Finite Group Databasebeta

← #30548504

Subgroups — #30548504

Order 15616.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459209C211yesmaximal, characteristic, complemented
2C2×#16840242C211yesmaximal, characteristic, complemented
3#21456098C214yesmaximal, complemented
4#21456083C214yesmaximal, complemented
5#21456035C214yesmaximal, complemented
6#21456020C214yesmaximal, complemented
7#21455744C212yesmaximal, complemented
8#21455626C211yesmaximal, characteristic, complemented
9#21455618C211yesmaximal, characteristic, complemented
10#21455293C211yesmaximal, characteristic, complemented
11#21455285C211yesmaximal, characteristic, complemented
12#21455064C212yesmaximal, complemented
13C4×#14519810C212yesmaximal, complemented
14C4×#14519805C212yesmaximal, complemented
15C61×#2921C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519810C2212yes—
18C2×#14519805C2212yes—
19#16840383C2212yescomplemented
20#16840383C2212yescomplemented
21#16840374C2212yescomplemented
22#16840367C2212yescomplemented
23#16840359—21no—
24#16840359—21no—
25#16840350—21no—
26#16840350—21no—
27#16840319C2211yescharacteristic
28#16840312C2211yescharacteristic
29#16840290—22no—
30#16840290—22no—
31#16840273C2212yes—
32#16840242—22no—
33#16840242—22no—
34#16840242C2214yes—
35#16840242C2214yes—
36C4×#11758222C2212yes—
37C2×C4×Dic122C2211yescharacteristic
38C2×C4×Dic122C2211yescharacteristic
39C2×C4×D244C2211yescharacteristic
40C2×C4×D244C2211yescharacteristic
41C2×#14519737—21no—
42C2×#14519737—21no—
43C2×#14519735—21no—
44C22×C4⋊Dic61C2211yescharacteristic
45C2×C4⋊C4×D61—21no—
46#16840098C2214yescomplemented
47#16840093C2214yescomplemented
48#16840081C2214yescomplemented
49#16840076C2214yescomplemented
50#16840070C2214yescomplemented
51#16840063C2214yescomplemented
52#16840058C2212yescomplemented
53#16840053C2212yescomplemented
54#16840048C2212yescomplemented
55#16840043C2212yescomplemented
56#16839985C2214yescomplemented
57#16839978C2214yescomplemented
58#16839973C2212yescomplemented
59#16839968C2212yescomplemented
60#16839963C2212yescomplemented
61#16839958C2212yescomplemented
62#16839926C2214yes—
63#16839926C2214yes—
64#16839909C2214yes—
65#16839909C2214yes—
66#16839875C2214yescomplemented
67#16839870C2214yescomplemented
68#16839864C2214yescomplemented
69#16839864C2214yescomplemented
70C4×Dic244C2214yescomplemented
71C4×#11758190C2214yescomplemented
72C4×#11758190C2214yescomplemented
73C4×D488C2214yescomplemented
74#16839804C2212yes—
75#16839804C2212yes—
76#16839772C2212yes—
77#16839768C2212yes—
78#16839764C2212yes—
79#16839764C2212yes—
80C2×#117×C61C2211yescharacteristic
81C61×#433C2214yescomplemented
82C61×#433C2214yescomplemented
83C61×#423C2211yescharacteristic
84C61×#423C2211yescharacteristic
85C61×#407C2212yes—
86C4×M16×C61C2212yes—
87C2×#11758222—22no—
88C2×#11758222—24no—
89C2×#11758222—24no—
90C2×#11758222C2312yes—
91C2×#11758222C2314yes—
92C22×Dic122C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×C22⋊D61—21no—
95C23×Dic61—21no—
96C22×C4×D61—21no—
97C22×C4×D61—21no—
98C22×C4×D61—21no—
99#14519810—28no—
100#14519805—28no—
101C2×Dic244C2314yes—
102C2×#11758190C2314yes—
103C2×#11758190C2314yes—
104C2×D488C2314yes—
