Finite Group Databasebeta

← C79×#14421 #34126110

Subgroups — C79×#14421 #34126110

Order 20224.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C79C211yesmaximal, characteristic
2C2×#391×C79C211yesmaximal, characteristic, complemented
3C2×#388×C79C211yesmaximal, characteristic, complemented
4C2×#386×C79C211yesmaximal, characteristic
5C2×#385×C79C211yesmaximal, characteristic, complemented
6C79×#1446C211yesmaximal, characteristic, complemented
7C79×#1440C211yesmaximal, characteristic, complemented
8C79×#1439C211yesmaximal, characteristic, complemented
9C79×#1439C211yesmaximal, characteristic, complemented
10C79×#1439C211yesmaximal, characteristic, complemented
11C79×#1438C211yesmaximal, characteristic
12C79×#1437C211yesmaximal, characteristic, complemented
13C79×C4⋊#95C211yesmaximal, characteristic, complemented
14C79×#1434C211yesmaximal, characteristic, complemented
15C79×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C79C2211yescharacteristic
17C23×D4×C79C2211yescharacteristic
18C24×C4×C79C2211yescharacteristic
19C2×#124×C79—24no—
20C2×#124×C79—24no—
21C2×#124×C79C418yescomplemented
22C22×C4⋊C4×C79C2211yescharacteristic
23C22×C4⋊C4×C79C2211yescharacteristic
24C22×C4⋊C4×C79C2211yescharacteristic
25C22×C22⋊C4×C79C2211yescharacteristic
26C22×C22⋊C4×C79C2211yescharacteristic
27C22×C22⋊C4×C79C2211yescharacteristic
28C22×C22⋊C4×C79C2211yescharacteristic
29C22×C22⋊C4×C79C2211yescharacteristic
30C22×C22⋊C4×C79C2211yescharacteristic
31C22×C22⋊C4×C79C2211yescharacteristic
32C22×C22⋊C4×C79C2211yescharacteristic
33C22×C22⋊C4×C79C2211yescharacteristic
34C22×C22⋊C4×C79C2211yescharacteristic
35C22×C22⋊C4×C79C2211yescharacteristic
36C22×C42×C79C2211yescharacteristic
37C22×C42×C79C2211yescharacteristic
38#391×C79—24no—
39#388×C79—24no—
40#386×C79—24no—
41#385×C79—24no—
42C2×#95×C79C2211yescharacteristic
43C2×#95×C79C2211yescharacteristic
44C2×#95×C79C2211yescharacteristic
45C2×#95×C79C2211yescharacteristic
46C2×#95×C79C2211yescharacteristic
47C2×#95×C79C2211yescharacteristic
48C2×#95×C79C2211yescharacteristic
49C2×#95×C79C2211yescharacteristic
50C2×#95×C79C2211yescharacteristic
51C2×#95×C79C2211yescharacteristic
52C2×#95×C79C2211yescharacteristic
53C2×#95×C79C2211yescharacteristic
54C2×#95×C79C2211yescharacteristic
55C2×#95×C79C2211yescharacteristic
56C2×#95×C79C2211yescharacteristic
57C2×#95×C79C2211yescharacteristic
58C25×C79C2311yescharacteristic
59C25×C79C2311yescharacteristic
60C22×Q8×C79—22no—
61C22×Q8×C79—22no—
62C22×Q8×C79—22no—
63C22×Q8×C79—22no—
64C22×Q8×C79—41no—
65C22×Q8×C79—41no—
66C22×Q8×C79C2×C414yescomplemented
67C22×D4×C79—22no—
68C22×D4×C79—22no—
69C22×D4×C79—22no—
70C22×D4×C79—22no—
71C22×D4×C79—41no—
