Finite Group Databasebeta

← D61×#3228 #30552065

Subgroups — D61×#3228 #30552065

Order 15616.

2058 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2#532×D61C211yesmaximal, characteristic
3#21456958C211yesmaximal, characteristic, complemented
4#21456957C211yesmaximal, characteristic, complemented
5#21456956C211yesmaximal, characteristic, complemented
6#21456955C211yesmaximal, characteristic, complemented
7#21456954C214yesmaximal, complemented
8#21456953C214yesmaximal, complemented
9#21456952C211yesmaximal, characteristic, complemented
10#21456951C211yesmaximal, characteristic, complemented
11#21456950C211yesmaximal, characteristic, complemented
12#500×D61C211yesmaximal, characteristic, complemented
13#498×D61C211yesmaximal, characteristic, complemented
14#486×D61C211yesmaximal, characteristic, complemented
15#486×D61C211yesmaximal, characteristic, complemented
16#482×D61C214yesmaximal, complemented
17#478×D61C214yesmaximal, complemented
18#431×D61C211yesmaximal, characteristic, complemented
19C61×#3228C211yesmaximal, characteristic, complemented
20C2×#41×D61—21no—
21#16840319C2211yescharacteristic, complemented
22#16840318C2212yescomplemented
23#16840317C2211yescharacteristic, complemented
24#16840317C2211yescharacteristic, complemented
25#16840316—21no—
26#16840316—21no—
27#16840315C2212yescomplemented
28#16840314—21no—
29#16840314—21no—
30#16840313C2211yescharacteristic
31#16840312C2211yescharacteristic
32#16840311—21no—
33#16840310C2211yescharacteristic
34#16840309—21no—
35#16840309C2212yes—
36#16840308—21no—
37#16840307—21no—
38#16840307C2212yes—
39C4⋊Q8×D61C2211yescharacteristic
40C4⋊Q8×D61C2211yescharacteristic
41C4⋊Q8×D61C2211yescharacteristic
42#127×D61C2211yescharacteristic
43#125×D61C2212yes—
44#124×D61—21no—
45C22⋊Q8×D61—21no—
46C22⋊Q8×D61—21no—
47#121×D61—21no—
48#121×D61C2212yes—
49C4×Q8×D61—21no—
50C4×Q8×D61—21no—
51C4×D4×D61—21no—
52C4×D4×D61C2212yes—
53#117×D61C2212yes—
54C2×C42×D61C2211yescharacteristic
55#16840167C2211yescharacteristic, complemented
56#16840166C2214yescomplemented
57#16840165C2211yescharacteristic, complemented
58#16840165C2211yescharacteristic, complemented
59#16840160C2211yescharacteristic, complemented
60#16840159C2214yescomplemented
61#16840158C2211yescharacteristic, complemented
62#16840158C2211yescharacteristic, complemented
63#16840110C2211yescharacteristic, complemented
64#16840110C2211yescharacteristic, complemented
65#16840109C2211yescharacteristic, complemented
66#16840109C2211yescharacteristic, complemented
67#16840108C2211yescharacteristic, complemented
68#16840108C2211yescharacteristic, complemented
69#16840107C2214yescomplemented
70#16840107C2214yescomplemented
71#16840089C2214yescomplemented
72#16840088C2214yescomplemented
73#16840087C2214yescomplemented
74#16840086C2214yescomplemented
75#16840085C2214yescomplemented
76#16840084C2214yescomplemented
77#16840083C2214yescomplemented
78#16840065C2214yescomplemented
79#16840064C2214yescomplemented
80#16840063C2214yescomplemented
81#16840062C2214yescomplemented
82#16840061C2214yescomplemented
