Finite Group Databasebeta

← C79×#24466 #34136155

Subgroups — C79×#24466 #34136155

Order 20224.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3489C211yesmaximal, characteristic
2C79×#3056C211yesmaximal, characteristic, complemented
3C2×#456×C79C211yesmaximal, characteristic, complemented
4C79×#3007C211yesmaximal, characteristic, complemented
5C22×#104×C79C211yesmaximal, characteristic, complemented
6C79×#2857C211yesmaximal, characteristic, complemented
7C79×#2039C211yesmaximal, characteristic, complemented
8C79×#2038C211yesmaximal, characteristic, complemented
9C79×#2007C211yesmaximal, characteristic, complemented
10C79×#2005C211yesmaximal, characteristic, complemented
11C79×#1901C211yesmaximal, characteristic, complemented
12C79×#1896C211yesmaximal, characteristic, complemented
13C79×#1882C211yesmaximal, characteristic, complemented
14C79×#1859C211yesmaximal, characteristic, complemented
15C79×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C79C2211yescharacteristic
17C22×#41×C79C2211yescharacteristic
18C2×#137×C79C2211yescharacteristic
19C2×#137×C79C2211yescharacteristic
20C2×#137×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×C4⋊Q8×C79C2211yescharacteristic, complemented
33#525×C79—21no—
34#525×C79C2211yescharacteristic
35C2×C22⋊Q8×C79—21no—
36C2×C22⋊Q8×C79C2211yescharacteristic
37C2×C22⋊Q8×C79C2211yescharacteristic
38#520×C79C2211yescharacteristic
39C22×C42×C79C2211yescharacteristic
40#470×C79—21no—
41#468×C79—21no—
42#467×C79—21no—
43#465×C79—21no—
44#456×C79—24no—
45#452×C79—21no—
46#452×C79—21no—
47#451×C79—21no—
48#450×C79—21no—
49#428×C79C2211yescharacteristic, complemented
50C2×#104×C79—24no—
51C2×#104×C79C2211yescharacteristic
52C2×#104×C79C2211yescharacteristic
53C2×#104×C79C2211yescharacteristic
54C2×#104×C79C2211yescharacteristic
55C2×#104×C79C2211yescharacteristic, complemented
56C2×#104×C79C2211yescharacteristic, complemented
57#419×C79C2211yescharacteristic, complemented
58#417×C79C2211yescharacteristic
59#417×C79C2211yescharacteristic
60#417×C79C2211yescharacteristic, complemented
61C2×#101×C79C2211yescharacteristic, complemented
62C2×#101×C79C2211yescharacteristic, complemented
63#407×C79C2211yescharacteristic
64#391×C79C2211yescharacteristic, complemented
65#391×C79C2211yescharacteristic, complemented
66#389×C79—22no—
67#384×C79C2211yescharacteristic, complemented
68#380×C79—22no—
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×Q8×C79C2311yescharacteristic
96C22×D4×C79—21no—
97C22×D4×C79D411yescharacteristic
98C23×C4×C79—21no—
99C23×C4×C79—21no—
100C23×C4×C79C2311yescharacteristic
101#137×C79—22no—
102#137×C79—22no—
103#137×C79—22no—
104#137×C79—41no—
105#137×C79—41no—
106#137×C79—41no—
107C2×Q16×C79—21no—
108C2×Q16×C79—21no—
109C2×Q16×C79—21no—
110C2×SD16×C79—21no—
111C2×SD16×C79—21no—
112C2×SD16×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—
123C4⋊Q8×C79—22no—
124C4⋊Q8×C79—41no—
125#124×C79—22no—
126#124×C79—21no—
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×C79—21no—
