Finite Group Databasebeta

← #29658470

Subgroups — #29658470

Order 15616.

818 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457161C211yesmaximal, characteristic, complemented
2#21456994C211yesmaximal, characteristic
3#21456560C211yesmaximal, characteristic, complemented
4#21445096C211yesmaximal, characteristic, complemented
5#21445089C211yesmaximal, characteristic, complemented
6#21445040C211yesmaximal, characteristic, complemented
7#21445033C211yesmaximal, characteristic, complemented
8#21444991C211yesmaximal, characteristic, complemented
9#21444977C211yesmaximal, characteristic, complemented
10#21444959C211yesmaximal, characteristic, complemented
11#21444953C211yesmaximal, characteristic, complemented
12#21444476C211yesmaximal, characteristic, complemented
13#21444240C211yesmaximal, characteristic, complemented
14#21444232C211yesmaximal, characteristic
15C61×#3555C211yesmaximal, characteristic
16#16840319C2211yescharacteristic
17#16840161—21no—
18#16840158C2211yescharacteristic
19#16840141C2211yescharacteristic
20#16840116—21no—
21#16840114C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840100—21no—
24#16840083—21no—
25#16840057C2211yescharacteristic
26#16840057C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840054—21no—
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840042C2211yescharacteristic
32#16840018—22no—
33#16840001—21no—
34#16840001—21no—
35#16839972C2211yescharacteristic
36#16839972C2211yescharacteristic
37#16839969—21no—
38#16839867—22no—
39#16839815C2211yescharacteristic
40C2×C4⋊#92418C2211yescharacteristic
41C4×#11758194C2211yescharacteristic
42#16839511C2211yescharacteristic
43#16839511C2211yescharacteristic
44#16839508C2211yescharacteristic
45#16839508C2211yescharacteristic
46Q8⋊#92418C2211yescharacteristic
47Q8⋊#92418C2211yescharacteristic
48Q8⋊#92418C2211yescharacteristic
49Q8⋊#92418C2211yescharacteristic
50Q8⋊#92418C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54C61×#563—22no—
55Q82×C61C2211yescharacteristic
56C61×#557—21no—
57C61×#557C2211yescharacteristic
58C61×#556—21no—
59C61×#556—21no—
60C61×#556C2211yescharacteristic
61C61×#554C2211yescharacteristic
62C61×#552—21no—
63C61×#544—21no—
64C61×#542—21no—
65C61×#541—21no—
66C61×#541—21no—
67C61×#541—22no—
68C61×#533C2211yescharacteristic
69C61×#533C2211yescharacteristic
70C61×#529C2211yescharacteristic
71C2×#11758202—22no—
72C2×#11758202—21no—
73C2×#11758202—21no—
74C2×#11758194—21no—
75C22×#92418—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519769—21no—
79#14519756—21no—
80#14519756—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83#14519736—21no—
84#14519710—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519708—22no—
89#14519708—21no—
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519701—21no—
97#14519701—21no—
98#14519701—22no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—22no—
104#14519698—21no—
105#14519698—21no—
106C22⋊#92418—21no—
107#14519688—21no—
108C4×#92418—21no—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C4⋊Q8×C61—22no—
112C4⋊Q8×C61—21no—
113C4⋊Q8×C61—22no—
114C4⋊Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61D411yescharacteristic
117C4⋊Q8×C61D411yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#126×C61—22no—
121#126×C61—22no—
122#126×C61—22no—
123#126×C61—22no—
124#126×C61—22no—
125#126×C61—22no—
126#126×C61—21no—
127#125×C61—22no—
128#125×C61—22no—
129#125×C61—22no—