105#14519777C2311yescharacteristic
106#14519777C2311yescharacteristic
107#14519777C2311yescharacteristic
108#14519774C2311yescharacteristic
109#14519772—22no—
110#14519772—22no—
111#14519770—22no—
112#14519770—22no—
113#14519769C2312yes—
114#14519767—22no—
115#14519767—22no—
116#14519765C2312yes—
117#14519763—22no—
118#14519763—22no—
119#14519762—22no—
120#14519762—22no—
121#14519760—22no—
122#14519759—22no—
123#14519759—22no—
124#14519756—21no—
125#14519756—21no—
126#14519756C2312yes—
127#14519756C2312yes—
128#14519755—22no—
129#14519755—22no—
130#14519751—21no—
131#14519751—21no—
132#14519751C2312yes—
133#14519751C2312yes—
134#14519750—22no—
135#14519750—22no—
136#14519746—22no—
137C4×Dic122—22no—
138C4×Dic122—21no—
139C4×Dic122—21no—
140C4×Dic122—21no—
141C4×Dic122—21no—
142C4×Dic122C2312yes—
143C4×Dic122C2312yes—
144C4×Dic122C2314yes—
145C4×Dic122C2312yes—
146C4×Dic122C2312yes—
147C4×D244—22no—
148C4×D244—21no—
149C4×D244—21no—
150C4×D244—21no—
151C4×D244—21no—
152C4×D244C2312yes—
153C4×D244C2312yes—
154C4×D244C2314yes—
155C4×D244C2312yes—
156C4×D244C2312yes—
157C4×C22⋊D61—22no—
158C4×C22⋊D61—22no—
159C4×C22⋊D61—22no—
160C4×C22⋊D61—22no—
161#14519737—24no—
162#14519737—24no—
163#14519737—24no—
164#14519737—24no—
165#14519736C2312yes—
166#14519735—24no—
167#14519735—24no—
168#14519734—22no—
169C2×C4⋊Dic61—21no—
170C2×C4⋊Dic61—22no—
171C2×C4⋊Dic61C2311yescharacteristic
172C2×C4⋊Dic61C2311yescharacteristic
173C2×C4⋊Dic61C2314yes—
174C2×#11758196—21no—
175C2×#11758196—21no—
176C4⋊C4×D61—24no—
177C4⋊C4×D61—24no—
178C2×#11758198—21no—
179C2×#11758198—21no—
180C2×C4×Dic61—21no—
181C2×C4×Dic61—21no—
182C42×D61—22no—
183#14519711C2314yes—
184#14519711C2314yes—
185#14519709C2314yes—
186#14519709C2314yes—
187#14519702C2314yes—
188#14519702C2314yes—
189#14519702C2314yes—
190#14519702C2314yes—
191#14519699C2314yes—
192#14519699C2314yes—
193#14519699C2314yes—
194#14519699C2314yes—
195C23×C4×C61C2311yescharacteristic
196C2×M16×C61C2312yes—
197C2×M16×C61C2312yes—
198#117×C61D412yes—
199#117×C61D412yes—
200#117×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61D411yescharacteristic
203C2×C4⋊C4×C61D411yescharacteristic
204C2×C22⋊C4×C61D411yescharacteristic
205C2×C22⋊C4×C61D411yescharacteristic
206C2×C42×C61C2311yescharacteristic
207C2×C42×C61C2311yescharacteristic
208C4⋊C8×C61C2312yes—
209C4⋊C8×C61C2312yes—
210C4⋊C8×C61C2312yes—
211C4⋊C8×C61C2312yes—
212C22⋊C8×C61C2314yes—
213C22⋊C8×C61C2314yes—
214#97×C61C2314yes—
215C4×C8×C61C2314yes—
216C24×C61C2×D411yescharacteristic
217C23×D61—21no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D412yes—
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2412yes—
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—28no—
229C2×C22⋊D61—24no—
230C2×C22⋊D61—22no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—22no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—24no—
237C22×Dic61—82no—
238#11758222—216no—
239#11758222—28no—
240#11758222—24no—
241#11758222—24no—
242#11758222—28no—
243C2×D244—21no—
244C2×D244—22no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244#4114yes—
248C2×D244C2412yes—
249C2×D244C2412yes—
250C2×C4×D61—28no—
251C2×C4×D61—24no—
252C2×C4×D61—22no—