72C22×D4×C79—41no—
73C22×D4×C79C2×C414yes—
74C23×C4×C79—22no—
75C23×C4×C79—22no—
76C23×C4×C79—22no—
77C23×C4×C79—41no—
78C23×C4×C79—41no—
79C23×C4×C79—41no—
80C23×C4×C79—41no—
81C23×C4×C79C2311yescharacteristic
82C23×C4×C79C2311yescharacteristic
83C23×C4×C79C2311yescharacteristic
84C23×C4×C79C2311yescharacteristic
85C23×C4×C79C2311yescharacteristic
86C23×C4×C79C2311yescharacteristic
87C23×C4×C79C2311yescharacteristic
88C23×C4×C79C2311yescharacteristic
89C23×C4×C79C2311yescharacteristic
90C23×C4×C79C2311yescharacteristic
91C23×C4×C79C2311yescharacteristic
92C23×C4×C79C2311yescharacteristic
93C23×C4×C79C2311yescharacteristic
94#124×C79—232no—
95C2×C4⋊C4×C79—22no—
96C2×C4⋊C4×C79—22no—
97C2×C4⋊C4×C79—22no—
98C2×C4⋊C4×C79—22no—
99C2×C4⋊C4×C79—22no—
100C2×C4⋊C4×C79—22no—
101C2×C4⋊C4×C79—41no—
102C2×C4⋊C4×C79—41no—
103C2×C4⋊C4×C79—41no—
104C2×C22⋊C4×C79—22no—
105C2×C22⋊C4×C79—22no—
106C2×C22⋊C4×C79—22no—
107C2×C22⋊C4×C79—22no—
108C2×C22⋊C4×C79—22no—
109C2×C22⋊C4×C79—22no—
110C2×C22⋊C4×C79—22no—
111C2×C22⋊C4×C79—22no—
112C2×C22⋊C4×C79—22no—
113C2×C22⋊C4×C79—22no—
114C2×C22⋊C4×C79—22no—
115C2×C22⋊C4×C79—22no—
116C2×C22⋊C4×C79—22no—
117C2×C22⋊C4×C79—22no—
118C2×C22⋊C4×C79—22no—
119C2×C22⋊C4×C79—41no—
120C2×C22⋊C4×C79—41no—
121C2×C22⋊C4×C79—41no—
122C2×C22⋊C4×C79—41no—
123C2×C22⋊C4×C79—41no—
124C2×C22⋊C4×C79—41no—
125C2×C22⋊C4×C79—41no—
126C2×C22⋊C4×C79—41no—
127C2×C22⋊C4×C79—41no—
128C2×C22⋊C4×C79—41no—
129C2×C22⋊C4×C79—41no—
130C2×C22⋊C4×C79—41no—
131C2×C22⋊C4×C79C2×C414yes—
132C2×C22⋊C4×C79C2×C414yes—
133C2×C22⋊C4×C79C2×C414yescomplemented
134C2×C22⋊C4×C79C2×C414yescomplemented
135C2×C22⋊C4×C79D414yes—
136C2×C22⋊C4×C79D414yes—
137C2×C42×C79—22no—
138C2×C42×C79—22no—
139C2×C42×C79—22no—
140C2×C42×C79—22no—
141C2×C42×C79—41no—
142C2×C42×C79C2×C414yescomplemented
143#95×C79—22no—
144#95×C79—22no—
145#95×C79—22no—
146#95×C79—22no—
147#95×C79—22no—
148#95×C79—22no—
149#95×C79—22no—
150#95×C79—22no—
151#95×C79—22no—
152#95×C79—41no—
153#95×C79—41no—
154#95×C79—41no—
155#95×C79—41no—
156#95×C79—41no—
157#95×C79—41no—
158#95×C79D414yes—
159C24×C79—21no—
160C24×C79—21no—
161C24×C79—21no—
162C24×C79—21no—
163C24×C79—21no—
164C24×C79—21no—
165C24×C79—21no—
166C24×C79—21no—
167C24×C79—21no—
168C24×C79—21no—
169C24×C79—21no—
170C24×C79—21no—
171C24×C79—21no—
172C24×C79—21no—
173C24×C79—21no—
174C24×C79—21no—
175C24×C79—21no—
176C24×C79—21no—
177C24×C79—21no—
178C24×C79—21no—
179C24×C79—21no—
180C24×C79—21no—
181C24×C79—21no—
182C24×C79—21no—
183C24×C79—21no—
184C24×C79—21no—
185C24×C79C22×C412yes—
186C24×C79C22×C412yes—
187C24×C79C2×D412yes—
188C24×C79C2×D412yes—
189C24×C79C2411yescharacteristic
190C2×Q8×C79—28no—
191C2×Q8×C79—28no—
192C2×Q8×C79—44no—
