Finite Group Databasebeta

← #30552191

Subgroups — #30552191

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459116C211yesmaximal, characteristic
2#533×D61C211yesmaximal, characteristic, complemented
3#21457062C212yesmaximal, complemented
4#21457060C212yesmaximal, complemented
5#21457050C212yesmaximal, complemented
6#21457041C212yesmaximal, complemented
7#21457034C212yesmaximal, complemented
8#21457026C212yesmaximal, complemented
9#21457018C212yesmaximal, complemented
10#21457010C212yesmaximal, complemented
11#21456341C211yesmaximal, characteristic, complemented
12#21456167C211yesmaximal, characteristic, complemented
13#21456165C211yesmaximal, characteristic, complemented
14#21455736C214yesmaximal, complemented
15#21455605C214yesmaximal, complemented
16C2×#16839817C211yesmaximal, characteristic, complemented
17C61×#3162C211yesmaximal, characteristic, complemented
18#16840319C2211yescharacteristic
19#16840318C2212yes—
20#16840317C2211yescharacteristic
21#16840317C2211yescharacteristic
22#16840317C2211yescharacteristic
23#16840317C2211yescharacteristic
24#16840316—21no—
25#16840316—21no—
26#16840315C2212yes—
27#16840314—21no—
28#16840314—21no—
29#16840313C2211yescharacteristic
30#16840313C2211yescharacteristic
31#16840312C2211yescharacteristic
32C4⋊Q8×D61C2211yescharacteristic
33C4⋊Q8×D61C2211yescharacteristic
34#16840299—21no—
35#16840299—21no—
36#16840298—21no—
37#16840298—21no—
38#16840297C2212yes—
39#16840297C2212yes—
40#125×D61C2212yes—
41#16840275—21no—
42#16840275—21no—
43#16840274C2212yes—
44C22⋊Q8×D61—21no—
45C22⋊Q8×D61—21no—
46C4×#11758226—21no—
47C4×#11758226—21no—
48#16840230C2212yes—
49C4×Q8×D61—21no—
50C4×Q8×D61—21no—
51#117×D61C2212yes—
52C2×C42×D61C2211yescharacteristic
53#16840172C2212yescomplemented
54#16840172C2212yescomplemented
55#16840168C2212yescomplemented
56#16840168C2212yescomplemented
57#16840132C2212yescomplemented
58#16840131C2212yescomplemented
59#16840128C2212yescomplemented
60#16840127C2212yescomplemented
61#16840124C2212yescomplemented
62#16840124C2212yescomplemented
63#16840122C2212yescomplemented
64#16840122C2212yescomplemented
65#16840106C2214yes—
66#16840105C2214yes—
67#16840099C2214yes—
68#16840094C2214yes—
69#16840089C2214yes—
70#16840088C2214yes—
71#16840082C2214yes—
72#16840077C2214yes—
73#16840072C2214yescomplemented
74#16840068C2214yescomplemented
75#16840065C2214yescomplemented
76#16840061C2214yescomplemented
77#16840056C2214yescomplemented
78#16840051C2214yescomplemented
79#16840046C2214yescomplemented
80#16840041C2214yescomplemented
81#16839817C2212yes—
82#16839817C2212yes—
83#16839817C2212yes—
84#16839817C2212yes—
85#16839798C2214yes—
86C2×#14519706C2212yes—
87#16839759C2214yes—
88#16839756C2214yes—
89C2×#14519689C2212yes—
90C2×#14519688C2211yescharacteristic
91C61×#533C2211yescharacteristic
92C61×#533C2211yescharacteristic
93C61×#501C2212yescomplemented
94C61×#501C2212yescomplemented
95C61×#501C2212yescomplemented
96C61×#501C2212yescomplemented
97C61×#427C2214yes—
98C2×#97×C61C2211yescharacteristic
99C2×#11758226—21no—
100C2×#11758226—21no—
101C2×#11758222C2312yes—
102C2×Q8×D61—21no—
103C2×Q8×D61—21no—
104C22×C4×D61D411yescharacteristic
