Finite Group Databasebeta

← #30548513

Subgroups — #30548513

Order 15616.

2002 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459208C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3#21456117C214yesmaximal, complemented
4#21456108C214yesmaximal, complemented
5#21456047C214yesmaximal, complemented
6#21456045C214yesmaximal, complemented
7#21455749C212yesmaximal, complemented
8#21455626C211yesmaximal, characteristic, complemented
9#21455624C211yesmaximal, characteristic, complemented
10#21455287C211yesmaximal, characteristic, complemented
11#21455051C212yesmaximal, complemented
12#21454643C212yesmaximal, complemented
13#137×Dic61C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3037C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×#14519807C2212yes—
18#16840381C2212yes—
19#16840381C2212yes—
20#16840373C2212yes—
21#16840366C2212yes—
22#16840357—21no—
23#16840357—21no—
24#16840349—21no—
25#16840349—21no—
26#16840319C2211yescharacteristic
27#16840292—22no—
28#16840292—22no—
29#16840269C2212yes—
30#16840238—22no—
31#16840238—22no—
32#16840238C2214yes—
33#16840238C2214yes—
34#41×Dic61C2212yes—
35C2×Q8×Dic61C2211yescharacteristic
36C2×C4×Dic122—21no—
37C2×C4×Dic122C2211yescharacteristic
38C2×#14519742—21no—
39C2×#14519742C2211yescharacteristic
40C2×#14519735—21no—
41C2×#14519735C2211yescharacteristic
42C2×#14519734—21no—
43C2×#14519734C2211yescharacteristic
44#16840102C2214yes—
45#16840101C2214yes—
46#16840085C2214yes—
47#16840084C2214yes—
48#16840070C2214yescomplemented
49#16840069C2214yescomplemented
50#16840058C2212yescomplemented
51#16840057C2212yescomplemented
52#16840048C2212yescomplemented
53#16840047C2212yescomplemented
54#16839981C2214yescomplemented
55#16839969C2212yescomplemented
56#16839959C2212yescomplemented
57#16839916C2214yes—
58#16839916C2214yes—
59#16839899C2214yes—
60#16839899C2214yes—
61#16839869C2214yescomplemented
62#16839866C2214yescomplemented
63#16839863C2214yescomplemented
64#16839859C2214yescomplemented
65Q16×Dic61C2214yescomplemented
66#16839854C2214yescomplemented
67#16839853C2214yescomplemented
68SD16×Dic61C2214yescomplemented
69#16839822C2214yes—
70#16839822C2214yes—
71#16839804C2212yes—
72#16839802C2212yes—
73#16839786C2211yescharacteristic
74#16839772C2212yes—
75#16839771C2212yes—
76#16839763C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C2×#137×C61C2212yes—
80C61×#532C2211yescharacteristic
81C2×C4×Q8×C61C2211yescharacteristic
82C61×#464C2214yescomplemented
83C61×#462C2212yescomplemented
84C61×#460C2212yescomplemented
85C61×#423C2211yescharacteristic
86C61×#417C2212yes—
87C22×Dic122—21no—
88C22×Dic122C2311yescharacteristic
89C2×Q8×D61—24no—
90C2×Q8×D61—22no—
91C2×Q8×D61—24no—
92C2×Q8×D61C2314yes—
93C22×C4×D61—21no—
94C22×C4×D61C2311yescharacteristic
95#14519807—28no—
96C2×#11758202C2314yes—
97C2×#11758200C2314yes—
98C2×#11758194C2312yes—
99#14519777C2311yescharacteristic
100#14519777C2311yescharacteristic
101#14519772—22no—
102#14519772—22no—
103#14519770—22no—
104#14519770—22no—
105#14519769C2312yes—
106#14519767—22no—
107#14519767—22no—
108#14519763—22no—
109#14519763—22no—
110#14519761—22no—
111#14519761—22no—
112#14519758—22no—
113#14519758—22no—
114#14519758—22no—
115#14519756—21no—
116#14519756—21no—
117#14519754—22no—
118#14519754—22no—
119#14519753C2312yes—
120#14519753C2312yes—
121#14519749—22no—
122#14519749—22no—
123#14519748C2312yes—
