Finite Group Databasebeta

← #29700802

Subgroups — #29700802

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#21455039C211yesmaximal, characteristic
2C2×#16839880C211yesmaximal, characteristic, complemented
3#21454543C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21454267C211yesmaximal, characteristic, complemented
6#21446709C211yesmaximal, characteristic, complemented
7#21446469C211yesmaximal, characteristic, complemented
8#21446266C211yesmaximal, characteristic, complemented
9#21446149C211yesmaximal, characteristic, complemented
10#21446147C211yesmaximal, characteristic, complemented
11#21446093C211yesmaximal, characteristic, complemented
12#21446025C211yesmaximal, characteristic, complemented
13#21445660C211yesmaximal, characteristic, complemented
14#21445586C211yesmaximal, characteristic, complemented
15C61×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519783C2211yescharacteristic
21C2×#14519783C2211yescharacteristic, complemented
22C2×M16×D61C2211yescharacteristic
23#16840274C2211yescharacteristic
24C2×#14519734C2211yescharacteristic
25#16839927C411yescharacteristic, complemented
26#16839925C411yescharacteristic, complemented
27#16839919C411yescharacteristic, complemented
28#16839914C411yescharacteristic, complemented
29#16839910C411yescharacteristic, complemented
30#16839908C411yescharacteristic, complemented
31#16839902C411yescharacteristic, complemented
32#16839897C411yescharacteristic, complemented
33#16839880—24no—
34#16839839—21no—
35#16839832—21no—
36#16839832—21no—
37#16839827—21no—
38C2×#14519713C2211yescharacteristic, complemented
39C2×#14519712C2211yescharacteristic, complemented
40#16839777—24no—
41C2×#14519705C2211yescharacteristic
42C2×#14519705C2211yescharacteristic, complemented
43C2×#14519704C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45C2×#14519703C2211yescharacteristic, complemented
46#16839756C2211yescharacteristic
47#16839730C2211yescharacteristic, complemented
48#16839729C2211yescharacteristic
49#16839727—21no—
50#16839727—21no—
51#16839725C2211yescharacteristic
52#16839724—21no—
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55C22⋊C8×D61—21no—
56#16839718C2211yescharacteristic, complemented
57C2×#14519688C2211yescharacteristic, complemented
58#16839526C2211yescharacteristic, complemented
59#16839521C2211yescharacteristic, complemented
60#16839516C2211yescharacteristic, complemented
61#16839516C2211yescharacteristic, complemented
62C61×#424C2211yescharacteristic, complemented
63C2×#104×C61C2211yescharacteristic
64C61×#416C2211yescharacteristic
65C61×#408C2211yescharacteristic
66C2×C4×C8×C61C2211yescharacteristic, complemented
67C61×#341C2211yescharacteristic, complemented
68C61×#339C2211yescharacteristic, complemented
69C2×#11758226C2×C411yescharacteristic
70C2×#11758222—21no—
71C2×#11758222C2311yescharacteristic
72C2×#11758222C2311yescharacteristic
73C2×#11758224—21no—
74C2×#11758224C2×C411yescharacteristic
75#41×D61—22no—
76#41×D61—22no—
77#41×D61—41no—
78#41×D61—41no—
79C2×Q8×D61C2×C411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84#14519799—22no—
85#14519799—22no—
86#14519797—41no—
87#14519797—41no—
88C2×Dic244C2×C411yescharacteristic
89C2×#11758202C2×C411yescharacteristic
90C2×#11758190C2×C411yescharacteristic
91C2×#11758190C2×C411yescharacteristic
92C2×#11758200C2×C411yescharacteristic
93C2×#11758201C2×C411yescharacteristic
94C2×D488C2×C411yescharacteristic
95C2×#11758199C2×C411yescharacteristic
96#14519785—22no—
97#14519785—41no—
98#14519783—22no—
99#14519783—22no—
100#14519783—41no—
101#14519783—41no—
102C2×#11758194C2311yescharacteristic
103C2×#11758194C2311yescharacteristic
104C2×#11758189—21no—
105C2×#11758189—21no—
106C2×#11758189—21no—
107C2×#11758189—21no—
108M16×D61—22no—
109M16×D61—41no—
110C22×#92418C2311yescharacteristic
111C22×#92418C2311yescharacteristic
112C2×C8×D61—21no—
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115C2×C8×D61—21no—
116#14519761—21no—
117#14519757C2×C411yescharacteristic
118#14519757C2×C411yescharacteristic