105C22×C4×D61D411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×#92418C2312yes—
108#14519777C2311yescharacteristic
109#14519777C2311yescharacteristic
110#14519777C2311yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776C2312yes—
114#14519776C2312yes—
115#14519775—21no—
116#14519775—21no—
117#14519774C2311yescharacteristic
118#14519772—22no—
119#14519772—22no—
120#14519769C2312yes—
121#14519768—21no—
122#14519768—21no—
123#14519768C2312yes—
124#14519768C2312yes—
125#14519767—22no—
126#14519767—22no—
127#14519766—21no—
128#14519766—21no—
129#14519765C2312yes—
130#14519762—22no—
131#14519762—22no—
132#14519761—22no—
133#14519757—21no—
134#14519757—21no—
135#14519757C2312yes—
136#14519757C2312yes—
137#14519756—21no—
138#14519756—21no—
139#14519755—22no—
140#14519755—22no—
141#14519754—22no—
142#14519754—22no—
143#14519753—21no—
144#14519753—21no—
145#14519753—21no—
146#14519753—21no—
147#14519752—21no—
148#14519752—21no—
149#14519752C2312yes—
150#14519752C2312yes—
151#14519751—21no—
152#14519751—21no—
153#14519747—22no—
154Q8×Dic61—21no—
155Q8×Dic61—21no—
156Q8×Dic61—21no—
157Q8×Dic61—21no—
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—22no—
161C4×Dic122—22no—
162#14519742—21no—
163#14519742—21no—
164#14519742—22no—
165#14519742—22no—
166#14519742C2312yes—
167#14519742C2312yes—
168C4×D244—22no—
169C4×D244—22no—
170C4×D244—21no—
171C4×D244—21no—
172#14519739—22no—
173#14519739—22no—
174#14519739—21no—
175#14519739—21no—
176#14519739C2312yes—
177#14519739C2312yes—
178#14519737—22no—
179#14519737—22no—
180#14519736C2312yes—
181#14519735—21no—
182#14519735—21no—
183#14519735—22no—
184#14519735—22no—
185#14519735C2312yes—
186#14519735C2312yes—
187#14519734—22no—
188#14519734—22no—
189#14519733—22no—
190C4⋊C4×D61—22no—
191C4⋊C4×D61—22no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2312yes—
195C4⋊C4×D61C2312yes—
196C22⋊C4×D61—22no—
197C2×C4×Dic61D411yescharacteristic
198C2×C4×Dic61D411yescharacteristic
199C2×C4×Dic61C2311yescharacteristic
200C42×D61—22no—
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—
227#14519688C2312yes—
228C22×C8×C61C2312yes—
229C4⋊Q8×C61C2311yescharacteristic
230C4⋊Q8×C61C2311yescharacteristic
231C4⋊Q8×C61C2311yescharacteristic
232C4⋊Q8×C61C2311yescharacteristic
233#125×C61C2312yes—
234#125×C61C2312yes—
235C22⋊Q8×C61—21no—
236C22⋊Q8×C61—21no—
237C22⋊Q8×C61—21no—
238C22⋊Q8×C61—21no—
239C4×Q8×C61—21no—
240C4×Q8×C61—21no—
241C4×Q8×C61—21no—
242C4×Q8×C61—21no—
243#117×C61C2312yes—
244#117×C61C2312yes—
245C2×C42×C61C2311yescharacteristic
246#107×C61C2314yes—
247#107×C61C2314yes—
248#106×C61C2314yes—
249#106×C61C2314yes—
250#97×C61C2312yes—
251#97×C61C2312yes—
252C23×D61C2×D411yescharacteristic
253C2×Q8×C61—21no—
254C2×Q8×C61—21no—
255C2×Q8×C61—21no—
256C2×Q8×C61—21no—
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260C2×C22⋊D61—22no—
261C22×Dic61C2×D411yescharacteristic
262C22×Dic61C2×D411yescharacteristic
263C22×Dic61C2×D411yescharacteristic
264#11758226—44no—
265#11758226—44no—
266Q8×D61—44no—
267Q8×D61—44no—
268#11758222—28no—
269C2×D244—22no—
270C2×D244—22no—
271C2×D244—21no—
272C2×D244—21no—
273C2×D244C2412yes—
274C2×C4×D61—24no—
