Finite Group Databasebeta

← C79×#24469 #34136158

Subgroups — C79×#24469 #34136158

Order 20224.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3489C211yesmaximal, characteristic, complemented
2C79×#3055C211yesmaximal, characteristic, complemented
3C2×#454×C79C211yesmaximal, characteristic, complemented
4C79×#3006C211yesmaximal, characteristic, complemented
5C2×#421×C79C211yesmaximal, characteristic, complemented
6C79×#2620C211yesmaximal, characteristic, complemented
7C79×#2039C211yesmaximal, characteristic, complemented
8C79×#2038C211yesmaximal, characteristic, complemented
9C79×#2006C211yesmaximal, characteristic, complemented
10C79×#2003C211yesmaximal, characteristic, complemented
11C79×#1901C211yesmaximal, characteristic, complemented
12C79×#1897C211yesmaximal, characteristic, complemented
13C79×#1883C211yesmaximal, characteristic, complemented
14C79×#1859C211yesmaximal, characteristic, complemented
15C79×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C79C2211yescharacteristic
17C22×#41×C79C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C79C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C79C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C79C2211yescharacteristic, complemented
21C22×M16×C79C2211yescharacteristic
22D4×Q8×C79—21no—
23#548×C79—21no—
24#547×C79—21no—
25#547×C79—22no—
26#546×C79—21no—
27#546×C79—22no—
28#537×C79—21no—
29#537×C79C2211yescharacteristic
30#536×C79—21no—
31#536×C79C2211yescharacteristic
32C2×#124×C79C2211yescharacteristic, complemented
33#525×C79—21no—
34#525×C79C2211yescharacteristic
35C2×C22⋊Q8×C79—21no—
36C2×C22⋊Q8×C79C2211yescharacteristic
37C2×#121×C79C2211yescharacteristic
38#520×C79C2211yescharacteristic
39C2×#117×C79C2211yescharacteristic
40#469×C79—21no—
41#468×C79—21no—
42#466×C79—21no—
43#465×C79—21no—
44#454×C79—24no—
45#449×C79—21no—
46#449×C79—21no—
47#448×C79—21no—
48#447×C79—21no—
49#428×C79C2211yescharacteristic, complemented
50#421×C79—24no—
51C2×#104×C79C2211yescharacteristic
52C2×#104×C79C2211yescharacteristic
53C2×#104×C79C2211yescharacteristic
54C2×#104×C79C2211yescharacteristic
55C2×#104×C79C2211yescharacteristic, complemented
56C2×#104×C79C2211yescharacteristic, complemented
57#418×C79C2211yescharacteristic, complemented
58#417×C79C2211yescharacteristic
59#417×C79C2211yescharacteristic
60#417×C79C2211yescharacteristic, complemented
61C2×#101×C79C2211yescharacteristic, complemented
62C2×#101×C79C2211yescharacteristic, complemented
63#407×C79C2211yescharacteristic
64#396×C79—22no—
65#394×C79—22no—
66#391×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
732−1+4×C79—22no—
742−1+4×C79—22no—
752−1+4×C79—41no—
762−1+4×C79—41no—
77C2×#41×C79—21no—
78C2×#41×C79—21no—
79C2×#41×C79—21no—
80C2×#41×C79—22no—
81C2×#41×C79—21no—
82C2×#41×C79—22no—
83C2×#41×C79—22no—
84C2×#41×C79—41no—
85C2×#41×C79—41no—
86C2×#41×C79D411yescharacteristic
87C2×#41×C79D411yescharacteristic
88C2×#41×C79C2311yescharacteristic
89C2×#41×C79C2311yescharacteristic
90C2×#41×C79C2311yescharacteristic
91C22×Q8×C79—21no—
92C22×Q8×C79—21no—
93C22×Q8×C79D411yescharacteristic
94C22×Q8×C79C2311yescharacteristic
95C22×D4×C79—21no—
96C22×D4×C79—21no—
97C22×D4×C79D411yescharacteristic
98C22×D4×C79C2311yescharacteristic
99C23×C4×C79—21no—