124#14519748C2312yes—
125#14519745—22no—
126Q8×Dic61—22no—
127Q8×Dic61C2314yes—
128Q8×Dic61C2312yes—
129Q8×Dic61C2312yes—
130C4×Dic122—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122—24no—
135C4×Dic122—24no—
136C4×Dic122C2312yes—
137C4×Dic122C2312yes—
138#14519742—24no—
139#14519742—24no—
140#14519742—22no—
141#14519742C2314yes—
142D4×Dic61—22no—
143D4×Dic61—22no—
144D4×Dic61C2312yes—
145D4×Dic61C2312yes—
146C4×C22⋊D61—22no—
147C4×C22⋊D61—22no—
148#14519736—22no—
149#14519736C2312yes—
150#14519735—22no—
151#14519735—24no—
152#14519735—24no—
153#14519735C2314yes—
154#14519734—24no—
155#14519734—24no—
156#14519734D412yes—
157#14519734D412yes—
158#14519734C2312yes—
159#14519734C2312yes—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61C2311yescharacteristic
162C2×#11758196—21no—
163C2×#11758196—21no—
164C2×#11758196D411yescharacteristic
165C2×#11758196D411yescharacteristic
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—22no—
174C2×C4×Dic61C2311yescharacteristic
175#14519711C2314yes—
176#14519710C2314yes—
177#14519709C2314yes—
178#14519708C2314yes—
179C4⋊#92418C2312yes—
180C4⋊#92418C2312yes—
181#14519702C2314yes—
182#14519702C2314yes—
183#14519701C2314yes—
184#14519701C2314yes—
185#14519701C2314yes—
186#14519698C2314yes—
187#14519689C2314yes—
188#14519689C2314yes—
189#14519687C2314yes—
190C8×Dic61C2314yes—
191C2×#41×C61C2312yes—
192C22×Q8×C61C2311yescharacteristic
193#137×C61—28no—
194C2×Q16×C61C2314yes—
195C2×SD16×C61C2314yes—
196C2×M16×C61C2312yes—
197C4⋊Q8×C61C2311yescharacteristic
198#127×C61C2311yescharacteristic
199#124×C61C2312yes—
200#121×C61—21no—
201#121×C61—21no—
202C4×Q8×C61—21no—
203C4×Q8×C61—21no—
204C4×Q8×C61C2312yes—
205C4×Q8×C61C2312yes—
206C4×D4×C61—21no—
207C4×D4×C61—21no—
208C2×C4⋊C4×C61—21no—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C42×C61—21no—
211C2×C42×C61C2311yescharacteristic
212C4⋊C8×C61C2312yes—
213C4⋊C8×C61C2312yes—
214#103×C61C2314yes—
215#102×C61C2314yes—
216C23×D61C2×D411yescharacteristic
217#41×C61—24no—
218#41×C61—24no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61#4114yes—
222C2×Q8×C61C2412yes—
223C2×Q8×C61C2412yes—
224C2×D4×C61—22no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61C2412yes—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—22no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—22no—
239C22×Dic61—22no—
240C22×Dic61C2×D411yescharacteristic
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243Q8×D61—216no—
244Q8×D61—28no—
245Q8×D61—28no—
246C2×C4×D61—28no—
247C2×C4×D61—24no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61C2×D412yes—
251C2×C4×D61C2412yes—
252C2×Dic122—28no—
253C2×Dic122—21no—
254C2×Dic122—22no—
255C2×Dic122—24no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122#4114yes—
259C2×Dic122C2412yes—
260Q16×C61—28no—
261SD16×C61—28no—
262M16×C61—24no—
263C2×C8×C61C2414yes—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C2412yes—
270C22⋊C4×C61—22no—
271C22⋊C4×C61—22no—
272C42×C61—22no—
273C42×C61—22no—
274C42×C61C2×D411yescharacteristic
275C42×C61C2×D411yescharacteristic
276C42×C61C2411yescharacteristic
277C42×C61C2411yescharacteristic
278C22⋊Dic61—22no—
279C22⋊Dic61—22no—
280C22⋊Dic61—22no—
281C22⋊Dic61—22no—
282C22⋊Dic61—22no—
283#11758202—28no—
284#11758200—28no—
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—24no—
316C4×Dic61—24no—
317C4×Dic61—24no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61C2×D412yes—
