Finite Group Databasebeta

← #35152246

Subgroups — #35152246

Order 20224.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099328C211yesmaximal, characteristic, complemented
2C2×#131×D79C211yesmaximal, characteristic, complemented
3#41×D316C211yesmaximal, characteristic
4#23772143C213yesmaximal, complemented
5#23772135C213yesmaximal, complemented
6#23772124C213yesmaximal, complemented
7#23772124C213yesmaximal, complemented
8#23772117C213yesmaximal, complemented
9#23772102C213yesmaximal, complemented
10#23772093C213yesmaximal, complemented
11C2×#19098633C213yesmaximal, complemented
12#23771847C211yesmaximal, characteristic, complemented
13#23771847C211yesmaximal, characteristic, complemented
14#23771828C211yesmaximal, characteristic, complemented
15C79×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D79C2211yescharacteristic
17C2×#41×D79C2211yescharacteristic
18#19099328—28no—
19C2×#14579169C2213yescomplemented
20C2×#14579169C2213yescomplemented
21C2×#14579168C2211yescharacteristic
22C2×#14579168C2211yescharacteristic
23C2×#14579167C2213yescomplemented
24C2×#14579167C2213yescomplemented
25#131×D79—28no—
26C22×#11929607C2213yescomplemented
27C2×M16×D79C2213yescomplemented
28C2×M16×D79C2213yescomplemented
29C22×C8×D79C2213yescomplemented
30#19099235C411yescharacteristic
31Q8×D316C411yescharacteristic
32#19099225C411yescharacteristic
33#19099225C411yescharacteristic
34#19099217C413yes—
35#19099208C413yes—
36#19099208C413yes—
37D4×D316C413yes—
38#19099113C2213yes—
39#19099075C2213yes—
40#19099075C2213yes—
41C2×C4×D316C2213yes—
42#19098640C2216yescomplemented
43#19098640C2216yescomplemented
44#19098633C2211yescharacteristic
45#19098633C2213yes—
46#19098633C2213yescomplemented
47#19098633C2213yescomplemented
48#19098633C2213yescomplemented
49#19098633C2213yescomplemented
50#19098633C2213yescomplemented
51#19098633C2213yescomplemented
52#19098633C2216yescomplemented
53#19098633C2216yescomplemented
54#19098633C2216yescomplemented
55#19098628C2216yescomplemented
56#19098628C2216yescomplemented
57#19098531C2213yescomplemented
58#19098531C2213yescomplemented
59#19098529C2213yescomplemented
60#19098529C2213yescomplemented
61#19098526C2213yescomplemented
62#19098526C2213yescomplemented
63C2×(C2×D79)⋊C8C2213yescomplemented
64C2×(C2×D79)⋊C8C2213yescomplemented
65#19098519C2213yescomplemented
66#19098519C2213yescomplemented
67C4×#11929608C2213yescomplemented
68C2×#14579072C2213yescomplemented
69C2×#131×C79C2211yescharacteristic
70C2×#131×C79C2211yescharacteristic
71C4×#41×C79C2211yescharacteristic
72#424×C79C2213yescomplemented
73#424×C79C2213yescomplemented
