Finite Group Databasebeta

← #29646175

Subgroups — #29646175

Order 15616.

1012 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840364C211yesmaximal, characteristic
2#21454846C211yesmaximal, characteristic, complemented
3#21454845C211yesmaximal, characteristic, complemented
4#21444180C211yesmaximal, characteristic, complemented
5#21444178C211yesmaximal, characteristic, complemented
6#21444177C212yesmaximal, complemented
7#21444167C211yesmaximal, characteristic, complemented
8#21444166C212yesmaximal, complemented
9#21444158C212yesmaximal, complemented
10#21444152C212yesmaximal, complemented
11C61×#1468C211yesmaximal, characteristic, complemented
12#16840364—22no—
13#16840364—22no—
14#16840364—22no—
15#16840364—22no—
16C2×#14519773C411yescharacteristic
17C2×#14519767C411yescharacteristic
18C2×#14519762C2211yescharacteristic
19C2×#14519761C411yescharacteristic
20C2×#14519759C411yescharacteristic
21C2×#14519752C411yescharacteristic
22C2×#14519751C2211yescharacteristic
23C2×#14519750C411yescharacteristic
24C2×#14519750C411yescharacteristic
25C2×#14519750C2211yescharacteristic
26C2×#14519749C411yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519737C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839836—22no—
31#16839833—22no—
32#16839831—22no—
33#16839830—22no—
34#16839816C2212yes—
35#16839816C2212yes—
36#16839726C2211yescharacteristic
37#16839724C2212yes—
38C2×C22⋊#92418C2211yescharacteristic
39C22⋊C8×D61C2212yes—
40#16839488C2212yes—
41#16839486C2212yes—
42#16839485C2212yes—
43#16839485C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C2×#123×C61C2211yescharacteristic
47C61×#407C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C61×#324C2212yes—
50C61×#323C2212yes—
51C22×D244C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×D244C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C22⋊D61C2×C411yescharacteristic
58C22×C22⋊D61C2×C411yescharacteristic
59C22×C22⋊D61C2×C411yescharacteristic
60C23×Dic61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758194—21no—
65C2×#11758189—22no—
66C22×#92418—21no—
67C2×C8×D61—22no—
68#14519773—22no—
69#14519773—22no—
70#14519767—22no—
71#14519767—22no—
72#14519762—22no—
73#14519762—22no—
74#14519761—22no—
75#14519761—22no—
76#14519759—22no—
77#14519759—22no—
78#14519752—22no—
79#14519752—22no—
80#14519751—21no—
81#14519751—21no—
82#14519751—21no—
83#14519751—21no—
84#14519750—22no—
85#14519750—22no—
86#14519750—22no—
87#14519750—22no—
88#14519750—22no—
89#14519750—22no—
90#14519749—22no—
91#14519749—22no—
92C4×C22⋊D61D412yes—
93C4×C22⋊D61D412yes—
94C4×C22⋊D61D412yes—
95C4×C22⋊D61D412yes—
96#14519737—22no—
97#14519737—22no—
98#14519735—22no—
99#14519735—22no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×C4⋊Dic61C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×#11758196C2×C411yescharacteristic
104C2×#11758196C2×C411yescharacteristic
105C2×#11758196C2×C411yescharacteristic
106C2×C22⋊Dic61C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2311yescharacteristic
112C2×#11758198C2311yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124#14519687—22no—
125C22×D4×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—21no—
128C22×C8×C61—21no—
129#123×C61—21no—
130#123×C61—21no—
131#123×C61—21no—
132#123×C61—21no—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61—21no—
