Finite Group Databasebeta

← C83×#26601 #35254425

Subgroups — C83×#26601 #35254425

Order 21248.

1084 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C83C211yesmaximal, characteristic, complemented
2C2×#442×C83C211yesmaximal, characteristic, complemented
3C83×#2445C211yesmaximal, characteristic, complemented
4C83×#2366C211yesmaximal, characteristic, complemented
5C83×#2065C211yesmaximal, characteristic, complemented
6C83×#2011C211yesmaximal, characteristic, complemented
7C83×#2011C211yesmaximal, characteristic, complemented
8C83×#2011C211yesmaximal, characteristic, complemented
9C83×#1972C211yesmaximal, characteristic, complemented
10C83×#1926C211yesmaximal, characteristic, complemented
11C83×#1926C211yesmaximal, characteristic, complemented
12C83×#1917C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1879C211yesmaximal, characteristic, complemented
15C83×#1864C211yesmaximal, characteristic, complemented
16C22×D8×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C2×#127×C83C2211yescharacteristic
21C2×#127×C83C2211yescharacteristic
22C2×#123×C83—21no—
23C2×C4×D4×C83—21no—
24C2×C4×D4×C83C2211yescharacteristic
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic
27#459×C83—24no—
28#442×C83—24no—
29C2×#106×C83C2211yescharacteristic
30C2×#106×C83C2211yescharacteristic
31C2×C4⋊C8×C83C2211yescharacteristic
32C2×#102×C83C2211yescharacteristic
33C2×#102×C83C2211yescharacteristic
34C2×#102×C83C2211yescharacteristic
35C2×#102×C83C2211yescharacteristic
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#97×C83C2211yescharacteristic
41#394×C83—21no—
42#394×C83—21no—
43#390×C83—21no—
44#390×C83C2211yescharacteristic
45#390×C83C2211yescharacteristic
46#390×C83C2211yescharacteristic
47#390×C83C2211yescharacteristic
48#390×C83C2211yescharacteristic
49#389×C83C2211yescharacteristic
50#386×C83—21no—
51#386×C83—21no—
52#386×C83—21no—
53C4×C4⋊C4×C83C2211yescharacteristic
54C4×C4⋊C4×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61C22×D4×C83—21no—
62C22×D4×C83—21no—
63C22×D4×C83—21no—
64C22×D4×C83—21no—
65C22×D4×C83C2311yescharacteristic
66C22×D4×C83C2311yescharacteristic
67C22×D4×C83C2311yescharacteristic
68C22×D4×C83C2311yescharacteristic
69C23×C4×C83—21no—
70C23×C4×C83—21no—
71C23×C4×C83—21no—
72C2×D8×C83—22no—
73C2×D8×C83—22no—
74C2×D8×C83—22no—
75C2×D8×C83—22no—
76C2×D8×C83—22no—
77C2×D8×C83—22no—
78C2×D8×C83—22no—
79C2×D8×C83—22no—
80C2×D8×C83—41no—
81C2×D8×C83—41no—
82C2×D8×C83—41no—
83C2×D8×C83—41no—
84C22×C8×C83C2311yescharacteristic
85C22×C8×C83C2311yescharacteristic
86C22×C8×C83C2311yescharacteristic
87C22×C8×C83C2311yescharacteristic
88#127×C83—22no—
89#127×C83—22no—
90#127×C83—22no—
91#127×C83—41no—
92#123×C83—44no—
93C4×D4×C83—22no—
94C4×D4×C83—22no—
95C4×D4×C83—22no—
96C4×D4×C83—41no—
97C4×D4×C83—41no—
98C4×D4×C83—41no—
99C4×D4×C83—44no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83D411yescharacteristic
102C2×C4⋊C4×C83D411yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C22⋊C4×C83—21no—
108C2×C22⋊C4×C83—21no—
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83—21no—