74#423×C79C2213yescomplemented
75C2×C4⋊C8×C79C2213yescomplemented
76C2×#11929625C2×C411yescharacteristic
77C2×#11929625C2×C411yescharacteristic
78C2×#11929624C2313yes—
79C2×#11929624C2313yes—
80C2×#11929623C2×C413yes—
81C2×#11929623C2×C413yes—
82#41×D79—24no—
83#41×D79—24no—
84#41×D79—24no—
85#41×D79—24no—
86C2×Q8×D79C2×C411yescharacteristic
87C2×Q8×D79C2×C411yescharacteristic
88C22×D316C2×C413yes—
89C2×D4×D79C2×C413yes—
90C2×D4×D79C2×C413yes—
91C22×C4×D79C2313yes—
92C22×C4×D79C2313yes—
93#14579169—212no—
94#14579169—212no—
95#14579168—24no—
96#14579168D418yescomplemented
97#14579167—212no—
98#14579167—212no—
99C2×#11929608C2313yes—
100C2×#11929608C2313yes—
101C2×#11929607—212no—
102C2×#11929607C2311yescharacteristic
103C2×#11929607C2313yes—
104C2×#11929607C2313yes—
105C2×#11929607C2316yes—
106C2×#11929607C2313yes—
107M16×D79—212no—
108M16×D79—212no—
109C22×C79⋊C8C2313yes—
110C22×C79⋊C8C2313yes—
111C2×C8×D79—212no—
112C2×C8×D79C2313yes—
113C2×C8×D79C2313yes—
114C2×C8×D79C2316yes—
115C2×C8×D79C2311yescharacteristic
116C2×C8×D79C2313yes—
117#14579161C2×C413yes—
118#14579158C2×C413yes—
119#14579149C2×C413yes—
120#14579149C2×C413yes—
121#14579145C2×C416yes—
122#14579145C2×C416yes—
123#14579141C2×C413yes—
124#14579141C2×C413yes—
125#14579141C2×C413yes—
126#14579141C2×C413yes—
127#14579136C2×C413yes—
128#14579136C2×C413yes—
129#14579136C2×C413yes—
130#14579136C2×C413yes—
131#14579135C2×C416yes—
132#14579135C2×C416yes—
133#14579131C2×C416yes—
134#14579131C2×C416yes—
135C4×D316C2×C413yes—
136C4×D316C2×C413yes—
137C4×D316C2×C413yes—
138C4×D316C2×C413yes—
139C4×D316C2313yes—
140C4×D316C2316yes—
141C4×D316C2311yescharacteristic
142C4×D316C2313yes—
143C4×D316C2313yes—
144C2×C4⋊Dic79C2×C413yes—
145C2×(C2×D79)⋊C4C2×C413yes—
146C2×(C2×D79)⋊C4C2×C413yes—
147(C2×D79)⋊C8C2313yes—
148(C2×D79)⋊C8C2313yes—
149(C2×D79)⋊C8C2316yes—
150(C2×D79)⋊C8C2316yes—
151(C2×D79)⋊C8C2311yescharacteristic
152(C2×D79)⋊C8C2311yescharacteristic
153(C2×D79)⋊C8C2313yes—
154(C2×D79)⋊C8C2313yes—
155(C2×D79)⋊C8C2313yes—
156(C2×D79)⋊C8C2313yes—
157#14579072C2311yescharacteristic
158#14579072C2313yes—
159#14579072C2313yes—
160#14579072C2313yes—
161C4×C79⋊C8C2316yes—
162C2×#41×C79C2311yescharacteristic
163#131×C79—24no—
164#131×C79—24no—
165C2×M16×C79C2313yes—
166C2×M16×C79C2313yes—
167C22×C8×C79C2313yes—
168C22×C8×C79C2313yes—
169C4×Q8×C79C2×C411yescharacteristic
170C4×Q8×C79C2×C411yescharacteristic
171C4×D4×C79C2×C413yes—
172C4×D4×C79C2×C413yes—
173#117×C79C2313yes—
174C2×C42×C79C2313yes—
175C4⋊C8×C79C2313yes—
176C4⋊C8×C79C2316yes—
177C4⋊C8×C79C2311yescharacteristic
178C4⋊C8×C79C2313yes—
179C4⋊C8×C79C2313yes—
