Finite Group Databasebeta

← C79×#33552 #34145241

Subgroups — C79×#33552 #34145241

Order 20224.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3533C211yesmaximal, characteristic, complemented
2C79×#3026C211yesmaximal, characteristic, complemented
3C2×#458×C79C211yesmaximal, characteristic, complemented
4C79×#3019C211yesmaximal, characteristic, complemented
5C79×#2201C212yesmaximal, complemented
6C79×#2200C212yesmaximal, complemented
7C79×#2198C212yesmaximal, complemented
8C79×#2197C212yesmaximal, complemented
9C79×#2127C211yesmaximal, characteristic, complemented
10C79×#2121C211yesmaximal, characteristic, complemented
11C2×#352×C79C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C79C2211yescharacteristic
13#575×C79—21no—
14#563×C79C2211yescharacteristic, complemented
15#562×C79—21no—
16#560×C79C2211yescharacteristic, complemented
17#559×C79C2211yescharacteristic, complemented
18#553×C79—21no—
19#552×C79—21no—
20#551×C79—21no—
21#551×C79C2211yescharacteristic, complemented
22#547×C79—21no—
23#546×C79—21no—
24#542×C79—21no—
25#540×C79—21no—
26#539×C79—21no—
27#538×C79—21no—
28#538×C79—21no—
29#535×C79C2211yescharacteristic
30#534×C79—21no—
31#534×C79C2211yescharacteristic
32#525×C79—21no—
33C2×#123×C79—21no—
34C2×#123×C79C2211yescharacteristic
35#458×C79—21no—
36#458×C79—21no—
37#458×C79—21no—
38#458×C79C2212yes—
39#458×C79C2212yes—
40#458×C79C2212yes—
41B(4,𝔽2)×C79—21no—
42B(4,𝔽2)×C79C2212yes—
43#455×C79—21no—
44#455×C79C2212yes—
45#453×C79—21no—
46#453×C79C2212yes—
47#421×C79—21no—
48C2×#100×C79C2211yescharacteristic
49C2×#99×C79—21no—
50C2×#99×C79—21no—
51C2×#99×C79C2211yescharacteristic
52C2×#99×C79C2211yescharacteristic
53#354×C79C2212yescomplemented
54#353×C79C2212yescomplemented
55#352×C79C2212yescomplemented
56#352×C79C2212yescomplemented
57#352×C79C2212yescomplemented
58AΣL(1,𝔽16)×C79C2212yescomplemented
59H(5,𝔽2)×C79—21no—
60H(5,𝔽2)×C79—21no—
61H(5,𝔽2)×C79—21no—
62H(5,𝔽2)×C79—42no—
63H(5,𝔽2)×C79C2312yes—
64C2×#41×C79—21no—
65C2×#41×C79—21no—
66C2×#41×C79—41no—
67C2×#41×C79D411yescharacteristic, complemented
68C22×D4×C79—21no—
69C22×D4×C79—21no—
70C22×D4×C79—41no—
71C22×D4×C79D411yescharacteristic
72C22×D4×C79C2311yescharacteristic
73C23×C4×C79D411yescharacteristic, complemented
74#137×C79—22no—
75#137×C79—41no—
76AGL(1,ℤ/8)×C79—22no—
77AGL(1,ℤ/8)×C79—41no—
78#135×C79—42no—
79C2×M16×C79—21no—
80C4⋊Q8×C79—21no—
81#127×C79D411yescharacteristic, complemented
82#127×C79C2311yescharacteristic
83#126×C79—21no—
84#126×C79—21no—
85#126×C79—21no—
86#126×C79—21no—
87#126×C79—21no—
88#126×C79—21no—
89#125×C79—21no—
90#125×C79—21no—
91#125×C79—21no—
92#124×C79—21no—
93#124×C79—21no—
94#124×C79—21no—
95#124×C79—21no—
96#124×C79D411yescharacteristic, complemented
97#124×C79C2311yescharacteristic
98#123×C79—21no—
99#123×C79—21no—
100#123×C79—21no—
101#123×C79—21no—
102#123×C79—21no—
103#123×C79—21no—
104#123×C79—21no—
105#123×C79—21no—
106#123×C79—21no—
107#123×C79—21no—
108#123×C79—21no—
109#123×C79—21no—
110#123×C79—22no—
111#123×C79—22no—
112#123×C79—22no—
113#123×C79—41no—
114#123×C79—42no—
115#123×C79D411yescharacteristic
116#123×C79D411yescharacteristic, complemented
117#123×C79D411yescharacteristic, complemented
118#123×C79C2311yescharacteristic
119#123×C79C2311yescharacteristic
120#123×C79C2311yescharacteristic
