Finite Group Databasebeta

← #30548502

Subgroups — #30548502

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
2#21456096C214yesmaximal, complemented
3#21456081C214yesmaximal, complemented
4#21456033C214yesmaximal, complemented
5#21456018C214yesmaximal, complemented
6#21455742C212yesmaximal, complemented
7#21455624C211yesmaximal, characteristic, complemented
8#21455616C211yesmaximal, characteristic, complemented
9#21455291C211yesmaximal, characteristic, complemented
10#21455283C211yesmaximal, characteristic, complemented
11#21455061C212yesmaximal, complemented
12C4×#14519808C212yesmaximal, complemented
13C4×#14519803C212yesmaximal, complemented
14#21454457C211yesmaximal, characteristic, complemented
15C2×C61×#520C211yesmaximal, characteristic, complemented
16C2×#14519808C2212yes—
17C2×#14519803C2212yes—
18#16840383C2212yescomplemented
19#16840383C2212yescomplemented
20#16840374C2212yescomplemented
21#16840367C2212yescomplemented
22#16840359—21no—
23#16840359—21no—
24#16840350—21no—
25#16840350—21no—
26#16840319C2211yescharacteristic
27#16840312C2211yescharacteristic
28#16840290—22no—
29#16840290—22no—
30#16840273C2212yes—
31C4×#11758222C2212yes—
32#16840097C2214yescomplemented
33#16840092C2214yescomplemented
34#16840080C2214yescomplemented
35#16840075C2214yescomplemented
36#16840069C2214yescomplemented
37#16840062C2214yescomplemented
38#16840057C2212yescomplemented
39#16840052C2212yescomplemented
40#16840047C2212yescomplemented
41#16840042C2212yescomplemented
42#16839984C2214yescomplemented
43#16839977C2214yescomplemented
44#16839972C2212yescomplemented
45#16839967C2212yescomplemented
46#16839962C2212yescomplemented
47#16839957C2212yescomplemented
48#16839924C2214yes—
49#16839924C2214yes—
50#16839907C2214yes—
51#16839907C2214yes—
52#16839872C2214yescomplemented
53#16839867C2214yescomplemented
54#16839862C2214yescomplemented
55#16839860C2214yescomplemented
56C4×#11758202C2214yescomplemented
57C4×#11758201C2214yescomplemented
58C4×#11758200C2214yescomplemented
59C4×#11758199C2214yescomplemented
60#16839823C2214yescomplemented
61#16839823C2214yescomplemented
62#16839802C2212yes—
63#16839802C2212yes—
64#16839786C2211yescharacteristic
65#16839786C2211yescharacteristic
66#16839771C2212yes—
67#16839767C2212yes—
68#16839761C2212yes—
69#16839761C2212yes—
70#16839726C2212yes—
71C4×#11758194C2212yes—
72C22×#41×C61C2211yescharacteristic
73C61×#520—22no—
74C61×#520—22no—
75C61×#520C2214yes—
76C61×#520C2214yes—
77C2×C4×Q8×C61C2211yescharacteristic
78C2×C4×Q8×C61C2211yescharacteristic
79C2×C4×D4×C61—21no—
80C2×C4×D4×C61—21no—
81C2×C4×D4×C61C2211yescharacteristic
82C2×C4×D4×C61C2211yescharacteristic
83C2×#117×C61—21no—
84C2×#117×C61C2211yescharacteristic
85C22×C4⋊C4×C61—21no—
86C22×C4⋊C4×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88#14519808—28no—
89#14519803—28no—
90C2×#11758202C2314yes—
91C2×#11758200C2314yes—
92C2×#11758201C2314yes—
93C2×#11758199C2314yes—
94C2×#11758194C2312yes—
95C2×#11758194C2312yes—
96#14519777C2311yescharacteristic
97#14519777C2311yescharacteristic
98#14519777C2311yescharacteristic
99#14519774C2311yescharacteristic
100#14519772—22no—
101#14519772—22no—
102#14519770—22no—
103#14519770—22no—
104#14519769C2312yes—
105#14519767—22no—
106#14519767—22no—
107#14519765C2312yes—
108#14519763—22no—
109#14519763—22no—
110#14519762—22no—
111#14519762—22no—
