Finite Group Databasebeta

← #30552348

Subgroups — #30552348

Order 15616.

1788 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic, complemented
2C2×#16840297C211yesmaximal, characteristic
3#21457062C212yesmaximal, complemented
4#21457060C212yesmaximal, complemented
5#21457050C212yesmaximal, complemented
6#21457041C212yesmaximal, complemented
7#21456999C214yesmaximal, complemented
8#21456988C214yesmaximal, complemented
9#21456368C211yesmaximal, characteristic, complemented
10#21456208C211yesmaximal, characteristic, complemented
11#21456206C211yesmaximal, characteristic, complemented
12#21455769C212yesmaximal, complemented
13#21455761C212yesmaximal
14#21455623C212yesmaximal, complemented
15#21455615C212yesmaximal, complemented
16#21454450C211yesmaximal, characteristic, complemented
17C61×#3166C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840318C2212yescomplemented
20#16840317C2211yescharacteristic, complemented
21#16840317C2211yescharacteristic, complemented
22#16840316—21no—
23#16840316—21no—
24#16840315C2212yes—
25#16840314—21no—
26#16840314—21no—
27C4⋊Q8×D61C2211yescharacteristic, complemented
28C4⋊Q8×D61C2211yescharacteristic, complemented
29#16840297—21no—
30#16840297—21no—
31#16840297—21no—
32#16840297—21no—
33#16840297C2212yes—
34#16840297C2212yes—
35#16840297C2212yes—
36#16840297C2212yes—
37C2×#14519772—21no—
38#125×D61C2212yescomplemented
39C2×#14519765C2211yescharacteristic
40C2×#14519762—21no—
41C2×#14519757C2211yescharacteristic
42C22⋊Q8×D61—21no—
43C22⋊Q8×D61—21no—
44C2×#14519752C2211yescharacteristic
45C2×#14519742C2211yescharacteristic
46C4×Q8×D61—21no—
47C4×Q8×D61—21no—
48C2×#14519739—21no—
49C2×#14519739C2211yescharacteristic
50C2×#14519735—21no—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840172C2212yescomplemented
55#16840161C2214yescomplemented
56#16840124C2212yescomplemented
57#16840124C2212yescomplemented
58#16840122C2212yescomplemented
59#16840122C2212yescomplemented
60#16840119C2214yescomplemented
61#16840117C2214yescomplemented
62#16840106C2214yescomplemented
63#16840105C2214yescomplemented
64#16840099C2214yescomplemented
65#16840094C2214yescomplemented
66#16840089C2214yes—
67#16840088C2214yes—
68#16840082C2214yes—
69#16840077C2214yes—
70#16840072C2214yescomplemented
71#16840068C2214yescomplemented
72#16840065C2214yescomplemented
73#16840061C2214yescomplemented
74#16840056C2214yescomplemented
75#16840051C2214yescomplemented
76#16840046C2214yescomplemented
77#16840041C2214yescomplemented
78#16839817C2212yescomplemented
79#16839817C2212yescomplemented
80#16839813C2212yescomplemented
81#16839813C2212yescomplemented
82#16839802C2212yes—
83#16839802C2212yes—
84#16839785C2212yes—
85#16839772C2212yes—
86#16839770C2212yes—
87#16839768C2212yes—
88#16839766C2212yes—
89#16839725C2212yes—
90C4×#11758194C2211yescharacteristic
91C61×#533C2211yescharacteristic
92C2×#125×C61C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#501C2212yescomplemented
95C61×#499C2214yescomplemented
