Finite Group Databasebeta

← #34310854

Subgroups — #34310854

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×#19098792C211yesmaximal, characteristic
2C2×C4×#11929613C211yesmaximal, characteristic, complemented
3C22×#14579093C211yesmaximal, characteristic, complemented
4#23766414C211yesmaximal, characteristic
5#23766403C211yesmaximal, characteristic, complemented
6#23764254C211yesmaximal, characteristic, complemented
7#23764128C211yesmaximal, characteristic, complemented
8#23764035C211yesmaximal, characteristic, complemented
9#23764028C211yesmaximal, characteristic, complemented
10#23763715C211yesmaximal, characteristic
11#23763705C211yesmaximal, characteristic, complemented
12#23763671C211yesmaximal, characteristic, complemented
13#23763664C211yesmaximal, characteristic, complemented
14C4×#14579093C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C79C211yesmaximal, characteristic, complemented
16C22×#11929613C2211yescharacteristic
17C2×#14579140C2211yescharacteristic
18C2×#14579135C2211yescharacteristic
19C2×C4×Dic158C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic
21C2×(C22⋊D79)⋊C4—21no—
22C22×C4⋊Dic79C2211yescharacteristic
23C22×C4⋊Dic79C2211yescharacteristic
24#19098792C418yescomplemented
25C4×#11929613—24no—
26C2×#14579093—24no—
27C2×#14579093C2211yescharacteristic
28C2×#14579093C2211yescharacteristic
29C2×#14579093C2211yescharacteristic
30C2×#14579093C2211yescharacteristic
31C2×#14579093C2211yescharacteristic
32C2×#14579086C2211yescharacteristic
33C2×#14579086C2211yescharacteristic
34C2×#14579086C2211yescharacteristic
35C2×#14579083C2211yescharacteristic
36C2×#14579083C2211yescharacteristic
37C2×#14579083C2211yescharacteristic
38#19098469C2211yescharacteristic
39#19098465C2211yescharacteristic
40#19098461C2211yescharacteristic
41#19098461C2211yescharacteristic
42#19098460—21no—
43#19098455—21no—
44#19098450—21no—
45#19098440—21no—
46#19098437—21no—
47#19098435—21no—
48C4×C4⋊Dic79C2211yescharacteristic
49C4×C4⋊Dic79C2211yescharacteristic
50C22⋊C4×Dic79—21no—
51#19098326C2211yescharacteristic
52#19098326C2211yescharacteristic
53#19098326C2211yescharacteristic
54#19098326C2211yescharacteristic
55C23×C8×C79C2211yescharacteristic
56C2×C22⋊C8×C79C2211yescharacteristic
57C2×C4×C8×C79C2211yescharacteristic
58C2×C4×C8×C79C2211yescharacteristic
59C4×C22⋊C4×C79C2211yescharacteristic
60#336×C79C2211yescharacteristic
61#336×C79C2211yescharacteristic
62C22×Dic158C2311yescharacteristic
63C22×D316C2311yescharacteristic
64C22×C22⋊D79—21no—
65C23×Dic79—21no—
66C23×Dic79—21no—
67C22×C4×D79—21no—
68C2×#11929613—22no—
69C2×#11929613—22no—
70C2×#11929613C2×C414yescomplemented
71#14579140—22no—
72#14579140C2×C414yescomplemented
73#14579135—22no—
74#14579135C2×C414yes—
75C4×Dic158—22no—
76C4×Dic158—41no—
77C4×D316—22no—
78C4×D316—41no—
79(C22⋊D79)⋊C4—44no—
80C2×C4⋊Dic79—22no—
81C2×C4⋊Dic79—22no—
82C2×C4⋊Dic79—21no—
83C2×C4⋊Dic79—21no—
84C2×C4⋊Dic79—41no—
85C2×C4⋊Dic79—41no—
86C2×C4⋊Dic79C2311yescharacteristic
87C2×C4⋊Dic79C2311yescharacteristic
88C2×C4⋊Dic79C2311yescharacteristic
89C2×C4⋊Dic79C2311yescharacteristic
90C2×C4⋊Dic79C2311yescharacteristic
91C2×C4⋊Dic79C2311yescharacteristic
92C2×Dic79⋊C4—21no—
93C2×Dic79⋊C4—21no—