321C4×Dic61C2412yes—
322#11758194—24no—
323C2×#92418C2414yes—
324C23×C61—22no—
325C23×C61C22×D411yescharacteristic
326C22×D61—22no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61C22×D412yes—
330Q8×C61—24no—
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—22no—
334Q8×C61C2×#4114yes—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—44no—
338D4×C61—81no—
339D4×C61—81no—
340C2×C4×C61—24no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—42no—
347C2×C4×C61—44no—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4112yes—
354C2×C4×C61C2×#4112yes—
355C2×C4×C61C2511yescharacteristic
356C22⋊D61—82no—
357C22⋊D61—82no—
358C2×Dic61—22no—
359C2×Dic61—24no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—42no—
367C2×Dic61—82no—
368C2×Dic61—82no—
369C2×Dic61C22×D412yes—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372C4×D61—216no—
373C4×D61—24no—
374C4×D61—22no—
375C4×D61—22no—
376Dic122—216no—
377Dic122—24no—
378Dic122—22no—
379Dic122—81no—
380Dic122—81no—
381Dic122C2×#4114yes—
382C8×C61—24no—
383#92418—24no—
384#60566—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—42no—
390C22×C61#52512yes—
391C22×C61C23×D411yescharacteristic
392C2×D61—22no—
393C2×D61—22no—
394C2×D61—22no—
395C2×D61—44no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—24no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61#52512yes—
404C4×C61C22×#4111yescharacteristic
405C4×C61C22×#4111yescharacteristic
406Dic61—22no—
407Dic61—22no—
408Dic61—22no—
409Dic61—24no—
410Dic61—42no—
411Dic61—42no—
412Dic61—42no—
413#3455—611no—
414C2×#519—611no—
415#3127—614no—
416#3126—614no—
417#3121—614no—
418#3121—614no—
419#3093—612no—
420#3078—611no—
421#3078—611no—
422#3037—611no—
423#3037D6111yescharacteristic, complemented
424#3004—612no—
425C4×#137—612no—
426C4×#137—612no—
427#2921—611no—
428C2×C61—22no—
429C2×C61—82no—
430C2×C61C2×#52511yescharacteristic
431C2×C61#358611yescharacteristic
432C2×C61#358611yescharacteristic
433D61—42no—
434C23×Q8—611no—
435C2×#137—612no—
436C2×#137C2×D6112yes—
437#542—612no—
438#542—612no—
439#541—612no—
440#540—612no—
441#539—1221no—
442#539—1221no—
443#538—1221no—
444#538—1221no—
445#533—611no—
446#532C2×D6111yescharacteristic
447#529—1222no—
448#529—1222no—
449#525—612no—
450#519—614no—
451#519—614no—
452#519—1222no—
453#519—1222no—
454C4×#41—612no—
455C2×C4×Q8—611no—
456C2×C4×Q8—611no—
457C2×C4×Q8—611no—
458C2×C4×Q8—1221no—
459C2×C4×Q8—1221no—
460C2×C4×Q8C2×D6111yescharacteristic
461C2×#117—611no—
462C2×#117—611no—
463C2×#117—1221no—
464C2×#117—1221no—
465#485—614no—
466#485—614no—
467#482—614no—
468#482—614no—
469#479—614no—
470#479—614no—
471#477—612no—
472#477—612no—
473#475—612no—
474#475—612no—
475#464—614no—
476#464C2×D6114yescomplemented
477#462—612no—
478#462C2×D6112yescomplemented
479#460—612no—
480#460C2×D6112yescomplemented
481#451—614no—
482#451—614no—
483#448—614no—
484#448—614no—
485#441—614no—
486#441—614no—
487#440—614no—
488#440—614no—
489C4×Q16—614no—
490C4×Q16—614no—
491C4×SD16—614no—
492C4×SD16—614no—
493#433—614no—
494#433—614no—
495#428—612no—
496#428—612no—
497#423—611no—
498#423C2×D6111yescharacteristic
499#419—612no—
500#419—612no—
501#417—612no—
502#417C2×D6112yes—
503#407—612no—
504C4×M16—612no—
505C61#6056611yescharacteristic, complemented, Sylow
506C2×#41C22×D6112yes—
507C22×Q8—614no—
508C22×Q8—611no—
509C22×Q8—1221no—