112#14519760—22no—
113#14519759—22no—
114#14519759—22no—
115#14519756—21no—
116#14519756—21no—
117#14519756C2312yes—
118#14519756C2312yes—
119#14519755—22no—
120#14519755—22no—
121#14519751—21no—
122#14519751—21no—
123#14519751C2312yes—
124#14519751C2312yes—
125#14519750—22no—
126#14519750—22no—
127#14519746—22no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122C2312yes—
131C4×Dic122C2312yes—
132C4×D244—21no—
133C4×D244—21no—
134C4×D244C2312yes—
135C4×D244C2312yes—
136C4×C22⋊D61—22no—
137C4×C22⋊D61—22no—
138C4×C22⋊D61—22no—
139C4×C22⋊D61—22no—
140#14519736C2312yes—
141#14519734—22no—
142C42×D61—22no—
143#14519710C2314yes—
144#14519710C2314yes—
145#14519708C2314yes—
146#14519708C2314yes—
147C4⋊#92418C2312yes—
148C4⋊#92418C2312yes—
149C4⋊#92418C2312yes—
150C4⋊#92418C2312yes—
151#14519701C2314yes—
152#14519701C2314yes—
153#14519700C2314yes—
154#14519700C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519697C2314yes—
158#14519697C2314yes—
159C22⋊#92418C2314yes—
160C22⋊#92418C2314yes—
161#14519688C2314yes—
162C4×#92418C2314yes—
163C2×#41×C61—24no—
164C2×#41×C61—24no—
165C2×#41×C61—22no—
166C2×#41×C61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61—21no—
173C23×C4×C61—21no—
174C23×C4×C61C2311yescharacteristic
175C4×Q8×C61—22no—
176C4×Q8×C61—21no—
177C4×Q8×C61—21no—
178C4×Q8×C61C2312yes—
179C4×Q8×C61C2312yes—
180C4×Q8×C61C2314yes—
181C4×D4×C61—24no—
182C4×D4×C61—24no—
183C4×D4×C61—24no—
184C4×D4×C61—24no—
185C4×D4×C61—22no—
186C4×D4×C61—21no—
187C4×D4×C61—21no—
188C4×D4×C61C2312yes—
189C4×D4×C61C2312yes—
190C4×D4×C61C2314yes—
191#117×C61—24no—
192#117×C61—24no—
193#117×C61D412yes—
194#117×C61D412yes—
195#117×C61C2312yes—
196#117×C61C2312yes—
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61—21no—
199C2×C4⋊C4×C61—21no—
200C2×C4⋊C4×C61—22no—
201C2×C4⋊C4×C61—24no—
202C2×C4⋊C4×C61—24no—
203C2×C4⋊C4×C61D411yescharacteristic
204C2×C4⋊C4×C61D411yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C4⋊C4×C61C2311yescharacteristic
207C2×C4⋊C4×C61C2314yes—
208C2×C22⋊C4×C61—21no—
209C2×C22⋊C4×C61—21no—
210C2×C22⋊C4×C61D411yescharacteristic
211C2×C22⋊C4×C61D411yescharacteristic
212C2×C42×C61—21no—
213C2×C42×C61—21no—
214C2×C42×C61C2311yescharacteristic
215C2×C42×C61C2311yescharacteristic
216C24×C61—21no—
217C24×C61C2×D411yescharacteristic
218#41×C61—216no—
219#41×C61—28no—
220#41×C61—28no—
221C2×Q8×C61—21no—
222C2×Q8×C61—22no—
223C2×Q8×C61#4114yes—
224C2×Q8×C61C2412yes—
225C2×D4×C61—28no—
226C2×D4×C61—24no—
227C2×D4×C61—21no—
228C2×D4×C61—22no—
229C2×D4×C61#4114yes—
230C2×D4×C61C2412yes—
231C22×C4×C61—28no—
232C22×C4×C61—21no—
233C22×C4×C61—24no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—24no—
239C22×C4×C61—24no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—82no—
243C22×C4×C61—82no—
244C22×C4×C61—82no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2412yes—
252C22×C4×C61C2411yescharacteristic
253C2×C22⋊D61—22no—
254C2×C22⋊D61—22no—
255C2×C22⋊D61—22no—
256#11758222—24no—
257#11758222—24no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244C2412yes—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—22no—
264C2×Dic122—21no—
265C2×Dic122—21no—
266C2×Dic122C2412yes—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—22no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61C2×D412yes—
274C4⋊C4×C61C2×D412yes—
275C4⋊C4×C61C2×D412yes—
276C4⋊C4×C61C2×D412yes—