193C2×Q8×C79—44no—
194C2×Q8×C79—44no—
195C2×Q8×C79—44no—
196C2×Q8×C79—44no—
197C2×D4×C79—28no—
198C2×D4×C79—28no—
199C2×D4×C79—44no—
200C2×D4×C79—44no—
201C2×D4×C79—44no—
202C2×D4×C79—44no—
203C2×D4×C79—44no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—21no—
210C22×C4×C79—21no—
211C22×C4×C79—21no—
212C22×C4×C79—21no—
213C22×C4×C79—21no—
214C22×C4×C79—21no—
215C22×C4×C79—21no—
216C22×C4×C79—21no—
217C22×C4×C79—21no—
218C22×C4×C79—21no—
219C22×C4×C79—21no—
220C22×C4×C79—21no—
221C22×C4×C79—21no—
222C22×C4×C79—21no—
223C22×C4×C79—21no—
224C22×C4×C79—21no—
225C22×C4×C79—21no—
226C22×C4×C79—21no—
227C22×C4×C79—21no—
228C22×C4×C79—21no—
229C22×C4×C79—21no—
230C22×C4×C79—21no—
231C22×C4×C79—21no—
232C22×C4×C79—21no—
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79—21no—
239C22×C4×C79—21no—
240C22×C4×C79—21no—
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
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—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79—21no—
261C22×C4×C79—21no—
262C22×C4×C79—21no—
263C22×C4×C79—21no—
264C22×C4×C79—21no—
265C22×C4×C79—21no—
266C22×C4×C79—21no—
267C22×C4×C79—21no—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—21no—
272C22×C4×C79—21no—
273C22×C4×C79—21no—
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—44no—
281C22×C4×C79—44no—
282C22×C4×C79—44no—
283C22×C4×C79—44no—
284C22×C4×C79—44no—
285C22×C4×C79—44no—
286C22×C4×C79—44no—
287C22×C4×C79C22×C412yes—
288C22×C4×C79C22×C412yes—
289C22×C4×C79C22×C412yes—
290C22×C4×C79C22×C412yes—
291C22×C4×C79C22×C412yes—
292C22×C4×C79C2×D412yes—
293C22×C4×C79C2×D412yes—
294C22×C4×C79C2×D412yes—
295C22×C4×C79C2×D412yes—
296C22×C4×C79C2×D412yes—
297C22×C4×C79C2×D412yes—
298C22×C4×C79C2×D412yes—
299C22×C4×C79#4112yes—
300C22×C4×C79#4112yes—
301C22×C4×C79#4112yes—
302C4⋊C4×C79—44no—
303C4⋊C4×C79—44no—
304C4⋊C4×C79—44no—
305C22⋊C4×C79—28no—
306C22⋊C4×C79—28no—
307C22⋊C4×C79—28no—
308C22⋊C4×C79—44no—
309C22⋊C4×C79—44no—
310C22⋊C4×C79—44no—
311C22⋊C4×C79—44no—
312C22⋊C4×C79—44no—
313C22⋊C4×C79—44no—
314C22⋊C4×C79—44no—
315C22⋊C4×C79C22⋊C4116yescomplemented
316C42×C79—28no—
317C42×C79—44no—
318C23×C79—22no—
319C23×C79—22no—
320C23×C79—22no—
321C23×C79—22no—
322C23×C79—22no—
323C23×C79—22no—
324C23×C79—22no—
325C23×C79—22no—
326C23×C79—22no—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79—22no—
331C23×C79—22no—
332C23×C79—22no—
333C23×C79—22no—
334C23×C79—22no—
335C23×C79—22no—
336C23×C79—22no—
337C23×C79—22no—
338C23×C79—22no—
339C23×C79—22no—
340C23×C79—22no—
341C23×C79—22no—
342C23×C79—22no—
343C23×C79—41no—
344C23×C79—41no—
345C23×C79—41no—
346C23×C79—41no—
347C23×C79—41no—
348C23×C79—41no—
349C23×C79—41no—
350C23×C79—41no—