130#125×C61—22no—
131#125×C61—21no—
132#125×C61—22no—
133#125×C61—21no—
134#125×C61—21no—
135#125×C61—21no—
136#125×C61D411yescharacteristic
137#124×C61—22no—
138#124×C61—21no—
139#124×C61D411yescharacteristic
140#123×C61—22no—
141#123×C61—21no—
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—22no—
144C22⋊Q8×C61—21no—
145C22⋊Q8×C61—21no—
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61—21no—
148C22⋊Q8×C61—21no—
149C22⋊Q8×C61D411yescharacteristic
150C22⋊Q8×C61D411yescharacteristic
151C22⋊Q8×C61D412yes—
152C22⋊Q8×C61D411yescharacteristic
153#121×C61D411yescharacteristic
154C4×Q8×C61—22no—
155C4×Q8×C61—21no—
156C4×Q8×C61—21no—
157C4×Q8×C61—21no—
158C4×Q8×C61—21no—
159C4×Q8×C61—21no—
160C4×Q8×C61—21no—
161C4×Q8×C61—21no—
162C4×Q8×C61D412yes—
163C4×Q8×C61C2311yescharacteristic
164C4×Q8×C61C2311yescharacteristic
165C4×Q8×C61C2311yescharacteristic
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61C2311yescharacteristic
169#117×C61—22no—
170#117×C61—21no—
171#117×C61—21no—
172#117×C61—21no—
173#117×C61—21no—
174C2×C4⋊C4×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C2×Q8×C61—22no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C2×D411yescharacteristic
180C2×Q8×C61C2×D411yescharacteristic
181C2×Q8×C61C2×D411yescharacteristic
182C2×Q8×C61C2×D412yes—
183C2×D4×C61—21no—
184C2×D4×C61C2×D411yescharacteristic
185C22×C4×C61—22no—
186C22×C4×C61—21no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C2×Dic122—21no—
191C2×Dic122—21no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C4⋊C4×C61—22no—
197C4⋊C4×C61—22no—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—22no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61C2×D411yescharacteristic
217C4⋊C4×C61C2×D411yescharacteristic
218C4⋊C4×C61C2×D411yescharacteristic
219C4⋊C4×C61C2×D411yescharacteristic
220C4⋊C4×C61C2×D412yes—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—21no—
225C22⋊C4×C61—22no—
226C22⋊C4×C61—21no—
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C42×C61—22no—
233C42×C61—22no—
234C42×C61—22no—
235C42×C61—22no—
236C42×C61—21no—
237C42×C61—21no—
238C42×C61—21no—
239C42×C61C2×D411yescharacteristic
240C42×C61C2×D411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2411yescharacteristic
243C22⋊Dic61—41no—
244#11758202—44no—
245#11758202—81no—
246#11758202—81no—
247C4⋊Dic61—21no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—21no—
251#11758196—41no—
252#11758196—41no—
253C4×Dic61—41no—
254#11758194—42no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—81no—
262C23×C61—21no—
263C23×C61#12011yescharacteristic
264Q8×C61—21no—
265Q8×C61—21no—
266Q8×C61—21no—
267Q8×C61—21no—
268Q8×C61—21no—
269Q8×C61—21no—
270Q8×C61—42no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—81no—
274Q8×C61—82no—
275D4×C61—21no—
276D4×C61—21no—
277D4×C61—81no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—21no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—82no—
295C2×C4×C61#12011yescharacteristic
296C2×C4×C61#12011yescharacteristic
297C2×C4×C61#12011yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×Dic61—41no—
302C2×Dic61—41no—
303Dic122—42no—
304Dic122—41no—
305Dic122—41no—
306#92418—22no—
307#92418—41no—
308#92418—41no—
309#92418—41no—
310#92418—41no—
311#92418—41no—
312#18745—611nomaximal, Sylow
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61C2×#12011yescharacteristic
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—41no—
325C4×C61—42no—