100C23×C4×C79C2311yescharacteristic
101AGL(1,ℤ/8)×C79—22no—
102AGL(1,ℤ/8)×C79—22no—
103AGL(1,ℤ/8)×C79—22no—
104AGL(1,ℤ/8)×C79—41no—
105AGL(1,ℤ/8)×C79—41no—
106AGL(1,ℤ/8)×C79—41no—
107C2×SD16×C79—21no—
108C2×SD16×C79—21no—
109C2×SD16×C79—21no—
110C2×D8×C79—21no—
111C2×D8×C79—21no—
112C2×D8×C79—21no—
113C2×M16×C79—21no—
114C2×M16×C79—22no—
115C2×M16×C79—41no—
116C2×M16×C79C2311yescharacteristic
117C2×M16×C79C2311yescharacteristic
118C2×M16×C79C2311yescharacteristic
119C2×M16×C79C2311yescharacteristic
120C22×C8×C79—21no—
121C4⋊Q8×C79—22no—
122C4⋊Q8×C79—21no—
123#124×C79—22no—
124#124×C79—21no—
125#124×C79—22no—
126#124×C79—41no—
127#123×C79—22no—
128#123×C79—22no—
129#123×C79—22no—
130#123×C79—21no—
131#123×C79—22no—
132C22⋊Q8×C79—22no—
133C22⋊Q8×C79—22no—
134C22⋊Q8×C79—22no—
135C22⋊Q8×C79—21no—
136C22⋊Q8×C79—21no—
137C22⋊Q8×C79—21no—
138C22⋊Q8×C79—21no—
139C22⋊Q8×C79—21no—
140C22⋊Q8×C79—21no—
141C22⋊Q8×C79—21no—
142C22⋊Q8×C79—21no—
143C22⋊Q8×C79D411yescharacteristic
144C22⋊Q8×C79D411yescharacteristic
145#121×C79—22no—
146#121×C79—22no—
147#121×C79—22no—
148#121×C79—21no—
149#121×C79—21no—
150#121×C79—22no—
151#121×C79—21no—
152#121×C79—21no—
153#121×C79—21no—
154#121×C79—21no—
155#121×C79D411yescharacteristic
156#121×C79D411yescharacteristic
157#120×C79—22no—
158#120×C79—21no—
159C4×Q8×C79—21no—
160C4×D4×C79—22no—
161C4×D4×C79—22no—
162C4×D4×C79—21no—
163C4×D4×C79—22no—
164C4×D4×C79—21no—
165C4×D4×C79—21no—
166#117×C79—21no—
167#117×C79—22no—
168#117×C79—41no—
169#117×C79C2311yescharacteristic
170C2×C4⋊C4×C79—22no—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79—22no—
174C2×C4⋊C4×C79D412yes—
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—22no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C22⋊C4×C79—22no—
181C2×C22⋊C4×C79—22no—
182C2×C22⋊C4×C79D412yes—
183C2×C42×C79C2311yescharacteristic
184C2×C42×C79C2311yescharacteristic
185#107×C79—21no—
186#106×C79—21no—
187#104×C79—22no—
188#104×C79—22no—
189#104×C79—22no—
190#104×C79—22no—
191#104×C79—41no—
192#104×C79D414yescomplemented
193#103×C79—21no—
194#103×C79—21no—
195#103×C79—21no—
196#102×C79—21no—
197#102×C79—21no—
198#102×C79—21no—
199#102×C79—21no—
200#102×C79—21no—
201#101×C79—22no—
202#101×C79—41no—
203C22⋊C8×C79—21no—
204C22⋊C8×C79—21no—
205#95×C79—22no—
206C24×C79—21no—
207C24×C79—21no—
208C24×C79C2×D411yescharacteristic
209#41×C79—21no—
210#41×C79—21no—
211#41×C79—22no—
212#41×C79—22no—
213#41×C79—21no—
214#41×C79—21no—
215#41×C79—21no—
216#41×C79—21no—
217#41×C79—21no—
218#41×C79—21no—
219#41×C79—21no—
220#41×C79—21no—
221#41×C79—42no—
222#41×C79—42no—
223#41×C79—41no—
224#41×C79—41no—
225#41×C79—42no—
226#41×C79—42no—
227#41×C79—42no—
228#41×C79—42no—
229#41×C79—44no—
230#41×C79—44no—
231#41×C79—42no—
232#41×C79—42no—
233#41×C79C2×D412yes—
234#41×C79#4112yes—
235C2×Q8×C79—22no—
236C2×Q8×C79—21no—
237C2×Q8×C79—21no—
238C2×Q8×C79—21no—
239C2×Q8×C79—21no—
240C2×Q8×C79—21no—
241C2×Q8×C79—21no—
242C2×Q8×C79—21no—
243C2×Q8×C79—22no—
244C2×Q8×C79—41no—
245C2×Q8×C79—42no—
246C2×Q8×C79—42no—
247C2×Q8×C79—42no—
248C2×Q8×C79—42no—
249C2×Q8×C79C2×D411yescharacteristic
250C2×Q8×C79C2×D411yescharacteristic
251C2×Q8×C79C2×D411yescharacteristic
252C2×D4×C79—21no—
253C2×D4×C79—22no—
254C2×D4×C79—22no—
255C2×D4×C79—21no—
256C2×D4×C79—21no—