115C2×C22⋊C4×C83—21no—
116C2×C22⋊C4×C83—21no—
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—21no—
120C2×C42×C83—21no—
121C2×C42×C83C2311yescharacteristic
122C2×C42×C83C2311yescharacteristic
123C2×C42×C83C2311yescharacteristic
124#106×C83—22no—
125#106×C83—41no—
126C4⋊C8×C83—22no—
127#102×C83—22no—
128#102×C83—22no—
129#102×C83—22no—
130#102×C83—22no—
131#102×C83—41no—
132#102×C83—41no—
133#102×C83—41no—
134#102×C83D414yescomplemented
135#97×C83—22no—
136#95×C83—21no—
137#95×C83—21no—
138#95×C83D411yescharacteristic
139#95×C83D411yescharacteristic
140C24×C83—21no—
141C24×C83—21no—
142C24×C83—21no—
143C24×C83—21no—
144C2×D4×C83—24no—
145C2×D4×C83—24no—
146C2×D4×C83—21no—
147C2×D4×C83—21no—
148C2×D4×C83—21no—
149C2×D4×C83—21no—
150C2×D4×C83—21no—
151C2×D4×C83—21no—
152C2×D4×C83—21no—
153C2×D4×C83—21no—
154C2×D4×C83—21no—
155C2×D4×C83—21no—
156C2×D4×C83—21no—
157C2×D4×C83—21no—
158C2×D4×C83—21no—
159C2×D4×C83—21no—
160C2×D4×C83—21no—
161C2×D4×C83—21no—
162C2×D4×C83—21no—
163C2×D4×C83—21no—
164C2×D4×C83—21no—
165C2×D4×C83—21no—
166C2×D4×C83—21no—
167C2×D4×C83—42no—
168C2×D4×C83—42no—
169C2×D4×C83—42no—
170C2×D4×C83—42no—
171C2×D4×C83—42no—
172C2×D4×C83—42no—
173C2×D4×C83—81no—
174C2×D4×C83—81no—
175C2×D4×C83—81no—
176C2×D4×C83—81no—
177C2×D4×C83C2×D412yes—
178C2×D4×C83#4112yes—
179C2×D4×C83#4112yes—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—42no—
185C22×C4×C83—42no—
186C22×C4×C83—42no—
187C22×C4×C83—42no—
188C22×C4×C83—42no—
189C22×C4×C83—42no—
190C22×C4×C83—81no—
191C22×C4×C83—81no—
192C22×C4×C83—81no—
193C22×C4×C83C2×D411yescharacteristic
194C22×C4×C83C2×D411yescharacteristic
195C22×C4×C83C2×D411yescharacteristic
196C22×C4×C83C2×D411yescharacteristic
197C22×C4×C83C2×D411yescharacteristic
198C22×C4×C83C2×D411yescharacteristic
199C22×C4×C83C2411yescharacteristic
200D8×C83—28no—
201D8×C83—44no—
202D8×C83—44no—
203D8×C83—44no—
204C2×C8×C83—21no—
205C2×C8×C83—21no—
206C2×C8×C83—21no—
207C2×C8×C83—21no—
208C2×C8×C83—21no—
209C2×C8×C83—21no—
210C2×C8×C83—21no—
211C2×C8×C83—21no—
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83C2×D412yes—
215C2×C8×C83#4112yes—
216C4⋊C4×C83—22no—
217C4⋊C4×C83—22no—
218C4⋊C4×C83—21no—
219C4⋊C4×C83—21no—
220C4⋊C4×C83—21no—
221C4⋊C4×C83—21no—
222C4⋊C4×C83—21no—
223C4⋊C4×C83—21no—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—42no—
226C4⋊C4×C83C2×D412yes—
227C22⋊C4×C83—42no—
228C22⋊C4×C83—42no—
229C22⋊C4×C83—42no—
230C22⋊C4×C83—42no—
231C22⋊C4×C83—42no—
232C22⋊C4×C83—42no—
233C22⋊C4×C83—42no—
234C22⋊C4×C83—42no—
235C22⋊C4×C83—81no—
236C22⋊C4×C83—81no—
237C22⋊C4×C83—81no—
238C22⋊C4×C83—81no—
239C22⋊C4×C83—81no—
240C42×C83—21no—
241C42×C83—21no—
242C42×C83—21no—
243C42×C83—21no—
244C42×C83—21no—
245C42×C83—21no—
246C42×C83—42no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—41no—
251C23×C83—41no—
252C23×C83—41no—
253C23×C83—41no—
254C23×C83—41no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—41no—
258C23×C83—41no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—41no—
267C23×C83—41no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—41no—