275C2×C4×D61—22no—
276C2×C4×D61—22no—
277C2×C4×D61—22no—
278C2×C4×D61—22no—
279C2×C4×D61—22no—
280C2×C4×D61—42no—
281C2×C4×D61—42no—
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×D61C2×D411yescharacteristic
292C2×C4×D61C2411yescharacteristic
293C2×C4×D61C2411yescharacteristic
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—22no—
297C2×Dic122—22no—
298C2×Dic122C2412yes—
299C2×C8×C61—24no—
300C2×C8×C61C2414yes—
301C4⋊C4×C61—22no—
302C4⋊C4×C61—22no—
303C4⋊C4×C61—22no—
304C4⋊C4×C61—22no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61C2412yes—
310C4⋊C4×C61C2412yes—
311C4⋊C4×C61C2412yes—
312C4⋊C4×C61C2412yes—
313C22⋊C4×C61—22no—
314C22⋊C4×C61—22no—
315C42×C61—22no—
316C42×C61—22no—
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C42×C61C2411yescharacteristic
320C42×C61C2411yescharacteristic
321C22⋊Dic61—22no—
322#11758198—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—
332C4⋊Dic61—21no—
333C4⋊Dic61—21no—
334C4⋊Dic61—21no—
335C4⋊Dic61—21no—
336C4⋊Dic61—22no—
337C4⋊Dic61—22no—
338C4⋊Dic61—22no—
339C4⋊Dic61—22no—
340C4⋊Dic61C2412yes—
341C4⋊Dic61C2412yes—
342#11758196—22no—
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—
352C4×Dic61—22no—
353C4×Dic61—22no—
354C4×Dic61—22no—
355C4×Dic61—22no—
356C4×Dic61—22no—
357C4×Dic61C2×D411yescharacteristic
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×Dic61C2411yescharacteristic
368C4×Dic61C2411yescharacteristic
369C2×#92418—24no—
370C2×#92418C2414yes—
371C23×C61C22×D411yescharacteristic
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—22no—
375C22×D61—41no—
376C22×D61C22×D411yescharacteristic
377C22×D61C22×D411yescharacteristic
378Q8×C61—42no—
379Q8×C61—42no—
380Q8×C61—42no—
381Q8×C61—42no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C612−1+414yes—
394C2×C4×C61C2511yescharacteristic
395C22⋊D61—44no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—41no—
402C2×Dic61C22×D411yescharacteristic
403C2×Dic61C22×D411yescharacteristic
404C2×Dic61C22×D411yescharacteristic
405C2×Dic61C22×D411yescharacteristic
406C2×Dic61C22×D411yescharacteristic
407C2×Dic61C22×D411yescharacteristic
408D244—24no—
409D244—42no—
410D244—42no—
411D244—44no—
412D244—44no—
413C4×D61—22no—
414C4×D61—22no—
415C4×D61—22no—
416C4×D61—22no—
417C4×D61—22no—
418C4×D61—22no—
419C4×D61—22no—
420C4×D61—22no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—44no—
426C4×D61—44no—
427C4×D61—44no—
428C4×D61—44no—
429C4×D61—44no—
430Dic122—24no—
431Dic122—44no—
432Dic122—42no—
433Dic122—42no—
434Dic122—44no—
435C8×C61—24no—
436#92418—24no—
437#60854—611nomaximal, Sylow
438C22×C61—21no—
439C22×C61—21no—
440C22×C61#53612yes—
441C22×C61C23×D411yescharacteristic
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—44no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61#57512yes—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—42no—
457C4×C61—42no—
458C4×C61—42no—
459C4×C61—42no—
460C4×C61#53612yes—
461C4×C61C2×2−1+412yes—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—42no—
468Dic61—42no—
469Dic61—42no—
470Dic61#57512yes—
471#3444—611no—
472C2×#533—611no—
473#3240—612no—
474#3240—612no—
475#3239—612no—
476#3238—612no—
477#3237—612no—
