Finite Group Databasebeta

← C83×#14729 #35242553

Subgroups — C83×#14729 #35242553

Order 21248.

2506 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C83C211yesmaximal, characteristic, complemented
2C2×#396×C83C212yesmaximal, complemented
3C2×#386×C83C211yesmaximal, characteristic
4C2×#386×C83C211yesmaximal, characteristic
5C2×#386×C83C211yesmaximal, characteristic
6C2×#385×C83C211yesmaximal, characteristic, complemented
7C2×#380×C83C211yesmaximal, characteristic, complemented
8C83×#1441C212yesmaximal, complemented
9C83×#1441C212yesmaximal, complemented
10C83×#1439C212yesmaximal, complemented
11C83×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C83C2211yescharacteristic
13C24×C4×C83C2211yescharacteristic
14C24×C4×C83C2211yescharacteristic
15C24×C4×C83C2211yescharacteristic
16C22×C4⋊C4×C83—24no—
17C22×C4⋊C4×C83—28no—
18C22×C4⋊C4×C83C2212yes—
19C22×C4⋊C4×C83C2212yes—
20C22×C4⋊C4×C83C2212yes—
21C22×C4⋊C4×C83C2212yes—
22C22×C22⋊C4×C83C2211yescharacteristic
23C22×C22⋊C4×C83C2211yescharacteristic
24C22×C22⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2212yes—
26C22×C22⋊C4×C83C2212yes—
27C22×C22⋊C4×C83C2211yescharacteristic
28C22×C22⋊C4×C83C2211yescharacteristic
29#396×C83—28no—
30#386×C83—24no—
31#386×C83—24no—
32#386×C83—24no—
33#385×C83—24no—
34#380×C83—24no—
35C2×#95×C83C2212yes—
36C2×#95×C83C2212yes—
37C2×#95×C83C2211yescharacteristic
38C2×#95×C83C2212yes—
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2212yes—
41C2×#95×C83C2212yes—
42C2×#95×C83C2212yes—
43C25×C83C2311yescharacteristic
44C25×C83C2311yescharacteristic
45C22×D4×C83—22no—
46C22×D4×C83—22no—
47C22×D4×C83—22no—
48C22×D4×C83—22no—
49C22×D4×C83—22no—
50C22×D4×C83—22no—
51C22×D4×C83Q814yes—
52C23×C4×C83—22no—
53C23×C4×C83—22no—
54C23×C4×C83—24no—
55C23×C4×C83—24no—
56C23×C4×C83—22no—
57C23×C4×C83—22no—
58C23×C4×C83—22no—
59C23×C4×C83—24no—
60C23×C4×C83—24no—
61C23×C4×C83—22no—
62C23×C4×C83—22no—
63C23×C4×C83—42no—
64C23×C4×C83—42no—
65C23×C4×C83D414yes—
66C23×C4×C83D414yes—
67C23×C4×C83C2311yescharacteristic
68C23×C4×C83C2312yes—
69C23×C4×C83C2311yescharacteristic
70C23×C4×C83C2312yes—
71C23×C4×C83C2311yescharacteristic
72C23×C4×C83C2312yes—
73C23×C4×C83C2311yescharacteristic
74C23×C4×C83C2311yescharacteristic
75C23×C4×C83C2312yes—
76C2×C4⋊C4×C83—232no—
77C2×C4⋊C4×C83—24no—
78C2×C4⋊C4×C83—24no—
79C2×C4⋊C4×C83—24no—
80C2×C4⋊C4×C83—24no—
81C2×C4⋊C4×C83—24no—
82C2×C4⋊C4×C83—24no—
83C2×C4⋊C4×C83—24no—
84C2×C4⋊C4×C83—24no—
85C2×C4⋊C4×C83—24no—
86C2×C4⋊C4×C83—24no—
87C2×C4⋊C4×C83—42no—
88C2×C4⋊C4×C83D418yescomplemented
89C2×C22⋊C4×C83—22no—
90C2×C22⋊C4×C83—22no—
91C2×C22⋊C4×C83—22no—
92C2×C22⋊C4×C83—22no—
93C2×C22⋊C4×C83—22no—
94C2×C22⋊C4×C83—22no—
95C2×C22⋊C4×C83—22no—
96C2×C22⋊C4×C83—22no—
97C2×C22⋊C4×C83—24no—
98C2×C22⋊C4×C83—22no—
99C2×C22⋊C4×C83—22no—
100C2×C22⋊C4×C83—24no—
101C2×C22⋊C4×C83—24no—
102C2×C22⋊C4×C83—24no—
103C2×C22⋊C4×C83—24no—
104C2×C22⋊C4×C83—24no—
105C2×C22⋊C4×C83—42no—
