Finite Group Databasebeta

← C79×#24464 #34136153

Subgroups — C79×#24464 #34136153

Order 20224.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3488C211yesmaximal, characteristic, complemented
2C79×#3055C211yesmaximal, characteristic, complemented
3C2×#453×C79C211yesmaximal, characteristic, complemented
4C79×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C79C211yesmaximal, characteristic, complemented
6C79×#2856C211yesmaximal, characteristic, complemented
7C79×#2039C211yesmaximal, characteristic, complemented
8C79×#2037C211yesmaximal, characteristic, complemented
9C79×#2006C211yesmaximal, characteristic, complemented
10C79×#2002C211yesmaximal, characteristic, complemented
11C79×#1900C211yesmaximal, characteristic, complemented
12C79×#1896C211yesmaximal, characteristic, complemented
13C79×#1883C211yesmaximal, characteristic, complemented
14C79×#1859C211yesmaximal, characteristic, complemented
15C79×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C79C2211yescharacteristic
17C22×#41×C79C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C79C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C79C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C79C2211yescharacteristic, complemented
21C22×M16×C79C2211yescharacteristic, complemented
22#550×C79—21no—
23#548×C79—21no—
24#546×C79—21no—
25#546×C79—22no—
26D42×C79—22no—
27D42×C79—21no—
28#537×C79—21no—
29#537×C79C2211yescharacteristic
30#535×C79—21no—
31#535×C79C2211yescharacteristic
32C2×#127×C79C2211yescharacteristic, complemented
33#525×C79—21no—
34#525×C79C2211yescharacteristic
35C2×#121×C79—21no—
36C2×#121×C79—22no—
37C2×#121×C79C2211yescharacteristic
38C2×#121×C79C2211yescharacteristic, complemented
39#520×C79C2211yescharacteristic
40C22×C42×C79C2211yescharacteristic, complemented
41#469×C79—21no—
42#468×C79—21no—
43#466×C79—21no—
44#465×C79—21no—
45#453×C79—24no—
46#449×C79—21no—
47#449×C79—21no—
48#448×C79—21no—
49#447×C79—21no—
50#428×C79C2211yescharacteristic, complemented
51C2×#104×C79—24no—
52C2×#104×C79C2211yescharacteristic
53C2×#104×C79C2211yescharacteristic
54C2×#104×C79C2211yescharacteristic, complemented
55C2×#104×C79C2211yescharacteristic, complemented
56C2×#104×C79C2211yescharacteristic, complemented
57C2×#104×C79C2211yescharacteristic, complemented
58#418×C79C2211yescharacteristic, complemented
59#417×C79C2211yescharacteristic
60#417×C79C2211yescharacteristic, complemented
61#417×C79C2211yescharacteristic, complemented
62C2×#100×C79C2211yescharacteristic, complemented
63C2×#100×C79C2211yescharacteristic, complemented
64#407×C79C2211yescharacteristic, complemented
65#390×C79—22no—
66#390×C79C2211yescharacteristic, complemented
67#390×C79C2211yescharacteristic, complemented
68#384×C79C2211yescharacteristic, complemented
69#343×C79C2211yescharacteristic, complemented
70#343×C79C2211yescharacteristic, complemented
71#339×C79C2211yescharacteristic, complemented
72#339×C79C2211yescharacteristic, complemented
73H(5,𝔽2)×C79—22no—
74H(5,𝔽2)×C79—22no—
75H(5,𝔽2)×C79—41no—
76H(5,𝔽2)×C79—41no—
77C2×#41×C79—21no—
78C2×#41×C79—21no—
79C2×#41×C79—21no—
80C2×#41×C79—21no—
81C2×#41×C79—22no—
82C2×#41×C79—22no—
83C2×#41×C79—41no—
84C2×#41×C79—41no—
85C2×#41×C79D411yescharacteristic, complemented