180C23×D79C22×C413yes—
181C23×D79C22×C413yes—
182#11929625—24no—
183#11929625—24no—
184#11929624—26no—
185#11929624—26no—
186#11929624—26no—
187#11929624—26no—
188#11929623—212no—
189#11929623—212no—
190C2×Dic158C22×C413yes—
191C2×Dic158C22×C413yes—
192Q8×D79—24no—
193Q8×D79—24no—
194C2×D316—46no—
195C2×D316C22×C413yes—
196C2×D316C22×C413yes—
197C2×D316C22×C411yescharacteristic
198C2×D316C22×C413yes—
199C2×D316C22×C413yes—
200C2×D316C22×C413yes—
201C2×D316C22×C416yes—
202C2×C22⋊D79C22×C416yes—
203C2×C22⋊D79C22×C416yes—
204D4×D79—212no—
205D4×D79—212no—
206C22×Dic79C22×C413yes—
207C22×Dic79C22×C413yes—
208C2×C4×D79—26no—
209C2×C4×D79—26no—
210C2×C4×D79—26no—
211C2×C4×D79—26no—
212C2×C4×D79C22×C413yes—
213C2×C4×D79C22×C413yes—
214C2×C4×D79C22×C413yes—
215C2×C4×D79C22×C413yes—
216C2×C4×D79C2413yes—
217C2×C4×D79C2413yes—
218C2×C4×D79C2411yescharacteristic
219C2×C4×D79C2411yescharacteristic
220#11929608—26no—
221#11929608C2×D4112yescomplemented
222#11929607—26no—
223#11929607—212no—
224#11929607—22no—
225#11929607—26no—
226#11929607—26no—
227C2×C79⋊C8—26no—
228C2×C79⋊C8C2×D4112yescomplemented
229C2×C79⋊C8C2413yes—
230C2×C79⋊C8C2411yescharacteristic
231C2×C79⋊C8C2413yes—
232C2×C79⋊C8C2411yescharacteristic
233C8×D79—22no—
234C8×D79—26no—
235C8×D79—26no—
236C8×D79—26no—
237C8×D79—212no—
238C4⋊Dic79C22×C411yescharacteristic
239C4⋊Dic79C22×C413yes—
240C4⋊Dic79C22×C413yes—
241C4⋊Dic79C22×C413yes—
242C4⋊Dic79C22×C416yes—
243(C2×D79)⋊C4C22×C411yescharacteristic
244(C2×D79)⋊C4C22×C411yescharacteristic
245(C2×D79)⋊C4C22×C413yes—
246(C2×D79)⋊C4C22×C413yes—
247(C2×D79)⋊C4C22×C413yes—
248(C2×D79)⋊C4C22×C413yes—
249(C2×D79)⋊C4C22×C413yes—
250(C2×D79)⋊C4C22×C413yes—
251(C2×D79)⋊C4C22×C416yes—
252(C2×D79)⋊C4C22×C416yes—
253#41×C79C2×D414yes—
254#41×C79#4114yes—
255C2×Q8×C79C22×C411yescharacteristic
256C2×D4×C79C22×C413yes—
257C22×C4×C79C22×C413yes—
258C22×C4×C79C22×C413yes—
259C22×C4×C79C2413yes—
260M16×C79—26no—
261M16×C79—26no—
262C2×C8×C79—26no—
263C2×C8×C79—26no—
264C2×C8×C79C2411yescharacteristic
265C2×C8×C79C2411yescharacteristic
266C2×C8×C79C2413yes—
267C2×C8×C79C2413yes—
268C4⋊C4×C79C22×C413yes—
269C4⋊C4×C79C22×C413yes—
270C22⋊C4×C79C22×C416yes—
271C42×C79C22×C413yes—
272C42×C79C22×C413yes—
273C42×C79C2411yescharacteristic
274C42×C79C2413yes—
275C23×C79C23×C413yes—
276C22×D79—26no—
277C22×D79—26no—
278C22×D79—26no—
279C22×D79—43no—
280C22×D79—43no—
281C22×D79—43no—
282C22×D79C23×C411yescharacteristic
283C22×D79C23×C413yes—
284C22×D79C23×C413yes—
285C22×D79C23×C411yescharacteristic
286Q8×C79C4×D414yes—
287D4×C79C4×D4112yes—
288C2×C4×C79—43no—
289C2×C4×C79—43no—
