Finite Group Databasebeta

← #29699232

Subgroups — #29699232

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic61C211yesmaximal, characteristic
2#21448791C211yesmaximal, characteristic, complemented
3#21448724C211yesmaximal, characteristic, complemented
4#21446519C211yesmaximal, characteristic, complemented
5#21446513C211yesmaximal, characteristic, complemented
6#21446391C211yesmaximal, characteristic, complemented
7#21446389C211yesmaximal, characteristic, complemented
8#21446169C211yesmaximal, characteristic
9#21445948C211yesmaximal, characteristic, complemented
10#21445827C211yesmaximal, characteristic, complemented
11#21445827C211yesmaximal, characteristic, complemented
12#21445685C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#21445644C211yesmaximal, characteristic, complemented
15C61×#1879C211yesmaximal, characteristic
16C2×D4×Dic61C2211yescharacteristic
17C2×D4×Dic61C2211yescharacteristic
18C2×D4×Dic61C2211yescharacteristic
19D8×Dic61C418yescomplemented
20C2×#14519711C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519688C2211yescharacteristic
27C2×#14519687C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839665C2211yescharacteristic
30#16839660C2211yescharacteristic
31#16839658C2211yescharacteristic
32#16839656—21no—
33#16839650—21no—
34#16839635—21no—
35#16839634—21no—
36#16839627C2211yescharacteristic
37#16839627C2211yescharacteristic
38#16839623—21no—
39#16839620—21no—
40C4⋊C4×Dic61C2211yescharacteristic
41C4×#11758196C2211yescharacteristic
42C4×C4⋊Dic61C2211yescharacteristic
43C22⋊C4×Dic61—21no—
44C2×#14519684—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C22×D8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C23×Dic61—21no—
61C23×Dic61—21no—
62C23×Dic61—21no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65D4×Dic61—22no—
66D4×Dic61—22no—
67D4×Dic61—22no—
68D4×Dic61—41no—
69D4×Dic61C2×C414yes—
70D4×Dic61C2×C414yescomplemented
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196D411yescharacteristic
78C2×#11758196D411yescharacteristic
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C22⋊Dic61—21no—
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61C2311yescharacteristic
87C2×C4×Dic61C2311yescharacteristic
88#14519711C2×C414yescomplemented
89#14519706—22no—
90#14519698—22no—
91#14519698—41no—
92#14519698C2×C414yes—
93#14519698C2×C414yescomplemented
94#14519688—41no—
95#14519687—41no—
96C8×Dic61C2×C414yescomplemented
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107C22×D4×C61C2311yescharacteristic
108C22×D4×C61C2311yescharacteristic
109C23×C4×C61—21no—
110C2×D8×C61—22no—
111C2×D8×C61—22no—
112C2×D8×C61C2×C414yes—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C4×D4×C61—22no—
116C4×D4×C61—41no—
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C42×C61C2311yescharacteristic
123#102×C61—22no—
124#102×C61—41no—
125C24×C61—21no—
126C24×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61C22×C412yes—
136C2×D4×C61C22×C412yes—
137C2×D4×C61#4112yes—
138C2×D4×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—42no—
142C22×C4×C61—42no—
143C22×C4×C61—81no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—24no—
150C22×Dic61—24no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—42no—
154C22×Dic61—42no—
155C22×Dic61—81no—
156C22×Dic61—81no—
157C22×Dic61—81no—
158C22×Dic61—81no—
159C22×Dic61—81no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C22×Dic61C2×D411yescharacteristic
164D8×C61—28no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61C22×C412yes—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C22⋊C4×C61—42no—
176C22⋊C4×C61—42no—
177C22⋊C4×C61—81no—
178C42×C61—21no—
179C42×C61—21no—
180C22⋊Dic61—24no—
181C22⋊Dic61—24no—
182C22⋊Dic61—42no—
183C22⋊Dic61—42no—
184C22⋊Dic61—81no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61C22×C412yes—
192C4⋊Dic61C22×C412yes—
193#11758196—41no—
194#11758196—41no—
195#11758196—81no—
196#11758196—81no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—81no—
200C4×Dic61—81no—
201C4×Dic61C22×C412yes—
202C4×Dic61#4112yes—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C22×C412yes—
209C23×C61—22no—
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—22no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—41no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61C22×D411yescharacteristic
224D4×C61—22no—
225D4×C61—22no—
226D4×C61—22no—
227D4×C61—22no—
228D4×C61—22no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61#11714yes—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
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—84no—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×C4×C612−1+411yescharacteristic
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—84no—
274C2×Dic61—84no—
275C2×Dic61—84no—
276C2×Dic61C4×D412yes—
277C2×Dic61C4×D412yes—
278C8×C61—22no—
279C8×C61—41no—
280#92418—22no—
281#92418—41no—
282#22764—611nomaximal, Sylow
283C22×C61—24no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61C2×C4×D411yescharacteristic
298C22×C61#54611yescharacteristic
299C22×C61#54811yescharacteristic
300C22×C61#57511yescharacteristic
301C22×C61#57511yescharacteristic
302C22×C61#57611yescharacteristic
303C22×C61#57611yescharacteristic
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61C2×#11711yescharacteristic
309C4×C61#52011yescharacteristic
310C4×C61#55211yescharacteristic
311C4×C61#55311yescharacteristic
312Dic61—22no—
313Dic61—22no—
314Dic61—42no—
315Dic61—42no—
316Dic61—41no—
317Dic61—41no—
