Finite Group Databasebeta

← C83×#24017 #35251841

Subgroups — C83×#24017 #35251841

Order 21248.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C83C211yesmaximal, characteristic
2C2×#485×C83C211yesmaximal, characteristic, complemented
3C2×#482×C83C211yesmaximal, characteristic, complemented
4C83×#2311C211yesmaximal, characteristic, complemented
5C83×#2036C211yesmaximal, characteristic, complemented
6C83×#2035C211yesmaximal, characteristic, complemented
7C83×#2034C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#1874C211yesmaximal, characteristic, complemented
10C83×#1872C211yesmaximal, characteristic, complemented
11C83×#1853C211yesmaximal, characteristic, complemented
12C83×#1852C211yesmaximal, characteristic, complemented
13C83×#1788C211yesmaximal, characteristic, complemented
14C83×#1788C211yesmaximal, characteristic, complemented
15C83×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×#41×C83C2211yescharacteristic
18#537×C83—24no—
19#537×C83—24no—
20C2×C22⋊Q8×C83—21no—
21C2×C22⋊Q8×C83C2211yescharacteristic
22C2×C22⋊Q8×C83C2211yescharacteristic
23C2×#121×C83—21no—
24C2×#121×C83—21no—
25C2×#121×C83—21no—
26C2×#121×C83C2211yescharacteristic
27C2×#121×C83C2211yescharacteristic
28C2×#117×C83C2211yescharacteristic
29C22×C4⋊C4×C83C2211yescharacteristic
30C22×C4⋊C4×C83C2211yescharacteristic
31#485×C83—24no—
32#482×C83—24no—
33C2×#107×C83C2211yescharacteristic
34C2×#107×C83C2211yescharacteristic
35C2×#106×C83C2211yescharacteristic
36C2×#106×C83C2211yescharacteristic
37C2×#103×C83C2211yescharacteristic
38C2×#103×C83C2211yescharacteristic
39C2×#103×C83C2211yescharacteristic
40C2×#103×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic
45C2×C22⋊C8×C83C2211yescharacteristic
46C2×C22⋊C8×C83C2211yescharacteristic
47C2×C22⋊C8×C83C2211yescharacteristic
48C2×C22⋊C8×C83C2211yescharacteristic
49C2×C22⋊C8×C83C2211yescharacteristic
50C2×C22⋊C8×C83C2211yescharacteristic
51#391×C83—21no—
52#390×C83—21no—
53#386×C83—21no—
54#386×C83—21no—
55#380×C83C2211yescharacteristic
56#380×C83C2211yescharacteristic
57#380×C83C2211yescharacteristic
58#380×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63C2×#41×C83—22no—
64C2×#41×C83—22no—
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—22no—
71C2×#41×C83—41no—
72C2×#41×C83—41no—
73C2×#41×C83—41no—
74C2×#41×C83—41no—
75C22×Q8×C83D411yescharacteristic
76C22×Q8×C83C2311yescharacteristic
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83D411yescharacteristic
81C22×D4×C83D411yescharacteristic
82C22×D4×C83D411yescharacteristic
83C22×D4×C83C2311yescharacteristic
84C23×C4×C83—21no—
85C23×C4×C83—21no—
86C23×C4×C83—21no—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C22×C8×C83C2311yescharacteristic
91C22×C8×C83C2311yescharacteristic
92C22×C8×C83C2311yescharacteristic
93C22×C8×C83C2311yescharacteristic
94C22⋊Q8×C83—28no—
95C22⋊Q8×C83—22no—
96C22⋊Q8×C83—22no—
97C22⋊Q8×C83—22no—
98C22⋊Q8×C83D414yes—
99#121×C83—28no—
100#121×C83—28no—
101#121×C83—28no—
102#121×C83—22no—
103#121×C83—22no—
104#121×C83—22no—
105#121×C83D414yes—
106#117×C83—22no—
107#117×C83—22no—
108C2×C4⋊C4×C83—21no—
109C2×C4⋊C4×C83—21no—
110C2×C4⋊C4×C83—21no—
111C2×C4⋊C4×C83—22no—
112C2×C4⋊C4×C83—22no—
113C2×C4⋊C4×C83—21no—
114C2×C4⋊C4×C83—41no—
115C2×C4⋊C4×C83—41no—
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83C2311yescharacteristic
118C2×C4⋊C4×C83C2311yescharacteristic
119C2×C4⋊C4×C83C2311yescharacteristic
120C2×C4⋊C4×C83C2311yescharacteristic
121C2×C4⋊C4×C83C2311yescharacteristic
122C2×C22⋊C4×C83—21no—
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83—21no—
127C2×C22⋊C4×C83—21no—
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—21no—