510C22×Q8—1222no—
511C22×Q8—1224no—
512C22×Q8—1224no—
513C22×Q8C22×D6111yescharacteristic
514C23×C4—611no—
515C23×C4—1221no—
516#137—28no—
517#137—1228no—
518C2×Q16—614no—
519C2×Q16C22×D6114yes—
520C2×SD16—614no—
521C2×SD16C22×D6114yes—
522C2×M16—612no—
523C2×M16C22×D6112yes—
524C4⋊Q8—611no—
525C4⋊Q8—611no—
526C4⋊Q8C22×D6111yescharacteristic
527#127C22×D6111yescharacteristic
528#126—1222no—
529#126—1222no—
530#126—1222no—
531#126—1222no—
532#125—612no—
533#125—1222no—
534#125—1222no—
535#124—1222no—
536#124—1222no—
537#124C22×D6112yes—
538#123—1222no—
539#123—1222no—
540#123—1222no—
541#123—1222no—
542#123—1222no—
543C22⋊Q8—612no—
544C22⋊Q8—612no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549#121—21no—
550#121—21no—
551#121—612no—
552#121—612no—
553#121—1222no—
554#121—1222no—
555#120—1222no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—614no—
559C4×Q8—612no—
560C4×Q8—612no—
561C4×Q8—614no—
562C4×Q8—612no—
563C4×Q8—612no—
564C4×Q8—1224no—
565C4×Q8—1224no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×Q8—1224no—
569C4×Q8—1224no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8C22×D6112yes—
575C4×Q8C22×D6112yes—
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—612no—
579C4×D4—612no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584#117—612no—
585#117—612no—
586#117—612no—
587#117—612no—
588#117—612no—
589#117—614no—
590#117—1224no—
591#117—1224no—
592#117—1222no—
593#117—1224no—
594#117—1224no—
595#117—1222no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4C22×D6111yescharacteristic
604C2×C22⋊C4—611no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—1221no—
607C2×C42—21no—
608C2×C42—611no—
609C2×C42—1222no—
610C2×C42—1221no—
611C2×C42—1221no—
612C2×C42—1221no—
613C2×C42—1221no—
614C2×C42C22×D6111yescharacteristic
615#107—614no—
616#107—614no—
617#106—614no—
618#106—614no—
619C4⋊C8—612no—
620C4⋊C8—612no—
621C4⋊C8C22×D6112yes—
622C4⋊C8C22×D6112yes—
623#103—614no—
624#103—614no—
625#103—614no—
626#103—614no—
627#103—614no—
628#103C22×D6114yes—
629#102—614no—
630#102C22×D6114yes—
631C22⋊C8—614no—
632C22⋊C8—614no—
633#97—614no—
634C4×C8—614no—
635C24—611no—
636#41—24no—
637#41—24no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—614no—
641C2×Q8—612no—
642C2×Q8—1224no—
643C2×Q8—1228no—
644C2×Q8—1228no—
645C2×Q8—12216no—
646C2×Q8—1228no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1222no—
651C2×Q8#1175822414yes—
652C2×Q8C23×D6112yes—
653C2×Q8C23×D6112yes—
654C2×D4—22no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—1222no—
658C2×D4—1222no—
659C2×D4C23×D6112yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—612no—
667C22×C4—612no—
668C22×C4—1224no—
669C22×C4—1228no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1221no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1221no—
676C22×C4D4×D6111yescharacteristic
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679Q16—28no—
680Q16—1228no—
681SD16—28no—
682SD16—1228no—
683M16—24no—
684M16—1224no—
685C2×C8—614no—
686C2×C8C23×D6114yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—612no—
693C4⋊C4—612no—
694C4⋊C4—612no—
695C4⋊C4—612no—
696C4⋊C4—612no—
697C4⋊C4—612no—
698C4⋊C4—612no—
699C4⋊C4—1224no—
700C4⋊C4—1224no—
701C4⋊C4—1222no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1221no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4C23×D6112yes—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—612no—