326C4×C61—41no—
327C4×C61—41no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—42no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61#57711yescharacteristic
334C4×C61#57811yescharacteristic
335C4×C61#57811yescharacteristic
336C4×C61#57811yescharacteristic
337Dic61—81no—
338Dic61—81no—
339#3555D6111yescharacteristic
340#3249—611no—
341#3233—611no—
342#3185—611no—
343#1653—611no—
344#1652—611no—
345#1645—611no—
346#1644—611no—
347#1638—611no—
348#1636—611no—
349#1633—611no—
350#1632—611no—
351#1542—611no—
352#1485—611no—
353#1483—611no—
354C2×C61—41no—
355C2×C61—81no—
356C2×C61#301111yescharacteristic
357C2×C61#301311yescharacteristic
358C2×C61#301811yescharacteristic
359#563—22no—
360Q82C2×D6111yescharacteristic
361#557—21no—
362#557C2×D6111yescharacteristic
363#556—21no—
364#556—21no—
365#556C2×D6111yescharacteristic
366#554C2×D6111yescharacteristic
367#552—21no—
368#544—21no—
369#542—21no—
370#541—21no—
371#541—21no—
372#541—22no—
373#533—611no—
374#533C2×D6111yescharacteristic
375#533C2×D6111yescharacteristic
376#529C2×D6111yescharacteristic
377#499—1221no—
378#498—611no—
379#494—611no—
380#488—1221no—
381#487—611no—
382#487—611no—
383#485—1221no—
384#482—1221no—
385#477—611no—
386#477—611no—
387#477—611no—
388#477—1221no—
389#476—611no—
390#475—611no—
391#474—611no—
392#470—1222no—
393#467—1221no—
394#467—1221no—
395#462—611no—
396#462—611no—
397#462—1221no—
398#441—1222no—
399#431—611no—
400C2×C4⋊C8—611no—
401C4×M16—611no—
402#333—611no—
403#333—611no—
404#332—611no—
405#332—611no—
406Q8⋊C8—611no—
407Q8⋊C8—611no—
408Q8⋊C8—611no—
409Q8⋊C8—611no—
410Q8⋊C8—611no—
411Q8⋊C8—611no—
412D4⋊C8—611no—
413D4⋊C8—611no—
414C61#1874511yescharacteristic, complemented, Sylow
415C2×Q16—1221no—
416C2×Q16—1221no—
417C2×Q16—1222no—
418C2×M16—1221no—
419C22×C8—1221no—
420C4⋊Q8—22no—
421C4⋊Q8—21no—
422C4⋊Q8—22no—
423C4⋊Q8—21no—
424C4⋊Q8—21no—
425C4⋊Q8—611no—
426C4⋊Q8—611no—
427C4⋊Q8C22⋊D6111yescharacteristic
428C4⋊Q8C22⋊D6111yescharacteristic
429C4⋊Q8C22×D6111yescharacteristic
430C4⋊Q8C22×D6111yescharacteristic
431#126—22no—
432#126—22no—
433#126—22no—
434#126—22no—
435#126—22no—
436#126—22no—
437#126—21no—
438#125—22no—
439#125—22no—
440#125—22no—
441#125—22no—
442#125—21no—
443#125—22no—
444#125—21no—
445#125—21no—
446#125—21no—
447#125—1221no—
448#125C22⋊D6111yescharacteristic
449#124—22no—
450#124—21no—
451#124C22⋊D6111yescharacteristic
452#123—22no—
453#123—21no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—1221no—
462C22⋊Q8—1221no—
463C22⋊Q8C22⋊D6111yescharacteristic
464C22⋊Q8C22⋊D6111yescharacteristic
465C22⋊Q8C22⋊D6111yescharacteristic
466C22⋊Q8C22⋊D6112yes—
467#121C22⋊D6111yescharacteristic
468C4×Q8—22no—
469C4×Q8—21no—
470C4×Q8—21no—
471C4×Q8—21no—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—1221no—
477C4×Q8—1221no—
478C4×Q8C22⋊D6112yes—
479C4×Q8C22×D6111yescharacteristic
480C4×Q8C22×D6111yescharacteristic
481C4×Q8C22×D6111yescharacteristic
482C4×D4—21no—
483C4×D4—21no—
484C4×D4C22×D6111yescharacteristic
485#117—22no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—1221no—
491C2×C4⋊C4—21no—
492C2×C42C22×D6111yescharacteristic
493#107—1221no—
494#107—1221no—
495#107—1221no—
496#107—1221no—
497#106—1222no—
498#106—1221no—
499#106—1221no—
500C4⋊C8—611no—
501C4⋊C8—611no—
502C4⋊C8—611no—
503C4⋊C8—611no—
504C4⋊C8—1221no—
505#103—1222no—
506#103—1221no—
507#103—1221no—
508#103—1221no—
509#103—1221no—
510#103—1222no—
511#103—1221no—
