Finite Group Databasebeta

← #29700794

Subgroups — #29700794

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455033C211yesmaximal, characteristic
2C2×#16839876C211yesmaximal, characteristic, complemented
3#21454549C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21454267C211yesmaximal, characteristic, complemented
6#21446520C211yesmaximal, characteristic, complemented
7#21446464C211yesmaximal, characteristic, complemented
8#21446264C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446148C211yesmaximal, characteristic, complemented
11#21446091C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445663C211yesmaximal, characteristic, complemented
14#21445588C211yesmaximal, characteristic, complemented
15C61×#1975C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C2×#14519784C2211yescharacteristic, complemented
20C2×#14519783C2211yescharacteristic
21C2×M16×D61C2211yescharacteristic
22#16840269C2211yescharacteristic
23C2×#14519734C2211yescharacteristic
24#16839923C411yescharacteristic, complemented
25#16839921C411yescharacteristic, complemented
26#16839916C411yescharacteristic, complemented
27#16839911C411yescharacteristic, complemented
28#16839906C411yescharacteristic, complemented
29#16839904C411yescharacteristic, complemented
30#16839899C411yescharacteristic, complemented
31#16839894C411yescharacteristic, complemented
32#16839876—24no—
33#16839837—21no—
34#16839836—21no—
35#16839830—21no—
36#16839825—21no—
37C2×#14519712C2211yescharacteristic, complemented
38#16839790C2211yescharacteristic, complemented
39#16839777—24no—
40C2×#14519705C2211yescharacteristic
41C2×#14519704C2211yescharacteristic
42C2×#14519704C2211yescharacteristic, complemented
43C2×#14519703C2211yescharacteristic
44#16839759C2211yescharacteristic
45#16839758C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839727—21no—
48#16839727—21no—
49#16839725C2211yescharacteristic
50#16839724—21no—
51C2×#14519689C2211yescharacteristic
52C2×#14519689C2211yescharacteristic
53C22⋊C8×D61—21no—
54#16839717C2211yescharacteristic, complemented
55C2×C4×#92418C2211yescharacteristic, complemented
56#16839527C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58#16839523C2211yescharacteristic, complemented
59#16839522C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C2×#135×C61C2211yescharacteristic
63C2×#108×C61C2211yescharacteristic, complemented
64C2×#104×C61C2211yescharacteristic
65C2×#104×C61C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic
67C61×#408C2211yescharacteristic, complemented
68C2×#97×C61C2211yescharacteristic, complemented
69C2×#11758226C2×C411yescharacteristic
70C2×#11758222—21no—
71C2×#11758222C2311yescharacteristic
72C2×#11758224—21no—
73C2×#11758224C2×C411yescharacteristic
74#41×D61—22no—
75#41×D61—22no—
76#41×D61—41no—
77#41×D61—41no—
78C2×Q8×D61C2×C411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61C2311yescharacteristic
83#14519797—22no—
84#14519797—22no—
85C2×#11758202C2×C411yescharacteristic
86C2×#11758200C2×C411yescharacteristic
87C2×#11758201C2×C411yescharacteristic
88C2×#11758199C2×C411yescharacteristic
89#14519785—22no—
90#14519785—41no—
91#14519784—22no—
92#14519784—41no—
93#14519783—22no—
94#14519783—41no—
95C2×#11758194—21no—
96C2×#11758194C2311yescharacteristic
97C2×#11758194C2311yescharacteristic
98C2×#11758189—21no—
99C2×#11758189—21no—
100C2×#11758189—21no—
101M16×D61—22no—
102M16×D61—41no—
103C22×#92418—21no—
104C22×#92418C2311yescharacteristic
105C22×#92418C2311yescharacteristic
106C2×C8×D61—21no—
107C2×C8×D61—21no—
108C2×C8×D61—21no—
109#14519758—21no—
110#14519753C2×C411yescharacteristic
111#14519753C2×C411yescharacteristic
112#14519748C2×C411yescharacteristic
113#14519748C2×C411yescharacteristic
114#14519745—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117#14519736C2311yescharacteristic
118#14519734—22no—
119#14519734—41no—
120C2×#11758196—21no—
121C2×#11758198—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519712—22no—
124#14519706—21no—
125#14519706—21no—
126#14519705D414yescomplemented
127#14519704—22no—
128#14519704—41no—
129#14519703—22no—
130#14519702C2×C411yescharacteristic
131#14519702C2×C411yescharacteristic
132#14519701C2×C411yescharacteristic
133#14519701C2×C411yescharacteristic
134#14519699C2×C411yescharacteristic
135#14519699C2×C411yescharacteristic