121C22⋊Q8×C79—21no—
122C22⋊Q8×C79—21no—
123C22⋊Q8×C79—21no—
124C22⋊Q8×C79—21no—
125C22⋊Q8×C79—21no—
126C22⋊Q8×C79—21no—
127C22⋊Q8×C79—21no—
128C22⋊Q8×C79—21no—
129#121×C79—21no—
130#121×C79—21no—
131#121×C79—21no—
132#121×C79—21no—
133#121×C79—21no—
134#121×C79—21no—
135#121×C79—21no—
136#121×C79—21no—
137#121×C79—21no—
138#121×C79—21no—
139#121×C79—21no—
140#121×C79—21no—
141#121×C79—42no—
142#120×C79—21no—
143#120×C79—21no—
144#120×C79—21no—
145#120×C79—21no—
146#120×C79—22no—
147#120×C79—41no—
148#120×C79D411yescharacteristic
149#120×C79C2311yescharacteristic
150C4×Q8×C79—21no—
151C4×D4×C79—21no—
152C4×D4×C79—21no—
153C4×D4×C79—21no—
154C4×D4×C79—21no—
155C4×D4×C79—21no—
156C4×D4×C79—21no—
157C4×D4×C79—21no—
158C4×D4×C79—21no—
159C4×D4×C79—21no—
160#117×C79—21no—
161#117×C79—21no—
162#117×C79—21no—
163#117×C79D411yescharacteristic, complemented
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—41no—
167C2×C22⋊C4×C79—21no—
168C2×C22⋊C4×C79—21no—
169C2×C22⋊C4×C79—21no—
170C2×C22⋊C4×C79—21no—
171C2×C22⋊C4×C79—41no—
172C2×C22⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic, complemented
174#104×C79—22no—
175#104×C79—22no—
176#100×C79—21no—
177#100×C79C2312yes—
178#99×C79—21no—
179#99×C79—21no—
180#99×C79—22no—
181#99×C79—22no—
182#99×C79—22no—
183#99×C79—22no—
184#99×C79C2312yes—
185#99×C79C2312yes—
186C24×C79—21no—
187C24×C79—21no—
188C24×C79C2×D411yescharacteristic
189C24×C79C2×D411yescharacteristic
190C24×C79C2×D411yescharacteristic
191#41×C79—22no—
192#41×C79—22no—
193#41×C79—42no—
194#41×C79—41no—
195#41×C79—42no—
196#41×C79—42no—
197#41×C79—41no—
198#41×C79—41no—
199#41×C79—42no—
200#41×C79—41no—
201#41×C79—81no—
202#41×C79—81no—
203C2×Q8×C79—21no—
204C2×Q8×C79—21no—
205C2×Q8×C79—21no—
206C2×Q8×C79C2×D411yescharacteristic
207C2×D4×C79—21no—
208C2×D4×C79—22no—
209C2×D4×C79—22no—
210C2×D4×C79—21no—
211C2×D4×C79—21no—
212C2×D4×C79—22no—
213C2×D4×C79—22no—
214C2×D4×C79—21no—
215C2×D4×C79—21no—
216C2×D4×C79—21no—
217C2×D4×C79—21no—
218C2×D4×C79—21no—
219C2×D4×C79—21no—
220C2×D4×C79—21no—
221C2×D4×C79—21no—
222C2×D4×C79—21no—
223C2×D4×C79—41no—
224C2×D4×C79—41no—
225C2×D4×C79—42no—
226C2×D4×C79—42no—
227C2×D4×C79—41no—
228C2×D4×C79—41no—
229C2×D4×C79—41no—
230C2×D4×C79—41no—
231C2×D4×C79—42no—
232C2×D4×C79—42no—
233C2×D4×C79—41no—
234C2×D4×C79—41no—
235C2×D4×C79—41no—
236C2×D4×C79—41no—
237C2×D4×C79—41no—
238C2×D4×C79—42no—
239C2×D4×C79C2×D411yescharacteristic
240C2×D4×C79C2×D411yescharacteristic
241C2×D4×C79C2×D411yescharacteristic
242C2×D4×C79C2×D411yescharacteristic
243C2×D4×C79C2411yescharacteristic
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—21no—
250C22×C4×C79—21no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—41no—
256C22×C4×C79—41no—
257C22×C4×C79—41no—
258C22×C4×C79—41no—
259C22×C4×C79—41no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264Q16×C79—42no—
265SD16×C79—42no—
266SD16×C79—42no—
267D8×C79—42no—
268M16×C79—22no—
269M16×C79—41no—
270C2×C8×C79—41no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79—21no—
277C4⋊C4×C79—21no—
278C4⋊C4×C79—21no—
279C4⋊C4×C79—21no—
280C4⋊C4×C79—21no—
281C4⋊C4×C79—21no—
282C4⋊C4×C79—21no—
283C4⋊C4×C79—21no—
284C4⋊C4×C79—21no—
285C4⋊C4×C79—21no—
286C4⋊C4×C79—21no—
287C4⋊C4×C79—21no—
288C4⋊C4×C79—21no—
289C4⋊C4×C79—21no—
290C4⋊C4×C79—42no—
291C4⋊C4×C79—42no—
