Finite Group Databasebeta

← #30547913

Subgroups — #30547913

Order 15616.

2106 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840335C211yesmaximal, characteristic
2#21459020C211yesmaximal, characteristic
3#21455787C214yesmaximal, complemented
4#21455785C214yesmaximal, complemented
5#21455783C214yesmaximal, complemented
6#21455781C214yesmaximal, complemented
7#21455769C212yesmaximal, complemented
8#21455768C211yesmaximal, characteristic, complemented
9#21455767C211yesmaximal, characteristic, complemented
10#21455765C212yesmaximal, complemented
11#21455763C211yesmaximal, characteristic, complemented
12#21454406C212yesmaximal, complemented
13#419×D61C212yesmaximal, complemented
14#21454262C211yesmaximal, characteristic
15C61×#3095C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Q8×D61C2211yescharacteristic
18C2×M16×D61C2212yes—
19#16840335—22no—
20#16840335—22no—
21#16840335C2214yes—
22#16840335C2214yes—
23C2×#14519776—21no—
24C2×#14519763—21no—
25C2×#14519762—21no—
26C2×#14519759—21no—
27C2×#14519757C2211yescharacteristic
28C2×#14519756C2211yescharacteristic
29C2×#14519753C2211yescharacteristic
30#16840243C2212yes—
31#16840243C2212yes—
32#16840242C2212yes—
33#16840242C2212yes—
34#16840239—21no—
35#16840236—21no—
36#16840235—21no—
37#16840235—21no—
38C4×#11758222—22no—
39#16840230—22no—
40C2×#14519736C2211yescharacteristic
41C2×#14519735C2211yescharacteristic
42#117×D61C2212yes—
43#117×D61C2212yes—
44#16840106C2214yescomplemented
45#16840105C2214yescomplemented
46#16840104C2214yescomplemented
47#16840103C2214yescomplemented
48#16840102C2214yescomplemented
49#16840101C2214yescomplemented
50#16840100C2214yescomplemented
51#16840099C2214yescomplemented
52#16840098C2212yescomplemented
53#16840097C2212yescomplemented
54#16840096C2214yescomplemented
55#16840095C2212yescomplemented
56#16840094C2214yescomplemented
57#16840093C2212yescomplemented
58#16840092C2212yescomplemented
59#16840091C2214yescomplemented
60#16840090C2212yescomplemented
61#16839805C2212yes—
62#16839804C2212yes—
63#16839803C2214yescomplemented
64#16839802C2212yes—
65#16839801C2214yescomplemented
66#16839799C2214yescomplemented
67#16839797C2214yescomplemented
68#16839772C2212yes—
69#16839771C2212yes—
70#16839770C2212yes—
71#16839769C2214yescomplemented
72#16839769C2214yescomplemented
73#103×D61C2214yescomplemented
74#103×D61C2214yescomplemented
75#16839727C2214yes—
76#16839727C2214yes—
77#16839726C2211yescharacteristic
78#16839725C2212yes—
79C2×C22⋊Q8×C61C2211yescharacteristic
80C2×#117×C61C2211yescharacteristic
81C61×#485C2214yescomplemented
82C61×#484C2212yescomplemented
83C61×#483C2212yescomplemented
84C61×#428C2212yes—
85C61×#419C2212yes—
86C61×#407C2211yescharacteristic
87C2×#11758222—28no—
88C2×#11758222D412yes—
89C2×#11758222D412yes—
90C2×#11758222C2312yes—
91C2×#11758222C2312yes—
92C22×Dic122—21no—
93C22×Dic122D411yescharacteristic
94C22×Dic122C2311yescharacteristic
95C2×Q8×D61—22no—
96C2×Q8×D61—28no—
97C2×Q8×D61C2314yes—
98C22×D244D411yescharacteristic
