Finite Group Databasebeta

← #30552097

Subgroups — #30552097

Order 15616.

1800 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#21459114C211yesmaximal, characteristic
2C2×#16840317C211yesmaximal, characteristic, complemented
3#21456996C214yesmaximal, complemented
4#21456984C214yesmaximal, complemented
5#21456979C212yesmaximal, complemented
6#21456972C211yesmaximal, characteristic, complemented
7#21456963C211yesmaximal, characteristic, complemented
8#21456950C212yesmaximal, complemented
9#21456944C211yesmaximal, characteristic, complemented
10#21456330C212yesmaximal, complemented
11#21456138C212yesmaximal, complemented
12#21455727C214yesmaximal, complemented
13#21455600C214yesmaximal, complemented
14#431×D61C211yesmaximal, characteristic, complemented
15C61×#3226C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840317—21no—
18#16840317—21no—
19#16840317—21no—
20#16840317—21no—
21#16840317C2211yescharacteristic
22#16840317C2212yes—
23#16840317C2212yes—
24#16840317C2212yes—
25#16840317C2212yes—
26#16840317C2211yescharacteristic
27#16840310C2211yescharacteristic
28#16840310C2211yescharacteristic
29C2×#14519777C2211yescharacteristic
30#16840294—21no—
31#16840294C2212yes—
32#16840293—21no—
33#16840293C2212yes—
34#16840291—21no—
35#16840291—21no—
36C2×#14519768C2212yes—
37#16840272—21no—
38#16840272C2212yes—
39#16840269—21no—
40C2×#14519757—21no—
41C2×#14519753—21no—
42#41×Dic61—21no—
43C4×#11758224—21no—
44C4×#11758224C2212yes—
45C2×Q8×Dic61—21no—
46C2×#14519742—21no—
47C2×#14519735C2212yes—
48C2×C42×D61C2211yescharacteristic
49#16840167C2212yescomplemented
50#16840163C2218yescomplemented
51#16840158C2212yescomplemented
52#16840158C2212yescomplemented
53#16840115C2218yescomplemented
54#16840114C2212yescomplemented
55#16840113C2212yescomplemented
56#16840108C2212yescomplemented
57#16840105C2218yes—
58#16840098C2214yes—
59#16840092C2214yes—
60#16840084C2218yes—
61#16840078C2214yes—
62#16840068C2218yescomplemented
63#16840060C2218yescomplemented
64#16840058C2214yescomplemented
65#16840052C2214yescomplemented
66#16840044C2214yescomplemented
67#16839815C2211yescharacteristic
68#16839814C2212yes—
69#16839813C2212yes—
70#16839812C2212yes—
71#16839799C2218yes—
72C4⋊C8×D61C2212yes—
73#16839755C2218yes—
74C22⋊C8×D61C2212yes—
75C4×C8×D61C2212yes—
76C61×#532C2211yescharacteristic
77C2×C4⋊Q8×C61C2211yescharacteristic
78C61×#500C2212yescomplemented
79C61×#486C2212yescomplemented
80C61×#480C2214yes—
81C61×#474C2214yescomplemented
82C61×#431C2211yescharacteristic
83C2×#11758224—21no—
84C2×#11758224C2312yes—
85C22×Dic122—21no—
86C22×C4×D61D411yescharacteristic
87C22×C4×D61D411yescharacteristic
88C22×C4×D61C2311yescharacteristic
89C2×C8×D61C2314yes—
90#14519777—21no—
91#14519777—21no—
92#14519777C2311yescharacteristic
93#14519777C2312yes—
94#14519777C2312yes—
95#14519777C2311yescharacteristic
96#14519770—22no—
97#14519770—22no—
98#14519769—21no—
99#14519768—22no—
100#14519768—22no—
101#14519768—21no—
102#14519768C2314yes—
103#14519768C2314yes—
104#14519768C2312yes—
105#14519764—21no—
106#14519764C2312yes—
107#14519759—22no—
108#14519759—22no—
109#14519758—22no—
110#14519757—22no—
111#14519757—22no—
112#14519757—22no—
113#14519757—22no—
114#14519757—21no—
115#14519757C2312yes—
116#14519756—21no—
117#14519756C2312yes—
118#14519753—22no—
119#14519753—22no—
120#14519753—22no—
121#14519753—22no—
