Finite Group Databasebeta

← #34310862

Subgroups — #34310862

Order 20224.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic79C211yesmaximal, characteristic, complemented
2C22×#14579093C211yesmaximal, characteristic, complemented
3#23766420C211yesmaximal, characteristic
4#23766409C211yesmaximal, characteristic, complemented
5#23764256C211yesmaximal, characteristic, complemented
6#23764129C211yesmaximal, characteristic, complemented
7#23764036C211yesmaximal, characteristic, complemented
8#23764029C211yesmaximal, characteristic, complemented
9#23763718C211yesmaximal, characteristic
10#23763708C211yesmaximal, characteristic, complemented
11#23763670C211yesmaximal, characteristic, complemented
12#23763663C211yesmaximal, characteristic, complemented
13#106×Dic79C211yesmaximal, characteristic, complemented
14C8×C22⋊Dic79C211yesmaximal, characteristic, complemented
15C2×#465×C79C211yesmaximal, characteristic
16C2×Q8×Dic79C2211yescharacteristic
17C2×D4×Dic79—21no—
18C2×D4×Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21SD16×Dic79—24no—
22C2×#14579093—24no—
23C2×#14579093C2211yescharacteristic
24C2×#14579093C2211yescharacteristic
25C2×#14579093C2211yescharacteristic
26C2×#14579093C2211yescharacteristic
27C2×#14579085C2211yescharacteristic
28C2×#14579085C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×C22⋊(C79⋊C8)C2211yescharacteristic
32C2×C8×Dic79C2211yescharacteristic
33C2×C8×Dic79C2211yescharacteristic
34#19098470C2211yescharacteristic
35#19098466C2211yescharacteristic
36#19098462—21no—
37#19098462C2211yescharacteristic
38#19098462C2211yescharacteristic
39#19098456—21no—
40#19098449—21no—
41#19098443—21no—
42#19098438—21no—
43#19098438—21no—
44C4⋊C4×Dic79C2211yescharacteristic
45C4⋊C4×Dic79C2211yescharacteristic
46C22⋊C4×Dic79—21no—
47C4×C22⋊Dic79C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51#19098325C2211yescharacteristic
52#19098317C2211yescharacteristic
53#19098317C2211yescharacteristic
54C22×SD16×C79C2211yescharacteristic
55C23×C8×C79C2211yescharacteristic
56C2×C22⋊Q8×C79C2211yescharacteristic
57C2×#121×C79C2211yescharacteristic
58#465×C79C418yescomplemented
59C2×#106×C79C2211yescharacteristic
60C2×#103×C79C2211yescharacteristic
61C2×#102×C79C2211yescharacteristic
62C23×Dic79—21no—
63C23×Dic79—21no—
64C23×Dic79—21no—
65C22×C79⋊C8C2311yescharacteristic
66C22×C79⋊C8C2311yescharacteristic
67Q8×Dic79—22no—
68Q8×Dic79—41no—
69D4×Dic79—22no—
70D4×Dic79—41no—
71D4×Dic79—44no—
72C2×C4⋊Dic79—22no—
73C2×C4⋊Dic79—22no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79—21no—
78C2×C4⋊Dic79—21no—
79C2×C4⋊Dic79—41no—
80C2×C4⋊Dic79—41no—
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C22⋊Dic79—21no—
86C2×C22⋊Dic79—21no—
87C2×C22⋊Dic79—21no—
88C2×C22⋊Dic79D411yescharacteristic
89C2×C22⋊Dic79D411yescharacteristic
90C2×C4×Dic79—21no—
91C2×C4×Dic79—21no—
92C2×C4×Dic79—21no—
93C2×C4×Dic79C2311yescharacteristic
94C2×C4×Dic79C2311yescharacteristic
95#14579093—22no—
96#14579093—22no—
97#14579093—22no—
98#14579093D414yescomplemented
99#14579085—22no—
100#14579085—41no—
101#14579082—22no—
102#14579082—41no—
103C22⋊(C79⋊C8)—22no—
104C8×Dic79—22no—
