Finite Group Databasebeta

← #29779568

Subgroups — #29779568

Order 15616.

862 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
1#21454128C211yesmaximal, characteristic
2#391×D61C211yesmaximal, characteristic
3#21447241C211yesmaximal, characteristic, complemented
4#21447240C211yesmaximal, characteristic, complemented
5#21446969C211yesmaximal, characteristic, complemented
6#21446968C211yesmaximal, characteristic, complemented
7#21446512C211yesmaximal, characteristic, complemented
8#21446509C211yesmaximal, characteristic, complemented
9#21446508C211yesmaximal, characteristic, complemented
10#21445908C211yesmaximal, characteristic
11#21445908C211yesmaximal, characteristic
12#21445752C211yesmaximal, characteristic
13#21445752C211yesmaximal, characteristic
14#21445582C211yesmaximal, characteristic
15C61×#1935C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20C2×#14519702C2211yescharacteristic
21C2×#14519702C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519700C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29#16839669C2211yescharacteristic
30#16839668C2211yescharacteristic
31#16839667C2211yescharacteristic
32#16839666—21no—
33#16839666—21no—
34#16839660C2211yescharacteristic
35#16839648—21no—
36#16839644—21no—
37#16839636—21no—
38#16839633—21no—
39#16839627C2211yescharacteristic
40#16839619C2211yescharacteristic
41#16839619C2211yescharacteristic
42#95×D61—21no—
43#95×D61—21no—
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#103×C61C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122—21no—
60C22×Dic122C2311yescharacteristic
61C2×Q8×D61—22no—
62C2×Q8×D61—22no—
63C2×Q8×D61—22no—
64C2×Q8×D61—22no—
65C2×Q8×D61—41no—
66C2×Q8×D61—41no—
67C22×C4×D61—21no—
68C22×C4×D61—21no—
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519768—41no—
75#14519768—41no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C4⋊C4×D61—22no—
84C4⋊C4×D61—22no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×C4×Dic61D411yescharacteristic
88C2×C4×Dic61D411yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90C42×D61—41no—
91C42×D61—41no—
92#14519702—22no—
93#14519702—41no—
94#14519701—22no—
95#14519701—41no—
96#14519700—22no—
97#14519700—41no—
98#14519689—22no—
99#14519689—22no—
100#14519688—41no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×Q8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#103×C61—22no—
121#103×C61—41no—
122#97×C61—41no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61C2×D411yescharacteristic
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61#4112yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147Q8×D61—44no—
148Q8×D61—44no—
149Q8×D61—44no—
150Q8×D61—44no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—24no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×C4×D61—42no—
163C2×C4×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61—42no—
167C2×C4×D61#4112yes—
168C2×C4×D61#4112yes—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—24no—
174C2×Dic122—21no—
175C2×Dic122—42no—
176C2×Dic122—42no—
177C2×Dic122#4112yes—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—42no—
191C42×C61—21no—
192C42×C61—21no—
193#11758198—42no—
194#11758198—42no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—42no—
202#11758196—42no—
203#11758196—42no—
204#11758196—42no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61—41no—
208C4×Dic61—41no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C23×C61C22×D411yescharacteristic
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61#12412yes—
221C22×D61#13712yes—
222C22×D61#13712yes—
223Q8×C61—22no—
224Q8×C61—22no—
225Q8×C61—41no—
226Q8×C61—41no—
227C2×C4×C61—22no—
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×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
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—41no—
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—22no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
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#12412yes—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—22no—
275C4×D61—22no—
276C4×D61—44no—
277C4×D61—44no—
278C4×D61—48no—
279C4×D61—84no—
280Dic122—22no—
281Dic122—22no—
282Dic122—48no—
283Dic122—41no—
284Dic122—41no—
285C8×C61—41no—
286C8×C61—41no—
287#92418—41no—
288#92418—41no—
289#29112—611nomaximal, Sylow
290C22×C61#52511yescharacteristic
291C22×C61C2×#12411yescharacteristic
292C22×C61#53411yescharacteristic
293C22×C61C2×#13711yescharacteristic
294C22×C61C2×#13711yescharacteristic
295C22×C61#57511yescharacteristic
296C22×C61#57511yescharacteristic
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61#49114yes—
304C4×C61—42no—
305C4×C61—41no—
306C4×C61—41no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61—81no—
310C4×C61#55111yescharacteristic
311C4×C61#55111yescharacteristic
312C4×C61#55111yescharacteristic
313C4×C61#55111yescharacteristic
314Dic61—22no—
315Dic61—42no—
316Dic61—41no—
317Dic61—41no—
318Dic61—81no—
319Dic61—81no—
320Dic61—81no—
321#2851—611no—
322C2×#391—611no—
323#2074—611no—
324#2074—611no—
325#2026—611no—
326#2026—611no—
327#1935—611no—
328#1935—611no—
329#1935—611no—
330#1935D6111yescharacteristic, complemented
331#1824—611no—
332#1824—611no—
333#1787—611no—
334#1787—611no—
335#1749—611no—
336C2×C61#256111yescharacteristic
337C2×C61#311711yescharacteristic
