Finite Group Databasebeta

← #29693899

Subgroups — #29693899

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456243C211yesmaximal, characteristic
2#21454535C211yesmaximal, characteristic, complemented
3#21454534C211yesmaximal, characteristic, complemented
4#21446649C211yesmaximal, characteristic, complemented
5#21446649C211yesmaximal, characteristic, complemented
6#21446149C211yesmaximal, characteristic, complemented
7#21446148C211yesmaximal, characteristic, complemented
8#21446147C211yesmaximal, characteristic, complemented
9#21446146C211yesmaximal, characteristic, complemented
10#21446145C211yesmaximal, characteristic, complemented
11#21446144C211yesmaximal, characteristic, complemented
12#21446143C211yesmaximal, characteristic, complemented
13#21445955C211yesmaximal, characteristic, complemented
14#21445569C211yesmaximal, characteristic, complemented
15C61×#1876C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519797C2211yescharacteristic
18C2×#14519797C2211yescharacteristic
19C2×#14519785C2211yescharacteristic
20C2×#14519784C2211yescharacteristic
21C2×#14519783C2211yescharacteristic
22#16840308C2211yescharacteristic
23#16840308C2211yescharacteristic
24#16840147C411yescharacteristic, complemented
25#16840145C411yescharacteristic, complemented
26#16840143C411yescharacteristic, complemented
27#16840143C411yescharacteristic, complemented
28#16840140C411yescharacteristic, complemented
29#16840137C411yescharacteristic, complemented
30#16840133C411yescharacteristic, complemented
31#16840133C411yescharacteristic, complemented
32#16839836—21no—
33#16839836—21no—
34#16839833—21no—
35#16839833—21no—
36#16839831—21no—
37#16839831—21no—
38#16839830—21no—
39#16839830—21no—
40#16839785C2211yescharacteristic
41#16839785C2211yescharacteristic
42C2×#14519705C2211yescharacteristic
43C2×#14519705C2211yescharacteristic
44C2×#14519704C2211yescharacteristic
45C2×#14519704C2211yescharacteristic
46C2×#14519703C2211yescharacteristic
47C2×#14519703C2211yescharacteristic
48#16839730C2211yescharacteristic
49#16839729C2211yescharacteristic
50#16839728C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×C8×Dic61C2211yescharacteristic
53#16839608C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839526C2211yescharacteristic
57#16839517C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#135×C61C2211yescharacteristic
61C2×#131×C61C2211yescharacteristic
62C2×#104×C61C2211yescharacteristic
63C2×#104×C61C2211yescharacteristic
64C61×#408C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519799—41no—
70#14519799—41no—
71#14519797—41no—
72#14519797—41no—
73#14519797—41no—
74#14519797—41no—
75C2×Dic244C2×C411yescharacteristic
76C2×#11758202C2×C411yescharacteristic
77C2×#11758202C2×C411yescharacteristic
78C2×#11758190C2×C411yescharacteristic
79C2×#11758190C2×C411yescharacteristic
80C2×#11758200C2×C411yescharacteristic
81C2×#11758200C2×C411yescharacteristic
82C2×#11758201C2×C411yescharacteristic
83C2×#11758201C2×C411yescharacteristic
84C2×D488C2×C411yescharacteristic
85C2×#11758199C2×C411yescharacteristic
86C2×#11758199C2×C411yescharacteristic
87#14519785—41no—
88#14519785—41no—
89#14519784—41no—
90#14519784—41no—
91#14519783—41no—
92#14519783—41no—
93C2×#11758194—21no—
94C2×#11758194C2311yescharacteristic
95C2×#11758194C2311yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98C22×#92418—21no—