140C22⋊C8×C61C2312yes—
141C22⋊C8×C61C2312yes—
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—81no—
150C22×C4×C61—81no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C2×C22⋊D61—21no—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—21no—
163C2×C22⋊D61—21no—
164C2×C22⋊D61—22no—
165C2×C22⋊D61—22no—
166C2×C22⋊D61—22no—
167C2×C22⋊D61—42no—
168C2×C22⋊D61—42no—
169C2×C22⋊D61—81no—
170C2×C22⋊D61—81no—
171C2×C22⋊D61—81no—
172C2×C22⋊D61—81no—
173C2×C22⋊D61C22⋊C412yes—
174C2×C22⋊D61C22⋊C412yes—
175C22×Dic61—22no—
176C22×Dic61—81no—
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—81no—
187C2×D244—81no—
188C2×D244—81no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—42no—
192C2×C4×D61—81no—
193C2×C4×D61—81no—
194C2×C4×D61C2×D412yes—
195C2×C4×D61C2×D412yes—
196M16×C61—81no—
197C2×C8×C61—22no—
198C2×C8×C61—22no—
199C2×C8×C61—81no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C22⋊C4×C61—21no—
205C22⋊C4×C61—21no—
206C22⋊C4×C61—21no—
207C22⋊C4×C61—21no—
208C22⋊C4×C61—21no—
209C22⋊C4×C61—21no—
210C22⋊Dic61C22⋊C412yes—
211C22⋊Dic61C22⋊C412yes—
212#11758198—22no—
213#11758198—21no—
214#11758198—21no—
215#11758198—21no—
216#11758198—21no—
217#11758198—22no—
218#11758198—22no—
219#11758198C22⋊C412yes—
220#11758198C22⋊C412yes—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—22no—
224#11758196—22no—
225#11758196—22no—
226#11758196—22no—
227#11758196C22⋊C412yes—
228#11758196C22⋊C412yes—
229C4×Dic61—22no—
230C4×Dic61C2×D412yes—
231C4×Dic61C2×D412yes—
232#11758194—81no—
233C2×#92418—22no—
234C2×#92418—22no—
235C2×#92418—81no—
236#11758189—82no—
237C8×D61—82no—
238C23×C61—22no—
239C23×C61—21no—
240C23×C61—22no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61C2×C22⋊C411yescharacteristic
246C23×C61C2×C22⋊C411yescharacteristic
247C23×C61C23×C411yescharacteristic
248C22×D61—22no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61C2×C22⋊C412yes—
260D4×C61—81no—
261D4×C61—81no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—22no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C2×C22⋊C411yescharacteristic
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C22⋊D61—42no—
279C22⋊D61—42no—
280C22⋊D61—44no—
281C22⋊D61—82no—
282C22⋊D61—82no—
283C22⋊D61—81no—
284C22⋊D61—81no—
285C22⋊D61—81no—
286C22⋊D61—81no—
287C2×Dic61—22no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—82no—
295C2×Dic61C2×C22⋊C412yes—
296C2×Dic61C2×C22⋊C412yes—
297C2×Dic61C2×C22⋊C412yes—
298D244—81no—
299D244—81no—
300D244—82no—
301D244—82no—
302C4×D61—42no—
303C4×D61—42no—
304C4×D61—44no—
305C4×D61—82no—
306C8×C61—42no—
307C8×C61—42no—
308#92418—42no—
309#92418—42no—
310#17408—611nomaximal, Sylow
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—82no—
323C22×C61—82no—
324C22×C61C22×C22⋊C411yescharacteristic
325C22×C61#56812yes—
326C2×D61—22no—
327C2×D61—22no—
328C2×D61—22no—
329C2×D61—41no—
330C2×D61—41no—
331C2×D61—41no—
332C2×D61—41no—
333C2×D61—41no—
334C2×D61—41no—
335C2×D61—82no—
336C2×D61—82no—
337C2×D61—82no—
338C4×C61—21no—
339C4×C61—21no—
340C4×C61—21no—
341C4×C61—21no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61—41no—
345Dic61—22no—
346Dic61—22no—
347Dic61—22no—
348Dic61—41no—
349Dic61—41no—
350C2×#540—611no—
351#2973—611no—
352#2973—611no—
353#1471—611no—
354#1471—611no—
355#1471—612no—