122#14519753—21no—
123#14519753—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748—21no—
127#14519748C2312yes—
128#14519745—22no—
129Q8×Dic61—22no—
130Q8×Dic61—22no—
131Q8×Dic61—22no—
132Q8×Dic61—22no—
133Q8×Dic61—21no—
134Q8×Dic61—21no—
135C4×Dic122—21no—
136C4×Dic122C2312yes—
137#14519742—22no—
138#14519742—22no—
139#14519742—22no—
140#14519742—22no—
141#14519742—21no—
142#14519742C2312yes—
143D4×Dic61—22no—
144D4×Dic61—22no—
145D4×Dic61—21no—
146D4×Dic61—21no—
147D4×Dic61—21no—
148D4×Dic61C2312yes—
149C4×C22⋊D61—22no—
150C4×C22⋊D61—22no—
151#14519737—22no—
152#14519737—22no—
153#14519736—21no—
154#14519736—22no—
155#14519735—22no—
156#14519735—22no—
157#14519735—21no—
158#14519735C2314yes—
159#14519735C2314yes—
160#14519735C2312yes—
161#14519733—22no—
162#14519733—22no—
163C2×C4⋊Dic61—21no—
164C2×C4⋊Dic61—22no—
165C2×C4⋊Dic61C2312yes—
166C2×#11758196—22no—
167C2×#11758198—22no—
168C2×C4×Dic61—22no—
169C2×C4×Dic61—22no—
170C2×C4×Dic61D411yescharacteristic
171C2×C4×Dic61D411yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173C42×D61D411yescharacteristic
174C42×D61D411yescharacteristic
175C42×D61D411yescharacteristic
176C42×D61D411yescharacteristic
177C42×D61C2311yescharacteristic
178C42×D61C2311yescharacteristic
179C42×D61C2311yescharacteristic
180C42×D61C2311yescharacteristic
181#14519711C2318yes—
182#14519708C2318yes—
183#14519708C2318yes—
184C4⋊#92418C2312yes—
185#14519706C2314yes—
186#14519702C2318yes—
187#14519700C2318yes—
188#14519698C2318yes—
189C22⋊#92418C2312yes—
190#14519689C2314yes—
191C4×#92418C2312yes—
192C8×Dic61C2314yes—
193C2×#41×C61—21no—
194C22×Q8×C61—21no—
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61—21no—
197C4⋊Q8×C61C2312yes—
198C4⋊Q8×C61C2312yes—
199C4⋊Q8×C61C2311yescharacteristic
200#127×C61C2311yescharacteristic
201#124×C61—21no—
202#121×C61—21no—
203#121×C61C2312yes—
204C4×D4×C61—21no—
205C4×D4×C61C2312yes—
206C2×C4⋊C4×C61—21no—
207C2×C4⋊C4×C61C2312yes—
208C2×C42×C61C2311yescharacteristic
209#107×C61C2318yes—
210C4⋊C8×C61C2312yes—
211#102×C61C2318yes—
212C22⋊C8×C61C2312yes—
213C4×C8×C61C2312yes—
214C23×D61C2×D411yescharacteristic
215#41×C61—44no—
216C2×Q8×C61—21no—
217C2×Q8×C61—22no—
218C2×Q8×C61—22no—
219C2×Q8×C61—44no—
220C2×D4×C61—22no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61C2412yes—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—22no—
230C2×C22⋊D61—22no—
231C22×Dic61—22no—
232C22×Dic61—22no—
233C22×Dic61—22no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237#11758224—28no—
238#11758224—44no—
239C2×C4×D61—24no—
240C2×C4×D61—24no—
241C2×C4×D61—42no—
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2411yescharacteristic
253C2×C4×D61C2411yescharacteristic
254C2×Dic122—22no—
255C2×Dic122—22no—
256C2×Dic122—21no—
257C2×Dic122—44no—
258C2×Dic122C2412yes—
259C2×C8×C61C2414yes—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C2414yes—
265C4⋊C4×C61C2412yes—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—22no—
268C42×C61C2×D411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2411yescharacteristic
271C42×C61C2411yescharacteristic
272C22⋊Dic61—22no—
273C22⋊Dic61—22no—
274C22⋊Dic61—22no—
275C22⋊Dic61—22no—
276C22⋊Dic61—22no—
277#11758198—24no—
278#11758198—24no—
279#11758198—22no—
280#11758198—22no—
281C4⋊Dic61—22no—
282C4⋊Dic61—22no—
283C4⋊Dic61—22no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—24no—
