Finite Group Databasebeta

← #29700793

Subgroups — #29700793

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×#16839877C211yesmaximal, characteristic, complemented
3#21454543C211yesmaximal, characteristic, complemented
4C2×#16839777C211yesmaximal, characteristic, complemented
5#21454266C211yesmaximal, characteristic, complemented
6#21446710C211yesmaximal, characteristic, complemented
7#21446522C211yesmaximal, characteristic, complemented
8#21446465C211yesmaximal, characteristic, complemented
9#21446266C211yesmaximal, characteristic, complemented
10#21446145C211yesmaximal, characteristic, complemented
11#21446144C211yesmaximal, characteristic, complemented
12#21446022C211yesmaximal, characteristic, complemented
13#21445666C211yesmaximal, characteristic, complemented
14#21445584C211yesmaximal, characteristic, complemented
15C61×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#14519799C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519784C2211yescharacteristic
20C2×#14519783C2211yescharacteristic, complemented
21C2×M16×D61C2211yescharacteristic
22#16840274C2211yescharacteristic
23C2×#14519734C2211yescharacteristic
24#16839927C411yescharacteristic, complemented
25#16839925C411yescharacteristic, complemented
26#16839919C411yescharacteristic, complemented
27#16839914C411yescharacteristic, complemented
28#16839910C411yescharacteristic, complemented
29#16839908C411yescharacteristic, complemented
30#16839902C411yescharacteristic, complemented
31#16839897C411yescharacteristic, complemented
32#16839877—24no—
33#16839839—21no—
34#16839832—21no—
35#16839832—21no—
36#16839827—21no—
37C2×#14519712C2211yescharacteristic, complemented
38#16839777—24no—
39C2×#14519705C2211yescharacteristic
40C2×#14519705C2211yescharacteristic, complemented
41C2×#14519704C2211yescharacteristic
42C2×#14519703C2211yescharacteristic
43C2×#14519703C2211yescharacteristic, complemented
44#16839756C2211yescharacteristic
45#16839730—21no—
46#16839730C2211yescharacteristic
47#16839730C2211yescharacteristic, complemented
48#16839728—21no—
49#16839728C2211yescharacteristic
50#16839725—21no—
51#16839725C2211yescharacteristic
52C2×#14519689—21no—
53C2×#14519689C2211yescharacteristic
54C2×#14519689C2211yescharacteristic
55#16839718C2211yescharacteristic, complemented
56C2×#14519687C2211yescharacteristic, complemented
57C2×C8×Dic61C2211yescharacteristic, complemented
58#16839527C2211yescharacteristic, complemented
59#16839526C2211yescharacteristic, complemented
60#16839521C2211yescharacteristic, complemented
61#16839517C2211yescharacteristic, complemented
62C2×#131×C61C2211yescharacteristic
63C2×#108×C61C2211yescharacteristic, complemented
64C61×#424C2211yescharacteristic, complemented
65C2×#104×C61C2211yescharacteristic
66C61×#416C2211yescharacteristic
67C61×#339C2211yescharacteristic, complemented
68C61×#336C2211yescharacteristic, 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—41no—
85#14519799—41no—
86#14519797—22no—
87#14519797—22no—
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#14519784—22no—
97#14519784—41no—
98#14519783—22no—
99#14519783—41no—
100C2×#11758194—21no—
101C2×#11758194C2311yescharacteristic
102C2×#11758194C2311yescharacteristic
103C2×#11758189—21no—
104C2×#11758189—21no—
105M16×D61—22no—
106M16×D61—41no—
107C22×#92418—21no—
108C22×#92418C2311yescharacteristic
109C22×#92418C2311yescharacteristic
110C2×C8×D61—21no—
111C2×C8×D61—21no—
112#14519761—21no—
113#14519757C2×C411yescharacteristic
114#14519757C2×C411yescharacteristic
115#14519752C2×C411yescharacteristic
116#14519752C2×C411yescharacteristic
117#14519747—21no—
118C4×D244—21no—
119C4×D244—21no—
120#14519734—22no—
121#14519734—41no—
122C2×#11758196—21no—
123C2×#11758198—21no—
124C2×C4×Dic61C2311yescharacteristic
125#14519712—22no—
126#14519705—22no—
127#14519705—41no—
128#14519704D414yescomplemented
129#14519703—22no—
130#14519703—22no—
131#14519700C2×C411yescharacteristic
132#14519700C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134#14519697C2×C411yescharacteristic
135#14519689—21no—
136#14519689—21no—
137#14519689—21no—
138#14519689—21no—
139#14519689—21no—
140#14519689—21no—
141#14519689—21no—
142#14519689—21no—
143#14519689C2×C411yescharacteristic
144#14519689C2×C411yescharacteristic
145#14519689C2×C411yescharacteristic
146#14519689C2×C411yescharacteristic
147#14519689D411yescharacteristic
148#14519689D411yescharacteristic
149#14519689D411yescharacteristic