257C2×D4×C79—21no—
258C2×D4×C79—21no—
259C2×D4×C79—21no—
260C2×D4×C79—22no—
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—41no—
270C2×D4×C79—42no—
271C2×D4×C79—42no—
272C2×D4×C79—41no—
273C2×D4×C79—41no—
274C2×D4×C79—82no—
275C2×D4×C79C2×D411yescharacteristic
276C2×D4×C79C2×D411yescharacteristic
277C2×D4×C79C2×D411yescharacteristic
278C22×C4×C79—21no—
279C22×C4×C79—21no—
280C22×C4×C79—21no—
281C22×C4×C79—21no—
282C22×C4×C79—21no—
283C22×C4×C79—22no—
284C22×C4×C79—22no—
285C22×C4×C79—21no—
286C22×C4×C79—21no—
287C22×C4×C79—22no—
288C22×C4×C79—21no—
289C22×C4×C79—21no—
290C22×C4×C79—21no—
291C22×C4×C79—21no—
292C22×C4×C79—21no—
293C22×C4×C79—21no—
294C22×C4×C79—42no—
295C22×C4×C79—42no—
296C22×C4×C79C2×D412yes—
297C22×C4×C79C2×D411yescharacteristic
298C22×C4×C79C2×D411yescharacteristic
299C22×C4×C79C2×D411yescharacteristic
300C22×C4×C79C2×D411yescharacteristic
301C22×C4×C79C2×D411yescharacteristic
302C22×C4×C79C2×D412yes—
303C22×C4×C79C2411yescharacteristic
304SD16×C79—42no—
305SD16×C79—42no—
306SD16×C79—42no—
307D8×C79—42no—
308D8×C79—42no—
309D8×C79—42no—
310M16×C79—21no—
311M16×C79—21no—
312M16×C79—21no—
313M16×C79—21no—
314M16×C79—21no—
315M16×C79—21no—
316M16×C79—21no—
317M16×C79—42no—
318M16×C79C2×D412yes—
319C2×C8×C79—21no—
320C2×C8×C79—21no—
321C2×C8×C79—21no—
322C2×C8×C79—21no—
323C2×C8×C79—42no—
324C4⋊C4×C79—22no—
325C4⋊C4×C79—22no—
326C4⋊C4×C79—22no—
327C4⋊C4×C79—22no—
328C4⋊C4×C79—21no—
329C4⋊C4×C79—22no—
330C4⋊C4×C79—22no—
331C4⋊C4×C79—21no—
332C4⋊C4×C79—21no—
333C4⋊C4×C79—21no—
334C4⋊C4×C79—21no—
335C4⋊C4×C79—21no—
336C4⋊C4×C79—42no—
337C4⋊C4×C79—82no—
338C4⋊C4×C79C2×D411yescharacteristic
339C4⋊C4×C79C2×D411yescharacteristic
340C22⋊C4×C79—22no—
341C22⋊C4×C79—22no—
342C22⋊C4×C79—22no—
343C22⋊C4×C79—22no—
344C22⋊C4×C79—22no—
345C22⋊C4×C79—21no—
346C22⋊C4×C79—22no—
347C22⋊C4×C79—22no—
348C22⋊C4×C79—21no—
349C22⋊C4×C79—21no—
350C22⋊C4×C79—21no—
351C22⋊C4×C79—21no—
352C22⋊C4×C79—44no—
353C22⋊C4×C79—42no—
354C22⋊C4×C79—41no—
355C22⋊C4×C79—41no—
356C22⋊C4×C79—82no—
357C42×C79—22no—
358C42×C79—21no—
359C42×C79—21no—
360C42×C79—21no—
361C42×C79—21no—
362C42×C79C2×D412yes—
363C23×C79—21no—
364C23×C79—21no—
365C23×C79—21no—
366C23×C79—21no—
367C23×C79—21no—
368C23×C79—41no—
369C23×C79—41no—
370C23×C79—42no—
371C23×C79—42no—
372C23×C79—42no—
373C23×C79—42no—
374C23×C79—41no—
375C23×C79—41no—
376C23×C79—41no—
377C23×C79—81no—
378C23×C79#12011yescharacteristic
379C23×C79#12011yescharacteristic
380C23×C79C22×D411yescharacteristic
381Q8×C79—21no—
382Q8×C79—21no—
383Q8×C79—21no—
384Q8×C79—21no—
385Q8×C79—21no—
386Q8×C79—42no—
387Q8×C79—44no—
388Q8×C79—41no—
389Q8×C79—41no—
390Q8×C79—41no—
391Q8×C79—41no—
392Q8×C79#12112yes—
393D4×C79—22no—
394D4×C79—22no—
395D4×C79—21no—
396D4×C79—21no—
397D4×C79—21no—
398D4×C79—21no—
399D4×C79—21no—
400D4×C79—42no—
401D4×C79—42no—
402D4×C79—42no—
403D4×C79—42no—
404D4×C79—44no—
405D4×C79—41no—
406D4×C79—41no—
407D4×C79—41no—
408D4×C79—41no—
409D4×C79—41no—
410D4×C79—41no—
411D4×C79—41no—
412D4×C79—41no—
413D4×C79—81no—
414D4×C79—82no—
415D4×C79—82no—
416D4×C79—82no—
417D4×C79#12112yes—
418C2×C4×C79—21no—
419C2×C4×C79—21no—
420C2×C4×C79—21no—
421C2×C4×C79—21no—
422C2×C4×C79—21no—
423C2×C4×C79—21no—
424C2×C4×C79—21no—
425C2×C4×C79—21no—
