Finite Group Databasebeta

← #1733×D79 #34285653

Subgroups — #1733×D79 #34285653

Order 20224.

2270 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D79C211yesmaximal, characteristic
2C2×#117×D79C211yesmaximal, characteristic
3C2×#117×D79C211yesmaximal, characteristic
4#23763111C211yesmaximal, characteristic, complemented
5#23763110C211yesmaximal, characteristic, complemented
6#23763109C211yesmaximal, characteristic, complemented
7#23763108C214yesmaximal, complemented
8#339×D79C214yesmaximal, complemented
9C79×#1733C211yesmaximal, characteristic, complemented
10C23×C4×D79C2211yescharacteristic
11C22×#11929608C2211yescharacteristic
12C22×#11929607—21no—
13C2×M16×D79—24no—
14C2×M16×D79—21no—
15C2×M16×D79—21no—
16C2×M16×D79C418yescomplemented
17C2×M16×D79C2212yes—
18C2×M16×D79C2212yes—
19C22×C8×D79—21no—
20C2×#14579120C2211yescharacteristic
21C2×#14579120C2211yescharacteristic
22C2×#14579119—21no—
23C2×#14579119C412yescomplemented
24C2×#14579118—21no—
25C2×#14579118C2212yes—
26C2×#14579117—21no—
27C2×#14579117—21no—
28#117×D79—21no—
29#117×D79—21no—
30#117×D79—21no—
31#117×D79—21no—
32#117×D79—24no—
33#117×D79C412yescomplemented
34#117×D79C412yescomplemented
35#117×D79C418yescomplemented
36#117×D79C2212yes—
37#117×D79C2212yes—
38C2×C4⋊C4×D79—21no—
39C2×C4⋊C4×D79C412yescomplemented
40C2×C22⋊C4×D79—21no—
41C2×C22⋊C4×D79—21no—
42C2×C42×D79—21no—
43C2×C42×D79C2212yes—
44#19098324C2214yescomplemented
45#19098323C2214yescomplemented
46#19098322C2214yescomplemented
47C22×M16×C79C2211yescharacteristic
48C2×#117×C79C2211yescharacteristic
49C2×#117×C79C2211yescharacteristic
50#339×C79C2214yescomplemented
51C24×D79D411yescharacteristic
52C23×Dic79D411yescharacteristic
53C22×C4×D79—22no—
54C22×C4×D79—22no—
55C22×C4×D79C2×C414yes—
56C22×C4×D79C2×C411yescharacteristic
57C22×C4×D79C2×C411yescharacteristic
58C22×C4×D79C2×C411yescharacteristic
59C22×C4×D79C2×C414yes—
60C22×C4×D79C2×C411yescharacteristic
61C22×C4×D79D411yescharacteristic
62C22×C4×D79D411yescharacteristic
63C22×C4×D79D411yescharacteristic
64C22×C4×D79D411yescharacteristic
65C22×C4×D79D414yes—
66C22×C4×D79D411yescharacteristic
67C22×C4×D79D411yescharacteristic
68C22×C4×D79Q814yes—
69C22×C4×D79C2311yescharacteristic
70C22×C4×D79C2311yescharacteristic
71C2×#11929608—22no—
72C2×#11929608—21no—
73C2×#11929608C2×C414yescomplemented
74C2×#11929608C2312yes—
75C2×#11929607—28no—
76C2×#11929607—22no—
77C2×#11929607—22no—
78M16×D79—28no—
79M16×D79—28no—
80M16×D79—24no—
81M16×D79—24no—
82M16×D79C2×C418yescomplemented
83M16×D79C2×C418yescomplemented