288C4⋊Dic61—24no—
289C4⋊Dic61—22no—
290C4⋊Dic61—22no—
291C4⋊Dic61C2414yes—
292C4⋊Dic61C2412yes—
293#11758196—22no—
294#11758196—22no—
295#11758196—24no—
296#11758196—24no—
297#11758196—22no—
298#11758196—22no—
299C4×Dic61—22no—
300C4×Dic61—22no—
301C4×Dic61—22no—
302C4×Dic61—24no—
303C4×Dic61—24no—
304C4×Dic61C2×D411yescharacteristic
305C4×Dic61C2×D411yescharacteristic
306C4×Dic61C2×D411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2411yescharacteristic
315C4×Dic61C2411yescharacteristic
316C2×#92418C2414yes—
317C8×D61—28no—
318C23×C61—22no—
319C23×C61C22×D411yescharacteristic
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—41no—
323C22×D61C22×D411yescharacteristic
324C22×D61C22×D411yescharacteristic
325Q8×C61—44no—
326Q8×C61—44no—
327Q8×C61—42no—
328D4×C61—24no—
329D4×C61—44no—
330D4×C61—42no—
331D4×C61—42no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—24no—
336C2×C4×C61—44no—
337C2×C4×C61—44no—
338C2×C4×C61#13514yes—
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2511yescharacteristic
345C22⋊D61—44no—
346C22⋊D61—44no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—24no—
352C2×Dic61—41no—
353C2×Dic61—44no—
354C2×Dic61—44no—
355C2×Dic61—44no—
356C2×Dic61C22×D411yescharacteristic
357C2×Dic61C22×D411yescharacteristic
358C2×Dic61C22×D411yescharacteristic
359C2×Dic61C22×D411yescharacteristic
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D612−1+414yes—
374Dic122—24no—
375Dic122—44no—
376Dic122—44no—
377Dic122—42no—
378C8×C61—24no—
379#92418—24no—
380#60846—611nomaximal, Sylow
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—42no—
386C22×C61C2×#13512yes—
387C22×C61C23×D411yescharacteristic
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—44no—
394C2×D61#53612yes—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—42no—
398C4×C61—44no—
399C4×C61C2×#13512yes—
400C4×C61C2×#13512yes—
401C4×C61#57512yes—
402C4×C61C2×2−1+412yes—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—42no—
409Dic61—44no—
410Dic61—42no—
411Dic61#53612yes—
412#3444—611no—
413C2×#533—611no—
414#3233—614no—
415#3232—614no—
416#3231—612no—
417#3230—611no—
418#3229—611no—
419#3228—612no—
420#3227—611no—
421#3226D6111yescharacteristic, complemented
422#3160—612no—
423#3131—612no—
424#3091—614no—
425#3076—614no—
426C2×#431—611no—
427C2×C61—22no—
428C2×C61—82no—
429C2×C61C2×#53611yescharacteristic
430C2×C61C22×#13511yescharacteristic
431C2×C61C2×#57511yescharacteristic
432D61—22no—
433D61—41no—
434#533—612no—
435#533—612no—
436#533—611no—
437#533—612no—
438#533—612no—
439#533—611no—
440#533—611no—
441#533—1221no—
442#533—1221no—
443#533—1221no—
444#533—1221no—
445#532—611no—
446#532—611no—
447#532C2×D6111yescharacteristic
448C2×C4⋊Q8—611no—
449C2×C4⋊Q8C2×D6111yescharacteristic
450#529—612no—
451#529—612no—
452#529—1221no—
453#529—1221no—
454#529—1221no—
455#529—1221no—
456C2×#125—612no—
457#525—612no—
458#525—1221no—
459#525—1221no—
460C2×C22⋊Q8—1221no—
461C2×C22⋊Q8—1221no—
462C4×#41—612no—
463C4×#41—1221no—
464C4×#41—1221no—
465C2×C4×Q8—1221no—
466C2×C4×Q8—1221no—
467C2×#117—612no—
468C22×C42—611no—
469#500—612no—
470#500C2×D6112yescomplemented
471#499—618no—
472#498—612no—
473#498—612no—
474#488—618no—
475#487—612no—
476#487—612no—
477#486—612no—
478#486C2×D6112yescomplemented
479#485—618no—
480#484—614no—
481#483—614no—
482#482—618no—
483#481—614no—
484#480C2×D6114yes—
485#479—618no—