119#14519752C2×C411yescharacteristic
120#14519752C2×C411yescharacteristic
121#14519747—21no—
122C4×D244—21no—
123C4×D244—21no—
124#14519734—22no—
125#14519734—41no—
126C2×#11758196—21no—
127C2×#11758198—21no—
128C2×C4×Dic61C2311yescharacteristic
129#14519713—22no—
130#14519712—41no—
131#14519705—22no—
132#14519705D414yescomplemented
133#14519704—22no—
134#14519703—22no—
135#14519703—41no—
136#14519700C2×C411yescharacteristic
137#14519700C2×C411yescharacteristic
138#14519697C2×C411yescharacteristic
139#14519697C2×C411yescharacteristic
140C22⋊#92418—21no—
141C22⋊#92418—21no—
142#14519689—21no—
143#14519689—21no—
144#14519689—21no—
145#14519689—21no—
146#14519689C2×C411yescharacteristic
147#14519689C2×C411yescharacteristic
148#14519689C2×C411yescharacteristic
149#14519689C2×C411yescharacteristic
150#14519689D411yescharacteristic
151#14519689D411yescharacteristic
152#14519689D411yescharacteristic
153#14519689D411yescharacteristic
154#14519688—21no—
155#14519688—41no—
156C4×#92418—21no—
157C2×#41×C61C2311yescharacteristic
158C2×M16×C61C2311yescharacteristic
159C2×M16×C61C2311yescharacteristic
160C22×C8×C61C2311yescharacteristic
161C22×C8×C61C2311yescharacteristic
162#117×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164C4⋊C8×C61—21no—
165C4⋊C8×C61—21no—
166#104×C61—22no—
167#103×C61C2×C411yescharacteristic
168#103×C61C2×C411yescharacteristic
169#102×C61C2×C411yescharacteristic
170#102×C61C2×C411yescharacteristic
171C22⋊C8×C61—21no—
172C22⋊C8×C61—21no—
173C4×C8×C61—22no—
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C2411yescharacteristic
186C2×C22⋊D61—21no—
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61#4111yescharacteristic
193#11758226—22no—
194#11758226—41no—
195Q8×D61—22no—
196Q8×D61—41no—
197#11758224—22no—
198#11758224—41no—
199#11758224—42no—
200#11758224—42no—
201D4×D61—22no—
202D4×D61—41no—
203D4×D61—42no—
204D4×D61—42no—
205#11758222—21no—
206#11758222—21no—
207#11758222—21no—
208#11758222—21no—
209#11758222—21no—
210#11758222—21no—
211#11758222—42no—
212#11758222—42no—
213#11758222C2×D412yes—
214#11758222#4112yes—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244C22×C411yescharacteristic
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
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—42no—
229C2×C4×D61—42no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122C22×C411yescharacteristic
236C2×Dic122C22×C411yescharacteristic
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61C22×C411yescharacteristic
248C2×C8×C61C22×C411yescharacteristic
249C2×C8×C61C2×D411yescharacteristic
250C2×C8×C61C2×D411yescharacteristic
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C22⋊C4×C61—21no—
254C42×C61—21no—
255C42×C61—21no—
256C42×C61C2×D412yes—
257#11758202—41no—
258#11758201—41no—
259#11758200—41no—
260#11758199—41no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—42no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268#11758196—42no—
269C4×Dic61—21no—
270C4×Dic61—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—21no—
274#11758194C2×D412yes—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418C22×C411yescharacteristic
282C2×#92418C22×C411yescharacteristic
283C2×#92418C2×D411yescharacteristic
284C2×#92418C2×D411yescharacteristic
285Dic244—22no—
286D488—22no—
287#11758190—22no—
288#11758190—22no—
289#11758189—42no—
290#11758189—42no—
291#11758189—42no—
292#11758189—42no—
293C8×D61—42no—
294C8×D61—42no—
295C8×D61—42no—
296C8×D61—42no—
297C23×C61—21no—
298C23×C61C2×#4111yescharacteristic
299C22×D61—21no—
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—
312D4×C61—21no—
313D4×C61—21no—
314D4×C61—41no—
315D4×C61—41no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61H(5,𝔽2)11yescharacteristic
329C2×C4×C61H(5,𝔽2)11yescharacteristic
330C22⋊D61—22no—
331C22⋊D61—22no—
332C22⋊D61—42no—
333C22⋊D61—42no—
334C22⋊D61—41no—
335C22⋊D61—41no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—42no—
341C2×Dic61—41no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61C4×D411yescharacteristic
