Finite Group Databasebeta

← #30553054

Subgroups — #30553054

Order 15616.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459208C211yesmaximal, characteristic, complemented
2C2×#16840377C211yesmaximal, characteristic, complemented
3#21457286C214yesmaximal, complemented
4#21457277C214yesmaximal, complemented
5#21457241C214yesmaximal, complemented
6#21457226C214yesmaximal, complemented
7#21455630C212yesmaximal, complemented
8#21455626C211yesmaximal, characteristic, complemented
9#21455616C211yesmaximal, characteristic, complemented
10#21455452C212yesmaximal, complemented
11#21455432C212yesmaximal, complemented
12#21455311C212yesmaximal, complemented
13#21455287C211yesmaximal, characteristic, complemented
14#21454381C211yesmaximal, characteristic, complemented
15C61×#3036C211yesmaximal, characteristic, complemented
16C2×#14519807C2212yes—
17C2×M16×D61C2212yes—
18#16840381C2212yescomplemented
19#16840381C2212yescomplemented
20#16840377—22no—
21#16840377—22no—
22#16840377C2214yes—
23#16840377C2214yes—
24#16840373C2212yescomplemented
25#16840366C2212yescomplemented
26#16840357—21no—
27#16840357—21no—
28#16840349—21no—
29#16840349—21no—
30#16840319C2211yescharacteristic
31C2×#14519776C2211yescharacteristic
32#16840292—22no—
33#16840292—22no—
34C2×#14519770—21no—
35C2×#14519764C2211yescharacteristic
36C2×#14519763—21no—
37#16840269C2212yes—
38C2×#14519760—21no—
39C2×#14519757C2211yescharacteristic
40C2×#14519756—21no—
41C2×#14519748C2211yescharacteristic
42#41×Dic61C2212yes—
43C2×C4×Dic122C2211yescharacteristic
44C2×#14519734C2211yescharacteristic
45#16840070C2214yescomplemented
46#16840062C2214yescomplemented
47#16840058C2212yescomplemented
48#16840055C2214yescomplemented
49#16840052C2212yescomplemented
50#16840050C2214yescomplemented
51#16840048C2212yescomplemented
52#16840045C2214yescomplemented
53#16840042C2212yescomplemented
54#16840040C2214yescomplemented
55#16840019C2214yescomplemented
56#16840012C2214yes—
57#16840007C2214yescomplemented
58#16840005C2214yes—
59#16840002C2214yescomplemented
60#16839995C2214yes—
61#16839990C2214yescomplemented
62#16839988C2214yes—
63#16839982C2214yescomplemented
64#16839982C2214yescomplemented
65#16839981C2214yescomplemented
66#16839975C2214yescomplemented
67#16839975C2214yescomplemented
68#16839969C2212yescomplemented
69#16839959C2212yescomplemented
70#16839804C2212yes—
71#16839802C2212yes—
72#16839787C2214yescomplemented
73#16839787C2214yescomplemented
74#16839786C2211yescharacteristic
75#16839785C2212yes—
76#16839772C2212yes—
77#16839767C2212yes—
78#16839763C2212yes—
79C2×AGL(1,ℤ/8)×C61C2212yes—
80C61×#532C2211yescharacteristic
81C2×C4×D4×C61C2211yescharacteristic
82C61×#463C2214yescomplemented
83C61×#461C2212yescomplemented
84C61×#459C2212yescomplemented
85C61×#423C2211yescharacteristic
86C61×#417C2212yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C22×C22⋊D61—21no—
90C22×C4×D61C2311yescharacteristic
91#14519807—44no—
92C2×#11758202C2314yes—
93C2×#11758200C2314yes—
94C2×#11758194C2312yes—
95C2×#11758189C2314yes—
96M16×D61—44no—
97C2×C8×D61C2314yes—
98#14519777C2311yescharacteristic
99#14519777C2311yescharacteristic
100#14519776—22no—
101#14519776C2314yes—
102#14519772—22no—
103#14519772—22no—
104#14519770—24no—
105#14519770—24no—
106#14519770—22no—
107#14519770—22no—
108#14519769C2312yes—
109#14519767—22no—
110#14519767—22no—
111#14519764—22no—
112#14519764C2314yes—
113#14519763—24no—
114#14519763—24no—
115#14519763—22no—
116#14519763—22no—
117#14519761—22no—
118#14519761—22no—
119#14519760—24no—
120#14519760—24no—
121#14519758—22no—