253C2×C4×D61—24no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×C4×D61—22no—
257C2×C4×D61—22no—
258C2×C4×D61—82no—
259C2×C4×D61—82no—
260C2×Dic122—21no—
261C2×Dic122—22no—
262C2×Dic122—21no—
263C2×Dic122—21no—
264C2×Dic122#4114yes—
265C2×Dic122C2412yes—
266C2×Dic122C2412yes—
267M16×C61—24no—
268M16×C61—24no—
269C2×C8×C61C2414yes—
270C2×C8×C61C2414yes—
271C4⋊C4×C61C2×D412yes—
272C4⋊C4×C61C2×D412yes—
273C4⋊C4×C61C2×D412yes—
274C4⋊C4×C61C2×D412yes—
275C22⋊C4×C61C2×D412yes—
276C22⋊C4×C61C2×D412yes—
277C22⋊C4×C61C2×D412yes—
278C22⋊C4×C61C2×D412yes—
279C42×C61C2×D412yes—
280C42×C61C2×D411yescharacteristic
281C42×C61C2×D411yescharacteristic
282C42×C61C2412yes—
283C42×C61C2411yescharacteristic
284C42×C61C2411yescharacteristic
285C22⋊Dic61—22no—
286C22⋊Dic61—22no—
287C22⋊Dic61—22no—
288#11758198—24no—
289#11758198—22no—
290#11758198—22no—
291#11758198—22no—
292#11758198—22no—
293#11758198—22no—
294#11758198—22no—
295#11758198—22no—
296#11758198—22no—
297C4⋊Dic61—24no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C2412yes—
305C4⋊Dic61C2412yes—
306C4⋊Dic61C2412yes—
307C4⋊Dic61C2412yes—
308#11758196—24no—
309#11758196—22no—
310#11758196—22no—
311#11758196—22no—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—22no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—24no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323Dic244—28no—
324D488—28no—
325#11758190—28no—
326#11758190—28no—
327C23×C61—22no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61C22×D412yes—
331C23×C61C22×D411yescharacteristic
332C22×D61—24no—
333C22×D61—22no—
334C22×D61—22no—
335C22×D61—42no—
336C22×D61—42no—
337C2×C4×C61—22no—
338C2×C4×C61—24no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61C22×D412yes—
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D412yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D412yes—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4112yes—
354C2×C4×C61C2×#4112yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—216no—
357C22⋊D61—44no—
358C22⋊D61—82no—
359C22⋊D61—82no—
360C2×Dic61—24no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61—84no—
370D244—24no—
371D244—22no—
372D244—22no—
373D244—22no—
374D244—81no—
375D244—81no—
376D244C2×#4114yes—
377C4×D61—216no—
378C4×D61—44no—
379C4×D61—82no—
380C4×D61—82no—
381C4×D61—82no—
382C4×D61—84no—
383C4×D61—82no—
384Dic122—24no—
385Dic122—22no—
386Dic122—22no—
387Dic122—22no—
388Dic122—81no—
389Dic122—81no—
390Dic122C2×#4114yes—
391C8×C61—24no—
392C8×C61—24no—
393#60565—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—44no—
400C22×C61#52512yes—
401C22×C61C23×D411yescharacteristic
402C2×D61—24no—
403C2×D61—48no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—42no—
409C4×C61—21no—
410C4×C61—22no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—22no—
414C4×C61—21no—
415C4×C61—22no—
416C4×C61#52512yes—
417C4×C61C22×#4111yescharacteristic
418C4×C61C22×#4111yescharacteristic
419Dic61—24no—
420Dic61—42no—
421Dic61—42no—
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425#3455—611no—
426C2×#520—611no—
427#3125—614no—
428#3124—614no—
429#3120—614no—
430#3119—614no—
431#3092—612no—
432#3078—611no—
433#3077—611no—