96C61×#428C2212yes—
97C61×#428C2212yes—
98C4×M16×C61C2211yescharacteristic
99C22×Dic122C2311yescharacteristic
100C2×Q8×D61—21no—
101C2×Q8×D61—21no—
102C22×D244—21no—
103C22×D244C2311yescharacteristic
104C22×C4×D61—21no—
105C22×C4×D61D411yescharacteristic
106C22×C4×D61D411yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C2×#11758194C2312yes—
109#14519777C2311yescharacteristic
110#14519777C2311yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776C2312yes—
114#14519776C2312yes—
115#14519775—21no—
116#14519775—21no—
117#14519772—22no—
118#14519772—22no—
119#14519772—22no—
120#14519772—22no—
121#14519769C2312yes—
122#14519768C2312yes—
123#14519768C2312yes—
124#14519767—22no—
125#14519767—22no—
126#14519765—21no—
127#14519765—21no—
128#14519765C2312yes—
129#14519765C2312yes—
130#14519762—22no—
131#14519762—22no—
132#14519762—22no—
133#14519762—22no—
134#14519757—21no—
135#14519757—21no—
136#14519757—21no—
137#14519757—21no—
138#14519757C2312yes—
139#14519757C2312yes—
140#14519756—21no—
141#14519756—21no—
142#14519755—22no—
143#14519755—22no—
144#14519754—22no—
145#14519754—22no—
146#14519753—21no—
147#14519753—21no—
148#14519752—21no—
149#14519752—21no—
150#14519752C2312yes—
151#14519752C2312yes—
152Q8×Dic61—21no—
153Q8×Dic61—21no—
154C4×Dic122—21no—
155C4×Dic122—21no—
156C4×Dic122—22no—
157C4×Dic122—22no—
158#14519742—21no—
159#14519742—21no—
160#14519742—22no—
161#14519742—22no—
162#14519742—21no—
163#14519742—21no—
164#14519742C2312yes—
165#14519742C2312yes—
166#14519739—22no—
167#14519739—22no—
168#14519739—22no—
169#14519739—22no—
170#14519739—21no—
171#14519739—21no—
172#14519739C2312yes—
173#14519739C2312yes—
174#14519736C2312yes—
175#14519735—22no—
176#14519735—22no—
177#14519735—22no—
178#14519735—22no—
179#14519735C2312yes—
180#14519735C2312yes—
181#14519734—22no—
182#14519733—22no—
183C2×C4⋊Dic61—21no—
184C2×#11758196—21no—
185C4⋊C4×D61—22no—
186C4⋊C4×D61—22no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61C2312yes—
190C4⋊C4×D61C2312yes—
191C2×#11758198—21no—
192C2×#11758198—21no—
193C2×#11758198—21no—
194C2×#11758198—21no—
195C2×#11758198—21no—
196C22⋊C4×D61—22no—
197C2×C4×Dic61—21no—
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61D411yescharacteristic
200C2×C4×Dic61C2311yescharacteristic
201C42×D61—22no—
202C42×D61D411yescharacteristic
203C42×D61D411yescharacteristic
204C42×D61D411yescharacteristic
205C42×D61D411yescharacteristic
206C42×D61C2311yescharacteristic
207C42×D61C2311yescharacteristic
208C42×D61C2311yescharacteristic
209C42×D61C2311yescharacteristic
210#14519710C2314yes—
211#14519710C2314yes—
212#14519708C2314yes—
213#14519708C2314yes—
214#14519706C2314yes—
215#14519706C2314yes—
216#14519702C2314yes—
217#14519702C2314yes—
218#14519700C2314yes—
219#14519700C2314yes—
220#14519699C2314yes—
221#14519699C2314yes—
222#14519697C2314yes—
223#14519697C2314yes—
224#14519689C2314yes—
225#14519689C2314yes—
226#14519688C2312yes—
227C4×#92418C2312yes—
228C2×M16×C61C2312yes—