99C22×C22⋊D61D411yescharacteristic
100C22×C22⋊D61D411yescharacteristic
101C22×C4×D61—21no—
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C2×#11758194C2312yes—
105C2×#11758189C2314yes—
106M16×D61—28no—
107C2×C8×D61C2314yes—
108#14519776—24no—
109#14519776—24no—
110#14519763—24no—
111#14519763—24no—
112#14519762—24no—
113#14519762—24no—
114#14519759—24no—
115#14519759—24no—
116#14519757—22no—
117#14519757C2314yes—
118#14519756—21no—
119#14519756—21no—
120#14519756C2312yes—
121#14519756C2312yes—
122#14519753—22no—
123#14519753C2314yes—
124C4×Dic122—22no—
125C4×Dic122—22no—
126#14519742—22no—
127#14519742—22no—
128C4×D244—22no—
129C4×D244—22no—
130#14519739—22no—
131#14519739—22no—
132C4×C22⋊D61—22no—
133C4×C22⋊D61—22no—
134C4×C22⋊D61—22no—
135C4×C22⋊D61—22no—
136#14519737—22no—
137#14519737—22no—
138#14519737—22no—
139#14519737—22no—
140#14519736—21no—
141#14519736—21no—
142#14519736C2312yes—
143#14519736C2312yes—
144#14519735—22no—
145#14519735C2312yes—
146#14519735C2312yes—
147#14519735C2312yes—
148#14519735C2312yes—
149#14519735C2314yes—
150#14519734—22no—
151#14519734—22no—
152#14519733—22no—
153#14519733—22no—
154C2×C4⋊Dic61—21no—
155C2×C4⋊Dic61C2311yescharacteristic
156C2×C4⋊Dic61C2311yescharacteristic
157C2×C4⋊Dic61C2311yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61C2312yes—
161C4⋊C4×D61C2312yes—
162C4⋊C4×D61C2312yes—
163C4⋊C4×D61C2312yes—
164C2×C22⋊Dic61—21no—
165C2×C22⋊Dic61—21no—
166C2×#11758198—21no—
167C2×#11758198—21no—
168C2×#11758198—21no—
169C22⋊C4×D61—22no—
170C22⋊C4×D61—22no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C42×D61—22no—
174C42×D61—22no—
175#14519711C2314yes—
176#14519710C2314yes—
177#14519710C2314yes—
178#14519709C2314yes—
179#14519708C2314yes—
180#14519708C2314yes—
181#14519702C2314yes—
182#14519702C2314yes—
183#14519701C2314yes—
184#14519701C2314yes—
185#14519700C2314yes—
186#14519700C2314yes—
187C22⋊#92418C2312yes—
188C22⋊#92418C2312yes—
189#14519689C2314yes—
190#14519689C2314yes—
191C22×Q8×C61C2311yescharacteristic
192C23×C4×C61C2311yescharacteristic
193C2×M16×C61C2312yes—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61C2312yes—
197C22⋊Q8×C61C2312yes—
198#117×C61—21no—
199#117×C61—21no—
200#117×C61C2312yes—
201#117×C61C2312yes—
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C4⋊C4×C61C2311yescharacteristic
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C42×C61—21no—
209#107×C61C2314yes—
210#106×C61C2314yes—
211#103×C61C2314yes—
212#103×C61C2314yes—
213C22⋊C8×C61C2312yes—
214C22⋊C8×C61C2312yes—
215C24×C61C2×D411yescharacteristic
216C23×D61C2×D411yescharacteristic
217C23×D61C2×D411yescharacteristic
218C2×Q8×C61—21no—
219C2×Q8×C61—24no—
220C2×Q8×C61C2412yes—
221C22×C4×C61—24no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—24no—
233C2×C22⋊D61—24no—
234C2×C22⋊D61C2×D412yes—
235C2×C22⋊D61C2×D412yes—
236C2×C22⋊D61C2×D412yes—
237C2×C22⋊D61C2×D412yes—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244Q8×D61—28no—
245Q8×D61—28no—
246Q8×D61—48no—
247#11758222—28no—
248#11758222—28no—