274C23×C83—41no—
275C23×C83C22×D411yescharacteristic
276D4×C83—22no—
277D4×C83—22no—
278D4×C83—22no—
279D4×C83—22no—
280D4×C83—22no—
281D4×C83—22no—
282D4×C83—48no—
283D4×C83—41no—
284D4×C83—41no—
285D4×C83—41no—
286D4×C83—41no—
287D4×C83—41no—
288D4×C83—41no—
289D4×C83—41no—
290D4×C83—41no—
291D4×C83—41no—
292D4×C83—41no—
293D4×C83—84no—
294D4×C83—84no—
295D4×C83—84no—
296C2×C4×C83—21no—
297C2×C4×C83—21no—
298C2×C4×C83—21no—
299C2×C4×C83—21no—
300C2×C4×C83—21no—
301C2×C4×C83—21no—
302C2×C4×C83—21no—
303C2×C4×C83—21no—
304C2×C4×C83—22no—
305C2×C4×C83—21no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—21no—
310C2×C4×C83—21no—
311C2×C4×C83—21no—
312C2×C4×C83—21no—
313C2×C4×C83—41no—
314C2×C4×C83—41no—
315C2×C4×C83—41no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
321C2×C4×C83—41no—
322C2×C4×C83—41no—
323C2×C4×C83—41no—
324C2×C4×C83—84no—
325C2×C4×C83—84no—
326C2×C4×C83—84no—
327C2×C4×C83AGL(1,ℤ/8)12yes—
328C2×C4×C83AGL(1,ℤ/8)12yes—
329C2×C4×C83C22×D411yescharacteristic
330C2×C4×C83C2×#4111yescharacteristic
331C2×C4×C83C2×#4111yescharacteristic
332C2×C4×C83C2×#4111yescharacteristic
333C2×C4×C83H(5,𝔽2)11yescharacteristic
334C2×C4×C83H(5,𝔽2)11yescharacteristic
335C8×C83—22no—
336C8×C83—22no—
337C8×C83—41no—
338C8×C83—41no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—42no—
344C22×C83—42no—
345C22×C83—42no—
346C22×C83—42no—
347C22×C83—42no—
348C22×C83—81no—
349C22×C83—81no—
350C22×C83—81no—
351C22×C83—81no—
352C22×C83—81no—
353C22×C83—81no—
354C22×C83—81no—
355C22×C83—81no—
356C22×C83—81no—
357C22×C83—81no—
358C22×C83—81no—
359C22×C83—81no—
360C22×C83—81no—
361C22×C83—81no—
362C22×C83—81no—
363C22×C83—81no—
364C22×C83—81no—
365C22×C83—81no—
366C22×C83—81no—
367C22×C83#52511yescharacteristic
368C22×C83D4211yescharacteristic
369C22×C83#55011yescharacteristic
370C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C83#57611yescharacteristic
373C22×C83#57611yescharacteristic
374C4×C83—22no—
375C4×C83—22no—
376C4×C83—41no—
377C4×C83—41no—
378C4×C83—42no—
379C4×C83—41no—
380C4×C83—41no—
381C4×C83—81no—
382C4×C83—81no—
383C4×C83—81no—
384C4×C83#52511yescharacteristic
385C4×C83#53811yescharacteristic
386C4×C83#54611yescharacteristic
387C4×C83#55311yescharacteristic
388#26601C8311yesmaximal, characteristic, direct product factor, Sylow
389C2×C83—82no—
390C2×C83—82no—
391C2×C83—82no—
392C2×C83—161no—
393C2×C83#245611yescharacteristic
394C2×C83#310911yescharacteristic
395C2×C83#312211yescharacteristic
396C2×C83#326411yescharacteristic
397C2×C83#327411yescharacteristic
398C2×C83#339911yescharacteristic
399C2×C83#339911yescharacteristic
400C2×#459C2×C8311yescharacteristic, complemented
401C2×#442C2×C8311yescharacteristic, complemented
402#2445C2×C8311yescharacteristic, complemented
403#2366C2×C8311yescharacteristic, complemented
404#2065C2×C8311yescharacteristic, complemented
405#2011C2×C8311yescharacteristic, complemented
406#2011C2×C8311yescharacteristic, complemented
407#2011C2×C8311yescharacteristic, complemented
408#1972C2×C8311yescharacteristic, complemented
409#1926C2×C8311yescharacteristic, complemented