106C2×C22⋊C4×C83—42no—
107C2×C22⋊C4×C83D414yes—
108#95×C83—24no—
109#95×C83—24no—
110#95×C83—24no—
111#95×C83—22no—
112#95×C83—22no—
113#95×C83—24no—
114#95×C83—24no—
115#95×C83—42no—
116C24×C83—22no—
117C24×C83—22no—
118C24×C83—22no—
119C24×C83—22no—
120C24×C83—22no—
121C24×C83—21no—
122C24×C83—21no—
123C24×C83—21no—
124C24×C83—22no—
125C24×C83—21no—
126C24×C83—21no—
127C24×C83—21no—
128C24×C83—22no—
129C24×C83—22no—
130C24×C83C2×D412yes—
131C24×C83C2×D412yes—
132C24×C83C2×D412yes—
133C24×C83C2×Q812yes—
134C24×C83C2×Q812yes—
135C24×C83#4112yes—
136C24×C83#4112yes—
137C24×C83#4112yes—
138C24×C83C2411yescharacteristic
139C2×D4×C83—28no—
140C2×D4×C83—28no—
141C2×D4×C83—28no—
142C2×D4×C83—44no—
143C2×D4×C83—44no—
144C2×D4×C83—44no—
145C2×D4×C83—44no—
146C22×C4×C83—28no—
147C22×C4×C83—216no—
148C22×C4×C83—28no—
149C22×C4×C83—28no—
150C22×C4×C83—22no—
151C22×C4×C83—22no—
152C22×C4×C83—21no—
153C22×C4×C83—22no—
154C22×C4×C83—22no—
155C22×C4×C83—21no—
156C22×C4×C83—22no—
157C22×C4×C83—216no—
158C22×C4×C83—28no—
159C22×C4×C83—28no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—22no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—22no—
172C22×C4×C83—21no—
173C22×C4×C83—22no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—22no—
180C22×C4×C83—22no—
181C22×C4×C83—22no—
182C22×C4×C83—28no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—22no—
186C22×C4×C83—21no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—22no—
194C22×C4×C83—22no—
195C22×C4×C83—22no—
196C22×C4×C83—22no—
197C22×C4×C83—22no—
198C22×C4×C83—22no—
199C22×C4×C83—22no—
200C22×C4×C83—44no—
201C22×C4×C83—48no—
202C22×C4×C83—48no—
203C22×C4×C83—48no—
204C22×C4×C83—48no—
205C22×C4×C83—44no—
206C22×C4×C83—44no—
207C22×C4×C83C2×D414yes—
208C22×C4×C83C2×D412yes—
209C22×C4×C83C2×D414yes—
210C22×C4×C83C2×D412yes—
211C22×C4×C83C2×D414yes—
212C22×C4×C83C2×D414yes—
213C22×C4×C83C2×D414yes—
214C22×C4×C83C2×Q812yes—
215C22×C4×C83#4114yes—
216C4⋊C4×C83—216no—
217C4⋊C4×C83—216no—
218C4⋊C4×C83—48no—
219C4⋊C4×C83—48no—
220C22⋊C4×C83—28no—
221C22⋊C4×C83—48no—
222C22⋊C4×C83—44no—
223C22⋊C4×C83—44no—
224C22⋊C4×C83—44no—
225C22⋊C4×C83—44no—
226C22⋊C4×C83—48no—
227C23×C83—22no—
228C23×C83—24no—
229C23×C83—22no—
230C23×C83—24no—
231C23×C83—22no—
232C23×C83—22no—
233C23×C83—24no—
234C23×C83—24no—
235C23×C83—24no—
236C23×C83—24no—
237C23×C83—24no—
238C23×C83—24no—
239C23×C83—24no—
240C23×C83—24no—
241C23×C83—24no—
242C23×C83—24no—
243C23×C83—22no—
244C23×C83—22no—
245C23×C83—22no—
246C23×C83—24no—
247C23×C83—24no—
248C23×C83—41no—
249C23×C83—42no—
250C23×C83—41no—
251C23×C83—41no—
252C23×C83—41no—
253C23×C83—41no—
254C23×C83—42no—
255C23×C83—41no—
256C23×C83—41no—
257C23×C83—41no—
258C23×C83—42no—
259C23×C83—42no—
260C23×C83—42no—
261C23×C83—42no—
262C23×C83—42no—
263C23×C83—42no—
264C23×C83—42no—
265C23×C83—42no—
266C23×C83#12114yes—
267C23×C83#12114yes—
268C23×C83#12114yes—
269C23×C83C22⋊Q814yes—
270C23×C83C22⋊Q814yes—
