Finite Group Databasebeta

← #30622864

Subgroups — #30622864

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462615C211yesmaximal, characteristic, complemented
2#21462564C211yesmaximal, characteristic
3#21461995C211yesmaximal, characteristic, complemented
4#21461984C211yesmaximal, characteristic
5#21461914C211yesmaximal, characteristic, complemented
6#21461913C211yesmaximal, characteristic, complemented
7#21461902C211yesmaximal, characteristic, complemented
8#21461901C211yesmaximal, characteristic, complemented
9#21461787C211yesmaximal, characteristic, complemented
10#21461786C211yesmaximal, characteristic, complemented
11#21461639C211yesmaximal, characteristic, complemented
12#21461617C211yesmaximal, characteristic, complemented
13#21461598C211yesmaximal, characteristic, complemented
14#21461596C211yesmaximal, characteristic, complemented
15#21456161C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519864C2211yescharacteristic
18#16840813—21no—
19#16840813—21no—
20#16840812—21no—
21#16840811—21no—
22#16840795—21no—
23#16840794—21no—
24#16840791—21no—
25#16840789—21no—
26C2×#14519848C2211yescharacteristic
27C2×#14519847C2211yescharacteristic
28#16840769C2211yescharacteristic
29#16840769C2211yescharacteristic
30D61⋊(C4⋊C8)C2211yescharacteristic
31C2×#14519842C2211yescharacteristic
32C2×#14519842C2211yescharacteristic
33C2×#14519841C2211yescharacteristic
34C2×#14519841C2211yescharacteristic
35#16840737C2211yescharacteristic
36#16840736C2211yescharacteristic
37#16840727C2211yescharacteristic
38#16840727C2211yescharacteristic
39C4×#11758213C2211yescharacteristic
40C4×#11758213C2211yescharacteristic
41C2×#14519831C2211yescharacteristic
42C2×C8×#6923C2211yescharacteristic
43C4×C4⋊#6923C2211yescharacteristic
44#16840638C2211yescharacteristic
45#16840638C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50(C2×#6923)⋊C8C2211yescharacteristic
51(C2×#6923)⋊C8C2211yescharacteristic
52#16840317C2211yescharacteristic
53#16840311C2211yescharacteristic
54#16840129C411yescharacteristic, complemented
55#16840129C411yescharacteristic, complemented
56#16840125C411yescharacteristic, complemented
57#16840125C411yescharacteristic, complemented
58#16840124C411yescharacteristic, complemented
59#16840122C411yescharacteristic, complemented
60#16840121C411yescharacteristic, complemented
61#16839757C2211yescharacteristic
62#16839757C2211yescharacteristic
63#16839755C2211yescharacteristic
64#16839755C2211yescharacteristic
65#97×D61C2211yescharacteristic
66C61×#489C411yescharacteristic, complemented
67#14519865—22no—
68#14519865—41no—
69#14519864—22no—
70#14519864—41no—
71C2×#11758213—21no—
72C2×#11758213C2311yescharacteristic
73C2×#11758213C2311yescharacteristic
74C2×#11758213C2311yescharacteristic
75C2×#11758213C2311yescharacteristic
76C2×#11758217—21no—
77C2×D61⋊C8—21no—
78C2×D61⋊C8C2311yescharacteristic
79C2×D61⋊C8C2311yescharacteristic
80C22×#92420—21no—
81C2×C4⋊#6923—21no—
82C2×C4×#6923C2311yescharacteristic
83C2×C4×#6923C2311yescharacteristic
84#14519848—22no—
85#14519847—22no—
86#14519844—21no—
87#14519844—21no—
88#14519844D411yescharacteristic
89#14519844D411yescharacteristic
90C4⋊#92420—21no—
91C4⋊#92420—21no—
92C4⋊#92420D411yescharacteristic
93C4⋊#92420D411yescharacteristic
94#14519842—22no—
95#14519842—41no—
96#14519841—22no—
97#14519841—41no—
98#14519834—21no—
99#14519834—21no—
100C22⋊#92420—21no—
101C22⋊#92420—21no—
102#14519832—21no—
103#14519832—21no—
104#14519832—21no—
105#14519832—21no—
106#14519831—41no—
107C4×#92420—21no—
108C4×#92420—21no—
109C4×#92420—21no—
110C4×#92420—21no—
111C8×#6923—41no—
112(C2×#6923)⋊C4—21no—
113C2×#11758226C2311yescharacteristic
114C2×#11758224C2311yescharacteristic
115C2×C8×D61C2311yescharacteristic
116C2×C8×D61C2311yescharacteristic