351C23×C79—41no—
352C23×C79—41no—
353C23×C79—41no—
354C23×C79—41no—
355C23×C79—41no—
356C23×C79—41no—
357C23×C79—41no—
358C23×C79—41no—
359C23×C79—41no—
360C23×C79—41no—
361C23×C79—41no—
362C23×C79—41no—
363C23×C79—41no—
364C23×C79—41no—
365C23×C79—41no—
366C23×C79—41no—
367C23×C79—41no—
368C23×C79—41no—
369C23×C79—41no—
370C23×C79—41no—
371C23×C79—41no—
372C23×C79—41no—
373C23×C79—41no—
374C23×C79—41no—
375C23×C79—41no—
376C23×C79—41no—
377C23×C79—41no—
378C23×C79—41no—
379C23×C79—41no—
380C23×C79—41no—
381C23×C79—41no—
382C23×C79—41no—
383C23×C79—41no—
384C23×C79—41no—
385C23×C79—41no—
386C23×C79—41no—
387C23×C79C2×C22⋊C414yes—
388C23×C79C23×C411yescharacteristic
389C23×C79C22×D411yescharacteristic
390C23×C79C22×D411yescharacteristic
391C23×C79C22×D411yescharacteristic
392C23×C79C2×#4111yescharacteristic
393C23×C79C2×#4111yescharacteristic
394C23×C79C2×#4111yescharacteristic
395C23×C79H(5,𝔽2)11yescharacteristic
396C23×C79H(5,𝔽2)11yescharacteristic
397C23×C79H(5,𝔽2)11yescharacteristic
398C23×C79H(5,𝔽2)11yescharacteristic
399C23×C79H(5,𝔽2)11yescharacteristic
400C23×C792−1+411yescharacteristic
401C23×C792−1+411yescharacteristic
402C23×C792−1+411yescharacteristic
403Q8×C79—416no—
404D4×C79—416no—
405C2×C4×C79—22no—
406C2×C4×C79—22no—
407C2×C4×C79—22no—
408C2×C4×C79—22no—
409C2×C4×C79—22no—
410C2×C4×C79—22no—
411C2×C4×C79—22no—
412C2×C4×C79—22no—
413C2×C4×C79—22no—
414C2×C4×C79—22no—
415C2×C4×C79—22no—
416C2×C4×C79—22no—
417C2×C4×C79—22no—
418C2×C4×C79—22no—
419C2×C4×C79—22no—
420C2×C4×C79—22no—
421C2×C4×C79—22no—
422C2×C4×C79—22no—
423C2×C4×C79—22no—
424C2×C4×C79—22no—
425C2×C4×C79—22no—
426C2×C4×C79—22no—
427C2×C4×C79—22no—
428C2×C4×C79—22no—
429C2×C4×C79—22no—
430C2×C4×C79—22no—
431C2×C4×C79—22no—
432C2×C4×C79—22no—
433C2×C4×C79—22no—
434C2×C4×C79—22no—
435C2×C4×C79—22no—
436C2×C4×C79—22no—
437C2×C4×C79—22no—
438C2×C4×C79—22no—
439C2×C4×C79—22no—
440C2×C4×C79—22no—
441C2×C4×C79—416no—
442C2×C4×C79—41no—
443C2×C4×C79—41no—
444C2×C4×C79—41no—
445C2×C4×C79—41no—
446C2×C4×C79—41no—
447C2×C4×C79—41no—
448C2×C4×C79—41no—
449C2×C4×C79—41no—
450C2×C4×C79—41no—
451C2×C4×C79—41no—
452C2×C4×C79—41no—
453C2×C4×C79—41no—
454C2×C4×C79—41no—
455C2×C4×C79—41no—
456C2×C4×C79—41no—
457C2×C4×C79—41no—
458C2×C4×C79—41no—
459C2×C4×C79—41no—
460C2×C4×C79—41no—
461C2×C4×C79—41no—
462C2×C4×C79—41no—
463C2×C4×C79—41no—
464C2×C4×C79—41no—
465C2×C4×C79—41no—
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—41no—
473C2×C4×C79—41no—
474C2×C4×C79—41no—
475C2×C4×C79—41no—
476C2×C4×C79—41no—
477C2×C4×C79—41no—
478C2×C4×C79—41no—
479C2×C4×C79—41no—
480C2×C4×C79—41no—
481C2×C4×C79—41no—
482C2×C4×C79—41no—
483C2×C4×C79—41no—
484C2×C4×C79—41no—
