Finite Group Databasebeta

← #30548517

Subgroups — #30548517

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#21459211C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3#21456121C214yesmaximal, complemented
4#21456112C214yesmaximal, complemented
5#21456055C214yesmaximal, complemented
6#21456053C214yesmaximal, complemented
7#21455753C212yesmaximal, complemented
8#21455620C211yesmaximal, characteristic, complemented
9#21455293C211yesmaximal, characteristic, complemented
10#21455291C211yesmaximal, characteristic, complemented
11#21455055C212yesmaximal, complemented
12#21454637C212yesmaximal, complemented
13#21454634C212yesmaximal, complemented
14#21454456C211yesmaximal, characteristic, complemented
15C61×#3078C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C2×#14519810C2212yes—
18C2×#14519808C2212yes—
19#16840386C2212yes—
20#16840386C2212yes—
21#16840375C2212yes—
22#16840368C2212yes—
23#16840361—21no—
24#16840361—21no—
25#16840352—21no—
26#16840352—21no—
27#16840312C2211yescharacteristic
28#16840299—22no—
29#16840299—22no—
30#16840274C2212yes—
31#16840238—22no—
32#16840238—22no—
33#16840238C2214yes—
34#16840238C2214yes—
35#16840230C2212yes—
36C2×Q8×Dic61C2211yescharacteristic
37C2×C4×Dic122—21no—
38C2×C4×Dic122C2211yescharacteristic
39C2×#14519742—21no—
40C2×#14519742C2211yescharacteristic
41C2×#14519735—21no—
42C2×#14519735C2211yescharacteristic
43C2×#14519734—21no—
44C2×#14519734C2211yescharacteristic
45#16840106C2214yes—
46#16840105C2214yes—
47#16840089C2214yes—
48#16840088C2214yes—
49#16840066C2214yescomplemented
50#16840054C2212yescomplemented
51#16840044C2212yescomplemented
52#16839985C2214yescomplemented
53#16839984C2214yescomplemented
54#16839973C2212yescomplemented
55#16839972C2212yescomplemented
56#16839963C2212yescomplemented
57#16839962C2212yescomplemented
58#16839919C2214yes—
59#16839919C2214yes—
60#16839902C2214yes—
61#16839902C2214yes—
62#16839868C2214yescomplemented
63#16839866C2214yescomplemented
64#16839865C2214yescomplemented
65#16839861C2214yescomplemented
66#16839856C2214yescomplemented
67#16839854C2214yescomplemented
68#16839849C2214yescomplemented
69#16839847C2214yescomplemented
70#16839822C2214yes—
71#16839822C2214yes—
72#16839805C2212yes—
73#16839786C2211yescharacteristic
74#16839770C2212yes—
75#16839764C2212yes—
76#16839761C2212yes—
77#16839725C2212yes—
78M16×Dic61C2212yes—
79C61×#533C2211yescharacteristic
80C2×C4×Q8×C61C2211yescharacteristic
81C61×#479C2214yescomplemented
82C61×#477C2212yescomplemented
83C61×#475C2212yescomplemented
84C61×#428C2212yes—
85C61×#423C2211yescharacteristic
86C61×#419C2212yes—
87C2×#11758222C2312yes—
88C22×Dic122—21no—
89C22×Dic122C2311yescharacteristic
90C2×Q8×D61—24no—
91C2×Q8×D61—22no—
92C2×Q8×D61—24no—
93C2×Q8×D61C2314yes—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96#14519810—28no—
97#14519808—28no—
98C2×Dic244C2314yes—
99C2×#11758202C2314yes—
100C2×#11758190C2314yes—
101C2×#11758201C2314yes—
102C2×#11758194C2312yes—
103#14519777C2311yescharacteristic
104#14519774C2311yescharacteristic
105#14519772—22no—
106#14519772—22no—
107#14519772—22no—
108#14519772—22no—
109#14519768—22no—
110#14519768—22no—
111#14519766—22no—
112#14519766—22no—
