Finite Group Databasebeta

← C83×#29460 #35257284

Subgroups — C83×#29460 #35257284

Order 21248.

912 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2854C211yesmaximal, characteristic, complemented
2C4×#121×C83C211yesmaximal, characteristic, complemented
3C83×#2075C211yesmaximal, characteristic, complemented
4C83×#2033C211yesmaximal, characteristic, complemented
5C83×#2033C211yesmaximal, characteristic, complemented
6C83×#1999C211yesmaximal, characteristic
7C83×#1970C211yesmaximal, characteristic, complemented
8C83×#1942C211yesmaximal, characteristic, complemented
9C83×#1934C211yesmaximal, characteristic, complemented
10C83×#1934C211yesmaximal, characteristic, complemented
11C83×#1925C211yesmaximal, characteristic, complemented
12C83×#1918C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1862C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C83C211yesmaximal, characteristic, complemented
16C22×D8×C83C2211yescharacteristic
17C2×#123×C83—21no—
18C2×#121×C83C2211yescharacteristic
19C2×#121×C83C2211yescharacteristic
20C2×C4×D4×C83—21no—
21C2×C4×D4×C83C2211yescharacteristic
22C22×C42×C83C2211yescharacteristic
23C2×#107×C83C2211yescharacteristic
24C2×#107×C83C2211yescharacteristic
25C2×#107×C83C2211yescharacteristic
26C2×#102×C83C2211yescharacteristic
27C2×#102×C83C2211yescharacteristic
28C2×#102×C83C2211yescharacteristic
29C2×#102×C83C2211yescharacteristic
30C2×#102×C83C2211yescharacteristic
31C2×#102×C83C2211yescharacteristic
32C2×C22⋊C8×C83C2211yescharacteristic
33C2×C22⋊C8×C83C2211yescharacteristic
34C2×C4×C8×C83C2211yescharacteristic
35C2×C4×C8×C83C2211yescharacteristic
36#390×C83C2211yescharacteristic
37#390×C83C2211yescharacteristic
38#390×C83C2211yescharacteristic
39#389×C83C2211yescharacteristic
40#389×C83C2211yescharacteristic
41#389×C83C2211yescharacteristic
42#388×C83—21no—
43#388×C83—21no—
44#388×C83—21no—
45#386×C83—21no—
46#386×C83—21no—
47#380×C83C2211yescharacteristic
48#380×C83C2211yescharacteristic
49C4×C4⋊C4×C83C2211yescharacteristic
50C4×C22⋊C4×C83—21no—
51#340×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×D4×C83—21no—
60C22×D4×C83—21no—
61C22×D4×C83C2311yescharacteristic
62C22×D4×C83C2311yescharacteristic
63C23×C4×C83—21no—
64C23×C4×C83D411yescharacteristic
65C23×C4×C83D411yescharacteristic
66C23×C4×C83C2311yescharacteristic
67C2×D8×C83—22no—
68C2×D8×C83—22no—
69C2×D8×C83—41no—
70C22×C8×C83C2311yescharacteristic
71C22×C8×C83C2311yescharacteristic
72C22×C8×C83C2311yescharacteristic
73C22×C8×C83C2311yescharacteristic
74#123×C83—44no—
75#121×C83—22no—
76#121×C83—22no—
77#121×C83—41no—
78#121×C83—41no—
79C4×D4×C83—41no—
80C4×D4×C83—41no—
81C4×D4×C83—44no—
82C2×C4⋊C4×C83—21no—
83C2×C4⋊C4×C83—21no—
84C2×C4⋊C4×C83—21no—
85C2×C4⋊C4×C83C2311yescharacteristic
86C2×C4⋊C4×C83C2311yescharacteristic
87C2×C4⋊C4×C83C2311yescharacteristic
88C2×C4⋊C4×C83C2311yescharacteristic
89C2×C4⋊C4×C83C2311yescharacteristic
90C2×C4⋊C4×C83C2311yescharacteristic
91C2×C22⋊C4×C83—21no—
92C2×C22⋊C4×C83—21no—
93C2×C22⋊C4×C83—21no—
94C2×C22⋊C4×C83—21no—
95C2×C22⋊C4×C83—21no—
96C2×C22⋊C4×C83—21no—
97C2×C22⋊C4×C83—21no—
98C2×C22⋊C4×C83—21no—
99C2×C22⋊C4×C83—21no—
100C2×C22⋊C4×C83—21no—
101C2×C22⋊C4×C83—21no—
102C2×C42×C83—21no—
103C2×C42×C83—41no—
104C2×C42×C83—41no—
105C2×C42×C83D411yescharacteristic
106C2×C42×C83D411yescharacteristic
107C2×C42×C83C2311yescharacteristic
108C2×C42×C83C2311yescharacteristic
109#107×C83—22no—
110#107×C83—22no—
111#107×C83—41no—
112#102×C83—22no—
113#102×C83—22no—
114#102×C83—22no—
115#102×C83—22no—
116#102×C83—41no—
117#102×C83—41no—