94C2×Dic79⋊C4—21no—
95C2×Dic79⋊C4—21no—
96C2×C22⋊Dic79—21no—
97C2×(C2×D79)⋊C4—21no—
98C2×(C2×D79)⋊C4—21no—
99C2×(C2×D79)⋊C4—21no—
100C2×(C2×D79)⋊C4—21no—
101C2×C4×Dic79—21no—
102C2×C4×Dic79—21no—
103C2×C4×Dic79—21no—
104#14579093—22no—
105#14579093—22no—
106#14579093—22no—
107#14579093C2×C414yescomplemented
108#14579093D414yescomplemented
109#14579086—22no—
110#14579086—41no—
111#14579086C2×C414yescomplemented
112#14579083—22no—
113#14579083—41no—
114#14579083C2×C414yescomplemented
115C79⋊#95—21no—
116C79⋊#95—21no—
117C79⋊#95—21no—
118C79⋊#95—21no—
119C79⋊#95—21no—
120C79⋊#95—21no—
121C23×C4×C79C2311yescharacteristic
122C22×C8×C79—22no—
123C22×C8×C79—22no—
124C22×C8×C79C2×C414yescomplemented
125C22×C8×C79C2311yescharacteristic
126C22×C8×C79C2311yescharacteristic
127C22×C8×C79C2311yescharacteristic
128C22×C8×C79C2311yescharacteristic
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133C22⋊C8×C79—22no—
134C4×C8×C79—22no—
135C4×C8×C79—22no—
136#95×C79D411yescharacteristic
137#95×C79D411yescharacteristic
138C23×D79—21no—
139C2×Dic158—21no—
140C2×Dic158—21no—
141C2×Dic158—21no—
142C2×Dic158—21no—
143C2×Dic158—21no—
144C2×Dic158C22×C412yes—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316C22×C412yes—
151C2×C22⋊D79—24no—
152C2×C22⋊D79—42no—
153C2×C22⋊D79—42no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C22×Dic79—21no—
157C22×Dic79—21no—
158C22×Dic79—21no—
159C22×Dic79—21no—
160C22×Dic79—21no—
161C22×Dic79—42no—
162C22×Dic79—42no—
163C22×Dic79—42no—
164C22×Dic79—42no—
165C22×Dic79—81no—
166C22×Dic79—81no—
167C2×C4×D79—42no—
168C2×C4×D79—42no—
169C2×C4×D79—81no—
170#11929613—28no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79—21no—
177C4⋊Dic79—21no—
178C4⋊Dic79—21no—
179C4⋊Dic79—42no—
180C4⋊Dic79—42no—
181C4⋊Dic79C22×C412yes—
182C4⋊Dic79C22×C412yes—
183C4⋊Dic79C2×D412yes—
184C4⋊Dic79C2×D412yes—
185Dic79⋊C4—24no—
186Dic79⋊C4—42no—
187Dic79⋊C4—42no—
188Dic79⋊C4—81no—
189C22⋊Dic79—24no—
190(C2×D79)⋊C4—24no—
191(C2×D79)⋊C4—42no—
192(C2×D79)⋊C4—42no—
193(C2×D79)⋊C4—81no—
194C4×Dic79—42no—
195C4×Dic79—42no—
196C4×Dic79—81no—
197C24×C79C2×D411yescharacteristic
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×D411yescharacteristic
205C22×C4×C79C2×D411yescharacteristic
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79#4112yes—
209C22×C4×C79C2411yescharacteristic
210C2×C8×C79—28no—
211C2×C8×C79—21no—
212C2×C8×C79—21no—
213C2×C8×C79—21no—
214C2×C8×C79—21no—
215C2×C8×C79—21no—
216C2×C8×C79—21no—
217C2×C8×C79—21no—
218C2×C8×C79—21no—
219C2×C8×C79C22×C412yes—
220C2×C8×C79C22×C412yes—
221C2×C8×C79C2×D412yes—
222C2×C8×C79#4112yes—
223C22⋊C4×C79—22no—
224C22⋊C4×C79SD1614yescomplemented
225C42×C79—21no—
226C42×C79—21no—
227C42×C79—21no—
228C42×C79—21no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79C4×D412yes—
234C23×C79C2×SD1612yes—
235C23×C79#13512yes—
236C23×C79C22×D411yescharacteristic
237C22×D79—22no—
238C22×D79—41no—
239C22×D79—41no—
240C22×D79—41no—
241C22×D79—41no—
242C22×D79—41no—
243C22×D79—41no—
244C2×C4×C79—21no—
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
249C2×C4×C79—21no—
250C2×C4×C79—22no—
251C2×C4×C79—22no—
252C2×C4×C79—22no—
253C2×C4×C79—22no—
254C2×C4×C79—21no—