229C4⋊Q8×C61C2311yescharacteristic
230C4⋊Q8×C61C2311yescharacteristic
231#125×C61—21no—
232#125×C61—21no—
233#125×C61C2312yes—
234#125×C61C2312yes—
235#125×C61C2312yes—
236C22⋊Q8×C61—21no—
237C22⋊Q8×C61—21no—
238C4×Q8×C61—21no—
239C4×Q8×C61—21no—
240#117×C61C2312yes—
241C2×C4⋊C4×C61—21no—
242C2×C4⋊C4×C61—21no—
243C2×C4⋊C4×C61C2311yescharacteristic
244C2×C4⋊C4×C61C2311yescharacteristic
245C2×C42×C61C2311yescharacteristic
246#107×C61C2314yes—
247#107×C61C2314yes—
248#106×C61C2314yes—
249#106×C61C2314yes—
250#97×C61C2312yes—
251C4×C8×C61C2312yes—
252C23×D61—21no—
253C23×D61C2×D411yescharacteristic
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2411yescharacteristic
261C22×Dic61—21no—
262C22×Dic61C2×D411yescharacteristic
263C22×Dic61C2×D411yescharacteristic
264C22×Dic61C2×D411yescharacteristic
265Q8×D61—44no—
266Q8×D61—44no—
267C2×D244—24no—
268C2×D244—22no—
269C2×D244—22no—
270C2×D244—21no—
271C2×D244—44no—
272C2×D244C2412yes—
273C2×C4×D61—24no—
274C2×C4×D61—22no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—22no—
278C2×C4×D61—42no—
279C2×C4×D61—42no—
280C2×C4×D61—44no—
281C2×C4×D61C2×D411yescharacteristic
282C2×C4×D61C2×D411yescharacteristic
283C2×C4×D61C2×D411yescharacteristic
284C2×C4×D61C2×D411yescharacteristic
285C2×C4×D61C2×D411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2411yescharacteristic
292C2×C4×D61C2411yescharacteristic
293C2×Dic122—24no—
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122—22no—
298C2×Dic122—22no—
299C2×Dic122C2412yes—
300M16×C61—24no—
301C2×C8×C61C2414yes—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—22no—
304C4⋊C4×C61—22no—
305C4⋊C4×C61—22no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—22no—
309C4⋊C4×C61—22no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61C2412yes—
313C4⋊C4×C61C2412yes—
314C4⋊C4×C61C2412yes—
315C4⋊C4×C61C2412yes—
316C22⋊C4×C61—22no—
317C42×C61—22no—
318C42×C61C2×D411yescharacteristic
319C42×C61C2×D411yescharacteristic
320C42×C61C2411yescharacteristic
321C42×C61C2411yescharacteristic
322C22⋊Dic61—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198—22no—
326#11758198—22no—
327#11758198—22no—
328#11758198—22no—
329#11758198—22no—
330#11758198—22no—
331#11758198—22no—
332#11758198—22no—
333#11758198—22no—
334#11758198—22no—
335C4⋊Dic61—21no—
336C4⋊Dic61—21no—
337C4⋊Dic61—22no—
338C4⋊Dic61—22no—
339C4⋊Dic61—22no—
340C4⋊Dic61—22no—
341C4⋊Dic61C2412yes—
342C4⋊Dic61C2412yes—
343#11758196—22no—
344#11758196—22no—
345#11758196—22no—
346#11758196—22no—
347#11758196—22no—
348#11758196—22no—
349#11758196—22no—
350#11758196—22no—
351#11758196—22no—
352#11758196—22no—
353C4×Dic61—22no—
354C4×Dic61—22no—
355C4×Dic61—22no—
356C4×Dic61—22no—
357C4×Dic61—22no—
358C4×Dic61C2×D411yescharacteristic
359C4×Dic61C2×D411yescharacteristic
360C4×Dic61C2×D411yescharacteristic
361C4×Dic61C2×D411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61C2×D411yescharacteristic
365C4×Dic61C2×D411yescharacteristic