86C2×#41×C79D411yescharacteristic, complemented
87C2×#41×C79C2311yescharacteristic
88C2×#41×C79C2311yescharacteristic
89C2×#41×C79C2311yescharacteristic
90C22×Q8×C79D411yescharacteristic, complemented
91C22×D4×C79—21no—
92C22×D4×C79—22no—
93C22×D4×C79—22no—
94C22×D4×C79—21no—
95C22×D4×C79—21no—
96C22×D4×C79—21no—
97C22×D4×C79—22no—
98C22×D4×C79D412yes—
99C22×D4×C79D411yescharacteristic, complemented
100C22×D4×C79C2311yescharacteristic
101C22×D4×C79C2311yescharacteristic
102C23×C4×C79—21no—
103C23×C4×C79—21no—
104C23×C4×C79C2311yescharacteristic
105AGL(1,ℤ/8)×C79—22no—
106AGL(1,ℤ/8)×C79—22no—
107AGL(1,ℤ/8)×C79—22no—
108AGL(1,ℤ/8)×C79—41no—
109AGL(1,ℤ/8)×C79—41no—
110AGL(1,ℤ/8)×C79—41no—
111C2×SD16×C79—21no—
112C2×SD16×C79—21no—
113C2×SD16×C79—21no—
114C2×D8×C79—21no—
115C2×D8×C79—21no—
116C2×D8×C79—21no—
117C2×M16×C79—21no—
118C2×M16×C79—22no—
119C2×M16×C79—41no—
120C2×M16×C79C2311yescharacteristic
121C2×M16×C79C2311yescharacteristic
122C2×M16×C79C2311yescharacteristic
123C2×M16×C79C2311yescharacteristic
124C22×C8×C79—21no—
125#127×C79—22no—
126#127×C79—21no—
127#127×C79—22no—
128#127×C79—41no—
129#124×C79—22no—
130#124×C79—21no—
131#123×C79—22no—
132#123×C79—21no—
133C22⋊Q8×C79—22no—
134C22⋊Q8×C79—21no—
135C22⋊Q8×C79—21no—
136C22⋊Q8×C79D411yescharacteristic, complemented
137C22⋊Q8×C79D411yescharacteristic, complemented
138#121×C79—22no—
139#121×C79—22no—
140#121×C79—22no—
141#121×C79—22no—
142#121×C79—22no—
143#121×C79—21no—
144#121×C79—21no—
145#121×C79—21no—
146#121×C79—21no—
147#121×C79—21no—
148#121×C79—21no—
149#121×C79—22no—
150#121×C79—21no—
151#121×C79—21no—
152#121×C79—21no—
153#121×C79—21no—
154#121×C79—21no—
155#121×C79—21no—
156#121×C79—48no—
157#121×C79D411yescharacteristic, complemented
158#121×C79D411yescharacteristic, complemented
159#120×C79—22no—
160#120×C79—22no—
161#120×C79—22no—
162#120×C79—21no—
163#120×C79—22no—
164C4×Q8×C79—21no—
165C4×D4×C79—22no—
166C4×D4×C79—22no—
167C4×D4×C79—21no—
168C4×D4×C79—22no—
169C4×D4×C79—21no—
170C4×D4×C79—21no—
171#117×C79—21no—
172#117×C79C2311yescharacteristic
173C2×C4⋊C4×C79—21no—
174C2×C4⋊C4×C79—22no—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—22no—
178C2×C22⋊C4×C79—22no—
179C2×C22⋊C4×C79—22no—
180C2×C22⋊C4×C79—21no—
181C2×C22⋊C4×C79D412yes—
182C2×C42×C79—22no—
183C2×C42×C79—21no—
184C2×C42×C79—41no—
185C2×C42×C79C2311yescharacteristic
186C2×C42×C79C2311yescharacteristic
187#107×C79—21no—
188#106×C79—21no—
189#104×C79—22no—
190#104×C79—22no—
191#104×C79—22no—
192#104×C79—22no—
193#104×C79—41no—
194#104×C79D414yescomplemented
195#103×C79—21no—
196#103×C79—21no—
197#103×C79—21no—
198#102×C79—21no—
199#102×C79—21no—
200#102×C79—21no—
201#102×C79—21no—
202#102×C79—21no—
203#100×C79—22no—
204#100×C79—41no—
205C22⋊C8×C79—21no—
206C22⋊C8×C79—21no—
207C24×C79—22no—
208C24×C79—21no—
209C24×C79—21no—
210C24×C79C2×D411yescharacteristic
211C24×C79C2×D412yes—
212#41×C79—21no—
213#41×C79—21no—
214#41×C79—22no—
215#41×C79—22no—
216#41×C79—21no—
217#41×C79—21no—
218#41×C79—21no—
219#41×C79—21no—
220#41×C79—21no—
221#41×C79—21no—
222#41×C79—21no—
223#41×C79—21no—
224#41×C79—42no—
225#41×C79—42no—
226#41×C79—41no—
227#41×C79—41no—
228#41×C79—42no—
229#41×C79—42no—
230#41×C79—42no—
231#41×C79—42no—
232#41×C79—42no—