83#16840060C2214yescomplemented
84#16840059C2214yescomplemented
85#16839815C2211yescharacteristic, complemented
86#16839814C2212yescomplemented
87#16839813C2211yescharacteristic, complemented
88#16839813C2211yescharacteristic, complemented
89#16839812C2212yescomplemented
90#107×D61C2214yes—
91#106×D61C2214yes—
92C4⋊C8×D61C2212yes—
93#102×D61C2214yes—
94#102×D61C2214yes—
95C22⋊C8×D61C2212yes—
96C4×C8×D61C2211yescharacteristic
97C4×C8×D61C2211yescharacteristic
98C61×#533C2211yescharacteristic, complemented
99C61×#532C2211yescharacteristic
100C61×#500C2211yescharacteristic, complemented
101C61×#498C2211yescharacteristic, complemented
102C61×#486C2211yescharacteristic, complemented
103C61×#486C2211yescharacteristic, complemented
104C61×#482C2214yescomplemented
105C61×#478C2214yescomplemented
106C61×#431C2211yescharacteristic, complemented
107C2×#11758226—21no—
108C2×#11758222—21no—
109C2×#11758222—22no—
110C2×#11758224—22no—
111C2×#11758224—21no—
112#41×D61—48no—
113C2×Q8×D61—21no—
114C2×Q8×D61—21no—
115C2×Q8×D61—21no—
116C2×D4×D61—22no—
117C2×D4×D61—21no—
118C2×D4×D61—21no—
119C2×D4×D61C2312yes—
120C22×C4×D61—22no—
121C22×C4×D61D411yescharacteristic
122C22×C4×D61D411yescharacteristic
123C22×C4×D61C2311yescharacteristic
124C2×C8×D61C2312yes—
125C2×C8×D61C2312yes—
126#14519777C2311yescharacteristic
127#14519777C2311yescharacteristic
128#14519777C2311yescharacteristic
129#14519776—21no—
130#14519776—21no—
131#14519776—21no—
132#14519776C2312yes—
133#14519776C2312yes—
134#14519776C2312yes—
135#14519775—21no—
136#14519775—21no—
137#14519775—21no—
138#14519774C2311yescharacteristic
139#14519773—21no—
140#14519773—21no—
141#14519773C2312yes—
142#14519769C2312yes—
143#14519768C2312yes—
144#14519768C2312yes—
145#14519767—22no—
146#14519767—22no—
147#14519766—21no—
148#14519765—21no—
149#14519764—21no—
150#14519763—22no—
151#14519763—22no—
152#14519757—21no—
153#14519757—21no—
154#14519756—21no—
155#14519756—21no—
156#14519755—22no—
157#14519755—22no—
158#14519754—22no—
159#14519754—22no—
160#14519753—21no—
161#14519753—21no—
162#14519752—21no—
163#14519752C2312yes—
164#14519751—21no—
165#14519751C2312yes—
166#14519750—22no—
167#14519750—22no—
168#14519749—22no—
169#14519749—22no—
170#14519748—21no—
171#14519748C2312yes—
172Q8×Dic61—21no—
173Q8×Dic61—21no—
174C4×Dic122—21no—
175C4×Dic122—21no—
176C4×Dic122—22no—
177C4×Dic122—22no—
178#14519742—21no—
179#14519742—21no—
180#14519742—22no—
181#14519742—22no—
182C4×D244—21no—
183C4×D244C2312yes—
184D4×Dic61—21no—
185D4×Dic61C2312yes—
186#14519739—21no—
187#14519739C2312yes—
188C4×C22⋊D61—22no—
189C4×C22⋊D61—22no—
190#14519737—22no—
191#14519737—22no—
192#14519736C2312yes—
193#14519735C2312yes—
194#14519735C2312yes—
195#14519734—22no—
196#14519733—22no—
197C4⋊C4×D61—21no—
198C4⋊C4×D61—22no—
199C4⋊C4×D61—22no—
200C4⋊C4×D61—21no—
201C4⋊C4×D61—21no—
202C4⋊C4×D61C2312yes—
203C4⋊C4×D61C2312yes—
204C4⋊C4×D61C2312yes—
205C22⋊C4×D61—22no—
206C22⋊C4×D61—22no—
207C22⋊C4×D61—22no—
208C2×C4×Dic61D411yescharacteristic
209C2×C4×Dic61D411yescharacteristic