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C2×C8×D61—21no—
102C2×C8×D61—21no—
103#14519775C2×C411yescharacteristic
104#14519775C2×C411yescharacteristic
105#14519773C2×C411yescharacteristic
106#14519773C2×C411yescharacteristic
107#14519766C2×C411yescharacteristic
108#14519766C2×C411yescharacteristic
109#14519764C2×C411yescharacteristic
110#14519764C2×C411yescharacteristic
111#14519749—21no—
112#14519749—21no—
113#14519749—21no—
114#14519749—21no—
115C4×C22⋊D61—21no—
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121#14519706—21no—
122#14519706—21no—
123#14519706—21no—
124#14519706—21no—
125#14519705—41no—
126#14519705—41no—
127#14519704—41no—
128#14519704—41no—
129#14519703—41no—
130#14519703—41no—
131C22⋊#92418—21no—
132C22⋊#92418—21no—
133#14519689—21no—
134#14519689—21no—
135#14519689—21no—
136#14519689—21no—
137#14519687D411yescharacteristic
138#14519687D411yescharacteristic
139#14519687D411yescharacteristic
140#14519687D411yescharacteristic
141C8×Dic61C2×C411yescharacteristic
142C8×Dic61C2×C411yescharacteristic
143C8×Dic61C2×C411yescharacteristic
144C8×Dic61C2×C411yescharacteristic
145#14519684—21no—
146#14519684—21no—
147C2×#41×C61C2311yescharacteristic
148C2×#41×C61C2311yescharacteristic
149#135×C61—41no—
150#135×C61—41no—
151C2×Q16×C61C2×C411yescharacteristic
152C2×SD16×C61C2×C411yescharacteristic
153C2×SD16×C61C2×C411yescharacteristic
154C2×D8×C61C2×C411yescharacteristic
155#131×C61—41no—
156#131×C61—41no—
157C2×M16×C61—21no—
158C2×M16×C61C2311yescharacteristic
159C2×M16×C61C2311yescharacteristic
160C22×C8×C61—21no—
161C22×C8×C61C2311yescharacteristic
162C22×C8×C61C2311yescharacteristic
163C2×C42×C61C2311yescharacteristic
164#104×C61—41no—
165#104×C61—41no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—21no—
174#41×C61—21no—
175#41×C61—21no—
176C2×Q8×C61C22×C411yescharacteristic
177C2×Q8×C61C22×C411yescharacteristic
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61C22×C411yescharacteristic
181C2×D4×C61C22×C411yescharacteristic
182C22×C4×C61—21no—
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—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61#4111yescharacteristic
194C22×Dic61#4111yescharacteristic
195#11758222—21no—
196#11758222—21no—
197#11758222—21no—
198#11758222—21no—
199#11758222—21no—
200#11758222—21no—
201#11758222—21no—
202#11758222—21no—
203C2×D244C22×C411yescharacteristic
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×Dic122C22×C411yescharacteristic
208C2×Dic122C22×C411yescharacteristic
209Q16×C61—41no—
210SD16×C61—41no—
211SD16×C61—41no—
212D8×C61—41no—
213M16×C61—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—42no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—42no—
225C2×C8×C61C22×C411yescharacteristic
226C2×C8×C61C22×C411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C2×C8×C61C2×D411yescharacteristic
229C42×C61—21no—
230C42×C61—21no—
231C22⋊Dic61—21no—
232C22⋊Dic61—21no—
233C22⋊Dic61—21no—
234C22⋊Dic61—21no—
235#11758202—41no—
236#11758202—41no—
237#11758201—41no—
238#11758201—41no—
239#11758200—41no—
240#11758200—41no—
241#11758199—41no—
242#11758199—41no—
243#11758198—21no—
244#11758198—21no—
245#11758198—21no—
246#11758198—21no—
247#11758196—21no—
248#11758196—21no—
249#11758196—21no—