290C2×C4×C79C23×C411yescharacteristic
291C2×C4×C79C23×C413yes—
292C2×C4×C79C23×C413yes—
293C2×C4×C79C23×C411yescharacteristic
294C2×C4×C79C23×C413yes—
295C2×C4×C79C22×D416yes—
296C2×C4×C79C2×#4116yes—
297C2×C4×C79C2511yescharacteristic
298C22⋊D79—212no—
299C22⋊D79—212no—
300C2×Dic79—26no—
301C2×Dic79—26no—
302C2×Dic79C23×C411yescharacteristic
303C2×Dic79C23×C411yescharacteristic
304C2×Dic79C23×C413yes—
305C2×Dic79C23×C413yes—
306D316—22no—
307D316—26no—
308D316—26no—
309D316—26no—
310D316—43no—
311D316—43no—
312D316—46no—
313C4×D79—26no—
314C4×D79—26no—
315C4×D79—26no—
316C4×D79—26no—
317C4×D79—21no—
318C4×D79—23no—
319C4×D79—23no—
320C4×D79—21no—
321C4×D79—21no—
322C4×D79—21no—
323C4×D79—23no—
324C4×D79—23no—
325Dic158—26no—
326Dic158—26no—
327C8×C79—21no—
328C8×C79—23no—
329C8×C79—23no—
330C8×C79—21no—
331C79⋊C8—21no—
332C79⋊C8—23no—
333C79⋊C8C22×D412yes—
334C79⋊C8C22×D416yes—
335C22×C79—23no—
336C22×C79—23no—
337C22×C79C2×C4×D416yes—
338C22×C79C24×C411yescharacteristic
339C2×D79—21no—
340C2×D79—21no—
341C2×D79—23no—
342C2×D79—23no—
343C2×D79—21no—
344C2×D79—23no—
345C2×D79—21no—
346C2×D79—23no—
347C2×D79—21no—
348C2×D79—23no—
349C2×D79—23no—
350C2×D79—412no—
351C2×D79—86no—
352C2×D79#56812yescomplemented
353C4×C79—21no—
354C4×C79—23no—
355C4×C79—21no—
356C4×C79—23no—
357C4×C79C2×C4×D416yes—
358C4×C79C23×D411yescharacteristic
359C4×C79C22×#4111yescharacteristic
360Dic79—23no—
361Dic79—23no—
362Dic79—21no—
363Dic79—21no—
364#60146—791nomaximal, Sylow
365C2×C79—26no—
366C2×C79C22×C4×D411yescharacteristic
367C2×C79C2×#56811yescharacteristic
368C2×C79#357311yescharacteristic
369D79—22no—
370D79—43no—
371D79—43no—
372D79—41no—
373C2×#568—791no—
374C22×#131—791no—
375D4×#41—791no—
376#2935—793no—
377D4×M16—793no—
378#2933—793no—
379#2933—793no—
380#2932—793no—
381#2930—793no—
382#2929—793no—
383C2×#435—793no—
384#2906D7911yescharacteristic, complemented
385#2880—791no—
386#2880—791no—
387#2875—791no—
388C79#6014611yescharacteristic, complemented, Sylow
389C22×#41—791no—
390C22×#41—791no—
391#568—1588no—
392C2×#131—791no—
393C2×#131—791no—
394C2×#131—793no—
395C2×#131—793no—
396C2×#131—793no—
397C2×#131—793no—
398C2×#131—1588no—
399C2×#131C2×D7911yescharacteristic
400C2×#131C2×D7911yescharacteristic
401C22×M16—793no—
402C22×M16—793no—
403C22×M16—793no—
404C23×C8—793no—
405#550—791no—
406D4×Q8—791no—
407#548—791no—
408#548—791no—
409#547—793no—
410#546—793no—
411#546—793no—
412D42—793no—
413#532—793no—
414#525—793no—
415#525—793no—
416C4×#41C2×D7911yescharacteristic
417C2×C4×D4—793no—
418#436—796no—
419#436—796no—
420#435—791no—
421#435—793no—
422#435—793no—
423#435—793no—