210C2×C4×Dic61C2311yescharacteristic
211C42×D61—22no—
212C42×D61D411yescharacteristic
213C42×D61D411yescharacteristic
214C42×D61D411yescharacteristic
215C42×D61D411yescharacteristic
216C42×D61C2311yescharacteristic
217C42×D61C2311yescharacteristic
218C42×D61C2311yescharacteristic
219C42×D61C2311yescharacteristic
220#14519711C2314yes—
221#14519710C2314yes—
222#14519710C2314yes—
223#14519709C2314yes—
224#14519708C2314yes—
225#14519708C2314yes—
226C4⋊#92418C2312yes—
227#14519706C2312yes—
228#14519706C2312yes—
229#14519699C2314yes—
230#14519699C2314yes—
231#14519698C2314yes—
232#14519698C2314yes—
233#14519697C2314yes—
234#14519697C2314yes—
235C22⋊#92418C2312yes—
236#14519689C2312yes—
237#14519689C2312yes—
238C4×#92418C2311yescharacteristic
239C4×#92418C2311yescharacteristic
240C8×Dic61C2312yes—
241C8×Dic61C2312yes—
242C2×#41×C61—21no—
243C4⋊Q8×C61C2311yescharacteristic
244C4⋊Q8×C61C2311yescharacteristic
245C4⋊Q8×C61C2311yescharacteristic
246#127×C61C2311yescharacteristic
247#125×C61C2312yes—
248#124×C61—21no—
249C22⋊Q8×C61—21no—
250C22⋊Q8×C61—21no—
251#121×C61—21no—
252#121×C61C2312yes—
253C4×Q8×C61—21no—
254C4×Q8×C61—21no—
255C4×D4×C61—21no—
256C4×D4×C61C2312yes—
257#117×C61C2312yes—
258C2×C42×C61C2311yescharacteristic
259#107×C61C2314yes—
260#106×C61C2314yes—
261C4⋊C8×C61C2312yes—
262#102×C61C2314yes—
263#102×C61C2314yes—
264C22⋊C8×C61C2312yes—
265C4×C8×C61C2311yescharacteristic
266C4×C8×C61C2311yescharacteristic
267C23×D61—22no—
268C23×D61C2×D411yescharacteristic
269#41×C61—44no—
270C2×Q8×C61—21no—
271C2×Q8×C61—21no—
272C2×Q8×C61—21no—
273C2×D4×C61—22no—
274C2×D4×C61—21no—
275C2×D4×C61—21no—
276C2×D4×C61C2412yes—
277C22×C4×C61—22no—
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2411yescharacteristic
281C2×C22⋊D61—22no—
282C2×C22⋊D61—22no—
283C2×C22⋊D61—22no—
284C2×C22⋊D61—22no—
285C2×C22⋊D61—22no—
286C22×Dic61—22no—
287C22×Dic61C2×D411yescharacteristic
288C22×Dic61C2×D411yescharacteristic
289C22×Dic61C2×D411yescharacteristic
290#11758226—44no—
291Q8×D61—44no—
292Q8×D61—44no—
293Q8×D61—44no—
294#11758224—44no—
295#11758224—48no—
296D4×D61—28no—
297D4×D61—48no—
298D4×D61—44no—
299D4×D61—44no—
300#11758222—48no—
301#11758222—44no—
302C2×D244—22no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244C2412yes—
306C2×C4×D61—24no—
307C2×C4×D61—24no—
308C2×C4×D61—24no—
309C2×C4×D61—22no—
310C2×C4×D61—22no—
311C2×C4×D61—22no—
312C2×C4×D61—22no—
313C2×C4×D61—22no—
314C2×C4×D61—48no—
315C2×C4×D61C2×D411yescharacteristic
316C2×C4×D61C2×D411yescharacteristic
317C2×C4×D61C2×D411yescharacteristic
318C2×C4×D61C2×D411yescharacteristic
319C2×C4×D61C2×D411yescharacteristic
320C2×C4×D61C2×D411yescharacteristic
321C2×C4×D61C2×D411yescharacteristic
322C2×C4×D61C2×D411yescharacteristic
323C2×C4×D61C2×D411yescharacteristic
324C2×C4×D61C2×D411yescharacteristic
325C2×C4×D61C2411yescharacteristic
326C2×C4×D61C2411yescharacteristic
327C2×Dic122—21no—
328C2×Dic122—21no—
329C2×Dic122—21no—
330C2×Dic122—22no—
331C2×Dic122—22no—
332C2×Dic122—22no—
333C2×C8×C61C2412yes—
334C2×C8×C61C2412yes—
335C4⋊C4×C61—21no—
336C4⋊C4×C61—22no—