118C22⋊C8×C83—22no—
119C22⋊C8×C83—22no—
120C4×C8×C83—41no—
121C4×C8×C83—41no—
122#95×C83—21no—
123#95×C83—21no—
124#95×C83—21no—
125#95×C83—21no—
126#95×C83—21no—
127#95×C83—21no—
128C24×C83—21no—
129C24×C83—21no—
130C24×C83C2×D411yescharacteristic
131C2×D4×C83—24no—
132C2×D4×C83—21no—
133C2×D4×C83—21no—
134C2×D4×C83—21no—
135C2×D4×C83—21no—
136C2×D4×C83—21no—
137C2×D4×C83—21no—
138C2×D4×C83—21no—
139C2×D4×C83—21no—
140C2×D4×C83—21no—
141C2×D4×C83—21no—
142C2×D4×C83—21no—
143C2×D4×C83—42no—
144C2×D4×C83—42no—
145C2×D4×C83—42no—
146C2×D4×C83—42no—
147C2×D4×C83—42no—
148C2×D4×C83#4112yes—
149C22×C4×C83—21no—
150C22×C4×C83—22no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—41no—
163C22×C4×C83—41no—
164C22×C4×C83—41no—
165C22×C4×C83—41no—
166C22×C4×C83—42no—
167C22×C4×C83—42no—
168C22×C4×C83—42no—
169C22×C4×C83D814yescomplemented
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2411yescharacteristic
176D8×C83—44no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—21no—
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83#4112yes—
188C2×C8×C83#4112yes—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83—42no—
201C4⋊C4×C83—42no—
202C4⋊C4×C83—42no—
203C4⋊C4×C83#4112yes—
204C22⋊C4×C83—24no—
205C22⋊C4×C83—42no—
206C22⋊C4×C83—42no—
207C22⋊C4×C83—42no—
208C22⋊C4×C83—42no—
209C22⋊C4×C83—42no—
210C22⋊C4×C83—42no—
211C22⋊C4×C83—42no—
212C22⋊C4×C83—42no—
213C22⋊C4×C83—42no—
214C22⋊C4×C83—42no—
215C42×C83—21no—
216C42×C83—21no—
217C42×C83—21no—
218C42×C83—21no—
219C42×C83—41no—
220C42×C83—41no—
221C42×C83—42no—
222C23×C83—21no—
223C23×C83—21no—
224C23×C83—21no—
225C23×C83—21no—
226C23×C83—21no—
227C23×C83—21no—
228C23×C83—22no—
229C23×C83—41no—
230C23×C83—41no—
231C23×C83—41no—
232C23×C83—41no—
233C23×C83—41no—
234C23×C83—41no—
235C23×C83—41no—
236C23×C83—41no—
237C23×C83—41no—
238C23×C83—41no—
239C23×C83—41no—
240C23×C83—41no—
241C23×C83—41no—
242C23×C83C2×D812yes—
243C23×C83C22×D411yescharacteristic
244D4×C83—22no—
245D4×C83—22no—
246D4×C83—48no—
247D4×C83—41no—
248D4×C83—41no—
249D4×C83—41no—
250D4×C83—41no—
251D4×C83—41no—
252D4×C83—41no—
253D4×C83—84no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—22no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—44no—
268C2×C4×C83—44no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—41no—
286C2×C4×C83—41no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—84no—
291C2×C4×C83C2×D812yes—
292C2×C4×C83C2×D812yes—
293C2×C4×C83#13512yes—
294C2×C4×C83C2×#4111yescharacteristic
295C2×C4×C83C2×#4111yescharacteristic
296C2×C4×C83C2×#4111yescharacteristic
297C2×C4×C83C2×#4111yescharacteristic
298C2×C4×C83H(5,𝔽2)11yescharacteristic
299C2×C4×C83H(5,𝔽2)11yescharacteristic
300C8×C83—22no—
301C8×C83—22no—
302C8×C83—41no—
303C8×C83—41no—
304C22×C83—22no—
305C22×C83—22no—
306C22×C83—22no—
307C22×C83—41no—
308C22×C83—41no—
309C22×C83—41no—
310C22×C83—41no—
311C22×C83—42no—
312C22×C83—42no—
313C22×C83—42no—
314C22×C83—81no—
315C22×C83—81no—
316C22×C83—81no—
317C22×C83—81no—
318C22×C83—81no—
319C22×C83—81no—
320C22×C83—81no—
321C22×C83—81no—
322C22×C83—81no—
323C22×C83—81no—
324C22×C83—81no—
325C22×C83#52511yescharacteristic
326C22×C83#53211yescharacteristic
327C22×C83#53411yescharacteristic
328C22×C83C22×D811yescharacteristic
329C22×C83C2×#13511yescharacteristic
330C22×C83#57511yescharacteristic
331C22×C83#57511yescharacteristic
332C4×C83—22no—
333C4×C83—22no—
334C4×C83—22no—
335C4×C83—42no—
336C4×C83—41no—
337C4×C83—41no—
338C4×C83—81no—
339C4×C83—81no—
340C4×C83—81no—
341C4×C83—81no—
342C4×C83—81no—
343C4×C83#55111yescharacteristic