144C22⋊Q8×C79—21no—
145C22⋊Q8×C79—21no—
146C22⋊Q8×C79—21no—
147C22⋊Q8×C79D411yescharacteristic
148C22⋊Q8×C79D411yescharacteristic
149#121×C79—22no—
150#121×C79—22no—
151#121×C79—22no—
152#121×C79—21no—
153#121×C79—21no—
154#121×C79—22no—
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×C79C2311yescharacteristic
168C2×C4⋊C4×C79—22no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—22no—
172C2×C4⋊C4×C79—22no—
173C2×C4⋊C4×C79D412yes—
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C22⋊C4×C79—22no—
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79D412yes—
179C2×C42×C79—22no—
180C2×C42×C79—21no—
181C2×C42×C79—41no—
182C2×C42×C79C2311yescharacteristic
183C2×C42×C79C2311yescharacteristic
184#107×C79—21no—
185#106×C79—21no—
186#104×C79—22no—
187#104×C79—22no—
188#104×C79—22no—
189#104×C79—22no—
190#104×C79—41no—
191#104×C79D414yescomplemented
192#103×C79—21no—
193#103×C79—21no—
194#103×C79—21no—
195#103×C79—21no—
196#103×C79—21no—
197#102×C79—21no—
198#102×C79—21no—
199#102×C79—21no—
200#101×C79—22no—
201#101×C79—41no—
202C22⋊C8×C79—21no—
203C22⋊C8×C79—21no—
204#95×C79—22no—
205#95×C79—22no—
206C24×C79—21no—
207C24×C79C2×D411yescharacteristic
208#41×C79—21no—
209#41×C79—21no—
210#41×C79—22no—
211#41×C79—22no—
212#41×C79—21no—
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—42no—
221#41×C79—42no—
222#41×C79—41no—
223#41×C79—41no—
224#41×C79—42no—
225#41×C79—42no—
226#41×C79—42no—
227#41×C79—42no—
228#41×C79—44no—
229#41×C79—44no—
230#41×C79—42no—
231#41×C79—42no—
232#41×C79C2×D412yes—
233#41×C79#4112yes—
234C2×Q8×C79—22no—
235C2×Q8×C79—21no—
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—22no—
243C2×Q8×C79—21no—
244C2×Q8×C79—21no—
245C2×Q8×C79—21no—
246C2×Q8×C79—21no—
247C2×Q8×C79—21no—
248C2×Q8×C79—21no—
249C2×Q8×C79—41no—
250C2×Q8×C79—42no—
251C2×Q8×C79—42no—
252C2×Q8×C79—42no—
253C2×Q8×C79—42no—
254C2×Q8×C79C2×D411yescharacteristic
255C2×Q8×C79C2×D411yescharacteristic
256C2×Q8×C79C2×D411yescharacteristic
257C2×D4×C79—21no—
258C2×D4×C79—22no—
259C2×D4×C79—22no—
260C2×D4×C79—21no—
261C2×D4×C79—21no—
262C2×D4×C79—21no—
263C2×D4×C79—21no—
264C2×D4×C79—21no—
265C2×D4×C79—22no—
266C2×D4×C79—21no—
267C2×D4×C79—21no—
268C2×D4×C79—41no—
269C2×D4×C79—42no—
270C2×D4×C79—42no—
271C2×D4×C79C2×D411yescharacteristic
272C2×D4×C79C2×D411yescharacteristic
273C2×D4×C79C2×D411yescharacteristic
274C22×C4×C79—21no—
275C22×C4×C79—21no—
276C22×C4×C79—21no—
277C22×C4×C79—21no—
278C22×C4×C79—21no—
279C22×C4×C79—21no—
280C22×C4×C79—22no—
281C22×C4×C79—22no—
282C22×C4×C79—24no—
283C22×C4×C79—21no—
284C22×C4×C79—21no—
285C22×C4×C79—22no—
286C22×C4×C79—21no—
287C22×C4×C79—21no—
288C22×C4×C79—21no—
289C22×C4×C79—21no—
290C22×C4×C79—21no—
291C22×C4×C79—21no—
292C22×C4×C79—42no—
293C22×C4×C79—42no—
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
304Q16×C79—42no—
305Q16×C79—42no—
306Q16×C79—42no—
307SD16×C79—42no—
308SD16×C79—42no—
309SD16×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—44no—