250#11758196—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61C22×C411yescharacteristic
254C4×Dic61C22×C411yescharacteristic
255C4×Dic61C2×D411yescharacteristic
256C4×Dic61C2×D411yescharacteristic
257#11758194—21no—
258#11758194—21no—
259#11758194—21no—
260#11758194—21no—
261#11758194—42no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418—21no—
265C2×#92418—21no—
266C2×#92418—21no—
267C2×#92418—21no—
268C2×#92418—42no—
269C2×#92418C22×C411yescharacteristic
270C2×#92418C22×C411yescharacteristic
271C2×#92418C2×D411yescharacteristic
272C2×#92418C2×D411yescharacteristic
273Dic244—41no—
274D488—41no—
275#11758190—41no—
276#11758190—41no—
277#11758189—42no—
278#11758189—42no—
279C8×D61—42no—
280C8×D61—42no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C2×#4111yescharacteristic
284C22×D61—21no—
285C22×D61—21no—
286Q8×C61—21no—
287Q8×C61—21no—
288Q8×C61—21no—
289Q8×C61—21no—
290D4×C61—21no—
291D4×C61—21no—
292D4×C61—21no—
293D4×C61—21no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—41no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61C23×C411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C61H(5,𝔽2)11yescharacteristic
313C22⋊D61—41no—
314C22⋊D61—41no—
315C22⋊D61—41no—
316C22⋊D61—41no—
317C22⋊D61—81no—
318C22⋊D61—81no—
319C22⋊D61—81no—
320C22⋊D61—81no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61C4×D411yescharacteristic
329C2×Dic61C4×D411yescharacteristic
330C2×Dic61C4×D411yescharacteristic
331C2×Dic61C4×D411yescharacteristic
332D244—21no—
333D244—21no—
334D244—21no—
335D244—21no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340Dic122—21no—
341Dic122—21no—
342Dic122—21no—
343Dic122—21no—
344C8×C61—21no—
345C8×C61—21no—
346C8×C61—21no—
347C8×C61—21no—
348C8×C61—41no—
349C8×C61—41no—
350#92418—21no—
351#92418—21no—
352#92418—21no—
353#92418—21no—
354#92418—41no—
355#92418—41no—
356#22282—611nomaximal, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61C2×C4×D411yescharacteristic
366C22×C61#54011yescharacteristic
367C22×C61#54011yescharacteristic
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C4×C61—41no—
375C4×C61—41no—
376C4×C61—81no—
377C4×C61#51811yescharacteristic
378C4×C61#51811yescharacteristic
379C4×C61#53511yescharacteristic
380C4×C61#53511yescharacteristic
381Dic61—21no—
382Dic61—21no—
383Dic61—21no—
384Dic61—21no—
385Dic61—41no—
386Dic61—41no—
387Dic61—81no—
388#3147—611no—
389#2932—611no—
390#2932—611no—
391#1963—611no—
392#1963—611no—
393#1876—611no—
394#1876—611no—
395#1876—611no—
396#1876—611no—
397#1876—611no—
398#1876—611no—
399#1876—611no—
400#1876D6111yescharacteristic, complemented
401#1837—611no—
402#1746—611no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—81no—
406C2×C61—81no—
407C2×C61#232811yescharacteristic
408C2×C61#295711yescharacteristic
409C2×C61#295711yescharacteristic
410D61—81no—
411D61—81no—
412C2×#135—611no—
413C2×#135—611no—
414C2×#135—611no—
415C2×#135C2×D6111yescharacteristic
416C2×#131—611no—
417C2×#131—611no—
418C2×#131—611no—
419C2×#131C2×D6111yescharacteristic
420#532—611no—
421#532—611no—
422#495—611no—
423#495—611no—
424#495—611no—
425#495—611no—
426#494—611no—
427#493—611no—
428#492—611no—
429#492—611no—
430#435—1221no—
431#435—1221no—
432#435—1221no—
433#435—1221no—
434#435—1221no—
435#435—1221no—
436#435—1221no—
437#435—1221no—
438#423—611no—
439#423—611no—
440C2×#104—611no—