337C4⋊C4×C61—22no—
338C4⋊C4×C61—21no—
339C4⋊C4×C61—21no—
340C4⋊C4×C61C2412yes—
341C4⋊C4×C61C2412yes—
342C4⋊C4×C61C2412yes—
343C22⋊C4×C61—22no—
344C22⋊C4×C61—22no—
345C22⋊C4×C61—22no—
346C42×C61—22no—
347C42×C61C2×D411yescharacteristic
348C42×C61C2×D411yescharacteristic
349C42×C61C2411yescharacteristic
350C42×C61C2411yescharacteristic
351C22⋊Dic61—22no—
352C22⋊Dic61—22no—
353C22⋊Dic61—22no—
354#11758198—22no—
355#11758198—22no—
356#11758198—22no—
357#11758198—22no—
358#11758198—22no—
359#11758198—22no—
360C4⋊Dic61—21no—
361C4⋊Dic61—21no—
362C4⋊Dic61—21no—
363C4⋊Dic61—22no—
364C4⋊Dic61—22no—
365C4⋊Dic61C2412yes—
366C4⋊Dic61C2412yes—
367C4⋊Dic61C2412yes—
368#11758196—22no—
369#11758196—22no—
370#11758196—22no—
371#11758196—22no—
372#11758196—22no—
373#11758196—22no—
374#11758196—22no—
375#11758196—22no—
376#11758196—22no—
377#11758196—22no—
378C4×Dic61—22no—
379C4×Dic61—22no—
380C4×Dic61—22no—
381C4×Dic61C2×D411yescharacteristic
382C4×Dic61C2×D411yescharacteristic
383C4×Dic61C2×D411yescharacteristic
384C4×Dic61C2×D411yescharacteristic
385C4×Dic61C2×D411yescharacteristic
386C4×Dic61C2×D411yescharacteristic
387C4×Dic61C2×D411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C4×Dic61C2×D411yescharacteristic
391C4×Dic61C2411yescharacteristic
392C4×Dic61C2411yescharacteristic
393C2×#92418C2412yes—
394C2×#92418C2412yes—
395C8×D61—24no—
396C8×D61—24no—
397C23×C61—22no—
398C23×C61C22×D411yescharacteristic
399C22×D61—22no—
400C22×D61—22no—
401C22×D61—22no—
402C22×D61—22no—
403C22×D61—44no—
404C22×D61—44no—
405C22×D61—44no—
406C22×D61C22×D411yescharacteristic
407C22×D61C22×D411yescharacteristic
408Q8×C61—42no—
409Q8×C61—42no—
410Q8×C61—42no—
411D4×C61—24no—
412D4×C61—44no—
413D4×C61—42no—
414D4×C61—42no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—44no—
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C22×D411yescharacteristic
424C2×C4×C61C22×D411yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C2511yescharacteristic
428C22⋊D61—44no—
429C22⋊D61—44no—
430C22⋊D61—44no—
431C22⋊D61—44no—
432C22⋊D61—44no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—22no—
438C2×Dic61—22no—
439C2×Dic61—44no—
440C2×Dic61C22×D411yescharacteristic
441C2×Dic61C22×D411yescharacteristic
442C2×Dic61C22×D411yescharacteristic
443C2×Dic61C22×D411yescharacteristic
444C2×Dic61C22×D411yescharacteristic
445C2×Dic61C22×D411yescharacteristic
446D244—24no—
447D244—44no—
448D244—42no—
449D244—42no—
450C4×D61—22no—
451C4×D61—22no—
452C4×D61—22no—
453C4×D61—22no—
454C4×D61—22no—
455C4×D61—22no—
456C4×D61—22no—
457C4×D61—22no—
458C4×D61—22no—
459C4×D61—44no—
460C4×D61—44no—
461C4×D61—44no—
462C4×D61—44no—
463C4×D61—44no—
464C4×D61#13514yes—
465C4×D61AGL(1,ℤ/8)14yes—
466C4×D612−1+414yes—
467Dic122—42no—
468Dic122—42no—
469Dic122—42no—
470Dic122—44no—
471Dic122—44no—
472Dic122—44no—
473C8×C61—22no—
474C8×C61—22no—
475#92418—22no—
476#92418—22no—
477C2×#3228—611nomaximal, Sylow
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—42no—
484C22×C61C23×D411yescharacteristic
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—44no—