337C4⋊C4×C79—44no—
338C4⋊C4×C79—41no—
339C4⋊C4×C79—41no—
340C4⋊C4×C79C2×D411yescharacteristic
341C4⋊C4×C79C2×D411yescharacteristic
342C22⋊C4×C79—22no—
343C22⋊C4×C79—22no—
344C22⋊C4×C79—22no—
345C22⋊C4×C79—22no—
346C22⋊C4×C79—22no—
347C22⋊C4×C79—21no—
348C22⋊C4×C79—22no—
349C22⋊C4×C79—22no—
350C22⋊C4×C79—21no—
351C22⋊C4×C79—21no—
352C22⋊C4×C79—21no—
353C22⋊C4×C79—21no—
354C22⋊C4×C79—41no—
355C22⋊C4×C79—41no—
356C42×C79—22no—
357C42×C79—21no—
358C42×C79—21no—
359C42×C79—21no—
360C42×C79—21no—
361C42×C79—42no—
362C42×C79C2×D412yes—
363C23×C79—21no—
364C23×C79—21no—
365C23×C79—21no—
366C23×C79—22no—
367C23×C79—21no—
368C23×C79—21no—
369C23×C79—41no—
370C23×C79—42no—
371C23×C79—42no—
372C23×C79—81no—
373C23×C79#12011yescharacteristic
374C23×C79#12011yescharacteristic
375C23×C79C22×D411yescharacteristic
376Q8×C79—21no—
377Q8×C79—21no—
378Q8×C79—21no—
379Q8×C79—21no—
380Q8×C79—21no—
381Q8×C79—42no—
382Q8×C79—44no—
383Q8×C79—41no—
384Q8×C79—41no—
385Q8×C79—41no—
386Q8×C79—41no—
387Q8×C79—41no—
388Q8×C79—41no—
389Q8×C79—41no—
390Q8×C79—41no—
391Q8×C79#12112yes—
392D4×C79—22no—
393D4×C79—22no—
394D4×C79—21no—
395D4×C79—21no—
396D4×C79—21no—
397D4×C79—21no—
398D4×C79—21no—
399D4×C79—42no—
400D4×C79—42no—
401D4×C79—42no—
402D4×C79—44no—
403D4×C79—41no—
404D4×C79—41no—
405D4×C79—41no—
406D4×C79—41no—
407D4×C79—42no—
408D4×C79—81no—
409D4×C79—82no—
410D4×C79#12112yes—
411C2×C4×C79—22no—
412C2×C4×C79—22no—
413C2×C4×C79—21no—
414C2×C4×C79—22no—
415C2×C4×C79—21no—
416C2×C4×C79—21no—
417C2×C4×C79—21no—
418C2×C4×C79—21no—
419C2×C4×C79—21no—
420C2×C4×C79—21no—
421C2×C4×C79—21no—
422C2×C4×C79—21no—
423C2×C4×C79—22no—
424C2×C4×C79—21no—
425C2×C4×C79—21no—
426C2×C4×C79—22no—
427C2×C4×C79—22no—
428C2×C4×C79—21no—
429C2×C4×C79—22no—
430C2×C4×C79—21no—
431C2×C4×C79—21no—
432C2×C4×C79—22no—
433C2×C4×C79—21no—
434C2×C4×C79—22no—
435C2×C4×C79—22no—
436C2×C4×C79—42no—
437C2×C4×C79—42no—
438C2×C4×C79—42no—
439C2×C4×C79—48no—
440C2×C4×C79—44no—
441C2×C4×C79—41no—
442C2×C4×C79—44no—
443C2×C4×C79—41no—
444C2×C4×C79—41no—
445C2×C4×C79—41no—
446C2×C4×C79—41no—
447C2×C4×C79—41no—
448C2×C4×C79—42no—
449C2×C4×C79—42no—
450C2×C4×C79—41no—
451C2×C4×C79—41no—
452C2×C4×C79—41no—
453C2×C4×C79—41no—
454C2×C4×C79—82no—
455C2×C4×C79#12011yescharacteristic
456C2×C4×C79#12011yescharacteristic
457C2×C4×C79C22×D411yescharacteristic
458C2×C4×C79C22×D411yescharacteristic
459C2×C4×C79C22×D411yescharacteristic
460C2×C4×C79C2×#4111yescharacteristic
461C2×C4×C79H(5,𝔽2)11yescharacteristic
462C2×C4×C79H(5,𝔽2)11yescharacteristic
463C8×C79—22no—
464C8×C79—41no—
465C8×C79—41no—
466C8×C79—41no—
467C22×C79—21no—
468C22×C79—21no—
469C22×C79—21no—
470C22×C79—21no—
471C22×C79—21no—
472C22×C79—22no—
473C22×C79—21no—
474C22×C79—21no—
475C22×C79—42no—
476C22×C79—42no—
477C22×C79—41no—
478C22×C79—41no—
479C22×C79—41no—
480C22×C79—41no—
481C22×C79—41no—
482C22×C79—41no—
483C22×C79—41no—
484C22×C79—41no—
485C22×C79—84no—
486C22×C79#45612yescomplemented
487C22×C79C2×#12011yescharacteristic