113#14519765C2312yes—
114#14519762—22no—
115#14519762—22no—
116#14519762—22no—
117#14519762—22no—
118#14519761—22no—
119#14519757C2312yes—
120#14519757C2312yes—
121#14519753—22no—
122#14519753—22no—
123#14519752—22no—
124#14519752—22no—
125#14519752C2312yes—
126#14519752C2312yes—
127#14519751—21no—
128#14519751—21no—
129#14519747—22no—
130Q8×Dic61—22no—
131Q8×Dic61C2314yes—
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—
142#14519742C2312yes—
143#14519742C2312yes—
144C4×D244—22no—
145C4×D244—22no—
146C4×D244—21no—
147C4×D244—21no—
148#14519739C2312yes—
149#14519739C2312yes—
150#14519737—22no—
151#14519737—22no—
152#14519735—22no—
153#14519735—24no—
154#14519735—24no—
155#14519735C2314yes—
156#14519734—24no—
157#14519734—24no—
158#14519734—22no—
159#14519734D412yes—
160#14519734D412yes—
161#14519734C2312yes—
162#14519734C2312yes—
163C2×C4⋊Dic61—21no—
164C2×C4⋊Dic61C2311yescharacteristic
165C2×#11758196—21no—
166C2×#11758196—21no—
167C2×#11758196D411yescharacteristic
168C2×#11758196D411yescharacteristic
169C2×#11758198—21no—
170C2×#11758198D411yescharacteristic
171C2×#11758198D411yescharacteristic
172C2×C4×Dic61—21no—
173C2×C4×Dic61—21no—
174C2×C4×Dic61—21no—
175C2×C4×Dic61—21no—
176C2×C4×Dic61C2311yescharacteristic
177C42×D61—22no—
178#14519710C2314yes—
179#14519708C2314yes—
180C4⋊#92418C2312yes—
181C4⋊#92418C2312yes—
182#14519702C2314yes—
183#14519700C2314yes—
184#14519700C2314yes—
185#14519700C2314yes—
186#14519699C2314yes—
187#14519697C2314yes—
188#14519689C2314yes—
189#14519689C2314yes—
190#14519687C2314yes—
191C8×Dic61C2314yes—
192C22×Q8×C61C2311yescharacteristic
193C2×M16×C61C2312yes—
194C4⋊Q8×C61C2311yescharacteristic
195C4⋊Q8×C61C2311yescharacteristic
196#125×C61C2312yes—
197C22⋊Q8×C61—21no—
198C22⋊Q8×C61—21no—
199C4×Q8×C61—21no—
200C4×Q8×C61—21no—
201C4×Q8×C61—21no—
202C4×Q8×C61—21no—
203C4×Q8×C61C2312yes—
204C4×Q8×C61C2312yes—
205#117×C61C2312yes—
206C2×C4⋊C4×C61—21no—
207C2×C4⋊C4×C61C2311yescharacteristic
208C2×C42×C61—21no—
209C2×C42×C61C2311yescharacteristic
210#107×C61C2314yes—
211#106×C61C2314yes—
212C4⋊C8×C61C2312yes—
213C4⋊C8×C61C2312yes—
214#103×C61C2314yes—
215#103×C61C2314yes—
216C23×D61C2×D411yescharacteristic
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61#4114yes—
222C2×Q8×C61C2412yes—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—22no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234Q8×D61—216no—
235Q8×D61—28no—
236Q8×D61—28no—
237#11758222—24no—
238#11758222—24no—
239C2×D244—22no—
240C2×D244—22no—
241C2×D244—21no—
242C2×D244—21no—
243C2×D244C2412yes—
244C2×C4×D61—28no—
245C2×C4×D61—24no—
246C2×C4×D61—22no—
247C2×C4×D61—22no—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—22no—
251C2×C4×D61C2×D412yes—
252C2×C4×D61C2412yes—
253C2×Dic122—28no—
254C2×Dic122—21no—
255C2×Dic122—22no—
256C2×Dic122—24no—
257C2×Dic122#4114yes—
258C2×Dic122C2412yes—
259C2×Dic122C2412yes—
260M16×C61—24no—
261C2×C8×C61C2414yes—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61C2412yes—
270C4⋊C4×C61C2412yes—
271C4⋊C4×C61C2412yes—
272C22⋊C4×C61—22no—
273C42×C61—22no—
274C42×C61—22no—
275C42×C61—22no—
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2411yescharacteristic
