Finite Group Databasebeta

← #29651315

Subgroups — #29651315

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455820C211yesmaximal, characteristic
2#21454885C211yesmaximal, characteristic, complemented
3#21454856C211yesmaximal, characteristic, complemented
4#21444732C211yesmaximal, characteristic, complemented
5#21444703C211yesmaximal, characteristic, complemented
6#21444682C211yesmaximal, characteristic, complemented
7#21444682C211yesmaximal, characteristic, complemented
8#21444647C211yesmaximal, characteristic, complemented
9#21444647C211yesmaximal, characteristic, complemented
10#21444642C211yesmaximal, characteristic, complemented
11#21444613C211yesmaximal, characteristic, complemented
12#21444287C211yesmaximal, characteristic, complemented
13#21444209C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1572C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17C2×C4×D244C2211yescharacteristic
18#16840076C411yescharacteristic
19#16840076C411yescharacteristic
20#16840043C411yescharacteristic
21#16840043C411yescharacteristic
22#16839958C411yescharacteristic
23#16839958C411yescharacteristic
24#16839898C411yescharacteristic
25#16839898C411yescharacteristic
26C4×D488C2211yescharacteristic
27C4×D488C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×D488C2211yescharacteristic
30#16839841—21no—
31#16839839C2211yescharacteristic
32#16839839C2211yescharacteristic
33#16839839C2211yescharacteristic, complemented
34#16839839C2211yescharacteristic, complemented
35#16839835—21no—
36#16839835—21no—
37C8×D244—21no—
38#16839827C2211yescharacteristic
39#16839827C2211yescharacteristic
40#16839827C2211yescharacteristic, complemented
41#16839827C2211yescharacteristic, complemented
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839727—21no—
45#16839727—21no—
46#16839724—21no—
47C22⋊C8×D61—21no—
48#16839489C2211yescharacteristic
49#16839489C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839489C2211yescharacteristic, complemented
53#16839489C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic, complemented
55#16839489C2211yescharacteristic, complemented
56#16839484C2211yescharacteristic, complemented
57#16839484C2211yescharacteristic, complemented
58#16839483C2211yescharacteristic, complemented
59C8×#92418C2211yescharacteristic, complemented
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#335C2211yescharacteristic, complemented
64C61×#335C2211yescharacteristic, complemented
65C61×#334C2211yescharacteristic, complemented
66C61×#334C2211yescharacteristic, complemented
67C2×#11758222—21no—
68C22×D244C2×C411yescharacteristic
69C22×C4×D61—21no—
70C2×D488C2×C411yescharacteristic
71C2×D488C2×C411yescharacteristic
72C2×D488C2×C411yescharacteristic
73C2×D488C2×C411yescharacteristic
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C2×#11758189—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82#14519777C2×C411yescharacteristic
83#14519774C2×C411yescharacteristic
84#14519765—21no—
85#14519751—21no—
86#14519751C2×C411yescharacteristic
87#14519751C2×C411yescharacteristic
88C4×D244—21no—
89C4×D244—21no—
90C4×D244—21no—
91C4×D244C2×C411yescharacteristic
92C4×D244C2×C411yescharacteristic
93C4×D244C2311yescharacteristic
94C4×D244C2311yescharacteristic
95C4×D244C2311yescharacteristic
96C4×D244C2311yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758198—21no—
99#14519711C2×C411yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519711C2×C411yescharacteristic
102#14519711C2×C411yescharacteristic
103C4⋊#92418—21no—
104C4⋊#92418D411yescharacteristic
105C4⋊#92418D411yescharacteristic
106#14519699C2×C411yescharacteristic
107#14519699C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519699C2×C411yescharacteristic
110#14519699C2×C411yescharacteristic
111#14519699C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117#14519689—21no—
118#14519689—21no—
119#14519689—21no—
120#14519689—21no—
121#14519689—21no—
122#14519689—21no—
123#14519689—21no—
124#14519689—21no—
125C4×#92418C2311yescharacteristic
126C4×#92418C2311yescharacteristic
127C4×#92418C2311yescharacteristic
128C4×#92418C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61C2×C411yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61C2×C411yescharacteristic
139C22⋊C8×C61C2×C411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151#11758222—81no—
152#11758222—81no—
153C2×D244—22no—
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—41no—
158C2×D244C22×C411yescharacteristic
