Finite Group Databasebeta

← C79×#25131 #34136820

Subgroups — C79×#25131 #34136820

Order 20224.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C79C211yesmaximal, characteristic, complemented
2C2×#449×C79C211yesmaximal, characteristic, complemented
3C2×#435×C79C211yesmaximal, characteristic, complemented
4C2×#416×C79C211yesmaximal, characteristic, complemented
5C79×#2414C211yesmaximal, characteristic, complemented
6C79×#2407C211yesmaximal, characteristic, complemented
7C79×#2067C211yesmaximal, characteristic, complemented
8C79×#2055C211yesmaximal, characteristic, complemented
9C79×#2035C211yesmaximal, characteristic, complemented
10C79×#1999C211yesmaximal, characteristic, complemented
11C79×#1972C211yesmaximal, characteristic, complemented
12C79×#1935C211yesmaximal, characteristic, complemented
13C79×#1895C211yesmaximal, characteristic, complemented
14C79×#1893C211yesmaximal, characteristic, complemented
15C79×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C79C2211yescharacteristic
17C22×SD16×C79C2211yescharacteristic
18C22×D8×C79C2211yescharacteristic
19C22×M16×C79C2211yescharacteristic
20C23×C8×C79C2211yescharacteristic
21C2×C22⋊Q8×C79C2211yescharacteristic
22C2×#121×C79C2211yescharacteristic
23C2×#121×C79C2211yescharacteristic
24C2×#121×C79C2211yescharacteristic
25C2×C4×D4×C79C2211yescharacteristic
26C2×#117×C79C2211yescharacteristic
27#468×C79—24no—
28#449×C79—24no—
29#435×C79—24no—
30C2×#107×C79C2211yescharacteristic
31C2×#106×C79C2211yescharacteristic
32C2×C4⋊C8×C79C2211yescharacteristic
33#416×C79—24no—
34C2×#103×C79C2211yescharacteristic
35C2×#103×C79C2211yescharacteristic
36C2×#103×C79C2211yescharacteristic
37C2×#102×C79C2211yescharacteristic
38C2×#102×C79C2211yescharacteristic
39C2×#102×C79C2211yescharacteristic
40C2×#102×C79C2211yescharacteristic
41C2×#102×C79C2211yescharacteristic
42C2×C22⋊C8×C79C2211yescharacteristic
43C2×C22⋊C8×C79C2211yescharacteristic
44C2×#97×C79C2211yescharacteristic
45#394×C79—21no—
46#394×C79—21no—
47#392×C79—21no—
48#392×C79—21no—
49#391×C79C2211yescharacteristic
50#390×C79—21no—
51#390×C79C2211yescharacteristic
52#390×C79C2211yescharacteristic
53#389×C79C2211yescharacteristic
54#388×C79—21no—
55#386×C79—21no—
56#385×C79—21no—
57#380×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#340×C79C2211yescharacteristic
60#340×C79C2211yescharacteristic
61#340×C79C2211yescharacteristic
62#340×C79C2211yescharacteristic
63C2×#41×C79—22no—
64C2×#41×C79—22no—
65C2×#41×C79—22no—
66C2×#41×C79—22no—
67C2×#41×C79—41no—
68C2×#41×C79—41no—
69C22×Q8×C79C2311yescharacteristic
70C22×D4×C79—21no—
71C22×D4×C79—21no—
72C22×D4×C79—21no—
73C22×D4×C79—21no—
74C22×D4×C79D411yescharacteristic
75C22×D4×C79C2311yescharacteristic
76C22×D4×C79C2311yescharacteristic
77C23×C4×C79—21no—
78C23×C4×C79C2311yescharacteristic
79C23×C4×C79C2311yescharacteristic
80C2×SD16×C79—22no—
81C2×SD16×C79—22no—
82C2×SD16×C79—41no—
83C2×D8×C79—22no—
84C2×D8×C79—22no—
85C2×D8×C79—41no—
86C2×M16×C79—22no—
87C2×M16×C79—22no—
88C2×M16×C79—41no—
89C22×C8×C79—22no—
90C22×C8×C79—22no—
91C22×C8×C79—41no—
92C22×C8×C79C2311yescharacteristic
93C22×C8×C79C2311yescharacteristic
94C22×C8×C79C2311yescharacteristic
