Finite Group Databasebeta

← #29650393

Subgroups — #29650393

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455862C211yesmaximal, characteristic
2#21454859C211yesmaximal, characteristic, complemented
3#21444731C211yesmaximal, characteristic, complemented
4#21444719C211yesmaximal, characteristic, complemented
5#21444709C211yesmaximal, characteristic, complemented
6#21444702C211yesmaximal, characteristic, complemented
7#21444697C211yesmaximal, characteristic, complemented
8#21444683C211yesmaximal, characteristic, complemented
9#21444662C211yesmaximal, characteristic, complemented
10#21444648C211yesmaximal, characteristic, complemented
11#21444610C211yesmaximal, characteristic, complemented
12#21444243C211yesmaximal, characteristic, complemented
13#21444227C211yesmaximal, characteristic, complemented
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2993C211yesmaximal, characteristic, complemented
16C2×C4×D244C2211yescharacteristic
17#16840095C411yescharacteristic
18#16840078C411yescharacteristic
19#16840059C411yescharacteristic
20#16840059C411yescharacteristic
21#16839974C411yescharacteristic
22#16839974C411yescharacteristic
23#16839912C411yescharacteristic
24#16839895C411yescharacteristic
25C4×#11758201C2211yescharacteristic
26C4×#11758201C2211yescharacteristic
27C4×#11758199C2211yescharacteristic
28C4×#11758199C2211yescharacteristic
29#16839841C2211yescharacteristic
30#16839841C2211yescharacteristic
31#16839841C2211yescharacteristic
32#16839841C2211yescharacteristic
33#16839839—21no—
34#16839839—21no—
35#16839815C2211yescharacteristic
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839724—21no—
39#16839724—21no—
40#16839514C2211yescharacteristic, complemented
41#16839514C2211yescharacteristic, complemented
42#16839512C2211yescharacteristic, complemented
43#16839512C2211yescharacteristic, complemented
44Q8⋊#92418C2211yescharacteristic, complemented
45Q8⋊#92418C2211yescharacteristic, complemented
46D4⋊#92418C2211yescharacteristic, complemented
47D4⋊#92418C2211yescharacteristic, complemented
48#16839489C2211yescharacteristic
49#16839489C2211yescharacteristic
50#16839489C2211yescharacteristic
51#16839489C2211yescharacteristic
52#16839484C2211yescharacteristic, complemented
53#16839484C2211yescharacteristic, complemented
54#16839483C2211yescharacteristic, complemented
55C8×#92418C2211yescharacteristic, complemented
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic, complemented
58C8×Q8×C61C2211yescharacteristic, complemented
59C61×#436—21no—
60C61×#436C2211yescharacteristic, complemented
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic, complemented
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C61×#423C2211yescharacteristic
67C22×D244C2×C411yescharacteristic
68C22×C4×D61—21no—
69C2×#11758201C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758199C2×C411yescharacteristic
72C2×#11758199C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C4×D244—21no—
78C4×D244—21no—
79C4×D244C2×C411yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244C2311yescharacteristic
82C4×D244C2311yescharacteristic
83C2×C4⋊Dic61C2×C411yescharacteristic
84C2×#11758198—21no—
85#14519710C2×C411yescharacteristic
86#14519710C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88#14519708C2×C411yescharacteristic
89C4⋊#92418—21no—
90C4⋊#92418C2×C411yescharacteristic
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519698C2×C411yescharacteristic
97#14519698C2×C411yescharacteristic
98#14519697C2×C411yescharacteristic
99#14519697C2×C411yescharacteristic
100#14519697C2×C411yescharacteristic
101#14519697C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106#14519689—21no—
107#14519689—21no—
108#14519689—21no—
109#14519689—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61C2×C411yescharacteristic
120#124×C61C2×C411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123#121×C61C2×C411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×D4×C61—21no—
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×Dic61—21no—
153C2×D244—21no—
154C2×D244—41no—