277C4⋊C4×C61C2412yes—
278C4⋊C4×C61C2412yes—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61C2×D412yes—
283C22⋊C4×C61C2×D412yes—
284C22⋊C4×C61C2×D412yes—
285C22⋊C4×C61C2×D412yes—
286C42×C61—24no—
287C42×C61—22no—
288C42×C61—22no—
289C42×C61C2×D412yes—
290C42×C61C2×D411yescharacteristic
291C42×C61C2×D411yescharacteristic
292C42×C61C2412yes—
293C42×C61C2411yescharacteristic
294C42×C61C2411yescharacteristic
295C22⋊Dic61—22no—
296C22⋊Dic61—22no—
297C22⋊Dic61—22no—
298#11758202—28no—
299#11758201—28no—
300#11758200—28no—
301#11758199—28no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305#11758198—22no—
306#11758198—22no—
307#11758198—22no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61C2412yes—
313C4⋊Dic61C2412yes—
314#11758196—22no—
315#11758196—22no—
316#11758196—22no—
317#11758196—22no—
318#11758196—22no—
319#11758196—22no—
320C4×Dic61—22no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323#11758194—24no—
324#11758194—24no—
325C2×#92418C2414yes—
326C2×#92418C2414yes—
327C23×C61—22no—
328C23×C61—24no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61C22×D412yes—
335C23×C61C22×D411yescharacteristic
336C22×D61—22no—
337Q8×C61—24no—
338Q8×C61—22no—
339Q8×C61C2×#4114yes—
340D4×C61—216no—
341D4×C61—24no—
342D4×C61—22no—
343D4×C61C2×#4114yes—
344C2×C4×C61—216no—
345C2×C4×C61—22no—
346C2×C4×C61—24no—
347C2×C4×C61—22no—
348C2×C4×C61—24no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61—82no—
360C2×C4×C61—84no—
361C2×C4×C61—82no—
362C2×C4×C61—84no—
363C2×C4×C61C22×D412yes—
364C2×C4×C61C22×D412yes—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D412yes—
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C2×#4112yes—
372C2×C4×C61C2×#4112yes—
373C2×C4×C61C2511yescharacteristic
374C22⋊D61—44no—
375C22⋊D61—82no—
376C22⋊D61—82no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380D244—22no—
381D244—22no—
382D244—81no—
383D244—81no—
384C4×D61—44no—
385C4×D61—82no—
386C4×D61—82no—
387Dic122—22no—
388Dic122—22no—
389Dic122—81no—
390Dic122—81no—
391#92418—24no—
392#92418—24no—
393#60565—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—24no—
400C22×C61—44no—
401C22×C61—48no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61#52512yes—
405C22×C61C23×D411yescharacteristic
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—24no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61#52512yes—
420C4×C61C22×#4111yescharacteristic
421C4×C61C22×#4111yescharacteristic
422Dic61—42no—
423Dic61—42no—
424Dic61—42no—
425#3455—611no—
426C2×#520D6111yescharacteristic, complemented
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#2921—611no—
440C2×C61—22no—
441C2×C61—42no—
442C2×C61—44no—
443C2×C61C2×#52511yescharacteristic
444C2×C61#358511yescharacteristic
445C2×C61#358611yescharacteristic
446D61—82no—
447C22×#41C2×D6111yescharacteristic
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—22no—
464#520—22no—
465#520C2×D6114yes—
466#520C2×D6114yes—
467C4×#41—612no—
468C2×C4×Q8C2×D6111yescharacteristic
469C2×C4×Q8C2×D6111yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4—21no—
472C2×C4×D4C2×D6111yescharacteristic
473C2×C4×D4C2×D6111yescharacteristic
474C2×#117—21no—
475C2×#117C2×D6111yescharacteristic
476C22×C4⋊C4—21no—
477C22×C4⋊C4C2×D6111yescharacteristic
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#433—614no—
507#433—614no—