410#1926C2×C8311yescharacteristic, complemented
411#1917C2×C8311yescharacteristic, complemented
412#1879C2×C8311yescharacteristic, complemented
413#1879C2×C8311yescharacteristic, complemented
414#1864C2×C8311yescharacteristic, complemented
415C83#2660111yescharacteristic, direct product factor, Sylow
416C22×D8C22×C8311yescharacteristic
417C22×D8C22×C8311yescharacteristic
418C22×D8C22×C8311yescharacteristic
419C22×D8C22×C8311yescharacteristic
420C2×#127C22×C8311yescharacteristic
421C2×#127C22×C8311yescharacteristic
422C2×#123—21no—
423C2×C4×D4—21no—
424C2×C4×D4C22×C8311yescharacteristic
425C2×C4×D4C22×C8311yescharacteristic
426C2×C4×D4C22×C8311yescharacteristic
427#459—24no—
428#442—24no—
429C2×#106C22×C8311yescharacteristic
430C2×#106C22×C8311yescharacteristic
431C2×C4⋊C8C22×C8311yescharacteristic
432C2×#102C22×C8311yescharacteristic
433C2×#102C22×C8311yescharacteristic
434C2×#102C22×C8311yescharacteristic
435C2×#102C22×C8311yescharacteristic
436C2×#102C22×C8311yescharacteristic
437C2×#102C22×C8311yescharacteristic
438C2×#102C22×C8311yescharacteristic
439C2×#102C22×C8311yescharacteristic
440C2×#97C22×C8311yescharacteristic
441#394—21no—
442#394—21no—
443#390—21no—
444#390C22×C8311yescharacteristic
445#390C22×C8311yescharacteristic
446#390C22×C8311yescharacteristic
447#390C22×C8311yescharacteristic
448#390C22×C8311yescharacteristic
449#389C22×C8311yescharacteristic
450#386—21no—
451#386—21no—
452#386—21no—
453C4×C4⋊C4C22×C8311yescharacteristic
454C4×C4⋊C4C22×C8311yescharacteristic
455#340C22×C8311yescharacteristic
456#340C22×C8311yescharacteristic
457#336C22×C8311yescharacteristic
458#336C22×C8311yescharacteristic
459#336C22×C8311yescharacteristic
460#336C22×C8311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4C23×C8311yescharacteristic
466C22×D4C23×C8311yescharacteristic
467C22×D4C23×C8311yescharacteristic
468C22×D4C23×C8311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—22no—
479C2×D8—22no—
480C2×D8—41no—
481C2×D8—41no—
482C2×D8—41no—
483C2×D8—41no—
484C22×C8C23×C8311yescharacteristic
485C22×C8C23×C8311yescharacteristic
486C22×C8C23×C8311yescharacteristic
487C22×C8C23×C8311yescharacteristic
488#127—22no—
489#127—22no—
490#127—22no—
491#127—41no—
492#123—44no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—41no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—44no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C8311yescharacteristic
502C2×C4⋊C4D4×C8311yescharacteristic
503C2×C4⋊C4C23×C8311yescharacteristic
504C2×C4⋊C4C23×C8311yescharacteristic
505C2×C4⋊C4C23×C8311yescharacteristic
506C2×C4⋊C4C23×C8311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C42—21no—
521C2×C42C23×C8311yescharacteristic
522C2×C42C23×C8311yescharacteristic
523C2×C42C23×C8311yescharacteristic
524#106—22no—
525#106—41no—
526C4⋊C8—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—41no—
532#102—41no—
533#102—41no—
534#102D4×C8314yescomplemented
535#97—22no—
536#95—21no—
537#95—21no—
538#95D4×C8311yescharacteristic
539#95D4×C8311yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4C2×D4×C8312yes—