155C2×D244—41no—
156C2×D244C22×C411yescharacteristic
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—81no—
163C2×C4×D61—81no—
164M16×C61—81no—
165M16×C61—81no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—21no—
184C42×C61—21no—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61#4111yescharacteristic
188C42×C61C2411yescharacteristic
189#11758201—41no—
190#11758201—41no—
191#11758199—41no—
192#11758199—41no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61C22×C411yescharacteristic
199C4⋊Dic61C22×C411yescharacteristic
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208#11758189—81no—
209#11758189—81no—
210#11758189—81no—
211#11758189—81no—
212C23×C61—21no—
213C23×C61C4×D411yescharacteristic
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—42no—
217C22×D61—81no—
218C22×D61—81no—
219Q8×C61—21no—
220Q8×C61—21no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—81no—
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—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—81no—
243D244—21no—
244D244—21no—
245D244—21no—
246D244—21no—
247D244—42no—
248C4×D61—41no—
249C4×D61—41no—
250C4×D61—41no—
251C4×D61—41no—
252C4×D61—81no—
253C4×D61—81no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—21no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#17946—611nomaximal, Sylow
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×C4×D411yescharacteristic
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—84no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61#56811yescharacteristic
291C4×C61#56811yescharacteristic
292C4×C61#57611yescharacteristic
293C4×C61#57711yescharacteristic
294Dic61—41no—
295Dic61—41no—
296#3105—611no—
297#2993D6111yescharacteristic, complemented
298#2975—611no—
299#1594—611no—
300#1592—611no—
301#1590—611no—
302#1589—611no—
303#1588—611no—
304#1586—611no—
305#1583—611no—
306#1581—611no—
307#1574—611no—
308#1486—611no—
309#1482—611no—
310#1454—611no—
311C2×C61—41no—
312C2×C61—81no—
313C2×C61#293011yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61#295711yescharacteristic
316D61—81no—
317D61—81no—
318#529C2×D6111yescharacteristic
319C2×C4×D4—611no—
320#484—611no—
321#481—611no—
322#478—611no—
323#478—611no—
324#463—611no—
325#463—611no—
326#450—611no—
327#447—611no—
328#446C2×D6111yescharacteristic, complemented
329C8×Q8C2×D6111yescharacteristic, complemented
330C4×SD16—611no—
331C4×SD16—611no—
332C4×D8—611no—
333C4×D8—611no—
334#436—21no—
335#436—611no—
336#436—611no—
337#436—611no—
338#436—611no—
339#436—1221no—
340#436—1221no—
341#436C2×D6111yescharacteristic, complemented
342#435—21no—
343C8×D4C2×D6111yescharacteristic, complemented
344#433—21no—
345#431—611no—
346#431—611no—
347#431—611no—
348#431C2×D6111yescharacteristic
349#424—21no—
350#423C2×D6111yescharacteristic
351#407—1221no—
352#407—1221no—
353#335—611no—
354#335—611no—
355#334—611no—
356#334—611no—
357Q8⋊C8—611no—
358Q8⋊C8—611no—
359D4⋊C8—611no—
360D4⋊C8—611no—
361D4⋊C8—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365#322—611no—
366#322—611no—
367#322—611no—
368C82—611no—
369C61#1794611yescharacteristic, complemented, Sylow
370C22×D4—611no—
371C23×C4—1221no—
372C2×SD16—611no—
373C2×SD16—611no—
374C2×D8—611no—
375C2×D8—611no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C22×C8—21no—
383#126—21no—
384#125C4×D6111yescharacteristic
385#124C4×D6111yescharacteristic
386#123—21no—
387C22⋊Q8C4×D6111yescharacteristic
388#121C4×D6111yescharacteristic
389C4×Q8C22×D6111yescharacteristic
390C4×D4—21no—
391C4×D4—611no—
392C4×D4—611no—
393C4×D4—611no—
394C4×D4—611no—
395C4×D4—1221no—
396C4×D4—1221no—
397C4×D4C22×D6111yescharacteristic
398#117—21no—
399C2×C4⋊C4—611no—
400C2×C22⋊C4—1221no—
401C2×C42C22×D6111yescharacteristic
402#107—611no—
403#107—611no—
404#106—611no—
405#106—611no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—1221no—
414C4⋊C8C22⋊D6111yescharacteristic
415C4⋊C8C22⋊D6111yescharacteristic
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418#103—611no—
419#103—611no—
420#102—611no—
421#102—611no—
422#102—611no—
