Finite Group Databasebeta

← #29571555

Subgroups — #29571555

Order 15616.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446248C211yesmaximal, characteristic, complemented
2#21446243C211yesmaximal, characteristic, complemented
3#21446112C211yesmaximal, characteristic, complemented
4#21445807C211yesmaximal, characteristic, complemented
5#21444391C211yesmaximal, characteristic, complemented
6#21444387C211yesmaximal, characteristic, complemented
7C61×#3505C211yesmaximal, characteristic
8C23×#92418C2211yescharacteristic
9C2×#14519701—21no—
10C2×#14519698—21no—
11C2×#14519692—21no—
12C2×C22⋊#92418—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839622C2211yescharacteristic
15#16839622C2211yescharacteristic
16#16839529—21no—
17#16839524—21no—
18#16839524—21no—
19#16839517—21no—
20#16839499—22no—
21#16839496—22no—
22C61×#553—22no—
23C61×#553—21no—
24C61×#552—21no—
25C61×#551—22no—
26C61×#548—21no—
27C61×#546—21no—
28C61×#539C412yescomplemented
29C61×#538C412yescomplemented
30C61×#534—21no—
31C61×#529—21no—
32C61×#525—21no—
33C2×C22⋊Q8×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C61×#518—21no—
36C2×C4×D4×C61C2211yescharacteristic
37C22×#92418—21no—
38C22×#92418—21no—
39C22×#92418—21no—
40C22×#92418—21no—
41C22×#92418—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46#14519701—42no—
47#14519698—42no—
48#14519692—42no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418—42no—
52#14519684—21no—
53#14519684—21no—
54C2×#41×C61—21no—
55C22×Q8×C61D411yescharacteristic
56C22×D4×C61—21no—
57C22×D4×C61D411yescharacteristic
58C22×D4×C61D411yescharacteristic
59C23×C4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61#126×C61—22no—
62#126×C61—22no—
63#126×C61—22no—
64#125×C61—21no—
65#125×C61—22no—
66#124×C61—21no—
67#124×C61—22no—
68#123×C61—22no—
69#123×C61—22no—
70#123×C61—22no—
71#123×C61—22no—
72#123×C61—22no—
73C22⋊Q8×C61—21no—
74C22⋊Q8×C61—22no—
75C22⋊Q8×C61—21no—
76C22⋊Q8×C61—21no—
77C22⋊Q8×C61C2×C412yes—
78C22⋊Q8×C61D412yes—
79#121×C61—22no—
80#121×C61—22no—
81#121×C61—21no—
82#121×C61—22no—
83#121×C61—21no—
84#121×C61—21no—
85#121×C61C2×C412yes—
86#121×C61D412yes—
87#120×C61—22no—
88#120×C61—22no—
89C4×Q8×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61—22no—
92C4×D4×C61—22no—
93C4×D4×C61—22no—
94C4×D4×C61—22no—
95C4×D4×C61—22no—
96C4×D4×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99C4×D4×C61—21no—
100#117×C61—22no—
101#117×C61—22no—
102#117×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61C2×C411yescharacteristic
105C2×C4⋊C4×C61D411yescharacteristic
106C2×C4⋊C4×C61D411yescharacteristic
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61C2×C411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61D411yescharacteristic
113C24×C61—21no—
114C24×C61C22⋊C411yescharacteristic
115C24×C61C2×D411yescharacteristic
116#41×C61—81no—
117#41×C61—81no—
118C2×Q8×C61—21no—
119C2×Q8×C61—41no—
120C2×Q8×C61—41no—
121C2×Q8×C61C22⋊C412yes—
122C2×D4×C61—22no—
123C2×D4×C61—21no—
124C2×D4×C61—21no—
125C2×D4×C61—22no—
126C2×D4×C61—21no—
127C2×D4×C61—21no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—22no—
131C2×D4×C61—22no—
132C2×D4×C61—21no—
133C2×D4×C61—41no—
134C2×D4×C61—41no—
135C2×D4×C61—41no—
136C2×D4×C61—41no—
137C2×D4×C61—41no—
138C2×D4×C61—41no—
139C2×D4×C61C22⋊C412yes—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61—41no—
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×C61C2×D411yescharacteristic
160C22×Dic61—41no—
161C22×Dic61—41no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C22⋊C412yes—
173C4⋊C4×C61C22⋊C412yes—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—21no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—22no—
188C42×C61—22no—
189C42×C61—22no—
190C42×C61—21no—