292C4⋊C4×C79—42no—
293C22⋊C4×C79—21no—
294C22⋊C4×C79—21no—
295C22⋊C4×C79—21no—
296C22⋊C4×C79—21no—
297C22⋊C4×C79—21no—
298C22⋊C4×C79—21no—
299C22⋊C4×C79—21no—
300C22⋊C4×C79—21no—
301C22⋊C4×C79—21no—
302C22⋊C4×C79—21no—
303C22⋊C4×C79—21no—
304C22⋊C4×C79—21no—
305C22⋊C4×C79—21no—
306C22⋊C4×C79—21no—
307C22⋊C4×C79—21no—
308C22⋊C4×C79—21no—
309C22⋊C4×C79—21no—
310C22⋊C4×C79—21no—
311C22⋊C4×C79—21no—
312C22⋊C4×C79—21no—
313C22⋊C4×C79—21no—
314C22⋊C4×C79—21no—
315C22⋊C4×C79—21no—
316C22⋊C4×C79—22no—
317C22⋊C4×C79—22no—
318C22⋊C4×C79—42no—
319C22⋊C4×C79—41no—
320C22⋊C4×C79—41no—
321C22⋊C4×C79—42no—
322C22⋊C4×C79—42no—
323C22⋊C4×C79—42no—
324C22⋊C4×C79C2×D411yescharacteristic
325C22⋊C4×C79C2×D411yescharacteristic
326C22⋊C4×C79C2×D411yescharacteristic
327C22⋊C4×C79C2×D411yescharacteristic
328C42×C79—21no—
329C42×C79—21no—
330C42×C79—21no—
331C42×C79—21no—
332C42×C79C2×D411yescharacteristic
333C42×C79C2×D411yescharacteristic
334C23×C79—21no—
335C23×C79—21no—
336C23×C79—21no—
337C23×C79—21no—
338C23×C79—22no—
339C23×C79—22no—
340C23×C79—21no—
341C23×C79—21no—
342C23×C79—41no—
343C23×C79—41no—
344C23×C79—41no—
345C23×C79—41no—
346C23×C79—81no—
347C23×C79—81no—
348C23×C79—81no—
349C23×C79—82no—
350C23×C79—161no—
351C23×C79#12011yescharacteristic
352C23×C79#12011yescharacteristic
353C23×C79#12011yescharacteristic
354C23×C79C22×D411yescharacteristic
355C23×C79C22×D411yescharacteristic
356Q8×C79—22no—
357Q8×C79—41no—
358Q8×C79—41no—
359Q8×C79—81no—
360Q8×C79—81no—
361D4×C79—22no—
362D4×C79—41no—
363D4×C79—41no—
364D4×C79—41no—
365D4×C79—41no—
366D4×C79—41no—
367D4×C79—41no—
368D4×C79—42no—
369D4×C79—42no—
370D4×C79—42no—
371D4×C79—42no—
372D4×C79—42no—
373D4×C79—42no—
374D4×C79—41no—
375D4×C79—41no—
376D4×C79—41no—
377D4×C79—41no—
378D4×C79—81no—
379D4×C79—81no—
380D4×C79—81no—
381D4×C79—81no—
382D4×C79—81no—
383D4×C79—81no—
384D4×C79—81no—
385D4×C79—81no—
386D4×C79—81no—
387D4×C79—162no—
388C2×C4×C79—21no—
389C2×C4×C79—21no—
390C2×C4×C79—22no—
391C2×C4×C79—22no—
392C2×C4×C79—21no—
393C2×C4×C79—21no—
394C2×C4×C79—21no—
395C2×C4×C79—21no—
396C2×C4×C79—21no—
397C2×C4×C79—21no—
398C2×C4×C79—21no—
399C2×C4×C79—21no—
400C2×C4×C79—21no—
401C2×C4×C79—21no—
402C2×C4×C79—42no—
403C2×C4×C79—42no—
404C2×C4×C79—41no—
405C2×C4×C79—41no—
406C2×C4×C79—41no—
407C2×C4×C79—41no—
408C2×C4×C79—41no—
409C2×C4×C79—41no—
410C2×C4×C79—41no—
411C2×C4×C79—41no—
412C2×C4×C79—42no—
413C2×C4×C79—42no—
414C2×C4×C79—81no—
415C2×C4×C79—81no—
416C2×C4×C79—81no—
417C2×C4×C79—81no—
418C2×C4×C79—81no—
419C2×C4×C79—81no—
420C2×C4×C79—81no—
421C2×C4×C79—81no—
422C2×C4×C79—82no—
423C2×C4×C79—161no—
424C2×C4×C79#12011yescharacteristic
425C2×C4×C79C22×D411yescharacteristic
426C8×C79—42no—
427C22×C79—21no—
428C22×C79—21no—
429C22×C79—21no—
430C22×C79—21no—
431C22×C79—41no—
432C22×C79—41no—
433C22×C79—41no—
434C22×C79—41no—
435C22×C79—41no—
436C22×C79—42no—
437C22×C79—41no—
438C22×C79—41no—
439C22×C79—41no—
440C22×C79—41no—
441C22×C79—42no—
442C22×C79—41no—
443C22×C79—41no—
444C22×C79—81no—
445C22×C79—81no—
446C22×C79—81no—
447C22×C79—82no—
448C22×C79—82no—
449C22×C79—82no—
450C22×C79—82no—
451C22×C79—161no—
452C22×C79—161no—
453C22×C79B(4,𝔽2)11yescharacteristic
454C22×C79B(4,𝔽2)11yescharacteristic
455C22×C79C2×#12011yescharacteristic
456C4×C79—21no—
457C4×C79—21no—
458C4×C79—41no—