159C2×D244C22×C411yescharacteristic
160C2×D244C22×C411yescharacteristic
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—81no—
169C2×C4×D61—81no—
170C2×Dic122—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61C22×C411yescharacteristic
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—21no—
190#11758198—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C22×C411yescharacteristic
194C4⋊Dic61C22×C411yescharacteristic
195C4⋊Dic61C22×C411yescharacteristic
196C4⋊Dic61C22×C411yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203D488—22no—
204D488—22no—
205D488—41no—
206D488—41no—
207#11758189—81no—
208#11758189—81no—
209#11758189—81no—
210#11758189—81no—
211C8×D61—81no—
212C8×D61—81no—
213C8×D61—81no—
214C8×D61—81no—
215C23×C61C4×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—42no—
221C22×D61—42no—
222C22×D61—81no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—41no—
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—81no—
235C22⋊D61—81no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—81no—
241D244—21no—
242D244—21no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—21no—
248D244—42no—
249D244—42no—
250D244—81no—
251D244#13112yes—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—81no—
261C4×D61—81no—
262Dic122—81no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—21no—
266C8×C61—21no—
267C8×C61—41no—
268C8×C61—41no—
269C8×C61—41no—
270C8×C61—41no—
271#92418—21no—
272#92418—21no—
273#92418—21no—
274#92418—21no—
275#92418—41no—
276#92418—41no—
277#18026—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61C2×C4×D411yescharacteristic
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—84no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61C2×#13111yescharacteristic
300C4×C61#56811yescharacteristic
301C4×C61#57611yescharacteristic
302C4×C61#57611yescharacteristic
303Dic61—41no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307#3100—611no—
308#2979—611no—
309#2974—611no—
310#1594—611no—
311#1589—611no—
312#1586—611no—
313#1586—611no—
314#1581—611no—
315#1581—611no—
316#1580—611no—
317C8×D8—611no—
318#1572D6111yescharacteristic, complemented
319#1496—611no—
320#1478—611no—
321#1454—611no—
322C2×C61—41no—
323C2×C61#293311yescharacteristic
324C2×C61#294811yescharacteristic
325C2×C61#295511yescharacteristic
326D61—42no—
327D61—81no—
328D61—81no—
329D61—81no—
330#532—611no—
331C2×C4×D4—611no—
332#480—611no—
333#480—611no—
334#474—611no—
335#474—611no—
336#459—611no—
337#459—611no—
338#447—611no—
339#447—611no—
340C4×D8—611no—
341C4×D8—611no—
342C4×D8—611no—
343C4×D8—611no—
344#436—611no—
345#436—611no—
346#436—611no—
347#436—611no—
348#436—1221no—
349#435—1221no—
350#435—1221no—
351C8×D4—611no—
352C8×D4—611no—
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—1221no—
356#432C2×D6111yescharacteristic
357#431—611no—
358#431—611no—
359#431C2×D6111yescharacteristic
360#431C2×D6111yescharacteristic
361#408—1221no—
362#408—1221no—
363#407—1221no—
364C2×C22⋊C8—1221no—
365#335C2×D6111yescharacteristic, complemented
366#335C2×D6111yescharacteristic, complemented
367#334C2×D6111yescharacteristic, complemented
368#334C2×D6111yescharacteristic, complemented
369D4⋊C8—611no—
370D4⋊C8—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322—611no—
378#322—611no—
379#322—611no—
380C82—611no—
381C61#1802611yescharacteristic, complemented, Sylow
382C2×#41—1221no—
383C22×D4—611no—
384C23×C4—1221no—
385C2×D8—611no—
386C2×D8—611no—
387C2×D8—611no—
388C2×D8—611no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—1221no—
394C22×C8—1221no—
395C22×C8—1221no—
396C22×C8—1221no—
397C4⋊Q8—611no—
398#127—611no—
399#124—1221no—
400#121—611no—
401#121—611no—
402#121—1221no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—611no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1221no—
411C4×D4—1221no—
412C2×C4⋊C4—611no—
413C2×C22⋊C4—1221no—
414C2×C42C22×D6111yescharacteristic
415#107—611no—
416#107—611no—
417#107—611no—
418#107—611no—
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—1221no—
422C4⋊C8C4×D6111yescharacteristic
423C4⋊C8C4×D6111yescharacteristic
424C4⋊C8C22×D6111yescharacteristic
425C4⋊C8C22×D6111yescharacteristic
426C4⋊C8C22×D6111yescharacteristic
427C4⋊C8C22×D6111yescharacteristic
428#102—611no—
429#102—611no—
430#102—611no—
431#102—611no—
432#102—611no—
433#102—611no—
434#102—611no—
435#102—611no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—611no—