424#435—793no—
425#435—793no—
426#435—793no—
427#435—793no—
428#435—796no—
429#435—796no—
430#435—796no—
431C8×D4—796no—
432C8×D4—796no—
433#424C2×D7913yescomplemented
434#424C2×D7913yescomplemented
435#423C2×D7913yescomplemented
436C2×C4⋊C8C2×D7913yescomplemented
437#408—793no—
438#408—793no—
439#408—793no—
440#408—793no—
441#407—793no—
442#407—793no—
443C2×C22⋊C8—793no—
444C2×C22⋊C8—793no—
445#405—793no—
446#405—793no—
447C4×M16—793no—
448C2×#97—793no—
449C2×#41—791no—
450C2×#41—791no—
451C2×#41—793no—
452C2×#41—793no—
453C2×#41—793no—
454C2×#41—793no—
455C2×#41—1584no—
456C2×#41—1584no—
457C2×#41—1584no—
458C2×#41—1584no—
459C2×#41C22×D7911yescharacteristic
460C22×Q8—791no—
461C22×Q8—791no—
462C22×D4—793no—
463C22×D4—793no—
464C22×D4—793no—
465C23×C4—793no—
466C23×C4—793no—
467#131—24no—
468#131—24no—
469#131—798no—
470#131—15812no—
471#131—15812no—
472#131—15812no—
473#131—15812no—
474#131—1584no—
475C2×M16—793no—
476C2×M16—793no—
477C2×M16—791no—
478C2×M16—793no—
479C2×M16—793no—
480C2×M16—796no—
481C2×M16—793no—
482C2×M16—15812no—
483C2×M16—15812no—
484C2×M16—15812no—
485C2×M16C22×D7913yes—
486C2×M16C22×D7913yes—
487C22×C8—793no—
488C22×C8—793no—
489C22×C8—791no—
490C22×C8—793no—
491C22×C8—793no—
492C22×C8—793no—
493C22×C8—796no—
494C22×C8—15812no—
495C22×C8C22×D7913yes—
496C22×C8C22×D7913yes—
497C4⋊Q8—793no—
498#127—793no—
499#124—793no—
500#124—793no—
501#123—796no—
502#123—796no—
503C22⋊Q8—793no—
504C22⋊Q8—793no—
505C22⋊Q8—793no—
506C22⋊Q8—793no—
507#121—796no—
508#121—796no—
509#121—793no—
510#121—793no—
511#121—793no—
512#121—793no—
513#120—796no—
514#120—796no—
515C4×Q8C4×D7911yescharacteristic
516C4×Q8C4×D7911yescharacteristic
517C4×D4—793no—
518C4×D4—793no—
519C4×D4—793no—
520C4×D4—793no—
521C4×D4—791no—
522C4×D4—793no—
523C4×D4—793no—
524C4×D4—793no—
525C4×D4—796no—
526C4×D4C4×D7913yes—
527C4×D4C4×D7913yes—
528#117C22×D7913yes—
529C2×C4⋊C4—793no—
530C2×C22⋊C4—793no—
531C2×C22⋊C4—793no—
532C2×C42C22×D7913yes—
533C4⋊C8C22×D7911yescharacteristic
534C4⋊C8C22×D7913yes—
535C4⋊C8C22×D7913yes—
536C4⋊C8C22×D7913yes—
537C4⋊C8C22×D7916yes—
538C22⋊C8—791no—
539C22⋊C8—791no—
540C22⋊C8—793no—
541C22⋊C8—793no—
542C22⋊C8—793no—
543C22⋊C8—793no—
544C22⋊C8—793no—
545C22⋊C8—793no—
546C22⋊C8—796no—
547C22⋊C8—796no—
548#97—791no—
549#97—793no—
550#97—793no—
551#97—793no—
552C4×C8—796no—
553C24—793no—
554C24—793no—
555#41—1584no—
556#41—1584no—
557#41—15812no—
558#41—15812no—
559#41—1586no—
560#41—1586no—
561#41—1586no—
562#41—1586no—
563#41D4×D7914yes—
564#41#1192962514yes—
565C2×Q8—793no—
566C2×Q8—793no—
567C2×Q8—1584no—
568C2×Q8—1584no—
569C2×Q8C2×C4×D7911yescharacteristic