105C8×Dic79—22no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C79⋊#95—21no—
111C79⋊#95—21no—
112C79⋊#95D411yescharacteristic
113C79⋊#95D411yescharacteristic
114C22×Q8×C79C2311yescharacteristic
115C22×D4×C79—21no—
116C22×D4×C79C2311yescharacteristic
117C23×C4×C79C2311yescharacteristic
118C2×SD16×C79—22no—
119C2×SD16×C79—22no—
120C2×SD16×C79C2×C414yescomplemented
121C22×C8×C79—22no—
122C22×C8×C79—22no—
123C22×C8×C79C2×C414yescomplemented
124C22×C8×C79C2311yescharacteristic
125C22×C8×C79C2311yescharacteristic
126C22⋊Q8×C79—22no—
127C22⋊Q8×C79C2×C414yescomplemented
128#121×C79—22no—
129#121×C79C2×C414yes—
130C2×C4⋊C4×C79—21no—
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79C2311yescharacteristic
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79—21no—
135#106×C79C2×C414yescomplemented
136#103×C79C2×C414yescomplemented
137#102×C79C2×C414yescomplemented
138C22×Dic79—21no—
139C22×Dic79—21no—
140C22×Dic79—21no—
141C22×Dic79—21no—
142C22×Dic79—42no—
143C22×Dic79—42no—
144C22×Dic79—42no—
145C22×Dic79—42no—
146C22×Dic79—42no—
147C22×Dic79—42no—
148C22×Dic79—81no—
149C22×Dic79—81no—
150C22×Dic79—81no—
151C22×Dic79C2×D411yescharacteristic
152C22×Dic79C2×D411yescharacteristic
153C22×Dic79C2×D411yescharacteristic
154C22×Dic79C2×D411yescharacteristic
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—42no—
168C4⋊Dic79—42no—
169C4⋊Dic79—42no—
170C4⋊Dic79—42no—
171C4⋊Dic79—81no—
172C4⋊Dic79C2×D412yes—
173C4⋊Dic79C2×D412yes—
174C22⋊Dic79—22no—
175C22⋊Dic79—42no—
176C22⋊Dic79—42no—
177C22⋊Dic79—81no—
178C22⋊Dic79SD1614yescomplemented
179C4×Dic79—21no—
180C4×Dic79—21no—
181C4×Dic79—21no—
182C4×Dic79—21no—
183C4×Dic79—42no—
184C4×Dic79—42no—
185C4×Dic79—81no—
186C24×C79—21no—
187C24×C79C2×D411yescharacteristic
188C2×Q8×C79—21no—
189C2×Q8×C79—21no—
190C2×Q8×C79—21no—
191C2×Q8×C79—21no—
192C2×Q8×C79—21no—
193C2×Q8×C79C22×C412yes—
194C2×D4×C79—24no—
195C2×D4×C79—21no—
196C2×D4×C79—21no—
197C2×D4×C79—21no—
198C2×D4×C79—21no—
199C2×D4×C79—21no—
200C2×D4×C79—42no—
201C2×D4×C79—42no—
202C2×D4×C79C22×C412yes—
203C22×C4×C79—21no—
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×C79C22×C412yes—
211C22×C4×C79C2×D411yescharacteristic
212C22×C4×C79#4112yes—
213C22×C4×C79C2411yescharacteristic
214SD16×C79—28no—
215C2×C8×C79—28no—
216C2×C8×C79—21no—
217C2×C8×C79—21no—
218C2×C8×C79C22×C412yes—
219C2×C8×C79C22×C412yes—
220C2×C8×C79C2×D412yes—
221C2×C8×C79#4112yes—
222C4⋊C4×C79—24no—
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79C22×C412yes—
226C4⋊C4×C79C22×C412yes—
227C22⋊C4×C79—24no—
228C22⋊C4×C79—24no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79—22no—
234C23×C79—41no—
235C23×C79—41no—
236C23×C79—41no—
237C23×C79—41no—
238C23×C79—41no—
239C23×C79—41no—
240C23×C79C4×D412yes—
241C23×C79C2×SD1612yes—
242C23×C79#13512yes—
243C23×C79C22×D411yescharacteristic
244Q8×C79—22no—
245Q8×C79—22no—
246Q8×C79—41no—
247Q8×C79—41no—
248D4×C79—22no—
249D4×C79—22no—
250D4×C79—48no—
251D4×C79—41no—
252D4×C79—41no—
253C2×C4×C79—21no—
254C2×C4×C79—21no—
255C2×C4×C79—22no—
256C2×C4×C79—22no—
257C2×C4×C79—22no—
258C2×C4×C79—22no—
259C2×C4×C79—22no—
260C2×C4×C79—22no—
261C2×C4×C79—22no—
262C2×C4×C79—41no—