136#14519698C2×C411yescharacteristic
137#14519698C2×C411yescharacteristic
138C22⋊#92418—21no—
139C22⋊#92418—21no—
140#14519689—21no—
141#14519689—21no—
142#14519689C2×C411yescharacteristic
143#14519689C2×C411yescharacteristic
144#14519689C2×C411yescharacteristic
145#14519689C2×C411yescharacteristic
146#14519689D411yescharacteristic
147#14519689D411yescharacteristic
148#14519689D411yescharacteristic
149#14519689D411yescharacteristic
150#14519687—21no—
151C4×#92418—22no—
152C8×Dic61—21no—
153C2×#41×C61C2311yescharacteristic
154C2×#41×C61C2311yescharacteristic
155#135×C61—41no—
156#135×C61—41no—
157C2×Q16×C61C2×C411yescharacteristic
158C2×SD16×C61C2×C411yescharacteristic
159C2×SD16×C61C2×C411yescharacteristic
160C2×D8×C61C2×C411yescharacteristic
161C2×M16×C61C2311yescharacteristic
162C2×M16×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164C22×C8×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166#108×C61—41no—
167#104×C61—22no—
168#104×C61—22no—
169C22⋊C8×C61—21no—
170C22⋊C8×C61—21no—
171C22⋊C8×C61—21no—
172C22⋊C8×C61—21no—
173#97×C61—41no—
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184C2×Q8×C61C22×C411yescharacteristic
185C2×Q8×C61C22×C411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61C22×C411yescharacteristic
189C2×D4×C61C22×C411yescharacteristic
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C22×Dic61—21no—
200C22×Dic61—21no—
201C22×Dic61#4111yescharacteristic
202#11758226—22no—
203#11758226—41no—
204Q8×D61—22no—
205Q8×D61—41no—
206#11758224—22no—
207#11758224—41no—
208#11758224—42no—
209#11758224—42no—
210D4×D61—22no—
211D4×D61—41no—
212D4×D61—42no—
213D4×D61—42no—
214#11758222—21no—
215#11758222—21no—
216#11758222—42no—
217#11758222—42no—
218#11758222C2×D412yes—
219#11758222#4112yes—
220C2×D244—21no—
221C2×D244C22×C411yescharacteristic
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C22×C411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122C22×C411yescharacteristic
237Q16×C61—41no—
238SD16×C61—41no—
239SD16×C61—41no—
240D8×C61—41no—
241M16×C61—21no—
242M16×C61—21no—
243M16×C61—21no—
244M16×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61C22×C411yescharacteristic
252C2×C8×C61C22×C411yescharacteristic
253C2×C8×C61C2×D411yescharacteristic
254C2×C8×C61C2×D411yescharacteristic
255C42×C61—21no—
256C42×C61C2×D412yes—
257C22⋊Dic61—21no—
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260#11758202—22no—
261#11758201—22no—
262#11758200—22no—
263#11758199—22no—
264#11758198—21no—
265#11758198—21no—
266#11758198—42no—
267C4⋊Dic61C22×C411yescharacteristic
268C4⋊Dic61C22×C411yescharacteristic
269#11758196—21no—
270#11758196—21no—
271#11758196—42no—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275#11758194—21no—
276#11758194—21no—
277#11758194—21no—
278#11758194—42no—
279#11758194C2×D412yes—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—42no—
287C2×#92418C22×C411yescharacteristic
288C2×#92418C22×C411yescharacteristic
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291#11758189—42no—
292#11758189—42no—
293#11758189—42no—
294C8×D61—42no—
295C8×D61—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61C2×#4111yescharacteristic
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—42no—
306C22×D61—42no—
307C22×D61—81no—
308C22×D61C4×D411yescharacteristic
309C22×D61C4×D411yescharacteristic
310Q8×C61—21no—
311Q8×C61—21no—
312Q8×C61—21no—
313Q8×C61—21no—
314D4×C61—21no—
315D4×C61—21no—
316D4×C61—21no—
317D4×C61—21no—
318D4×C61—41no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—41no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61C23×C411yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61H(5,𝔽2)11yescharacteristic
336C2×C4×C61H(5,𝔽2)11yescharacteristic
337C22⋊D61—22no—
338C22⋊D61—22no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C22⋊D61—81no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—21no—
346C2×Dic61—21no—
347C2×Dic61—21no—
348C2×Dic61—42no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—41no—
352C2×Dic61C4×D411yescharacteristic
353C2×Dic61C4×D411yescharacteristic
354D244—21no—
355D244—42no—
356D244C4×D412yes—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—21no—
362C4×D61—22no—
363C4×D61—21no—
364C4×D61—22no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—42no—
368C4×D61—42no—