318Dic61—81no—
319Dic61—81no—
320C2×C4×D8—611no—
321#2357—611no—
322#2349—611no—
323#1936—611no—
324#1936—611no—
325#1918—611no—
326#1918—611no—
327#1879—611no—
328#1879D6111yescharacteristic
329#1835—611no—
330#1804—611no—
331#1804—611no—
332#1770—611no—
333#1762—611no—
334#1762—611no—
335C2×C61—44no—
336C2×C61—82no—
337C2×C61#235211yescharacteristic
338C2×C61#294311yescharacteristic
339C2×C61#294811yescharacteristic
340C2×C61#332211yescharacteristic
341C2×C61#332211yescharacteristic
342C2×C61#337011yescharacteristic
343C2×C61#337011yescharacteristic
344C22×D8C2×D6111yescharacteristic
345C2×C4×D4—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4C2×D6111yescharacteristic
349C4×D8—618no—
350C2×#107—611no—
351C2×C4⋊C8—611no—
352C2×#102—611no—
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102C2×D6111yescharacteristic
357C2×#102C2×D6111yescharacteristic
358C2×#97—611no—
359C2×#97—611no—
360C2×C4×C8—611no—
361#390—611no—
362#390C2×D6111yescharacteristic
363#389—611no—
364#389—611no—
365#388—1221no—
366#388—1221no—
367#385—1221no—
368#385—1221no—
369#382—611no—
370#382—611no—
371#381—1221no—
372#380—1221no—
373C4×C4⋊C4—611no—
374C4×C4⋊C4—611no—
375C4×C4⋊C4—611no—
376C4×C22⋊C4—1221no—
377C2×#95—1221no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340C2×D6111yescharacteristic
386#336—611no—
387#336C2×D6111yescharacteristic
388C61#2276411yescharacteristic, complemented, Sylow
389C22×D4C22×D6111yescharacteristic
390C22×D4C22×D6111yescharacteristic
391C23×C4—21no—
392C23×C4—1221no—
393C23×C4—1221no—
394C23×C4—1221no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8C4×D6114yes—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4×D4—22no—
403C4×D4—41no—
404C4×D4—614no—
405C4×D4—614no—
406C4×D4—1222no—
407C4×D4—1222no—
408C4×D4—1222no—
409C4×D4—2441no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—1221no—
431C2×C42—1221no—
432C2×C42C22×D6111yescharacteristic
433#107—614no—
434C4⋊C8—1222no—
435#102—22no—
436#102—41no—
437#102—614no—
438#102—614no—
439#102—1222no—
440#102—2441no—
441#97—2441no—
442#97—2441no—
443C4×C8—614no—
444#95—611no—
445#95—611no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454C24—21no—
455C24—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4C2×C4×D6112yes—
465C2×D4C2×C4×D6112yes—
466C2×D4#1175822412yes—
467C2×D4#1175822412yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—1224no—
478C22×C4—1224no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4—4881no—
488C22×C4—2442no—
489C22×C4—2442no—
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4C23×D6111yescharacteristic
493D8—28no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—612no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8C2×C4×D6112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—612no—
511C4⋊C4—612no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—4881no—
519C4⋊C4—4881no—
520C4⋊C4—2441no—
521C4⋊C4—2441no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—1224no—
526C22⋊C4—1224no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C22⋊C4—2442no—
530C42—21no—
531C42—21no—
532C42—612no—
533C42—612no—
534C42—1221no—
535C42—1221no—
536C42—4881no—
537C42—4881no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×D4×D6111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4#1451973314yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—612no—
575C2×C4—612no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—4884no—
589C2×C4—4884no—
590C2×C4—4884no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4#41×D6111yescharacteristic
603C2×C4C2×#1175822411yescharacteristic
604C2×C4C2×#1175822411yescharacteristic
605C2×C4#1451982211yescharacteristic
606C2×C4#1451982411yescharacteristic
607C8—22no—
608C8—41no—
609C8—1222no—
610C8—2441no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C4×D4×D6111yescharacteristic
626C22#1684039911yescharacteristic
627C22#1684041811yescharacteristic
628C22#1684055811yescharacteristic
629C22#1684055811yescharacteristic
630C22#1684056311yescharacteristic
631C22#1684056411yescharacteristic
632C4—41no—
633C4—41no—
634C4—81no—
635C4—81no—
636C4—1222no—
637C4—1222no—
638C4—4881no—
639C4—4881no—
640C4—2442no—
641C4—2442no—
642C4—2441no—
643C4—2441no—
644C4C2×#1451973311yescharacteristic
645C4#1684024111yescharacteristic
646C4#1684044911yescharacteristic
647C4#1684045511yescharacteristic
648C2—44no—
649C2—82no—
650C2#2144874611yescharacteristic
651C2#2145461611yescharacteristic
652C2#2145466611yescharacteristic
653C2#2145801311yescharacteristic
654C2#2145802411yescharacteristic
655C2#2145856511yescharacteristic
656C2#2145856911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1879C2
socleC23×C61C22×D4
prime radicalC22×D8×C61C22
cosocleC22×C4×C61C24
hypercenter#1879D61
hypocenterC61#22764
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #21448791C2semidirect
3. #21448724C2semidirect
4. #21446519C2semidirect
5. #21446513C2semidirect
6. #21446391C2semidirect
7. #21446389C2semidirect
9. #21445948C2semidirect
10. #21445827C2semidirect
11. #21445827C2semidirect
12. #21445685C2semidirect
13. #21445646C2semidirect
14. #21445644C2semidirect
19. D8×Dic61C4semidirect
70. D4×Dic61C2×C4semidirect
88. #14519711C2×C4semidirect
93. #14519698C2×C4semidirect
96. C8×Dic61C2×C4semidirect
388. C61#22764semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic612
#214487912
#214487242
#214465192
#214465132
#214463912
#214463892
#214461692
#214459482
#214458272
#214456852
#214456462
#214456442
C61×#18792
#2276461