271C23×C83C22⋊Q814yes—
272C23×C83#12614yes—
273C23×C83C22×D411yescharacteristic
274C23×C83C22×D412yes—
275C23×C83C22×D411yescharacteristic
276C23×C83C22×D411yescharacteristic
277C23×C83C22×Q811yescharacteristic
278C23×C83C2×#4111yescharacteristic
279C23×C83C2×#4111yescharacteristic
280C23×C83C2×#4111yescharacteristic
281C23×C83C2×#4112yes—
282C23×C83H(5,𝔽2)12yes—
283C23×C832−1+412yes—
284D4×C83—416no—
285C2×C4×C83—232no—
286C2×C4×C83—24no—
287C2×C4×C83—24no—
288C2×C4×C83—24no—
289C2×C4×C83—22no—
290C2×C4×C83—24no—
291C2×C4×C83—24no—
292C2×C4×C83—24no—
293C2×C4×C83—22no—
294C2×C4×C83—24no—
295C2×C4×C83—24no—
296C2×C4×C83—22no—
297C2×C4×C83—24no—
298C2×C4×C83—24no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—24no—
305C2×C4×C83—24no—
306C2×C4×C83—24no—
307C2×C4×C83—24no—
308C2×C4×C83—416no—
309C2×C4×C83—416no—
310C2×C4×C83—42no—
311C2×C4×C83—42no—
312C2×C4×C83—41no—
313C2×C4×C83—41no—
314C2×C4×C83—41no—
315C2×C4×C83—41no—
316C2×C4×C83—42no—
317C2×C4×C83—42no—
318C2×C4×C83—42no—
319C2×C4×C83—42no—
320C2×C4×C83—42no—
321C2×C4×C83—42no—
322C2×C4×C83—42no—
323C2×C4×C83—42no—
324C2×C4×C83—41no—
325C2×C4×C83—41no—
326C2×C4×C83—41no—
327C2×C4×C83—42no—
328C2×C4×C83—42no—
329C2×C4×C83—42no—
330C2×C4×C83—41no—
331C2×C4×C83—42no—
332C2×C4×C83—41no—
333C2×C4×C83—41no—
334C2×C4×C83—42no—
335C2×C4×C83—42no—
336C2×C4×C83—42no—
337C2×C4×C83—42no—
338C2×C4×C83—42no—
339C2×C4×C83—42no—
340C2×C4×C83—42no—
341C2×C4×C83#12014yes—
342C2×C4×C83#12118yes—
343C22×C83—24no—
344C22×C83—24no—
345C22×C83—24no—
346C22×C83—24no—
347C22×C83—24no—
348C22×C83—24no—
349C22×C83—28no—
350C22×C83—28no—
351C22×C83—28no—
352C22×C83—28no—
353C22×C83—42no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—44no—
357C22×C83—44no—
358C22×C83—81no—
359C22×C83—81no—
360C22×C83—81no—
361C22×C83—81no—
362C22×C83—82no—
363C22×C83—82no—
364C22×C83#39618yescomplemented
365C22×C83C2×#12011yescharacteristic
366C22×C83C2×#12111yescharacteristic
367C22×C83C2×#12112yes—
368C22×C83C2×#12111yescharacteristic
369C22×C83C2×#12111yescharacteristic
370C22×C83C2×C22⋊Q811yescharacteristic
371C22×C83C2×C22⋊Q811yescharacteristic
372C22×C83C2×C22⋊Q811yescharacteristic
373C22×C83#52511yescharacteristic
374C22×C83#52512yes—
375C22×C83C2×#12611yescharacteristic
376C22×C83#53411yescharacteristic
377C22×C83#53611yescharacteristic
378C22×C83#53712yes—
379C22×C83#53912yes—
380C22×C83D4212yes—
381C22×C83#54612yes—
382C22×C83#54712yes—
383C22×C83#54812yes—
384C22×C83D4×Q812yes—
385C22×C83#55212yes—
386C22×C83#55312yes—
387C22×C83#55412yes—
388C4×C83—28no—
389C4×C83—24no—
390C4×C83—42no—
391C4×C83—42no—
392C4×C83—44no—
393C4×C83—44no—
394C4×C83—81no—
395C4×C83—81no—
396C4×C83—82no—
397#14729C8311yesmaximal, characteristic, direct product factor, Sylow
398C2×C83—28no—
399C2×C83—82no—
400C2×C83C2×#39611yescharacteristic
401C2×C83#240911yescharacteristic
402C2×C83#241011yescharacteristic
403C2×C83#241311yescharacteristic
404C2×C83#241612yes—