485C2×C4×C79—41no—
486C2×C4×C79—41no—
487C2×C4×C79—41no—
488C2×C4×C79—41no—
489C2×C4×C79—41no—
490C2×C4×C79—41no—
491C2×C4×C79—41no—
492C2×C4×C79—41no—
493C2×C4×C79—41no—
494C2×C4×C79C2×C22⋊C414yes—
495C2×C4×C79C2×C22⋊C414yes—
496C2×C4×C79C4×D414yes—
497C22×C79—24no—
498C22×C79—24no—
499C22×C79—24no—
500C22×C79—42no—
501C22×C79—42no—
502C22×C79—42no—
503C22×C79—42no—
504C22×C79—42no—
505C22×C79—42no—
506C22×C79—42no—
507C22×C79—42no—
508C22×C79—42no—
509C22×C79—42no—
510C22×C79—42no—
511C22×C79—42no—
512C22×C79—42no—
513C22×C79—42no—
514C22×C79—42no—
515C22×C79—42no—
516C22×C79—42no—
517C22×C79—42no—
518C22×C79—42no—
519C22×C79—81no—
520C22×C79—81no—
521C22×C79—81no—
522C22×C79—81no—
523C22×C79—81no—
524C22×C79—81no—
525C22×C79—81no—
526C22×C79—81no—
527C22×C79C22×C22⋊C411yescharacteristic
528C22×C79C2×C4×D411yescharacteristic
529C22×C79C4×#4111yescharacteristic
530C22×C79#51811yescharacteristic
531C22×C79#52011yescharacteristic
532C22×C79#52011yescharacteristic
533C22×C79#52011yescharacteristic
534C22×C79#53511yescharacteristic
535C22×C79#53511yescharacteristic
536C22×C79#53611yescharacteristic
537C22×C79#53611yescharacteristic
538C22×C79#53711yescharacteristic
539C22×C79#53711yescharacteristic
540C22×C79#53811yescharacteristic
541C22×C79#53811yescharacteristic
542C22×C79#54211yescharacteristic
543C22×C79#54211yescharacteristic
544C22×C79#54211yescharacteristic
545C22×C79#54211yescharacteristic
546C22×C79D4211yescharacteristic
547C22×C79D4211yescharacteristic
548C22×C79#54611yescharacteristic
549C22×C79#54611yescharacteristic
550C22×C79#54611yescharacteristic
551C22×C79#54611yescharacteristic
552C22×C79#54611yescharacteristic
553C22×C79#54711yescharacteristic
554C22×C79#54711yescharacteristic
555C22×C79#54811yescharacteristic
556C22×C79#55611yescharacteristic
557C22×C79#55911yescharacteristic
558C22×C79H(3,𝔽4)11yescharacteristic
559C22×C79#56211yescharacteristic
560C22×C79#56211yescharacteristic
561C22×C79#56311yescharacteristic
562C4×C79—24no—
563C4×C79—24no—
564C4×C79—24no—
565C4×C79—42no—
566C4×C79—42no—
567C4×C79—42no—
568C4×C79—42no—
569C4×C79—42no—
570C4×C79—42no—
571C4×C79—81no—
572C4×C79—81no—
573C4×C79—81no—
574C4×C79—81no—
575#14421C7911yesmaximal, characteristic, direct product factor, Sylow
576C2×C79—44no—
577C2×C79—82no—
578C2×C79#231111yescharacteristic
579C2×C79#232611yescharacteristic
580C2×C79#233711yescharacteristic
581C2×C79D4×C22⋊C411yescharacteristic
582C2×C79#233911yescharacteristic
583C2×C79#236711yescharacteristic
584C2×C79#237911yescharacteristic
585C2×C79#267011yescharacteristic
586C2×C79#267211yescharacteristic
587C2×C79#267411yescharacteristic
588C2×C79#267611yescharacteristic
589C2×C79#270011yescharacteristic