233#41×C79—42no—
234#41×C79C2×D412yes—
235#41×C79#4112yes—
236C2×Q8×C79—21no—
237C2×Q8×C79—22no—
238C2×Q8×C79—41no—
239C2×Q8×C79C2×D411yescharacteristic
240C2×Q8×C79C2×D411yescharacteristic
241C2×Q8×C79C2×D411yescharacteristic
242C2×D4×C79—21no—
243C2×D4×C79—22no—
244C2×D4×C79—22no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79—21no—
248C2×D4×C79—21no—
249C2×D4×C79—21no—
250C2×D4×C79—21no—
251C2×D4×C79—21no—
252C2×D4×C79—22no—
253C2×D4×C79—22no—
254C2×D4×C79—22no—
255C2×D4×C79—21no—
256C2×D4×C79—22no—
257C2×D4×C79—21no—
258C2×D4×C79—21no—
259C2×D4×C79—21no—
260C2×D4×C79—21no—
261C2×D4×C79—21no—
262C2×D4×C79—21no—
263C2×D4×C79—21no—
264C2×D4×C79—21no—
265C2×D4×C79—21no—
266C2×D4×C79—21no—
267C2×D4×C79—21no—
268C2×D4×C79—21no—
269C2×D4×C79—21no—
270C2×D4×C79—41no—
271C2×D4×C79—42no—
272C2×D4×C79—42no—
273C2×D4×C79—44no—
274C2×D4×C79—44no—
275C2×D4×C79—44no—
276C2×D4×C79—42no—
277C2×D4×C79—42no—
278C2×D4×C79—44no—
279C2×D4×C79—44no—
280C2×D4×C79—42no—
281C2×D4×C79—42no—
282C2×D4×C79—44no—
283C2×D4×C79—44no—
284C2×D4×C79—41no—
285C2×D4×C79—41no—
286C2×D4×C79—84no—
287C2×D4×C79C2×D411yescharacteristic
288C2×D4×C79C2×D411yescharacteristic
289C2×D4×C79C2×D411yescharacteristic
290C22×C4×C79—21no—
291C22×C4×C79—21no—
292C22×C4×C79—21no—
293C22×C4×C79—21no—
294C22×C4×C79—21no—
295C22×C4×C79—21no—
296C22×C4×C79—22no—
297C22×C4×C79—24no—
298C22×C4×C79—21no—
299C22×C4×C79—21no—
300C22×C4×C79—22no—
301C22×C4×C79—21no—
302C22×C4×C79—21no—
303C22×C4×C79—21no—
304C22×C4×C79—21no—
305C22×C4×C79—21no—
306C22×C4×C79—42no—
307C22×C4×C79—42no—
308C22×C4×C79—42no—
309C22×C4×C79—42no—
310C22×C4×C79C2×D411yescharacteristic
311C22×C4×C79C2×D411yescharacteristic
312C22×C4×C79C2×D411yescharacteristic
313C22×C4×C79C2×D411yescharacteristic
314C22×C4×C79C2×D411yescharacteristic
315C22×C4×C79C2×D412yes—
316C22×C4×C79C2411yescharacteristic
317SD16×C79—42no—
318SD16×C79—42no—
319SD16×C79—42no—
320D8×C79—42no—
321D8×C79—42no—
322D8×C79—42no—
323M16×C79—21no—
324M16×C79—21no—
325M16×C79—21no—
326M16×C79—21no—
327M16×C79—21no—
328M16×C79—21no—
329M16×C79—21no—
330M16×C79—42no—
331M16×C79C2×D412yescomplemented
332C2×C8×C79—21no—
333C2×C8×C79—21no—
334C2×C8×C79—21no—
335C2×C8×C79—21no—
336C2×C8×C79—42no—
337C4⋊C4×C79—22no—
338C4⋊C4×C79—22no—
339C4⋊C4×C79—21no—
340C4⋊C4×C79—21no—
341C4⋊C4×C79—21no—
342C4⋊C4×C79—21no—
343C4⋊C4×C79—21no—
344C4⋊C4×C79—21no—
345C4⋊C4×C79—44no—
346C4⋊C4×C79C2×D411yescharacteristic
347C4⋊C4×C79C2×D411yescharacteristic
348C22⋊C4×C79—22no—
349C22⋊C4×C79—22no—
350C22⋊C4×C79—22no—
351C22⋊C4×C79—22no—
352C22⋊C4×C79—22no—
353C22⋊C4×C79—21no—
354C22⋊C4×C79—21no—
355C22⋊C4×C79—21no—
356C22⋊C4×C79—21no—
357C22⋊C4×C79—22no—
358C22⋊C4×C79—22no—
359C22⋊C4×C79—21no—
360C22⋊C4×C79—44no—
361C22⋊C4×C79—44no—
362C22⋊C4×C79—41no—
363C22⋊C4×C79—41no—
364C42×C79—22no—
365C42×C79—21no—
366C42×C79—21no—
367C42×C79—21no—
368C42×C79—21no—
369C42×C79—42no—
370C42×C79C2×D412yescomplemented
371C23×C79—21no—
372C23×C79—21no—
373C23×C79—21no—
374C23×C79—22no—
375C23×C79—22no—
376C23×C79—21no—
377C23×C79—21no—
378C23×C79—22no—
379C23×C79—22no—
380C23×C79—41no—
381C23×C79—42no—
382C23×C79—44no—
383C23×C79—42no—
384C23×C79—42no—
385C23×C79—42no—
386C23×C79—42no—
387C23×C79—42no—
388C23×C79—41no—
389C23×C79—41no—
