Finite Group Databasebeta

← #29783172

Subgroups — #29783172

Order 15616.

708 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#21451782C211yesmaximal, characteristic, complemented
2#21448456C211yesmaximal, characteristic, complemented
3#21447311C211yesmaximal, characteristic, complemented
4#21447194C211yesmaximal, characteristic, complemented
5#21447189C211yesmaximal, characteristic, complemented
6#21447128C211yesmaximal, characteristic
7#21446684C211yesmaximal, characteristic
8#21446544C211yesmaximal, characteristic, complemented
9#21446516C211yesmaximal, characteristic, complemented
10#21446444C211yesmaximal, characteristic, complemented
11#21446388C211yesmaximal, characteristic, complemented
12#21446165C211yesmaximal, characteristic
13#21446078C211yesmaximal, characteristic, complemented
14#21445679C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C22×#11758199C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×#14519710C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×C4×#92418C2211yescharacteristic
28#16839691—21no—
29#16839689—21no—
30#16839688—21no—
31#16839684—21no—
32#16839665C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839663C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839661C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839658C2211yescharacteristic
39#16839658C2211yescharacteristic
40#16839656—21no—
41#16839650—21no—
42#16839623—21no—
43#16839620—21no—
44C4⋊C4×Dic61C2211yescharacteristic
45#16839608C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C23×Dic61—21no—
61C2×#11758199—22no—
62C2×#11758199—22no—
63C2×#11758199—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66D4×Dic61—22no—
67D4×Dic61—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77C2×C22⋊Dic61—21no—
78C2×#11758198—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519710—22no—
88#14519708—22no—
89#14519708—41no—
90#14519706—22no—
91#14519706—22no—
92#14519699—22no—
93#14519699—41no—
94#14519698—22no—
95#14519697—22no—
96C4×#92418—41no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684D411yescharacteristic
103#14519684D411yescharacteristic
104#14519684D411yescharacteristic
105#14519684D411yescharacteristic
106C22×D4×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#102×C61—22no—
117#102×C61—41no—
118#97×C61—41no—
119#95×C61—21no—
120C24×C61—21no—
121C23×D61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—21no—
126C2×D4×C61—21no—
127C2×D4×C61#4112yes—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—24no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—81no—
139C22×Dic61—81no—
140C22×Dic61C2×D411yescharacteristic
141C22×Dic61C2×D411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—81no—
163C22⋊C4×C61—81no—
164C22⋊C4×C61—81no—
165C42×C61—21no—
166C42×C61—21no—
167C22⋊Dic61—24no—
168C22⋊Dic61—81no—
169C22⋊Dic61—81no—
170#11758199—44no—
171#11758198—81no—
172#11758198—81no—
173#11758198—81no—
174#11758198—81no—
175#11758198—81no—
176#11758198—81no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—81no—
183C4⋊Dic61#4112yes—
184#11758196—81no—
185#11758196—81no—
186#11758196—81no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—81no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418#4112yes—
197C2×#92418#4112yes—
198C23×C61—22no—
199C23×C61—41no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61C22×D411yescharacteristic
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C22×D61—41no—
213D4×C61—22no—
214D4×C61—22no—
215D4×C61—41no—
216D4×C61—41no—
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—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61H(5,𝔽2)11yescharacteristic
237C2×C4×C612−1+411yescharacteristic
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—22no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
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—84no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—41no—
264C8×C61—41no—
265C8×C61—41no—
266#92418—22no—
267#92418—22no—
268#29437—611nomaximal, Sylow
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61#52511yescharacteristic
277C22×C61#53211yescharacteristic
278C22×C61#53711yescharacteristic
279C22×C61#57611yescharacteristic
280C22×C61#57611yescharacteristic
281C22×C61#57711yescharacteristic
282C22×C61#57711yescharacteristic
283C2×D61—81no—
284C2×D61—81no—
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—81no—
293C4×C61—81no—
294C4×C61—81no—
295C4×C61#55111yescharacteristic
296C4×C61#55211yescharacteristic
297C4×C61#55311yescharacteristic
298C4×C61#55611yescharacteristic
299Dic61—41no—
300Dic61—42no—
301Dic61—41no—
302Dic61—41no—
303Dic61—41no—
304Dic61—81no—
305Dic61—81no—
306#2644—611no—
307#2319—611no—
308#2086—611no—
309#2065—611no—
310#2065—611no—
311#2054—611no—
312#1970—611no—
313#1941—611no—
314#1936—611no—
315#1936D6111yescharacteristic, complemented
316#1926—611no—
317#1918—611no—
318#1879—611no—
319#1864—611no—
320#1768—611no—
321C2×C61—82no—
322C2×C61#260111yescharacteristic
323C2×C61#311811yescharacteristic
324C2×C61#311911yescharacteristic
325C2×C61#317311yescharacteristic
326C2×C61#317611yescharacteristic
327C2×C61#325711yescharacteristic