84C22×C79⋊C8—21no—
85C2×C8×D79—28no—
86C2×C8×D79—22no—
87C2×C8×D79—22no—
88#14579120—21no—
89#14579120—21no—
90#14579120—22no—
91#14579120C2×C412yescomplemented
92#14579120C2×C414yescomplemented
93#14579120C2312yes—
94#14579119—22no—
95#14579119—22no—
96#14579119—28no—
97#14579119C2×C414yes—
98#14579119C2×C414yescomplemented
99#14579118—22no—
100#14579118—22no—
101#14579118—24no—
102#14579118—22no—
103#14579118—22no—
104#14579118C2×C418yescomplemented
105#14579117—22no—
106#14579117—22no—
107#14579117—28no—
108#14579117—22no—
109#14579117—22no—
110C2×C4⋊Dic79—21no—
111C2×C4⋊Dic79C2×C412yescomplemented
112C2×Dic79⋊C4—22no—
113C2×Dic79⋊C4—22no—
114C4⋊C4×D79—28no—
115C4⋊C4×D79—22no—
116C4⋊C4×D79—22no—
117C4⋊C4×D79C2×C414yes—
118C4⋊C4×D79C2×C414yescomplemented
119C2×C22⋊Dic79—21no—
120C2×C22⋊Dic79—21no—
121C2×(C2×D79)⋊C4—22no—
122C2×(C2×D79)⋊C4—22no—
123C22⋊C4×D79—22no—
124C22⋊C4×D79—22no—
125C22⋊C4×D79—28no—
126C22⋊C4×D79—22no—
127C22⋊C4×D79—22no—
128C2×C4×Dic79—21no—
129C2×C4×Dic79—22no—
130C2×C4×Dic79—22no—
131C2×C4×Dic79C2312yes—
132C42×D79—22no—
133C42×D79—22no—
134C42×D79—22no—
135C42×D79—22no—
136C42×D79—24no—
137C42×D79C2×C418yescomplemented
138C23×C4×C79C2311yescharacteristic
139C2×M16×C79—22no—
140C2×M16×C79—21no—
141C2×M16×C79C2×C414yescomplemented
142C2×M16×C79C2312yes—
143C22×C8×C79—21no—
144#117×C79—21no—
145#117×C79—21no—
146#117×C79—22no—
147#117×C79C2×C412yescomplemented
148#117×C79C2×C414yescomplemented
149#117×C79C2312yes—
150C2×C4⋊C4×C79—21no—
151C2×C4⋊C4×C79C2×C412yescomplemented
152C2×C22⋊C4×C79—21no—
153C2×C22⋊C4×C79—21no—
154C2×C42×C79—21no—
155C2×C42×C79C2312yes—
156C23×D79—44no—
157C23×D79C22⋊C411yescharacteristic
158C23×D79C22⋊C411yescharacteristic
159C23×D79C22⋊C414yes—
160C23×D79C22⋊C411yescharacteristic
161C23×D79C22⋊C411yescharacteristic
162C23×D79C4⋊C414yes—
163C23×D79C2×D411yescharacteristic
164C23×D79C2×D411yescharacteristic
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79C22⋊C411yescharacteristic
168C22×Dic79C22⋊C411yescharacteristic
169C22×Dic79C22⋊C411yescharacteristic
170C22×Dic79C22⋊C411yescharacteristic
171C22×Dic79C22⋊C414yes—
172C22×Dic79C4⋊C414yes—
173C22×Dic79C2×D411yescharacteristic
174C22×Dic79C2×D411yescharacteristic
175C2×C4×D79—24no—
176C2×C4×D79—24no—
177C2×C4×D79—28no—
178C2×C4×D79—48no—
179C2×C4×D79—48no—
180C2×C4×D79C4214yes—
181C2×C4×D79C4214yes—
182C2×C4×D79C4214yes—
183C2×C4×D79C4214yes—
184C2×C4×D79C22⋊C414yes—
185C2×C4×D79C22⋊C414yes—
186C2×C4×D79C22⋊C414yes—
187C2×C4×D79C22⋊C414yes—
188C2×C4×D79C22⋊C411yescharacteristic
189C2×C4×D79C22⋊C411yescharacteristic