488C22×C79D4211yescharacteristic
489C22×C79#54611yescharacteristic
490C4×C79—24no—
491C4×C79—21no—
492C4×C79—21no—
493C4×C79—22no—
494C4×C79—42no—
495C4×C79—42no—
496C4×C79—41no—
497C4×C79—41no—
498C4×C79—41no—
499C4×C79—42no—
500C4×C79—41no—
501C4×C79—81no—
502C4×C79—81no—
503C4×C79C2×#12111yescharacteristic
504C4×C79#53411yescharacteristic
505C4×C79D4211yescharacteristic
506C4×C79#54611yescharacteristic
507#24466C7911yesmaximal, characteristic, direct product factor, Sylow
508C2×C79—21no—
509C2×C79—22no—
510C2×C79—21no—
511C2×C79—41no—
512C2×C79—42no—
513C2×C79—81no—
514C2×C79—81no—
515C2×C79#241011yescharacteristic
516C2×C79C2×#45611yescharacteristic
517C2×C79#301811yescharacteristic
518#3489C2×C7911yescharacteristic
519#3056C2×C7911yescharacteristic, complemented
520C2×#456C2×C7911yescharacteristic, complemented
521#3007C2×C7911yescharacteristic, complemented
522C22×#104C2×C7911yescharacteristic, complemented
523#2857C2×C7911yescharacteristic, complemented
524#2039C2×C7911yescharacteristic, complemented
525#2038C2×C7911yescharacteristic, complemented
526#2007C2×C7911yescharacteristic, complemented
527#2005C2×C7911yescharacteristic, complemented
528#1901C2×C7911yescharacteristic, complemented
529#1896C2×C7911yescharacteristic, complemented
530#1882C2×C7911yescharacteristic, complemented
531#1859C2×C7911yescharacteristic, complemented
532#1793C2×C7911yescharacteristic, complemented
533C79#2446611yescharacteristic, direct product factor, Sylow
534C2×2−1+4C22×C7911yescharacteristic
535C22×#41C22×C7911yescharacteristic
536C2×#137C22×C7911yescharacteristic
537C2×#137C22×C7911yescharacteristic
538C2×#137C22×C7911yescharacteristic, complemented
539C22×M16C22×C7911yescharacteristic
540D4×Q8—21no—
541#548—21no—
542#547—21no—
543#547—22no—
544#546—21no—
545#546—22no—
546#537—21no—
547#537C22×C7911yescharacteristic
548#536—21no—
549#536C22×C7911yescharacteristic
550C2×C4⋊Q8C22×C7911yescharacteristic, complemented
551#525—21no—
552#525C22×C7911yescharacteristic
553C2×C22⋊Q8—21no—
554C2×C22⋊Q8C22×C7911yescharacteristic
555C2×C22⋊Q8C22×C7911yescharacteristic
556#520C22×C7911yescharacteristic
557C22×C42C22×C7911yescharacteristic
558#470—21no—
559#468—21no—
560#467—21no—
561#465—21no—
562#456—24no—
563#452—21no—
564#452—21no—
565#451—21no—
566#450—21no—
567#428C22×C7911yescharacteristic, complemented
568C2×#104—24no—
569C2×#104C22×C7911yescharacteristic
570C2×#104C22×C7911yescharacteristic
571C2×#104C22×C7911yescharacteristic
572C2×#104C22×C7911yescharacteristic
573C2×#104C22×C7911yescharacteristic, complemented
574C2×#104C22×C7911yescharacteristic, complemented
575#419C22×C7911yescharacteristic, complemented
576#417C22×C7911yescharacteristic
577#417C22×C7911yescharacteristic
578#417C22×C7911yescharacteristic, complemented
579C2×#101C22×C7911yescharacteristic, complemented
580C2×#101C22×C7911yescharacteristic, complemented
581#407C22×C7911yescharacteristic
582#391C22×C7911yescharacteristic, complemented