426C2×C4×C79—21no—
427C2×C4×C79—22no—
428C2×C4×C79—21no—
429C2×C4×C79—21no—
430C2×C4×C79—22no—
431C2×C4×C79—21no—
432C2×C4×C79—22no—
433C2×C4×C79—21no—
434C2×C4×C79—21no—
435C2×C4×C79—22no—
436C2×C4×C79—21no—
437C2×C4×C79—22no—
438C2×C4×C79—22no—
439C2×C4×C79—22no—
440C2×C4×C79—42no—
441C2×C4×C79—42no—
442C2×C4×C79—42no—
443C2×C4×C79—44no—
444C2×C4×C79—41no—
445C2×C4×C79—41no—
446C2×C4×C79—44no—
447C2×C4×C79—41no—
448C2×C4×C79—41no—
449C2×C4×C79—41no—
450C2×C4×C79—41no—
451C2×C4×C79—42no—
452C2×C4×C79—41no—
453C2×C4×C79—42no—
454C2×C4×C79—41no—
455C2×C4×C79—41no—
456C2×C4×C79—41no—
457C2×C4×C79—82no—
458C2×C4×C79#12011yescharacteristic
459C2×C4×C79#12011yescharacteristic
460C2×C4×C79C22×D411yescharacteristic
461C2×C4×C79C22×D411yescharacteristic
462C2×C4×C79C22×D411yescharacteristic
463C2×C4×C79C2×#4111yescharacteristic
464C2×C4×C79H(5,𝔽2)11yescharacteristic
465C2×C4×C79H(5,𝔽2)11yescharacteristic
466C8×C79—22no—
467C8×C79—41no—
468C8×C79—41no—
469C8×C79—41no—
470C22×C79—21no—
471C22×C79—21no—
472C22×C79—21no—
473C22×C79—21no—
474C22×C79—22no—
475C22×C79—21no—
476C22×C79—21no—
477C22×C79—21no—
478C22×C79—21no—
479C22×C79—41no—
480C22×C79—41no—
481C22×C79—41no—
482C22×C79—41no—
483C22×C79—41no—
484C22×C79—41no—
485C22×C79—41no—
486C22×C79—41no—
487C22×C79—81no—
488C22×C79—81no—
489C22×C79—82no—
490C22×C79—82no—
491C22×C79—84no—
492C22×C79—81no—
493C22×C79—81no—
494C22×C79—81no—
495C22×C79C2×#12011yescharacteristic
496C22×C79D4211yescharacteristic
497C22×C79#54611yescharacteristic
498C4×C79—21no—
499C4×C79—21no—
500C4×C79—22no—
501C4×C79—42no—
502C4×C79—42no—
503C4×C79—41no—
504C4×C79—41no—
505C4×C79—41no—
506C4×C79—42no—
507C4×C79—41no—
508C4×C79—81no—
509C4×C79—81no—
510C4×C79C2×#12111yescharacteristic
511C4×C79#53411yescharacteristic
512C4×C79D4211yescharacteristic
513C4×C79#54611yescharacteristic
514#24469C7911yesmaximal, characteristic, direct product factor, Sylow
515C2×C79—21no—
516C2×C79—21no—
517C2×C79—41no—
518C2×C79—41no—
519C2×C79—42no—
520C2×C79—81no—
521C2×C79—81no—
522C2×C79—161no—
523C2×C79#241011yescharacteristic
524C2×C79#302011yescharacteristic
525C2×C79#302111yescharacteristic
526#3489C2×C7911yescharacteristic, complemented
527#3055C2×C7911yescharacteristic, complemented
528C2×#454C2×C7911yescharacteristic, complemented
529#3006C2×C7911yescharacteristic, complemented
530C2×#421C2×C7911yescharacteristic, complemented
531#2620C2×C7911yescharacteristic, complemented
532#2039C2×C7911yescharacteristic, complemented
533#2038C2×C7911yescharacteristic, complemented
534#2006C2×C7911yescharacteristic, complemented
535#2003C2×C7911yescharacteristic, complemented
536#1901C2×C7911yescharacteristic, complemented
537#1897C2×C7911yescharacteristic, complemented
538#1883C2×C7911yescharacteristic, complemented
539#1859C2×C7911yescharacteristic, complemented
540#1793C2×C7911yescharacteristic, complemented
541C79#2446911yescharacteristic, direct product factor, Sylow
542C2×2−1+4C22×C7911yescharacteristic
543C22×#41C22×C7911yescharacteristic
544C2×AGL(1,ℤ/8)C22×C7911yescharacteristic
545C2×AGL(1,ℤ/8)C22×C7911yescharacteristic
546C2×AGL(1,ℤ/8)C22×C7911yescharacteristic, complemented
547C22×M16C22×C7911yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C7911yescharacteristic
556#536—21no—