345C2×Dic61C4×D411yescharacteristic
346D244—21no—
347D244—21no—
348D244—21no—
349D244—42no—
350D244—42no—
351D244—81no—
352D244C4×D412yes—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—22no—
359C4×D61—21no—
360C4×D61—22no—
361C4×D61—21no—
362C4×D61—21no—
363C4×D61—42no—
364C4×D61—42no—
365C4×D61—41no—
366C4×D61—41no—
367Dic122—21no—
368Dic122—21no—
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—22no—
381#92418—21no—
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×C61C2×C4×D411yescharacteristic
391C22×C61#54611yescharacteristic
392C22×C61#55111yescharacteristic
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—22no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—21no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
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×C61—41no—
412C4×C61C2×C4×D411yescharacteristic
413C4×C61#51811yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416Dic61—22no—
417Dic61—21no—
418Dic61—21no—
419Dic61—41no—
420Dic61—81no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937D6111yescharacteristic, complemented
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#235811yescharacteristic
440C2×C61#295511yescharacteristic
441C2×C61#295711yescharacteristic
442D61—41no—
443D61—41no—
444D61—42no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
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×#108—611no—
470#424C2×D6111yescharacteristic, complemented
471#421—1224no—
472C2×#104—611no—
473C2×#104—611no—
474C2×#104—611no—
475C2×#104—611no—
476C2×#104—611no—
477C2×#104C2×D6111yescharacteristic
478#416—611no—
479#416C2×D6111yescharacteristic
480#408—611no—
481#408—611no—
482#408—1221no—
483#408—1221no—
484#408C2×D6111yescharacteristic
485#407—611no—
486#407—1221no—
487C2×C22⋊C8—611no—
488C2×C22⋊C8—611no—
489C2×C22⋊C8—1221no—
490#405—611no—
491C2×#97—611no—
492C2×C4×C8C2×D6111yescharacteristic, complemented
493#341—611no—
494#341C2×D6111yescharacteristic, complemented
495#339—611no—
496#339C2×D6111yescharacteristic, complemented
497#336—611no—
498#336—611no—
499C61#2288911yescharacteristic, complemented, Sylow
500C2×#41—611no—
501C2×#41—611no—
502C2×#41—611no—
503C2×#41—611no—
504C2×#41—1221no—
505C2×#41—1221no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—2441no—
509C2×#41—2441no—
510C2×#41C22×D6111yescharacteristic
511C22×Q8—611no—
512C22×D4—611no—
513C22×D4—1221no—
514C23×C4—611no—
515C23×C4—1221no—
516#135—1222no—
517#135—1222no—
518#135—2441no—
519#135—2441no—
520C2×Q16—611no—
521C2×Q16—611no—
522C2×SD16—611no—
523C2×SD16—611no—
524C2×SD16—611no—
525C2×SD16—611no—
526C2×D8—611no—
527C2×D8—611no—
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—1222no—
561#117—2441no—
562#117C22×D6111yescharacteristic
563C2×C4⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C42—611no—
566C2×C42C22×D6111yescharacteristic
567#108—1222no—
568#108—2441no—
569C4⋊C8—21no—
570C4⋊C8—21no—
571#104—22no—
572#104—614no—
573#104—1222no—
574#104—1222no—
575#104—1222no—
576#104—2441no—
577#103—611no—
578#103—611no—
579#103C4×D6111yescharacteristic
580#103C4×D6111yescharacteristic
581#102—611no—
582#102—611no—
583#102C4×D6111yescharacteristic
584#102C4×D6111yescharacteristic
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—611no—
594C22⋊C8—611no—
595C22⋊C8—1221no—
596C22⋊C8—1221no—
597C22⋊C8—1221no—
598C22⋊C8—1221no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—1221no—
602#97—2441no—
603C4×C8—22no—
604C4×C8—1221no—
605C24—611no—
606C24—1221no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—612no—
612#41—612no—
613#41—1221no—
614#41—1221no—
615#41—1222no—
616#41—1222no—
617#41—1221no—
618#41—1221no—
619#41—1221no—
620#41—1221no—
621#41—2442no—
622#41—2442no—
623#41—2441no—
624#41—2442no—
625#41—2442no—
626#41—2441no—
627C2×Q8—611no—
628C2×Q8—611no—
629C2×Q8—1221no—
630C2×Q8—1222no—
631C2×Q8—2441no—
632C2×Q8C2×C4×D6111yescharacteristic
633C2×D4—21no—
634C2×D4—611no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1222no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2441no—