423#102—611no—
424#102—611no—
425#102—611no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—611no—
429C22⋊C8—611no—
430C22⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C22⋊C8—1221no—
436C22⋊C8C22⋊D6111yescharacteristic
437C22⋊C8C22⋊D6111yescharacteristic
438#97—21no—
439C4×C8—21no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8—1221no—
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447C24—1221no—
448C2×Q8C2×C4×D6111yescharacteristic
449C2×D4—21no—
450C2×D4—611no—
451C2×D4—611no—
452C2×D4—1221no—
453C2×D4—2441no—
454C2×D4—2441no—
455C2×D4C2×C4×D6111yescharacteristic
456C22×C4—21no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—4881no—
463C22×C4—4881no—
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4#1175822211yescharacteristic
466C22×C4C2×C22⋊D6111yescharacteristic
467SD16—2441no—
468SD16—2441no—
469D8—2441no—
470D8—2441no—
471M16—81no—
472M16—81no—
473M16—4881no—
474M16—4881no—
475M16—4881no—
476M16—4881no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—611no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8C2×C22⋊D6111yescharacteristic
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—1221no—
499C4⋊C4C2×C4×D6111yescharacteristic
500C4⋊C4C2×C4×D6111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C42—21no—
511C42C2×C4×D6111yescharacteristic
512C42#1175822211yescharacteristic
513C42C2×C22⋊D6111yescharacteristic
514C42C23×D6111yescharacteristic
515C23—21no—
516C23—1221no—
517C23—1221no—
518C23—4881no—
519C23—4881no—
520C23—2442no—
521C23C4×C22⋊D6111yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—1221no—
528D4—1221no—
529D4—1221no—
530D4—1221no—
531D4—2442no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—4881no—
545C2×C4—4881no—
546C2×C4—4881no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4C4×C22⋊D6111yescharacteristic
552C2×C4C4×C22⋊D6111yescharacteristic
553C2×C4C4×C22⋊D6111yescharacteristic
554C2×C4C22×C4×D6111yescharacteristic
555C2×C4C22×C22⋊D6111yescharacteristic
556C2×C4C2×#1175822211yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—1221no—
564C8—1221no—
565C8—1221no—
566C8—1221no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—4884no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22—2441no—
582C22—2441no—
583C22—2441no—
584C22C2×C4×C22⋊D6111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—2441no—
593C4—2441no—
594C4#1684052711yescharacteristic
595C4#1684052711yescharacteristic
596C4#1684056511yescharacteristic
597C4#1684057011yescharacteristic
598C2—41no—
599C2—81no—
600C2—4881no—
601C2—4881no—
602C2#2145452011yescharacteristic
603C2#2145464711yescharacteristic
604C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2993C2
socleC22×C61C2×C4×D4
prime radical#16839895C4
cosocleC42×C61C24
hypercenter#2993D61
hypocenterC61#17946
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #21454859C2semidirect
3. #21444731C2semidirect
4. #21444719C2semidirect
5. #21444709C2semidirect
6. #21444702C2semidirect
7. #21444697C2semidirect
8. #21444683C2semidirect
9. #21444662C2semidirect
10. #21444648C2semidirect
11. #21444610C2semidirect
12. #21444243C2semidirect
13. #21444227C2semidirect
14. #21444119C2semidirect
15. C61×#2993C2semidirect
40. #16839514C22semidirect
41. #16839514C22semidirect
42. #16839512C22semidirect
43. #16839512C22semidirect
44. Q8⋊#92418C22semidirect
45. Q8⋊#92418C22semidirect
46. D4⋊#92418C22semidirect
47. D4⋊#92418C22semidirect
52. #16839484C22semidirect
53. #16839484C22semidirect
54. #16839483C22semidirect
55. C8×#92418C22semidirect
57. C61×#446C22semidirect
58. C8×Q8×C61C22semidirect
60. C61×#436C22semidirect
62. C8×D4×C61C22semidirect
297. #2993D61semidirect
328. #446C2×D61semidirect
329. C8×Q8C2×D61semidirect
341. #436C2×D61semidirect
343. C8×D4C2×D61semidirect
369. C61#17946semidirect

Maximal subgroups

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

subgroupindex
#214558622
#214548592
#214447312
#214447192
#214447092
#214447022
#214446972
#214446832
#214446622
#214446482
#214446102
#214442432
#214442272
#214441192
C61×#29932
#1794661