557#536C22×C7911yescharacteristic
558C2×#124C22×C7911yescharacteristic, complemented
559#525—21no—
560#525C22×C7911yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C7911yescharacteristic
563C2×#121C22×C7911yescharacteristic
564#520C22×C7911yescharacteristic
565C2×#117C22×C7911yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C7911yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C7911yescharacteristic
578C2×#104C22×C7911yescharacteristic
579C2×#104C22×C7911yescharacteristic
580C2×#104C22×C7911yescharacteristic
581C2×#104C22×C7911yescharacteristic, complemented
582C2×#104C22×C7911yescharacteristic, complemented
583#418C22×C7911yescharacteristic, complemented
584#417C22×C7911yescharacteristic
585#417C22×C7911yescharacteristic
586#417C22×C7911yescharacteristic, complemented
587C2×#101C22×C7911yescharacteristic, complemented
588C2×#101C22×C7911yescharacteristic, complemented
589#407C22×C7911yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C7911yescharacteristic, complemented
593#390C22×C7911yescharacteristic, complemented
594#384C22×C7911yescharacteristic, complemented
595#343C22×C7911yescharacteristic, complemented
596#343C22×C7911yescharacteristic, complemented
597#339C22×C7911yescharacteristic, complemented
598#339C22×C7911yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C7911yescharacteristic
613C2×#41D4×C7911yescharacteristic
614C2×#41C23×C7911yescharacteristic
615C2×#41C23×C7911yescharacteristic
616C2×#41C23×C7911yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C7911yescharacteristic
620C22×Q8C23×C7911yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C7911yescharacteristic
624C22×D4C23×C7911yescharacteristic
625C23×C4—21no—
626C23×C4C23×C7911yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C7911yescharacteristic
643C2×M16C23×C7911yescharacteristic
644C2×M16C23×C7911yescharacteristic
645C2×M16C23×C7911yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C7911yescharacteristic
670C22⋊Q8D4×C7911yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C7911yescharacteristic
682#121D4×C7911yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C7911yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C7912yes—
701C2×C4⋊C4C23×C7911yescharacteristic
702C2×C4⋊C4C23×C7911yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C7912yes—
709C2×C42C23×C7911yescharacteristic
710C2×C42C23×C7911yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C7914yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C7911yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C7912yes—
760#41#41×C7912yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C7911yescharacteristic
776C2×Q8C2×D4×C7911yescharacteristic
777C2×Q8C2×D4×C7911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C7911yescharacteristic
802C2×D4C2×D4×C7911yescharacteristic
803C2×D4C2×D4×C7911yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C7912yes—
823C22×C4C2×D4×C7911yescharacteristic
824C22×C4C2×D4×C7911yescharacteristic
825C22×C4C2×D4×C7911yescharacteristic
826C22×C4C2×D4×C7911yescharacteristic
827C22×C4C2×D4×C7911yescharacteristic
828C22×C4C2×D4×C7912yes—
829C22×C4C24×C7911yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C7912yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C7911yescharacteristic