590C2×C79#271011yescharacteristic
591C2×C79#271211yescharacteristic
592C2×C79#271511yescharacteristic
593C22×#124C2×C7911yescharacteristic
594C2×#391C2×C7911yescharacteristic, complemented
595C2×#388C2×C7911yescharacteristic, complemented
596C2×#386C2×C7911yescharacteristic
597C2×#385C2×C7911yescharacteristic, complemented
598#1446C2×C7911yescharacteristic, complemented
599#1440C2×C7911yescharacteristic, complemented
600#1439C2×C7911yescharacteristic, complemented
601#1439C2×C7911yescharacteristic, complemented
602#1439C2×C7911yescharacteristic, complemented
603#1438C2×C7911yescharacteristic
604#1437C2×C7911yescharacteristic, complemented
605C4⋊#95C2×C7911yescharacteristic, complemented
606#1434C2×C7911yescharacteristic, complemented
607C22⋊#95C2×C7911yescharacteristic, complemented
608C79#1442111yescharacteristic, direct product factor, Sylow
609C23×Q8C22×C7911yescharacteristic
610C23×D4C22×C7911yescharacteristic
611C24×C4C22×C7911yescharacteristic
612C2×#124—24no—
613C2×#124—24no—
614C2×#124C4×C7918yescomplemented
615C22×C4⋊C4C22×C7911yescharacteristic
616C22×C4⋊C4C22×C7911yescharacteristic
617C22×C4⋊C4C22×C7911yescharacteristic
618C22×C22⋊C4C22×C7911yescharacteristic
619C22×C22⋊C4C22×C7911yescharacteristic
620C22×C22⋊C4C22×C7911yescharacteristic
621C22×C22⋊C4C22×C7911yescharacteristic
622C22×C22⋊C4C22×C7911yescharacteristic
623C22×C22⋊C4C22×C7911yescharacteristic
624C22×C22⋊C4C22×C7911yescharacteristic
625C22×C22⋊C4C22×C7911yescharacteristic
626C22×C22⋊C4C22×C7911yescharacteristic
627C22×C22⋊C4C22×C7911yescharacteristic
628C22×C22⋊C4C22×C7911yescharacteristic
629C22×C42C22×C7911yescharacteristic
630C22×C42C22×C7911yescharacteristic
631#391—24no—
632#388—24no—
633#386—24no—
634#385—24no—
635C2×#95C22×C7911yescharacteristic
636C2×#95C22×C7911yescharacteristic
637C2×#95C22×C7911yescharacteristic
638C2×#95C22×C7911yescharacteristic
639C2×#95C22×C7911yescharacteristic
640C2×#95C22×C7911yescharacteristic
641C2×#95C22×C7911yescharacteristic
642C2×#95C22×C7911yescharacteristic
643C2×#95C22×C7911yescharacteristic
644C2×#95C22×C7911yescharacteristic
645C2×#95C22×C7911yescharacteristic
646C2×#95C22×C7911yescharacteristic
647C2×#95C22×C7911yescharacteristic
648C2×#95C22×C7911yescharacteristic
649C2×#95C22×C7911yescharacteristic
650C2×#95C22×C7911yescharacteristic
651C25C23×C7911yescharacteristic
652C25C23×C7911yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C7914yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C7914yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C7911yescharacteristic
675C23×C4C23×C7911yescharacteristic
676C23×C4C23×C7911yescharacteristic
677C23×C4C23×C7911yescharacteristic