279C42×C61C2411yescharacteristic
280#11758202—28no—
281#11758201—28no—
282#11758198—24no—
283#11758198—22no—
284#11758198—22no—
285#11758198—22no—
286#11758198—22no—
287#11758198—22no—
288#11758198—22no—
289#11758198—22no—
290#11758198—22no—
291#11758198C2×D412yes—
292#11758198C2×D412yes—
293#11758198C2×D412yes—
294#11758198C2×D412yes—
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—24no—
299C4⋊Dic61—22no—
300C4⋊Dic61—22no—
301C4⋊Dic61C2412yes—
302#11758196—22no—
303#11758196—22no—
304#11758196—24no—
305#11758196—22no—
306#11758196—22no—
307#11758196C2×D412yes—
308#11758196C2×D412yes—
309#11758196C2×D412yes—
310#11758196C2×D412yes—
311C4×Dic61—22no—
312C4×Dic61—22no—
313C4×Dic61—22no—
314C4×Dic61—22no—
315C4×Dic61—24no—
316C4×Dic61—24no—
317C4×Dic61—24no—
318C4×Dic61C2×D412yes—
319C4×Dic61C2412yes—
320#11758194—24no—
321C2×#92418C2414yes—
322Dic244—28no—
323#11758190—28no—
324C23×C61C22×D411yescharacteristic
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61C22×D412yes—
330Q8×C61—24no—
331Q8×C61—22no—
332Q8×C61—81no—
333Q8×C61—81no—
334Q8×C61C2×#4114yes—
335C2×C4×C61—24no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—42no—
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C22×D411yescharacteristic
346C2×C4×C61C22×D411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C2×#4112yes—
349C2×C4×C61C2×#4112yes—
350C2×C4×C61C2511yescharacteristic
351C22⋊D61—44no—
352C2×Dic61—22no—
353C2×Dic61—24no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—22no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—42no—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362C2×Dic61C22×D412yes—
363D244—22no—
364D244—22no—
365D244—81no—
366D244—81no—
367D244—82no—
368D244—82no—
369C4×D61—216no—
370C4×D61—24no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—44no—
374C4×D61—82no—
375C4×D61—82no—
376Dic122—216no—
377Dic122—24no—
378Dic122—22no—
379Dic122—22no—
380Dic122—22no—
381Dic122C2×#4114yes—
382C8×C61—24no—
383#92418—24no—
384#60566—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61#52512yes—
388C22×C61C23×D411yescharacteristic
389C2×D61—22no—
390C2×D61—22no—
391C2×D61—22no—
392C2×D61—44no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—24no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61#52512yes—
405C4×C61C22×#4111yescharacteristic
406C4×C61C22×#4111yescharacteristic
407Dic61—22no—
408Dic61—22no—
409Dic61—22no—
410Dic61—24no—
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#3078D6111yescharacteristic, complemented
422#3037—611no—
423#3037—611no—
424#3004—612no—
425C4×#137—612no—
426C4×#137—612no—
427#2921—611no—
428C2×C61—22no—
429C2×C61C2×#52511yescharacteristic
430C2×C61#358611yescharacteristic
431C2×C61#358611yescharacteristic
432D61—42no—
433D61—82no—
434C23×Q8—611no—
435C2×#137—612no—
436C2×#137—612no—
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#533C2×D6111yescharacteristic
446#532—611no—
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#479C2×D6114yescomplemented
471#477—612no—
472#477C2×D6112yescomplemented
473#475—612no—
474#475C2×D6112yescomplemented
475#464—614no—
476#464—614no—
477#462—612no—
478#462—612no—
479#460—612no—
480#460—612no—