405C2×C83#241712yes—
406C2×C83#244912yes—
407C2×C83#248112yes—
408C2×C83#257911yescharacteristic
409C2×C83#261811yescharacteristic
410C2×C83#284711yescharacteristic
411C23×C4⋊C4C2×C8311yescharacteristic, complemented
412C2×#396C2×C8312yescomplemented
413C2×#386C2×C8311yescharacteristic
414C2×#386C2×C8311yescharacteristic
415C2×#386C2×C8311yescharacteristic
416C2×#385C2×C8311yescharacteristic, complemented
417C2×#380C2×C8311yescharacteristic, complemented
418#1441C2×C8312yescomplemented
419#1441C2×C8312yescomplemented
420#1439C2×C8312yescomplemented
421C22⋊#95C2×C8311yescharacteristic, complemented
422C83#1472911yescharacteristic, direct product factor, Sylow
423C23×D4C22×C8311yescharacteristic
424C24×C4C22×C8311yescharacteristic
425C24×C4C22×C8311yescharacteristic
426C24×C4C22×C8311yescharacteristic
427C22×C4⋊C4—24no—
428C22×C4⋊C4—28no—
429C22×C4⋊C4C22×C8312yes—
430C22×C4⋊C4C22×C8312yes—
431C22×C4⋊C4C22×C8312yes—
432C22×C4⋊C4C22×C8312yes—
433C22×C22⋊C4C22×C8311yescharacteristic
434C22×C22⋊C4C22×C8312yes—
435C22×C22⋊C4C22×C8311yescharacteristic
436C22×C22⋊C4C22×C8311yescharacteristic
437C22×C22⋊C4C22×C8312yes—
438C22×C22⋊C4C22×C8311yescharacteristic
439C22×C22⋊C4C22×C8311yescharacteristic
440#396—28no—
441#386—24no—
442#386—24no—
443#386—24no—
444#385—24no—
445#380—24no—
446C2×#95C22×C8312yes—
447C2×#95C22×C8312yes—
448C2×#95C22×C8312yes—
449C2×#95C22×C8311yescharacteristic
450C2×#95C22×C8312yes—
451C2×#95C22×C8311yescharacteristic
452C2×#95C22×C8312yes—
453C2×#95C22×C8312yes—
454C25C23×C8311yescharacteristic
455C25C23×C8311yescharacteristic
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4Q8×C8314yes—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—24no—
471C23×C4—24no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—42no—
475C23×C4—42no—
476C23×C4D4×C8314yes—
477C23×C4D4×C8314yes—
478C23×C4C23×C8311yescharacteristic
479C23×C4C23×C8312yes—
480C23×C4C23×C8311yescharacteristic
481C23×C4C23×C8312yes—
482C23×C4C23×C8311yescharacteristic
483C23×C4C23×C8312yes—
484C23×C4C23×C8311yescharacteristic
485C23×C4C23×C8311yescharacteristic
486C23×C4C23×C8312yes—
487C2×C4⋊C4—232no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4D4×C8318yescomplemented
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4D4×C8314yes—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—22no—
523#95—22no—
524#95—24no—
525#95—24no—
526#95—42no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24C2×D4×C8312yes—
542C24C2×D4×C8312yes—
543C24C2×D4×C8312yes—
544C24C2×Q8×C8312yes—
545C24C2×Q8×C8312yes—
546C24#41×C8312yes—
547C24#41×C8312yes—
548C24#41×C8312yes—
549C24C24×C8311yescharacteristic
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C22×C4—28no—
558C22×C4—216no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—216no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4C2×D4×C8314yes—
619C22×C4C2×D4×C8312yes—
620C22×C4C2×D4×C8314yes—
621C22×C4C2×D4×C8312yes—
622C22×C4C2×D4×C8314yes—