122#14519758—22no—
123#14519758—22no—
124#14519757—22no—
125#14519757C2314yes—
126#14519756—21no—
127#14519756—21no—
128#14519756—24no—
129#14519756—24no—
130#14519754—22no—
131#14519754—22no—
132#14519753C2312yes—
133#14519753C2312yes—
134#14519749—22no—
135#14519749—22no—
136#14519748—22no—
137#14519748C2314yes—
138#14519748C2312yes—
139#14519748C2312yes—
140#14519745—22no—
141Q8×Dic61C2312yes—
142Q8×Dic61C2312yes—
143C4×Dic122—21no—
144C4×Dic122—21no—
145C4×Dic122—21no—
146C4×Dic122—21no—
147C4×Dic122C2312yes—
148C4×Dic122C2312yes—
149D4×Dic61—22no—
150D4×Dic61—22no—
151D4×Dic61C2312yes—
152D4×Dic61C2312yes—
153C4×C22⋊D61—22no—
154C4×C22⋊D61—22no—
155#14519736—22no—
156#14519736C2312yes—
157#14519734D412yes—
158#14519734D412yes—
159#14519734C2312yes—
160#14519734C2312yes—
161C2×C4⋊Dic61—21no—
162C2×C4⋊Dic61C2311yescharacteristic
163C2×#11758196—21no—
164C2×#11758196—21no—
165C2×#11758196D411yescharacteristic
166C2×#11758196D411yescharacteristic
167C2×C22⋊Dic61—21no—
168C2×C22⋊Dic61—21no—
169C2×C22⋊Dic61—21no—
170C2×#11758198—21no—
171C2×#11758198D411yescharacteristic
172C2×#11758198D411yescharacteristic
173C2×C4×Dic61—21no—
174C2×C4×Dic61—22no—
175C2×C4×Dic61C2311yescharacteristic
176#14519711C2314yes—
177#14519710C2314yes—
178#14519709C2314yes—
179#14519708C2314yes—
180C4⋊#92418C2312yes—
181C4⋊#92418C2312yes—
182#14519706C2314yes—
183#14519706C2314yes—
184#14519702C2314yes—
185#14519702C2314yes—
186#14519701C2314yes—
187#14519698C2314yes—
188#14519698C2314yes—
189#14519698C2314yes—
190C2×#41×C61C2312yes—
191C22×D4×C61C2311yescharacteristic
192C23×C4×C61—21no—
193AGL(1,ℤ/8)×C61—44no—
194C2×SD16×C61C2314yes—
195C2×D8×C61C2314yes—
196C2×M16×C61C2312yes—
197C4⋊Q8×C61C2311yescharacteristic
198#127×C61C2311yescharacteristic
199#124×C61C2312yes—
200#121×C61—21no—
201#121×C61—21no—
202C4×D4×C61—21no—
203C4×D4×C61—21no—
204C4×D4×C61—21no—
205C4×D4×C61—21no—
206C4×D4×C61C2312yes—
207C4×D4×C61C2312yes—
208C2×C4⋊C4×C61C2311yescharacteristic
209C2×C22⋊C4×C61—21no—
210C2×C42×C61C2311yescharacteristic
211C4⋊C8×C61C2312yes—
212C4⋊C8×C61C2312yes—
213#103×C61C2314yes—
214#102×C61C2314yes—
215C24×C61—21no—
216C23×D61C2×D411yescharacteristic
217#41×C61—24no—
218#41×C61—24no—
219C2×Q8×C61C2412yes—
220C2×D4×C61—22no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—22no—
225C2×D4×C61—22no—
226C2×D4×C61C2412yes—
227C2×D4×C61C2412yes—
228C22×C4×C61—21no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—82no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2411yescharacteristic
236C2×C22⋊D61—24no—
237C2×C22⋊D61—22no—
238C2×C22⋊D61—22no—
239C2×C22⋊D61—82no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—22no—
243C22×Dic61—22no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2412yes—
251C2×Dic122—22no—
252C2×Dic122—22no—
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—24no—
257C2×Dic122—82no—
258C2×Dic122C2412yes—
259SD16×C61—44no—
260D8×C61—44no—
261M16×C61—24no—
262C2×C8×C61C2414yes—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61C2412yes—
267C22⋊C4×C61—22no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—22no—
270C22⋊C4×C61—22no—
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274C42×C61C2411yescharacteristic
275C22⋊Dic61—22no—
276C22⋊Dic61—24no—
277C22⋊Dic61—24no—
278C22⋊Dic61—24no—
279C22⋊Dic61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283#11758202—44no—
284#11758200—44no—
285#11758198—24no—
286#11758198—22no—
287#11758198—22no—
288#11758198C2×D412yes—
289#11758198C2×D412yes—
290#11758198C2×D412yes—
291#11758198C2×D412yes—