255C2×C4×C79—21no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79C4×D412yes—
261C2×C4×C79C2×SD1612yes—
262C2×C4×C79C2×SD1612yes—
263C2×C4×C79C23×C411yescharacteristic
264C2×C4×C79C22×D411yescharacteristic
265C2×C4×C79C2×#4111yescharacteristic
266C2×C4×C79C2×#4111yescharacteristic
267C2×C4×C79H(5,𝔽2)11yescharacteristic
268C2×C4×C792−1+411yescharacteristic
269C22⋊D79—48no—
270C2×Dic79—22no—
271C2×Dic79—22no—
272C2×Dic79—22no—
273C2×Dic79—22no—
274C2×Dic79—22no—
275C2×Dic79—41no—
276C2×Dic79—41no—
277C2×Dic79—41no—
278C2×Dic79—41no—
279C2×Dic79—41no—
280C2×Dic79—41no—
281C2×Dic79—41no—
282C2×Dic79—41no—
283C2×Dic79—41no—
284C2×Dic79—41no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—41no—
290C2×Dic79—41no—
291C2×Dic79—84no—
292C2×Dic79—84no—
293D316—22no—
294D316—22no—
295D316—41no—
296D316—41no—
297C4×D79—84no—
298Dic158—22no—
299Dic158—22no—
300Dic158—41no—
301Dic158—41no—
302C8×C79—22no—
303C8×C79—41no—
304C8×C79—41no—
305C8×C79C4×D414yescomplemented
306C22×C79—22no—
307C22×C79—22no—
308C22×C79—22no—
309C22×C79—22no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79C4×SD1614yescomplemented
313C22×C79C2×C4×D411yescharacteristic
314C22×C79D4211yescharacteristic
315C22×C79#54711yescharacteristic
316C22×C79C22×SD1611yescharacteristic
317C22×C79C2×#13511yescharacteristic
318C22×C79#57711yescharacteristic
319C22×C79#57711yescharacteristic
320C2×D79—42no—
321C2×D79—42no—
322C2×D79—42no—
323C2×D79—81no—
324C2×D79—81no—
325C2×D79—81no—
326C2×D79—81no—
327C4×C79—22no—
328C4×C79—22no—
329C4×C79—22no—
330C4×C79—41no—
331C4×C79—41no—
332C4×C79C2×C4×D411yescharacteristic
333C4×C79#52011yescharacteristic
334C4×C79#54811yescharacteristic
335C4×C79#55311yescharacteristic
336Dic79—42no—
337Dic79—42no—
338Dic79—42no—
339Dic79—42no—
340Dic79—42no—
341Dic79—81no—
342Dic79—81no—
343#23022—791nomaximal, Sylow
344C2×C79—24no—
345C2×C79#236111yescharacteristic
346C2×C79C2×C4×SD1611yescharacteristic
347C2×C79#295211yescharacteristic
348C2×C79D4×SD1611yescharacteristic
349C2×C79#328211yescharacteristic
350C2×C79#333511yescharacteristic
351C2×C79#333711yescharacteristic
352D79—82no—
353C2×#465—791no—
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⋊C4D7911yescharacteristic, complemented
368C79#2302211yescharacteristic, complemented, Sylow
369C22×SD16—791no—
370C23×C8C2×D7911yescharacteristic
371C2×C22⋊Q8—791no—
372C2×#121—791no—
373C2×C4×Q8—791no—
374C2×C4×D4—791no—
375C2×C4×D4—1581no—
376C22×C4⋊C4—791no—
377C22×C4⋊C4—791no—
378#465—798no—
379C4×SD16—1584no—
380C2×#106—791no—
381C2×#106—791no—
382C2×#106—791no—
383C2×#106—791no—
384C2×#106—791no—
385C2×#106—1584no—
386C2×#103—791no—
387C2×#103—791no—
388C2×#103—791no—
389C2×#102—791no—
390C2×#102—791no—
391C2×#102—791no—
392C2×C22⋊C8C2×D7911yescharacteristic
393C2×C4×C8C2×D7911yescharacteristic
394C2×C4×C8C2×D7911yescharacteristic
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—1581no—
408C4×C22⋊C4C2×D7911yescharacteristic
409#340—791no—
410#340—791no—
411#340—791no—
412#340—791no—
413#336C2×D7911yescharacteristic
414#336C2×D7911yescharacteristic
415C22×Q8—791no—
416C22×D4—791no—
417C22×D4—1581no—
418C23×C4—1581no—
419C23×C4—1581no—
420C23×C4—1581no—
421C23×C4C22×D7911yescharacteristic
422C2×SD16—794no—