249#11758222—24no—
250#11758222—24no—
251#11758222—24no—
252#11758222—24no—
253C2×D244—24no—
254C2×D244C2×D412yes—
255C2×D244C2×D412yes—
256C2×C4×D61—24no—
257C2×C4×D61—24no—
258C2×C4×D61—22no—
259C2×C4×D61—22no—
260C2×C4×D61—22no—
261C2×C4×D61—22no—
262C2×C4×D61—44no—
263C2×C4×D61C2×D412yes—
264C2×C4×D61C2×D412yes—
265C2×C4×D61#4118yes—
266C2×C4×D61C2412yes—
267C2×C4×D61C2412yes—
268C2×Dic122—24no—
269C2×Dic122—24no—
270C2×Dic122—21no—
271C2×Dic122—24no—
272C2×Dic122—44no—
273C2×Dic122C2×D412yes—
274C2×Dic122C2×D412yes—
275C2×Dic122C2412yes—
276M16×C61—24no—
277C2×C8×C61C2414yes—
278C4⋊C4×C61—22no—
279C4⋊C4×C61—22no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61C2412yes—
284C4⋊C4×C61C2412yes—
285C4⋊C4×C61C2412yes—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—22no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—22no—
290C42×C61—22no—
291C42×C61—22no—
292C22⋊Dic61—22no—
293C22⋊Dic61—22no—
294C22⋊Dic61—22no—
295C22⋊Dic61—22no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—24no—
301#11758198—24no—
302#11758198—24no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—24no—
307C4⋊Dic61C2412yes—
308C4⋊Dic61C2412yes—
309C4⋊Dic61C2412yes—
310#11758196—22no—
311#11758196—22no—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—24no—
317C4×Dic61—22no—
318C4×Dic61—22no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61—24no—
324#11758194—24no—
325C2×#92418C2414yes—
326#11758189—28no—
327C8×D61—28no—
328C23×C61—22no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C22×D61—22no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61#12314yes—
340C22×D61C22×D412yes—
341C22×D61C22×D412yes—
342Q8×C61—24no—
343Q8×C61—42no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—81no—
356C2×C4×C61—81no—
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4114yes—
361C2×C4×C61C2511yescharacteristic
362C22⋊D61—24no—
363C22⋊D61—24no—
364C22⋊D61—24no—
365C22⋊D61—24no—
366C2×Dic61—22no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—81no—
374C2×Dic61—81no—
375C2×Dic61#12314yes—
376C2×Dic61C22×D412yes—
377C2×Dic61C22×D412yes—
378D244—24no—
379D244—24no—
380C4×D61—24no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—48no—
384C4×D61—82no—
385C4×D61—82no—
386C4×D61—82no—
387C4×D61—82no—
388C4×D61#12318yes—
389C4×D61C2×#4114yes—
390C4×D61C2×#4114yes—
391Dic122—24no—
392Dic122—24no—
393Dic122—24no—
394Dic122—42no—
395Dic122—48no—
396C8×C61—24no—
397#92418—24no—
398#60519—611nomaximal, Sylow
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—82no—
408C22×C61C2×#12312yes—
409C22×C61C23×D411yescharacteristic
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—44no—
416C2×D61—82no—
417C2×D61C2×#12314yes—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—42no—
421C4×C61—42no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61C2×#12312yes—
425C4×C61C22×#4112yes—
426Dic61—22no—
427Dic61—42no—
428Dic61—42no—
429Dic61—42no—
430Dic61—42no—
431Dic61C2×#12314yes—
432C2×#536—611no—
433#3428—611no—
434#3097—614no—
435#3097—614no—