150#14519689D411yescharacteristic
151#14519688—21no—
152#14519687—41no—
153C4×#92418—21no—
154C8×Dic61—22no—
155C2×#41×C61C2311yescharacteristic
156#131×C61—22no—
157#131×C61—41no—
158C2×M16×C61—21no—
159C2×M16×C61C2311yescharacteristic
160C2×M16×C61C2311yescharacteristic
161C22×C8×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#117×C61C2311yescharacteristic
165C2×C42×C61C2311yescharacteristic
166#108×C61—41no—
167C4⋊C8×C61—21no—
168C4⋊C8×C61—21no—
169#104×C61—22no—
170#103×C61C2×C411yescharacteristic
171#103×C61C2×C411yescharacteristic
172#102×C61C2×C411yescharacteristic
173#102×C61C2×C411yescharacteristic
174C23×D61—21no—
175C23×D61#4111yescharacteristic
176#41×C61—21no—
177#41×C61—21no—
178#41×C61C2×D412yes—
179#41×C61#4112yes—
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—21no—
212#11758222—21no—
213#11758222—42no—
214#11758222—42no—
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—
241M16×C61—42no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—42no—
249C2×C8×C61C22×C411yescharacteristic
250C2×C8×C61C22×C411yescharacteristic
251C2×C8×C61C2×D411yescharacteristic
252C2×C8×C61C2×D411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C22⋊C4×C61—21no—
256C42×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259#11758202—22no—
260#11758201—22no—
261#11758200—22no—
262#11758199—22no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—42no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270#11758196—42no—
271C4×Dic61—21no—
272C4×Dic61C2×D412yes—
273#11758194—21no—
274#11758194—21no—
275#11758194—21no—
276#11758194—42no—
277#11758194C2×D412yes—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—42no—
285C2×#92418C22×C411yescharacteristic
286C2×#92418C22×C411yescharacteristic
287C2×#92418C2×D411yescharacteristic
288C2×#92418C2×D411yescharacteristic
289Dic244—41no—
290D488—41no—
291#11758190—41no—
292#11758190—41no—
293#11758189—42no—
294#11758189—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×C61C4×D412yes—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—21no—
315D4×C61C4×D412yes—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
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—42no—
331C22⋊D61—42no—
332C22⋊D61—41no—
333C22⋊D61—41no—
334C22⋊D61—41no—
335C22⋊D61—41no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—22no—
341C2×Dic61—42no—
342C2×Dic61—41no—
343C2×Dic61—41no—
344C2×Dic61C4×D411yescharacteristic
345C2×Dic61C4×D411yescharacteristic
346D244—21no—
347D244—21no—
348D244—21no—
349D244—21no—
350D244—42no—
351D244—42no—
352D244—81no—
353C4×D61—21no—
354C4×D61—21no—
355C4×D61—21no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122—21no—
371Dic122—42no—
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—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61C2×C4×D411yescharacteristic
391C22×C61#54611yescharacteristic
392C22×C61#55111yescharacteristic
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—21no—
398C2×D61—21no—
399C2×D61—41no—
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—22no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61—81no—
412C4×C61C2×C4×D411yescharacteristic
413C4×C61#51811yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416Dic61—21no—
417Dic61—21no—
418Dic61—42no—
419Dic61—41no—
420Dic61—41no—
421#3002—611no—
422C2×#443—611no—
423#2933—611no—
424C2×#421—611no—
425#2880—611no—
426#1975—611no—
427#1937—611no—
428#1929—611no—
429#1897—611no—
430#1876—611no—
431#1876—611no—
432#1866D6111yescharacteristic, complemented
433#1855—611no—
434#1765—611no—
435#1750—611no—
436C2×C61—21no—
437C2×C61—21no—
438C2×C61—42no—
439C2×C61#235811yescharacteristic
440C2×C61#295511yescharacteristic
441C2×C61#295711yescharacteristic
442D61—41no—
443D61—41no—
444D61—81no—
445D61—81no—
446C22×#41—611no—
447C2×#135—611no—
448C2×#135—611no—
449C2×#131—611no—
450C2×#131—611no—
451C2×#131C2×D6111yescharacteristic
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#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—611no—
483#408—1221no—
484#408—1221no—
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×C8—611no—
493#341—611no—
494#341—611no—
495#339—611no—
496#339C2×D6111yescharacteristic, complemented
497#336—611no—
498#336C2×D6111yescharacteristic, complemented
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—22no—
529#131—41no—
530#131—1222no—
531#131—1222no—
532#131—2441no—
533#131—2441no—
534C2×M16—21no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—1221no—
