Finite Group Databasebeta

← #30617305

Subgroups — #30617305

Order 15616.

834 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
1C2×#16840813C211yesmaximal, characteristic, complemented
2C2×#16840726C211yesmaximal, characteristic
3#21461988C211yesmaximal, characteristic, complemented
4#21461918C211yesmaximal, characteristic, complemented
5#21461878C211yesmaximal, characteristic, complemented
6#21461877C211yesmaximal, characteristic, complemented
7#21461763C211yesmaximal, characteristic
8#21461762C211yesmaximal, characteristic
9#21461677C211yesmaximal, characteristic
10#21461618C211yesmaximal, characteristic, complemented
11#21461618C211yesmaximal, characteristic, complemented
12#21461611C211yesmaximal, characteristic, complemented
13#21461561C211yesmaximal, characteristic
14#21461561C211yesmaximal, characteristic
15#21449086C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18#16840813—24no—
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27#16840726—24no—
28C2×#14519832C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×#14519832C2211yescharacteristic
32C2×C4×#92420C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×Q8×Dic61C2211yescharacteristic
47C2×#14519733C2211yescharacteristic
48#16839702C411yescharacteristic
49#16839698C411yescharacteristic
50#16839696C411yescharacteristic
51#16839696C411yescharacteristic
52#16839685C411yescharacteristic
53#16839685C411yescharacteristic
54#16839681C411yescharacteristic
55#16839613C2211yescharacteristic
56#16839613C2211yescharacteristic
57#16839613C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60C61×#393C411yescharacteristic
61C2×#11758217—22no—
62C2×#11758217—22no—
63C2×#11758217Q814yescomplemented
64C22×#92420—22no—
65C22×#92420—22no—
66C22×#92420—22no—
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75#14519844—22no—
76#14519844—22no—
77#14519844—22no—
78C4⋊#92420—22no—
79C4⋊#92420—22no—
80C4⋊#92420—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83#14519832—22no—
84#14519832—22no—
85#14519832—22no—
86#14519832D414yes—
87C4×#92420—22no—
88C4×#92420—22no—
89C4×#92420—22no—
90C4×#92420—22no—
91C23×Dic61C2311yescharacteristic
92Q8×Dic61—22no—
93Q8×Dic61—22no—
94#14519733—22no—
95#14519733—22no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×#11758196C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×#11758196C2×C411yescharacteristic
107C2×C22⋊Dic61C2×C411yescharacteristic
108C2×C22⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120#14519684C2×C411yescharacteristic
121#14519684C2×C411yescharacteristic
122#14519684C2×C411yescharacteristic
123C22×Q8×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127#95×C61C2×C411yescharacteristic
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130C24×C61C22×C411yescharacteristic
131C2×Q8×C61—22no—
132C2×Q8×C61—22no—
133C2×Q8×C61—41no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C2×Q812yes—
152C22×Dic61#4112yes—
153C22×Dic61C2411yescharacteristic
154#11758217—28no—
155C2×#92420—28no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420—21no—
174C2×#92420C2×D412yes—
175C2×#92420C2×D412yes—
176C2×#92420C2×Q812yes—
177C2×#92420C2×Q812yes—
178C2×#92420#4112yes—
179C2×#92420#4112yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—41no—
183C22⋊Dic61—22no—
184C22⋊Dic61—22no—
185C22⋊Dic61—41no—
186C4⋊Dic61—22no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189#11758196—22no—
190#11758196—22no—
191#11758196—22no—
192#11758196—22no—
193#11758196—22no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C2×D412yes—
208C4×Dic61#4112yes—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C4×Q812yes—
216C23×C61C23×C411yescharacteristic
217Q8×C61—44no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
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—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61C4×D412yes—
235C2×C4×C61#13112yes—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61C4×D412yes—
259C2×Dic61C4×Q812yes—
260C2×Dic61#13112yes—
261C2×Dic61C22×D411yescharacteristic
262C2×Dic61C22×Q811yescharacteristic
263C2×Dic61C2×#4111yescharacteristic
264C2×Dic61C2×#4111yescharacteristic
265C2×Dic61C2×#4111yescharacteristic
266C2×Dic61C2×#4111yescharacteristic
267#92420—22no—
268#92420—22no—
269#92420—22no—
270#92420—41no—
271#92420—41no—
272#92420—41no—
273#92420—41no—
274#92420C22⋊Q814yes—
275#21606—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61C2×C4×D411yescharacteristic
284C22×C61C2×C4×Q811yescharacteristic
285C22×C61C4×#4111yescharacteristic
286C22×C61C2×#13111yescharacteristic
287C22×C61C2×#13111yescharacteristic
288C22×C61#56811yescharacteristic
289C22×C61#56811yescharacteristic
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296Dic61—22no—
297Dic61—22no—
298Dic61—22no—
299Dic61—41no—
300Dic61—41no—
301Dic61—41no—
302Dic61—41no—
303Dic61C2×C22⋊Q811yescharacteristic
304Dic61#52511yescharacteristic
305Dic61#52911yescharacteristic
306Dic61#53311yescharacteristic
307C2×#446—611no—
308C2×#405—611no—
309#2396—611no—
310#1984—611no—
311#1939—611no—
312#1917—611no—
313#1917—611no—
314#1850—611no—
315#1850—611no—
316#1798—611no—
317#1771—611no—
318#1771—611no—