716C22⋊C4—612no—
717C22⋊C4—612no—
718C22⋊C4—612no—
719C22⋊C4—1224no—
720C22⋊C4—1222no—
721C22⋊C4—1222no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C22⋊C4—1222no—
727C42—22no—
728C42—22no—
729C42—612no—
730C42—612no—
731C42—1224no—
732C42—1224no—
733C42—1224no—
734C42—1222no—
735C42—1222no—
736C42—1222no—
737C42—1222no—
738C42—1222no—
739C42D4×D6111yescharacteristic
740C42D4×D6111yescharacteristic
741C42C23×D6111yescharacteristic
742C42C23×D6111yescharacteristic
743C23—22no—
744C23—612no—
745C23—1222no—
746C23—2441no—
747C23—2441no—
748C23C2×D4×D6111yescharacteristic
749Q8—24no—
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—614no—
754Q8—12216no—
755Q8—1224no—
756Q8—1222no—
757Q8—4881no—
758Q8—4881no—
759Q8C2×#1175822414yes—
760D4—22no—
761D4—22no—
762D4—44no—
763D4—81no—
764D4—81no—
765D4—4882no—
766D4—4882no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—612no—
776C2×C4—612no—
777C2×C4—612no—
778C2×C4—12216no—
779C2×C4—1222no—
780C2×C4—1224no—
781C2×C4—1222no—
782C2×C4—1224no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—4882no—
789C2×C4—4882no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4C2×D4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C2×C4#41×D6112yes—
799C2×C4C2×#1175822412yes—
800C2×C4C24×D6111yescharacteristic
801C8—24no—
802C8—1224no—
803C22—21no—
804C22—21no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—1222no—
809C22—1222no—
810C22—1222no—
811C22—2444no—
812C22#1684027212yes—
813C22C22×D4×D6111yescharacteristic
814C4—24no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1224no—
823C4—1222no—
824C4—1222no—
825C4—2442no—
826C4—2442no—
827C4—2442no—
828C4#1684027212yes—
829C4C2×#41×D6111yescharacteristic
830C4C22×#1175822411yescharacteristic
831C2—22no—
832C2—82no—
833C2—2442no—
834C2C2×#1684027211yescharacteristic
835C2#2146060211yescharacteristic
836C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3037C2
socleC22×C61C23×D4
prime radical#21459208C2
hypercenter#3037D61
hypocenterC61#60566
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
2. C2×#16840238C2semidirect
3. #21456117C2semidirect
4. #21456108C2semidirect
5. #21456047C2semidirect
6. #21456045C2semidirect
7. #21455749C2semidirect
8. #21455626C2semidirect
9. #21455624C2semidirect
10. #21455287C2semidirect
11. #21455051C2semidirect
12. #21454643C2semidirect
13. #137×Dic61C2semidirect
14. #21454456C2semidirect
15. C61×#3037C2semidirect
48. #16840070C22semidirect
49. #16840069C22semidirect
50. #16840058C22semidirect
51. #16840057C22semidirect
52. #16840048C22semidirect
53. #16840047C22semidirect
54. #16839981C22semidirect
55. #16839969C22semidirect
56. #16839959C22semidirect
61. #16839869C22semidirect
62. #16839866C22semidirect
63. #16839863C22semidirect
64. #16839859C22semidirect
65. Q16×Dic61C22semidirect
66. #16839854C22semidirect
67. #16839853C22semidirect
68. SD16×Dic61C22semidirect
82. C61×#464C22semidirect
83. C61×#462C22semidirect
84. C61×#460C22semidirect
423. #3037D61semidirect
476. #464C2×D61semidirect
478. #462C2×D61semidirect
480. #460C2×D61semidirect
505. C61#60566semidirect

Maximal subgroups

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

subgroupindex
#214592082
C2×#168402382
#214561172
#214561082
#214560472
#214560452
#214557492
#214556262
#214556242
#214552872
#214550512
#214546432
#137×Dic612
#214544562
C61×#30372
#6056661