436#3097—614no—
437#3097—614no—
438#3095—612no—
439#3095—612no—
440#3095—611no—
441#3095—611no—
442#3095—611no—
443#3095D6111yescharacteristic, complemented
444#2911—612no—
445C2×#419—612no—
446#2879—611no—
447C2×C61—22no—
448C2×C61—41no—
449C2×C61—41no—
450C2×C61C22×#12311yescharacteristic
451C2×C61#358611yescharacteristic
452C2×C61#358611yescharacteristic
453D61—24no—
454D61—42no—
455C22×#41—611no—
456C23×Q8—611no—
457C22×M16—612no—
458#536—614no—
459#536—614no—
460#536—1222no—
461#536—1222no—
462C2×C4⋊Q8—1221no—
463C2×#124—1221no—
464C2×#123—1221no—
465C2×#123—1221no—
466C2×C22⋊Q8—611no—
467C2×C22⋊Q8—611no—
468C2×C22⋊Q8—611no—
469C2×C22⋊Q8C2×D6111yescharacteristic
470#520—612no—
471#520—612no—
472#520—612no—
473#520—612no—
474#519—1221no—
475#518—1221no—
476#518—1221no—
477#518—1221no—
478C4×#41—1222no—
479C4×#41—1222no—
480C2×#117—611no—
481C2×#117—612no—
482C2×#117—612no—
483C2×#117—611no—
484C2×#117C2×D6111yescharacteristic
485#485—614no—
486#485—614no—
487#485—614no—
488#485—614no—
489#485—614no—
490#485—614no—
491#485—614no—
492#485C2×D6114yescomplemented
493#484—612no—
494#484—612no—
495#484—614no—
496#484—614no—
497#484—612no—
498#484C2×D6112yescomplemented
499#483—612no—
500#483—612no—
501#483—614no—
502#483—614no—
503#483—612no—
504#483C2×D6112yescomplemented
505#428—612no—
506#428—612no—
507#428—612no—
508#428—614no—
509#428—614no—
510#428C2×D6112yes—
511#427—614no—
512#427—614no—
513#419—612no—
514#419—612no—
515#419—612no—
516#419—614no—
517#419—614no—
518#419C2×D6112yes—
519C2×#103—614no—
520C2×#103—614no—
521#408—614no—
522#408—614no—
523#407—611no—
524#407—612no—
525#407C2×D6111yescharacteristic
526C61#6051911yescharacteristic, complemented, Sylow
527C2×#41—612no—
528C2×#41—612no—
529C2×#41—612no—
530C2×#41—612no—
531C2×#41—1228no—
532C22×Q8—611no—
533C22×Q8—614no—
534C22×Q8—611no—
535C22×Q8—1221no—
536C22×Q8—1222no—
537C22×Q8—1228no—
538C22×Q8C22×D6111yescharacteristic
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—611no—
542C23×C4—611no—
543C23×C4—611no—
544C23×C4—1221no—
545C23×C4C22×D6111yescharacteristic
546C2×M16—612no—
547C2×M16—614no—
548C2×M16—1228no—
549C2×M16C22×D6112yes—
550C22×C8—614no—
551C4⋊Q8—1224no—
552C4⋊Q8—1224no—
553#124—1224no—
554#124—1224no—
555#123—1224no—
556#123—1224no—
557#123—1224no—
558#123—1224no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—614no—
562C22⋊Q8—612no—
563C22⋊Q8—612no—
564C22⋊Q8—614no—
565C22⋊Q8—1222no—
566C22⋊Q8—1222no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8C22×D6112yes—
570C22⋊Q8C22×D6112yes—
571C4×Q8—1222no—
572C4×Q8—1222no—
573C4×Q8—1222no—
574C4×Q8—1222no—
575C4×D4—1222no—
576C4×D4—1222no—
577C4×D4—1222no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4—1222no—
581C4×D4—1222no—
582C4×D4—1222no—
583C4×D4—1222no—
584C4×D4—1222no—
585C4×D4—1222no—
586C4×D4—1222no—
587#117—21no—
588#117—21no—
589#117—612no—
590#117—612no—
591#117—612no—
592#117—612no—
593#117—612no—
594#117—612no—
595#117—614no—
596#117—1222no—
597#117—1222no—
598#117—1222no—
599#117—1222no—