486#478—618no—
487#477—614no—
488#476—614no—
489#475—614no—
490#474C2×D6114yescomplemented
491#431—611no—
492#431—612no—
493#431—612no—
494#431—612no—
495#431C2×D6111yescharacteristic
496#427—618no—
497C2×C4⋊C8—612no—
498#416—618no—
499C2×C22⋊C8—612no—
500C2×C4×C8—612no—
501C61#6084611yescharacteristic, complemented, Sylow
502C2×#41—21no—
503C2×#41—612no—
504C2×#41—1221no—
505C22×Q8—21no—
506C22×Q8—1221no—
507C23×C4—611no—
508C23×C4—611no—
509C23×C4—611no—
510C22×C8—614no—
511C4⋊Q8—21no—
512C4⋊Q8—21no—
513C4⋊Q8—612no—
514C4⋊Q8—612no—
515C4⋊Q8—611no—
516C4⋊Q8—611no—
517C4⋊Q8—1221no—
518C4⋊Q8—1221no—
519C4⋊Q8C22×D6112yes—
520C4⋊Q8C22×D6112yes—
521C4⋊Q8C22×D6111yescharacteristic
522#127C22×D6111yescharacteristic
523#126—1222no—
524#126—1222no—
525#125—614no—
526#125—614no—
527#125—612no—
528#125—1222no—
529#125—1222no—
530#125—1221no—
531#125—1221no—
532#124—21no—
533#124—612no—
534#124—1221no—
535#123—1222no—
536#123—1222no—
537#123—1222no—
538C22⋊Q8—612no—
539C22⋊Q8—612no—
540C22⋊Q8—1222no—
541C22⋊Q8—1222no—
542C22⋊Q8—1222no—
543C22⋊Q8—1222no—
544C22⋊Q8—1221no—
545C22⋊Q8—1222no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552#121—21no—
553#121—612no—
554#121—1221no—
555#121—1221no—
556#121—1221no—
557#121C22×D6112yes—
558#120—1222no—
559C4×Q8—612no—
560C4×Q8—612no—
561C4×Q8—1222no—
562C4×Q8—1222no—
563C4×Q8—1222no—
564C4×Q8—1222no—
565C4×Q8—1221no—
566C4×Q8—1222no—
567C4×Q8—1222no—
568C4×Q8—1222no—
569C4×Q8—1222no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×D4—21no—
574C4×D4—612no—
575C4×D4—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4C22×D6112yes—
585#117—614no—
586#117—614no—
587#117—612no—
588#117—1222no—
589#117—1222no—
590#117—1222no—
591#117—1222no—
592#117—1222no—
593#117—1221no—
594#117—1221no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—612no—
597C2×C4⋊C4—1222no—
598C2×C4⋊C4—1222no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4C22×D6112yes—
601C2×C22⋊C4—1222no—
602C2×C42—611no—
603C2×C42—611no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42—611no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—1222no—
614C2×C42—1222no—
615C2×C42C22×D6111yescharacteristic
616#107—618no—
617#107C22×D6118yes—
618#106—618no—
619#106—618no—
620C4⋊C8—614no—
621C4⋊C8—612no—
622C4⋊C8C22×D6112yes—
623#103—618no—
624#103—618no—
625#102—618no—
626#102C22×D6118yes—
627C22⋊C8—612no—
628C22⋊C8—614no—
629C22⋊C8C22×D6112yes—
630C4×C8—614no—
631C4×C8—612no—
632C4×C8C22×D6112yes—
633C24—611no—
634#41—44no—
635#41—1228no—
636#41—2444no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—44no—
641C2×Q8—612no—
642C2×Q8—1221no—
643C2×Q8—1222no—
644C2×Q8—1222no—
645C2×Q8—2444no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—1222no—
650C2×D4—1222no—
651C2×D4C23×D6112yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—1224no—
670C22×C4—1222no—
671C22×C4—1222no—
672C22×C4—1224no—
673C22×C4—1222no—
674C22×C4—2442no—
675C22×C4D4×D6111yescharacteristic
676C22×C4D4×D6111yescharacteristic
677C22×C4C23×D6111yescharacteristic
678C2×C8—614no—
679C2×C8—1228no—
680C2×C8C23×D6114yes—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—614no—
686C4⋊C4—612no—
687C4⋊C4—1224no—
688C4⋊C4—1224no—
689C4⋊C4—1224no—
690C4⋊C4—1224no—
691C4⋊C4—1222no—
692C4⋊C4—1222no—
693C4⋊C4—1222no—
694C4⋊C4—1222no—
695C4⋊C4—1222no—