191C42×C61—21no—
192C22⋊Dic61—41no—
193C22⋊Dic61—41no—
194C22⋊Dic61—41no—
195C22⋊Dic61—41no—
196C4⋊Dic61—41no—
197C4⋊Dic61—41no—
198C4⋊Dic61—41no—
199C4⋊Dic61—41no—
200C2×#92418—22no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—41no—
204C2×#92418—41no—
205C2×#92418—41no—
206C2×#92418—41no—
207C2×#92418—41no—
208C2×#92418—41no—
209C2×#92418—41no—
210C23×C61—21no—
211C23×C61—22no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—41no—
215C23×C61—41no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—81no—
221C23×C61—81no—
222C23×C61C2×C22⋊C411yescharacteristic
223C23×C61#12011yescharacteristic
224C23×C61#12011yescharacteristic
225C23×C61#13511yescharacteristic
226C23×C61#13511yescharacteristic
227C23×C61AGL(1,ℤ/8)11yescharacteristic
228C23×C61#13711yescharacteristic
229Q8×C61—42no—
230Q8×C61—41no—
231Q8×C61—41no—
232D4×C61—42no—
233D4×C61—42no—
234D4×C61—42no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—42no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—42no—
241D4×C61—41no—
242D4×C61—41no—
243D4×C61—82no—
244D4×C61—82no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—22no—
254C2×C4×C61—21no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
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—81no—
269C2×C4×C61—81no—
270C2×C4×C61—81no—
271C2×C4×C61—82no—
272C2×C4×C61—82no—
273C2×C4×C61C2×C22⋊C411yescharacteristic
274C2×C4×C61C2×C22⋊C411yescharacteristic
275C2×C4×C61#12011yescharacteristic
276C2×C4×C61#12011yescharacteristic
277C2×Dic61—81no—
278C2×Dic61—81no—
279C2×Dic61—81no—
280C2×Dic61—81no—
281C2×Dic61—81no—
282C2×Dic61—81no—
283#92418—42no—
284#92418—81no—
285#8352—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—21no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—42no—
301C22×C61—41no—
302C22×C61—42no—
303C22×C61—81no—
304C22×C61—161no—
305C22×C61—161no—
306C22×C61#37911yescharacteristic
307C22×C61#41611yescharacteristic
308C22×C61#41711yescharacteristic
309C22×C61#44911yescharacteristic
310C22×C61#44911yescharacteristic
311C22×C61#45211yescharacteristic
312C22×C61#45211yescharacteristic
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—41no—
317C4×C61—42no—
318C4×C61—41no—
319C4×C61—42no—
320C4×C61—41no—
321C4×C61—42no—
322C4×C61B(4,𝔽2)11yescharacteristic
323C4×C61#45811yescharacteristic
324Dic61—161no—
325Dic61—161no—
326#3505D6111yescharacteristic
327#1893—611no—
328#1892—611no—
329#1869—611no—
330#1799—611no—
331#1520—611no—
332#1519—611no—
333C2×C61—21no—
334C2×C61—21no—
335C2×C61—21no—
336C2×C61—21no—
337C2×C61—21no—
338C2×C61—21no—
339C2×C61—81no—
340C2×C61—82no—
341C2×C61#178811yescharacteristic
342C2×C61#179011yescharacteristic
343C2×C61#179411yescharacteristic
344C23×C8—611no—
345#553—22no—
346#553—21no—
347#552—21no—
348#551—22no—
349#548—21no—
350#546—21no—
351#539Dic6112yescomplemented
352#538Dic6112yescomplemented
353#534—21no—
354#529—21no—
355#525—21no—
356C2×C22⋊Q8C2×D6111yescharacteristic
357C2×#121C2×D6111yescharacteristic
358#518—21no—
359C2×C4×D4C2×D6111yescharacteristic
360C2×#103—1221no—
361C2×#102—1221no—
362C2×#99—1221no—
363C2×C22⋊C8—611no—
364C2×C22⋊C8—1221no—
365#380—611no—
366#380—611no—
367#342—1221no—
368#340—1221no—
369#340—1221no—
370#336—1221no—
371#328—1222no—
372#327—1222no—
373C61#835211yescharacteristic, complemented, Sylow
374C2×#41—21no—
375C22×Q8C22⋊D6111yescharacteristic
376C22×D4—21no—
377C22×D4C22⋊D6111yescharacteristic
378C22×D4C22⋊D6111yescharacteristic
379C23×C4C22⋊D6111yescharacteristic
380C23×C4C22×D6111yescharacteristic
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—2442no—
386#126—22no—
387#126—22no—
388#126—22no—
389#125—21no—
390#125—22no—
391#124—21no—
392#124—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8C2×Dic6112yes—