600#117—1222no—
601#117—1221no—
602#117—1221no—
603#117C22×D6112yes—
604#117C22×D6112yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—612no—
610C2×C4⋊C4—612no—
611C2×C4⋊C4—612no—
612C2×C4⋊C4—612no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4C22×D6111yescharacteristic
617C2×C4⋊C4C22×D6111yescharacteristic
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1221no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C42—21no—
629C2×C42—1222no—
630C2×C42—1222no—
631C2×C42—1221no—
632C2×C42—1221no—
633#107—614no—
634#107—614no—
635#107—614no—
636#107C22×D6114yes—
637#106—614no—
638#106—614no—
639#106—614no—
640#106C22×D6114yes—
641#103—614no—
642#103—614no—
643#103—614no—
644#103—614no—
645#103—614no—
646#103—614no—
647#103C22×D6114yes—
648#103C22×D6114yes—
649C22⋊C8—612no—
650C22⋊C8—612no—
651C22⋊C8—614no—
652C22⋊C8—614no—
653C22⋊C8C22×D6112yes—
654C22⋊C8C22×D6112yes—
655C24—611no—
656C24—611no—
657C24D4×D6111yescharacteristic
658#41—1228no—
659#41—1228no—
660#41—1224no—
661#41—1224no—
662#41—1224no—
663#41—1224no—
664C2×Q8—21no—
665C2×Q8—24no—
666C2×Q8—612no—
667C2×Q8—612no—
668C2×Q8—612no—
669C2×Q8—1224no—
670C2×Q8—1224no—
671C2×Q8—1228no—
672C2×Q8—1228no—
673C2×Q8—1221no—
674C2×Q8—1224no—
675C2×Q8—2444no—
676C2×Q8—2448no—
677C2×Q8C23×D6112yes—
678C2×D4—612no—
679C2×D4—612no—
680C2×D4—612no—
681C2×D4—612no—
682C2×D4—612no—
683C2×D4—612no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1224no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—611no—
693C22×C4—612no—
694C22×C4—618no—
695C22×C4—612no—
696C22×C4—611no—
697C22×C4—612no—
698C22×C4—612no—
699C22×C4—1222no—
700C22×C4—1222no—
701C22×C4—1222no—
702C22×C4—1222no—
703C22×C4—1224no—
704C22×C4—1224no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4—2444no—
710C22×C4D4×D6111yescharacteristic
711C22×C4D4×D6111yescharacteristic
712C22×C4D4×D6111yescharacteristic
713C22×C4C23×D6111yescharacteristic
714C22×C4C23×D6111yescharacteristic
715C22×C4C23×D6111yescharacteristic
716M16—24no—
717M16—1228no—
718M16—1224no—
719C2×C8—614no—
720C2×C8—1228no—
721C2×C8C23×D6114yes—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—612no—
728C4⋊C4—612no—
729C4⋊C4—612no—
730C4⋊C4—1222no—
731C4⋊C4—1222no—
732C4⋊C4—1222no—
733C4⋊C4—1222no—
734C4⋊C4—1224no—
735C4⋊C4—1224no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1222no—
740C4⋊C4—1222no—
741C4⋊C4C23×D6112yes—
742C4⋊C4C23×D6112yes—
743C4⋊C4C23×D6112yes—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—1222no—
749C22⋊C4—1222no—
750C22⋊C4—1222no—
751C22⋊C4—1222no—
752C22⋊C4—1224no—
753C22⋊C4—1224no—
754C22⋊C4—1224no—
755C22⋊C4—1222no—
756C22⋊C4—1222no—
757C22⋊C4—1222no—
758C22⋊C4—1222no—
759C42—22no—
760C42—22no—
761C42—1222no—
762C42—1222no—
763C42—1222no—
764C42—1222no—
765C42—1224no—
766C42—1222no—
767C42—1222no—
768C23—22no—
769C23—41no—
770C23—41no—
771C23—612no—
772C23—614no—
773C23—612no—
774C23—1222no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23C2×D4×D6111yescharacteristic
780C23C2×D4×D6111yescharacteristic