441C2×#104—611no—
442C2×#104—611no—
443C2×#104—611no—
444C2×#104—611no—
445C2×#104—611no—
446C2×#104C2×D6111yescharacteristic
447C2×#104C2×D6111yescharacteristic
448#408—611no—
449#408—611no—
450#408—611no—
451#408C2×D6111yescharacteristic
452C2×#97—611no—
453C2×C4×C8—611no—
454#376—611no—
455#341—611no—
456#341—611no—
457#341—611no—
458#341C2×D6111yescharacteristic
459#336—611no—
460#336—611no—
461#336—611no—
462#336C2×D6111yescharacteristic
463C61#2228211yescharacteristic, complemented, Sylow
464C2×#41—611no—
465C2×#41—611no—
466C2×#41C22×D6111yescharacteristic
467C2×#41C22×D6111yescharacteristic
468#135—41no—
469#135—41no—
470#135—2441no—
471#135—2441no—
472#135—2441no—
473#135—2441no—
474#135—2441no—
475#135—2441no—
476C2×Q16—611no—
477C2×Q16—611no—
478C2×Q16—611no—
479C2×Q16C4×D6111yescharacteristic
480C2×SD16—611no—
481C2×SD16—611no—
482C2×SD16—611no—
483C2×SD16—611no—
484C2×SD16—611no—
485C2×SD16—611no—
486C2×SD16C4×D6111yescharacteristic
487C2×SD16C4×D6111yescharacteristic
488C2×D8—611no—
489C2×D8—611no—
490C2×D8—611no—
491C2×D8C4×D6111yescharacteristic
492#131—41no—
493#131—41no—
494#131—2441no—
495#131—2441no—
496#131—2441no—
497#131—2441no—
498#131—2441no—
499#131—2441no—
500C2×M16—21no—
501C2×M16—611no—
502C2×M16—611no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16—1221no—
506C2×M16C22×D6111yescharacteristic
507C2×M16C22×D6111yescharacteristic
508C22×C8—21no—
509C22×C8—611no—
510C22×C8—611no—
511C22×C8—1221no—
512C22×C8—1221no—
513C22×C8—1221no—
514C22×C8C22×D6111yescharacteristic
515C22×C8C22×D6111yescharacteristic
516C4⋊Q8—611no—
517C4⋊Q8—611no—
518#127—611no—
519#127—611no—
520#124—611no—
521#124—611no—
522#124—611no—
523#124—611no—
524#121—1221no—
525#121—1221no—
526#121—1221no—
527#121—1221no—
528C4×D4—1221no—
529C4×D4—1221no—
530C4×D4—1221no—
531C4×D4—1221no—
532C2×C42—611no—
533C2×C42—611no—
534C2×C42C22×D6111yescharacteristic
535C4⋊C8—1221no—
536C4⋊C8—1221no—
537C4⋊C8—1221no—
538C4⋊C8—1221no—
539#104—41no—
540#104—41no—
541#104—2441no—
542#104—2441no—
543#104—2441no—
544#104—2441no—
545#104—2441no—
546#104—2441no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—1221no—
550C22⋊C8—1221no—
551C22⋊C8—1221no—
552C22⋊C8—1221no—
553C22⋊C8—1221no—
554C22⋊C8—1221no—
555#97—611no—
556#97—611no—
557#97—611no—
558#97—611no—
559C4×C8—611no—
560C4×C8—611no—
561C4×C8—611no—
562C4×C8—611no—
563#95—1221no—
564#95—1221no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—1221no—
574#41—1221no—
575#41—1221no—
576#41—1221no—
577#41—1221no—
578#41—1221no—
579#41—1221no—
580#41—1221no—
581C2×Q8—611no—
582C2×Q8—611no—
583C2×Q8C2×C4×D6111yescharacteristic
584C2×Q8C2×C4×D6111yescharacteristic
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—611no—
588C2×D4—611no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4—1221no—
594C2×D4—1221no—
595C2×D4C2×C4×D6111yescharacteristic
596C2×D4C2×C4×D6111yescharacteristic
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4C23×D6111yescharacteristic
606Q16—41no—
607Q16—2441no—
608Q16—2441no—
609Q16—2441no—
610SD16—41no—
611SD16—41no—
612SD16—2441no—
613SD16—2441no—
614SD16—2441no—
615SD16—2441no—
616SD16—2441no—
617SD16—2441no—
618D8—41no—
619D8—2441no—
620D8—2441no—
621D8—2441no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—42no—
627M16—1221no—
628M16—1221no—
629M16—1221no—