623C22×C4C2×D4×C8314yes—
624C22×C4C2×D4×C8314yes—
625C22×C4C2×Q8×C8312yes—
626C22×C4#41×C8314yes—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C22⋊C4—28no—
632C22⋊C4—48no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—48no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23#121×C8314yes—
678C23#121×C8314yes—
679C23#121×C8314yes—
680C23C22⋊Q8×C8314yes—
681C23C22⋊Q8×C8314yes—
682C23C22⋊Q8×C8314yes—
683C23#126×C8314yes—
684C23C22×D4×C8311yescharacteristic
685C23C22×D4×C8312yes—
686C23C22×D4×C8311yescharacteristic
687C23C22×D4×C8311yescharacteristic
688C23C22×Q8×C8311yescharacteristic
689C23C2×#41×C8311yescharacteristic
690C23C2×#41×C8311yescharacteristic
691C23C2×#41×C8311yescharacteristic
692C23C2×#41×C8312yes—
693C23H(5,𝔽2)×C8312yes—
694C232−1+4×C8312yes—
695D4—416no—
696C2×C4—232no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4#120×C8314yes—
753C2×C4#121×C8318yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—82no—
774C22—82no—
775C22#396×C8318yescomplemented
776C22C2×#120×C8311yescharacteristic
777C22C2×#121×C8311yescharacteristic
778C22C2×#121×C8312yes—
779C22C2×#121×C8311yescharacteristic
780C22C2×#121×C8311yescharacteristic
781C22C2×C22⋊Q8×C8311yescharacteristic
782C22C2×C22⋊Q8×C8311yescharacteristic
783C22C2×C22⋊Q8×C8311yescharacteristic
784C22#525×C8311yescharacteristic
785C22#525×C8312yes—
786C22C2×#126×C8311yescharacteristic
787C22#534×C8311yescharacteristic
788C22#536×C8311yescharacteristic
789C22#537×C8312yes—
790C22#539×C8312yes—
791C22D42×C8312yes—
792C22#546×C8312yes—
793C22#547×C8312yes—
794C22#548×C8312yes—
795C22D4×Q8×C8312yes—
796C22#552×C8312yes—
797C22#553×C8312yes—
798C22#554×C8312yes—
799C4—28no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—82no—
808C2—28no—
809C2—82no—
810C2C2×#396×C8311yescharacteristic
811C2C83×#240911yescharacteristic
812C2C83×#241011yescharacteristic
813C2C83×#241311yescharacteristic
814C2C83×#241612yes—
815C2C83×#241712yes—
816C2C83×#244912yes—
817C2C83×#248112yes—
818C2C83×#257911yescharacteristic
819C2C83×#261811yescharacteristic
820C2C83×#284711yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC23×D4×C83C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C4⋊C4×C83C2semidirect
2. C2×#396×C83C2semidirect
6. C2×#385×C83C2semidirect
7. C2×#380×C83C2semidirect
8. C83×#1441C2semidirect
9. C83×#1441C2semidirect
10. C83×#1439C2semidirect
11. C83×C22⋊#95C2semidirect
88. C2×C4⋊C4×C83D4semidirect
364. C22×C83#396semidirect
397. #14729C83direct (N × H)
411. C23×C4⋊C4C2×C83semidirect
412. C2×#396C2×C83semidirect
416. C2×#385C2×C83semidirect
417. C2×#380C2×C83semidirect
418. #1441C2×C83semidirect
419. #1441C2×C83semidirect
420. #1439C2×C83semidirect
421. C22⋊#95C2×C83semidirect
422. C83#14729direct (N × H)
499. C2×C4⋊C4D4×C83semidirect
775. C22#396×C83semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C832
C2×#396×C832
C2×#386×C832
C2×#385×C832
C2×#380×C832
C83×#14412
C83×#14392
C83×C22⋊#952
#1472983