95C22×C8×C79C2311yescharacteristic
96C22⋊Q8×C79—22no—
97C22⋊Q8×C79—41no—
98#121×C79—22no—
99#121×C79—22no—
100#121×C79—22no—
101#121×C79—22no—
102#121×C79—41no—
103#121×C79—41no—
104C4×D4×C79—22no—
105C4×D4×C79—22no—
106#117×C79—22no—
107#117×C79—41no—
108C2×C4⋊C4×C79—21no—
109C2×C4⋊C4×C79—21no—
110C2×C4⋊C4×C79D411yescharacteristic
111C2×C4⋊C4×C79C2311yescharacteristic
112C2×C4⋊C4×C79C2311yescharacteristic
113C2×C4⋊C4×C79C2311yescharacteristic
114C2×C4⋊C4×C79C2311yescharacteristic
115C2×C4⋊C4×C79C2311yescharacteristic
116C2×C22⋊C4×C79—21no—
117C2×C22⋊C4×C79—21no—
118C2×C22⋊C4×C79—21no—
119C2×C22⋊C4×C79—21no—
120C2×C22⋊C4×C79—21no—
121C2×C22⋊C4×C79—21no—
122C2×C22⋊C4×C79—21no—
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C22⋊C4×C79D411yescharacteristic
128C2×C22⋊C4×C79D411yescharacteristic
129C2×C42×C79—21no—
130C2×C42×C79C2311yescharacteristic
131#107×C79—22no—
132#106×C79—41no—
133C4⋊C8×C79—22no—
134#103×C79—22no—
135#103×C79—22no—
136#103×C79D414yescomplemented
137#102×C79—22no—
138#102×C79—22no—
139#102×C79—22no—
140#102×C79—22no—
141#102×C79—41no—
142C22⋊C8×C79—22no—
143C22⋊C8×C79D414yescomplemented
144#97×C79—22no—
145#95×C79—21no—
146#95×C79—21no—
147#95×C79—21no—
148#95×C79—21no—
149#95×C79—21no—
150C24×C79—21no—
151C24×C79—21no—
152C24×C79C2×D411yescharacteristic
153C24×C79C2×D411yescharacteristic
154#41×C79—28no—
155#41×C79—44no—
156#41×C79—44no—
157#41×C79—44no—
158C2×Q8×C79—21no—
159C2×Q8×C79—21no—
160C2×Q8×C79—21no—
161C2×Q8×C79—21no—
162C2×Q8×C79—21no—
163C2×Q8×C79C2×D412yes—
164C2×D4×C79—22no—
165C2×D4×C79—21no—
166C2×D4×C79—21no—
167C2×D4×C79—21no—
168C2×D4×C79—21no—
169C2×D4×C79—21no—
170C2×D4×C79—21no—
171C2×D4×C79—21no—
172C2×D4×C79—21no—
173C2×D4×C79—21no—
174C2×D4×C79—21no—
175C2×D4×C79—21no—
176C2×D4×C79—41no—
177C2×D4×C79—41no—
178C2×D4×C79—42no—
179C2×D4×C79—42no—
180C2×D4×C79—42no—
181C2×D4×C79—42no—
182C2×D4×C79—42no—
183C2×D4×C79—42no—
184C2×D4×C79—42no—
185C2×D4×C79—42no—
186C2×D4×C79—81no—
187C2×D4×C79—81no—
188C2×D4×C79—81no—
189C2×D4×C79—81no—
190C2×D4×C79#4112yes—
191C22×C4×C79—21no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—42no—
208C22×C4×C79—42no—
209C22×C4×C79—42no—
210C22×C4×C79C2×D411yescharacteristic
211C22×C4×C79C2×D411yescharacteristic
212C22×C4×C79C2×D411yescharacteristic
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D412yes—
215C22×C4×C79#4112yes—
216C22×C4×C79C2411yescharacteristic
217SD16×C79—44no—
218D8×C79—44no—
219M16×C79—44no—
220C2×C8×C79—21no—
221C2×C8×C79—21no—
222C2×C8×C79—21no—
223C2×C8×C79—21no—
224C2×C8×C79—21no—
225C2×C8×C79—21no—
226C2×C8×C79—21no—
227C2×C8×C79—21no—
228C2×C8×C79—21no—
229C2×C8×C79—44no—
230C2×C8×C79C2×D412yes—
231C2×C8×C79C2×D412yes—
232C2×C8×C79C2×D412yes—
233C4⋊C4×C79—22no—
234C4⋊C4×C79—21no—
235C4⋊C4×C79—21no—
236C4⋊C4×C79—21no—
237C4⋊C4×C79—21no—
238C4⋊C4×C79—21no—
239C4⋊C4×C79—21no—
240C4⋊C4×C79—21no—
241C4⋊C4×C79—21no—
242C4⋊C4×C79—21no—
243C4⋊C4×C79—42no—
244C4⋊C4×C79—81no—
245C4⋊C4×C79C2×D412yes—
246C22⋊C4×C79—22no—
247C22⋊C4×C79—22no—
248C22⋊C4×C79—42no—
249C22⋊C4×C79—42no—
250C22⋊C4×C79—42no—
251C22⋊C4×C79—42no—
252C22⋊C4×C79—42no—
253C22⋊C4×C79—42no—
254C22⋊C4×C79—42no—
255C22⋊C4×C79—81no—
256C22⋊C4×C79—81no—
257C22⋊C4×C79—81no—
