Finite Group Databasebeta

← #29685873

Subgroups — #29685873

Order 15616.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic, complemented
2#21455039C211yesmaximal, characteristic
3C2×#16839881C211yesmaximal, characteristic, complemented
4C2×#16839878C211yesmaximal, characteristic, complemented
5#21454521C211yesmaximal, characteristic, complemented
6#21446146C211yesmaximal, characteristic, complemented
7#21446145C211yesmaximal, characteristic, complemented
8#21446120C211yesmaximal, characteristic, complemented
9#21446093C211yesmaximal, characteristic, complemented
10#21446022C211yesmaximal, characteristic, complemented
11#21445761C211yesmaximal, characteristic, complemented
12#21445660C211yesmaximal, characteristic, complemented
13#21445659C211yesmaximal, characteristic, complemented
14#21445601C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19#16840527—24no—
20#16840527—24no—
21C2×#14519785—21no—
22C2×#14519785C2211yescharacteristic
23C2×#14519785C2211yescharacteristic, complemented
24C2×#14519784C2211yescharacteristic
25C2×#14519783—21no—
26C2×#14519783C2211yescharacteristic
27C22×#11758189—21no—
28C22×#11758189C2211yescharacteristic
29C2×M16×D61—21no—
30C2×M16×D61C2211yescharacteristic
31#16840274C2211yescharacteristic
32#16839927C411yescharacteristic, complemented
33#16839925C411yescharacteristic, complemented
34#16839919C411yescharacteristic, complemented
35#16839914C411yescharacteristic, complemented
36#16839910C411yescharacteristic, complemented
37#16839908C411yescharacteristic, complemented
38#16839902C411yescharacteristic, complemented
39#16839897C411yescharacteristic, complemented
40#16839881—24no—
41#16839878—24no—
42#16839839—21no—
43#16839839—21no—
44#16839832—21no—
45#16839832—21no—
46C2×#14519712C2211yescharacteristic, complemented
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic, complemented
49C2×#14519704C2211yescharacteristic
50C2×#14519703C2211yescharacteristic
51C2×#14519703C2211yescharacteristic, complemented
52#16839756C2211yescharacteristic
53#16839728C2211yescharacteristic, complemented
54#16839725C2211yescharacteristic
55C2×#14519689C2211yescharacteristic
56#16839718C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58C2×C8×Dic61C2211yescharacteristic, complemented
59C4×#11758198C2211yescharacteristic
60#16839527C2211yescharacteristic, complemented
61#16839526C2211yescharacteristic, complemented
62#16839521C2211yescharacteristic, complemented
63#16839516C2211yescharacteristic, complemented
64C2×#131×C61C2211yescharacteristic
65C2×#108×C61C2211yescharacteristic, complemented
66C61×#424C2211yescharacteristic, complemented
67C2×#104×C61C2211yescharacteristic
68C61×#416C2211yescharacteristic
69C61×#339C2211yescharacteristic, complemented
70C61×#336C2211yescharacteristic, complemented
71C2×#11758226C2×C411yescharacteristic
72C2×#11758222—21no—
73C2×#11758222C2311yescharacteristic
74C2×#11758222C2311yescharacteristic
75C2×#11758224—21no—
76C2×#11758224C2×C411yescharacteristic
77#41×D61—22no—
78#41×D61—22no—
79#41×D61—22no—
80#41×D61—22no—
81C2×Q8×D61C2×C411yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61C2×C411yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86#14519799—22no—
87#14519799—22no—
88#14519797—22no—
89#14519797—22no—
90C2×Dic244C2×C411yescharacteristic
91C2×#11758202C2×C411yescharacteristic
92C2×#11758190C2×C411yescharacteristic
93C2×#11758190C2×C411yescharacteristic
94C2×#11758200C2×C411yescharacteristic
95C2×#11758201C2×C411yescharacteristic
96C2×D488C2×C411yescharacteristic
97C2×#11758199C2×C411yescharacteristic
98#14519785—28no—
99#14519785—22no—
100#14519785—22no—
101#14519785—22no—
102#14519785D414yescomplemented
