Finite Group Databasebeta

← #29779637

Subgroups — #29779637

Order 15616.

842 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451649C211yesmaximal, characteristic, complemented
2#21447227C211yesmaximal, characteristic, complemented
3#21447222C211yesmaximal, characteristic, complemented
4#21446970C211yesmaximal, characteristic, complemented
5#21446965C211yesmaximal, characteristic, complemented
6#21446519C211yesmaximal, characteristic, complemented
7#21446512C211yesmaximal, characteristic, complemented
8#21446505C211yesmaximal, characteristic, complemented
9#21446498C211yesmaximal, characteristic, complemented
10#21445909C211yesmaximal, characteristic, complemented
11#21445905C211yesmaximal, characteristic, complemented
12#21445759C211yesmaximal, characteristic
13#21445759C211yesmaximal, characteristic
14#21445585C211yesmaximal, characteristic, complemented
15C61×#2311C211yesmaximal, characteristic
16C2×#14519769C2211yescharacteristic
17C2×#14519701C2211yescharacteristic
18C2×#14519701C2211yescharacteristic
19C2×#14519701C2211yescharacteristic
20C2×#14519701C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×#14519688C2211yescharacteristic
28C2×C4×#92418C2211yescharacteristic
29#16839695—21no—
30#16839695—21no—
31#16839685—21no—
32#16839685—21no—
33#16839660C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839632C2211yescharacteristic
36#16839622C2211yescharacteristic
37#16839622C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C22×#41×C61C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C22×C4⋊C4×C61C2211yescharacteristic
51C61×#391C2211yescharacteristic
52C61×#391C2211yescharacteristic
53C61×#390C2211yescharacteristic
54C61×#390C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C61×#380—21no—
58C61×#380—21no—
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519769—41no—
64#14519769—41no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×C22⋊Dic61—21no—
76C2×C22⋊Dic61—21no—
77#14519701—22no—
78#14519701—22no—
79#14519701—41no—
80#14519701—41no—
81#14519698—22no—
82#14519698—22no—
83#14519698—41no—
84#14519698—41no—
85C22⋊#92418—22no—
86C22⋊#92418—22no—
87#14519688—41no—
88C4×#92418—41no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93C2×#41×C61—22no—
94C2×#41×C61—22no—
95C2×#41×C61—22no—
96C2×#41×C61—22no—
97C2×#41×C61—41no—
98C2×#41×C61—41no—
99C22×Q8×C61C2311yescharacteristic
100C22×D4×C61—21no—
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61C2311yescharacteristic
105#117×C61—41no—
106#117×C61—41no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—22no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61D411yescharacteristic
119C2×C22⋊C4×C61D411yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61—21no—
127C24×C61C2×D411yescharacteristic
128#41×C61—44no—
129#41×C61—44no—
130#41×C61—44no—
131#41×C61—44no—
132C2×Q8×C61—21no—
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61#4112yes—
138C2×D4×C61—24no—
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—42no—
145C2×D4×C61—42no—
146C2×D4×C61#4112yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—24no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—42no—
156C22×C4×C61—42no—
157C22×C4×C61—42no—
158C22×C4×C61—81no—
159C22×C4×C61—81no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61#4112yes—
166C22×C4×C61#4112yes—
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—42no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—81no—
182C22⋊C4×C61—81no—
183C22⋊C4×C61—81no—
184C22⋊C4×C61—81no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C22⋊Dic61—81no—
190C22⋊Dic61—81no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—81no—
200C4⋊Dic61—81no—
201#11758196—42no—
202#11758196—42no—
203#11758196—81no—
204#11758196—81no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—22no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61#12412yes—
231C23×C61C22×D411yescharacteristic
232Q8×C61—22no—
233Q8×C61—22no—
234Q8×C61—41no—
235Q8×C61—41no—
236D4×C61—22no—
237D4×C61—22no—
238D4×C61—48no—
239D4×C61—41no—
240D4×C61—41no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—48no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—84no—
270C2×C4×C61#12412yes—
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61H(5,𝔽2)11yescharacteristic
276C2×C4×C61H(5,𝔽2)11yescharacteristic
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289#92418—41no—
290#92418—41no—
291#92418—41no—
292#92418—41no—
293#29119—611nomaximal, Sylow
294C22×C61—22no—
295C22×C61—22no—
296C22×C61—22no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61#52511yescharacteristic
309C22×C61C2×#12411yescharacteristic
310C22×C61#53411yescharacteristic
311C22×C61#57611yescharacteristic
312C22×C61#57711yescharacteristic
313C22×C61#57711yescharacteristic
314C22×C61#57811yescharacteristic
315C4×C61—22no—
316C4×C61—42no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—81no—
322C4×C61—81no—
323C4×C61#55111yescharacteristic
324C4×C61#55111yescharacteristic
325C4×C61#55111yescharacteristic
326C4×C61#55111yescharacteristic
327Dic61—81no—
328Dic61—81no—
329Dic61—81no—
330Dic61—81no—
331#2629—611no—
332#2311D6111yescharacteristic
333#2072—611no—
334#2071—611no—
335#2026—611no—
336#2025—611no—
337#1936—611no—
338#1935—611no—
339#1934—611no—
340#1933—611no—
341#1824—611no—
342#1823—611no—