508#428—612no—
509#428—612no—
510#423—611no—
511#423—611no—
512#419—612no—
513#418—612no—
514#417—612no—
515#417—612no—
516#407—612no—
517C4×M16—612no—
518C61#6056511yescharacteristic, complemented, Sylow
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—612no—
523C2×#41C22×D6114yes—
524C22×Q8C22×D6111yescharacteristic
525C22×D4—21no—
526C22×D4C22×D6111yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D6111yescharacteristic
532#137—1228no—
533AGL(1,ℤ/8)—1228no—
534C2×Q16—614no—
535C2×SD16—614no—
536C2×SD16—614no—
537C2×D8—614no—
538C2×M16—612no—
539C2×M16—612no—
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—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—612no—
576C4×Q8—612no—
577C4×Q8—1221no—
578C4×Q8—1221no—
579C4×Q8C22×D6114yes—
580C4×Q8C22×D6112yes—
581C4×Q8C22×D6112yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—612no—
590C4×D4—612no—
591C4×D4—1222no—
592C4×D4—1222no—
593C4×D4—1222no—
594C4×D4—1222no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4C22×D6114yes—
598C4×D4C22×D6112yes—
599C4×D4C22×D6112yes—
600#117—24no—
601#117—24no—
602#117—612no—
603#117—1222no—
604#117C22⋊D6112yes—
605#117C22⋊D6112yes—
606#117C22×D6112yes—
607#117C22×D6112yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D6111yescharacteristic
615C2×C4⋊C4C22⋊D6111yescharacteristic
616C2×C4⋊C4C22×D6111yescharacteristic
617C2×C4⋊C4C22×D6111yescharacteristic
618C2×C4⋊C4C22×D6114yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D6111yescharacteristic
622C2×C22⋊C4C22⋊D6111yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—1222no—
626C2×C42C22×D6111yescharacteristic
627C2×C42C22×D6111yescharacteristic
628#107—614no—
629#107—614no—
630#106—614no—
631#106—614no—
632C4⋊C8—612no—
633C4⋊C8—612no—
634C4⋊C8—612no—
635C4⋊C8—612no—
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⋊C8—614no—
645C22⋊C8—614no—
646#97—614no—
647C4×C8—614no—
648C24—21no—
649C24C2×C22⋊D6111yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—1224no—
654#41—1224no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—612no—
658C2×Q8—1221no—
659C2×Q8—1221no—
660C2×Q8#1175822214yes—
661C2×Q8C23×D6112yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—612no—
667C2×D4—1222no—
668C2×D4—1222no—
669C2×D4—1222no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4#1175822214yes—
673C2×D4C23×D6112yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—1222no—
689C22×C4—1222no—
690C22×C4—1222no—
691C22×C4C2×C22⋊D6111yescharacteristic
692C22×C4C2×C22⋊D6112yes—
693C22×C4C2×C22⋊D6111yescharacteristic
694C22×C4C2×C22⋊D6111yescharacteristic
695C22×C4C2×C22⋊D6111yescharacteristic
696C22×C4C2×C22⋊D6111yescharacteristic
697C22×C4C23×D6112yes—
698C22×C4C23×D6111yescharacteristic
699Q16—1228no—
700SD16—1228no—
701SD16—1228no—
702D8—1228no—
703M16—1224no—
704M16—1224no—
705C2×C8—614no—
706C2×C8—614no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—612no—
714C4⋊C4—612no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C4⋊C4—1222no—
720C4⋊C4—1222no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4C2×C22⋊D6112yes—
726C4⋊C4C2×C22⋊D6112yes—
727C4⋊C4C2×C22⋊D6112yes—
728C4⋊C4C2×C22⋊D6112yes—
729C4⋊C4C23×D6112yes—
730C4⋊C4C23×D6112yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—1222no—
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×C22⋊D6112yes—
744C22⋊C4C2×C22⋊D6112yes—
745C22⋊C4C2×C22⋊D6112yes—