366C4×Dic61C2×D411yescharacteristic
367C4×Dic61C2×D411yescharacteristic
368C4×Dic61C2411yescharacteristic
369C4×Dic61C2411yescharacteristic
370#11758194—24no—
371C2×#92418C2414yes—
372C23×C61C22×D411yescharacteristic
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—22no—
376C22×D61—41no—
377C22×D61—42no—
378C22×D61—42no—
379C22×D61—42no—
380C22×D61C22×D411yescharacteristic
381C22×D61C22×D411yescharacteristic
382Q8×C61—42no—
383Q8×C61—42no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—42no—
391C2×C4×C61—42no—
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C612−1+414yes—
398C2×C4×C61C2511yescharacteristic
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—41no—
405C2×Dic61—42no—
406C2×Dic61C22×D411yescharacteristic
407C2×Dic61C22×D411yescharacteristic
408C2×Dic61C22×D411yescharacteristic
409C2×Dic61C22×D411yescharacteristic
410C2×Dic61C22×D411yescharacteristic
411C2×Dic61C22×D411yescharacteristic
412D244—24no—
413D244—44no—
414D244—44no—
415D244—42no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—22no—
422C4×D61—22no—
423C4×D61—22no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—41no—
428C4×D61—44no—
429C4×D61—44no—
430C4×D61—44no—
431C4×D61—44no—
432Dic122—24no—
433Dic122—44no—
434Dic122—42no—
435Dic122—42no—
436Dic122—42no—
437Dic122—44no—
438C8×C61—24no—
439#92418—24no—
440#60866—611nomaximal, Sylow
441C22×C61—21no—
442C22×C61—21no—
443C22×C61#53612yes—
444C22×C61C23×D411yescharacteristic
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—44no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—84no—
455C2×D61#57512yes—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—42no—
461C4×C61—42no—
462C4×C61—42no—
463C4×C61—42no—
464C4×C61#53612yes—
465C4×C61C2×2−1+412yes—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—42no—
472Dic61—42no—
473Dic61—42no—
474Dic61#57512yes—
475C2×#533—611no—
476C2×#529—611no—
477#3240—612no—
478#3240—612no—
479#3239—612no—
480#3238—612no—
481#3233—614no—
482#3232—614no—
483#3166—611no—
484#3166D6111yescharacteristic, complemented
485#3140—611no—
486#3140—611no—
487#3095—612no—
488#3094—612no—
489#3078—612no—
490#3077—612no—
491#2920—611no—
492C2×C61—22no—
493C2×C61C2×#53611yescharacteristic
494C2×C61C2×#57511yescharacteristic
495C2×C61C2×#57511yescharacteristic
496D61—22no—
497D61—41no—
498D61—82no—
499#533—611no—
500#533—611no—
501#533—612no—
502#533—612no—
503#533—611no—
504#533—1221no—
505#533—1221no—
506#533—1221no—
507#533—1221no—
508#533C2×D6111yescharacteristic
509C2×C4⋊Q8—611no—
510C2×C4⋊Q8—611no—
511#529—612no—
512#529—612no—
513#529—612no—
514#529—612no—
515#529—1221no—
516#529—1221no—
517#529—1221no—
518#529—1221no—
519C2×#126—1221no—
520C2×#125—612no—
521C2×#125C2×D6111yescharacteristic
522C2×#124—611no—
523C2×#123—1221no—
524C2×C22⋊Q8—611no—
525C2×C22⋊Q8—1221no—
526C2×C22⋊Q8—1221no—
527C2×#121—611no—
528C2×C4×Q8—611no—
529C2×C4×Q8—1221no—
530C2×C4×Q8—1221no—
531C2×C4×D4—611no—
532C2×C4×D4—1221no—
533C2×#117—612no—
534C2×#117—1221no—