328C2×C61#325711yescharacteristic
329D61—161no—
330C22×D8—611no—
331C2×C4×D4—611no—
332C2×#107—611no—
333C2×#106—611no—
334C2×#106—611no—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—611no—
337C2×#102—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102C2×D6111yescharacteristic
342C2×#102C2×D6111yescharacteristic
343C2×#97C2×D6111yescharacteristic
344C2×C4×C8—611no—
345#397—1221no—
346#397—1221no—
347#397—1221no—
348#396—1221no—
349#390—611no—
350#390—611no—
351#390—611no—
352#390—611no—
353#390C2×D6111yescharacteristic
354#389—611no—
355#389—611no—
356#389—611no—
357#389—611no—
358#389C2×D6111yescharacteristic
359#388—1221no—
360#388—1221no—
361#381—1221no—
362#380—1221no—
363C4×C4⋊C4—611no—
364#376—611no—
365#340—611no—
366#340—611no—
367#340—611no—
368#340—611no—
369#340C2×D6111yescharacteristic
370#340C2×D6111yescharacteristic
371#336—611no—
372#336—611no—
373C61#2943711yescharacteristic, complemented, Sylow
374C22×D4—611no—
375C22×D4C22×D6111yescharacteristic
376C23×C4—1221no—
377C2×D8—1222no—
378C2×D8—1222no—
379C2×D8—2441no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8C22×D6111yescharacteristic
383C22×C8C22×D6111yescharacteristic
384C4×D4—1222no—
385C4×D4—1222no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C4⋊C4C22×D6111yescharacteristic
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—1221no—
400C2×C22⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C22⋊C4—1221no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—1221no—
411C2×C42C22×D6111yescharacteristic
412#107—1222no—
413#106—1222no—
414#106—2441no—
415C4⋊C8—1222no—
416C4⋊C8—1222no—
417#102—22no—
418#102—41no—
419#102—1222no—
420#102—1222no—
421#102—1222no—
422#102—2441no—
423#97—41no—
424C4×C8—2441no—
425#95—21no—
426#95—611no—
427#95—611no—
428#95—611no—
429#95—611no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433#95—1221no—
434#95—1221no—
435C24—21no—
436C24—1221no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4#1175822212yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1224no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—4881no—
461C22×C4—4881no—
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4C23×D6111yescharacteristic
465D8—2444no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—612no—
473C2×C8—612no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—81no—
485C4⋊C4—612no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—4881no—
492C4⋊C4—4881no—
493C4⋊C4—4881no—
494C4⋊C4—4881no—
495C22⋊C4—81no—
496C22⋊C4—81no—
497C22⋊C4—1224no—
498C22⋊C4—4881no—
499C22⋊C4—4881no—
500C22⋊C4—4881no—
501C22⋊C4—4881no—
502C22⋊C4—4881no—
503C22⋊C4—4881no—
504C22⋊C4—4881no—
505C22⋊C4—4881no—
506C42—21no—
507C42—21no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42—4881no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—2441no—
521C23—2441no—
522C23—2441no—
523C23—2441no—
524C23—2441no—
525C23—2441no—
526C23—2441no—
527C23C2×D4×D6111yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—2441no—
533D4—2441no—
534D4—2441no—
535D4—2441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1222no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—4884no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4#41×D6111yescharacteristic
574C2×C4#41×D6111yescharacteristic
575C2×C4#41×D6111yescharacteristic
576C2×C4C2×#1175822211yescharacteristic
577C2×C4#1451982211yescharacteristic
578C2×C4#1451982411yescharacteristic
579C8—41no—
580C8—41no—
581C8—1222no—
582C8—1222no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—4881no—
591C22—4881no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—4881no—
597C22#1684027111yescharacteristic
598C22#1684031111yescharacteristic
599C22#1684033911yescharacteristic
600C22#1684056611yescharacteristic
601C22#1684056611yescharacteristic
602C22#1684057111yescharacteristic
603C22#1684057211yescharacteristic
604C4—41no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4—4881no—
610C4—4881no—
611C4—2441no—
612C4—2441no—
613C4—2441no—
614C4—2442no—
615C4—2441no—
616C4#1684044111yescharacteristic
617C4#1684044511yescharacteristic
618C4#1684045711yescharacteristic
619C4#1684047911yescharacteristic
620C2—82no—
621C2—9761no—
622C2#2145142111yescharacteristic
623C2#2145600711yescharacteristic
624C2#2145602211yescharacteristic
625C2#2145643511yescharacteristic
626C2#2145646811yescharacteristic
627C2#2145722511yescharacteristic
628C2#2145723111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#1936D61
hypocenterC61#29437
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
1. #21451782C2semidirect
2. #21448456C2semidirect
3. #21447311C2semidirect
4. #21447194C2semidirect
5. #21447189C2semidirect
8. #21446544C2semidirect
9. #21446516C2semidirect
10. #21446444C2semidirect
11. #21446388C2semidirect
13. #21446078C2semidirect
14. #21445679C2semidirect
15. C61×#1936C2semidirect
315. #1936D61semidirect
373. C61#29437semidirect

Maximal subgroups

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

subgroupindex
#214517822
#214484562
#214473112
#214471942
#214471892
#214471282
#214466842
#214465442
#214465162
#214464442
#214463882
#214461652
#214460782
#214456792
C61×#19362
#2943761