478#3236—612no—
479#3235—612no—
480#3234—612no—
481#3162—611no—
482#3162D6111yescharacteristic, complemented
483#3135—611no—
484#3135—611no—
485#3091—614no—
486#3076—614no—
487C2×#432—611no—
488C2×C61—22no—
489C2×C61C2×#53611yescharacteristic
490C2×C61C2×#57511yescharacteristic
491C2×C61C2×#57511yescharacteristic
492D61—22no—
493D61—41no—
494D61—82no—
495#533—611no—
496#533—611no—
497#533—612no—
498#533—612no—
499#533—611no—
500#533—611no—
501#533—611no—
502#533—1221no—
503#533—1221no—
504#533—1221no—
505#533—1221no—
506#533C2×D6111yescharacteristic
507#533C2×D6111yescharacteristic
508#532—611no—
509#532—611no—
510#532—611no—
511C2×C4⋊Q8—611no—
512C2×C4⋊Q8—611no—
513#529—612no—
514#529—612no—
515#529—1221no—
516#529—1221no—
517#529—1221no—
518#529—1221no—
519C2×#125—612no—
520#525—612no—
521#525—1221no—
522#525—1221no—
523C2×C22⋊Q8—1221no—
524C2×C22⋊Q8—1221no—
525C4×#41—612no—
526C4×#41—1221no—
527C4×#41—1221no—
528C2×C4×Q8—1221no—
529C2×C4×Q8—1221no—
530C2×#117—612no—
531C22×C42—611no—
532#501—612no—
533#501—612no—
534#501—612no—
535#501—612no—
536#501C2×D6112yescomplemented
537#501C2×D6112yescomplemented
538#501C2×D6112yescomplemented
539#501C2×D6112yescomplemented
540#491—612no—
541#491—612no—
542#490—612no—
543#490—612no—
544#489—612no—
545#489—612no—
546#489—612no—
547#489—612no—
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#432—612no—
567#432—612no—
568#427—614no—
569#427C2×D6114yes—
570C2×C4⋊C8—612no—
571#416—614no—
572#416—614no—
573C2×C22⋊C8—612no—
574C2×#97—611no—
575C2×#97C2×D6111yescharacteristic
576C61#6085411yescharacteristic, complemented, Sylow
577C2×#41—612no—
578C2×#41—1221no—
579C2×#41—1221no—
580C22×Q8—1221no—
581C22×Q8—1221no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C22×C8—612no—
586C22×C8C22×D6112yes—
587C4⋊Q8—612no—
588C4⋊Q8—612no—
589C4⋊Q8—611no—
590C4⋊Q8—611no—
591C4⋊Q8—611no—
592C4⋊Q8—1221no—
593C4⋊Q8—1221no—
594C4⋊Q8—1221no—
595C4⋊Q8—1221no—
596C4⋊Q8C22×D6111yescharacteristic
597C4⋊Q8C22×D6111yescharacteristic
598C4⋊Q8C22×D6111yescharacteristic
599C4⋊Q8C22×D6111yescharacteristic
600#127—611no—
601#126—1222no—
602#126—1222no—
603#125—612no—
604#125—612no—
605#125—612no—
606#125—1222no—
607#125—1222no—
608#125—1221no—
609#125—1221no—
610#125C22×D6112yes—
611#125C22×D6112yes—
612#124—612no—
613#124—1221no—
614#124—1221no—
615#123—1222no—
616#123—1222no—
617#123—1222no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—612no—
623C22⋊Q8—612no—
624C22⋊Q8—1222no—
625C22⋊Q8—1222no—
626C22⋊Q8—1222no—
627C22⋊Q8—1222no—
628C22⋊Q8—1221no—
629C22⋊Q8—1221no—
630C22⋊Q8—1221no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C22⋊Q8—1221no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636#121—612no—
637#121—612no—
638#121—1221no—
639#121—1221no—
640#121—1221no—
641#121—1221no—
642#120—1222no—
643C4×Q8—21no—
644C4×Q8—21no—
645C4×Q8—21no—
646C4×Q8—21no—
647C4×Q8—612no—
648C4×Q8—612no—
649C4×Q8—1222no—
650C4×Q8—1222no—
651C4×Q8—1221no—
652C4×Q8—1222no—
653C4×Q8—1222no—
654C4×Q8—1221no—
655C4×Q8—1221no—
656C4×Q8—1221no—
657C4×Q8—1221no—
658C4×Q8—1221no—
659C4×Q8—1221no—
660C4×Q8—1221no—
661C4×D4—612no—
662C4×D4—612no—
663C4×D4—1222no—