434#3037—611no—
435#3036—611no—
436#3005—612no—
437C4×#137—612no—
438C4×AGL(1,ℤ/8)—612no—
439#2921D6111yescharacteristic, complemented
440C2×C61—22no—
441C2×C61—42no—
442C2×C61C2×#52511yescharacteristic
443C2×C61#358511yescharacteristic
444C2×C61#358611yescharacteristic
445D61—44no—
446D61—82no—
447C22×#41—611no—
448C2×#137—612no—
449C2×AGL(1,ℤ/8)—612no—
450#542—612no—
451#542—612no—
452#541—612no—
453#540—612no—
454#539—1221no—
455#539—1221no—
456#538—1221no—
457#538—1221no—
458#533—611no—
459#532—611no—
460#529—1222no—
461#529—1222no—
462#525—612no—
463#520—614no—
464#520—614no—
465#520—1222no—
466#520—1222no—
467C4×#41—612no—
468C2×C4×Q8—611no—
469C2×C4×Q8—611no—
470C2×C4×D4—611no—
471C2×C4×D4—611no—
472C2×C4×D4—1221no—
473C2×C4×D4—1221no—
474C2×#117—1221no—
475C2×#117C2×D6111yescharacteristic
476C22×C4⋊C4—611no—
477C22×C4⋊C4—1221no—
478#484—614no—
479#483—614no—
480#481—614no—
481#480—614no—
482#479—614no—
483#478—614no—
484#477—612no—
485#476—612no—
486#475—612no—
487#474—612no—
488#464—614no—
489#463—614no—
490#462—612no—
491#461—612no—
492#460—612no—
493#459—612no—
494#452—614no—
495#452—614no—
496#449—614no—
497#449—614no—
498#442—614no—
499#441—614no—
500#440—614no—
501#440—614no—
502C4×Q16—614no—
503C4×SD16—614no—
504C4×SD16—614no—
505C4×D8—614no—
506#433C2×D6114yescomplemented
507#433C2×D6114yescomplemented
508#428—612no—
509#428—612no—
510#423C2×D6111yescharacteristic
511#423C2×D6111yescharacteristic
512#419—612no—
513#418—612no—
514#417—612no—
515#417—612no—
516#407C2×D6112yes—
517C4×M16C2×D6112yes—
518C61#6056511yescharacteristic, complemented, Sylow
519C2×#41—612no—
520C2×#41—614no—
521C2×#41—1224no—
522C2×#41—1224no—
523C2×#41—1222no—
524C22×Q8—611no—
525C22×D4—611no—
526C22×D4—1221no—
527C23×C4—1221no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532#137—1228no—
533AGL(1,ℤ/8)—1228no—
534C2×Q16—614no—
535C2×SD16—614no—
536C2×SD16—614no—
537C2×D8—614no—
538C2×M16C22×D6112yes—
539C2×M16C22×D6112yes—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—611no—
543#127—611no—
544#126—1222no—
545#126—1222no—
546#126—1222no—
547#126—1222no—
548#125—612no—
549#125—1222no—
550#125—1222no—
551#124—612no—
552#124—1222no—
553#124—1222no—
554#123—1222no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123—1222no—
559C22⋊Q8—612no—
560C22⋊Q8—612no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565#121—612no—
566#121—612no—
567#121—1221no—
568#121—1221no—
569#121—1222no—
570#121—1222no—
571#120—1222no—
572C4×Q8—614no—
573C4×Q8—612no—
574C4×Q8—612no—
575C4×Q8—612no—
576C4×Q8—612no—
577C4×Q8—1222no—
578C4×Q8—1221no—
579C4×Q8—1221no—
580C4×Q8—1221no—
581C4×Q8—1221no—
582C4×D4—614no—
583C4×D4—612no—
584C4×D4—612no—
585C4×D4—612no—
586C4×D4—612no—
587C4×D4—1222no—
588C4×D4—1222no—
589C4×D4—1222no—
590C4×D4—1222no—
591C4×D4—1224no—
592C4×D4—1224no—
593C4×D4—1224no—
594C4×D4—1224no—
595C4×D4—1222no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1221no—
599C4×D4—1221no—
600#117—612no—
601#117—1224no—
602#117—1224no—
603#117—1222no—
604#117D24412yes—
605#117D24412yes—
606#117C22×D6112yes—
607#117C22×D6112yes—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—611no—