538C2×M16—1221no—
539C2×M16—1221no—
540C2×M16—1222no—
541C2×M16—2441no—
542C2×M16C22×D6111yescharacteristic
543C2×M16C22×D6111yescharacteristic
544C22×C8—21no—
545C22×C8—611no—
546C22×C8—611no—
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—41no—
568#108—1222no—
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—611no—
586C22⋊C8—611no—
587C22⋊C8—611no—
588C22⋊C8—611no—
589C22⋊C8—611no—
590C22⋊C8—611no—
591C22⋊C8—611no—
592C22⋊C8—611no—
593C22⋊C8—1221no—
594C22⋊C8—1221no—
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—1221no—
604C4×C8—1222no—
605C24—611no—
606C24—1221no—
607#41—21no—
608#41—21no—
609#41—1222no—
610#41—1222no—
611#41—1221no—
612#41—1221no—
613#41—1221no—
614#41—1221no—
615#41—1221no—
616#41—1221no—
617#41—1221no—
618#41—1221no—
619#41—2442no—
620#41—2442no—
621#41—2441no—
622#41—2442no—
623#41—2442no—
624#41—2441no—
625#41D4×D6112yes—
626#41#1175822612yes—
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—42no—
681M16—612no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
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—42no—
695C2×C8—611no—
696C2×C8—611no—
697C2×C8—611no—
698C2×C8—611no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—1221no—
704C2×C8—1221no—
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—21no—
726C42—612no—
727C42—1221no—
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—1221no—
743Q8—1221no—
744Q8—1221no—
745Q8—1221no—
746Q8—2442no—
747Q8#1451973912yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—1221no—
752D4—1221no—
753D4—1221no—
754D4—1221no—
755D4—4881no—
756D4—2442no—
757D4—2442no—
758D4—2442no—
759D4—2442no—
760D4—2441no—
761D4—2441no—
762D4—2441no—
763D4—2441no—
764D4#1451973912yes—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
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—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—2442no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2441no—
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×C4C2×#1175822611yescharacteristic
801C2×C4#1451982211yescharacteristic
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—22no—
818C22—41no—
819C22—41no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—1221no—
825C22—1221no—
826C22—4881no—
827C22—4881no—
828C22—4884no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22—2441no—
833C22—2441no—
834C22—2441no—
835C22C4×D4×D6111yescharacteristic
836C22#1684040411yescharacteristic
837C22#1684043911yescharacteristic
838C4—22no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—1221no—
843C4—1221no—
844C4—2442no—
845C4—2441no—
846C4—2441no—
847C4C2×#1451973911yescharacteristic
848C4#1684023411yescharacteristic
849C4#1684039411yescharacteristic
850C4#1684040311yescharacteristic
851C2—21no—
852C2—21no—
853C2—42no—
854C2—4881no—
855C2—4881no—
856C2—2441no—
857C2—2441no—
858C2#2144879511yescharacteristic
859C2#2145471711yescharacteristic
860C2#2145473311yescharacteristic
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#22889
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
2. C2×#16839877C2semidirect
3. #21454543C2semidirect
4. C2×#16839777C2semidirect
5. #21454266C2semidirect
6. #21446710C2semidirect
7. #21446522C2semidirect
8. #21446465C2semidirect
9. #21446266C2semidirect
10. #21446145C2semidirect
11. #21446144C2semidirect
12. #21446022C2semidirect
13. #21445666C2semidirect
14. #21445584C2semidirect
15. C61×#1866C2semidirect
20. C2×#14519783C22semidirect
24. #16839927C4semidirect
25. #16839925C4semidirect
26. #16839919C4semidirect
27. #16839914C4semidirect
28. #16839910C4semidirect
29. #16839908C4semidirect
30. #16839902C4semidirect
31. #16839897C4semidirect
37. C2×#14519712C22semidirect
40. C2×#14519705C22semidirect
43. C2×#14519703C22semidirect
47. #16839730C22semidirect
55. #16839718C22semidirect
56. C2×#14519687C22semidirect
57. C2×C8×Dic61C22semidirect
58. #16839527C22semidirect
59. #16839526C22semidirect
60. #16839521C22semidirect
61. #16839517C22semidirect
63. C2×#108×C61C22semidirect
64. C61×#424C22semidirect
67. C61×#339C22semidirect
68. C61×#336C22semidirect
128. #14519704D4semidirect
432. #1866D61semidirect
469. C2×#108C2×D61semidirect
470. #424C2×D61semidirect
496. #339C2×D61semidirect
498. #336C2×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×#168398772
#214545432
C2×#168397772
#214542662
#214467102
#214465222
#214464652
#214462662
#214461452
#214461442
#214460222
#214456662
#214455842
C61×#18662
#2288961