578C2×D4#41×C8312yes—
579C2×D4#41×C8312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C8311yescharacteristic
594C22×C4C2×D4×C8311yescharacteristic
595C22×C4C2×D4×C8311yescharacteristic
596C22×C4C2×D4×C8311yescharacteristic
597C22×C4C2×D4×C8311yescharacteristic
598C22×C4C2×D4×C8311yescharacteristic
599C22×C4C24×C8311yescharacteristic
600D8—28no—
601D8—44no—
602D8—44no—
603D8—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8C2×D4×C8312yes—
615C2×C8#41×C8312yes—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C8312yes—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—42no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23C22×D4×C8311yescharacteristic
676D4—22no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—84no—
695D4—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4AGL(1,ℤ/8)×C8312yes—
728C2×C4AGL(1,ℤ/8)×C8312yes—
729C2×C4C22×D4×C8311yescharacteristic
730C2×C4C2×#41×C8311yescharacteristic
731C2×C4C2×#41×C8311yescharacteristic
732C2×C4C2×#41×C8311yescharacteristic
733C2×C4H(5,𝔽2)×C8311yescharacteristic
734C2×C4H(5,𝔽2)×C8311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22#525×C8311yescharacteristic
768C22D42×C8311yescharacteristic
769C22#550×C8311yescharacteristic
770C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
771C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
772C22#576×C8311yescharacteristic
773C22#576×C8311yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—41no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#525×C8311yescharacteristic
785C4#538×C8311yescharacteristic
786C4#546×C8311yescharacteristic
787C4#553×C8311yescharacteristic
788C2—82no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C83×#245611yescharacteristic
793C2C83×#310911yescharacteristic
794C2C83×#312211yescharacteristic
795C2C83×#326411yescharacteristic
796C2C83×#327411yescharacteristic
797C2C83×#339911yescharacteristic
798C2C83×#339911yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C4⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C83C2semidirect
2. C2×#442×C83C2semidirect
3. C83×#2445C2semidirect
4. C83×#2366C2semidirect
5. C83×#2065C2semidirect
6. C83×#2011C2semidirect
7. C83×#2011C2semidirect
8. C83×#2011C2semidirect
9. C83×#1972C2semidirect
10. C83×#1926C2semidirect
11. C83×#1926C2semidirect
12. C83×#1917C2semidirect
13. C83×#1879C2semidirect
14. C83×#1879C2semidirect
15. C83×#1864C2semidirect
134. #102×C83D4semidirect
388. #26601C83direct (N × H)
400. C2×#459C2×C83semidirect
401. C2×#442C2×C83semidirect
402. #2445C2×C83semidirect
403. #2366C2×C83semidirect
404. #2065C2×C83semidirect
405. #2011C2×C83semidirect
406. #2011C2×C83semidirect
407. #2011C2×C83semidirect
408. #1972C2×C83semidirect
409. #1926C2×C83semidirect
410. #1926C2×C83semidirect
411. #1917C2×C83semidirect
412. #1879C2×C83semidirect
413. #1879C2×C83semidirect
414. #1864C2×C83semidirect
415. C83#26601direct (N × H)
534. #102D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C832
C2×#442×C832
C83×#24452
C83×#23662
C83×#20652
C83×#20112
C83×#19722
C83×#19262
C83×#19172
C83×#18792
C83×#18642
#2660183