356#1468—612no—
357#1468—611no—
358#1468D6111yescharacteristic, complemented
359#1466—612no—
360#1464—612no—
361C2×C61—22no—
362C2×C61—41no—
363C2×C61—41no—
364C2×C61—81no—
365C2×C61#287911yescharacteristic
366C2×C61#288311yescharacteristic
367C2×C61#288811yescharacteristic
368D61—42no—
369D61—81no—
370D61—81no—
371#540—1222no—
372#540—1222no—
373#540—1222no—
374#540—1222no—
375C2×#127—611no—
376C2×#125—611no—
377C2×#123—611no—
378C2×#123—611no—
379C2×#123—611no—
380C2×#123C2×D6111yescharacteristic
381C2×#121—611no—
382C2×#121—611no—
383C2×#121—611no—
384C2×#121—611no—
385C2×#121—611no—
386C2×#121—611no—
387C2×C4×D4—611no—
388C2×C4×D4—611no—
389C2×#117—611no—
390#435—1222no—
391#435—1222no—
392#435—1222no—
393#435—1222no—
394#432—612no—
395#432—612no—
396#407—611no—
397#407—612no—
398#407C2×D6111yescharacteristic
399C2×C22⋊C8—611no—
400C2×C22⋊C8—612no—
401C2×C22⋊C8C2×D6111yescharacteristic
402#324—612no—
403#324C2×D6112yes—
404#323—612no—
405#323—612no—
406#323—612no—
407#323—612no—
408#323—612no—
409#323C2×D6112yes—
410C61#1740811yescharacteristic, complemented, Sylow
411C22×D4—611no—
412C22×D4—611no—
413C22×D4—611no—
414C22×D4—611no—
415C22×D4—611no—
416C22×D4—611no—
417C22×D4—611no—
418C22×D4—611no—
419C22×D4—611no—
420C22×D4C4×D6111yescharacteristic
421C23×C4—611no—
422C23×C4—611no—
423C23×C4—611no—
424C23×C4—611no—
425C23×C4C22×D6111yescharacteristic
426C2×M16—21no—
427C2×M16—1222no—
428C2×M16—1221no—
429C22×C8—21no—
430C22×C8—1222no—
431C22×C8—1221no—
432#127—1222no—
433#127—1222no—
434#125—1222no—
435#125—1222no—
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—1222no—
441#123—1222no—
442#123—1222no—
443#123—1222no—
444#123—1222no—
445#123—1222no—
446#121—1222no—
447#121—1222no—
448#121—1222no—
449#121—1222no—
450#121—1222no—
451#121—1222no—
452#121—1222no—
453#121—1222no—
454#121—1222no—
455#121—1222no—
456#121—1221no—
457#121—1221no—
458#121—1221no—
459#121—1221no—
460C4×D4—612no—
461C4×D4—612no—
462C4×D4—612no—
463C4×D4—612no—
464C4×D4—1222no—
465C4×D4—1222no—
466#117—1222no—
467#117—1222no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4C4×D6111yescharacteristic
475C2×C4⋊C4C22×D6111yescharacteristic
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4C4×D6111yescharacteristic
484C2×C22⋊C4C4×D6111yescharacteristic
485C2×C22⋊C4C22×D6111yescharacteristic
486C2×C42—611no—
487C2×C42—611no—
488C4⋊C8—1222no—
489C4⋊C8—1222no—
490C22⋊C8—21no—
491C22⋊C8—21no—
492C22⋊C8—612no—
493C22⋊C8—612no—
494C22⋊C8—1222no—
495C22⋊C8—1222no—
496C22⋊C8—1221no—
497C22⋊C8—1221no—
498C22⋊C8C22×D6112yes—
499C22⋊C8C22×D6112yes—
500#97—1222no—
501#97—1222no—
502C24—611no—
503C24—611no—
504C24—611no—
505C24C2×C4×D6111yescharacteristic
506C24C2×C4×D6111yescharacteristic
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—81no—
510C2×D4—612no—
511C2×D4—612no—
512C2×D4—1222no—
513C2×D4—1222no—
514C2×D4—1222no—
515C2×D4—1222no—
516C2×D4—1222no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—1221no—
520C2×D4—1221no—
521C2×D4—1221no—
522C2×D4—1221no—
523C2×D4—4881no—
524C2×D4—4881no—
525C2×D4—4881no—
526C2×D4—4881no—
527C2×D4—4881no—
528C2×D4—4881no—
529C2×D4—4881no—
530C2×D4—2442no—
531C2×D4—2442no—
532C22×C4—81no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—4881no—
544C22×C4—4881no—
545C22×C4—4881no—
546C22×C4—2442no—
