Finite Group Databasebeta

← #30620063

Subgroups — #30620063

Order 15616.

774 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#21461992C211yesmaximal, characteristic, complemented
2#21461991C211yesmaximal, characteristic, complemented
3#21461895C211yesmaximal, characteristic, complemented
4#21461895C211yesmaximal, characteristic, complemented
5#21461893C211yesmaximal, characteristic, complemented
6#21461892C211yesmaximal, characteristic, complemented
7#21461794C211yesmaximal, characteristic
8#21461793C211yesmaximal, characteristic
9#21461764C211yesmaximal, characteristic, complemented
10#21461763C211yesmaximal, characteristic, complemented
11#21461747C211yesmaximal, characteristic, complemented
12#21461604C211yesmaximal, characteristic, complemented
13#21461557C211yesmaximal, characteristic, complemented
14#21461556C211yesmaximal, characteristic, complemented
15#21448360C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×#14519834C2211yescharacteristic
23C2×#14519834C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×#14519832C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×#14519832C2211yescharacteristic
31C2×#14519832C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519763C411yescharacteristic
45C2×#14519742C2211yescharacteristic
46C2×#14519737C2211yescharacteristic
47#16839666C411yescharacteristic
48#16839662C411yescharacteristic
49#16839656C411yescharacteristic
50#16839653C411yescharacteristic
51#16839652C411yescharacteristic
52#16839626C411yescharacteristic
53C22⋊C4×Dic61C2211yescharacteristic
54C22⋊C4×Dic61C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839609C2211yescharacteristic
57C42×Dic61C2211yescharacteristic
58C61×#388C411yescharacteristic
59C2×D61⋊C8—22no—
60C2×D61⋊C8—41no—
61C2×D61⋊C8—41no—
62C22×#92420—22no—
63C22×#92420—41no—
64C22×#92420—41no—
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73#14519844—22no—
74#14519844—22no—
75#14519844—41no—
76C4⋊#92420—41no—
77#14519834—22no—
78#14519834—41no—
79#14519834—41no—
80C22⋊#92420—22no—
81C22⋊#92420—41no—
82C22⋊#92420—41no—
83#14519832—41no—
84#14519832—41no—
85#14519832—41no—
86#14519832—41no—
87C22×Dic122C2×C411yescharacteristic
88C22×C22⋊D61C2×C411yescharacteristic
89C23×Dic61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91#14519763—24no—
92#14519742—41no—
93#14519742—41no—
94#14519737—41no—
95#14519737—41no—
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×#11758198C2×C411yescharacteristic
102C2×#11758198C2×C411yescharacteristic
103C2×#11758198C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117#14519684C2×C411yescharacteristic
118#14519684C2×C411yescharacteristic
119#14519684C2×C411yescharacteristic
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C42×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127C24×C61C22×C411yescharacteristic
128C23×D61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C2×C22⋊D61—41no—
136C2×C22⋊D61—41no—
137C2×C22⋊D61M1614yes—
138C22×Dic61—21no—
139C22×Dic61—21no—
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×Dic61C2411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×Dic122—22no—
158C2×Dic122—41no—
159C2×Dic122—41no—
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×#92420—21no—
175C2×#92420—21no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—21no—
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—44no—
183C2×#92420#4112yes—
184C2×#92420#4112yes—
185D61⋊C8—44no—
186C4⋊C4×C61—41no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C42×C61—41no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196#11758198—41no—
197#11758198—41no—
198#11758196—41no—
199#11758196—41no—
200#11758196—41no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—41no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61C2×M1612yes—
221C23×C61C23×C411yescharacteristic
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61C2×M1612yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
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—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C22⋊D61—44no—
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×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61C2×M1612yes—
269C2×Dic61#13112yes—
270C2×Dic61C2×#4111yescharacteristic
271C2×Dic61C2×#4111yescharacteristic
272C2×Dic61H(5,𝔽2)11yescharacteristic
273C2×Dic61H(5,𝔽2)11yescharacteristic
274C2×Dic61H(5,𝔽2)11yescharacteristic
275C2×Dic612−1+411yescharacteristic
276C4×D61—41no—
277C4×D61—41no—
278C4×D61—41no—
279C4×D61—41no—
280Dic122—44no—
281#92420—22no—
282#92420—22no—
283#92420—41no—
284#92420—41no—
285#92420—41no—
286#92420—41no—
287#92420—41no—
288#92420—41no—
289#22395—611nomaximal, Sylow
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61C4×#4111yescharacteristic
298C22×C61#51811yescharacteristic
299C22×C61#52011yescharacteristic
300C22×C61C22×M1611yescharacteristic
301C22×C61C2×#13111yescharacteristic
302C22×C61#56811yescharacteristic
303C22×C61#56811yescharacteristic
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61—41no—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317Dic61—22no—
318Dic61—22no—
319Dic61—41no—
320Dic61—41no—
321Dic61—41no—
322Dic61—41no—
323Dic61#53811yescharacteristic
324Dic61#53811yescharacteristic
325Dic61#54211yescharacteristic
326Dic61#54211yescharacteristic
327C4×#124—611no—