512#103—1221no—
513#102—1221no—
514#102—1221no—
515C22⋊C8—1221no—
516#97—1221no—
517C4×C8—611no—
518C4×C8—611no—
519C4×C8—1221no—
520C2×Q8—22no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8C2×C22⋊D6111yescharacteristic
526C2×Q8C2×C22⋊D6111yescharacteristic
527C2×Q8C2×C22⋊D6111yescharacteristic
528C2×Q8C2×C22⋊D6112yes—
529C2×D4—21no—
530C2×D4C2×C22⋊D6111yescharacteristic
531C22×C4—22no—
532C22×C4—21no—
533C22×C4C2×C22⋊D6111yescharacteristic
534C22×C4C2×C22⋊D6111yescharacteristic
535C22×C4C2×C22⋊D6111yescharacteristic
536Q16—4881no—
537Q16—4881no—
538Q16—2444no—
539M16—2442no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—4881no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—22no—
571C4⋊C4—1221no—
572C4⋊C4—1221no—
573C4⋊C4—1221no—
574C4⋊C4—1221no—
575C4⋊C4—2441no—
576C4⋊C4—2441no—
577C4⋊C4C2×C22⋊D6112yes—
578C4⋊C4C2×C22⋊D6111yescharacteristic
579C4⋊C4C2×C22⋊D6111yescharacteristic
580C4⋊C4C2×C22⋊D6111yescharacteristic
581C4⋊C4C2×C22⋊D6111yescharacteristic
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—21no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—21no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—2441no—
594C42—22no—
595C42—22no—
596C42—22no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—22no—
601C42—2441no—
602C42C2×C22⋊D6111yescharacteristic
603C42C2×C22⋊D6111yescharacteristic
604C42C2×C22⋊D6111yescharacteristic
605C42C23×D6111yescharacteristic
606C23—21no—
607C23#1451974611yescharacteristic
608Q8—21no—
609Q8—21no—
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—42no—
615Q8—41no—
616Q8—41no—
617Q8—81no—
618Q8—82no—
619Q8—2442no—
620Q8—2441no—
621Q8—2441no—
622D4—21no—
623D4—21no—
624D4—81no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—82no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4#1451974611yescharacteristic
645C2×C4#1451974611yescharacteristic
646C2×C4#1451974611yescharacteristic
647C2×C4C22×C22⋊D6111yescharacteristic
648C2×C4C22×C22⋊D6111yescharacteristic
649C2×C4C22×C22⋊D6111yescharacteristic
650C8—1222no—
651C8—2441no—
652C8—2441no—
653C8—2441no—
654C8—2441no—
655C8—2441no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22C2×#1451974611yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—41no—
668C4—42no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—4881no—
677C4—4881no—
678C4#1684057011yescharacteristic
679C4#1684057711yescharacteristic
680C4#1684057711yescharacteristic
681C4#1684057711yescharacteristic
682C2—41no—
683C2—81no—
684C2#2145511411yescharacteristic
685C2#2145513411yescharacteristic
686C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3555C2
socleC22×C61C2×#120
prime radical#121×C61D4
hypercenter#3555D61
hypocenterC61#18745
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3555

Complements

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

NH ≅ G/Ntype
1. #21457161C2semidirect
3. #21456560C2semidirect
4. #21445096C2semidirect
5. #21445089C2semidirect
6. #21445040C2semidirect
7. #21445033C2semidirect
8. #21444991C2semidirect
9. #21444977C2semidirect
10. #21444959C2semidirect
11. #21444953C2semidirect
12. #21444476C2semidirect
13. #21444240C2semidirect
414. C61#18745semidirect

Maximal subgroups

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

subgroupindex
#214571612
#214569942
#214565602
#214450962
#214450892
#214450402
#214450332
#214449912
#214449772
#214449592
#214449532
#214444762
#214442402
#214442322
C61×#35552
#1874561