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#428C2×D6112yes—
497#423—611no—
498#423C2×D6111yescharacteristic
499#419—612no—
500#419C2×D6112yes—
501#417—612no—
502#417—612no—
503#407—612no—
504C4×M16—612no—
505C61#6056611yescharacteristic, complemented, Sylow
506C2×#41—612no—
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—1228no—
517#137—1228no—
518C2×Q16—614no—
519C2×Q16—614no—
520C2×SD16—614no—
521C2×SD16—614no—
522C2×M16—612no—
523C2×M16C22×D6112yes—
524C4⋊Q8—611no—
525C4⋊Q8C22×D6111yescharacteristic
526C4⋊Q8C22×D6111yescharacteristic
527#127—611no—
528#126—1222no—
529#126—1222no—
530#126—1222no—
531#126—1222no—
532#125—1222no—
533#125—1222no—
534#125C22×D6112yes—
535#124—612no—
536#124—1222no—
537#124—1222no—
538#123—1222no—
539#123—1222no—
540#123—1222no—
541#123—1222no—
542#123—1222no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—612no—
546C22⋊Q8—612no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549#121—612no—
550#121—612no—
551#121—1222no—
552#121—1222no—
553#121—1221no—
554#121—1221no—
555#120—1222no—
556C4×Q8—21no—
557C4×Q8—21no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8—614no—
561C4×Q8—614no—
562C4×Q8—612no—
563C4×Q8—612no—
564C4×Q8—612no—
565C4×Q8—612no—
566C4×Q8—1224no—
567C4×Q8—1224no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8—1224no—
571C4×Q8—1224no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8C22×D6112yes—
575C4×Q8C22×D6112yes—
576C4×D4—612no—
577C4×D4—612no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1221no—
583C4×D4—1221no—
584#117—612no—
585#117—612no—
586#117—612no—
587#117—612no—
588#117—614no—
589#117—1222no—
590#117—1224no—
591#117—1224no—
592#117—1224no—
593#117—1224no—
594#117—1222no—
595#117C22×D6112yes—
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#107C22×D6114yes—
617#106—614no—
618#106C22×D6114yes—
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#103C22×D6114yes—
628#103C22×D6114yes—
629#102—614no—
630#102—614no—
631C22⋊C8—614no—
632C22⋊C8—614no—
633#97—614no—
634C4×C8—614no—
635C24—611no—
636#41—1224no—
637#41—1224no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—22no—
642C2×Q8—614no—
643C2×Q8—612no—
644C2×Q8—612no—
645C2×Q8—1224no—
646C2×Q8—1228no—
647C2×Q8—1228no—
648C2×Q8—12216no—
649C2×Q8—1228no—
650C2×Q8—1221no—
651C2×Q8—1222no—
652C2×Q8#1175822614yes—
653C2×Q8C23×D6112yes—
654C2×D4—612no—
655C2×D4—1222no—
656C2×D4—1222no—
657C2×D4—1222no—
658C2×D4—1221no—
659C2×D4—1221no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1224no—
670C22×C4—1228no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1221no—
675C22×C4—1222no—
676C22×C4D4×D6111yescharacteristic
677C22×C4D4×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679Q16—1228no—
680Q16—1228no—
681SD16—1228no—
682SD16—1228no—
683M16—24no—
684M16—1224no—
685C2×C8—614no—
686C2×C8C23×D6114yes—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—21no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
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—1221no—
709C4⋊C4—1221no—
710C4⋊C4C23×D6112yes—
711C4⋊C4C23×D6112yes—
712C4⋊C4C23×D6112yes—
713C22⋊C4—22no—
714C22⋊C4—612no—
715C22⋊C4—612no—
716C22⋊C4—612no—
717C22⋊C4—612no—
718C22⋊C4—1222no—