781C23C2×D4×D6111yescharacteristic
782Q8—24no—
783Q8—42no—
784Q8—1224no—
785Q8—1224no—
786Q8—1224no—
787Q8—2448no—
788Q8—2442no—
789D4—1224no—
790D4—1224no—
791D4—1224no—
792D4—1224no—
793D4—1224no—
794D4—1224no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—614no—
809C2×C4—612no—
810C2×C4—618no—
811C2×C4—614no—
812C2×C4—614no—
813C2×C4—612no—
814C2×C4—1222no—
815C2×C4—1224no—
816C2×C4—1222no—
817C2×C4—1222no—
818C2×C4—1222no—
819C2×C4—1222no—
820C2×C4—1222no—
821C2×C4—1222no—
822C2×C4—4882no—
823C2×C4—4882no—
824C2×C4—4882no—
825C2×C4—4882no—
826C2×C4—4881no—
827C2×C4—4881no—
828C2×C4—2448no—
829C2×C4—2442no—
830C2×C4—2442no—
831C2×C4C2×D4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4#41×D6114yes—
835C2×C4C24×D6111yescharacteristic
836C8—24no—
837C8—1224no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—82no—
847C22—614no—
848C22—1222no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—4882no—
854C22—2444no—
855C22#123×D6112yes—
856C22C22×D4×D6111yescharacteristic
857C4—21no—
858C4—21no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—614no—
864C4—1222no—
865C4—2442no—
866C4—2442no—
867C4—2442no—
868C4—2442no—
869C4#123×D6112yes—
870C4C2×#41×D6112yes—
871C2—22no—
872C2—41no—
873C2—41no—
874C2—1224no—
875C2—2442no—
876C2C2×#123×D6111yescharacteristic
877C2#2146060211yescharacteristic
878C2#2146060311yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3095C2
socleC22×C61C23×D4
prime radicalC22×#11758222C22
hypercenter#3095D61
hypocenterC61#60519
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
3. #21455787C2semidirect
4. #21455785C2semidirect
5. #21455783C2semidirect
6. #21455781C2semidirect
7. #21455769C2semidirect
8. #21455768C2semidirect
9. #21455767C2semidirect
10. #21455765C2semidirect
11. #21455763C2semidirect
12. #21454406C2semidirect
13. #419×D61C2semidirect
15. C61×#3095C2semidirect
44. #16840106C22semidirect
45. #16840105C22semidirect
46. #16840104C22semidirect
47. #16840103C22semidirect
48. #16840102C22semidirect
49. #16840101C22semidirect
50. #16840100C22semidirect
51. #16840099C22semidirect
52. #16840098C22semidirect
53. #16840097C22semidirect
54. #16840096C22semidirect
55. #16840095C22semidirect
56. #16840094C22semidirect
57. #16840093C22semidirect
58. #16840092C22semidirect
59. #16840091C22semidirect
60. #16840090C22semidirect
63. #16839803C22semidirect
65. #16839801C22semidirect
66. #16839799C22semidirect
67. #16839797C22semidirect
71. #16839769C22semidirect
72. #16839769C22semidirect
73. #103×D61C22semidirect
74. #103×D61C22semidirect
81. C61×#485C22semidirect
82. C61×#484C22semidirect
83. C61×#483C22semidirect
443. #3095D61semidirect
492. #485C2×D61semidirect
498. #484C2×D61semidirect
504. #483C2×D61semidirect
526. C61#60519semidirect

Maximal subgroups

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

subgroupindex
C2×#168403352
#214590202
#214557872
#214557852
#214557832
#214557812
#214557692
#214557682
#214557672
#214557652
#214557632
#214544062
#419×D612
#214542622
C61×#30952
#6051961