130C2×C22⋊C4×C83—21no—
131C2×C42×C83—21no—
132#107×C83—22no—
133#107×C83—22no—
134#106×C83—22no—
135#106×C83—22no—
136#103×C83—22no—
137#103×C83—22no—
138#103×C83—41no—
139#103×C83—41no—
140#102×C83—22no—
141#102×C83—22no—
142#102×C83—41no—
143#102×C83—41no—
144C22⋊C8×C83—22no—
145C22⋊C8×C83—22no—
146C22⋊C8×C83—22no—
147C22⋊C8×C83—22no—
148C22⋊C8×C83—41no—
149C22⋊C8×C83—41no—
150#95×C83—21no—
151#95×C83—21no—
152#95×C83—21no—
153#95×C83—21no—
154C24×C83—21no—
155C24×C83C2×D411yescharacteristic
156C24×C83C2×D411yescharacteristic
157C24×C83C2×D411yescharacteristic
158#41×C83—44no—
159#41×C83—44no—
160#41×C83—44no—
161#41×C83—44no—
162#41×C83—44no—
163#41×C83—44no—
164#41×C83—44no—
165#41×C83—44no—
166C2×Q8×C83—22no—
167C2×Q8×C83—22no—
168C2×Q8×C83—21no—
169C2×Q8×C83—21no—
170C2×Q8×C83—21no—
171C2×Q8×C83—21no—
172C2×Q8×C83—21no—
173C2×Q8×C83—41no—
174C2×Q8×C83C2×D412yes—
175C2×D4×C83—24no—
176C2×D4×C83—22no—
177C2×D4×C83—22no—
178C2×D4×C83—22no—
179C2×D4×C83—22no—
180C2×D4×C83—24no—
181C2×D4×C83—24no—
182C2×D4×C83—22no—
183C2×D4×C83—22no—
184C2×D4×C83—21no—
185C2×D4×C83—21no—
186C2×D4×C83—21no—
187C2×D4×C83—21no—
188C2×D4×C83—21no—
189C2×D4×C83—41no—
190C2×D4×C83—41no—
191C2×D4×C83—41no—
192C2×D4×C83—42no—
193C2×D4×C83—42no—
194C2×D4×C83—81no—
195C2×D4×C83—81no—
196C2×D4×C83—81no—
197C2×D4×C83—81no—
198C2×D4×C83C2×D412yes—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—24no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—24no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—42no—
223C22×C4×C83—42no—
224C22×C4×C83—42no—
225C22×C4×C83—81no—
226C22×C4×C83—81no—
227C22×C4×C83—81no—
228C22×C4×C83—81no—
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2×D412yes—
232C22×C4×C83C2×D412yes—
233C22×C4×C83C2×D411yescharacteristic
234C22×C4×C83#4112yes—
235C22×C4×C83#4112yes—
236C22×C4×C83C2411yescharacteristic
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83—21no—
247C2×C8×C83—21no—
248C2×C8×C83—21no—
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—24no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—21no—
256C4⋊C4×C83—21no—
257C4⋊C4×C83—21no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—42no—
263C4⋊C4×C83C2×D412yes—
264C4⋊C4×C83C2×D412yes—
265C22⋊C4×C83—24no—
266C22⋊C4×C83—24no—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—42no—
270C22⋊C4×C83—81no—
271C22⋊C4×C83—81no—
272C22⋊C4×C83—81no—
273C22⋊C4×C83—81no—
274C42×C83—42no—
275C23×C83—21no—
276C23×C83—21no—
277C23×C83—21no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—21no—
283C23×C83—21no—
284C23×C83—21no—
285C23×C83—21no—
286C23×C83—21no—
287C23×C83—21no—
288C23×C83—22no—
289C23×C83—21no—
290C23×C83—21no—
291C23×C83—21no—
292C23×C83—21no—
293C23×C83—21no—
294C23×C83—21no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83#12012yes—
302C23×C83#12312yes—
303C23×C83C22×D411yescharacteristic
304Q8×C83—22no—
305Q8×C83—22no—
306Q8×C83—44no—
307Q8×C83—41no—
308Q8×C83—41no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—44no—
312D4×C83—44no—
313D4×C83—44no—
314D4×C83—48no—
315D4×C83—41no—
316D4×C83—41no—
317D4×C83—84no—
318D4×C83—84no—
319C2×C4×C83—21no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—21no—
335C2×C4×C83—21no—
336C2×C4×C83—21no—
337C2×C4×C83—48no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—84no—
361C2×C4×C83—84no—
362C2×C4×C83#12012yes—
363C2×C4×C83#12312yes—
364C2×C4×C83C22×D411yescharacteristic
365C2×C4×C83C22×D411yescharacteristic
366C2×C4×C83C2×#4111yescharacteristic
367C2×C4×C83C2×#4111yescharacteristic
368C2×C4×C83H(5,𝔽2)11yescharacteristic
369C2×C4×C83H(5,𝔽2)11yescharacteristic
370C8×C83—41no—
371C8×C83—41no—
372C8×C83—41no—