103#14519784—22no—
104#14519784D414yescomplemented
105#14519783—28no—
106#14519783—22no—
107#14519783—22no—
108C2×#11758194—21no—
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758189—28no—
112C2×#11758189—21no—
113C2×#11758189—21no—
114C2×#11758189—21no—
115C2×#11758189—22no—
116C2×#11758189—22no—
117C2×#11758189—21no—
118C2×#11758189D411yescharacteristic
119C2×#11758189D411yescharacteristic
120C2×#11758189D411yescharacteristic
121C2×#11758189D411yescharacteristic
122M16×D61—28no—
123M16×D61—22no—
124M16×D61—22no—
125C22×#92418—21no—
126C22×#92418C2311yescharacteristic
127C22×#92418C2311yescharacteristic
128C2×C8×D61—21no—
129C2×C8×D61—21no—
130C2×C8×D61—21no—
131C2×C8×D61—21no—
132#14519761—21no—
133#14519757C2×C411yescharacteristic
134#14519757C2×C411yescharacteristic
135#14519752C2×C411yescharacteristic
136#14519752C2×C411yescharacteristic
137#14519747—21no—
138C4×D244—21no—
139C4×D244—21no—
140C2×#11758198—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519712—22no—
143#14519705—22no—
144#14519705—22no—
145#14519704—22no—
146#14519703—22no—
147#14519703—22no—
148#14519700C2×C411yescharacteristic
149#14519700C2×C411yescharacteristic
150#14519697C2×C411yescharacteristic
151#14519697C2×C411yescharacteristic
152#14519689—21no—
153#14519689—21no—
154#14519689—21no—
155#14519689—21no—
156#14519689C2×C411yescharacteristic
157#14519689C2×C411yescharacteristic
158#14519689C2×C411yescharacteristic
159#14519689C2×C411yescharacteristic
160#14519688—22no—
161#14519688—21no—
162C4×#92418—21no—
163C8×Dic61—22no—
164#14519684—21no—
165C2×#41×C61C2311yescharacteristic
166#131×C61—22no—
167#131×C61—22no—
168C2×M16×C61—21no—
169C2×M16×C61C2311yescharacteristic
170C2×M16×C61C2311yescharacteristic
171C22×C8×C61—21no—
172C22×C8×C61C2311yescharacteristic
173C22×C8×C61C2311yescharacteristic
174#117×C61C2311yescharacteristic
175C2×C42×C61C2311yescharacteristic
176#108×C61—22no—
177C4⋊C8×C61—21no—
178C4⋊C8×C61—21no—
179#104×C61—22no—
180#103×C61C2×C411yescharacteristic
181#103×C61C2×C411yescharacteristic
182#102×C61C2×C411yescharacteristic
183#102×C61C2×C411yescharacteristic
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186#41×C61—21no—
187#41×C61—21no—
188#41×C61C2×D412yes—
189#41×C61#4112yes—
190C2×Q8×C61C22×C411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61C22×C411yescharacteristic
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61#4111yescharacteristic
203#11758226—22no—
204#11758226—22no—
205Q8×D61—22no—
206Q8×D61—22no—
207#11758224—24no—
208#11758224—24no—
209#11758224—22no—
210#11758224—22no—
211D4×D61—24no—
212D4×D61—24no—
213D4×D61—22no—
214D4×D61—22no—
215#11758222—24no—
216#11758222—24no—
217#11758222—21no—
218#11758222—21no—
219#11758222—21no—
220#11758222—21no—
221#11758222—21no—
222#11758222—21no—
223#11758222C2×D412yes—
224#11758222#4112yes—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244C22×C411yescharacteristic
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—24no—
231C2×C4×D61—24no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61C22×C411yescharacteristic
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×Dic122—21no—
245C2×Dic122C22×C411yescharacteristic
246C2×Dic122C22×C411yescharacteristic
247M16×C61—24no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61C2×D412yes—
252C2×C8×C61—24no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61C22×C411yescharacteristic
260C2×C8×C61C22×C411yescharacteristic
261C2×C8×C61C2×D411yescharacteristic
262C2×C8×C61C2×D411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C4⋊C4×C61C22×C411yescharacteristic
265C22⋊C4×C61—21no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—21no—
