
327#1862—611no—
328#1804—611no—
329C4×#102—611no—
330C2×C61#246011yescharacteristic
331C2×C61#310511yescharacteristic
332C2×C61#311811yescharacteristic
333C2×C61#330411yescharacteristic
334C2×C61#331811yescharacteristic
335C2×C61#336111yescharacteristic
336C2×C61#336811yescharacteristic
337D61—82no—
338D61—82no—
339C2×#127—611no—
340C2×C4×D4—611no—
341C2×C4×D4—611no—
342C2×C4×D4—1221no—
343C2×#107—611no—
344C2×#106—611no—
345C2×C4⋊C8—611no—
346C2×#102—611no—
347C2×#102—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×C4×C8—611no—
355#400—21no—
356#400—21no—
357#390—611no—
358#390—611no—
359#390—1221no—
360#389—21no—
361#389C2×D6111yescharacteristic
362#389C2×D6111yescharacteristic
363#389C2×D6111yescharacteristic
364#389C2×D6111yescharacteristic
365#387—21no—
366#386—1221no—
367#386—1221no—
368#382C2×D6111yescharacteristic
369C4×C4⋊C4—611no—
370C4×C4⋊C4C2×D6111yescharacteristic
371C4×C4⋊C4C2×D6111yescharacteristic
372#340—611no—
373#340—611no—
374#340—611no—
375#340—611no—
376#340—611no—
377#340—611no—
378#336—611no—
379#336—611no—
380#336—611no—
381#336—611no—
382C61#2675511yescharacteristic, complemented, Sylow
383C22×D4—611no—
384C22×D4—611no—
385C22×D4—1221no—
386C22×D4—1221no—
387C23×C4—1221no—
388C23×C4—1221no—
389C22×C8—611no—
390C22×C8—611no—
391C22×C8—611no—
392C22×C8—611no—
393#127—1222no—
394#127—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—2441no—
398C4×D4—2441no—
399C4×D4—2444no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4C22⋊D6111yescharacteristic
407C2×C4⋊C4C22⋊D6111yescharacteristic
408C2×C4⋊C4C22×D6111yescharacteristic
409C2×C4⋊C4C22×D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
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×C42—21no—
419C2×C42—1221no—
420C2×C42C22×D6111yescharacteristic
421C2×C42C22×D6111yescharacteristic
422C2×C42C22×D6111yescharacteristic
423#107—1222no—
424#106—1222no—
425C4⋊C8—2441no—
426#102—1222no—
427#102—1222no—
428#102—1222no—
429#102—1222no—
430#102—1222no—
431#102—1222no—
432#102—2441no—
433#102—2441no—
434C4×C8—2441no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—1221no—
443#95C22⋊D6111yescharacteristic
444#95C22⋊D6111yescharacteristic
445C24—1221no—
446C24—1221no—
447C2×D4—612no—
448C2×D4—612no—
449C2×D4—1224no—
450C2×D4—1224no—
451C2×D4—1221no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—4881no—
462C2×D4—4881no—
463C2×D4—2442no—
464C2×D4—2442no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—4881no—
472C22×C4—4881no—
473C22×C4—2442no—
474C22×C4—2442no—
475C22×C4—2442no—
476C22×C4—2442no—
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479C22×C4C2×C22⋊D6111yescharacteristic
480C22×C4C2×C22⋊D6111yescharacteristic
481C22×C4C2×C22⋊D6111yescharacteristic
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C23×D6111yescharacteristic
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—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C4⋊C4—612no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4#1175822612yes—
514C22⋊C4—4881no—
515C22⋊C4—4881no—
516C22⋊C4—2442no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2442no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—81no—
527C42—2442no—
528C23—1222no—
529C23—1222no—
530C23—2441no—
531C23—2441no—
532C23—2441no—
533C23—2441no—
534C23—2441no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23—2441no—
542C23C22×C22⋊D6111yescharacteristic
543D4—1222no—
544D4—1222no—
545D4—1222no—
546D4—1222no—
547D4—4884no—
548D4—2448no—
549D4—2441no—
550D4—2441no—
551D4—2441no—
552D4—2441no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—1222no—
582C2×C4—4884no—
583C2×C4—4884no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4#1451979712yes—
590C2×C4#1451980212yes—
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4C2×#1175822611yescharacteristic
595C2×C4#1451982311yescharacteristic
596C2×C4#1451982511yescharacteristic
597C8—2441no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C22—4881no—
602C22—4881no—
603C22—4881no—
604C22—4881no—
605C22—4881no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—2442no—
610C22—2442no—
611C22—2442no—
612C22—2442no—
613C22—2442no—
614C22—2442no—
615C22#1684026911yescharacteristic
616C22#1684040011yescharacteristic
617C22#1684042311yescharacteristic
618C22C2×#1451979711yescharacteristic
619C22C2×#1451980211yescharacteristic
620C22#1684056511yescharacteristic
621C22#1684057011yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—4881no—
633C4—2442no—
634C4#1684029711yescharacteristic
635C4#1684036011yescharacteristic
636C4#1684044411yescharacteristic
637C4#1684046511yescharacteristic
638C2—4882no—
639C2—4882no—
640C2#2144976711yescharacteristic
641C2#2145586211yescharacteristic
642C2#2145599711yescharacteristic
643C2#2145775211yescharacteristic
644C2#2145795411yescharacteristic
645C2#2145847911yescharacteristic
646C2#2145854811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2509C2
socleC23×C61C22×D4
prime radicalC2×#14519774C22
hypercenter#2509D61
hypocenterC61#26755
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2509

Complements

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

NH ≅ G/Ntype
2. #21447233C2semidirect
3. #21447190C2semidirect
6. #21446501C2semidirect
7. #21446446C2semidirect
8. #21446408C2semidirect
9. #21446394C2semidirect
10. #21446378C2semidirect
11. #21446065C2semidirect
12. #21446065C2semidirect
13. #21445826C2semidirect
14. C4×#14519697C2semidirect
15. C61×#2509C2semidirect
315. #2509D61semidirect
382. C61#26755semidirect

Maximal subgroups

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

subgroupindex
#214488832
#214472332
#214471902
#214470532
#214465012
#214464462
#214464082
#214463942
#214463782
#214460652
#214458262
C4×#145196972
C61×#25092
#2675561