610C2×C4⋊C4—614no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1224no—
616C2×C4⋊C4—1224no—
617C2×C4⋊C4D24411yescharacteristic
618C2×C4⋊C4D24411yescharacteristic
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4D24411yescharacteristic
622C2×C22⋊C4D24411yescharacteristic
623C2×C42—1221no—
624C2×C42—1221no—
625C2×C42—1222no—
626C2×C42C22×D6111yescharacteristic
627C2×C42C22×D6111yescharacteristic
628#107—614no—
629#107—614no—
630#106—614no—
631#106—614no—
632C4⋊C8C22×D6112yes—
633C4⋊C8C22×D6112yes—
634C4⋊C8C22×D6112yes—
635C4⋊C8C22×D6112yes—
636#103—614no—
637#103—614no—
638#103—614no—
639#103—614no—
640#102—614no—
641#102—614no—
642#102—614no—
643#102—614no—
644C22⋊C8C22×D6114yes—
645C22⋊C8C22×D6114yes—
646#97C22×D6114yes—
647C4×C8C22×D6114yes—
648C24—1221no—
649C24C2×D24411yescharacteristic
650#41—1228no—
651#41—1228no—
652#41—12216no—
653#41—1224no—
654#41—1224no—
655C2×Q8—614no—
656C2×Q8—612no—
657C2×Q8—612no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8—1221no—
661C2×Q8—1222no—
662C2×D4—614no—
663C2×D4—612no—
664C2×D4—612no—
665C2×D4—1228no—
666C2×D4—1224no—
667C2×D4—1222no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1221no—
673C2×D4—1222no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—1228no—
677C22×C4—1221no—
678C22×C4—1224no—
679C22×C4—1224no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1222no—
683C22×C4—1222no—
684C22×C4—1224no—
685C22×C4—1222no—
686C22×C4—1222no—
687C22×C4—1222no—
688C22×C4—4882no—
689C22×C4—4882no—
690C22×C4—4882no—
691C22×C4C2×D24411yescharacteristic
692C22×C4C2×D24412yes—
693C22×C4C2×D24411yescharacteristic
694C22×C4C2×D24411yescharacteristic
695C22×C4C2×D24411yescharacteristic
696C22×C4C2×D24411yescharacteristic
697C22×C4C23×D6112yes—
698C22×C4C23×D6111yescharacteristic
699Q16—1228no—
700SD16—1228no—
701SD16—1228no—
702D8—1228no—
703M16—24no—
704M16—24no—
705C2×C8C23×D6114yes—
706C2×C8C23×D6114yes—
707C4⋊C4—612no—
708C4⋊C4—612no—
709C4⋊C4—612no—
710C4⋊C4—612no—
711C4⋊C4—1224no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1224no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1222no—
722C4⋊C4—1222no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4C2×D24412yes—
728C4⋊C4C2×D24412yes—
729C4⋊C4C2×D24412yes—
730C4⋊C4C2×D24412yes—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4—1224no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C22⋊C4—1222no—
739C22⋊C4—1222no—
740C22⋊C4—1222no—
741C22⋊C4—1222no—
742C22⋊C4—1222no—
743C22⋊C4C2×D24412yes—
744C22⋊C4C2×D24412yes—
745C22⋊C4C2×D24412yes—
746C22⋊C4C2×D24412yes—
747C42—1222no—
748C42—1224no—
749C42—1222no—
750C42—1222no—
751C42—1222no—
752C42—1222no—
753C42C2×D24412yes—
754C42C2×D24411yescharacteristic
755C42C2×D24411yescharacteristic
756C42C23×D6112yes—
757C42C23×D6111yescharacteristic
758C42C23×D6111yescharacteristic
759C23—22no—
760C23—41no—
761C23—41no—
762C23—1224no—
763C23—1222no—
764C23—1222no—
765C23—2442no—
766C23—2442no—
767C23C22×D24412yes—
768C23C22×D24411yescharacteristic
769Q8—614no—
770Q8—1224no—
771Q8—1222no—
772Q8—1222no—
773Q8—1222no—
774Q8—4881no—
775Q8—4881no—
776D4—614no—
777D4—12216no—
778D4—1224no—
779D4—1222no—
780D4—1222no—
781D4—1222no—
782D4—4881no—
783D4—4881no—
784D4—4882no—
785D4—4882no—