746C22⋊C4C2×C22⋊D6112yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—1222no—
751C42—1222no—
752C42—1222no—
753C42C2×C22⋊D6112yes—
754C42C2×C22⋊D6111yescharacteristic
755C42C2×C22⋊D6111yescharacteristic
756C42C23×D6112yes—
757C42C23×D6111yescharacteristic
758C42C23×D6111yescharacteristic
759C23—22no—
760C23—24no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—1222no—
767C23C22×C22⋊D6112yes—
768C23C22×C22⋊D6111yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—1222no—
772Q8—1222no—
773Q8—4881no—
774Q8—4881no—
775Q8C2×#1175822214yes—
776D4—216no—
777D4—24no—
778D4—22no—
779D4—1222no—
780D4—1222no—
781D4—4881no—
782D4—4881no—
783D4—4882no—
784D4—4882no—
785D4—2444no—
786D4C2×#1175822214yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4882no—
810C2×C4—4882no—
811C2×C4—2444no—
812C2×C4C22×C22⋊D6112yes—
813C2×C4C22×C22⋊D6111yescharacteristic
814C2×C4C22×C22⋊D6111yescharacteristic
815C2×C4C22×C22⋊D6112yes—
816C2×C4C22×C22⋊D6111yescharacteristic
817C2×C4C22×C22⋊D6111yescharacteristic
818C2×C4C22×C22⋊D6112yes—
819C2×C4C22×C22⋊D6111yescharacteristic
820C2×C4C2×#1175822212yes—
821C2×C4C2×#1175822212yes—
822C2×C4C24×D6111yescharacteristic
823C8—1224no—
824C8—1224no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—2442no—
836C22—2442no—
837C22—2442no—
838C22#1684027312yes—
839C22C23×C22⋊D6111yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—2442no—
851C4—2442no—
852C4—2442no—
853C4#1684027312yes—
854C4C22×#1175822211yescharacteristic
855C4C22×#1175822211yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—4882no—
860C2C2×#1684027311yescharacteristic
861C2#2146059911yescharacteristic
862C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#520C2
socleC22×C61C23×D4
hypercenterC2×#520D61
hypocenterC61#60565
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #21459209C2semidirect
2. #21456096C2semidirect
3. #21456081C2semidirect
4. #21456033C2semidirect
5. #21456018C2semidirect
6. #21455742C2semidirect
7. #21455624C2semidirect
8. #21455616C2semidirect
9. #21455291C2semidirect
10. #21455283C2semidirect
11. #21455061C2semidirect
12. C4×#14519808C2semidirect
13. C4×#14519803C2semidirect
14. #21454457C2semidirect
15. C2×C61×#520C2semidirect
18. #16840383C22semidirect
19. #16840383C22semidirect
20. #16840374C22semidirect
21. #16840367C22semidirect
32. #16840097C22semidirect
33. #16840092C22semidirect
34. #16840080C22semidirect
35. #16840075C22semidirect
36. #16840069C22semidirect
37. #16840062C22semidirect
38. #16840057C22semidirect
39. #16840052C22semidirect
40. #16840047C22semidirect
41. #16840042C22semidirect
42. #16839984C22semidirect
43. #16839977C22semidirect
44. #16839972C22semidirect
45. #16839967C22semidirect
46. #16839962C22semidirect
47. #16839957C22semidirect
52. #16839872C22semidirect
53. #16839867C22semidirect
54. #16839862C22semidirect
55. #16839860C22semidirect
56. C4×#11758202C22semidirect
57. C4×#11758201C22semidirect
58. C4×#11758200C22semidirect
59. C4×#11758199C22semidirect
60. #16839823C22semidirect
61. #16839823C22semidirect
426. C2×#520D61semidirect
518. C61#60565semidirect

Maximal subgroups

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

subgroupindex
#214592092
#214560962
#214560812
#214560332
#214560182
#214557422
#214556242
#214556162
#214552912
#214552832
#214550612
C4×#145198082
C4×#145198032
#214544572
C2×C61×#5202
#6056561