535C22×C42—611no—
536#501—612no—
537#501—612no—
538#501C2×D6112yescomplemented
539#501C2×D6112yescomplemented
540#499—614no—
541#499C2×D6114yescomplemented
542#489—612no—
543#489—612no—
544#489—612no—
545#489—612no—
546#488—614no—
547#488—614no—
548#485—614no—
549#485—614no—
550#484—614no—
551#483—614no—
552#482—614no—
553#482—614no—
554#481—614no—
555#480—614no—
556#479—614no—
557#479—614no—
558#478—614no—
559#478—614no—
560#477—614no—
561#476—614no—
562#475—614no—
563#474—614no—
564#432—612no—
565#432—612no—
566#431—612no—
567#431—612no—
568#428—612no—
569#428—612no—
570#428C2×D6112yes—
571#428C2×D6112yes—
572#423—612no—
573#419—612no—
574#419—612no—
575#418—612no—
576#418—612no—
577#407—612no—
578C4×M16—611no—
579C4×M16C2×D6111yescharacteristic
580C61#6086611yescharacteristic, complemented, Sylow
581C22×Q8—611no—
582C22×Q8—1221no—
583C22×Q8—1221no—
584C22×D4—611no—
585C22×D4—1221no—
586C23×C4—611no—
587C23×C4—611no—
588C23×C4—611no—
589C23×C4—1221no—
590C2×M16—612no—
591C2×M16C22×D6112yes—
592C4⋊Q8—612no—
593C4⋊Q8—612no—
594C4⋊Q8—611no—
595C4⋊Q8—611no—
596C4⋊Q8—1221no—
597C4⋊Q8—1221no—
598C4⋊Q8—1221no—
599C4⋊Q8—1221no—
600C4⋊Q8C22×D6111yescharacteristic
601C4⋊Q8C22×D6111yescharacteristic
602#126—1222no—
603#126—1222no—
604#126—1222no—
605#126—1222no—
606#125—21no—
607#125—21no—
608#125—612no—
609#125—612no—
610#125—612no—
611#125—1222no—
612#125—1222no—
613#125C22×D6112yes—
614#125C22×D6112yes—
615#125C22×D6112yes—
616#124—612no—
617#124—612no—
618#124—1221no—
619#124—1221no—
620#123—1222no—
621#123—1222no—
622#123—1222no—
623#123—1222no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8—612no—
627C22⋊Q8—612no—
628C22⋊Q8—1222no—
629C22⋊Q8—1222no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1222no—
633C22⋊Q8—1222no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8—1221no—
638C22⋊Q8—1221no—
639C22⋊Q8—1221no—
640#121—612no—
641#121—612no—
642#121—1221no—
643#121—1221no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—612no—
647C4×Q8—612no—
648C4×Q8—1222no—
649C4×Q8—1222no—
650C4×Q8—1221no—
651C4×Q8—1221no—
652C4×Q8—1222no—
653C4×Q8—1221no—
654C4×Q8—1222no—
655C4×Q8—1221no—
656C4×Q8—1221no—
657C4×Q8—1221no—
658C4×Q8—1221no—
659C4×Q8—1221no—
660C4×D4—612no—
661C4×D4—612no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1222no—
665C4×D4—1222no—
666C4×D4—1222no—
667C4×D4—1222no—
668#117—612no—
669#117—612no—
670#117—612no—
671#117—1222no—
672#117—1222no—
673#117—1222no—
674#117—1222no—
675#117—1222no—
676#117—1222no—
677#117C22×D6112yes—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—612no—
681C2×C4⋊C4—612no—
682C2×C4⋊C4—1222no—
683C2×C4⋊C4—1222no—
684C2×C4⋊C4—1221no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4—1221no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4C22×D6111yescharacteristic
689C2×C4⋊C4C22×D6111yescharacteristic
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1221no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C22⋊C4—1221no—
696C2×C42—611no—