190C2×C4×D79C22⋊C414yes—
191C2×C4×D79C22⋊C411yescharacteristic
192C2×C4×D79C22⋊C411yescharacteristic
193C2×C4×D79C22⋊C411yescharacteristic
194C2×C4×D79C22⋊C411yescharacteristic
195C2×C4×D79C22⋊C411yescharacteristic
196C2×C4×D79C22⋊C411yescharacteristic
197C2×C4×D79C22⋊C414yes—
198C2×C4×D79C4⋊C414yes—
199C2×C4×D79C4⋊C414yes—
200C2×C4×D79C4⋊C414yes—
201C2×C4×D79C4⋊C414yes—
202C2×C4×D79C4⋊C414yes—
203C2×C4×D79C4⋊C414yes—
204C2×C4×D79C4⋊C414yes—
205C2×C4×D79C4⋊C414yes—
206C2×C4×D79C4⋊C414yes—
207C2×C4×D79C4⋊C414yes—
208C2×C4×D79C22×C412yes—
209C2×C4×D79C22×C411yescharacteristic
210C2×C4×D79C22×C411yescharacteristic
211C2×C4×D79C22×C412yes—
212C2×C4×D79C22×C411yescharacteristic
213C2×C4×D79C22×C411yescharacteristic
214C2×C4×D79C22×C412yes—
215C2×C4×D79C22×C412yes—
216C2×C4×D79C2×D411yescharacteristic
217C2×C4×D79C2×D412yes—
218C2×C4×D79C2×D411yescharacteristic
219C2×C4×D79C2×D411yescharacteristic
220C2×C4×D79C2×D412yes—
221C2×C4×D79C2×D411yescharacteristic
222C2×C4×D79C2×Q812yes—
223C2×C4×D79C2×Q812yes—
224#11929608—24no—
225#11929608—22no—
226#11929608C22×C414yescomplemented
227#11929607—28no—
228#11929607—28no—
229C2×C79⋊C8—24no—
230C2×C79⋊C8—22no—
231C8×D79—28no—
232C8×D79—28no—
233C4⋊Dic79—24no—
234C4⋊Dic79—22no—
235C4⋊Dic79C22×C414yes—
236Dic79⋊C4—28no—
237Dic79⋊C4—24no—
238Dic79⋊C4—24no—
239C22⋊Dic79—22no—
240C22⋊Dic79—24no—
241C22⋊Dic79—22no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—28no—
245C4×Dic79—24no—
246C4×Dic79—24no—
247C4×Dic79—28no—
248C4×Dic79—22no—
249C4×Dic79—22no—
250C4×Dic79—22no—
251C4×Dic79C22×C414yescomplemented
252C24×C79C2×D411yescharacteristic
253C22×C4×C79—22no—
254C22×C4×C79—22no—
255C22×C4×C79C22×C412yes—
256C22×C4×C79C22×C411yescharacteristic
257C22×C4×C79C22×C411yescharacteristic
258C22×C4×C79C22×C412yes—
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D412yes—
263C22×C4×C79C2×Q812yes—
264C22×C4×C79C2411yescharacteristic
265M16×C79—24no—
266M16×C79—22no—
267M16×C79C22×C414yescomplemented
268C2×C8×C79—24no—
269C2×C8×C79—22no—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—22no—
272C4⋊C4×C79C22×C414yes—
273C22⋊C4×C79—22no—
274C22⋊C4×C79—24no—
275C22⋊C4×C79—22no—
276C42×C79—22no—
277C42×C79—22no—
278C42×C79—22no—
279C42×C79C22×C414yescomplemented
280C23×C79—42no—
281C23×C79C2×C22⋊C411yescharacteristic
282C23×C79C2×C22⋊C411yescharacteristic
283C23×C79C2×C22⋊C412yes—
284C23×C79C2×C4⋊C412yes—
285C23×C79C22×D411yescharacteristic
286C22×D79—24no—
287C22×D79—24no—
288C22×D79—24no—
289C22×D79—48no—
290C22×D79—48no—
291C22×D79—42no—