786D4—2444no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—12216no—
796C2×C4—1224no—
797C2×C4—1222no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—4882no—
804C2×C4—4882no—
805C2×C4—4884no—
806C2×C4—4882no—
807C2×C4—4882no—
808C2×C4—4884no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2444no—
812C2×C4C22×D24412yes—
813C2×C4C22×D24411yescharacteristic
814C2×C4C22×D24411yescharacteristic
815C2×C4C22×D24412yes—
816C2×C4C22×D24411yescharacteristic
817C2×C4C22×D24411yescharacteristic
818C2×C4C22×D24412yes—
819C2×C4C22×D24411yescharacteristic
820C2×C4#41×D6112yes—
821C2×C4#41×D6112yes—
822C2×C4C24×D6111yescharacteristic
823C8—24no—
824C8—24no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—44no—
831C22—1224no—
832C22—2448no—
833C22—2442no—
834C22—2442no—
835C22—2442no—
836C22—2442no—
837C22—2442no—
838C22#1684027412yes—
839C22C23×D24411yescharacteristic
840C4—22no—
841C4—22no—
842C4—21no—
843C4—21no—
844C4—22no—
845C4—21no—
846C4—21no—
847C4—1224no—
848C4—2442no—
849C4—2442no—
850C4—2442no—
851C4—2442no—
852C4—2442no—
853C4#1684027412yes—
854C4C2×#41×D6111yescharacteristic
855C4C2×#41×D6111yescharacteristic
856C2—22no—
857C2—42no—
858C2—4882no—
859C2—2444no—
860C2C2×#1684027411yescharacteristic
861C2#2146060011yescharacteristic
862C2#2146060711yescharacteristic
subgroupG/H
centerC22C23×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#2921C2
socleC22×C61C23×D4
hypercenter#2921D61
hypocenterC61#60565
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2921

Complements

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

NH ≅ G/Ntype
1. #21459209C2semidirect
2. C2×#16840242C2semidirect
3. #21456098C2semidirect
4. #21456083C2semidirect
5. #21456035C2semidirect
6. #21456020C2semidirect
7. #21455744C2semidirect
8. #21455626C2semidirect
9. #21455618C2semidirect
10. #21455293C2semidirect
11. #21455285C2semidirect
12. #21455064C2semidirect
13. C4×#14519810C2semidirect
14. C4×#14519805C2semidirect
15. C61×#2921C2semidirect
19. #16840383C22semidirect
20. #16840383C22semidirect
21. #16840374C22semidirect
22. #16840367C22semidirect
46. #16840098C22semidirect
47. #16840093C22semidirect
48. #16840081C22semidirect
49. #16840076C22semidirect
50. #16840070C22semidirect
51. #16840063C22semidirect
52. #16840058C22semidirect
53. #16840053C22semidirect
54. #16840048C22semidirect
55. #16840043C22semidirect
56. #16839985C22semidirect
57. #16839978C22semidirect
58. #16839973C22semidirect
59. #16839968C22semidirect
60. #16839963C22semidirect
61. #16839958C22semidirect
66. #16839875C22semidirect
67. #16839870C22semidirect
68. #16839864C22semidirect
69. #16839864C22semidirect
70. C4×Dic244C22semidirect
71. C4×#11758190C22semidirect
72. C4×#11758190C22semidirect
73. C4×D488C22semidirect
81. C61×#433C22semidirect
82. C61×#433C22semidirect
439. #2921D61semidirect
506. #433C2×D61semidirect
507. #433C2×D61semidirect
518. C61#60565semidirect

Maximal subgroups

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

subgroupindex
#214592092
C2×#168402422
#214560982
#214560832
#214560352
#214560202
#214557442
#214556262
#214556182
#214552932
#214552852
#214550642
C4×#145198102
C4×#145198052
C61×#29212
#6056561