258C22⋊C4×C79—81no—
259C42×C79—21no—
260C42×C79—21no—
261C42×C79—42no—
262C23×C79—21no—
263C23×C79—21no—
264C23×C79—21no—
265C23×C79—21no—
266C23×C79—21no—
267C23×C79—21no—
268C23×C79—21no—
269C23×C79—21no—
270C23×C79—22no—
271C23×C79—21no—
272C23×C79—21no—
273C23×C79—21no—
274C23×C79—21no—
275C23×C79—21no—
276C23×C79—41no—
277C23×C79—41no—
278C23×C79—41no—
279C23×C79—41no—
280C23×C79—41no—
281C23×C79—41no—
282C23×C79—41no—
283C23×C79—41no—
284C23×C79—41no—
285C23×C79—41no—
286C23×C79—41no—
287C23×C79—41no—
288C23×C79—41no—
289C23×C79#12112yes—
290C23×C79C22×D411yescharacteristic
291Q8×C79—22no—
292Q8×C79—22no—
293Q8×C79—41no—
294Q8×C79—41no—
295D4×C79—22no—
296D4×C79—22no—
297D4×C79—44no—
298D4×C79—48no—
299D4×C79—41no—
300D4×C79—41no—
301D4×C79—41no—
302D4×C79—41no—
303D4×C79—41no—
304D4×C79—41no—
305D4×C79—84no—
306D4×C79—84no—
307D4×C79—84no—
308C2×C4×C79—21no—
309C2×C4×C79—21no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—21no—
315C2×C4×C79—21no—
316C2×C4×C79—21no—
317C2×C4×C79—22no—
318C2×C4×C79—21no—
319C2×C4×C79—22no—
320C2×C4×C79—21no—
321C2×C4×C79—21no—
322C2×C4×C79—21no—
323C2×C4×C79—21no—
324C2×C4×C79—21no—
325C2×C4×C79—48no—
326C2×C4×C79—41no—
327C2×C4×C79—41no—
328C2×C4×C79—41no—
329C2×C4×C79—41no—
330C2×C4×C79—41no—
331C2×C4×C79—41no—
332C2×C4×C79—41no—
333C2×C4×C79—41no—
334C2×C4×C79—41no—
335C2×C4×C79—41no—
336C2×C4×C79—41no—
337C2×C4×C79—41no—
338C2×C4×C79—41no—
339C2×C4×C79—41no—
340C2×C4×C79—41no—
341C2×C4×C79—41no—
342C2×C4×C79—41no—
343C2×C4×C79—41no—
344C2×C4×C79—41no—
345C2×C4×C79—41no—
346C2×C4×C79#12112yes—
347C2×C4×C79C22×D411yescharacteristic
348C2×C4×C79C22×D411yescharacteristic
349C2×C4×C79C2×#4111yescharacteristic
350C2×C4×C79C2×#4111yescharacteristic
351C2×C4×C79H(5,𝔽2)11yescharacteristic
352C2×C4×C79H(5,𝔽2)11yescharacteristic
353C8×C79—22no—
354C8×C79—22no—
355C8×C79—22no—
356C8×C79—41no—
357C22×C79—22no—
358C22×C79—22no—
359C22×C79—22no—
360C22×C79—41no—
361C22×C79—41no—
362C22×C79—41no—
363C22×C79—41no—
364C22×C79—42no—
365C22×C79—41no—
366C22×C79—41no—
367C22×C79—41no—
368C22×C79—41no—
369C22×C79—42no—
370C22×C79—41no—
371C22×C79—41no—
372C22×C79—41no—
373C22×C79—42no—
374C22×C79—81no—
375C22×C79—81no—
376C22×C79—81no—
377C22×C79—81no—
378C22×C79—81no—
379C22×C79—81no—
380C22×C79—81no—
381C22×C79—81no—
382C22×C79—81no—
383C22×C79—81no—
384C22×C79—81no—
385C22×C79C2×#12111yescharacteristic
386C22×C79D4211yescharacteristic
387C22×C79#54611yescharacteristic
388C22×C79#57511yescharacteristic
389C22×C79#57511yescharacteristic
390C22×C79#57611yescharacteristic
391C22×C79#57711yescharacteristic
392C4×C79—22no—
393C4×C79—41no—
394C4×C79—42no—
395C4×C79—42no—
396C4×C79—41no—
397C4×C79—41no—
398C4×C79—81no—
399C4×C79—81no—
400C4×C79—81no—
401C4×C79—81no—
402C4×C79#52511yescharacteristic
403C4×C79#53811yescharacteristic
404C4×C79D4211yescharacteristic
405C4×C79#54611yescharacteristic
406#25131C7911yesmaximal, characteristic, direct product factor, Sylow
407C2×C79—42no—
408C2×C79—81no—
409C2×C79—82no—
410C2×C79—161no—
411C2×C79#242411yescharacteristic
412C2×C79#305411yescharacteristic
413C2×C79#306211yescharacteristic
414C2×C79#326811yescharacteristic
415C2×C79#327111yescharacteristic