263C2×C4×C79—41no—
264C2×C4×C79—41no—
265C2×C4×C79—41no—
266C2×C4×C79—41no—
267C2×C4×C79—41no—
268C2×C4×C79C4×D412yes—
269C2×C4×C79C23×C411yescharacteristic
270C2×C4×C79C22×D411yescharacteristic
271C2×C4×C79C2×#4111yescharacteristic
272C2×C4×C79C2×#4111yescharacteristic
273C2×C4×C79H(5,𝔽2)11yescharacteristic
274C2×C4×C792−1+411yescharacteristic
275C2×Dic79—21no—
276C2×Dic79—21no—
277C2×Dic79—21no—
278C2×Dic79—21no—
279C2×Dic79—21no—
280C2×Dic79—22no—
281C2×Dic79—22no—
282C2×Dic79—21no—
283C2×Dic79—21no—
284C2×Dic79—21no—
285C2×Dic79—21no—
286C2×Dic79—21no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—41no—
292C2×Dic79—41no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297C2×Dic79—84no—
298C2×Dic79—84no—
299C2×Dic79—84no—
300C2×Dic79C2×SD1612yes—
301C2×Dic79C2×SD1612yes—
302C8×C79—22no—
303C8×C79C4×D414yescomplemented
304C79⋊C8—41no—
305C79⋊C8—41no—
306C22×C79—22no—
307C22×C79—22no—
308C22×C79—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79—42no—
313C22×C79—42no—
314C22×C79—42no—
315C22×C79—81no—
316C22×C79—81no—
317C22×C79—81no—
318C22×C79—81no—
319C22×C79C4×SD1614yescomplemented
320C22×C79C2×C4×D411yescharacteristic
321C22×C79D4211yescharacteristic
322C22×C79#54711yescharacteristic
323C22×C79C22×SD1611yescharacteristic
324C22×C79C2×#13511yescharacteristic
325C22×C79#57711yescharacteristic
326C22×C79#57711yescharacteristic
327C4×C79—22no—
328C4×C79—42no—
329C4×C79—42no—
330C4×C79—42no—
331C4×C79C2×C4×D411yescharacteristic
332C4×C79#52011yescharacteristic
333C4×C79#54811yescharacteristic
334C4×C79#55311yescharacteristic
335Dic79—22no—
336Dic79—22no—
337Dic79—41no—
338Dic79—42no—
339Dic79—41no—
340Dic79—42no—
341Dic79—81no—
342Dic79—81no—
343#23022—791nomaximal, Sylow
344C2×C79—24no—
345C2×C79—82no—
346C2×C79#236111yescharacteristic
347C2×C79C2×C4×SD1611yescharacteristic
348C2×C79#295211yescharacteristic
349C2×C79D4×SD1611yescharacteristic
350C2×C79#328211yescharacteristic
351C2×C79#333511yescharacteristic
352C2×C79#333711yescharacteristic
353C2×#465D7911yescharacteristic
354C2×C4×SD16—791no—
355C22×#106—791no—
356#2361—791no—
357#2360—791no—
358#1968—791no—
359#1941—791no—
360#1927—791no—
361#1926—791no—
362#1874—791no—
363#1872—791no—
364#1865—791no—
365#1864—791no—
366C4×#106—791no—
367C8×C22⋊C4—791no—
368C79#2302211yescharacteristic, complemented, Sylow
369C22×SD16C2×D7911yescharacteristic
370C23×C8C2×D7911yescharacteristic
371C2×C22⋊Q8C2×D7911yescharacteristic
372C2×#121C2×D7911yescharacteristic
373C2×C4×Q8—791no—
374C2×C4×D4—791no—
375C2×C4×D4—1581no—
376C22×C4⋊C4—791no—
377C22×C4⋊C4—791no—
378#465Dic7918yescomplemented
379C4×SD16—1584no—
380C2×#106—791no—
381C2×#106—791no—
382C2×#106—791no—
383C2×#106—791no—
384C2×#106—1584no—
385C2×#106C2×D7911yescharacteristic
386C2×#103—791no—
387C2×#103—791no—
388C2×#103C2×D7911yescharacteristic
389C2×#102—791no—
390C2×#102—791no—
391C2×#102C2×D7911yescharacteristic
392C2×C22⋊C8—791no—
393C2×C4×C8—791no—
394C2×C4×C8—791no—
395#391—791no—
396#390—791no—
397#389—791no—
398#389—791no—
399#389—1581no—
400#388—1581no—
401#387—1581no—
402#386—1581no—
403#385—1581no—
404#385—1581no—
405C4×C4⋊C4—791no—
406C4×C4⋊C4—791no—