338C2×C61#311711yescharacteristic
339C2×C61C2×#49111yescharacteristic
340C2×C61#314011yescharacteristic
341C2×C61#319611yescharacteristic
342C2×C61#319611yescharacteristic
343D61—24no—
344C23×Q8—611no—
345C2×#125—611no—
346C22×C4⋊C4—611no—
347C22×C42—611no—
348C2×#103—611no—
349C2×#103—611no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#103—611no—
353C2×#103—611no—
354C2×#103C2×D6111yescharacteristic
355C2×#103C2×D6111yescharacteristic
356C2×C22⋊C8—611no—
357C2×C22⋊C8—611no—
358C2×#97—611no—
359C2×#97C2×D6111yescharacteristic
360#391—611no—
361#391—611no—
362#391—611no—
363#391—1221no—
364#391—1221no—
365#391C2×D6111yescharacteristic
366#389—611no—
367#389C2×D6111yescharacteristic
368#387—1221no—
369#387—1221no—
370#385—1221no—
371#385—1221no—
372#382—611no—
373#380—611no—
374#380—611no—
375C2×#95—1221no—
376C2×#95—1221no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340C2×D6111yescharacteristic
384#340C2×D6111yescharacteristic
385#336—611no—
386#336—611no—
387C61#2911211yescharacteristic, complemented, Sylow
388C22×Q8—611no—
389C22×Q8—1221no—
390C22×Q8—1222no—
391C22×Q8—1222no—
392C22×Q8—1222no—
393C22×Q8—1222no—
394C22×Q8—2441no—
395C22×Q8—2441no—
396C22×Q8C22×D6111yescharacteristic
397C23×C4—611no—
398C23×C4—611no—
399C23×C4—611no—
400C23×C4—1221no—
401C23×C4—1221no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406#125—2441no—
407#125—2441no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—1222no—
413C2×C4⋊C4—1222no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C22×D6111yescharacteristic
419C2×C4⋊C4C22×D6111yescharacteristic
420C2×C4⋊C4C22×D6111yescharacteristic
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—2441no—
427C2×C42—2441no—
428C2×C42C22×D6111yescharacteristic
429#103—22no—
430#103—41no—
431#103—1222no—
432#103—1222no—
433#103—1222no—
434#103—2441no—
435#103—2441no—
436#103—2441no—
437C22⋊C8—1222no—
438C22⋊C8—1222no—
439#97—41no—
440#97—2441no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—1221no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453#95—1221no—
454#95—1221no—
455C24—611no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—612no—
462C2×Q8—1224no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×Q8—1221no—
468C2×Q8—2442no—
469C2×Q8—2442no—
470C2×Q8—2444no—
471C2×Q8—2444no—
472C2×Q8—2444no—
473C2×Q8—2444no—
474C2×Q8#1175822212yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—611no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1222no—
485C22×C4—1222no—
486C22×C4—1224no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—2441no—
496C22×C4—2441no—
497C22×C4—2441no—
498C22×C4—2441no—
499C22×C4—2442no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4—2442no—
504C22×C4D4×D6111yescharacteristic
505C22×C4D4×D6111yescharacteristic
506C22×C4C23×D6111yescharacteristic
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—2442no—
533C4⋊C4—2442no—
534C4⋊C4—2442no—
535C4⋊C4—2442no—
536C22⋊C4—2442no—
537C22⋊C4—2442no—
538C42—21no—
539C42—21no—
540C42—1221no—
541C42—1221no—
542C42—2441no—
543C42—2441no—
544C23—612no—
545C23—612no—
546C23—612no—
547C23—1221no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23C2×D4×D6111yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8—1222no—
557Q8—1222no—
558Q8—2448no—
559Q8—2441no—
560Q8—2441no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—612no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—4884no—
594C2×C4—2444no—
595C2×C4—2444no—
596C2×C4—2448no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4#41×D6111yescharacteristic
609C2×C4#41×D6111yescharacteristic
610C2×C4#41×D6111yescharacteristic
611C2×C4C2×#1175822211yescharacteristic
612C2×C4#1451982211yescharacteristic
613C2×C4#1451982311yescharacteristic
614C8—41no—
615C8—41no—
616C8—2441no—
617C8—2441no—
618C22—614no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—1222no—
624C22—1222no—
625C22#1684027111yescharacteristic
626C22#124×D6111yescharacteristic
627C22#1684032011yescharacteristic
628C22#137×D6111yescharacteristic
629C22#137×D6111yescharacteristic
630C22#1684055811yescharacteristic
631C22#1684056111yescharacteristic
632C4—41no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—1222no—
639C4—4881no—
640C4—4881no—
641C4—4881no—
642C4—2441no—
643C4—2441no—
644C4—2442no—
645C4#1684043611yescharacteristic
646C4#1684043711yescharacteristic
647C4#1684044011yescharacteristic
648C4#1684044111yescharacteristic
649C2—1224no—
650C2#2145097511yescharacteristic
651C2#2145598811yescharacteristic
652C2#2145599411yescharacteristic
653C2#491×D6111yescharacteristic
654C2#2145620411yescharacteristic
655C2#2145664411yescharacteristic
656C2#2145665011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1935C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1935D61
hypocenterC61#29112
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
3. #21447241C2semidirect
4. #21447240C2semidirect
5. #21446969C2semidirect
6. #21446968C2semidirect
7. #21446512C2semidirect
8. #21446509C2semidirect
9. #21446508C2semidirect
15. C61×#1935C2semidirect
330. #1935D61semidirect
387. C61#29112semidirect

Maximal subgroups

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

subgroupindex
#214541282
#391×D612
#214472412
#214472402
#214469692
#214469682
#214465122
#214465092
#214465082
#214459082
#214457522
#214455822
C61×#19352
#2911261