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—24no—
296C4⋊Dic61—22no—
297C4⋊Dic61—22no—
298C4⋊Dic61C2412yes—
299C4⋊Dic61C2412yes—
300C4⋊Dic61C2412yes—
301#11758196—22no—
302#11758196—22no—
303#11758196—22no—
304#11758196—22no—
305#11758196—24no—
306#11758196—22no—
307#11758196—22no—
308#11758196C2×D412yes—
309#11758196C2×D412yes—
310#11758196C2×D412yes—
311#11758196C2×D412yes—
312C4×Dic61—22no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317C4×Dic61C2×D412yes—
318C4×Dic61C2412yes—
319#11758194—24no—
320C2×#92418C2414yes—
321#11758189—44no—
322C8×D61—44no—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—42no—
326C23×C61—42no—
327C23×C61—42no—
328C23×C61C22×D411yescharacteristic
329C22×D61—22no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61C22×D412yes—
333Q8×C61—22no—
334Q8×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—44no—
340D4×C61—42no—
341D4×C61—81no—
342D4×C61—81no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—42no—
348C2×C4×C61—44no—
349C2×C4×C61—82no—
350C2×C4×C61—82no—
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61H(5,𝔽2)12yes—
357C2×C4×C612−1+412yes—
358C2×C4×C61C2511yescharacteristic
359C22⋊D61—82no—
360C22⋊D61—82no—
361C22⋊D61—84no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—22no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—42no—
370C2×Dic61—42no—
371C2×Dic61—82no—
372C2×Dic61—82no—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376C4×D61—24no—
377C4×D61—22no—
378C4×D61—22no—
379Dic122—22no—
380Dic122—22no—
381Dic122—42no—
382Dic122—84no—
383Dic122—81no—
384Dic122—81no—
385C8×C61—24no—
386#92418—24no—
387#60919—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—84no—
397C22×C61#53712yes—
398C22×C61C23×D411yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—82no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61#53712yes—
410C4×C61C2×H(5,𝔽2)11yescharacteristic
411C4×C61C2×2−1+411yescharacteristic
412Dic61—22no—
413Dic61—22no—
414Dic61—22no—
415Dic61—42no—
416Dic61—42no—
417Dic61—42no—
418Dic61—42no—
419#3455—611no—
420C2×#542—611no—
421#3263—614no—
422#3262—614no—
423#3258—614no—
424#3257—614no—
425#3079—612no—
426#3078—611no—
427#3077—611no—
428#3056—612no—
429#3055—612no—
430#3040—612no—
431#3037—611no—
432#3036D6111yescharacteristic, complemented
433#2905—611no—
434C2×C61—22no—
435C2×C61—82no—
436C2×C61—82no—
437C2×C61C2×#53711yescharacteristic
438C2×C61#358511yescharacteristic
439C2×C61#358611yescharacteristic
440D61—42no—
441C2×#137—612no—
442C2×AGL(1,ℤ/8)C2×D6112yes—
443C22×M16—612no—
444#542—612no—
445#542—612no—
446#542—614no—
447#542—614no—
448#542—1222no—
449#542—1222no—
450#541—612no—
451#540—612no—
452#539—1221no—
453#539—1221no—
454#538—1221no—
455#538—1221no—
456#533—611no—
457#532C2×D6111yescharacteristic
458C2×C4⋊Q8—611no—
459#529—1222no—
460#529—1222no—
461C2×#126—1221no—
462C2×#124—611no—
463C2×#124—1221no—
464#525—612no—
465C2×#123—1221no—
466C2×C22⋊Q8—611no—
467C2×C22⋊Q8—1221no—
468C2×#121—611no—
469C4×#41—612no—
470C2×C4×Q8—611no—
471C2×C4×D4C2×D6111yescharacteristic
472C2×#117—611no—
473#479—614no—
474#478—614no—
475#477—612no—
476#477—614no—
477#476—612no—
478#476—614no—
479#475—612no—
480#475—614no—
481#474—612no—
482#474—614no—
483#470—614no—
484#469—614no—
485#468—614no—
486#468—614no—
487#467—614no—
488#466—614no—
489#465—614no—
490#465—614no—
491#464—614no—
492#464—614no—
493#464—614no—
494#463—614no—
495#463—614no—
496#463C2×D6114yescomplemented
497#462—612no—
498#461C2×D6112yescomplemented
499#460—612no—
500#459C2×D6112yescomplemented
501#428—612no—
502#428—612no—