664C4×D4—1222no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1222no—
668C4×D4—1222no—
669C4×D4—1222no—
670C4×D4—1222no—
671C4×D4—1221no—
672C4×D4—1221no—
673#117—612no—
674#117—612no—
675#117—612no—
676#117—1222no—
677#117—1222no—
678#117—1222no—
679#117—1222no—
680#117—1222no—
681#117—1221no—
682#117—1221no—
683#117C22×D6112yes—
684#117C22×D6112yes—
685C2×C4⋊C4—612no—
686C2×C4⋊C4—612no—
687C2×C4⋊C4—1222no—
688C2×C4⋊C4—1222no—
689C2×C4⋊C4—1221no—
690C2×C4⋊C4—1221no—
691C2×C22⋊C4—1222no—
692C2×C42—611no—
693C2×C42—611no—
694C2×C42—611no—
695C2×C42—611no—
696C2×C42—611no—
697C2×C42—611no—
698C2×C42—611no—
699C2×C42—611no—
700C2×C42—611no—
701C2×C42—611no—
702C2×C42—611no—
703C2×C42—1222no—
704C2×C42—1222no—
705C2×C42C22×D6111yescharacteristic
706#107—614no—
707#107—614no—
708#107C22×D6114yes—
709#107C22×D6114yes—
710#106—614no—
711#106—614no—
712#106C22×D6114yes—
713#106C22×D6114yes—
714C4⋊C8—614no—
715C4⋊C8—614no—
716#103—614no—
717#103—614no—
718#103—614no—
719#103—614no—
720#102—614no—
721#102—614no—
722#102—614no—
723#102—614no—
724C22⋊C8—614no—
725C22⋊C8—614no—
726#97—612no—
727#97—612no—
728#97C22×D6112yes—
729#97C22×D6112yes—
730C24—611no—
731#41—1228no—
732#41—2444no—
733#41—2444no—
734C2×Q8—21no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—612no—
739C2×Q8—1222no—
740C2×Q8—1222no—
741C2×Q8—1221no—
742C2×Q8—1221no—
743C2×Q8—2444no—
744C2×Q8—2444no—
745C2×D4—612no—
746C2×D4—1222no—
747C2×D4—1222no—
748C2×D4—1222no—
749C2×D4—1221no—
750C2×D4—1221no—
751C22×C4—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
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—1222no—
767C22×C4—1222no—
768C22×C4—1222no—
769C22×C4—1222no—
770C22×C4—1224no—
771C22×C4—1222no—
772C22×C4—2442no—
773C22×C4—2442no—
774C22×C4D4×D6111yescharacteristic
775C22×C4D4×D6111yescharacteristic
776C22×C4C23×D6111yescharacteristic
777C2×C8—24no—
778C2×C8—614no—
779C2×C8—1224no—
780C2×C8C23×D6114yes—
781C4⋊C4—22no—
782C4⋊C4—22no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—22no—
788C4⋊C4—22no—
789C4⋊C4—612no—
790C4⋊C4—612no—
791C4⋊C4—1222no—
792C4⋊C4—1222no—
793C4⋊C4—1222no—
794C4⋊C4—1222no—
795C4⋊C4—1222no—
796C4⋊C4—1222no—
797C4⋊C4—1222no—
798C4⋊C4—1222no—
799C4⋊C4—1222no—
800C4⋊C4—1222no—
801C4⋊C4—1222no—
802C4⋊C4—1222no—
803C4⋊C4—1222no—
804C4⋊C4—1222no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4C23×D6112yes—
810C4⋊C4C23×D6112yes—
811C4⋊C4C23×D6112yes—
812C4⋊C4C23×D6112yes—
813C22⋊C4—22no—
814C22⋊C4—22no—
815C22⋊C4—1222no—
816C22⋊C4—1222no—
817C22⋊C4—1222no—
818C22⋊C4—1222no—
819C22⋊C4—1222no—
820C22⋊C4—1222no—
821C22⋊C4—1222no—
822C22⋊C4—1222no—
823C22⋊C4—1222no—
824C22⋊C4—1222no—
825C22⋊C4—1222no—
826C42—22no—
827C42—22no—
828C42—611no—
829C42—611no—
830C42—611no—
831C42—611no—
832C42—611no—
833C42—611no—
834C42—611no—
835C42—611no—
836C42—611no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—1222no—
841C42—1222no—
842C42—1222no—
843C42—1222no—
844C42—1222no—
845C42D4×D6111yescharacteristic
846C42D4×D6111yescharacteristic
847C42C23×D6111yescharacteristic
848C42C23×D6111yescharacteristic
849C23—611no—
850C23—611no—
851C23—1222no—
852C23—1222no—
853C23—1222no—
854C23—2441no—
855C23C2×D4×D6111yescharacteristic