390C23×C79—41no—
391C23×C79—81no—
392C23×C79—82no—
393C23×C79—82no—
394C23×C79#12011yescharacteristic
395C23×C79#12011yescharacteristic
396C23×C79C22×D411yescharacteristic
397Q8×C79—21no—
398Q8×C79—21no—
399Q8×C79—21no—
400Q8×C79—21no—
401Q8×C79—21no—
402Q8×C79—42no—
403Q8×C79#12112yescomplemented
404D4×C79—22no—
405D4×C79—22no—
406D4×C79—21no—
407D4×C79—21no—
408D4×C79—21no—
409D4×C79—21no—
410D4×C79—21no—
411D4×C79—42no—
412D4×C79—42no—
413D4×C79—44no—
414D4×C79—42no—
415D4×C79—44no—
416D4×C79—41no—
417D4×C79—41no—
418D4×C79—41no—
419D4×C79—41no—
420D4×C79—44no—
421D4×C79—42no—
422D4×C79—41no—
423D4×C79—41no—
424D4×C79—41no—
425D4×C79—41no—
426D4×C79—41no—
427D4×C79—41no—
428D4×C79—41no—
429D4×C79—41no—
430D4×C79—88no—
431D4×C79—81no—
432D4×C79—82no—
433D4×C79—82no—
434D4×C79—82no—
435D4×C79—82no—
436D4×C79—82no—
437D4×C79—82no—
438D4×C79#12112yescomplemented
439C2×C4×C79—22no—
440C2×C4×C79—22no—
441C2×C4×C79—21no—
442C2×C4×C79—22no—
443C2×C4×C79—21no—
444C2×C4×C79—21no—
445C2×C4×C79—21no—
446C2×C4×C79—21no—
447C2×C4×C79—21no—
448C2×C4×C79—21no—
449C2×C4×C79—21no—
450C2×C4×C79—21no—
451C2×C4×C79—22no—
452C2×C4×C79—21no—
453C2×C4×C79—21no—
454C2×C4×C79—22no—
455C2×C4×C79—22no—
456C2×C4×C79—21no—
457C2×C4×C79—22no—
458C2×C4×C79—21no—
459C2×C4×C79—21no—
460C2×C4×C79—21no—
461C2×C4×C79—42no—
462C2×C4×C79—42no—
463C2×C4×C79—42no—
464C2×C4×C79—48no—
465C2×C4×C79—44no—
466C2×C4×C79—41no—
467C2×C4×C79—41no—
468C2×C4×C79—41no—
469C2×C4×C79—41no—
470C2×C4×C79—41no—
471C2×C4×C79—41no—
472C2×C4×C79—42no—
473C2×C4×C79—42no—
474C2×C4×C79—41no—
475C2×C4×C79—82no—
476C2×C4×C79#12011yescharacteristic
477C2×C4×C79#12011yescharacteristic
478C2×C4×C79C22×D411yescharacteristic
479C2×C4×C79C22×D411yescharacteristic
480C2×C4×C79C22×D411yescharacteristic
481C2×C4×C79C2×#4111yescharacteristic
482C2×C4×C79H(5,𝔽2)11yescharacteristic
483C2×C4×C79H(5,𝔽2)11yescharacteristic
484C8×C79—22no—
485C8×C79—41no—
486C8×C79—41no—
487C8×C79—41no—
488C22×C79—21no—
489C22×C79—21no—
490C22×C79—21no—
491C22×C79—21no—
492C22×C79—21no—
493C22×C79—22no—
494C22×C79—21no—
495C22×C79—21no—
496C22×C79—42no—
497C22×C79—42no—
498C22×C79—41no—
499C22×C79—41no—
500C22×C79—41no—
501C22×C79—41no—
502C22×C79—42no—
503C22×C79—42no—
504C22×C79—41no—
505C22×C79—41no—
506C22×C79—41no—
507C22×C79—42no—
508C22×C79—41no—
509C22×C79—84no—
510C22×C79—82no—
511C22×C79—82no—
512C22×C79—82no—
513C22×C79—82no—
514C22×C79—81no—
515C22×C79—81no—
516C22×C79—81no—
517C22×C79—164no—
518C22×C79#45312yescomplemented
519C22×C79C2×#12011yescharacteristic
520C22×C79D4211yescharacteristic
521C22×C79#54611yescharacteristic
522C4×C79—24no—
523C4×C79—21no—
524C4×C79—21no—
525C4×C79—22no—
526C4×C79—42no—
527C4×C79—41no—
528C4×C79—41no—
529C4×C79—42no—
530C4×C79—41no—
531C4×C79—41no—
532C4×C79—81no—
533C4×C79C2×#12111yescharacteristic
534C4×C79#53411yescharacteristic
535C4×C79D4211yescharacteristic
536C4×C79#54611yescharacteristic
537#24464C7911yesmaximal, characteristic, direct product factor, Sylow
538C2×C79—21no—
539C2×C79—21no—
540C2×C79—22no—
541C2×C79—41no—
542C2×C79—42no—
543C2×C79—81no—
544C2×C79—82no—
545C2×C79—81no—
546C2×C79—161no—
547C2×C79#241011yescharacteristic
548C2×C79C2×#45311yescharacteristic
549C2×C79#301811yescharacteristic