678C23×C4C23×C7911yescharacteristic
679C23×C4C23×C7911yescharacteristic
680C23×C4C23×C7911yescharacteristic
681C23×C4C23×C7911yescharacteristic
682C23×C4C23×C7911yescharacteristic
683C23×C4C23×C7911yescharacteristic
684C23×C4C23×C7911yescharacteristic
685C23×C4C23×C7911yescharacteristic
686C23×C4C23×C7911yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4C2×C4×C7914yes—
725C2×C22⋊C4C2×C4×C7914yes—
726C2×C22⋊C4C2×C4×C7914yescomplemented
727C2×C22⋊C4C2×C4×C7914yescomplemented
728C2×C22⋊C4D4×C7914yes—
729C2×C22⋊C4D4×C7914yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735C2×C42C2×C4×C7914yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95D4×C7914yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C7912yes—
779C24C22×C4×C7912yes—
780C24C2×D4×C7912yes—
781C24C2×D4×C7912yes—
782C24C24×C7911yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4C22×C4×C7912yes—
881C22×C4C22×C4×C7912yes—
882C22×C4C22×C4×C7912yes—
883C22×C4C22×C4×C7912yes—
884C22×C4C22×C4×C7912yes—
885C22×C4C2×D4×C7912yes—
886C22×C4C2×D4×C7912yes—
887C22×C4C2×D4×C7912yes—
888C22×C4C2×D4×C7912yes—
889C22×C4C2×D4×C7912yes—
890C22×C4C2×D4×C7912yes—
891C22×C4C2×D4×C7912yes—
892C22×C4#41×C7912yes—
893C22×C4#41×C7912yes—
894C22×C4#41×C7912yes—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4C22⋊C4×C79116yescomplemented
909C42—28no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C7914yes—
981C23C23×C4×C7911yescharacteristic
982C23C22×D4×C7911yescharacteristic
983C23C22×D4×C7911yescharacteristic
984C23C22×D4×C7911yescharacteristic
985C23C2×#41×C7911yescharacteristic
986C23C2×#41×C7911yescharacteristic
987C23C2×#41×C7911yescharacteristic
988C23H(5,𝔽2)×C7911yescharacteristic
989C23H(5,𝔽2)×C7911yescharacteristic
990C23H(5,𝔽2)×C7911yescharacteristic
991C23H(5,𝔽2)×C7911yescharacteristic
992C23H(5,𝔽2)×C7911yescharacteristic
993C232−1+4×C7911yescharacteristic
994C232−1+4×C7911yescharacteristic
995C232−1+4×C7911yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—416no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C7914yes—
1088C2×C4C2×C22⋊C4×C7914yes—
1089C2×C4C4×D4×C7914yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C7911yescharacteristic
1121C22C2×C4×D4×C7911yescharacteristic
1122C22C4×#41×C7911yescharacteristic
1123C22#518×C7911yescharacteristic
1124C22#520×C7911yescharacteristic
1125C22#520×C7911yescharacteristic
1126C22#520×C7911yescharacteristic
1127C22#535×C7911yescharacteristic
1128C22#535×C7911yescharacteristic
1129C22#536×C7911yescharacteristic
1130C22#536×C7911yescharacteristic
1131C22#537×C7911yescharacteristic
1132C22#537×C7911yescharacteristic
1133C22#538×C7911yescharacteristic
1134C22#538×C7911yescharacteristic
1135C22#542×C7911yescharacteristic