697C2×C42—611no—
698C2×C42—611no—
699C2×C42—611no—
700C2×C42—611no—
701C2×C42—611no—
702C2×C42—611no—
703C2×C42—611no—
704C2×C42—611no—
705C2×C42—611no—
706C2×C42—611no—
707C2×C42—1222no—
708C2×C42—1221no—
709C2×C42C22×D6111yescharacteristic
710#107—614no—
711#107—614no—
712#107C22×D6114yes—
713#107C22×D6114yes—
714#106—614no—
715#106—614no—
716#106C22×D6114yes—
717#106C22×D6114yes—
718C4⋊C8—614no—
719C4⋊C8—614no—
720#103—614no—
721#103—614no—
722#103—614no—
723#103—614no—
724#102—614no—
725#102—614no—
726#102—614no—
727#102—614no—
728C22⋊C8—614no—
729C22⋊C8—614no—
730#97—612no—
731#97C22×D6112yes—
732C4×C8—612no—
733C4×C8C22×D6112yes—
734C24—611no—
735C24—1221no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—612no—
739C2×Q8—1222no—
740C2×Q8—1222no—
741C2×Q8—1221no—
742C2×Q8—1221no—
743C2×Q8—1221no—
744C2×Q8—1224no—
745C2×Q8—2444no—
746C2×Q8—2444no—
747C2×D4—612no—
748C2×D4—1222no—
749C2×D4—1222no—
750C2×D4—1221no—
751C2×D4—1224no—
752C2×D4—2444no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—611no—
763C22×C4—611no—
764C22×C4—611no—
765C22×C4—611no—
766C22×C4—611no—
767C22×C4—611no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—1222no—
771C22×C4—1222no—
772C22×C4—1222no—
773C22×C4—1222no—
774C22×C4—1224no—
775C22×C4—1221no—
776C22×C4—2442no—
777C22×C4—2442no—
778C22×C4—2444no—
779C22×C4D4×D6111yescharacteristic
780C22×C4D4×D6111yescharacteristic
781C22×C4C23×D6111yescharacteristic
782M16—24no—
783M16—1224no—
784C2×C8—614no—
785C2×C8C23×D6114yes—
786C4⋊C4—22no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—612no—
797C4⋊C4—612no—
798C4⋊C4—1222no—
799C4⋊C4—1222no—
800C4⋊C4—1222no—
801C4⋊C4—1222no—
802C4⋊C4—1222no—
803C4⋊C4—1222no—
804C4⋊C4—1222no—
805C4⋊C4—1222no—
806C4⋊C4—1222no—
807C4⋊C4—1222no—
808C4⋊C4—1222no—
809C4⋊C4—1222no—
810C4⋊C4—1222no—
811C4⋊C4—1222no—
812C4⋊C4—1221no—
813C4⋊C4—1221no—
814C4⋊C4C23×D6112yes—
815C4⋊C4C23×D6112yes—
816C4⋊C4C23×D6112yes—
817C4⋊C4C23×D6112yes—
818C22⋊C4—22no—
819C22⋊C4—1222no—
820C22⋊C4—1222no—
821C22⋊C4—1222no—
822C22⋊C4—1222no—
823C22⋊C4—1222no—
824C22⋊C4—1222no—
825C22⋊C4—1222no—
826C22⋊C4—1222no—
827C22⋊C4—1222no—
828C22⋊C4—1222no—
829C22⋊C4—1222no—
830C22⋊C4—1222no—
831C22⋊C4—1222no—
832C42—22no—
833C42—611no—
834C42—611no—
835C42—611no—
836C42—611no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—611no—
843C42—611no—
844C42—611no—
845C42—1222no—
846C42—1222no—
847C42—1222no—
848C42—1222no—
849C42—1222no—
850C42D4×D6111yescharacteristic
851C42D4×D6111yescharacteristic
852C42C23×D6111yescharacteristic
853C42C23×D6111yescharacteristic
854C23—611no—
855C23—611no—
856C23—1222no—
857C23—1222no—
858C23—1222no—
859C23—2441no—
860C23—2442no—
861C23—2442no—
862C23—2442no—
863C23C2×D4×D6111yescharacteristic
864Q8—42no—
865Q8—42no—
866Q8—1224no—
867Q8—2442no—
868Q8—2442no—
869Q8—2444no—
870Q8—2444no—
871Q8—2442no—
872D4—1224no—
873D4—2444no—
874D4—2444no—
875D4—2442no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—1222no—