328#1985—611no—
329#1985—611no—
330#1924—611no—
331#1924—611no—
332#1924—611no—
333#1924—611no—
334#1869—611no—
335#1869—611no—
336#1850—611no—
337#1850—611no—
338#1839—611no—
339#1767—611no—
340#1752—611no—
341#1752—611no—
342C2×C61—42no—
343C2×C61#233711yescharacteristic
344C2×C61#296811yescharacteristic
345C2×C61#297011yescharacteristic
346C2×C61#297311yescharacteristic
347C2×C61#298111yescharacteristic
348C2×C61#299011yescharacteristic
349C2×C61#299511yescharacteristic
350D61—42no—
351C23×C8—611no—
352C23×C8—611no—
353C2×#124—611no—
354C2×C4×Q8—611no—
355C2×C4×D4—611no—
356C2×C4⋊C8—611no—
357C2×C4⋊C8—611no—
358C2×C4⋊C8—611no—
359C2×C4⋊C8—611no—
360C2×C22⋊C8—611no—
361C2×C22⋊C8—611no—
362C2×C22⋊C8—611no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8—611no—
365C2×C22⋊C8—611no—
366C2×#97—611no—
367C2×#97—611no—
368C2×#97—611no—
369C2×#97—611no—
370#391—611no—
371#390—611no—
372#388—611no—
373#388—611no—
374#388—611no—
375#388#692311yescharacteristic
376#382—611no—
377C4×C22⋊C4—611no—
378C4×C22⋊C4—611no—
379C4×C22⋊C4—611no—
380C4×C22⋊C4—611no—
381C43—611no—
382#336—611no—
383#336—611no—
384#336—611no—
385#336—611no—
386#336—611no—
387#336—611no—
388#336—611no—
389#336—611no—
390#336—611no—
391#336—611no—
392#336—611no—
393#336—611no—
394C61#2239511yescharacteristic, complemented, Sylow
395C22×Q8—611no—
396C22×D4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407C22×C8—1222no—
408C22×C8—1222no—
409C22×C8—2441no—
410C22×C8—2441no—
411C22×C8—2441no—
412C22×C8—2441no—
413#124—1224no—
414C4×Q8—2441no—
415C4×Q8—2441no—
416C4×D4—2441no—
417C4×D4—2441no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4C2×#692311yescharacteristic
422C2×C22⋊C4—611no—
423C2×C22⋊C4—611no—
424C2×C22⋊C4—611no—
425C2×C22⋊C4—611no—
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4C2×#692311yescharacteristic
430C2×C22⋊C4C2×#692311yescharacteristic
431C2×C22⋊C4C2×#692311yescharacteristic
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42C2×#692311yescharacteristic
441C4⋊C8—1222no—
442C4⋊C8—1222no—
443C4⋊C8—2441no—
444C4⋊C8—2441no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447C22⋊C8—2441no—
448C22⋊C8—2441no—
449C22⋊C8—2441no—
450C22⋊C8—2441no—
451#97—2441no—
452#97—2441no—
453#97—2441no—
454#97—2441no—
455#95—611no—
456#95—611no—
457#95—611no—
458#95—611no—
459#95—611no—
460#95—611no—
461#95C2×#692311yescharacteristic
462#95C2×#692311yescharacteristic
463C24—611no—
464C24C22×#692311yescharacteristic
465C2×Q8—1222no—
466C2×Q8—2441no—
467C2×Q8—2441no—
468C2×D4—614no—
469C2×D4—2441no—
470C2×D4—2441no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4C22×#692311yescharacteristic
491C22×C4C22×#692311yescharacteristic
492C22×C4C22×#692311yescharacteristic
493C22×C4C22×#692311yescharacteristic
494C22×C4C22×#692311yescharacteristic
495C22×C4C22×#692311yescharacteristic
496C2×C8—612no—
497C2×C8—612no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—2444no—
521C2×C8—2444no—
522C4⋊C4—41no—
523C4⋊C4—2441no—
524C4⋊C4—2441no—
525C4⋊C4—2441no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—2441no—
535C22⋊C4—2441no—
536C42—41no—
537C42—1221no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42—1222no—
546C42—1221no—
547C42—1221no—
548C42—1222no—
549C42—2441no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—612no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23D61⋊M1612yes—
564C23C23×#692311yescharacteristic
565Q8—2444no—
566D4—2444no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—611no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—611no—
591C2×C4—612no—
592C2×C4—612no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—1221no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C8—1222no—
618C8—1222no—
619C8—2441no—
620C8—2441no—
621C8—2441no—
622C8—2441no—
623C8—2441no—
624C8—2441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—1222no—
633C22—1222no—
634C22—1222no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22#41×#692311yescharacteristic
640C22#1684082911yescharacteristic
641C22#1684083111yescharacteristic
642C22C2×D61⋊M1611yescharacteristic
643C22D61⋊#13111yescharacteristic
644C22#1684084011yescharacteristic
645C22#1684084111yescharacteristic
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—611no—
653C4—611no—
654C4—611no—
655C4—611no—
656C4—1222no—
657C4—1222no—
658C4—2441no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C2—42no—
663C2—2442no—
664C2#2146232011yescharacteristic
665C2#2146264911yescharacteristic
666C2#2146265911yescharacteristic
667C2#2146267111yescharacteristic
668C2#2146270711yescharacteristic
669C2#2146274811yescharacteristic
670C2#2146277311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61#22395
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #21461992C2semidirect
2. #21461991C2semidirect
3. #21461895C2semidirect
4. #21461895C2semidirect
5. #21461893C2semidirect
6. #21461892C2semidirect
9. #21461764C2semidirect
10. #21461763C2semidirect
11. #21461747C2semidirect
12. #21461604C2semidirect
13. #21461557C2semidirect
14. #21461556C2semidirect
394. C61#22395semidirect

Maximal subgroups

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

subgroupindex
#214619922
#214619912
#214618952
#214618932
#214618922
#214617942
#214617932
#214617642
#214617632
#214617472
#214616042
#214615572
#214615562
#214483602
#2239561