489C2×D61—42no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—88no—
493C2×D61#53612yes—
494C2×D61C2×#13512yes—
495C2×D61C2×AGL(1,ℤ/8)12yes—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—42no—
502C4×C61C2×#13512yes—
503C4×C61C2×AGL(1,ℤ/8)12yes—
504C4×C61C2×2−1+412yes—
505Dic61—21no—
506Dic61—21no—
507Dic61—21no—
508Dic61—42no—
509Dic61—42no—
510Dic61—42no—
511Dic61#53612yes—
512Dic61C2×#13512yes—
513Dic61C2×AGL(1,ℤ/8)12yes—
514C2×#533—611no—
515C2×#532—611no—
516#3228—611no—
517#3228—611no—
518#3228—611no—
519#3228—611no—
520#3228—614no—
521#3228—614no—
522#3228—611no—
523#3228—611no—
524#3228—611no—
525#3228D6111yescharacteristic, direct product factor
526C2×#500—611no—
527C2×#498—611no—
528C2×#486—611no—
529C2×#486—611no—
530C2×#482—614no—
531C2×#478—614no—
532C2×#431—611no—
533C2×C61—41no—
534C2×C61—82no—
535C2×C61C2×#53611yescharacteristic
536C2×C61C22×#13511yescharacteristic
537C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
538D61—41no—
539D61—82no—
540D61#322814yesdirect product factor
541C22×#41—1221no—
542#533—611no—
543#533—611no—
544#533—612no—
545#533—612no—
546#533—611no—
547#533—1221no—
548#533—1221no—
549#533—1221no—
550#533—1221no—
551#533C2×D6111yescharacteristic, complemented
552#532—611no—
553#532—611no—
554#532—612no—
555#532—612no—
556#532—611no—
557#532—1221no—
558#532—1221no—
559#532—1221no—
560#532—1221no—
561#532C2×D6111yescharacteristic
562C2×C4⋊Q8—611no—
563C2×C4⋊Q8—611no—
564C2×C4⋊Q8—611no—
565C2×#127—611no—
566C2×#125—612no—
567C2×#124—1221no—
568C2×C22⋊Q8—1221no—
569C2×C22⋊Q8—1221no—
570C2×#121—612no—
571C2×#121—1221no—
572C2×C4×Q8—1221no—
573C2×C4×Q8—1221no—
574C2×C4×D4—612no—
575C2×C4×D4—1221no—
576C2×#117—612no—
577C22×C42—611no—
578#500—611no—
579#500—611no—
580#500—614no—
581#500—611no—
582#500C2×D6111yescharacteristic, complemented
583#498—611no—
584#498—611no—
585#498—614no—
586#498—611no—
587#498C2×D6111yescharacteristic, complemented
588#486—611no—
589#486—611no—
590#486—611no—
591#486—611no—
592#486—614no—
593#486—614no—
594#486—611no—
595#486—611no—
596#486C2×D6111yescharacteristic, complemented
597#486C2×D6111yescharacteristic, complemented
598#482—614no—
599#482—614no—
600#482—614no—
601#482—614no—
602#482—614no—
603#482—614no—
604#482—614no—
605#482C2×D6114yescomplemented
606#478—614no—
607#478—614no—
608#478—614no—
609#478—614no—
610#478—614no—
611#478—614no—
612#478—614no—
613#478C2×D6114yescomplemented
614#431—611no—
615#431—612no—
616#431—612no—
617#431—611no—
618#431—611no—
619#431C2×D6111yescharacteristic, complemented
620C2×#107—614no—
621C2×#106—614no—
622C2×C4⋊C8—612no—
623C2×#102—614no—
624C2×#102—614no—
625C2×C22⋊C8—612no—
626C2×C4×C8—611no—
627C2×C4×C8—611no—
628C61C2×#322811yescharacteristic, complemented, Sylow
629C2×#41—21no—
630C2×#41—1222no—
631C2×#41—1222no—
632C2×#41—1221no—
633C2×#41—1221no—
634C2×#41—1221no—
635C2×#41—2448no—
636C22×Q8—1221no—
637C22×Q8—1221no—
638C22×Q8—1221no—
639C22×D4—612no—
640C22×D4—1221no—
641C22×D4—1221no—
642C22×D4—1222no—
643C23×C4—611no—
644C23×C4—611no—
645C23×C4—611no—