423C2×SD16—1582no—
424C2×SD16—1582no—
425C22×C8—22no—
426C22×C8—22no—
427C22×C8C4×D7914yescomplemented
428C22×C8C22×D7911yescharacteristic
429C22×C8C22×D7911yescharacteristic
430C22×C8C22×D7911yescharacteristic
431C22×C8C22×D7911yescharacteristic
432C22⋊Q8—794no—
433C22⋊Q8—1582no—
434#121—794no—
435#121—1582no—
436C4×Q8—3161no—
437C4×Q8—1582no—
438C4×D4—3161no—
439C4×D4—3164no—
440C4×D4—1582no—
441C2×C4⋊C4—3161no—
442C2×C4⋊C4—3161no—
443C2×C4⋊C4—791no—
444C2×C4⋊C4—791no—
445C2×C4⋊C4—791no—
446C2×C4⋊C4—791no—
447C2×C4⋊C4—791no—
448C2×C4⋊C4—791no—
449C2×C4⋊C4—1581no—
450C2×C4⋊C4—1581no—
451C2×C4⋊C4—1581no—
452C2×C4⋊C4—1581no—
453C2×C4⋊C4—1582no—
454C2×C4⋊C4—1582no—
455C2×C4⋊C4—1581no—
456C2×C4⋊C4—1581no—
457C2×C22⋊C4—1581no—
458C2×C22⋊C4—1581no—
459C2×C22⋊C4—1581no—
460C2×C22⋊C4—1581no—
461C2×C22⋊C4—1581no—
462C2×C22⋊C4D31611yescharacteristic
463C2×C22⋊C4D31611yescharacteristic
464C2×C42—1581no—
465C2×C42—1581no—
466C2×C42—1581no—
467C2×C42C22×D7911yescharacteristic
468C2×C42C22×D7911yescharacteristic
469#106—794no—
470#106—794no—
471#106—1582no—
472#106—1582no—
473#106—1582no—
474#103—3161no—
475#103—794no—
476#103—1582no—
477#102—3161no—
478#102—794no—
479#102—1582no—
480C22⋊C8—22no—
481C4×C8—22no—
482C4×C8—22no—
483#95—1581no—
484#95—1581no—
485#95—1581no—
486#95—1581no—
487#95—1581no—
488#95—1581no—
489#95D31611yescharacteristic
490#95D31611yescharacteristic
491C24—1581no—
492C24C2×D31611yescharacteristic
493C2×Q8—792no—
494C2×Q8—1581no—
495C2×Q8—1581no—
496C2×Q8—1581no—
497C2×Q8—1581no—
498C2×Q8—1581no—
499C2×D4—3162no—
500C2×D4—3162no—
501C2×D4—792no—
502C2×D4—1584no—
503C2×D4—1581no—
504C2×D4—1581no—
505C2×D4—1581no—
506C2×D4—1581no—
507C2×D4—1581no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—3162no—
513C22×C4—3162no—
514C22×C4—3162no—
515C22×C4—3162no—
516C22×C4—3162no—
517C22×C4—3162no—
518C22×C4—6321no—
519C22×C4—6321no—
520C22×C4—6321no—
521C22×C4—1581no—
522C22×C4—1581no—
523C22×C4—1581no—
524C22×C4—1581no—
525C22×C4—1581no—
526C22×C4—1581no—
527C22×C4—1581no—
528C22×C4C2×C4×D7912yes—
529C22×C4C2×D31611yescharacteristic
530C22×C4C2×D31611yescharacteristic
531C22×C4C2×D31611yescharacteristic
532C22×C4C2×D31611yescharacteristic
533C22×C4C2×D31611yescharacteristic
534C22×C4#1192962412yes—
535C22×C4C23×D7911yescharacteristic
536SD16—1588no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C2×C4×D7912yes—
547C2×C8C2×C4×D7912yes—
548C2×C8D4×D7912yes—
549C2×C8#1192962312yes—
550C4⋊C4—3162no—
551C4⋊C4—3162no—
552C4⋊C4—3162no—
553C4⋊C4—3162no—
554C4⋊C4—792no—
555C4⋊C4—792no—
556C4⋊C4—792no—
557C4⋊C4—792no—
558C4⋊C4—6321no—
559C4⋊C4—1581no—
560C4⋊C4—1581no—
561C4⋊C4—1581no—
562C4⋊C4—1581no—
563C4⋊C4—1581no—
564C4⋊C4—1581no—
565C4⋊C4—1581no—
566C4⋊C4—1581no—
567C4⋊C4—1584no—
568C22⋊C4—22no—
569C22⋊C4—3162no—
570C22⋊C4—3162no—
571C22⋊C4—6321no—
572C22⋊C4—1584no—
573C22⋊C4—1584no—
574C22⋊C4#1192961314yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—3162no—
580C42—3162no—
581C42—6321no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—3161no—
587C23—3161no—
588C23—3161no—
589C23—3161no—
590C23—3161no—
591C23—3161no—
592C23—1582no—
593C23C4×D31612yes—
594C23C2×#1192961312yes—
595C23#1457918312yes—
596C23C22×D31611yescharacteristic