269#11758202—22no—
270#11758201—22no—
271#11758200—22no—
272#11758199—22no—
273#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—42no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282#11758194—21no—
283#11758194—24no—
284#11758194—21no—
285#11758194—21no—
286#11758194C2×D412yes—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—24no—
291C2×#92418—21no—
292C2×#92418C22×C411yescharacteristic
293C2×#92418C22×C411yescharacteristic
294C2×#92418C2×D412yes—
295C2×#92418C2×D411yescharacteristic
296C2×#92418C2×D411yescharacteristic
297C2×#92418C2×D412yes—
298Dic244—22no—
299D488—22no—
300#11758190—22no—
301#11758190—22no—
302#11758189—24no—
303#11758189—24no—
304#11758189—22no—
305#11758189—22no—
306#11758189—24no—
307#11758189—22no—
308#11758189—22no—
309#11758189—42no—
310C8×D61—24no—
311C8×D61—24no—
312C8×D61—24no—
313C8×D61—42no—
314C23×C61—21no—
315C23×C61C2×#4111yescharacteristic
316C22×D61—21no—
317C22×D61—24no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—81no—
324C22×D61—81no—
325C22×D61C4×D411yescharacteristic
326C22×D61C4×D411yescharacteristic
327Q8×C61—21no—
328Q8×C61C4×D412yes—
329D4×C61—22no—
330D4×C61—22no—
331D4×C61—21no—
332D4×C61C4×D412yes—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C22⋊D61—24no—
348C22⋊D61—24no—
349C22⋊D61—22no—
350C22⋊D61—22no—
351C22⋊D61—41no—
352C22⋊D61—41no—
353C2×Dic61—24no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61C4×D411yescharacteristic
362C2×Dic61C4×D411yescharacteristic
363D244—24no—
364D244—21no—
365D244—21no—
366D244—21no—
367D244—81no—
368D244—81no—
369D244C4×D412yes—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—22no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—22no—
381C4×D61—21no—
382C4×D61—41no—
383C4×D61—41no—
384Dic122—24no—
385Dic122—21no—
386Dic122—21no—
387Dic122—21no—
388Dic122C4×D412yes—
389C8×C61—21no—
390C8×C61—21no—
391C8×C61—22no—
392C8×C61—21no—
393C8×C61—21no—
394C8×C61—41no—
395#92418—21no—
396#92418—21no—
397#92418—22no—
398#92418—41no—
399#92418#12012yes—
400#92418#12012yes—
401#21468—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—22no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61C2×C4×D411yescharacteristic
408C22×C61#52511yescharacteristic
409C22×C61#52511yescharacteristic
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—22no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—84no—
425C4×C61—22no—
426C4×C61—41no—
427C4×C61—41no—
428C4×C61—81no—
429C4×C61C2×C4×D411yescharacteristic
430C4×C61C2×C4×D411yescharacteristic
431C4×C61C2×#12011yescharacteristic
432C4×C61#52511yescharacteristic
433Dic61—21no—
434Dic61—22no—
435Dic61—21no—
436Dic61—42no—
437Dic61—41no—
438C2×#568—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#443—611no—
442#2930—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866D6111yescharacteristic, complemented
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1764—611no—
452#1753—611no—
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—42no—
456C2×C61C4×#12011yescharacteristic
457C2×C61#295611yescharacteristic
458C2×C61#295711yescharacteristic
459D61—41no—
460D61—41no—
461D61—42no—
462D61—81no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466#568—1224no—
467#568—1224no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—611no—
472C2×#131—1221no—
473C2×#131—1221no—
474C2×#131C2×D6111yescharacteristic
475C22×M16—611no—
476C22×M16—611no—
477C22×M16—1221no—
478C22×M16—1221no—
479#525—611no—
480#452—611no—
481#452—611no—
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447—611no—
488#444—1224no—
489#443—1224no—
490#436—1221no—
491#436—1221no—
492#435—1221no—
493#435—1221no—
494C2×#108—611no—