696C4⋊C4—1222no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4—1222no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4C23×D6114yes—
704C4⋊C4C23×D6112yes—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1222no—
710C22⋊C4—1222no—
711C22⋊C4—1222no—
712C22⋊C4—1222no—
713C22⋊C4—1222no—
714C22⋊C4—1222no—
715C22⋊C4—1222no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—1222no—
729C42—1224no—
730C42—1224no—
731C42—1222no—
732C42—1222no—
733C42D4×D6111yescharacteristic
734C42D4×D6111yescharacteristic
735C42C23×D6111yescharacteristic
736C42C23×D6111yescharacteristic
737C23—22no—
738C23—611no—
739C23—611no—
740C23—1222no—
741C23—1222no—
742C23—2441no—
743C23C2×D4×D6111yescharacteristic
744Q8—44no—
745Q8—44no—
746Q8—42no—
747Q8—1224no—
748Q8—2444no—
749Q8—2444no—
750Q8—2442no—
751D4—24no—
752D4—44no—
753D4—42no—
754D4—42no—
755D4—2444no—
756D4—2444no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—611no—
764C2×C4—614no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1222no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1224no—
784C2×C4—2441no—
785C2×C4—2441no—
786C2×C4—2444no—
787C2×C4—2441no—
788C2×C4—2444no—
789C2×C4—2444no—
790C2×C4#1451979614yes—
791C2×C4C2×D4×D6111yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C2×D4×D6111yescharacteristic
795C2×C4C2×D4×D6111yescharacteristic
796C2×C4C24×D6111yescharacteristic
797C8—24no—
798C8—1224no—
799C22—21no—
800C22—21no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—612no—
805C22—1221no—
806C22—1221no—
807C22—1221no—
808C22—1221no—
809C22—1221no—
810C22—2444no—
811C22C2×#1451979612yes—
812C22C22×D4×D6111yescharacteristic
813C4—21no—
814C4—21no—
815C4—42no—
816C4—44no—
817C4—612no—
818C4—1221no—
819C4—1221no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—2442no—
824C4—2444no—
825C4—2442no—
826C4C2×#1451979612yes—
827C4C2×#1451979612yes—
828C4#1684056112yes—
829C42−1+4×D6112yes—
830C2—22no—
831C2—82no—
832C2—1222no—
833C2—2441no—
834C2#536×D6111yescharacteristic
835C2C22×#1451979611yescharacteristic
836C2C2×#1684056111yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3226C2
socleC22×C61C23×D4
prime radical#21459114C2
hypercenter#3226D61
hypocenterC61#60846
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. C2×#16840317C2semidirect
3. #21456996C2semidirect
4. #21456984C2semidirect
5. #21456979C2semidirect
6. #21456972C2semidirect
7. #21456963C2semidirect
8. #21456950C2semidirect
9. #21456944C2semidirect
10. #21456330C2semidirect
11. #21456138C2semidirect
12. #21455727C2semidirect
13. #21455600C2semidirect
14. #431×D61C2semidirect
15. C61×#3226C2semidirect
49. #16840167C22semidirect
50. #16840163C22semidirect
51. #16840158C22semidirect
52. #16840158C22semidirect
53. #16840115C22semidirect
54. #16840114C22semidirect
55. #16840113C22semidirect
56. #16840108C22semidirect
62. #16840068C22semidirect
63. #16840060C22semidirect
64. #16840058C22semidirect
65. #16840052C22semidirect
66. #16840044C22semidirect
78. C61×#500C22semidirect
79. C61×#486C22semidirect
81. C61×#474C22semidirect
421. #3226D61semidirect
470. #500C2×D61semidirect
478. #486C2×D61semidirect
490. #474C2×D61semidirect
501. C61#60846semidirect

Maximal subgroups

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

subgroupindex
#214591142
C2×#168403172
#214569962
#214569842
#214569792
#214569722
#214569632
#214569502
#214569442
#214563302
#214561382
#214557272
#214556002
#431×D612
C61×#32262
#6084661