583#391C22×C7911yescharacteristic, complemented
584#389—22no—
585#384C22×C7911yescharacteristic, complemented
586#380—22no—
587#343C22×C7911yescharacteristic, complemented
588#343C22×C7911yescharacteristic, complemented
589#339C22×C7911yescharacteristic, complemented
590#339C22×C7911yescharacteristic, complemented
5912−1+4—22no—
5922−1+4—22no—
5932−1+4—41no—
5942−1+4—41no—
595C2×#41—21no—
596C2×#41—21no—
597C2×#41—21no—
598C2×#41—22no—
599C2×#41—21no—
600C2×#41—22no—
601C2×#41—22no—
602C2×#41—41no—
603C2×#41—41no—
604C2×#41D4×C7911yescharacteristic
605C2×#41D4×C7911yescharacteristic
606C2×#41C23×C7911yescharacteristic
607C2×#41C23×C7911yescharacteristic
608C2×#41C23×C7911yescharacteristic
609C22×Q8—21no—
610C22×Q8—21no—
611C22×Q8D4×C7911yescharacteristic
612C22×Q8C23×C7911yescharacteristic
613C22×Q8C23×C7911yescharacteristic
614C22×D4—21no—
615C22×D4D4×C7911yescharacteristic
616C23×C4—21no—
617C23×C4—21no—
618C23×C4C23×C7911yescharacteristic
619#137—22no—
620#137—22no—
621#137—22no—
622#137—41no—
623#137—41no—
624#137—41no—
625C2×Q16—21no—
626C2×Q16—21no—
627C2×Q16—21no—
628C2×SD16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×M16—21no—
632C2×M16—22no—
633C2×M16—41no—
634C2×M16C23×C7911yescharacteristic
635C2×M16C23×C7911yescharacteristic
636C2×M16C23×C7911yescharacteristic
637C2×M16C23×C7911yescharacteristic
638C22×C8—21no—
639C4⋊Q8—22no—
640C4⋊Q8—21no—
641C4⋊Q8—22no—
642C4⋊Q8—41no—
643#124—22no—
644#124—21no—
645#123—22no—
646#123—22no—
647#123—22no—
648#123—21no—
649#123—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—21no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658C22⋊Q8—21no—
659C22⋊Q8—21no—
660C22⋊Q8—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8D4×C7911yescharacteristic
666C22⋊Q8D4×C7911yescharacteristic
667#121—22no—
668#121—22no—
669#121—22no—
670#121—21no—
671#121—21no—
672#121—22no—
673#121D4×C7911yescharacteristic
674#121D4×C7911yescharacteristic
675#120—22no—
676#120—21no—
677C4×Q8—21no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—21no—
681C4×D4—22no—
682C4×D4—21no—
683C4×D4—21no—
684#117—21no—
685#117C23×C7911yescharacteristic
686C2×C4⋊C4—22no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4D4×C7912yes—
692C2×C4⋊C4C23×C7911yescharacteristic
693C2×C4⋊C4C23×C7911yescharacteristic
694C2×C22⋊C4—22no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4D4×C7912yes—
697C2×C42—22no—
698C2×C42—21no—
699C2×C42—41no—
700C2×C42C23×C7911yescharacteristic
701C2×C42C23×C7911yescharacteristic
702#107—21no—
703#106—21no—
704#104—22no—
705#104—22no—
706#104—22no—
707#104—22no—
708#104—41no—
709#104D4×C7914yescomplemented
710#103—21no—
711#103—21no—
712#103—21no—
713#103—21no—
714#103—21no—
715#102—21no—
716#102—21no—
717#102—21no—
718#101—22no—
719#101—41no—
720C22⋊C8—21no—
721C22⋊C8—21no—
722#95—22no—
723#95—22no—
724C24—21no—
725C24C2×D4×C7911yescharacteristic
726#41—21no—
727#41—21no—
728#41—22no—
729#41—22no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—21no—
738#41—42no—