495C2×#108C2×D6111yescharacteristic, complemented
496#424C2×D6111yescharacteristic, complemented
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104C2×D6111yescharacteristic
503#416—611no—
504#416C2×D6111yescharacteristic
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×C4×C8—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339C2×D6111yescharacteristic, complemented
516#336—611no—
517#336C2×D6111yescharacteristic, complemented
518C61#2146811yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—1221no—
524C2×#41—1221no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41C22×D6111yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16—611no—
545C2×D8—611no—
546C2×D8—611no—
547#131—22no—
548#131—22no—
549#131—614no—
550#131—614no—
551#131—1222no—
552#131—1222no—
553#131—1228no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1222no—
558#131—1228no—
559C2×M16—21no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—611no—
564C2×M16—611no—
565C2×M16—611no—
566C2×M16—1222no—
567C2×M16—1222no—
568C2×M16—1221no—
569C2×M16—1221no—
570C2×M16—1221no—
571C2×M16—1228no—
572C2×M16—1221no—
573C2×M16—1222no—
574C2×M16—1228no—
575C2×M16—1222no—
576C2×M16—1221no—
577C2×M16C22×D6111yescharacteristic
578C2×M16C22×D6111yescharacteristic
579C22×C8—21no—
580C22×C8—611no—
581C22×C8—611no—
582C22×C8—1221no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8C22×D6111yescharacteristic
588C22×C8C22×D6111yescharacteristic
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592#121—611no—
593#121—611no—
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117C22×D6111yescharacteristic
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42C22×D6111yescharacteristic
601#108—22no—
602#108—1222no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—22no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103C4×D6111yescharacteristic
614#103C4×D6111yescharacteristic
615#102—611no—
616#102—611no—
617#102C4×D6111yescharacteristic
618#102C4×D6111yescharacteristic
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—611no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8—1221no—
627#97—1222no—
628#97—1221no—
629C4×C8—1221no—
630C4×C8—1222no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—21no—
635#41—21no—
636#41—612no—
637#41—612no—
638#41—1224no—
639#41—1224no—
640#41—1222no—
641#41—1224no—
642#41—1224no—
643#41—1222no—
644#41—1222no—
645#41—1222no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41D4×D6112yes—
653#41#1175822612yes—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—1221no—
657C2×Q8—1222no—
658C2×Q8—1222no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1222no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1222no—
673C2×D4—1221no—
674C2×D4C2×C4×D6111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1224no—
685C22×C4—1224no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C23×D6111yescharacteristic
695Q16—1222no—
696Q16—1222no—
697SD16—1222no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—612no—
708M16—1222no—
709M16—1222no—
710M16—1222no—
711M16—1222no—
712M16—1224no—
713M16—1224no—
714M16—1224no—
715M16—1224no—
716M16—1221no—
717M16—1221no—
718M16—1221no—
719M16—2442no—
720M16D4×D6112yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—612no—
729C2×C8—612no—
730C2×C8—611no—
731C2×C8—611no—
732C2×C8—611no—
733C2×C8—611no—
734C2×C8—1224no—
735C2×C8—1224no—
736C2×C8—1224no—
737C2×C8—1224no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—2442no—
743C2×C8C2×C4×D6111yescharacteristic
744C2×C8C2×C4×D6111yescharacteristic
745C2×C8D4×D6111yescharacteristic
746C2×C8D4×D6111yescharacteristic
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4C2×C4×D6111yescharacteristic