856Q8—42no—
857Q8—42no—
858Q8—42no—
859Q8—42no—
860Q8—1224no—
861Q8—2442no—
862Q8—2442no—
863Q8—2444no—
864Q8—2444no—
865D4—1224no—
866D4—2442no—
867D4—2442no—
868D4—2444no—
869D4—2444no—
870D4—2444no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—1222no—
887C2×C4—1222no—
888C2×C4—1222no—
889C2×C4—1222no—
890C2×C4—1222no—
891C2×C4—1222no—
892C2×C4—1222no—
893C2×C4—1222no—
894C2×C4—1222no—
895C2×C4—1222no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2444no—
901C2×C4—2444no—
902C2×C4—2444no—
903C2×C4—2444no—
904C2×C4—2441no—
905C2×C4—2444no—
906C2×C4C2×D4×D6111yescharacteristic
907C2×C4C2×D4×D6111yescharacteristic
908C2×C4C2×D4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4C2×D4×D6111yescharacteristic
911C2×C4#1451982514yes—
912C2×C4C24×D6111yescharacteristic
913C8—24no—
914C8—1224no—
915C22—21no—
916C22—21no—
917C22—612no—
918C22—1221no—
919C22—1221no—
920C22—1221no—
921C22—1221no—
922C22—1221no—
923C22—2444no—
924C22—2442no—
925C22—2442no—
926C22—2442no—
927C22#1684033712yes—
928C22C22×D4×D6111yescharacteristic
929C4—21no—
930C4—21no—
931C4—21no—
932C4—21no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—612no—
938C4—1221no—
939C4—1221no—
940C4—1221no—
941C4—1221no—
942C4—1221no—
943C4—2442no—
944C4—2442no—
945C4—2442no—
946C4#1684033712yes—
947C4C2×#1451982512yes—
948C2—22no—
949C2—1222no—
950C2—4882no—
951C2—2441no—
952C2C2×#1684033711yescharacteristic
953C2#575×D6111yescharacteristic
954C2#575×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3162C2
socleC22×C61C23×D4
prime radical#21459116C2
hypercenter#3162D61
hypocenterC61#60854
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
2. #533×D61C2semidirect
3. #21457062C2semidirect
4. #21457060C2semidirect
5. #21457050C2semidirect
6. #21457041C2semidirect
7. #21457034C2semidirect
8. #21457026C2semidirect
9. #21457018C2semidirect
10. #21457010C2semidirect
11. #21456341C2semidirect
12. #21456167C2semidirect
13. #21456165C2semidirect
14. #21455736C2semidirect
15. #21455605C2semidirect
16. C2×#16839817C2semidirect
17. C61×#3162C2semidirect
53. #16840172C22semidirect
54. #16840172C22semidirect
55. #16840168C22semidirect
56. #16840168C22semidirect
57. #16840132C22semidirect
58. #16840131C22semidirect
59. #16840128C22semidirect
60. #16840127C22semidirect
61. #16840124C22semidirect
62. #16840124C22semidirect
63. #16840122C22semidirect
64. #16840122C22semidirect
73. #16840072C22semidirect
74. #16840068C22semidirect
75. #16840065C22semidirect
76. #16840061C22semidirect
77. #16840056C22semidirect
78. #16840051C22semidirect
79. #16840046C22semidirect
80. #16840041C22semidirect
93. C61×#501C22semidirect
94. C61×#501C22semidirect
95. C61×#501C22semidirect
96. C61×#501C22semidirect
482. #3162D61semidirect
536. #501C2×D61semidirect
537. #501C2×D61semidirect
538. #501C2×D61semidirect
539. #501C2×D61semidirect
576. C61#60854semidirect

Maximal subgroups

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

subgroupindex
#214591162
#533×D612
#214570622
#214570602
#214570502
#214570412
#214570342
#214570262
#214570182
#214570102
#214563412
#214561672
#214561652
#214557362
#214556052
C2×#168398172
C61×#31622
#6085461