550#3488C2×C7911yescharacteristic, complemented
551#3055C2×C7911yescharacteristic, complemented
552C2×#453C2×C7911yescharacteristic, complemented
553#3006C2×C7911yescharacteristic, complemented
554C22×#104C2×C7911yescharacteristic, complemented
555#2856C2×C7911yescharacteristic, complemented
556#2039C2×C7911yescharacteristic, complemented
557#2037C2×C7911yescharacteristic, complemented
558#2006C2×C7911yescharacteristic, complemented
559#2002C2×C7911yescharacteristic, complemented
560#1900C2×C7911yescharacteristic, complemented
561#1896C2×C7911yescharacteristic, complemented
562#1883C2×C7911yescharacteristic, complemented
563#1859C2×C7911yescharacteristic, complemented
564#1792C2×C7911yescharacteristic, complemented
565C79#2446411yescharacteristic, direct product factor, Sylow
566C2×H(5,𝔽2)C22×C7911yescharacteristic
567C22×#41C22×C7911yescharacteristic
568C2×AGL(1,ℤ/8)C22×C7911yescharacteristic
569C2×AGL(1,ℤ/8)C22×C7911yescharacteristic, complemented
570C2×AGL(1,ℤ/8)C22×C7911yescharacteristic, complemented
571C22×M16C22×C7911yescharacteristic, complemented
572#550—21no—
573#548—21no—
574#546—21no—
575#546—22no—
576D42—22no—
577D42—21no—
578#537—21no—
579#537C22×C7911yescharacteristic
580#535—21no—
581#535C22×C7911yescharacteristic
582C2×#127C22×C7911yescharacteristic, complemented
583#525—21no—
584#525C22×C7911yescharacteristic
585C2×#121—21no—
586C2×#121—22no—
587C2×#121C22×C7911yescharacteristic
588C2×#121C22×C7911yescharacteristic, complemented
589#520C22×C7911yescharacteristic
590C22×C42C22×C7911yescharacteristic, complemented
591#469—21no—
592#468—21no—
593#466—21no—
594#465—21no—
595#453—24no—
596#449—21no—
597#449—21no—
598#448—21no—
599#447—21no—
600#428C22×C7911yescharacteristic, complemented
601C2×#104—24no—
602C2×#104C22×C7911yescharacteristic
603C2×#104C22×C7911yescharacteristic
604C2×#104C22×C7911yescharacteristic, complemented
605C2×#104C22×C7911yescharacteristic, complemented
606C2×#104C22×C7911yescharacteristic, complemented
607C2×#104C22×C7911yescharacteristic, complemented
608#418C22×C7911yescharacteristic, complemented
609#417C22×C7911yescharacteristic
610#417C22×C7911yescharacteristic, complemented
611#417C22×C7911yescharacteristic, complemented
612C2×#100C22×C7911yescharacteristic, complemented
613C2×#100C22×C7911yescharacteristic, complemented
614#407C22×C7911yescharacteristic, complemented
615#390—22no—
616#390C22×C7911yescharacteristic, complemented
617#390C22×C7911yescharacteristic, complemented
618#384C22×C7911yescharacteristic, complemented
619#343C22×C7911yescharacteristic, complemented
620#343C22×C7911yescharacteristic, complemented
621#339C22×C7911yescharacteristic, complemented
622#339C22×C7911yescharacteristic, complemented
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C7911yescharacteristic, complemented
636C2×#41D4×C7911yescharacteristic, complemented
637C2×#41C23×C7911yescharacteristic
638C2×#41C23×C7911yescharacteristic
639C2×#41C23×C7911yescharacteristic
640C22×Q8D4×C7911yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C7912yes—
649C22×D4D4×C7911yescharacteristic, complemented
650C22×D4C23×C7911yescharacteristic
651C22×D4C23×C7911yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C7911yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C7911yescharacteristic