630M16—1221no—
631M16—2442no—
632M16—2442no—
633M16—2442no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—42no—
641C2×C8—611no—
642C2×C8—611no—
643C2×C8—611no—
644C2×C8—611no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—1221no—
648C2×C8—1221no—
649C2×C8—1221no—
650C2×C8—1221no—
651C2×C8—2442no—
652C2×C8—2442no—
653C2×C8—2442no—
654C2×C8C2×C4×D6111yescharacteristic
655C2×C8C2×C4×D6111yescharacteristic
656C2×C8D4×D6111yescharacteristic
657C2×C8D4×D6111yescharacteristic
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C22⋊C4—1221no—
663C22⋊C4—1221no—
664C22⋊C4—1221no—
665C22⋊C4—1221no—
666C22⋊C4—1221no—
667C22⋊C4—1221no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C42—21no—
671C42—21no—
672C42—611no—
673C42—611no—
674C42—611no—
675C42—611no—
676C42—1221no—
677C42—1221no—
678C23—21no—
679C23—21no—
680C23—1221no—
681C23—1221no—
682C23#41×D6111yescharacteristic
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—1221no—
688Q8—1221no—
689Q8—1221no—
690Q8—1221no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—1221no—
700D4—1221no—
701D4—1221no—
702D4—1221no—
703D4—4881no—
704D4—4881no—
705D4—4881no—
706D4—4881no—
707D4—2441no—
708D4—2441no—
709D4—2441no—
710D4—2441no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4C22×C4×D6111yescharacteristic
736C2×C4C2×D4×D6111yescharacteristic
737C2×C4#1451982211yescharacteristic
738C2×C4#1451982211yescharacteristic
739C2×C4#1451982211yescharacteristic
740C2×C4#1451982311yescharacteristic
741C8—21no—
742C8—21no—
743C8—21no—
744C8—21no—
745C8—41no—
746C8—41no—
747C8—1221no—
748C8—1221no—
749C8—1221no—
750C8—1221no—
751C8—2441no—
752C8—2441no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22—2441no—
767C22C4×D4×D6111yescharacteristic
768C22#1684036211yescharacteristic
769C22#1684036411yescharacteristic
770C4—41no—
771C4—41no—
772C4—81no—
773C4—1221no—
774C4—1221no—
775C4—1221no—
776C4—1221no—
777C4—4881no—
778C4—2441no—
779C4—2441no—
780C4#1684023411yescharacteristic
781C4#1684023511yescharacteristic
782C4#1684032711yescharacteristic
783C4#1684032811yescharacteristic
784C2—21no—
785C2—21no—
786C2—81no—
787C2—81no—
788C2—4881no—
789C2—4881no—
790C2#2144854011yescharacteristic
791C2#2145473111yescharacteristic
792C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1876C2
socleC22×C61C2×C4×D4
prime radical#21456243C2
cosocleC22×C4×C61C24
hypercenter#1876D61
hypocenterC61#22282
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #21454535C2semidirect
3. #21454534C2semidirect
4. #21446649C2semidirect
5. #21446649C2semidirect
6. #21446149C2semidirect
7. #21446148C2semidirect
8. #21446147C2semidirect
9. #21446146C2semidirect
10. #21446145C2semidirect
11. #21446144C2semidirect
12. #21446143C2semidirect
13. #21445955C2semidirect
14. #21445569C2semidirect
15. C61×#1876C2semidirect
24. #16840147C4semidirect
25. #16840145C4semidirect
26. #16840143C4semidirect
27. #16840143C4semidirect
28. #16840140C4semidirect
29. #16840137C4semidirect
30. #16840133C4semidirect
31. #16840133C4semidirect
400. #1876D61semidirect
463. C61#22282semidirect

Maximal subgroups

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

subgroupindex
#214562432
#214545352
#214545342
#214466492
#214461492
#214461482
#214461472
#214461462
#214461452
#214461442
#214461432
#214459552
#214455692
C61×#18762
#2228261