750C4⋊C4C2×C4×D6111yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—611no—
764C23—611no—
765C23—1224no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—4881no—
771C23—4881no—
772C23—2441no—
773C23—2441no—
774C23#41×D6111yescharacteristic
775Q8—21no—
776Q8—612no—
777Q8—1224no—
778Q8—1221no—
779Q8—1221no—
780Q8—1221no—
781Q8#1451973912yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—612no—
786D4—1224no—
787D4—1224no—
788D4—1224no—
789D4—1222no—
790D4—1222no—
791D4—1221no—
792D4—1221no—
793D4—1221no—
794D4—4881no—
795D4—4881no—
796D4—2441no—
797D4—2441no—
798D4#1451973912yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—1224no—
810C2×C4—1224no—
811C2×C4—1224no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1222no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1221no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4C22×C4×D6111yescharacteristic
832C2×C4C2×D4×D6111yescharacteristic
833C2×C4C2×D4×D6111yescharacteristic
834C2×C4C2×D4×D6111yescharacteristic
835C2×C4#41×D6111yescharacteristic
836C2×C4C2×#1175822611yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—22no—
841C8—21no—
842C8—41no—
843C8—612no—
844C8—612no—
845C8—1221no—
846C8—1221no—
847C8—1222no—
848C8—2441no—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—1221no—
855C22—1222no—
856C22—1221no—
857C22—1221no—
858C22—1221no—
859C22—1221no—
860C22—1221no—
861C22—4881no—
862C22—4881no—
863C22—4884no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22C4×D4×D6111yescharacteristic
870C22#1684027011yescharacteristic
871C22#1684027511yescharacteristic
872C4—22no—
873C4—41no—
874C4—41no—
875C4—81no—
876C4—1221no—
877C4—1221no—
878C4—1222no—
879C4—2442no—
880C4—2441no—
881C4C4×D4×D6111yescharacteristic
882C4C2×#1451973911yescharacteristic
883C4#120×D6111yescharacteristic
884C4#1684027511yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—4881no—
889C2—2441no—
890C2—2441no—
891C2—2442no—
892C2#2144832011yescharacteristic
893C2#2145472711yescharacteristic
894C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1866C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1866D61
hypocenterC61#21468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. C2×#16840527C2semidirect
3. C2×#16839881C2semidirect
4. C2×#16839878C2semidirect
5. #21454521C2semidirect
6. #21446146C2semidirect
7. #21446145C2semidirect
8. #21446120C2semidirect
9. #21446093C2semidirect
10. #21446022C2semidirect
11. #21445761C2semidirect
12. #21445660C2semidirect
13. #21445659C2semidirect
14. #21445601C2semidirect
15. C61×#1866C2semidirect
23. C2×#14519785C22semidirect
32. #16839927C4semidirect
33. #16839925C4semidirect
34. #16839919C4semidirect
35. #16839914C4semidirect
36. #16839910C4semidirect
37. #16839908C4semidirect
38. #16839902C4semidirect
39. #16839897C4semidirect
46. C2×#14519712C22semidirect
48. C2×#14519705C22semidirect
51. C2×#14519703C22semidirect
53. #16839728C22semidirect
56. #16839718C22semidirect
57. C2×#14519688C22semidirect
58. C2×C8×Dic61C22semidirect
60. #16839527C22semidirect
61. #16839526C22semidirect
62. #16839521C22semidirect
63. #16839516C22semidirect
65. C2×#108×C61C22semidirect
66. C61×#424C22semidirect
69. C61×#339C22semidirect
70. C61×#336C22semidirect
102. #14519785D4semidirect
104. #14519784D4semidirect
447. #1866D61semidirect
495. C2×#108C2×D61semidirect
496. #424C2×D61semidirect
515. #339C2×D61semidirect
517. #336C2×D61semidirect
518. C61#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#214550392
C2×#168398812
C2×#168398782
#214545212
#214461462
#214461452
#214461202
#214460932
#214460222
#214457612
#214456602
#214456592
#214456012
C61×#18662
#2146861