739#41—42no—
740#41—41no—
741#41—41no—
742#41—42no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—44no—
747#41—44no—
748#41—42no—
749#41—42no—
750#41C2×D4×C7912yes—
751#41#41×C7912yes—
752C2×Q8—22no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—22no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—41no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—42no—
771C2×Q8—42no—
772C2×Q8C2×D4×C7911yescharacteristic
773C2×Q8C2×D4×C7911yescharacteristic
774C2×Q8C2×D4×C7911yescharacteristic
775C2×D4—21no—
776C2×D4—22no—
777C2×D4—22no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—41no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4C2×D4×C7911yescharacteristic
790C2×D4C2×D4×C7911yescharacteristic
791C2×D4C2×D4×C7911yescharacteristic
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—24no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4C2×D4×C7912yes—
815C22×C4C2×D4×C7911yescharacteristic
816C22×C4C2×D4×C7911yescharacteristic
817C22×C4C2×D4×C7911yescharacteristic
818C22×C4C2×D4×C7911yescharacteristic
819C22×C4C2×D4×C7911yescharacteristic
820C22×C4C2×D4×C7912yes—
821C22×C4C24×C7911yescharacteristic
822Q16—42no—
823Q16—42no—
824Q16—42no—
825SD16—42no—
826SD16—42no—
827SD16—42no—
828M16—21no—
829M16—21no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—42no—
836M16C2×D4×C7912yes—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—41no—
857C4⋊C4—41no—
858C4⋊C4C2×D4×C7911yescharacteristic
859C4⋊C4C2×D4×C7911yescharacteristic
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—22no—
865C22⋊C4—21no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—41no—
873C22⋊C4—41no—
874C42—22no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—42no—
880C42C2×D4×C7912yes—
881C23—22no—
882C23—21no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—81no—
891C23#120×C7911yescharacteristic
892C23#120×C7911yescharacteristic
893C23C22×D4×C7911yescharacteristic
894Q8—21no—
895Q8—21no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—42no—
900Q8—44no—
901Q8—41no—
902Q8—41no—
903Q8—41no—
904Q8—41no—
905Q8—41no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8#121×C7912yes—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—42no—
918D4—42no—
919D4—42no—
920D4—44no—
921D4—42no—
922D4—41no—
923D4—41no—
924D4—41no—
925D4—41no—
926D4—81no—
927D4—82no—
928D4#121×C7912yes—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—22no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—48no—
958C2×C4—44no—
959C2×C4—41no—
960C2×C4—44no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—82no—
973C2×C4#120×C7911yescharacteristic
974C2×C4#120×C7911yescharacteristic
975C2×C4C22×D4×C7911yescharacteristic
976C2×C4C22×D4×C7911yescharacteristic
977C2×C4C22×D4×C7911yescharacteristic
978C2×C4C2×#41×C7911yescharacteristic
979C2×C4H(5,𝔽2)×C7911yescharacteristic
980C2×C4H(5,𝔽2)×C7911yescharacteristic
981C8—22no—
982C8—41no—
983C8—41no—
984C8—41no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—21no—