369Dic122—21no—
370Dic122—42no—
371Dic122C4×D412yes—
372C8×C61—21no—
373C8×C61—21no—
374C8×C61—21no—
375C8×C61—21no—
376C8×C61—41no—
377C8×C61—41no—
378#92418—21no—
379#92418—21no—
380#92418—21no—
381#92418—22no—
382#92418—21no—
383#92418—41no—
384#22889—611nomaximal, Sylow
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61C2×C4×D411yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#55111yescharacteristic
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—22no—
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—81no—
406C2×D61—81no—
407C2×D61—84no—
408C4×C61—42no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61C2×C4×D411yescharacteristic
412C4×C61#51811yescharacteristic
413C4×C61D4211yescharacteristic
414C4×C61#54611yescharacteristic
415Dic61—22no—
416Dic61—21no—
417Dic61—21no—
418Dic61—41no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975D6111yescharacteristic, complemented
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866—611no—
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—81no—
439C2×C61—81no—
440C2×C61#235811yescharacteristic
441C2×C61#295511yescharacteristic
442C2×C61#295711yescharacteristic
443D61—41no—
444D61—41no—
445D61—42no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135C2×D6111yescharacteristic
449C2×#131—611no—
450C2×#131—611no—
451C2×#131—611no—
452C22×M16—611no—
453#525—611no—
454C2×#117—611no—
455#452—611no—
456#452—611no—
457#451—611no—
458#450—611no—
459#449—611no—
460#449—611no—
461#448—611no—
462#447—611no—
463#443—1224no—
464#436—1221no—
465#435—1221no—
466#435—1221no—
467C8×D4—1221no—
468C2×#108—611no—
469C2×#108C2×D6111yescharacteristic, complemented
470#424—611no—
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104C2×D6111yescharacteristic
477C2×#104C2×D6111yescharacteristic, complemented
478#416—611no—
479#416—611no—
480#408—611no—
481#408—1221no—
482#408—1221no—
483#408C2×D6111yescharacteristic
484#408C2×D6111yescharacteristic, complemented
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97C2×D6111yescharacteristic, complemented
492C2×C4×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339—611no—
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—1221no—
504C2×#41—1221no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—2441no—
508C2×#41—2441no—
509C2×#41C22×D6111yescharacteristic
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—1221no—
516#135—41no—
517#135—41no—
518#135—1222no—
519#135—1222no—
520C2×Q16—611no—
521C2×Q16C4×D6111yescharacteristic
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16C4×D6111yescharacteristic
525C2×SD16C4×D6111yescharacteristic
526C2×D8—611no—
527C2×D8C4×D6111yescharacteristic
528#131—1222no—
529#131—1222no—
530#131—1222no—
531#131—2441no—
532#131—2441no—
533#131—2441no—
534C2×M16—611no—
535C2×M16—611no—
536C2×M16—1221no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—611no—
545C22×C8—611no—
546C22×C8—1221no—
547C22×C8—1221no—
548C22×C8—1221no—
549C22×C8—1221no—
550C22×C8C22×D6111yescharacteristic
551C22×C8C22×D6111yescharacteristic
552#123—1221no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555#121—611no—
556#121—611no—
557#120—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560#117—611no—
561#117—1222no—
562#117—2441no—
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42C22×D6111yescharacteristic
567#108—41no—
568#108—1222no—
569C4⋊C8—1221no—
570C4⋊C8—1221no—
571#104—22no—
572#104—22no—
573#104—614no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
577#103—611no—
578#103—611no—
579#103—611no—
580#103—611no—
581#102—611no—
582#102—611no—
583#102—611no—
584#102—611no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—41no—
602#97—1221no—
603C4×C8—1221no—
604C4×C8—1222no—
605C24—611no—
606C24—1221no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—612no—
616#41—612no—
617#41—1221no—
618#41—1221no—
619#41—1222no—
620#41—1222no—
621#41—2442no—
622#41—2442no—
623#41—2441no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627C2×Q8—611no—
628C2×Q8—1221no—
629C2×Q8—1222no—
630C2×Q8—2441no—
631C2×Q8C2×C4×D6111yescharacteristic
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1222no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—2441no—
644C2×D4—2442no—
645C2×D4—2442no—
646C2×D4C2×C4×D6111yescharacteristic