547C22×C4C2×C4×D6111yescharacteristic
548C22×C4C2×C4×D6111yescharacteristic
549C22×C4C2×C4×D6111yescharacteristic
550C22×C4C2×C4×D6111yescharacteristic
551C22×C4D4×D6111yescharacteristic
552C22×C4D4×D6111yescharacteristic
553C22×C4D4×D6111yescharacteristic
554C22×C4D4×D6111yescharacteristic
555C22×C4C23×D6111yescharacteristic
556M16—81no—
557M16—4882no—
558M16—4881no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—81no—
562C2×C8—1222no—
563C2×C8—1222no—
564C2×C8—4882no—
565C2×C8—4881no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—612no—
571C4⋊C4—612no—
572C4⋊C4—1222no—
573C4⋊C4—1222no—
574C4⋊C4—1222no—
575C4⋊C4—1222no—
576C4⋊C4—1221no—
577C4⋊C4—1221no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—612no—
585C22⋊C4—612no—
586C22⋊C4—612no—
587C22⋊C4—612no—
588C22⋊C4—1222no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4—1221no—
592C22⋊C4—1221no—
593C22⋊C4—1221no—
594C22⋊C4—1221no—
595C42—612no—
596C42—612no—
597C42—1222no—
598C23—22no—
599C23—21no—
600C23—22no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—612no—
606C23—1222no—
607C23—1222no—
608C23—1222no—
609C23—1221no—
610C23—1221no—
611C23—2441no—
612C23—2441no—
613C23—2441no—
614C23—2441no—
615C23—2441no—
616C23—2441no—
617C23C22⋊C4×D6111yescharacteristic
618C23C22⋊C4×D6111yescharacteristic
619C23C22×C4×D6111yescharacteristic
620D4—81no—
621D4—81no—
622D4—4881no—
623D4—4881no—
624D4—4882no—
625D4—4882no—
626D4—4882no—
627D4—4881no—
628D4—4881no—
629D4—4881no—
630D4—4881no—
631D4—4882no—
632D4—2442no—
633D4—2442no—
634D4—2444no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—612no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—1222no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—4882no—
654C2×C4—4882no—
655C2×C4—2442no—
656C2×C4—2442no—
657C2×C4—2444no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4C22⋊C4×D6111yescharacteristic
663C2×C4C22⋊C4×D6111yescharacteristic
664C2×C4C2×D4×D6111yescharacteristic
665C2×C4C2×D4×D6111yescharacteristic
666C8—42no—
667C8—42no—
668C8—2442no—
669C8—2442no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—82no—
682C22—82no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—4882no—
687C22—4882no—
688C22—4882no—
689C22—2441no—
690C22—2441no—
691C22—2441no—
692C22—2441no—
693C22—2441no—
694C22—2441no—
695C22C2×C22⋊C4×D6111yescharacteristic
696C22#1684052712yes—
697C4—21no—
698C4—21no—
699C4—21no—
700C4—21no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—1222no—
705C4—1222no—
706C4—1222no—
707C4—2441no—
708C4—2441no—
709C2—22no—
710C2—41no—
711C2—41no—
712C2—81no—
713C2—4881no—
714C2—4881no—
715C2—2442no—
716C2#2145426111yescharacteristic
717C2#2145427711yescharacteristic
718C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840364C2
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454846C2semidirect
3. #21454845C2semidirect
4. #21444180C2semidirect
5. #21444178C2semidirect
6. #21444177C2semidirect
7. #21444167C2semidirect
8. #21444166C2semidirect
9. #21444158C2semidirect
10. #21444152C2semidirect
11. C61×#1468C2semidirect
358. #1468D61semidirect
410. C61#17408semidirect

Maximal subgroups

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

subgroupindex
C2×#168403642
#214548462
#214548452
#214441802
#214441782
#214441772
#214441672
#214441662
#214441582
#214441522
C61×#14682
#1740861