344C4×C83#55311yescharacteristic
345C4×C83#55311yescharacteristic
346C4×C83#55911yescharacteristic
347#29460C8311yesmaximal, characteristic, direct product factor, Sylow
348C2×C83—42no—
349C2×C83—82no—
350C2×C83—161no—
351C2×C83#260211yescharacteristic
352C2×C83#310011yescharacteristic
353C2×C83#310211yescharacteristic
354C2×C83#316911yescharacteristic
355C2×C83#318311yescharacteristic
356C2×C83#318611yescharacteristic
357C2×C83#319111yescharacteristic
358#2854C2×C8311yescharacteristic, complemented
359C4×#121C2×C8311yescharacteristic, complemented
360#2075C2×C8311yescharacteristic, complemented
361#2033C2×C8311yescharacteristic, complemented
362#2033C2×C8311yescharacteristic, complemented
363#1999C2×C8311yescharacteristic
364#1970C2×C8311yescharacteristic, complemented
365#1942C2×C8311yescharacteristic, complemented
366#1934C2×C8311yescharacteristic, complemented
367#1934C2×C8311yescharacteristic, complemented
368#1925C2×C8311yescharacteristic, complemented
369#1918C2×C8311yescharacteristic, complemented
370#1879C2×C8311yescharacteristic, complemented
371#1862C2×C8311yescharacteristic, complemented
372C4×C22⋊C8C2×C8311yescharacteristic, complemented
373C83#2946011yescharacteristic, direct product factor, Sylow
374C22×D8C22×C8311yescharacteristic
375C2×#123—21no—
376C2×#121C22×C8311yescharacteristic
377C2×#121C22×C8311yescharacteristic
378C2×C4×D4—21no—
379C2×C4×D4C22×C8311yescharacteristic
380C22×C42C22×C8311yescharacteristic
381C2×#107C22×C8311yescharacteristic
382C2×#107C22×C8311yescharacteristic
383C2×#107C22×C8311yescharacteristic
384C2×#102C22×C8311yescharacteristic
385C2×#102C22×C8311yescharacteristic
386C2×#102C22×C8311yescharacteristic
387C2×#102C22×C8311yescharacteristic
388C2×#102C22×C8311yescharacteristic
389C2×#102C22×C8311yescharacteristic
390C2×C22⋊C8C22×C8311yescharacteristic
391C2×C22⋊C8C22×C8311yescharacteristic
392C2×C4×C8C22×C8311yescharacteristic
393C2×C4×C8C22×C8311yescharacteristic
394#390C22×C8311yescharacteristic
395#390C22×C8311yescharacteristic
396#390C22×C8311yescharacteristic
397#389C22×C8311yescharacteristic
398#389C22×C8311yescharacteristic
399#389C22×C8311yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#386—21no—
404#386—21no—
405#380C22×C8311yescharacteristic
406#380C22×C8311yescharacteristic
407C4×C4⋊C4C22×C8311yescharacteristic
408C4×C22⋊C4—21no—
409#340C22×C8311yescharacteristic
410#340C22×C8311yescharacteristic
411#340C22×C8311yescharacteristic
412#340C22×C8311yescharacteristic
413#340C22×C8311yescharacteristic
414#340C22×C8311yescharacteristic
415#336C22×C8311yescharacteristic
416#336C22×C8311yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C8311yescharacteristic
420C22×D4C23×C8311yescharacteristic
421C23×C4—21no—
422C23×C4D4×C8311yescharacteristic
423C23×C4D4×C8311yescharacteristic
424C23×C4C23×C8311yescharacteristic
425C2×D8—22no—
426C2×D8—22no—
427C2×D8—41no—
428C22×C8C23×C8311yescharacteristic
429C22×C8C23×C8311yescharacteristic
430C22×C8C23×C8311yescharacteristic
431C22×C8C23×C8311yescharacteristic
432#123—44no—
433#121—22no—
434#121—22no—
435#121—41no—
436#121—41no—
437C4×D4—41no—
438C4×D4—41no—
439C4×D4—44no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4C23×C8311yescharacteristic
444C2×C4⋊C4C23×C8311yescharacteristic
445C2×C4⋊C4C23×C8311yescharacteristic
446C2×C4⋊C4C23×C8311yescharacteristic
447C2×C4⋊C4C23×C8311yescharacteristic
448C2×C4⋊C4C23×C8311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C42—21no—
461C2×C42—41no—
462C2×C42—41no—
463C2×C42D4×C8311yescharacteristic