671C2×M16C23×C7911yescharacteristic
672C2×M16C23×C7911yescharacteristic
673C2×M16C23×C7911yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C7911yescharacteristic, complemented
687C22⋊Q8D4×C7911yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C7911yescharacteristic, complemented
708#121D4×C7911yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C7911yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C7911yescharacteristic
726C2×C4⋊C4C23×C7911yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C7912yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C7911yescharacteristic
736C2×C42C23×C7911yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C7914yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C7911yescharacteristic
761C24C2×D4×C7912yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C7912yes—
785#41#41×C7912yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C7911yescharacteristic
790C2×Q8C2×D4×C7911yescharacteristic
791C2×Q8C2×D4×C7911yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C7911yescharacteristic
838C2×D4C2×D4×C7911yescharacteristic
839C2×D4C2×D4×C7911yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C7911yescharacteristic
861C22×C4C2×D4×C7911yescharacteristic
862C22×C4C2×D4×C7911yescharacteristic
863C22×C4C2×D4×C7911yescharacteristic
864C22×C4C2×D4×C7911yescharacteristic
865C22×C4C2×D4×C7912yes—
866C22×C4C24×C7911yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C7912yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C7911yescharacteristic
897C4⋊C4C2×D4×C7911yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C7912yescomplemented
921C23—22no—
922C23—21no—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C7911yescharacteristic
945C23#120×C7911yescharacteristic
946C23C22×D4×C7911yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C7912yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—44no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C7912yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C7911yescharacteristic
1027C2×C4#120×C7911yescharacteristic
1028C2×C4C22×D4×C7911yescharacteristic
1029C2×C4C22×D4×C7911yescharacteristic
1030C2×C4C22×D4×C7911yescharacteristic
1031C2×C4C2×#41×C7911yescharacteristic
1032C2×C4H(5,𝔽2)×C7911yescharacteristic
1033C2×C4H(5,𝔽2)×C7911yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—22no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—42no—
1052C22—41no—
1053C22—41no—
1054C22—41no—
1055C22—42no—
1056C22—42no—
1057C22—41no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22#453×C7912yescomplemented
1069C22C2×#120×C7911yescharacteristic
1070C22D42×C7911yescharacteristic
1071C22#546×C7911yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—41no—
1080C4—42no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C7911yescharacteristic
1084C4#534×C7911yescharacteristic
1085C4D42×C7911yescharacteristic
1086C4#546×C7911yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C79×#241011yescharacteristic
1097C2C2×#453×C7911yescharacteristic
1098C2C79×#301811yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC22×C4C24×C79
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C79 ◁ C23×C4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3488C2semidirect