292C22×D79—42no—
293C22×D79—42no—
294C22×D79#9514yes—
295C22×D79#9514yes—
296C22×D79#9514yes—
297C22×D79#9514yes—
298C22×D79C2×C22⋊C411yescharacteristic
299C22×D79C2×C22⋊C411yescharacteristic
300C22×D79C2×C22⋊C411yescharacteristic
301C22×D79C2×C22⋊C412yes—
302C22×D79C2×C22⋊C412yes—
303C22×D79C2×C22⋊C411yescharacteristic
304C22×D79C2×C4⋊C412yes—
305C22×D79C2×C4⋊C412yes—
306C2×C4×C79—24no—
307C2×C4×C79—24no—
308C2×C4×C79—44no—
309C2×C4×C79—44no—
310C2×C4×C79C2×C4212yes—
311C2×C4×C79C2×C4212yes—
312C2×C4×C79C2×C22⋊C412yes—
313C2×C4×C79C2×C22⋊C412yes—
314C2×C4×C79C2×C22⋊C411yescharacteristic
315C2×C4×C79C2×C22⋊C412yes—
316C2×C4×C79C2×C22⋊C411yescharacteristic
317C2×C4×C79C2×C4⋊C412yes—
318C2×C4×C79C2×C4⋊C412yes—
319C2×C4×C79C2×C4⋊C412yes—
320C2×C4×C79C2×C4⋊C412yes—
321C2×C4×C79C2×C4⋊C412yes—
322C2×C4×C79C23×C411yescharacteristic
323C2×C4×C79C23×C411yescharacteristic
324C2×C4×C79C23×C411yescharacteristic
325C2×C4×C79C22×D411yescharacteristic
326C2×C4×C79C22×D411yescharacteristic
327C2×C4×C79C22×Q811yescharacteristic
328C2×Dic79—24no—
329C2×Dic79—24no—
330C2×Dic79—44no—
331C2×Dic79—44no—
332C2×Dic79#9514yes—
333C2×Dic79#9514yes—
334C2×Dic79#9514yes—
335C2×Dic79#9514yes—
336C2×Dic79C2×C22⋊C412yes—
337C2×Dic79C2×C22⋊C411yescharacteristic
338C2×Dic79C2×C22⋊C411yescharacteristic
339C2×Dic79C2×C22⋊C412yes—
340C2×Dic79C2×C22⋊C411yescharacteristic
341C2×Dic79C2×C22⋊C411yescharacteristic
342C2×Dic79C2×C4⋊C412yes—
343C2×Dic79C2×C4⋊C412yes—
344C4×D79—416no—
345C4×D79—48no—
346C4×D79—48no—
347C4×D79#9514yes—
348C4×D79#9514yes—
349C4×D79#9514yes—
350C4×D79#9514yes—
351C4×D79#9514yes—
352C4×D79#9514yes—
353C4×D79#9514yes—
354C4×D79#9514yes—
355C4×D79C2×C4212yes—
356C4×D79C2×C4212yes—
357C4×D79C2×C4212yes—
358C4×D79C2×C4212yes—
359C4×D79C2×C22⋊C412yes—
360C4×D79C2×C22⋊C412yes—
361C4×D79C2×C22⋊C412yes—
362C4×D79C2×C22⋊C412yes—
363C4×D79C2×C4⋊C412yes—
364C4×D79C2×C4⋊C412yes—
365C4×D79C2×C4⋊C412yes—
366C4×D79C2×C4⋊C412yes—
367C4×D79C2×C4⋊C412yes—
368C4×D79C2×C4⋊C412yes—
369C4×D79C2×C4⋊C412yes—
370C4×D79C2×C4⋊C412yes—
371C8×C79—24no—
372C79⋊C8—24no—
373C22×C79—22no—
374C22×C79—22no—
375C22×C79—22no—
376C22×C79—42no—
377C22×C79—42no—
378C22×C79C2×#9512yes—
379C22×C79C2×#9512yes—
380C22×C79C22×C22⋊C411yescharacteristic
381C22×C79C22×C22⋊C411yescharacteristic
382C22×C79C22×C4⋊C411yescharacteristic
383C2×D79—22no—
384C2×D79—22no—
385C2×D79—22no—
386C2×D79—28no—
387C2×D79—28no—
388C2×D79—24no—
389C2×D79—24no—
390C2×D79—44no—
391C2×D79—44no—
392C2×D79—42no—
393C2×D79—42no—
394C2×D79C2×#9512yes—
395C2×D79C2×#9512yes—
396C2×D79C2×#9512yes—