373C8×C83—41no—
374C22×C83—22no—
375C22×C83—22no—
376C22×C83—22no—
377C22×C83—22no—
378C22×C83—22no—
379C22×C83—22no—
380C22×C83—41no—
381C22×C83—41no—
382C22×C83—41no—
383C22×C83—41no—
384C22×C83—41no—
385C22×C83—41no—
386C22×C83—41no—
387C22×C83—41no—
388C22×C83—41no—
389C22×C83—41no—
390C22×C83—42no—
391C22×C83—41no—
392C22×C83—41no—
393C22×C83—41no—
394C22×C83—41no—
395C22×C83—42no—
396C22×C83—41no—
397C22×C83—42no—
398C22×C83—81no—
399C22×C83—81no—
400C22×C83—81no—
401C22×C83—81no—
402C22×C83C2×#12011yescharacteristic
403C22×C83C2×#12311yescharacteristic
404C22×C83#53411yescharacteristic
405C22×C83#57611yescharacteristic
406C22×C83#57711yescharacteristic
407C22×C83#57711yescharacteristic
408C22×C83#57811yescharacteristic
409C4×C83—22no—
410C4×C83—22no—
411C4×C83—41no—
412C4×C83—42no—
413C4×C83—42no—
414C4×C83—42no—
415C4×C83—81no—
416C4×C83—81no—
417C4×C83—81no—
418C4×C83—81no—
419C4×C83#54611yescharacteristic
420C4×C83#54611yescharacteristic
421C4×C83#54611yescharacteristic
422C4×C83#54611yescharacteristic
423#24017C8311yesmaximal, characteristic, direct product factor, Sylow
424C2×C83—42no—
425C2×C83—42no—
426C2×C83—81no—
427C2×C83—82no—
428C2×C83#240511yescharacteristic
429C2×C83#301211yescharacteristic
430C2×C83#301311yescharacteristic
431C2×C83#309811yescharacteristic
432C2×C83#309911yescharacteristic
433C2×C83#319811yescharacteristic
434C2×C83#320111yescharacteristic
435C2×#537C2×C8311yescharacteristic
436C2×#485C2×C8311yescharacteristic, complemented
437C2×#482C2×C8311yescharacteristic, complemented
438#2311C2×C8311yescharacteristic, complemented
439#2036C2×C8311yescharacteristic, complemented
440#2035C2×C8311yescharacteristic, complemented
441#2034C2×C8311yescharacteristic, complemented
442#2033C2×C8311yescharacteristic, complemented
443#1874C2×C8311yescharacteristic, complemented
444#1872C2×C8311yescharacteristic, complemented
445#1853C2×C8311yescharacteristic, complemented
446#1852C2×C8311yescharacteristic, complemented
447#1788C2×C8311yescharacteristic, complemented
448#1788C2×C8311yescharacteristic, complemented
449#1780C2×C8311yescharacteristic, complemented
450C83#2401711yescharacteristic, direct product factor, Sylow
451C22×#41C22×C8311yescharacteristic
452C22×#41C22×C8311yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C8311yescharacteristic
457C2×C22⋊Q8C22×C8311yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C8311yescharacteristic
462C2×#121C22×C8311yescharacteristic
463C2×#117C22×C8311yescharacteristic
464C22×C4⋊C4C22×C8311yescharacteristic
465C22×C4⋊C4C22×C8311yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C8311yescharacteristic
469C2×#107C22×C8311yescharacteristic
470C2×#106C22×C8311yescharacteristic
471C2×#106C22×C8311yescharacteristic
472C2×#103C22×C8311yescharacteristic
473C2×#103C22×C8311yescharacteristic
474C2×#103C22×C8311yescharacteristic
475C2×#103C22×C8311yescharacteristic
476C2×#102C22×C8311yescharacteristic
477C2×#102C22×C8311yescharacteristic
478C2×#102C22×C8311yescharacteristic
479C2×#102C22×C8311yescharacteristic
480C2×C22⋊C8C22×C8311yescharacteristic
481C2×C22⋊C8C22×C8311yescharacteristic
482C2×C22⋊C8C22×C8311yescharacteristic
483C2×C22⋊C8C22×C8311yescharacteristic
484C2×C22⋊C8C22×C8311yescharacteristic
485C2×C22⋊C8C22×C8311yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C8311yescharacteristic
491#380C22×C8311yescharacteristic
492#380C22×C8311yescharacteristic
493#380C22×C8311yescharacteristic
494#340C22×C8311yescharacteristic
495#340C22×C8311yescharacteristic
496#340C22×C8311yescharacteristic
497#340C22×C8311yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C8311yescharacteristic