597Q8—3161no—
598Q8—3161no—
599Q8—1582no—
600Q8—1582no—
601D4—3168no—
602D4—3161no—
603D4—3161no—
604D4—1582no—
605D4—1582no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
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—3161no—
632C2×C4—3161no—
633C2×C4—3161no—
634C2×C4—3161no—
635C2×C4—3161no—
636C2×C4—3161no—
637C2×C4—3161no—
638C2×C4—6324no—
639C2×C4—6324no—
640C2×C4—6324no—
641C2×C4—1582no—
642C2×C4—1582no—
643C2×C4—1582no—
644C2×C4—1582no—
645C2×C4—1582no—
646C2×C4C4×D31612yes—
647C2×C4C2×#1192961312yes—
648C2×C4C2×#1192961312yes—
649C2×C4C22×C4×D7911yescharacteristic
650C2×C4C2×D4×D7911yescharacteristic
651C2×C4C2×#1192962311yescharacteristic
652C2×C4C2×#1192962411yescharacteristic
653C2×C4#1457920711yescharacteristic
654C2×C4#1457920811yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8(C22⋊D79)⋊C414yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—3162no—
666C22—3162no—
667C22—3162no—
668C22—6321no—
669C22—6321no—
670C22—6321no—
671C22—6321no—
672C22C4×#1192961314yescomplemented
673C22C2×C4×D31611yescharacteristic
674C22D4×D31611yescharacteristic
675C22#1909921711yescharacteristic
676C22C22×#1192961311yescharacteristic
677C22C2×#1457918311yescharacteristic
678C22#1909937511yescharacteristic
679C22#1909937511yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—41no—
685C4—3162no—
686C4—3162no—
687C4—3162no—
688C4—3162no—
689C4—3162no—
690C4—6321no—
691C4—6321no—
692C4C2×(C22⋊D79)⋊C411yescharacteristic
693C4#1909904311yescharacteristic
694C4#1909922211yescharacteristic
695C4#1909925911yescharacteristic
696C2—24no—
697C2—6322no—
698C2#2376641411yescharacteristic
699C2C2×C4×#1192961311yescharacteristic
700C2#2377228511yescharacteristic
701C2D4×#1192961311yescharacteristic
702C2#2377511211yescharacteristic
703C2#2377575811yescharacteristic
704C2#2377578111yescharacteristic
subgroupG/H
centerC23C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC8×C22⋊C4×C79C2
socleC23×C79C22×D4
prime radicalC2×#14579135C22
cosocleC22×C4×C79C24
hypercenterC8×C22⋊C4D79
hypocenterC79#23022
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11929613C2semidirect
3. C22×#14579093C2semidirect
5. #23766403C2semidirect
6. #23764254C2semidirect
7. #23764128C2semidirect
8. #23764035C2semidirect
9. #23764028C2semidirect
11. #23763705C2semidirect
12. #23763671C2semidirect
13. #23763664C2semidirect
14. C4×#14579093C2semidirect
15. C8×C22⋊C4×C79C2semidirect
24. #19098792C4semidirect
70. C2×#11929613C2×C4semidirect
72. #14579140C2×C4semidirect
107. #14579093C2×C4semidirect
108. #14579093D4semidirect
111. #14579086C2×C4semidirect
114. #14579083C2×C4semidirect
124. C22×C8×C79C2×C4semidirect
224. C22⋊C4×C79SD16semidirect
305. C8×C79C4×D4semidirect
312. C22×C79C4×SD16semidirect
367. C8×C22⋊C4D79semidirect
368. C79#23022semidirect
427. C22×C8C4×D79semidirect
574. C22⋊C4#11929613semidirect
658. C8(C22⋊D79)⋊C4semidirect
672. C22C4×#11929613semidirect

Maximal subgroups

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

subgroupindex
C2×#190987922
C2×C4×#119296132
C22×#145790932
#237664142
#237664032
#237642542
#237641282
#237640352
#237640282
#237637152
#237637052
#237636712
#237636642
C4×#145790932
C8×C22⋊C4×C792
#2302279