397C2×D79C2×#9512yes—
398C2×D79#42114yes—
399C4×C79—44no—
400C4×C79—44no—
401C4×C79C2×#9512yes—
402C4×C79C2×#9512yes—
403C4×C79C22×C4211yescharacteristic
404C4×C79C22×C22⋊C411yescharacteristic
405C4×C79C22×C4⋊C411yescharacteristic
406C4×C79C22×C4⋊C411yescharacteristic
407Dic79—44no—
408Dic79—44no—
409Dic79C2×#9512yes—
410Dic79C2×#9512yes—
411Dic79C2×#9512yes—
412Dic79C2×#9512yes—
413C2×#1733—791nomaximal, Sylow
414C2×C79—21no—
415C2×C79—21no—
416C2×C79—22no—
417C2×C79—22no—
418C2×C79C22×#9511yescharacteristic
419C2×C79C2×#42112yes—
420D79—22no—
421D79—22no—
422D79—22no—
423D79#173314yesdirect product factor
424C23×M16—791no—
425C22×#117—791no—
426C22×#117—791no—
427#1733—794no—
428#1733—791no—
429#1733—791no—
430#1733—791no—
431#1733D7911yescharacteristic, direct product factor
432C2×#339—794no—
433C79C2×#173311yescharacteristic, complemented, Sylow
434C24×C4—791no—
435C22×M16—791no—
436C22×M16—792no—
437C22×M16—792no—
438C22×M16—798no—
439C22×M16—1581no—
440C22×M16—1584no—
441C22×M16—1581no—
442C22×M16—1581no—
443C22×M16C2×D7911yescharacteristic
444C23×C8—1581no—
445C2×#117—791no—
446C2×#117—798no—
447C2×#117—792no—
448C2×#117—791no—
449C2×#117—792no—
450C2×#117—792no—
451C2×#117—792no—
452C2×#117—792no—
453C2×#117—792no—
454C2×#117—1581no—
455C2×#117—1581no—
456C2×#117—1581no—
457C2×#117—1581no—
458C2×#117—1581no—
459C2×#117—1581no—
460C2×#117—1581no—
461C2×#117—1581no—
462C2×#117—1584no—
463C2×#117C2×D7911yescharacteristic
464C2×#117C2×D7911yescharacteristic
465C22×C4⋊C4—792no—
466C22×C4⋊C4—1581no—
467C22×C22⋊C4—1581no—
468C22×C22⋊C4—1581no—
469C22×C42—792no—
470C22×C42—1581no—
471#339—794no—
472#339—794no—
473#339—794no—
474#339C2×D7914yescomplemented
475C25—791no—
476C23×C4—791no—
477C23×C4—791no—
478C23×C4—791no—
479C23×C4—791no—
480C23×C4—791no—
481C23×C4—794no—
482C23×C4—794no—
483C23×C4—791no—
484C23×C4—791no—
485C23×C4—791no—
486C23×C4—791no—
487C23×C4—794no—
488C23×C4—791no—
489C23×C4—791no—
490C23×C4—794no—
491C23×C4—791no—
492C23×C4—791no—
493C23×C4—1582no—
494C23×C4—1582no—
495C23×C4C22×D7911yescharacteristic
496C2×M16—22no—
497C2×M16—21no—
498C2×M16—794no—
499C2×M16—792no—
500C2×M16—798no—
501C2×M16—798no—
502C2×M16—1588no—
503C2×M16—1582no—
504C2×M16—1582no—
505C2×M16—1588no—
506C2×M16—1588no—
507C2×M16—1584no—
508C2×M16—1584no—
509C2×M16—1582no—
510C2×M16—1581no—
511C2×M16C4×D7914yescomplemented
512C2×M16C22×D7912yes—
513C22×C8—21no—
514C22×C8—1588no—
515C22×C8—1582no—
516C22×C8—1582no—
517C22×C8—1581no—
518#117—21no—
519#117—22no—
520#117—21no—
521#117—794no—
522#117—798no—