416C2×C79#330711yescharacteristic
417C2×C79#331911yescharacteristic
418C2×#468C2×C7911yescharacteristic, complemented
419C2×#449C2×C7911yescharacteristic, complemented
420C2×#435C2×C7911yescharacteristic, complemented
421C2×#416C2×C7911yescharacteristic, complemented
422#2414C2×C7911yescharacteristic, complemented
423#2407C2×C7911yescharacteristic, complemented
424#2067C2×C7911yescharacteristic, complemented
425#2055C2×C7911yescharacteristic, complemented
426#2035C2×C7911yescharacteristic, complemented
427#1999C2×C7911yescharacteristic, complemented
428#1972C2×C7911yescharacteristic, complemented
429#1935C2×C7911yescharacteristic, complemented
430#1895C2×C7911yescharacteristic, complemented
431#1893C2×C7911yescharacteristic, complemented
432#1854C2×C7911yescharacteristic, complemented
433C79#2513111yescharacteristic, direct product factor, Sylow
434C22×#41C22×C7911yescharacteristic
435C22×SD16C22×C7911yescharacteristic
436C22×D8C22×C7911yescharacteristic
437C22×M16C22×C7911yescharacteristic
438C23×C8C22×C7911yescharacteristic
439C2×C22⋊Q8C22×C7911yescharacteristic
440C2×#121C22×C7911yescharacteristic
441C2×#121C22×C7911yescharacteristic
442C2×#121C22×C7911yescharacteristic
443C2×C4×D4C22×C7911yescharacteristic
444C2×#117C22×C7911yescharacteristic
445#468—24no—
446#449—24no—
447#435—24no—
448C2×#107C22×C7911yescharacteristic
449C2×#106C22×C7911yescharacteristic
450C2×C4⋊C8C22×C7911yescharacteristic
451#416—24no—
452C2×#103C22×C7911yescharacteristic
453C2×#103C22×C7911yescharacteristic
454C2×#103C22×C7911yescharacteristic
455C2×#102C22×C7911yescharacteristic
456C2×#102C22×C7911yescharacteristic
457C2×#102C22×C7911yescharacteristic
458C2×#102C22×C7911yescharacteristic
459C2×#102C22×C7911yescharacteristic
460C2×C22⋊C8C22×C7911yescharacteristic
461C2×C22⋊C8C22×C7911yescharacteristic
462C2×#97C22×C7911yescharacteristic
463#394—21no—
464#394—21no—
465#392—21no—
466#392—21no—
467#391C22×C7911yescharacteristic
468#390—21no—
469#390C22×C7911yescharacteristic
470#390C22×C7911yescharacteristic
471#389C22×C7911yescharacteristic
472#388—21no—
473#386—21no—
474#385—21no—
475#380C22×C7911yescharacteristic
476#380C22×C7911yescharacteristic
477#340C22×C7911yescharacteristic
478#340C22×C7911yescharacteristic
479#340C22×C7911yescharacteristic
480#340C22×C7911yescharacteristic
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C7911yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C7911yescharacteristic
493C22×D4C23×C7911yescharacteristic
494C22×D4C23×C7911yescharacteristic
495C23×C4—21no—
496C23×C4C23×C7911yescharacteristic
497C23×C4C23×C7911yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C7911yescharacteristic
511C22×C8C23×C7911yescharacteristic
512C22×C8C23×C7911yescharacteristic
513C22×C8C23×C7911yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C7911yescharacteristic
529C2×C4⋊C4C23×C7911yescharacteristic
530C2×C4⋊C4C23×C7911yescharacteristic
531C2×C4⋊C4C23×C7911yescharacteristic
532C2×C4⋊C4C23×C7911yescharacteristic
533C2×C4⋊C4C23×C7911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C7911yescharacteristic
546C2×C22⋊C4D4×C7911yescharacteristic
547C2×C42—21no—