319C8×C4⋊C4—611no—
320#1753—611no—
321#1753—611no—
322C2×C61—42no—
323C2×C61C4×C22⋊Q811yescharacteristic
324C2×C61#293311yescharacteristic
325C2×C61#293511yescharacteristic
326C2×C61#296211yescharacteristic
327C2×C61#296211yescharacteristic
328C2×C61#296611yescharacteristic
329C2×C61#296711yescharacteristic
330C22×M16—611no—
331C23×C8—611no—
332C2×C4×Q8—611no—
333C2×#117—611no—
334#446—1224no—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C22⋊C8—611no—
342C2×C22⋊C8—611no—
343#405—1224no—
344C2×#97—611no—
345C2×#97—611no—
346C2×#97—611no—
347C2×#97—611no—
348C2×C4×C8—611no—
349C2×C4×C8—611no—
350C2×C4×C8—611no—
351C2×C4×C8—611no—
352#400—611no—
353#399—611no—
354#398—611no—
355#398—611no—
356#396—611no—
357#396—611no—
358#395—611no—
359#393#692311yescharacteristic
360C4×C4⋊C4—611no—
361C4×C4⋊C4—611no—
362C4×C4⋊C4—611no—
363C4×C22⋊C4—611no—
364C4×C22⋊C4—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370#336—611no—
371#336—611no—
372#336—611no—
373#336—611no—
374#336—611no—
375C61#2160611yescharacteristic, complemented, Sylow
376C22×Q8C2×#692311yescharacteristic
377C23×C4—611no—
378C2×M16—614no—
379C2×M16—1222no—
380C2×M16—1222no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—611no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—611no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8—1222no—
390C22×C8—1222no—
391C22×C8—1222no—
392C4×Q8—1222no—
393C4×Q8—1222no—
394#117—1222no—
395#117—1222no—
396C2×C4⋊C4—611no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—611no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—611no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C22⋊C4—611no—
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4C2×#692311yescharacteristic
411C2×C22⋊C4C2×#692311yescharacteristic
412C2×C22⋊C4C2×#692311yescharacteristic
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C4⋊C8—1222no—
420C4⋊C8—1222no—
421C4⋊C8—1222no—
422C4⋊C8—1222no—
423C4⋊C8—1222no—
424C4⋊C8—1222no—
425C22⋊C8—1222no—
426C22⋊C8—1222no—
427#97—614no—
428#97—1222no—
429#97—1222no—
430#97—1222no—
431C4×C8—1222no—
432C4×C8—1222no—
433C4×C8—1222no—
434C4×C8—1222no—
435#95—611no—
436#95—611no—
437#95—611no—
438#95—611no—
439#95—611no—
440#95—611no—
441#95—611no—
442#95C2×#692311yescharacteristic
443#95C2×#692311yescharacteristic
444#95C2×#692311yescharacteristic
445C24C22×#692311yescharacteristic
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—41no—
449C22×C4—611no—
450C22×C4—612no—
451C22×C4—612no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1221no—
462C22×C4—1221no—
463C22×C4C22×#692311yescharacteristic
464C22×C4C22×#692311yescharacteristic
465C22×C4C22×#692311yescharacteristic
466C22×C4C22×#692311yescharacteristic
467C22×C4C22×#692311yescharacteristic
468C22×C4C22×#692311yescharacteristic
469M16—1228no—
470C2×C8—612no—
471C2×C8—612no—
472C2×C8—612no—
473C2×C8—612no—
474C2×C8—612no—
475C2×C8—612no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1228no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—2441no—
504C4⋊C4—2441no—
505C4⋊C4—2441no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—41no—
509C22⋊C4—1222no—
510C22⋊C4—1222no—
511C22⋊C4—2441no—
512C42—612no—
513C42—612no—
514C42—1221no—
515C42—1221no—
516C42—1221no—
517C42—1221no—
518C42—1221no—
519C42—1221no—
520C42—1221no—
521C42—1221no—
522C42—1221no—
523C42—1221no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23Q8×#692312yes—
531C23C23×#692311yescharacteristic
532Q8—44no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—612no—
556C2×C4—612no—
557C2×C4—612no—
558C2×C4—1222no—
559C2×C4—1222no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4D4×#692312yes—
581C2×C4#1451986412yes—
582C8—614no—
583C8—1222no—
584C8—1222no—
585C8—1222no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C2×D4×#692311yescharacteristic
598C22C2×Q8×#692311yescharacteristic
599C22#41×#692311yescharacteristic
600C22C2×#1451986411yescharacteristic
601C22D61⋊#13111yescharacteristic
602C22#1684084011yescharacteristic
603C22#1684084111yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—611no—
611C4—611no—
612C4—611no—
613C4—611no—
614C4—1222no—
615C4—1222no—
616C4—1222no—
617C4—2441no—
618C4—2441no—
619C4—2441no—
620C4—2441no—
621C2—42no—
622C2C22⋊Q8×#692311yescharacteristic
623C2#2146255111yescharacteristic
624C2#2146256411yescharacteristic
625C2#2146261411yescharacteristic
626C2#2146261611yescharacteristic
627C2#2146263311yescharacteristic
628C2#2146263911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#393C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenter#393#6923
hypocenterC61#21606
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#16840813C2semidirect
3. #21461988C2semidirect
4. #21461918C2semidirect
5. #21461878C2semidirect
6. #21461877C2semidirect
10. #21461618C2semidirect
11. #21461618C2semidirect
12. #21461611C2semidirect
63. C2×#11758217Q8semidirect
375. C61#21606semidirect

Maximal subgroups

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

subgroupindex
C2×#168408132
C2×#168407262
#214619882
#214619182
#214618782
#214618772
#214617632
#214617622
#214616772
#214616182
#214616112
#214615612
#214490862
#2160661