719C22⋊C4—1222no—
720C22⋊C4—1222no—
721C22⋊C4—1222no—
722C22⋊C4—1224no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C22⋊C4—1222no—
727C42—22no—
728C42—22no—
729C42—22no—
730C42—612no—
731C42—612no—
732C42—1224no—
733C42—1224no—
734C42—1224no—
735C42—1222no—
736C42—1222no—
737C42—1222no—
738C42—1222no—
739C42D4×D6111yescharacteristic
740C42D4×D6111yescharacteristic
741C42C23×D6111yescharacteristic
742C42C23×D6111yescharacteristic
743C23—612no—
744C23—1222no—
745C23—1222no—
746C23—2441no—
747C23—2441no—
748C23C2×D4×D6111yescharacteristic
749Q8—24no—
750Q8—22no—
751Q8—81no—
752Q8—81no—
753Q8—614no—
754Q8—12216no—
755Q8—1224no—
756Q8—1222no—
757Q8—1222no—
758Q8—1222no—
759Q8C2×#1175822614yes—
760D4—1222no—
761D4—1222no—
762D4—4881no—
763D4—4881no—
764D4—4882no—
765D4—4882no—
766D4—2444no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
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—4882no—
788C2×C4—4882no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2442no—
792C2×C4—2444no—
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×#1175822612yes—
800C2×C4C24×D6111yescharacteristic
801C8—24no—
802C8—1224no—
803C22—21no—
804C22—21no—
805C22—1222no—
806C22—1222no—
807C22—1222no—
808C22—2444no—
809C22—2442no—
810C22—2442no—
811C22—2442no—
812C22#1684027512yes—
813C22C22×D4×D6111yescharacteristic
814C4—24no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1222no—
823C4—1224no—
824C4—1222no—
825C4—1222no—
826C4—2442no—
827C4—2442no—
828C4#1684027512yes—
829C4C2×#41×D6111yescharacteristic
830C4C22×#1175822611yescharacteristic
831C2—22no—
832C2—4882no—
833C2—2442no—
834C2C2×#1684027511yescharacteristic
835C2#2146060211yescharacteristic
836C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3078C2
socleC22×C61C23×D4
prime radical#21459211C2
hypercenter#3078D61
hypocenterC61#60566
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
2. C2×#16840238C2semidirect
3. #21456121C2semidirect
4. #21456112C2semidirect
5. #21456055C2semidirect
6. #21456053C2semidirect
7. #21455753C2semidirect
8. #21455620C2semidirect
9. #21455293C2semidirect
10. #21455291C2semidirect
11. #21455055C2semidirect
12. #21454637C2semidirect
13. #21454634C2semidirect
14. #21454456C2semidirect
15. C61×#3078C2semidirect
49. #16840066C22semidirect
50. #16840054C22semidirect
51. #16840044C22semidirect
52. #16839985C22semidirect
53. #16839984C22semidirect
54. #16839973C22semidirect
55. #16839972C22semidirect
56. #16839963C22semidirect
57. #16839962C22semidirect
62. #16839868C22semidirect
63. #16839866C22semidirect
64. #16839865C22semidirect
65. #16839861C22semidirect
66. #16839856C22semidirect
67. #16839854C22semidirect
68. #16839849C22semidirect
69. #16839847C22semidirect
81. C61×#479C22semidirect
82. C61×#477C22semidirect
83. C61×#475C22semidirect
421. #3078D61semidirect
470. #479C2×D61semidirect
472. #477C2×D61semidirect
474. #475C2×D61semidirect
505. C61#60566semidirect

Maximal subgroups

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

subgroupindex
#214592112
C2×#168402382
#214561212
#214561122
#214560552
#214560532
#214557532
#214556202
#214552932
#214552912
#214550552
#214546372
#214546342
#214544562
C61×#30782
#6056661