897C2×C4—1222no—
898C2×C4—1222no—
899C2×C4—1222no—
900C2×C4—1222no—
901C2×C4—1222no—
902C2×C4—1222no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2444no—
908C2×C4—2444no—
909C2×C4—2444no—
910C2×C4—2444no—
911C2×C4—2441no—
912C2×C4—2442no—
913C2×C4C2×D4×D6111yescharacteristic
914C2×C4C2×D4×D6111yescharacteristic
915C2×C4C2×D4×D6111yescharacteristic
916C2×C4C2×D4×D6111yescharacteristic
917C2×C4C2×D4×D6111yescharacteristic
918C2×C4#1451982514yes—
919C2×C4C24×D6111yescharacteristic
920C8—24no—
921C8—1224no—
922C22—21no—
923C22—21no—
924C22—612no—
925C22—1221no—
926C22—1221no—
927C22—1221no—
928C22—1221no—
929C22—1221no—
930C22—4884no—
931C22—2444no—
932C22—2442no—
933C22—2442no—
934C22—2442no—
935C22#1684033712yes—
936C22C22×D4×D6111yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—612no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—1221no—
950C4—1221no—
951C4—2442no—
952C4—2442no—
953C4—2442no—
954C4#1684033712yes—
955C4C2×#1451982512yes—
956C2—22no—
957C2—1222no—
958C2—4882no—
959C2—2441no—
960C2C2×#1684033711yescharacteristic
961C2#575×D6111yescharacteristic
962C2#575×D6111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3166C2
socleC22×C61C23×D4
prime radicalC2×#14519752C22
hypercenter#3166D61
hypocenterC61#60866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
1. #533×D61C2semidirect
3. #21457062C2semidirect
4. #21457060C2semidirect
5. #21457050C2semidirect
6. #21457041C2semidirect
7. #21456999C2semidirect
8. #21456988C2semidirect
9. #21456368C2semidirect
10. #21456208C2semidirect
11. #21456206C2semidirect
12. #21455769C2semidirect
14. #21455623C2semidirect
15. #21455615C2semidirect
16. #21454450C2semidirect
17. C61×#3166C2semidirect
19. #16840318C22semidirect
20. #16840317C22semidirect
21. #16840317C22semidirect
27. C4⋊Q8×D61C22semidirect
28. C4⋊Q8×D61C22semidirect
38. #125×D61C22semidirect
53. #16840172C22semidirect
54. #16840172C22semidirect
55. #16840161C22semidirect
56. #16840124C22semidirect
57. #16840124C22semidirect
58. #16840122C22semidirect
59. #16840122C22semidirect
60. #16840119C22semidirect
61. #16840117C22semidirect
62. #16840106C22semidirect
63. #16840105C22semidirect
64. #16840099C22semidirect
65. #16840094C22semidirect
70. #16840072C22semidirect
71. #16840068C22semidirect
72. #16840065C22semidirect
73. #16840061C22semidirect
74. #16840056C22semidirect
75. #16840051C22semidirect
76. #16840046C22semidirect
77. #16840041C22semidirect
78. #16839817C22semidirect
79. #16839817C22semidirect
80. #16839813C22semidirect
81. #16839813C22semidirect
93. C61×#501C22semidirect
94. C61×#501C22semidirect
95. C61×#499C22semidirect
484. #3166D61semidirect
538. #501C2×D61semidirect
539. #501C2×D61semidirect
541. #499C2×D61semidirect
580. C61#60866semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×#168402972
#214570622
#214570602
#214570502
#214570412
#214569992
#214569882
#214563682
#214562082
#214562062
#214557692
#214557612
#214556232
#214556152
#214544502
C61×#31662
#6086661