407C4×C22⋊C4—791no—
408C4×C22⋊C4—1581no—
409#340—791no—
410#340—791no—
411#340—791no—
412#340—791no—
413#336—791no—
414#336—791no—
415C22×Q8C22×D7911yescharacteristic
416C22×D4—21no—
417C22×D4C22×D7911yescharacteristic
418C23×C4—1581no—
419C23×C4—1581no—
420C23×C4—1581no—
421C23×C4C22×D7911yescharacteristic
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16C2×Dic7914yescomplemented
425C22×C8—22no—
426C22×C8—22no—
427C22×C8—791no—
428C22×C8—791no—
429C22×C8C2×Dic7914yescomplemented
430C22×C8C22×D7911yescharacteristic
431C22×C8C22×D7911yescharacteristic
432C22⋊Q8—22no—
433C22⋊Q8C2×Dic7914yescomplemented
434#121—22no—
435#121C2×Dic7914yes—
436C4×Q8—3161no—
437C4×Q8—1582no—
438C4×D4—3164no—
439C4×D4—3161no—
440C4×D4—1582no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—3161no—
443C2×C4⋊C4—3161no—
444C2×C4⋊C4—791no—
445C2×C4⋊C4—791no—
446C2×C4⋊C4—791no—
447C2×C4⋊C4—791no—
448C2×C4⋊C4—1581no—
449C2×C4⋊C4—1581no—
450C2×C4⋊C4—1581no—
451C2×C4⋊C4—1581no—
452C2×C4⋊C4—1582no—
453C2×C4⋊C4—1582no—
454C2×C4⋊C4—1581no—
455C2×C4⋊C4C22×D7911yescharacteristic
456C2×C4⋊C4C22×D7911yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—791no—
460C2×C22⋊C4—791no—
461C2×C22⋊C4—1581no—
462C2×C22⋊C4—1581no—
463C2×C22⋊C4—1581no—
464C2×C42—791no—
465C2×C42—791no—
466C2×C42—1581no—
467C2×C42—1581no—
468C2×C42—1581no—
469#106—794no—
470#106—1582no—
471#106—1582no—
472#106—1582no—
473#106C2×Dic7914yescomplemented
474#103—3161no—
475#103—1582no—
476#103C2×Dic7914yescomplemented
477#102—3161no—
478#102—1582no—
479#102C2×Dic7914yescomplemented
480C22⋊C8—1582no—
481C4×C8—1582no—
482C4×C8—1582no—
483#95—791no—
484#95—791no—
485#95—1581no—
486#95—1581no—
487#95—1581no—
488#95—1581no—
489#95—1581no—
490#95—1581no—
491C24—21no—
492C24D4×D7911yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×Dic7912yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×Dic7912yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—3162no—
516C22×C4—3162no—
517C22×C4—3162no—
518C22×C4—3162no—
519C22×C4—3162no—
520C22×C4—3162no—
521C22×C4—791no—
522C22×C4—791no—
523C22×C4—791no—
524C22×C4—791no—
525C22×C4—6321no—
526C22×C4—6321no—
527C22×C4—6321no—
528C22×C4—1581no—
529C22×C4—1581no—
530C22×C4—1581no—
531C22×C4—1581no—
532C22×C4C22×Dic7912yes—
533C22×C4D4×D7911yescharacteristic
534C22×C4#1192962312yes—
535C22×C4C23×D7911yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—1581no—
541C2×C8—1581no—
542C2×C8—1581no—
543C2×C8—1581no—
544C2×C8—1581no—
545C2×C8—1581no—
546C2×C8C22×Dic7912yes—
547C2×C8C22×Dic7912yes—
548C2×C8D4×D7912yes—
549C2×C8#1192962312yes—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—24no—
553C4⋊C4—3162no—
554C4⋊C4—3162no—
555C4⋊C4—3162no—
556C4⋊C4—3162no—
557C4⋊C4—792no—
558C4⋊C4—792no—
559C4⋊C4—6321no—
560C4⋊C4—1581no—
561C4⋊C4—1581no—
562C4⋊C4—1581no—
563C4⋊C4—1581no—
564C4⋊C4—1581no—
565C4⋊C4—1581no—
566C4⋊C4C22×Dic7912yes—
567C4⋊C4C22×Dic7912yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—3162no—
571C22⋊C4—3162no—
572C22⋊C4—794no—
573C22⋊C4—6321no—
574C22⋊C4—1582no—
575C42—3162no—
576C42—3162no—
577C42—6321no—
578C42—1581no—
579C42—1581no—
580C42—1581no—