548C2×C42C23×C7911yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C7914yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C7914yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C7911yescharacteristic
571C24C2×D4×C7911yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C7912yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C7912yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C7911yescharacteristic
629C22×C4C2×D4×C7911yescharacteristic
630C22×C4C2×D4×C7911yescharacteristic
631C22×C4C2×D4×C7911yescharacteristic
632C22×C4C2×D4×C7912yes—
633C22×C4#41×C7912yes—
634C22×C4C24×C7911yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C7912yes—
649C2×C8C2×D4×C7912yes—
650C2×C8C2×D4×C7912yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C7912yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C7912yes—
708C23C22×D4×C7911yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C7912yes—
765C2×C4C22×D4×C7911yescharacteristic
766C2×C4C22×D4×C7911yescharacteristic
767C2×C4C2×#41×C7911yescharacteristic
768C2×C4C2×#41×C7911yescharacteristic
769C2×C4H(5,𝔽2)×C7911yescharacteristic
770C2×C4H(5,𝔽2)×C7911yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C7911yescharacteristic
804C22D42×C7911yescharacteristic
805C22#546×C7911yescharacteristic
806C22#575×C7911yescharacteristic
807C22#575×C7911yescharacteristic
808C22#576×C7911yescharacteristic
809C22#577×C7911yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#525×C7911yescharacteristic
821C4#538×C7911yescharacteristic
822C4D42×C7911yescharacteristic
823C4#546×C7911yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C79×#242411yescharacteristic
829C2C79×#305411yescharacteristic
830C2C79×#306211yescharacteristic
831C2C79×#326811yescharacteristic
832C2C79×#327111yescharacteristic
833C2C79×#330711yescharacteristic
834C2C79×#331911yescharacteristic
subgroupG/H
center, socleC23×C79C22×D4
commutator, Frattini, cosocleC22×C4C24×C79
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C79 ◁ C2×C4×D4×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C79C2semidirect
2. C2×#449×C79C2semidirect
3. C2×#435×C79C2semidirect
4. C2×#416×C79C2semidirect
5. C79×#2414C2semidirect
6. C79×#2407C2semidirect
7. C79×#2067C2semidirect
8. C79×#2055C2semidirect
9. C79×#2035C2semidirect
10. C79×#1999C2semidirect
11. C79×#1972C2semidirect
12. C79×#1935C2semidirect
13. C79×#1895C2semidirect
14. C79×#1893C2semidirect
15. C79×#1854C2semidirect
136. #103×C79D4semidirect
143. C22⋊C8×C79D4semidirect
406. #25131C79direct (N × H)
418. C2×#468C2×C79semidirect
419. C2×#449C2×C79semidirect
420. C2×#435C2×C79semidirect
421. C2×#416C2×C79semidirect
422. #2414C2×C79semidirect
423. #2407C2×C79semidirect
424. #2067C2×C79semidirect
425. #2055C2×C79semidirect
426. #2035C2×C79semidirect
427. #1999C2×C79semidirect
428. #1972C2×C79semidirect
429. #1935C2×C79semidirect
430. #1895C2×C79semidirect
431. #1893C2×C79semidirect
432. #1854C2×C79semidirect
433. C79#25131direct (N × H)
554. #103D4×C79semidirect
561. C22⋊C8D4×C79semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C792
C2×#449×C792
C2×#435×C792
C2×#416×C792
C79×#24142
C79×#24072
C79×#20672
C79×#20552
C79×#20352
C79×#19992
C79×#19722
C79×#19352
C79×#18952
C79×#18932
C79×#18542
#2513179