523#117—792no—
524#117—792no—
525#117—794no—
526#117—794no—
527#117—1582no—
528#117—1582no—
529#117—1584no—
530#117—1582no—
531#117—1582no—
532#117—1588no—
533#117—1582no—
534#117—1582no—
535#117—1582no—
536#117—1582no—
537#117—1588no—
538#117—1582no—
539#117—1582no—
540#117—1581no—
541#117—1582no—
542#117—1581no—
543#117C4×D7912yescomplemented
544#117C4×D7914yescomplemented
545#117C22×D7912yes—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—792no—
548C2×C4⋊C4—794no—
549C2×C4⋊C4—794no—
550C2×C4⋊C4—1582no—
551C2×C4⋊C4—1582no—
552C2×C4⋊C4—1588no—
553C2×C4⋊C4—1582no—
554C2×C4⋊C4—1582no—
555C2×C4⋊C4—1581no—
556C2×C4⋊C4C4×D7912yescomplemented
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1588no—
560C2×C22⋊C4—1582no—
561C2×C22⋊C4—1582no—
562C2×C22⋊C4—1582no—
563C2×C22⋊C4—1582no—
564C2×C22⋊C4—1582no—
565C2×C22⋊C4—1582no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C42—21no—
569C2×C42—792no—
570C2×C42—798no—
571C2×C42—1582no—
572C2×C42—1582no—
573C2×C42—1582no—
574C2×C42—1582no—
575C2×C42—1584no—
576C2×C42—1582no—
577C2×C42—1582no—
578C2×C42—1581no—
579C2×C42C22×D7912yes—
580C24—3164no—
581C24—791no—
582C24—791no—
583C24—794no—
584C24—794no—
585C24—791no—
586C24—791no—
587C24—791no—
588C24—791no—
589C24D4×D7911yescharacteristic
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—3168no—
593C22×C4—3168no—
594C22×C4—791no—
595C22×C4—791no—
596C22×C4—791no—
597C22×C4—791no—
598C22×C4—794no—
599C22×C4—794no—
600C22×C4—791no—
601C22×C4—791no—
602C22×C4—792no—
603C22×C4—792no—
604C22×C4—794no—
605C22×C4—794no—
606C22×C4—794no—
607C22×C4—794no—
608C22×C4—791no—
609C22×C4—791no—
610C22×C4—791no—
611C22×C4—791no—
612C22×C4—794no—
613C22×C4—794no—
614C22×C4—791no—
615C22×C4—791no—
616C22×C4—791no—
617C22×C4—791no—
618C22×C4—794no—
619C22×C4—794no—
620C22×C4—794no—
621C22×C4—794no—
622C22×C4—794no—
623C22×C4—794no—
624C22×C4—794no—
625C22×C4—794no—
626C22×C4—794no—
627C22×C4—794no—
628C22×C4—794no—
629C22×C4—794no—
630C22×C4—794no—
631C22×C4—794no—
632C22×C4—792no—
633C22×C4—791no—
634C22×C4—791no—
635C22×C4—791no—
636C22×C4—791no—
637C22×C4—792no—
638C22×C4—792no—
639C22×C4—792no—
640C22×C4—792no—
641C22×C4—792no—
642C22×C4—791no—
643C22×C4—791no—
644C22×C4—791no—
645C22×C4—791no—
646C22×C4—1588no—
647C22×C4—1584no—
648C22×C4—1584no—
649C22×C4—1582no—
650C22×C4—1582no—
651C22×C4C2×C4×D7912yes—
652C22×C4C2×C4×D7911yescharacteristic
653C22×C4C2×C4×D7911yescharacteristic
654C22×C4C2×C4×D7912yes—
655C22×C4D4×D7911yescharacteristic
656C22×C4D4×D7912yes—
657C22×C4D4×D7911yescharacteristic