581C42—1581no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23D4×Dic7912yes—
594C23SD16×D7912yes—
595C23#1457918212yes—
596C23C2×D4×D7911yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—3161no—
622C2×C4—3161no—
623C2×C4—3161no—
624C2×C4—3161no—
625C2×C4—3161no—
626C2×C4—3161no—
627C2×C4—3161no—
628C2×C4—3161no—
629C2×C4—3161no—
630C2×C4—3161no—
631C2×C4—792no—
632C2×C4—792no—
633C2×C4—6324no—
634C2×C4—6324no—
635C2×C4—6324no—
636C2×C4—1582no—
637C2×C4—1581no—
638C2×C4—1582no—
639C2×C4—1581no—
640C2×C4—1581no—
641C2×C4—1581no—
642C2×C4—1581no—
643C2×C4—1581no—
644C2×C4—1581no—
645C2×C4—1581no—
646C2×C4—1581no—
647C2×C4—1581no—
648C2×C4D4×Dic7912yes—
649C2×C4C23×Dic7911yescharacteristic
650C2×C4C2×D4×D7911yescharacteristic
651C2×C4C2×#1192962311yescharacteristic
652C2×C4C2×#1192962311yescharacteristic
653C2×C4#1457920711yescharacteristic
654C2×C4#1457920811yescharacteristic
655C8—22no—
656C8—3161no—
657C8—3161no—
658C8D4×Dic7914yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22SD16×Dic7914yescomplemented
673C22C2×D4×Dic7911yescharacteristic
674C22#1909919711yescharacteristic
675C22#1909921311yescharacteristic
676C22C2×SD16×D7911yescharacteristic
677C22C2×#1457918211yescharacteristic
678C22#1909937011yescharacteristic
679C22#1909937011yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—3161no—
685C4—3162no—
686C4—3162no—
687C4—3161no—
688C4—6321no—
689C4—6321no—
690C4—1582no—
691C4—1582no—
692C4C2×D4×Dic7911yescharacteristic
693C4#1909904611yescharacteristic
694C4#1909921911yescharacteristic
695C4#1909926511yescharacteristic
696C2—24no—
697C2—82no—
698C2#2376642011yescharacteristic
699C2C2×SD16×Dic7911yescharacteristic
700C2#2377228411yescharacteristic
701C2#2377509311yescharacteristic
702C2#2377510411yescharacteristic
703C2#2377575211yescharacteristic
704C2#2377578511yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#465×C79C2
socleC23×C79C22×D4
prime radicalC2×#121×C79C22
cosocleC22×C4×C79C24
hypercenterC2×#465D79
hypocenterC79#23022
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic79C2semidirect
2. C22×#14579093C2semidirect
4. #23766409C2semidirect
5. #23764256C2semidirect
6. #23764129C2semidirect
7. #23764036C2semidirect
8. #23764029C2semidirect
10. #23763708C2semidirect
11. #23763670C2semidirect
12. #23763663C2semidirect
13. #106×Dic79C2semidirect
14. C8×C22⋊Dic79C2semidirect
58. #465×C79C4semidirect
98. #14579093D4semidirect
120. C2×SD16×C79C2×C4semidirect
123. C22×C8×C79C2×C4semidirect
127. C22⋊Q8×C79C2×C4semidirect
135. #106×C79C2×C4semidirect
136. #103×C79C2×C4semidirect
137. #102×C79C2×C4semidirect
178. C22⋊Dic79SD16semidirect
303. C8×C79C4×D4semidirect
319. C22×C79C4×SD16semidirect
368. C79#23022semidirect
378. #465Dic79semidirect
424. C2×SD16C2×Dic79semidirect
429. C22×C8C2×Dic79semidirect
433. C22⋊Q8C2×Dic79semidirect
473. #106C2×Dic79semidirect
476. #103C2×Dic79semidirect
479. #102C2×Dic79semidirect
658. C8D4×Dic79semidirect
672. C22SD16×Dic79semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic792
C22×#145790932
#237664202
#237664092
#237642562
#237641292
#237640362
#237640292
#237637182
#237637082
#237636702
#237636632
#106×Dic792
C8×C22⋊Dic792
C2×#465×C792
#2302279