343#1788—611no—
344#1788—611no—
345#1750—611no—
346C2×C61—42no—
347C2×C61—82no—
348C2×C61#256111yescharacteristic
349C2×C61#311911yescharacteristic
350C2×C61#312011yescharacteristic
351C2×C61#313611yescharacteristic
352C2×C61#313711yescharacteristic
353C2×C61#320311yescharacteristic
354C2×C61#320411yescharacteristic
355C22×#41C2×D6111yescharacteristic
356C2×#125—611no—
357C2×#117C2×D6111yescharacteristic
358C22×C4⋊C4C2×D6111yescharacteristic
359C2×#103—611no—
360C2×#103—611no—
361C2×#103—611no—
362C2×#103—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×#102—611no—
367C2×C22⋊C8—611no—
368C2×C22⋊C8—611no—
369C2×#97—611no—
370C2×C4×C8—611no—
371#398—1221no—
372#398—1221no—
373#396—1221no—
374#396—1221no—
375#391C2×D6111yescharacteristic
376#391C2×D6111yescharacteristic
377#390C2×D6111yescharacteristic
378#390C2×D6111yescharacteristic
379#389—611no—
380#389—611no—
381#386—21no—
382#386—21no—
383#384—611no—
384#380—21no—
385#380—21no—
386#380—611no—
387#380—611no—
388#340—611no—
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#340—611no—
396#336—611no—
397#336—611no—
398C61#2911911yescharacteristic, complemented, Sylow
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—22no—
402C2×#41—22no—
403C2×#41—41no—
404C2×#41—41no—
405C22×Q8C22×D6111yescharacteristic
406C22×D4—21no—
407C22×D4C22×D6111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4C22×D6111yescharacteristic
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8—611no—
415#125—2441no—
416#125—2441no—
417#117—41no—
418#117—41no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C22⋊D6111yescharacteristic
433C2×C4⋊C4C22⋊D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C4⋊C4C22×D6111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4C22⋊D6111yescharacteristic
443C2×C22⋊C4C22⋊D6111yescharacteristic
444C2×C42C22×D6111yescharacteristic
445C2×C42C22×D6111yescharacteristic
446#103—1222no—
447#103—1222no—
448#103—2441no—
449#103—2441no—
450#102—1222no—
451#102—1222no—
452#102—2441no—
453#102—2441no—
454C22⋊C8—1222no—
455C22⋊C8—1222no—
456#97—2441no—
457C4×C8—2441no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466C24—21no—
467C24C2×C22⋊D6111yescharacteristic
468#41—44no—
469#41—44no—
470#41—44no—
471#41—44no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8#1175822212yes—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4#1175822212yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4#1175822412yes—
505C22×C4#1175822412yes—
506C22×C4C2×C22⋊D6111yescharacteristic
507C22×C4C2×C22⋊D6111yescharacteristic
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C22×C4C2×C22⋊D6111yescharacteristic
511C22×C4C23×D6111yescharacteristic
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—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—42no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—4881no—
540C4⋊C4—4881no—
541C4⋊C4—4881no—
542C4⋊C4—4881no—
543C4⋊C4—2442no—
544C4⋊C4—2442no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—4881no—
552C22⋊C4—4881no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—22no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23#1451976412yes—
571C23C22×C22⋊D6111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576D4—22no—
577D4—22no—
578D4—48no—
579D4—41no—
580D4—41no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4#1451976412yes—
623C2×C4C2×#1175822411yescharacteristic
624C2×C4C2×#1175822411yescharacteristic
625C2×C4C2×#1175822211yescharacteristic
626C2×C4C2×#1175822211yescharacteristic
627C2×C4#1451982211yescharacteristic
628C2×C4#1451982211yescharacteristic
629C8—2441no—
630C8—2441no—
631C8—2441no—
632C8—2441no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22#1684027311yescharacteristic
648C22C2×#1451976411yescharacteristic
649C22#1684032111yescharacteristic
650C22#1684056511yescharacteristic
651C22#1684057011yescharacteristic
652C22#1684057311yescharacteristic
653C22#1684057711yescharacteristic
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—4881no—
663C4—4881no—
664C4—4881no—
665C4—4881no—
666C4#1684043811yescharacteristic
667C4#1684043811yescharacteristic
668C4#1684043811yescharacteristic
669C4#1684043811yescharacteristic
670C2—42no—
671C2—82no—
672C2#2145097711yescharacteristic
673C2#2145601811yescharacteristic
674C2#2145603311yescharacteristic
675C2#2145617311yescharacteristic
676C2#2145618411yescharacteristic
677C2#2145671611yescharacteristic
678C2#2145672511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2311C2
socleC23×C61C22×D4
prime radicalC22×#41×C61C22
hypercenter#2311D61
hypocenterC61#29119
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2311

Complements

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

NH ≅ G/Ntype
1. #21451649C2semidirect
2. #21447227C2semidirect
3. #21447222C2semidirect
4. #21446970C2semidirect
5. #21446965C2semidirect
6. #21446519C2semidirect
7. #21446512C2semidirect
8. #21446505C2semidirect
9. #21446498C2semidirect
10. #21445909C2semidirect
11. #21445905C2semidirect
14. #21445585C2semidirect
398. C61#29119semidirect

Maximal subgroups

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

subgroupindex
#214516492
#214472272
#214472222
#214469702
#214469652
#214465192
#214465122
#214465052
#214464982
#214459092
#214459052
#214457592
#214455852
C61×#23112
#2911961