439C22⋊C8—611no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C22⋊C8—1221no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—1221no—
448C22⋊C8—1221no—
449C22⋊C8C4×D6111yescharacteristic
450C22⋊C8C4×D6111yescharacteristic
451#97—21no—
452C4×C8—21no—
453C4×C8—611no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8C22×D6111yescharacteristic
458C4×C8C22×D6111yescharacteristic
459C24—1221no—
460#41—4881no—
461#41—4881no—
462C2×Q8—1221no—
463C2×D4—611no—
464C2×D4—611no—
465C2×D4—611no—
466C2×D4—611no—
467C2×D4—1222no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C2×D4—2441no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—4881no—
482C22×C4—4881no—
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4D4×D6111yescharacteristic
485C22×C4#1175822611yescharacteristic
486D8—1222no—
487D8—1222no—
488D8—2441no—
489D8—2441no—
490M16—4881no—
491M16—4881no—
492M16—4881no—
493M16—4881no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—611no—
501C2×C8—611no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—4881no—
505C2×C8—4881no—
506C2×C8—4881no—
507C2×C8—4881no—
508C2×C8C2×C4×D6111yescharacteristic
509C2×C8C2×C4×D6111yescharacteristic
510C2×C8C2×C4×D6111yescharacteristic
511C2×C8C2×C4×D6111yescharacteristic
512C4⋊C4—611no—
513C4⋊C4—611no—
514C4⋊C4—611no—
515C4⋊C4—611no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1221no—
520C22⋊C4—1221no—
521C22⋊C4—1221no—
522C22⋊C4—1221no—
523C22⋊C4—1221no—
524C22⋊C4—1221no—
525C22⋊C4—1221no—
526C42C2×C4×D6111yescharacteristic
527C42D4×D6111yescharacteristic
528C42#1175822611yescharacteristic
529C42C23×D6111yescharacteristic
530C23—1221no—
531C23—1221no—
532C23—1221no—
533C23—1221no—
534C23—4881no—
535C23—2442no—
536C23—2442no—
537C23#1451973911yescharacteristic
538Q8—4881no—
539D4—612no—
540D4—1221no—
541D4—1221no—
542D4—1221no—
543D4—1221no—
544D4—1221no—
545D4—1221no—
546D4—1221no—
547D4—4881no—
548D4—4881no—
549D4—4881no—
550D4—2442no—
551D4—2442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—4881no—
562C2×C4—4881no—
563C2×C4—4881no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4#1451973911yescharacteristic
573C2×C4#1451973911yescharacteristic
574C2×C4#1451973911yescharacteristic
575C2×C4C22×C4×D6111yescharacteristic
576C2×C4C2×D4×D6111yescharacteristic
577C2×C4C2×#1175822611yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—1221no—
587C8—1221no—
588C8—1221no—
589C8—1221no—
590C8—2441no—
591C8—2441no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—1222no—
596C22—4884no—
597C22—2441no—
598C22—2441no—
599C22—2441no—
600C22—2441no—
601C22—2441no—
602C22—2441no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2441no—
608C22C2×#1451973911yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—2441no—
614C4—2441no—
615C4—2441no—
616C4—2441no—
617C4#131×D6111yescharacteristic
618C4#1684052711yescharacteristic
619C4#1684056411yescharacteristic
620C4#1684056411yescharacteristic
621C2—41no—
622C2—4881no—
623C2—4881no—
624C2—4881no—
625C2—2442no—
626C2#2145454311yescharacteristic
627C2#2145467011yescharacteristic
628C2#2145472111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1572C2
socleC22×C61C2×C4×D4
prime radical#21455820C2
cosocleC42×C61C24
hypercenter#1572D61
hypocenterC61#18026
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #21454885C2semidirect
3. #21454856C2semidirect
4. #21444732C2semidirect
5. #21444703C2semidirect
6. #21444682C2semidirect
7. #21444682C2semidirect
8. #21444647C2semidirect
9. #21444647C2semidirect
10. #21444642C2semidirect
11. #21444613C2semidirect
12. #21444287C2semidirect
13. #21444209C2semidirect
14. #21444119C2semidirect
15. C61×#1572C2semidirect
33. #16839839C22semidirect
34. #16839839C22semidirect
40. #16839827C22semidirect
41. #16839827C22semidirect
52. #16839489C22semidirect
53. #16839489C22semidirect
54. #16839489C22semidirect
55. #16839489C22semidirect
56. #16839484C22semidirect
57. #16839484C22semidirect
58. #16839483C22semidirect
59. C8×#92418C22semidirect
63. C61×#335C22semidirect
64. C61×#335C22semidirect
65. C61×#334C22semidirect
66. C61×#334C22semidirect
318. #1572D61semidirect
365. #335C2×D61semidirect
366. #335C2×D61semidirect
367. #334C2×D61semidirect
368. #334C2×D61semidirect
381. C61#18026semidirect

Maximal subgroups

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

subgroupindex
#214558202
#214548852
#214548562
#214447322
#214447032
#214446822
#214446472
#214446422
#214446132
#214442872
#214442092
#214441192
C61×#15722
#1802661