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—2442no—
666C22×C4—2442no—
667C22×C4C23×D6111yescharacteristic
668Q16—41no—
669Q16—1222no—
670SD16—41no—
671SD16—41no—
672SD16—1222no—
673SD16—1222no—
674D8—41no—
675D8—1222no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—612no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—2442no—
685M16—2442no—
686M16—2442no—
687M16—2442no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—611no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—2442no—
705C2×C8—2442no—
706C2×C8—2442no—
707C2×C8—2442no—
708C2×C8C2×C4×D6111yescharacteristic
709C2×C8C2×C4×D6111yescharacteristic
710C2×C8D4×D6111yescharacteristic
711C2×C8D4×D6111yescharacteristic
712C4⋊C4—611no—
713C4⋊C4—611no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—2442no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—2442no—
723C42—21no—
724C42—1221no—
725C42—1221no—
726C42—1221no—
727C42D4×D6112yes—
728C23—21no—
729C23—21no—
730C23—611no—
731C23—611no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23#41×D6111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—612no—
746Q8—1221no—
747Q8—2442no—
748D4—21no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—612no—
757D4—1222no—
758D4—1222no—
759D4—1221no—
760D4—4881no—
761D4—2442no—
762D4—2442no—
763D4—2442no—
764D4—2442no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1222no—
785C2×C4—1221no—
786C2×C4—1222no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—2442no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2441no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4C22×C4×D6111yescharacteristic
798C2×C4C2×D4×D6111yescharacteristic
799C2×C4C2×D4×D6111yescharacteristic
800C2×C4#41×D6111yescharacteristic
801C2×C4#1451982211yescharacteristic
802C2×C4#1451982211yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—1221no—
810C8—1221no—
811C8—1221no—
812C8—1221no—
813C8—1222no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—1221no—
824C22—1221no—
825C22—1222no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—4881no—
831C22—4881no—
832C22—4884no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22#1684040111yescharacteristic
837C22#1684044211yescharacteristic
838C4—42no—
839C4—41no—
840C4—41no—
841C4—1221no—
842C4—1221no—
843C4—1222no—
844C4—4881no—
845C4—2441no—
846C4—2441no—
847C4C4×D4×D6111yescharacteristic
848C4#1684023511yescharacteristic
849C4#1684039711yescharacteristic
850C4#1684040111yescharacteristic
851C2—21no—
852C2—21no—
853C2—81no—
854C2—81no—
855C2—2441no—
856C2—2441no—
857C2—2442no—
858C2#2144880011yescharacteristic
859C2#2145471911yescharacteristic
860C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1975C2
socleC22×C61C2×C4×D4
prime radical#21455033C2
cosocleC22×C4×C61C24
hypercenter#1975D61
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1975

Complements

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

NH ≅ G/Ntype
2. C2×#16839876C2semidirect
3. #21454549C2semidirect
4. C2×#16839777C2semidirect
5. #21454267C2semidirect
6. #21446520C2semidirect
7. #21446464C2semidirect
8. #21446264C2semidirect
9. #21446149C2semidirect
10. #21446148C2semidirect
11. #21446091C2semidirect
12. #21446022C2semidirect
13. #21445663C2semidirect
14. #21445588C2semidirect
15. C61×#1975C2semidirect
19. C2×#14519784C22semidirect
24. #16839923C4semidirect
25. #16839921C4semidirect
26. #16839916C4semidirect
27. #16839911C4semidirect
28. #16839906C4semidirect
29. #16839904C4semidirect
30. #16839899C4semidirect
31. #16839894C4semidirect
37. C2×#14519712C22semidirect
38. #16839790C22semidirect
42. C2×#14519704C22semidirect
54. #16839717C22semidirect
55. C2×C4×#92418C22semidirect
56. #16839527C22semidirect
57. #16839526C22semidirect
58. #16839523C22semidirect
59. #16839522C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
63. C2×#108×C61C22semidirect
65. C2×#104×C61C22semidirect
67. C61×#408C22semidirect
68. C2×#97×C61C22semidirect
126. #14519705D4semidirect
426. #1975D61semidirect
469. C2×#108C2×D61semidirect
477. C2×#104C2×D61semidirect
484. #408C2×D61semidirect
491. C2×#97C2×D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550332
C2×#168398762
#214545492
C2×#168397772
#214542672
#214465202
#214464642
#214462642
#214461492
#214461482
#214460912
#214460222
#214456632
#214455882
C61×#19752
#2288961