658C22×C4D4×D7911yescharacteristic
659C22×C4Q8×D7912yes—
660C22×C4C23×D7911yescharacteristic
661M16—24no—
662M16—22no—
663M16—794no—
664M16—1588no—
665M16—1588no—
666M16—1584no—
667M16—1582no—
668M16C2×C4×D7914yescomplemented
669C2×C8—24no—
670C2×C8—22no—
671C2×C8—1588no—
672C2×C8—1588no—
673C2×C8—1584no—
674C2×C8—1582no—
675C4⋊C4—24no—
676C4⋊C4—22no—
677C4⋊C4—794no—
678C4⋊C4—1584no—
679C4⋊C4—1584no—
680C4⋊C4—1588no—
681C4⋊C4—1582no—
682C4⋊C4—1584no—
683C4⋊C4C2×C4×D7914yes—
684C22⋊C4—22no—
685C22⋊C4—24no—
686C22⋊C4—22no—
687C22⋊C4—1584no—
688C22⋊C4—1584no—
689C22⋊C4—1588no—
690C22⋊C4—1584no—
691C22⋊C4—1582no—
692C22⋊C4—1582no—
693C42—22no—
694C42—22no—
695C42—22no—
696C42—794no—
697C42—1588no—
698C42—1584no—
699C42—1584no—
700C42—1582no—
701C42—1582no—
702C42—1582no—
703C42C2×C4×D7914yescomplemented
704C23—42no—
705C23—3162no—
706C23—3162no—
707C23—3162no—
708C23—3168no—
709C23—3168no—
710C23—794no—
711C23—794no—
712C23—792no—
713C23—792no—
714C23—791no—
715C23—794no—
716C23—794no—
717C23—791no—
718C23—791no—
719C23—792no—
720C23—791no—
721C23—792no—
722C23—1584no—
723C23—1584no—
724C23—1584no—
725C23C22⋊C4×D7911yescharacteristic
726C23C22⋊C4×D7911yescharacteristic
727C23C22⋊C4×D7912yes—
728C23C4⋊C4×D7912yes—
729C23C2×D4×D7911yescharacteristic
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—3168no—
735C2×C4—31616no—
736C2×C4—3168no—
737C2×C4—3164no—
738C2×C4—3164no—
739C2×C4—794no—
740C2×C4—794no—
741C2×C4—794no—
742C2×C4—794no—
743C2×C4—792no—
744C2×C4—791no—
745C2×C4—791no—
746C2×C4—792no—
747C2×C4—791no—
748C2×C4—791no—
749C2×C4—792no—
750C2×C4—792no—
751C2×C4—794no—
752C2×C4—794no—
753C2×C4—794no—
754C2×C4—794no—
755C2×C4—794no—
756C2×C4—794no—
757C2×C4—794no—
758C2×C4—794no—
759C2×C4—792no—
760C2×C4—792no—
761C2×C4—792no—
762C2×C4—792no—
763C2×C4—792no—
764C2×C4—792no—
765C2×C4—792no—
766C2×C4—792no—
767C2×C4—792no—
768C2×C4—792no—
769C2×C4—792no—
770C2×C4—792no—
771C2×C4—792no—
772C2×C4—792no—
773C2×C4—792no—
774C2×C4—792no—
775C2×C4—1584no—
776C2×C4—1584no—
777C2×C4C42×D7912yes—
778C2×C4C42×D7912yes—
779C2×C4C22⋊C4×D7911yescharacteristic
780C2×C4C22⋊C4×D7912yes—
781C2×C4C22⋊C4×D7911yescharacteristic
782C2×C4C22⋊C4×D7912yes—
783C2×C4C22⋊C4×D7912yes—
784C2×C4C4⋊C4×D7912yes—
785C2×C4C4⋊C4×D7912yes—
786C2×C4C4⋊C4×D7912yes—
787C2×C4C4⋊C4×D7912yes—
788C2×C4C4⋊C4×D7912yes—
789C2×C4C22×C4×D7911yescharacteristic
790C2×C4C22×C4×D7911yescharacteristic
791C2×C4C22×C4×D7911yescharacteristic
792C2×C4C2×D4×D7911yescharacteristic
793C2×C4C2×D4×D7911yescharacteristic
794C2×C4C2×Q8×D7911yescharacteristic