503#424—614no—
504#424—614no—
505#423—612no—
506#423—611no—
507#423C2×D6111yescharacteristic
508#419—612no—
509#418—612no—
510#417—612no—
511#417C2×D6112yes—
512C61#6091911yescharacteristic, complemented, Sylow
513C2×#41C22×D6112yes—
514C22×Q8—611no—
515C22×Q8—1221no—
516C22×D4—1221no—
517C22×D4C22×D6111yescharacteristic
518C23×C4—21no—
519C23×C4—611no—
520#137—2444no—
521AGL(1,ℤ/8)—44no—
522C2×Q16—614no—
523C2×SD16—614no—
524C2×SD16C22×D6114yes—
525C2×D8C22×D6114yes—
526C2×M16—612no—
527C2×M16—614no—
528C2×M16—2444no—
529C2×M16C22×D6112yes—
530C22×C8—614no—
531C4⋊Q8—614no—
532C4⋊Q8—611no—
533C4⋊Q8—611no—
534C4⋊Q8—1222no—
535C4⋊Q8C22×D6111yescharacteristic
536#127C22×D6111yescharacteristic
537#126—1224no—
538#126—1224no—
539#126—1222no—
540#126—1222no—
541#126—1222no—
542#126—1222no—
543#125—612no—
544#125—1222no—
545#125—1222no—
546#124—614no—
547#124—1222no—
548#124—1224no—
549#124—1224no—
550#124—1222no—
551#124—1222no—
552#124C22×D6112yes—
553#123—1222no—
554#123—1222no—
555#123—1224no—
556#123—1224no—
557#123—1222no—
558#123—1222no—
559#123—1222no—
560C22⋊Q8—612no—
561C22⋊Q8—612no—
562C22⋊Q8—614no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1222no—
566C22⋊Q8—1224no—
567C22⋊Q8—1224no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570#121—21no—
571#121—21no—
572#121—614no—
573#121—612no—
574#121—612no—
575#121—1222no—
576#121—1222no—
577#121—1222no—
578#120—1222no—
579C4×Q8—612no—
580C4×Q8—612no—
581C4×Q8—612no—
582C4×Q8—612no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—612no—
592C4×D4—612no—
593C4×D4—1222no—
594C4×D4—1222no—
595C4×D4—1222no—
596C4×D4—1222no—
597C4×D4C22×D6112yes—
598C4×D4C22×D6112yes—
599#117—612no—
600#117—612no—
601#117—612no—
602#117—612no—
603#117—612no—
604#117—1222no—
605C2×C4⋊C4—611no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—1221no—
609C2×C4⋊C4—1221no—
610C2×C4⋊C4—1221no—
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—611no—
614C2×C22⋊C4—611no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C22⋊C4—1221no—
618C2×C22⋊C4—1221no—
619C2×C42—611no—
620C2×C42—1222no—
621C2×C42—1221no—
622C2×C42C22×D6111yescharacteristic
623#107—614no—
624#107—614no—
625#106—614no—
626#106—614no—
627C4⋊C8—614no—
628C4⋊C8—614no—
629C4⋊C8—612no—
630C4⋊C8—612no—
631C4⋊C8C22×D6112yes—
632C4⋊C8C22×D6112yes—
633#103—614no—
634#103—614no—
635#103—614no—
636#103C22×D6114yes—
637#102—614no—
638#102—614no—
639#102—614no—
640#102C22×D6114yes—
641C24—21no—
642C24—611no—
643#41—24no—
644#41—24no—
645C2×Q8—612no—
646C2×Q8—1224no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1222no—
651C2×Q8—1222no—
652C2×Q8—4882no—
653C2×Q8C23×D6112yes—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1224no—
663C2×D4—4882no—
664C2×D4C23×D6112yes—
665C2×D4C23×D6112yes—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—82no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—612no—
675C22×C4—612no—
676C22×C4—1222no—
677C22×C4—1222no—
678C22×C4—1222no—
679C22×C4—1222no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685Q16—2444no—
686SD16—44no—
687SD16—2444no—
688D8—44no—
689M16—24no—
690M16—1224no—
691M16—2444no—
692C2×C8—614no—
693C2×C8—2444no—
694C2×C8C23×D6114yes—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—612no—
699C4⋊C4—612no—
700C4⋊C4—612no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—612no—
704C4⋊C4—612no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1221no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4C23×D6112yes—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—612no—
724C22⋊C4—612no—
725C22⋊C4—612no—