646C23×C4—1222no—
647C22×C8—612no—
648C22×C8—612no—
649C4⋊Q8—612no—
650C4⋊Q8—612no—
651C4⋊Q8—612no—
652C4⋊Q8—611no—
653C4⋊Q8—611no—
654C4⋊Q8—611no—
655C4⋊Q8—1221no—
656C4⋊Q8—1221no—
657C4⋊Q8—1221no—
658C4⋊Q8—1221no—
659C4⋊Q8—1221no—
660C4⋊Q8—1221no—
661C4⋊Q8C22×D6111yescharacteristic
662C4⋊Q8C22×D6111yescharacteristic
663C4⋊Q8C22×D6111yescharacteristic
664#127—612no—
665#127—611no—
666#127—1221no—
667#127—1221no—
668#127C22×D6111yescharacteristic
669#125—612no—
670#125—612no—
671#125—612no—
672#125—1222no—
673#125—1222no—
674#125C22×D6112yes—
675#124—21no—
676#124—1222no—
677#124—1222no—
678#124—1221no—
679#124—1221no—
680#124—1221no—
681C22⋊Q8—21no—
682C22⋊Q8—21no—
683C22⋊Q8—1222no—
684C22⋊Q8—1222no—
685C22⋊Q8—1222no—
686C22⋊Q8—1222no—
687C22⋊Q8—1221no—
688C22⋊Q8—1221no—
689C22⋊Q8—1221no—
690C22⋊Q8—1221no—
691C22⋊Q8—1221no—
692C22⋊Q8—1221no—
693#121—21no—
694#121—612no—
695#121—612no—
696#121—612no—
697#121—1222no—
698#121—1222no—
699#121—1221no—
700#121—1222no—
701#121—1221no—
702#121—1222no—
703#121—1221no—
704#121C22×D6112yes—
705C4×Q8—21no—
706C4×Q8—21no—
707C4×Q8—1222no—
708C4×Q8—1222no—
709C4×Q8—1222no—
710C4×Q8—1221no—
711C4×Q8—1222no—
712C4×Q8—1221no—
713C4×Q8—1221no—
714C4×Q8—1221no—
715C4×Q8—1221no—
716C4×Q8—1221no—
717C4×D4—21no—
718C4×D4—612no—
719C4×D4—612no—
720C4×D4—612no—
721C4×D4—1222no—
722C4×D4—1222no—
723C4×D4—1221no—
724C4×D4—1222no—
725C4×D4—1222no—
726C4×D4—1221no—
727C4×D4—1221no—
728C4×D4C22×D6112yes—
729#117—612no—
730#117—612no—
731#117—612no—
732#117—1222no—
733#117—1222no—
734#117C22×D6112yes—
735C2×C4⋊C4—612no—
736C2×C4⋊C4—612no—
737C2×C4⋊C4—612no—
738C2×C4⋊C4—1221no—
739C2×C4⋊C4—1222no—
740C2×C4⋊C4—1222no—
741C2×C4⋊C4—1221no—
742C2×C4⋊C4—1221no—
743C2×C22⋊C4—1222no—
744C2×C22⋊C4—1222no—
745C2×C22⋊C4—1222no—
746C2×C42—611no—
747C2×C42—611no—
748C2×C42—611no—
749C2×C42—611no—
750C2×C42—611no—
751C2×C42—611no—
752C2×C42—611no—
753C2×C42—611no—
754C2×C42—611no—
755C2×C42—611no—
756C2×C42—611no—
757C2×C42—1222no—
758C2×C42C22×D6111yescharacteristic
759#107—614no—
760#107—614no—
761#107—614no—
762#107C22×D6114yes—
763#106—614no—
764#106—614no—
765#106—614no—
766#106C22×D6114yes—
767C4⋊C8—612no—
768C4⋊C8—612no—
769C4⋊C8—612no—
770C4⋊C8C22×D6112yes—
771#102—614no—
772#102—614no—
773#102—614no—
774#102—614no—
775#102—614no—
776#102—614no—
777#102C22×D6114yes—
778#102C22×D6114yes—
779C22⋊C8—612no—
780C22⋊C8—612no—
781C22⋊C8—612no—
782C22⋊C8C22×D6112yes—
783C4×C8—612no—
784C4×C8—612no—
785C4×C8—611no—
786C4×C8—611no—
787C4×C8C22×D6111yescharacteristic
788C4×C8C22×D6111yescharacteristic
789C24—611no—
790C24—1222no—
791#41—44no—
792#41—2444no—
793#41—2448no—
794#41—2448no—
795#41—2444no—
796#41—2444no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—1222no—
801C2×Q8—1222no—
802C2×Q8—1222no—
803C2×Q8—1221no—
804C2×Q8—1221no—
805C2×Q8—1221no—
806C2×Q8—2444no—
807C2×Q8—2444no—
808C2×Q8—2444no—
809C2×D4—22no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—612no—
813C2×D4—1222no—
814C2×D4—1228no—
815C2×D4—1222no—
816C2×D4—1222no—
817C2×D4—1222no—
818C2×D4—1222no—
819C2×D4—1222no—