645C2×D4—2442no—
646C2×D4—2442no—
647C2×D4C2×C4×D6111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—611no—
651C22×C4—611no—
652C22×C4—611no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—1221no—
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—1222no—
669Q16—2441no—
670SD16—1222no—
671SD16—1222no—
672SD16—2441no—
673SD16—2441no—
674D8—1222no—
675D8—2441no—
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—1221no—
713C4⋊C4—1221no—
714C4⋊C4—2442no—
715C4⋊C4C2×C4×D6111yescharacteristic
716C4⋊C4C2×C4×D6111yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—2442no—
723C42—21no—
724C42—21no—
725C42—1221no—
726C42—1221no—
727C42D4×D6112yes—
728C23—21no—
729C23—611no—
730C23—611no—
731C23—1221no—
732C23—1221no—
733C23—1221no—
734C23—1221no—
735C23—4881no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23#41×D6111yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—612no—
744Q8—1221no—
745Q8—1221no—
746Q8—1221no—
747Q8—2442no—
748D4—21no—
749D4—21no—
750D4—41no—
751D4—41no—
752D4—612no—
753D4—1222no—
754D4—1222no—
755D4—1221no—
756D4—1221no—
757D4—1221no—
758D4—4881no—
759D4—2442no—
760D4—2442no—
761D4—2442no—
762D4—2442no—
763D4—2441no—
764D4—2441no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1222no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4—2441no—
793C2×C4—2441no—
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#1451982311yescharacteristic
802C2×C4#1451982311yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—1221no—
810C8—1221no—
811C8—1222no—
812C8—1221no—
813C8—1221no—
814C8—2441no—
815C22—21no—
816C22—21no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—1221no—
821C22—1221no—
822C22—1222no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—1221no—
827C22—4881no—
828C22—4881no—
829C22—4884no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22#1684040411yescharacteristic
837C22#1684043711yescharacteristic
838C4—42no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—1221no—
843C4—1221no—
844C4—1222no—
845C4—4881no—
846C4—2441no—
847C4C4×D4×D6111yescharacteristic
848C4#1684023611yescharacteristic
849C4#1684039611yescharacteristic
850C4#1684040511yescharacteristic
851C2—21no—
852C2—21no—
853C2—81no—
854C2—4881no—
855C2—2441no—
856C2—2441no—
857C2—2442no—
858C2#2144879711yescharacteristic
859C2#2145471711yescharacteristic
860C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1937C2
socleC22×C61C2×C4×D4
prime radical#21455039C2
cosocleC22×C4×C61C24
hypercenter#1937D61
hypocenterC61#22889
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. C2×#16839880C2semidirect
3. #21454543C2semidirect
4. C2×#16839777C2semidirect
5. #21454267C2semidirect
6. #21446709C2semidirect
7. #21446469C2semidirect
8. #21446266C2semidirect
9. #21446149C2semidirect
10. #21446147C2semidirect
11. #21446093C2semidirect
12. #21446025C2semidirect
13. #21445660C2semidirect
14. #21445586C2semidirect
15. C61×#1937C2semidirect
21. C2×#14519783C22semidirect
25. #16839927C4semidirect
26. #16839925C4semidirect
27. #16839919C4semidirect
28. #16839914C4semidirect
29. #16839910C4semidirect
30. #16839908C4semidirect
31. #16839902C4semidirect
32. #16839897C4semidirect
38. C2×#14519713C22semidirect
39. C2×#14519712C22semidirect
42. C2×#14519705C22semidirect
45. C2×#14519703C22semidirect
47. #16839730C22semidirect
56. #16839718C22semidirect
57. C2×#14519688C22semidirect
58. #16839526C22semidirect
59. #16839521C22semidirect
60. #16839516C22semidirect
61. #16839516C22semidirect
62. C61×#424C22semidirect
66. C2×C4×C8×C61C22semidirect
67. C61×#341C22semidirect
68. C61×#339C22semidirect
132. #14519705D4semidirect
427. #1937D61semidirect
470. #424C2×D61semidirect
492. C2×C4×C8C2×D61semidirect
494. #341C2×D61semidirect
496. #339C2×D61semidirect
499. C61#22889semidirect

Maximal subgroups

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

subgroupindex
#214550392
C2×#168398802
#214545432
C2×#168397772
#214542672
#214467092
#214464692
#214462662
#214461492
#214461472
#214460932
#214460252
#214456602
#214455862
C61×#19372
#2288961