459C4×C79—41no—
460C4×C79—41no—
461C4×C79—41no—
462C4×C79—41no—
463C4×C79—41no—
464C4×C79—42no—
465C4×C79—41no—
466C4×C79—41no—
467C4×C79—41no—
468C4×C79—41no—
469C4×C79—82no—
470C4×C79—82no—
471#33552C7911yesmaximal, characteristic, direct product factor, Sylow
472C2×C79—21no—
473C2×C79—21no—
474C2×C79—21no—
475C2×C79—41no—
476C2×C79—41no—
477C2×C79—41no—
478C2×C79—41no—
479C2×C79—81no—
480C2×C79—81no—
481C2×C79—82no—
482C2×C79C2×B(4,𝔽2)11yescharacteristic
483#3533C2×C7911yescharacteristic, complemented
484#3026C2×C7911yescharacteristic, complemented
485C2×#458C2×C7911yescharacteristic, complemented
486#3019C2×C7911yescharacteristic, complemented
487#2201C2×C7912yescomplemented
488#2200C2×C7912yescomplemented
489#2198C2×C7912yescomplemented
490#2197C2×C7912yescomplemented
491#2127C2×C7911yescharacteristic, complemented
492#2121C2×C7911yescharacteristic, complemented
493C2×#352C2×C7911yescharacteristic, complemented
494C79#3355211yescharacteristic, direct product factor, Sylow
495C2×H(5,𝔽2)C22×C7911yescharacteristic
496#575—21no—
497#563C22×C7911yescharacteristic, complemented
498#562—21no—
499#560C22×C7911yescharacteristic, complemented
500#559C22×C7911yescharacteristic, complemented
501#553—21no—
502#552—21no—
503#551—21no—
504#551C22×C7911yescharacteristic, complemented
505#547—21no—
506#546—21no—
507#542—21no—
508#540—21no—
509#539—21no—
510#538—21no—
511#538—21no—
512#535C22×C7911yescharacteristic
513#534—21no—
514#534C22×C7911yescharacteristic
515#525—21no—
516C2×#123—21no—
517C2×#123C22×C7911yescharacteristic
518#458—21no—
519#458—21no—
520#458—21no—
521#458C22×C7912yes—
522#458C22×C7912yes—
523#458C22×C7912yes—
524B(4,𝔽2)—21no—
525B(4,𝔽2)C22×C7912yes—
526#455—21no—
527#455C22×C7912yes—
528#453—21no—
529#453C22×C7912yes—
530#421—21no—
531C2×#100C22×C7911yescharacteristic
532C2×#99—21no—
533C2×#99—21no—
534C2×#99C22×C7911yescharacteristic
535C2×#99C22×C7911yescharacteristic
536#354C22×C7912yescomplemented
537#353C22×C7912yescomplemented
538#352C22×C7912yescomplemented
539#352C22×C7912yescomplemented
540#352C22×C7912yescomplemented
541AΣL(1,𝔽16)C22×C7912yescomplemented
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C7912yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C7911yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C7911yescharacteristic
555C22×D4C23×C7911yescharacteristic
556C23×C4D4×C7911yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C7911yescharacteristic, complemented
565#127C23×C7911yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C7911yescharacteristic, complemented
580#124C23×C7911yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C7911yescharacteristic
599#123D4×C7911yescharacteristic, complemented
600#123D4×C7911yescharacteristic, complemented
601#123C23×C7911yescharacteristic
602#123C23×C7911yescharacteristic
603#123C23×C7911yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C7911yescharacteristic
632#120C23×C7911yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C7911yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C7911yescharacteristic
656C2×C22⋊C4D4×C7911yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C7912yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C7912yes—
668#99C23×C7912yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C7911yescharacteristic