2. C79×#3055C2semidirect
3. C2×#453×C79C2semidirect
4. C79×#3006C2semidirect
5. C22×#104×C79C2semidirect
6. C79×#2856C2semidirect
7. C79×#2039C2semidirect
8. C79×#2037C2semidirect
9. C79×#2006C2semidirect
10. C79×#2002C2semidirect
11. C79×#1900C2semidirect
12. C79×#1896C2semidirect
13. C79×#1883C2semidirect
14. C79×#1859C2semidirect
15. C79×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C79C22semidirect
20. C2×AGL(1,ℤ/8)×C79C22semidirect
21. C22×M16×C79C22semidirect
32. C2×#127×C79C22semidirect
38. C2×#121×C79C22semidirect
40. C22×C42×C79C22semidirect
50. #428×C79C22semidirect
54. C2×#104×C79C22semidirect
55. C2×#104×C79C22semidirect
56. C2×#104×C79C22semidirect
57. C2×#104×C79C22semidirect
58. #418×C79C22semidirect
60. #417×C79C22semidirect
61. #417×C79C22semidirect
62. C2×#100×C79C22semidirect
63. C2×#100×C79C22semidirect
64. #407×C79C22semidirect
66. #390×C79C22semidirect
67. #390×C79C22semidirect
68. #384×C79C22semidirect
69. #343×C79C22semidirect
70. #343×C79C22semidirect
71. #339×C79C22semidirect
72. #339×C79C22semidirect
85. C2×#41×C79D4semidirect
86. C2×#41×C79D4semidirect
90. C22×Q8×C79D4semidirect
99. C22×D4×C79D4semidirect
136. C22⋊Q8×C79D4semidirect
137. C22⋊Q8×C79D4semidirect
157. #121×C79D4semidirect
158. #121×C79D4semidirect
194. #104×C79D4semidirect
331. M16×C79C2×D4semidirect
370. C42×C79C2×D4semidirect
403. Q8×C79#121semidirect
438. D4×C79#121semidirect
518. C22×C79#453semidirect
537. #24464C79direct (N × H)
550. #3488C2×C79semidirect
551. #3055C2×C79semidirect
552. C2×#453C2×C79semidirect
553. #3006C2×C79semidirect
554. C22×#104C2×C79semidirect
555. #2856C2×C79semidirect
556. #2039C2×C79semidirect
557. #2037C2×C79semidirect
558. #2006C2×C79semidirect
559. #2002C2×C79semidirect
560. #1900C2×C79semidirect
561. #1896C2×C79semidirect
562. #1883C2×C79semidirect
563. #1859C2×C79semidirect
564. #1792C2×C79semidirect
565. C79#24464direct (N × H)
569. C2×AGL(1,ℤ/8)C22×C79semidirect
570. C2×AGL(1,ℤ/8)C22×C79semidirect
571. C22×M16C22×C79semidirect
582. C2×#127C22×C79semidirect
588. C2×#121C22×C79semidirect
590. C22×C42C22×C79semidirect
600. #428C22×C79semidirect
604. C2×#104C22×C79semidirect
605. C2×#104C22×C79semidirect
606. C2×#104C22×C79semidirect
607. C2×#104C22×C79semidirect
608. #418C22×C79semidirect
610. #417C22×C79semidirect
611. #417C22×C79semidirect
612. C2×#100C22×C79semidirect
613. C2×#100C22×C79semidirect
614. #407C22×C79semidirect
616. #390C22×C79semidirect
617. #390C22×C79semidirect
618. #384C22×C79semidirect
619. #343C22×C79semidirect
620. #343C22×C79semidirect
621. #339C22×C79semidirect
622. #339C22×C79semidirect
635. C2×#41D4×C79semidirect
636. C2×#41D4×C79semidirect
640. C22×Q8D4×C79semidirect
649. C22×D4D4×C79semidirect
686. C22⋊Q8D4×C79semidirect
687. C22⋊Q8D4×C79semidirect
707. #121D4×C79semidirect
708. #121D4×C79semidirect
744. #104D4×C79semidirect
881. M16C2×D4×C79semidirect
920. C42C2×D4×C79semidirect
953. Q8#121×C79semidirect
988. D4#121×C79semidirect
1068. C22#453×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#34882
C79×#30552
C2×#453×C792
C79×#30062
C22×#104×C792
C79×#28562
C79×#20392
C79×#20372
C79×#20062
C79×#20022
C79×#19002
C79×#18962
C79×#18832
C79×#18592
C79×#17922
#2446479