117#14519777C2×C411yescharacteristic
118#14519775C2×C411yescharacteristic
119#14519773C2×C411yescharacteristic
120#14519768C2×C411yescharacteristic
121#14519768C2×C411yescharacteristic
122#14519765C2×C411yescharacteristic
123#14519757—21no—
124#14519753—21no—
125#14519750—21no—
126#14519750—21no—
127Q8×Dic61—21no—
128#14519742—21no—
129#14519737—21no—
130#14519737—21no—
131#14519735C2311yescharacteristic
132#14519735C2311yescharacteristic
133C42×D61C2311yescharacteristic
134#14519702C2×C411yescharacteristic
135#14519702C2×C411yescharacteristic
136#14519701C2×C411yescharacteristic
137#14519701C2×C411yescharacteristic
138#14519700C2×C411yescharacteristic
139#14519700C2×C411yescharacteristic
140#14519699C2×C411yescharacteristic
141#14519699C2×C411yescharacteristic
142#14519698C2×C411yescharacteristic
143#14519698C2×C411yescharacteristic
144#14519697C2×C411yescharacteristic
145#14519697C2×C411yescharacteristic
146#14519688C2×C411yescharacteristic
147#14519687C2×C411yescharacteristic
148#14519687C2×C411yescharacteristic
149C4⋊Q8×C61C2×C411yescharacteristic
150#124×C61C2×C411yescharacteristic
151#103×C61C2×C411yescharacteristic
152#103×C61C2×C411yescharacteristic
153#102×C61C2×C411yescharacteristic
154#102×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic
156C22×#6923—21no—
157C22×#6923—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22×C411yescharacteristic
160C2×D4×C61C22×C411yescharacteristic
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C22×Dic61—21no—
165#11758226—21no—
166#11758226—21no—
167#11758226—21no—
168#11758226—21no—
169#11758224—21no—
170#11758224—21no—
171#11758224—21no—
172#11758224—21no—
173C2×D244—21no—
174C2×D244C22×C411yescharacteristic
175C2×C4×D61—21no—
176C2×C4×D61#4111yescharacteristic
177C2×C4×D61#4111yescharacteristic
178C2×C4×D61C2411yescharacteristic
179C2×Dic122—21no—
180C2×Dic122C22×C411yescharacteristic
181#11758217—42no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—21no—
185C2×#92420—21no—
186C2×#92420—42no—
187C2×#92420C2×D411yescharacteristic
188C2×#92420C2×D411yescharacteristic
189C2×#92420C2×D411yescharacteristic
190C2×#92420C2×D411yescharacteristic
191C4⋊#6923—42no—
192C4×#6923—21no—
193C4×#6923—21no—
194C4×#6923—21no—
195C4×#6923—21no—
196#11758213—21no—
197#11758213—21no—
198#11758213—21no—
199#11758213—21no—
200#11758213—21no—
201#11758213—21no—
202#11758213—42no—
203#11758213#4112yes—
204#11758213#4112yes—
205D61⋊C8—21no—
206D61⋊C8—21no—
207D61⋊C8—21no—
208D61⋊C8—21no—
209D61⋊C8—42no—
210C2×C8×C61C22×C411yescharacteristic
211C2×C8×C61C22×C411yescharacteristic
212C4⋊C4×C61—21no—
213C4⋊C4×C61C22×C411yescharacteristic
214C4⋊C4×C61C22×C411yescharacteristic
215C22⋊C4×C61—21no—
216C22⋊C4×C61—21no—
217C42×C61C22×C411yescharacteristic
218#11758198—21no—
219#11758198—21no—
220#11758198—21no—
221#11758198—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61C22×C411yescharacteristic
226C4⋊Dic61C22×C411yescharacteristic
227#11758196—21no—
228#11758196—21no—
229#11758196—21no—
230#11758196—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61C22×C411yescharacteristic
234C4×Dic61C2×D411yescharacteristic
235C4×Dic61C2×D411yescharacteristic
236C2×#92418C22×C411yescharacteristic
237C2×#92418C22×C411yescharacteristic
238C8×D61—21no—
239C8×D61—21no—
240C8×D61—21no—
241C8×D61—21no—
242C23×C61—21no—
243C22×D61—21no—
244C22×D61C2×#4111yescharacteristic
245C2×#6923—22no—
246C2×#6923—41no—
247C2×#6923—41no—
248C2×#6923—41no—
249C2×#6923—41no—
250C2×#6923—41no—
251Q8×C61—21no—
252Q8×C61—21no—
253Q8×C61—81no—
254D4×C61—21no—
255D4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61C4×D411yescharacteristic
260C2×C4×C61C4×D411yescharacteristic
261C2×C4×C61C23×C411yescharacteristic
262C22⋊D61—42no—
263C22⋊D61—41no—
264C22⋊D61—41no—