865C4⋊C4C2×D4×C7911yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C7912yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C7911yescharacteristic
905C23#120×C7911yescharacteristic
906C23C22×D4×C7911yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C7912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C7912yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C7911yescharacteristic
985C2×C4#120×C7911yescharacteristic
986C2×C4C22×D4×C7911yescharacteristic
987C2×C4C22×D4×C7911yescharacteristic
988C2×C4C22×D4×C7911yescharacteristic
989C2×C4C2×#41×C7911yescharacteristic
990C2×C4H(5,𝔽2)×C7911yescharacteristic
991C2×C4H(5,𝔽2)×C7911yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C7911yescharacteristic
1022C22D42×C7911yescharacteristic
1023C22#546×C7911yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—41no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C7911yescharacteristic
1037C4#534×C7911yescharacteristic
1038C4D42×C7911yescharacteristic
1039C4#546×C7911yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C79×#241011yescharacteristic
1049C2C79×#302011yescharacteristic
1050C2C79×#302111yescharacteristic
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×#3489C2semidirect
2. C79×#3055C2semidirect
3. C2×#454×C79C2semidirect
4. C79×#3006C2semidirect
5. C2×#421×C79C2semidirect
6. C79×#2620C2semidirect
7. C79×#2039C2semidirect
8. C79×#2038C2semidirect
9. C79×#2006C2semidirect
10. C79×#2003C2semidirect
11. C79×#1901C2semidirect
12. C79×#1897C2semidirect
13. C79×#1883C2semidirect
14. C79×#1859C2semidirect
15. C79×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C79C22semidirect
32. C2×#124×C79C22semidirect
49. #428×C79C22semidirect
55. C2×#104×C79C22semidirect
56. C2×#104×C79C22semidirect
57. #418×C79C22semidirect
60. #417×C79C22semidirect
61. C2×#101×C79C22semidirect
62. C2×#101×C79C22semidirect
66. #391×C79C22semidirect
67. #390×C79C22semidirect
68. #384×C79C22semidirect
69. #343×C79C22semidirect
70. #343×C79C22semidirect
71. #339×C79C22semidirect
72. #339×C79C22semidirect
192. #104×C79D4semidirect
514. #24469C79direct (N × H)
526. #3489C2×C79semidirect
527. #3055C2×C79semidirect
528. C2×#454C2×C79semidirect
529. #3006C2×C79semidirect
530. C2×#421C2×C79semidirect
531. #2620C2×C79semidirect
532. #2039C2×C79semidirect
533. #2038C2×C79semidirect
534. #2006C2×C79semidirect
535. #2003C2×C79semidirect
536. #1901C2×C79semidirect
537. #1897C2×C79semidirect
538. #1883C2×C79semidirect
539. #1859C2×C79semidirect
540. #1793C2×C79semidirect
541. C79#24469direct (N × H)
546. C2×AGL(1,ℤ/8)C22×C79semidirect
558. C2×#124C22×C79semidirect
575. #428C22×C79semidirect
581. C2×#104C22×C79semidirect
582. C2×#104C22×C79semidirect
583. #418C22×C79semidirect
586. #417C22×C79semidirect
587. C2×#101C22×C79semidirect
588. C2×#101C22×C79semidirect
592. #391C22×C79semidirect
593. #390C22×C79semidirect
594. #384C22×C79semidirect
595. #343C22×C79semidirect
596. #343C22×C79semidirect
597. #339C22×C79semidirect
598. #339C22×C79semidirect
718. #104D4×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#34892
C79×#30552
C2×#454×C792
C79×#30062
C2×#421×C792
C79×#26202
C79×#20392
C79×#20382
C79×#20062
C79×#20032
C79×#19012
C79×#18972
C79×#18832
C79×#18592
C79×#17932
#2446979