511C22×Q8C23×C8311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C8311yescharacteristic
516C22×D4D4×C8311yescharacteristic
517C22×D4D4×C8311yescharacteristic
518C22×D4C23×C8311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C8311yescharacteristic
523C23×C4C23×C8311yescharacteristic
524C23×C4C23×C8311yescharacteristic
525C22×C8C23×C8311yescharacteristic
526C22×C8C23×C8311yescharacteristic
527C22×C8C23×C8311yescharacteristic
528C22×C8C23×C8311yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C8314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C8314yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C8311yescharacteristic
552C2×C4⋊C4C23×C8311yescharacteristic
553C2×C4⋊C4C23×C8311yescharacteristic
554C2×C4⋊C4C23×C8311yescharacteristic
555C2×C4⋊C4C23×C8311yescharacteristic
556C2×C4⋊C4C23×C8311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C8311yescharacteristic
591C24C2×D4×C8311yescharacteristic
592C24C2×D4×C8311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C8312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C8312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C8311yescharacteristic
665C22×C4C2×D4×C8311yescharacteristic
666C22×C4C2×D4×C8312yes—
667C22×C4C2×D4×C8312yes—
668C22×C4C2×D4×C8311yescharacteristic
669C22×C4#41×C8312yes—
670C22×C4#41×C8312yes—
671C22×C4C24×C8311yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C8312yes—
699C4⋊C4C2×D4×C8312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C8312yes—
737C23#123×C8312yes—
738C23C22×D4×C8311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—84no—
797C2×C4#120×C8312yes—
798C2×C4#123×C8312yes—
799C2×C4C22×D4×C8311yescharacteristic
800C2×C4C22×D4×C8311yescharacteristic
801C2×C4C2×#41×C8311yescharacteristic
802C2×C4C2×#41×C8311yescharacteristic
803C2×C4H(5,𝔽2)×C8311yescharacteristic
804C2×C4H(5,𝔽2)×C8311yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C8311yescharacteristic
838C22C2×#123×C8311yescharacteristic
839C22#534×C8311yescharacteristic
840C22#576×C8311yescharacteristic
841C22#577×C8311yescharacteristic
842C22#577×C8311yescharacteristic
843C22#578×C8311yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C8311yescharacteristic
855C4#546×C8311yescharacteristic
856C4#546×C8311yescharacteristic
857C4#546×C8311yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C83×#240511yescharacteristic
863C2C83×#301211yescharacteristic
864C2C83×#301311yescharacteristic
865C2C83×#309811yescharacteristic
866C2C83×#309911yescharacteristic
867C2C83×#319811yescharacteristic
868C2C83×#320111yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#537×C83C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C83C2semidirect
3. C2×#482×C83C2semidirect
4. C83×#2311C2semidirect
5. C83×#2036C2semidirect
6. C83×#2035C2semidirect
7. C83×#2034C2semidirect
8. C83×#2033C2semidirect
9. C83×#1874C2semidirect
10. C83×#1872C2semidirect
11. C83×#1853C2semidirect
12. C83×#1852C2semidirect
13. C83×#1788C2semidirect
14. C83×#1788C2semidirect
15. C83×#1780C2semidirect
423. #24017C83direct (N × H)
436. C2×#485C2×C83semidirect
437. C2×#482C2×C83semidirect
438. #2311C2×C83semidirect
439. #2036C2×C83semidirect
440. #2035C2×C83semidirect
441. #2034C2×C83semidirect
442. #2033C2×C83semidirect
443. #1874C2×C83semidirect
444. #1872C2×C83semidirect
445. #1853C2×C83semidirect
446. #1852C2×C83semidirect
447. #1788C2×C83semidirect
448. #1788C2×C83semidirect
449. #1780C2×C83semidirect
450. C83#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#537×C832
C2×#485×C832
C2×#482×C832
C83×#23112
C83×#20362
C83×#20352
C83×#20342
C83×#20332
C83×#18742
C83×#18722
C83×#18532
C83×#18522
C83×#17882
C83×#17802
#2401783