726C22⋊C4—612no—
727C22⋊C4—1224no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C22⋊C4—1224no—
731C22⋊C4—1224no—
732C22⋊C4—1224no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1222no—
737C22⋊C4—1222no—
738C42—612no—
739C42—612no—
740C42—1222no—
741C42—1222no—
742C42—1222no—
743C42—1222no—
744C42—1222no—
745C42D4×D6111yescharacteristic
746C42D4×D6111yescharacteristic
747C42C23×D6111yescharacteristic
748C42C23×D6111yescharacteristic
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—612no—
755C23—1222no—
756C23—2441no—
757C23—2441no—
758C23C2×D4×D6111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—1222no—
762Q8—1222no—
763Q8—4881no—
764Q8—4881no—
765Q8—4884no—
766Q8—2442no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—42no—
773D4—81no—
774D4—81no—
775D4—4882no—
776D4—4882no—
777D4—4884no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4—612no—
787C2×C4—612no—
788C2×C4—612no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1224no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—4882no—
798C2×C4—4882no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×D4×D6111yescharacteristic
808C2×C4#1451982212yes—
809C2×C4#1451982412yes—
810C2×C4C24×D6111yescharacteristic
811C8—24no—
812C8—1224no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—84no—
822C22—1222no—
823C22—1222no—
824C22—1222no—
825C22—4882no—
826C22#1684034112yes—
827C22C22×D4×D6111yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—42no—
833C4—42no—
834C4—1222no—
835C4—1222no—
836C4—1222no—
837C4—2442no—
838C4—2442no—
839C4—2442no—
840C4—2442no—
841C4#1684034112yes—
842C4C2×#1451982211yescharacteristic
843C4C2×#1451982411yescharacteristic
844C2—22no—
845C2—82no—
846C2—82no—
847C2—2442no—
848C2C2×#1684034111yescharacteristic
849C2#2146059511yescharacteristic
850C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3036C2
socleC22×C61C23×D4
hypercenter#3036D61
hypocenterC61#60919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #21459208C2semidirect
2. C2×#16840377C2semidirect
3. #21457286C2semidirect
4. #21457277C2semidirect
5. #21457241C2semidirect
6. #21457226C2semidirect
7. #21455630C2semidirect
8. #21455626C2semidirect
9. #21455616C2semidirect
10. #21455452C2semidirect
11. #21455432C2semidirect
12. #21455311C2semidirect
13. #21455287C2semidirect
14. #21454381C2semidirect
15. C61×#3036C2semidirect
18. #16840381C22semidirect
19. #16840381C22semidirect
24. #16840373C22semidirect
25. #16840366C22semidirect
45. #16840070C22semidirect
46. #16840062C22semidirect
47. #16840058C22semidirect
48. #16840055C22semidirect
49. #16840052C22semidirect
50. #16840050C22semidirect
51. #16840048C22semidirect
52. #16840045C22semidirect
53. #16840042C22semidirect
54. #16840040C22semidirect
55. #16840019C22semidirect
57. #16840007C22semidirect
59. #16840002C22semidirect
61. #16839990C22semidirect
63. #16839982C22semidirect
64. #16839982C22semidirect
65. #16839981C22semidirect
66. #16839975C22semidirect
67. #16839975C22semidirect
68. #16839969C22semidirect
69. #16839959C22semidirect
72. #16839787C22semidirect
73. #16839787C22semidirect
82. C61×#463C22semidirect
83. C61×#461C22semidirect
84. C61×#459C22semidirect
432. #3036D61semidirect
496. #463C2×D61semidirect
498. #461C2×D61semidirect
500. #459C2×D61semidirect
512. C61#60919semidirect

Maximal subgroups

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

subgroupindex
#214592082
C2×#168403772
#214572862
#214572772
#214572412
#214572262
#214556302
#214556262
#214556162
#214554522
#214554322
#214553112
#214552872
#214543812
C61×#30362
#6091961