464C2×C42D4×C8311yescharacteristic
465C2×C42C23×C8311yescharacteristic
466C2×C42C23×C8311yescharacteristic
467#107—22no—
468#107—22no—
469#107—41no—
470#102—22no—
471#102—22no—
472#102—22no—
473#102—22no—
474#102—41no—
475#102—41no—
476C22⋊C8—22no—
477C22⋊C8—22no—
478C4×C8—41no—
479C4×C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486C24—21no—
487C24—21no—
488C24C2×D4×C8311yescharacteristic
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4#41×C8312yes—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4D8×C8314yescomplemented
528C22×C4C2×D4×C8311yescharacteristic
529C22×C4C2×D4×C8311yescharacteristic
530C22×C4C2×D4×C8311yescharacteristic
531C22×C4C2×D4×C8311yescharacteristic
532C22×C4C2×D4×C8311yescharacteristic
533C22×C4C24×C8311yescharacteristic
534D8—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8#41×C8312yes—
546C2×C8#41×C8312yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4#41×C8312yes—
562C22⋊C4—24no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—41no—
578C42—41no—
579C42—42no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×D8×C8312yes—
601C23C22×D4×C8311yescharacteristic
602D4—22no—
603D4—22no—
604D4—48no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—41no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4C2×D8×C8312yes—
650C2×C4C2×D8×C8312yes—
651C2×C4#135×C8312yes—
652C2×C4C2×#41×C8311yescharacteristic
653C2×C4C2×#41×C8311yescharacteristic
654C2×C4C2×#41×C8311yescharacteristic
655C2×C4C2×#41×C8311yescharacteristic
656C2×C4H(5,𝔽2)×C8311yescharacteristic
657C2×C4H(5,𝔽2)×C8311yescharacteristic
658C8—22no—
659C8—22no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#525×C8311yescharacteristic
684C22#532×C8311yescharacteristic
685C22#534×C8311yescharacteristic
686C22C22×D8×C8311yescharacteristic
687C22C2×#135×C8311yescharacteristic
688C22#575×C8311yescharacteristic
689C22#575×C8311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—42no—
694C4—41no—
695C4—41no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4#551×C8311yescharacteristic
702C4#553×C8311yescharacteristic
703C4#553×C8311yescharacteristic
704C4#559×C8311yescharacteristic
705C2—42no—
706C2—82no—
707C2—161no—
708C2C83×#260211yescharacteristic
709C2C83×#310011yescharacteristic
710C2C83×#310211yescharacteristic
711C2C83×#316911yescharacteristic
712C2C83×#318311yescharacteristic
713C2C83×#318611yescharacteristic
714C2C83×#319111yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC83×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#2854C2semidirect
2. C4×#121×C83C2semidirect
3. C83×#2075C2semidirect
4. C83×#2033C2semidirect
5. C83×#2033C2semidirect
7. C83×#1970C2semidirect
8. C83×#1942C2semidirect
9. C83×#1934C2semidirect
10. C83×#1934C2semidirect
11. C83×#1925C2semidirect
12. C83×#1918C2semidirect
13. C83×#1879C2semidirect
14. C83×#1862C2semidirect
15. C4×C22⋊C8×C83C2semidirect
169. C22×C4×C83D8semidirect
347. #29460C83direct (N × H)
358. #2854C2×C83semidirect
359. C4×#121C2×C83semidirect
360. #2075C2×C83semidirect
361. #2033C2×C83semidirect
362. #2033C2×C83semidirect
364. #1970C2×C83semidirect
365. #1942C2×C83semidirect
366. #1934C2×C83semidirect
367. #1934C2×C83semidirect
368. #1925C2×C83semidirect
369. #1918C2×C83semidirect
370. #1879C2×C83semidirect
371. #1862C2×C83semidirect
372. C4×C22⋊C8C2×C83semidirect
373. C83#29460direct (N × H)
527. C22×C4D8×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#28542
C4×#121×C832
C83×#20752
C83×#20332
C83×#19992
C83×#19702
C83×#19422
C83×#19342
C83×#19252
C83×#19182
C83×#18792
C83×#18622
C4×C22⋊C8×C832
#2946083