672C24C2×D4×C7911yescharacteristic
673C24C2×D4×C7911yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C7911yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C7911yescharacteristic
723C2×D4C2×D4×C7911yescharacteristic
724C2×D4C2×D4×C7911yescharacteristic
725C2×D4C2×D4×C7911yescharacteristic
726C2×D4C24×C7911yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C7911yescharacteristic
744C22×C4C2×D4×C7911yescharacteristic
745C22×C4C2×D4×C7911yescharacteristic
746C22×C4C2×D4×C7911yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C7911yescharacteristic
808C22⋊C4C2×D4×C7911yescharacteristic
809C22⋊C4C2×D4×C7911yescharacteristic
810C22⋊C4C2×D4×C7911yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C7911yescharacteristic
816C42C2×D4×C7911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C7911yescharacteristic
835C23#120×C7911yescharacteristic
836C23#120×C7911yescharacteristic
837C23C22×D4×C7911yescharacteristic
838C23C22×D4×C7911yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C7911yescharacteristic
908C2×C4C22×D4×C7911yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22B(4,𝔽2)×C7911yescharacteristic
937C22B(4,𝔽2)×C7911yescharacteristic
938C22C2×#120×C7911yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×B(4,𝔽2)×C7911yescharacteristic
subgroupG/H
center, socleC2×C79C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C79
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C79 ◁ C23×C79 ◁ C22×D4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C79×#3533C2semidirect
2. C79×#3026C2semidirect
3. C2×#458×C79C2semidirect
4. C79×#3019C2semidirect
5. C79×#2201C2semidirect
6. C79×#2200C2semidirect
7. C79×#2198C2semidirect
8. C79×#2197C2semidirect
9. C79×#2127C2semidirect
10. C79×#2121C2semidirect
11. C2×#352×C79C2semidirect
14. #563×C79C22semidirect
16. #560×C79C22semidirect
17. #559×C79C22semidirect
21. #551×C79C22semidirect
53. #354×C79C22semidirect
54. #353×C79C22semidirect
55. #352×C79C22semidirect
56. #352×C79C22semidirect
57. #352×C79C22semidirect
58. AΣL(1,𝔽16)×C79C22semidirect
67. C2×#41×C79D4semidirect
73. C23×C4×C79D4semidirect
81. #127×C79D4semidirect
96. #124×C79D4semidirect
116. #123×C79D4semidirect
117. #123×C79D4semidirect
163. #117×C79D4semidirect
173. C2×C22⋊C4×C79D4semidirect
471. #33552C79direct (N × H)
483. #3533C2×C79semidirect
484. #3026C2×C79semidirect
485. C2×#458C2×C79semidirect
486. #3019C2×C79semidirect
487. #2201C2×C79semidirect
488. #2200C2×C79semidirect
489. #2198C2×C79semidirect
490. #2197C2×C79semidirect
491. #2127C2×C79semidirect
492. #2121C2×C79semidirect
493. C2×#352C2×C79semidirect
494. C79#33552direct (N × H)
497. #563C22×C79semidirect
499. #560C22×C79semidirect
500. #559C22×C79semidirect
504. #551C22×C79semidirect
536. #354C22×C79semidirect
537. #353C22×C79semidirect
538. #352C22×C79semidirect
539. #352C22×C79semidirect
540. #352C22×C79semidirect
541. AΣL(1,𝔽16)C22×C79semidirect
550. C2×#41D4×C79semidirect
556. C23×C4D4×C79semidirect
564. #127D4×C79semidirect
579. #124D4×C79semidirect
599. #123D4×C79semidirect
600. #123D4×C79semidirect
646. #117D4×C79semidirect
656. C2×C22⋊C4D4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#35332
C79×#30262
C2×#458×C792
C79×#30192
C79×#22012
C79×#22002
C79×#21982
C79×#21972
C79×#21272
C79×#21212
C2×#352×C792
#3355279