403C22⋊Q8C22⋊D6112yes—
404#121—21no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—21no—
409#121—21no—
410#121C2×Dic6112yes—
411#121C22⋊D6112yes—
412#120—22no—
413#120—22no—
414C4×Q8—21no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425#117—22no—
426#117—21no—
427#117—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4C2×Dic6111yescharacteristic
432C2×C4⋊C4C22⋊D6111yescharacteristic
433C2×C4⋊C4C22⋊D6111yescharacteristic
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4C2×Dic6111yescharacteristic
440C2×C22⋊C4C22⋊D6111yescharacteristic
441C2×C42C22⋊D6111yescharacteristic
442#103—2442no—
443#102—2442no—
444#99—2442no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C22⋊C8—2442no—
448#95—1221no—
449#95—1221no—
450C24—21no—
451C24C22⋊Dic6111yescharacteristic
452C24C2×C22⋊D6111yescharacteristic
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C22⋊Dic6112yes—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C22⋊Dic6112yes—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—2441no—
489C22×C4—2441no—
490C22×C4C22⋊Dic6111yescharacteristic
491C22×C4C22⋊Dic6111yescharacteristic
492C22×C4C22⋊Dic6111yescharacteristic
493C22×C4C22×Dic6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—2441no—
503C2×C8—2441no—
504C2×C8—2441no—
505C2×C8—2441no—
506C2×C8—2441no—
507C2×C8—2441no—
508C2×C8—2441no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—2441no—
520C4⋊C4—2441no—
521C4⋊C4—2441no—
522C4⋊C4—2441no—
523C4⋊C4C22⋊Dic6112yes—
524C4⋊C4C22⋊Dic6112yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—2441no—
540C22⋊C4—2441no—
541C22⋊C4—2441no—
542C22⋊C4—2441no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—21no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23C2×C22⋊Dic6111yescharacteristic
560C23#1451974611yescharacteristic
561C23#1451974611yescharacteristic
562C23#1451979711yescharacteristic
563C23#1451979711yescharacteristic
564C23#1451980211yescharacteristic
565C23#1451980711yescharacteristic
566Q8—42no—
567Q8—41no—
568Q8—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—41no—
576D4—41no—
577D4—42no—
578D4—41no—
579D4—41no—
580D4—82no—
581D4—82no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—4881no—
611C2×C4—4881no—
612C2×C4—4881no—
613C2×C4—4881no—
614C2×C4—4881no—
615C2×C4—4881no—
616C2×C4C2×C22⋊Dic6111yescharacteristic
617C2×C4C2×C22⋊Dic6111yescharacteristic
618C2×C4#1451974611yescharacteristic
619C2×C4#1451974611yescharacteristic
620C8—4881no—
621C8—2442no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—81no—
640C22—161no—
641C22—161no—
642C22#1683961811yescharacteristic
643C22#1683975811yescharacteristic
644C22#1683976311yescharacteristic
645C22#1683990711yescharacteristic
646C22#1683990711yescharacteristic
647C22#1683992411yescharacteristic
648C22#1683992411yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—9761no—
659C4—9761no—
660C4#1683994911yescharacteristic
661C4#1683995211yescharacteristic
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2#2144575911yescharacteristic
671C2#2144576711yescharacteristic
672C2#2144578311yescharacteristic
subgroupG/H
centerC22#16839618
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#3505C2
socleC22×C61#379
cosocleC23×C4×C61C23
hypercenter#3505D61
hypocenterC61#8352
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. #21446248C2semidirect
2. #21446243C2semidirect
3. #21446112C2semidirect
4. #21445807C2semidirect
5. #21444391C2semidirect
6. #21444387C2semidirect
28. C61×#539C4semidirect
29. C61×#538C4semidirect
351. #539Dic61semidirect
352. #538Dic61semidirect
373. C61#8352semidirect

Maximal subgroups

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

subgroupindex
#214462482
#214462432
#214461122
#214458072
#214443912
#214443872
C61×#35052
#835261