820C2×D4—1221no—
821C2×D4—1221no—
822C2×D4—2444no—
823C2×D4—2444no—
824C2×D4—2448no—
825C2×D4C23×D6112yes—
826C22×C4—22no—
827C22×C4—611no—
828C22×C4—611no—
829C22×C4—611no—
830C22×C4—611no—
831C22×C4—611no—
832C22×C4—611no—
833C22×C4—611no—
834C22×C4—611no—
835C22×C4—611no—
836C22×C4—611no—
837C22×C4—611no—
838C22×C4—611no—
839C22×C4—611no—
840C22×C4—611no—
841C22×C4—611no—
842C22×C4—1224no—
843C22×C4—1224no—
844C22×C4—1224no—
845C22×C4—1222no—
846C22×C4—1222no—
847C22×C4—1222no—
848C22×C4—1222no—
849C22×C4—1222no—
850C22×C4—1222no—
851C22×C4—2448no—
852C22×C4D4×D6111yescharacteristic
853C22×C4D4×D6111yescharacteristic
854C22×C4C23×D6111yescharacteristic
855C2×C8—612no—
856C2×C8—612no—
857C2×C8—1224no—
858C2×C8—1224no—
859C2×C8C23×D6112yes—
860C2×C8C23×D6112yes—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—612no—
867C4⋊C4—612no—
868C4⋊C4—612no—
869C4⋊C4—1222no—
870C4⋊C4—1222no—
871C4⋊C4—1222no—
872C4⋊C4—1222no—
873C4⋊C4—1222no—
874C4⋊C4—1222no—
875C4⋊C4—1222no—
876C4⋊C4—1222no—
877C4⋊C4—1222no—
878C4⋊C4—1222no—
879C4⋊C4—1222no—
880C4⋊C4—1222no—
881C4⋊C4—1221no—
882C4⋊C4—1221no—
883C4⋊C4—1221no—
884C4⋊C4C23×D6112yes—
885C4⋊C4C23×D6112yes—
886C4⋊C4C23×D6112yes—
887C22⋊C4—22no—
888C22⋊C4—22no—
889C22⋊C4—22no—
890C22⋊C4—1222no—
891C22⋊C4—1222no—
892C22⋊C4—1222no—
893C22⋊C4—1222no—
894C22⋊C4—1222no—
895C22⋊C4—1222no—
896C22⋊C4—1222no—
897C22⋊C4—1222no—
898C22⋊C4—1222no—
899C42—22no—
900C42—611no—
901C42—611no—
902C42—611no—
903C42—611no—
904C42—611no—
905C42—611no—
906C42—611no—
907C42—611no—
908C42—611no—
909C42—611no—
910C42—611no—
911C42—611no—
912C42—1222no—
913C42—1222no—
914C42—1222no—
915C42D4×D6111yescharacteristic
916C42D4×D6111yescharacteristic
917C42C23×D6111yescharacteristic
918C42C23×D6111yescharacteristic
919C23—22no—
920C23—611no—
921C23—611no—
922C23—1222no—
923C23—1222no—
924C23—1222no—
925C23—1222no—
926C23—2444no—
927C23—2444no—
928C23—2444no—
929C23C2×D4×D6111yescharacteristic
930Q8—42no—
931Q8—42no—
932Q8—42no—
933Q8—2444no—
934Q8—2444no—
935Q8—2444no—
936Q8—2442no—
937Q8—2442no—
938Q8—2442no—
939D4—24no—
940D4—44no—
941D4—42no—
942D4—42no—
943D4—1224no—
944D4—2444no—
945D4—2444no—
946D4—2444no—
947D4—2444no—
948D4—2444no—
949D4—2444no—
950D4—2442no—
951D4—2442no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—44no—
959C2×C4—611no—
960C2×C4—611no—
961C2×C4—611no—
962C2×C4—614no—
963C2×C4—614no—
964C2×C4—614no—
965C2×C4—611no—
966C2×C4—611no—
967C2×C4—611no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1222no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1222no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—1222no—
982C2×C4—1222no—
983C2×C4—2444no—
984C2×C4—2444no—
985C2×C4—2444no—
986C2×C4—2444no—
987C2×C4—2444no—
988C2×C4—2444no—
989C2×C4C2×D4×D6111yescharacteristic
990C2×C4C2×D4×D6111yescharacteristic
991C2×C4C2×D4×D6111yescharacteristic
992C2×C4C2×D4×D6111yescharacteristic
993C2×C4C2×D4×D6111yescharacteristic
994C2×C4C24×D6111yescharacteristic
995C8—22no—
996C8—22no—
997C8—1222no—
998C8—1222no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—612no—