570C2×D4—3166no—
571C2×D4—796no—
572C2×D4—796no—
573C2×D4—793no—
574C2×D4—793no—
575C2×D4—796no—
576C2×D4—791no—
577C2×D4—793no—
578C2×D4—793no—
579C2×D4—793no—
580C2×D4—15812no—
581C2×D4—15812no—
582C2×D4C2×C4×D7913yes—
583C22×C4—793no—
584C22×C4—793no—
585C22×C4—791no—
586C22×C4—793no—
587C22×C4—793no—
588C22×C4—791no—
589C22×C4—793no—
590C22×C4—793no—
591C22×C4—793no—
592C22×C4—793no—
593C22×C4—1586no—
594C22×C4—1586no—
595C22×C4—1586no—
596C22×C4—1586no—
597C22×C4C2×C4×D7913yes—
598C22×C4C2×C4×D7913yes—
599C22×C4C23×D7913yes—
600M16—26no—
601M16—26no—
602M16—7912no—
603M16—1582no—
604M16—1586no—
605M16—1586no—
606M16—1586no—
607M16—15812no—
608M16—1586no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—793no—
612C2×C8—791no—
613C2×C8—7912no—
614C2×C8—793no—
615C2×C8—791no—
616C2×C8—1582no—
617C2×C8—1586no—
618C2×C8—1586no—
619C2×C8—1586no—
620C2×C8—15812no—
621C2×C8—1586no—
622C2×C8C23×D7911yescharacteristic
623C2×C8C23×D7913yes—
624C2×C8C23×D7913yes—
625C2×C8C23×D7911yescharacteristic
626C4⋊C4—791no—
627C4⋊C4—793no—
628C4⋊C4—793no—
629C4⋊C4—793no—
630C4⋊C4—796no—
631C4⋊C4C2×C4×D7913yes—
632C4⋊C4C2×C4×D7913yes—
633C22⋊C4—791no—
634C22⋊C4—791no—
635C22⋊C4—793no—
636C22⋊C4—793no—
637C22⋊C4—793no—
638C22⋊C4—793no—
639C22⋊C4—793no—
640C22⋊C4—793no—
641C22⋊C4—796no—
642C22⋊C4—796no—
643C22⋊C4C2×C4×D7916yes—
644C42C2×C4×D7913yes—
645C42C2×C4×D7913yes—
646C42C23×D7913yes—
647C42C23×D7911yescharacteristic
648C23—3163no—
649C23—3163no—
650C23—3163no—
651C23—791no—
652C23—791no—
653C23—793no—
654C23—793no—
655C23—1586no—
656C23—1586no—
657C23—1586no—
658C23C22×C4×D7913yes—
659Q8—1586no—
660Q8—1586no—
661Q8#1457912314yes—
662D4—3163no—
663D4—3163no—
664D4—3166no—
665D4—1582no—
666D4—1586no—
667D4—15812no—
668D4—15812no—
669D4—1586no—
670D4—1586no—
671D4#14579123112yes—
672C2×C4—43no—
673C2×C4—43no—
674C2×C4—791no—
675C2×C4—791no—
676C2×C4—793no—
677C2×C4—793no—
678C2×C4—1586no—
679C2×C4—1586no—
680C2×C4—1586no—
681C2×C4—1586no—
682C2×C4—1586no—
683C2×C4—1586no—
684C2×C4—1581no—
685C2×C4—1583no—
686C2×C4—1583no—
687C2×C4—1581no—
688C2×C4—1581no—
689C2×C4—1581no—
690C2×C4—1583no—
691C2×C4—1583no—
692C2×C4C22×C4×D7911yescharacteristic
693C2×C4C22×C4×D7911yescharacteristic
694C2×C4C22×C4×D7913yes—
695C2×C4C22×C4×D7913yes—
696C2×C4C22×C4×D7913yes—
697C2×C4C2×D4×D7916yes—
698C2×C4C2×#1192962516yes—
699C2×C4C24×D7911yescharacteristic
700C8—21no—
701C8—21no—
702C8—23no—
703C8—23no—
704C8—792no—
705C8—796no—
706C8—1581no—
707C8—1583no—
708C22—23no—
709C22—23no—
710C22—31612no—
711C22—792no—
712C22—6326no—
713C22—1581no—
714C22—1583no—
715C22—1583no—