1136C22#542×C7911yescharacteristic
1137C22#542×C7911yescharacteristic
1138C22#542×C7911yescharacteristic
1139C22D42×C7911yescharacteristic
1140C22D42×C7911yescharacteristic
1141C22#546×C7911yescharacteristic
1142C22#546×C7911yescharacteristic
1143C22#546×C7911yescharacteristic
1144C22#546×C7911yescharacteristic
1145C22#546×C7911yescharacteristic
1146C22#547×C7911yescharacteristic
1147C22#547×C7911yescharacteristic
1148C22#548×C7911yescharacteristic
1149C22#556×C7911yescharacteristic
1150C22#559×C7911yescharacteristic
1151C22H(3,𝔽4)×C7911yescharacteristic
1152C22#562×C7911yescharacteristic
1153C22#562×C7911yescharacteristic
1154C22#563×C7911yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C79×#231111yescharacteristic
1171C2C79×#232611yescharacteristic
1172C2C79×#233711yescharacteristic
1173C2D4×C22⋊C4×C7911yescharacteristic
1174C2C79×#233911yescharacteristic
1175C2C79×#236711yescharacteristic
1176C2C79×#237911yescharacteristic
1177C2C79×#267011yescharacteristic
1178C2C79×#267211yescharacteristic
1179C2C79×#267411yescharacteristic
1180C2C79×#267611yescharacteristic
1181C2C79×#270011yescharacteristic
1182C2C79×#271011yescharacteristic
1183C2C79×#271211yescharacteristic
1184C2C79×#271511yescharacteristic
subgroupG/H
center, socleC24×C79C24
commutatorC23C23×C4×C79
Frattini, cosocleC24C24×C79
prime radicalC23×D4×C79C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C79C2semidirect
3. C2×#388×C79C2semidirect
5. C2×#385×C79C2semidirect
6. C79×#1446C2semidirect
7. C79×#1440C2semidirect
8. C79×#1439C2semidirect
9. C79×#1439C2semidirect
10. C79×#1439C2semidirect
12. C79×#1437C2semidirect
13. C79×C4⋊#95C2semidirect
14. C79×#1434C2semidirect
15. C79×C22⋊#95C2semidirect
21. C2×#124×C79C4semidirect
66. C22×Q8×C79C2×C4semidirect
133. C2×C22⋊C4×C79C2×C4semidirect
134. C2×C22⋊C4×C79C2×C4semidirect
142. C2×C42×C79C2×C4semidirect
315. C22⋊C4×C79C22⋊C4semidirect
575. #14421C79direct (N × H)
594. C2×#391C2×C79semidirect
595. C2×#388C2×C79semidirect
597. C2×#385C2×C79semidirect
598. #1446C2×C79semidirect
599. #1440C2×C79semidirect
600. #1439C2×C79semidirect
601. #1439C2×C79semidirect
602. #1439C2×C79semidirect
604. #1437C2×C79semidirect
605. C4⋊#95C2×C79semidirect
606. #1434C2×C79semidirect
607. C22⋊#95C2×C79semidirect
608. C79#14421direct (N × H)
614. C2×#124C4×C79semidirect
659. C22×Q8C2×C4×C79semidirect
726. C2×C22⋊C4C2×C4×C79semidirect
727. C2×C22⋊C4C2×C4×C79semidirect
735. C2×C42C2×C4×C79semidirect
908. C22⋊C4C22⋊C4×C79semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C792
C2×#391×C792
C2×#388×C792
C2×#386×C792
C2×#385×C792
C79×#14462
C79×#14402
C79×#14392
C79×#14382
C79×#14372
C79×C4⋊#952
C79×#14342
C79×C22⋊#952
#1442179