1006C22—612no—
1007C22—612no—
1008C22—1221no—
1009C22—1221no—
1010C22—1221no—
1011C22—4888no—
1012C22—2444no—
1013C22—2442no—
1014C22—2442no—
1015C22—2442no—
1016C22C22×D4×D6111yescharacteristic
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—612no—
1024C4—612no—
1025C4—612no—
1026C4—1221no—
1027C4—1221no—
1028C4—1221no—
1029C4—2442no—
1030C4—2442no—
1031C4—2442no—
1032C4#135×D6112yes—
1033C4AGL(1,ℤ/8)×D6112yes—
1034C42−1+4×D6112yes—
1035C2—41no—
1036C2—82no—
1037C2—614no—
1038C2—4882no—
1039C2—2441no—
1040C2#536×D6111yescharacteristic
1041C2C2×#135×D6111yescharacteristic
1042C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3228C2
socleC22×C61C23×D4
prime radical#532×D61C2
hypercenter#3228D61
hypocenterC61C2×#3228
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21456958C2semidirect
4. #21456957C2semidirect
5. #21456956C2semidirect
6. #21456955C2semidirect
7. #21456954C2semidirect
8. #21456953C2semidirect
9. #21456952C2semidirect
10. #21456951C2semidirect
11. #21456950C2semidirect
12. #500×D61C2semidirect
13. #498×D61C2semidirect
14. #486×D61C2semidirect
15. #486×D61C2semidirect
16. #482×D61C2semidirect
17. #478×D61C2semidirect
18. #431×D61C2semidirect
19. C61×#3228C2semidirect
21. #16840319C22semidirect
22. #16840318C22semidirect
23. #16840317C22semidirect
24. #16840317C22semidirect
27. #16840315C22semidirect
55. #16840167C22semidirect
56. #16840166C22semidirect
57. #16840165C22semidirect
58. #16840165C22semidirect
59. #16840160C22semidirect
60. #16840159C22semidirect
61. #16840158C22semidirect
62. #16840158C22semidirect
63. #16840110C22semidirect
64. #16840110C22semidirect
65. #16840109C22semidirect
66. #16840109C22semidirect
67. #16840108C22semidirect
68. #16840108C22semidirect
69. #16840107C22semidirect
70. #16840107C22semidirect
71. #16840089C22semidirect
72. #16840088C22semidirect
73. #16840087C22semidirect
74. #16840086C22semidirect
75. #16840085C22semidirect
76. #16840084C22semidirect
77. #16840083C22semidirect
78. #16840065C22semidirect
79. #16840064C22semidirect
80. #16840063C22semidirect
81. #16840062C22semidirect
82. #16840061C22semidirect
83. #16840060C22semidirect
84. #16840059C22semidirect
85. #16839815C22semidirect
86. #16839814C22semidirect
87. #16839813C22semidirect
88. #16839813C22semidirect
89. #16839812C22semidirect
98. C61×#533C22semidirect
100. C61×#500C22semidirect
101. C61×#498C22semidirect
102. C61×#486C22semidirect
103. C61×#486C22semidirect
104. C61×#482C22semidirect
105. C61×#478C22semidirect
106. C61×#431C22semidirect
525. #3228D61direct (N × H)
540. D61#3228direct (N × H)
551. #533C2×D61semidirect
582. #500C2×D61semidirect
587. #498C2×D61semidirect
596. #486C2×D61semidirect
597. #486C2×D61semidirect
605. #482C2×D61semidirect
613. #478C2×D61semidirect
619. #431C2×D61semidirect
628. C61C2×#3228semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#532×D612
#214569582
#214569572
#214569562
#214569552
#214569542
#214569532
#214569522
#214569512
#214569502
#500×D612
#498×D612
#486×D612
#482×D612
#478×D612
#431×D612
C61×#32282
C2×#322861