795C8—24no—
796C8—1584no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—3162no—
803C22—3164no—
804C22—3164no—
805C22—3162no—
806C22—794no—
807C22—792no—
808C22—792no—
809C22—792no—
810C22—792no—
811C22—1584no—
812C22—1588no—
813C22—1588no—
814C22—1584no—
815C22—1582no—
816C22—1582no—
817C22—1582no—
818C22#95×D7912yes—
819C22#95×D7912yes—
820C22C2×C22⋊C4×D7911yescharacteristic
821C22C2×C22⋊C4×D7911yescharacteristic
822C22C2×C4⋊C4×D7911yescharacteristic
823C4—44no—
824C4—44no—
825C4—3164no—
826C4—3164no—
827C4—792no—
828C4—792no—
829C4—792no—
830C4—792no—
831C4#95×D7912yes—
832C4#95×D7912yes—
833C4C2×C42×D7911yescharacteristic
834C4C2×C22⋊C4×D7911yescharacteristic
835C4C2×C4⋊C4×D7911yescharacteristic
836C4C2×C4⋊C4×D7911yescharacteristic
837C2—21no—
838C2—22no—
839C2—22no—
840C2—21no—
841C2—794no—
842C2—1582no—
843C2—1582no—
844C2—1582no—
845C2C2×#95×D7911yescharacteristic
846C2#421×D7912yes—
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC4×C79C22×C42
FrattiniC22×C4C23×D79
FittingC79×#1733C2
socleC22×C79C22×C22⋊C4
prime radicalC24×D79D4
cosocleC22×C4×C79C24
hypercenter#1733D79
hypocenterC79C2×#1733
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #23763111C2semidirect
5. #23763110C2semidirect
6. #23763109C2semidirect
7. #23763108C2semidirect
8. #339×D79C2semidirect
9. C79×#1733C2semidirect
16. C2×M16×D79C4semidirect
23. C2×#14579119C4semidirect
33. #117×D79C4semidirect
34. #117×D79C4semidirect
35. #117×D79C4semidirect
39. C2×C4⋊C4×D79C4semidirect
44. #19098324C22semidirect
45. #19098323C22semidirect
46. #19098322C22semidirect
50. #339×C79C22semidirect
73. C2×#11929608C2×C4semidirect
82. M16×D79C2×C4semidirect
83. M16×D79C2×C4semidirect
91. #14579120C2×C4semidirect
92. #14579120C2×C4semidirect
98. #14579119C2×C4semidirect
104. #14579118C2×C4semidirect
111. C2×C4⋊Dic79C2×C4semidirect
118. C4⋊C4×D79C2×C4semidirect
137. C42×D79C2×C4semidirect
141. C2×M16×C79C2×C4semidirect
147. #117×C79C2×C4semidirect
148. #117×C79C2×C4semidirect
151. C2×C4⋊C4×C79C2×C4semidirect
226. #11929608C22×C4semidirect
251. C4×Dic79C22×C4semidirect
267. M16×C79C22×C4semidirect
279. C42×C79C22×C4semidirect
423. D79#1733direct (N × H)
431. #1733D79direct (N × H)
433. C79C2×#1733semidirect
474. #339C2×D79semidirect
511. C2×M16C4×D79semidirect
543. #117C4×D79semidirect
544. #117C4×D79semidirect
556. C2×C4⋊C4C4×D79semidirect
668. M16C2×C4×D79semidirect
703. C42C2×C4×D79semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D792
C2×#117×D792
#237631112
#237631102
#237631092
#237631082
#339×D792
C79×#17332
C2×#173379