991C22—22no—
992C22—21no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—41no—
1001C22—41no—
1002C22—41no—
1003C22—84no—
1004C22#456×C7912yescomplemented
1005C22C2×#120×C7911yescharacteristic
1006C22D42×C7911yescharacteristic
1007C22#546×C7911yescharacteristic
1008C4—24no—
1009C4—21no—
1010C4—21no—
1011C4—22no—
1012C4—42no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—41no—
1017C4—41no—
1018C4—41no—
1019C4—81no—
1020C4—81no—
1021C4C2×#121×C7911yescharacteristic
1022C4#534×C7911yescharacteristic
1023C4D42×C7911yescharacteristic
1024C4#546×C7911yescharacteristic
1025C2—21no—
1026C2—22no—
1027C2—21no—
1028C2—41no—
1029C2—42no—
1030C2—81no—
1031C2—81no—
1032C2C79×#241011yescharacteristic
1033C2C2×#456×C7911yescharacteristic
1034C2C79×#301811yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC22×C4C24×C79
prime radicalC79×#3489C2
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
2. C79×#3056C2semidirect
3. C2×#456×C79C2semidirect
4. C79×#3007C2semidirect
5. C22×#104×C79C2semidirect
6. C79×#2857C2semidirect
7. C79×#2039C2semidirect
8. C79×#2038C2semidirect
9. C79×#2007C2semidirect
10. C79×#2005C2semidirect
11. C79×#1901C2semidirect
12. C79×#1896C2semidirect
13. C79×#1882C2semidirect
14. C79×#1859C2semidirect
15. C79×#1793C2semidirect
20. C2×#137×C79C22semidirect
32. C2×C4⋊Q8×C79C22semidirect
49. #428×C79C22semidirect
55. C2×#104×C79C22semidirect
56. C2×#104×C79C22semidirect
57. #419×C79C22semidirect
60. #417×C79C22semidirect
61. C2×#101×C79C22semidirect
62. C2×#101×C79C22semidirect
64. #391×C79C22semidirect
65. #391×C79C22semidirect
67. #384×C79C22semidirect
69. #343×C79C22semidirect
70. #343×C79C22semidirect
71. #339×C79C22semidirect
72. #339×C79C22semidirect
191. #104×C79D4semidirect
486. C22×C79#456semidirect
507. #24466C79direct (N × H)
519. #3056C2×C79semidirect
520. C2×#456C2×C79semidirect
521. #3007C2×C79semidirect
522. C22×#104C2×C79semidirect
523. #2857C2×C79semidirect
524. #2039C2×C79semidirect
525. #2038C2×C79semidirect
526. #2007C2×C79semidirect
527. #2005C2×C79semidirect
528. #1901C2×C79semidirect
529. #1896C2×C79semidirect
530. #1882C2×C79semidirect
531. #1859C2×C79semidirect
532. #1793C2×C79semidirect
533. C79#24466direct (N × H)
538. C2×#137C22×C79semidirect
550. C2×C4⋊Q8C22×C79semidirect
567. #428C22×C79semidirect
573. C2×#104C22×C79semidirect
574. C2×#104C22×C79semidirect
575. #419C22×C79semidirect
578. #417C22×C79semidirect
579. C2×#101C22×C79semidirect
580. C2×#101C22×C79semidirect
582. #391C22×C79semidirect
583. #391C22×C79semidirect
585. #384C22×C79semidirect
587. #343C22×C79semidirect
588. #343C22×C79semidirect
589. #339C22×C79semidirect
590. #339C22×C79semidirect
709. #104D4×C79semidirect
1004. C22#456×C79semidirect

Maximal subgroups

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

subgroupindex
C79×#34892
C79×#30562
C2×#456×C792
C79×#30072
C22×#104×C792
C79×#28572
C79×#20392
C79×#20382
C79×#20072
C79×#20052
C79×#19012
C79×#18962
C79×#18822
C79×#18592
C79×#17932
#2446679