265C22⋊D61—81no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61C4×D411yescharacteristic
272C2×Dic61C4×D411yescharacteristic
273C2×Dic61C22×D411yescharacteristic
274D244—21no—
275D244—21no—
276D244—41no—
277D244—41no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61C2×#4111yescharacteristic
283C4×D61C2×#4111yescharacteristic
284C4×D61H(5,𝔽2)11yescharacteristic
285C4×D612−1+411yescharacteristic
286Dic122—21no—
287Dic122—21no—
288Dic122—42no—
289#92420—21no—
290#92420—21no—
291#92420—21no—
292#92420—21no—
293#92420—22no—
294#92420—22no—
295#92420—41no—
296#92420—41no—
297C8×C61—21no—
298C8×C61—21no—
299#92418—21no—
300#92418—21no—
301#23236—611nomaximal, Sylow
302C22×C61—41no—
303C22×C61—41no—
304C22×C61—41no—
305C22×C61C2×C4×D411yescharacteristic
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61#55611yescharacteristic
312C2×D61#55911yescharacteristic
313#6923—42no—
314#6923—81no—
315C4×C61—21no—
316C4×C61—21no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61C4×#4111yescharacteristic
321C4×C61#52011yescharacteristic
322Dic61—21no—
323Dic61—21no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61#54611yescharacteristic
328Dic61#54811yescharacteristic
329#3135—611no—
330#2962—611no—
331#2935—611no—
332#1986—611no—
333#1980—611no—
334#1938—611no—
335#1937—611no—
336#1929—611no—
337#1929—611no—
338#1866—611no—
339#1866—611no—
340#1778—611no—
341#1771—611no—
342#1765—611no—
343#1764—611no—
344C2×C61—81no—
345C2×C61#236711yescharacteristic
346C2×C61#295511yescharacteristic
347C2×C61#295611yescharacteristic
348D61—21no—
349D61—21no—
350D61—81no—
351C2×#131—611no—
352C2×#131—611no—
353#533—611no—
354#532—611no—
355#491—611no—
356#491—611no—
357#490—611no—
358#490—611no—
359#489—611no—
360#489—611no—
361#489—611no—
362#489#692311yescharacteristic, complemented
363#446—1221no—
364#446—1221no—
365#446—1221no—
366C8×Q8—1221no—
367#436—1221no—
368#435—1221no—
369#435—1221no—
370C8×D4—1221no—
371C2×#108—611no—
372C2×#108—611no—
373#424—611no—
374#424—611no—
375C2×C4⋊C8—611no—
376C2×#104—611no—
377C2×#104—611no—
378C2×#104—611no—
379C2×#104—611no—
380#416—611no—
381#416—611no—
382#416—611no—
383#416—611no—
384#408—611no—
385#408—611no—
386#405—611no—
387#405—611no—
388C4×M16—611no—
389C4×M16—611no—
390C2×#97—611no—
391C2×#97—611no—
392C2×C4×C8—611no—
393C4×C4⋊C4—611no—
394#341—611no—
395#341—611no—
396#339—611no—
397#339—611no—
398#339—611no—
399#339—611no—
400#336—611no—
401#336—611no—
402C61#2323611yescharacteristic, complemented, Sylow
403C2×#41—611no—
404C2×#41—611no—
405#131—1222no—
406#131—1222no—
407#131—2441no—
408#131—2441no—
409C2×M16—611no—
410C2×M16—611no—
411C2×M16—611no—
412C2×M16—611no—
413C2×M16—1221no—
414C2×M16—1221no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—1221no—
420C22×C8—1221no—
421C4⋊Q8—611no—
422C4⋊Q8—611no—
423C4⋊Q8C2×#692311yescharacteristic
424#127—611no—
425#125—611no—
426#125—611no—
427#124—611no—
428#124C2×#692311yescharacteristic
429C22⋊Q8—1221no—
430C22⋊Q8—1221no—
431#121—1221no—
432#121—1221no—
433C4×Q8—1221no—
434C4×Q8—1221no—
435C4×D4—1221no—
436C4×D4—1221no—
437#117—611no—
438#117—611no—
439C2×C4⋊C4—1221no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443#108—1222no—
444#108—1222no—
445C4⋊C8—611no—
446C4⋊C8—611no—
447C4⋊C8—611no—
448C4⋊C8—611no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452C4⋊C8—1221no—
453#104—1222no—
454#104—1222no—
455#104—2441no—
456#104—2441no—
457#103—611no—
458#103—611no—
459#103—611no—
460#103—611no—
461#103—611no—
462#103—611no—
463#103C2×#692311yescharacteristic
464#103C2×#692311yescharacteristic
465#102—611no—
466#102—611no—
467#102—611no—
468#102—611no—
469#102—611no—
470#102—611no—
471#102C2×#692311yescharacteristic
472#102C2×#692311yescharacteristic
473C22⋊C8—1221no—
474C22⋊C8—1221no—