716C22—1581no—
717C22—1583no—
718C22—1583no—
719C22—1583no—
720C22—1583no—
721C22—1581no—
722C22—1581no—
723C22—1581no—
724C22C2×#1457912316yes—
725C22C23×C4×D7911yescharacteristic
726C4—21no—
727C4—23no—
728C4—21no—
729C4—23no—
730C4—1581no—
731C4—1581no—
732C4—1583no—
733C4—1583no—
734C4C2×#1457912316yes—
735C4C22×D4×D7911yescharacteristic
736C4C22×#1192962511yescharacteristic
737C2—26no—
738C2—3163no—
739C2—3161no—
740C2—3163no—
741C2—1582no—
742C2C22×#1457912311yescharacteristic
743C2#568×D7911yescharacteristic
744C2#2377811111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
FittingC79×#2906C2
prime radical#41×D316C2
cosocleC2×C4×C79C25
hypercenter#2906D79
hypocenterC79#60146
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
1. C2×#19099328C2semidirect
2. C2×#131×D79C2semidirect
4. #23772143C2semidirect
5. #23772135C2semidirect
6. #23772124C2semidirect
7. #23772124C2semidirect
8. #23772117C2semidirect
9. #23772102C2semidirect
10. #23772093C2semidirect
11. C2×#19098633C2semidirect
12. #23771847C2semidirect
13. #23771847C2semidirect
14. #23771828C2semidirect
15. C79×#2906C2semidirect
19. C2×#14579169C22semidirect
20. C2×#14579169C22semidirect
23. C2×#14579167C22semidirect
24. C2×#14579167C22semidirect
26. C22×#11929607C22semidirect
27. C2×M16×D79C22semidirect
28. C2×M16×D79C22semidirect
29. C22×C8×D79C22semidirect
42. #19098640C22semidirect
43. #19098640C22semidirect
46. #19098633C22semidirect
47. #19098633C22semidirect
48. #19098633C22semidirect
49. #19098633C22semidirect
50. #19098633C22semidirect
51. #19098633C22semidirect
52. #19098633C22semidirect
53. #19098633C22semidirect
54. #19098633C22semidirect
55. #19098628C22semidirect
56. #19098628C22semidirect
57. #19098531C22semidirect
58. #19098531C22semidirect
59. #19098529C22semidirect
60. #19098529C22semidirect
61. #19098526C22semidirect
62. #19098526C22semidirect
63. C2×(C2×D79)⋊C8C22semidirect
64. C2×(C2×D79)⋊C8C22semidirect
65. #19098519C22semidirect
66. #19098519C22semidirect
67. C4×#11929608C22semidirect
68. C2×#14579072C22semidirect
72. #424×C79C22semidirect
73. #424×C79C22semidirect
74. #423×C79C22semidirect
75. C2×C4⋊C8×C79C22semidirect
96. #14579168D4semidirect
221. #11929608C2×D4semidirect
228. C2×C79⋊C8C2×D4semidirect
352. C2×D79#568semidirect
384. #2906D79semidirect
388. C79#60146semidirect
433. #424C2×D79semidirect
434. #424C2×D79semidirect
435. #423C2×D79semidirect
436. C2×C4⋊C8C2×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190993282
C2×#131×D792
#41×D3162
#237721432
#237721352
#237721242
#237721172
#237721022
#237720932
C2×#190986332
#237718472
#237718282
C79×#29062
#6014679