475C22⋊C8—1221no—
476C22⋊C8—1221no—
477#97—611no—
478#97—611no—
479#97—611no—
480#97—1221no—
481#97—1221no—
482#97—1221no—
483#97—1221no—
484#97—2441no—
485#97C2×#692311yescharacteristic
486C4×C8—1221no—
487C4×C8—1221no—
488C4×C8—1221no—
489C4×C8—1221no—
490C4×C8—2441no—
491#95—1221no—
492#41—1221no—
493#41—1221no—
494#41—1221no—
495#41—1221no—
496#41—1221no—
497#41—1221no—
498#41—1221no—
499#41—1221no—
500C2×Q8—21no—
501C2×Q8—611no—
502C2×Q8—1221no—
503C2×Q8C22×#692311yescharacteristic
504C2×D4—611no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—1221no—
509C2×D4C22×#692311yescharacteristic
510C22×C4—611no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517M16—612no—
518M16—612no—
519M16—1221no—
520M16—1221no—
521M16—1221no—
522M16—1221no—
523M16—1221no—
524M16—1221no—
525M16—2442no—
526M16—2442no—
527C2×C8—611no—
528C2×C8—611no—
529C2×C8—611no—
530C2×C8—611no—
531C2×C8—611no—
532C2×C8—611no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—2442no—
546C2×C8—2442no—
547C2×C8C22×#692311yescharacteristic
548C2×C8C22×#692311yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—611no—
551C4⋊C4—611no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—1221no—
559C4⋊C4—2442no—
560C4⋊C4C22×#692311yescharacteristic
561C4⋊C4C22×#692311yescharacteristic
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—1221no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42C22×#692311yescharacteristic
578C23—21no—
579C23—611no—
580C23—1221no—
581Q8—21no—
582Q8—21no—
583Q8—81no—
584Q8—1221no—
585Q8—1221no—
586Q8—2442no—
587D4—21no—
588D4—21no—
589D4—1221no—
590D4—1221no—
591D4—4881no—
592D4—2441no—
593D4—2441no—
594D4—2442no—
595D4—2441no—
596D4—2441no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—611no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—1222no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4D4×#692311yescharacteristic
623C2×C4D4×#692311yescharacteristic
624C2×C4C23×#692311yescharacteristic
625C8—21no—
626C8—21no—
627C8—1221no—
628C8—1221no—
629C8—1221no—
630C8—1221no—
631C8—1222no—
632C8—1222no—
633C8—1221no—
634C8—1221no—
635C8—2441no—
636C8—2441no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—611no—
641C22—611no—
642C22—1221no—
643C22—1221no—
644C22—2441no—
645C22—2441no—
646C22—2441no—
647C22C2×D4×#692311yescharacteristic
648C4—21no—
649C4—21no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—611no—
654C4—611no—
655C4—1221no—
656C4—1221no—
657C4—4881no—
658C4—2442no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C4#41×#692311yescharacteristic
663C4#1684083111yescharacteristic
664C2—81no—
665C2—1221no—
666C2—1221no—
667C2—4881no—
668C2#2146235011yescharacteristic
669C2#2146259211yescharacteristic
670C2#2146259311yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#489C4
socleC22×C61C2×C4×D4
prime radical#16840311C22
cosocleC2×C4×D61C24
hypercenter#489#6923
hypocenterC61#23236
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #21462615C2semidirect
3. #21461995C2semidirect
5. #21461914C2semidirect
6. #21461913C2semidirect
7. #21461902C2semidirect
8. #21461901C2semidirect
9. #21461787C2semidirect
10. #21461786C2semidirect
11. #21461639C2semidirect
12. #21461617C2semidirect
13. #21461598C2semidirect
14. #21461596C2semidirect
54. #16840129C4semidirect
55. #16840129C4semidirect
56. #16840125C4semidirect
57. #16840125C4semidirect
58. #16840124C4semidirect
59. #16840122C4semidirect
60. #16840121C4semidirect
66. C61×#489C4semidirect
362. #489#6923semidirect
402. C61#23236semidirect

Maximal subgroups

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

subgroupindex
#214626152
#214625642
#214619952
#214619842
#214619142
#214619132
#214619022
#214619012
#214617872
#214617862
#214616392
#214616172
#214615982
#214615962
#214561612
#2323661