Finite Group Databasebeta

← C83×#24390 #35252214

Subgroups — C83×#24390 #35252214

Order 21248.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C83C211yesmaximal, characteristic, complemented
2C2×#469×C83C211yesmaximal, characteristic, complemented
3C2×#466×C83C211yesmaximal, characteristic, complemented
4C2×#447×C83C211yesmaximal, characteristic, complemented
5C2×#408×C83C211yesmaximal, characteristic, complemented
6C83×#2615C211yesmaximal, characteristic, complemented
7C83×#2034C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#1999C211yesmaximal, characteristic, complemented
10C83×#1999C211yesmaximal, characteristic, complemented
11C83×#1895C211yesmaximal, characteristic, complemented
12C83×#1893C211yesmaximal, characteristic, complemented
13C83×#1875C211yesmaximal, characteristic, complemented
14C83×#1854C211yesmaximal, characteristic, complemented
15C83×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×M16×C83C2211yescharacteristic, complemented
21C23×C8×C83C2211yescharacteristic, complemented
22#535×C83—24no—
23#535×C83—24no—
24C2×#127×C83—21no—
25C2×#124×C83—21no—
26C2×#121×C83C2211yescharacteristic
27C2×#121×C83C2211yescharacteristic
28C2×#121×C83C2211yescharacteristic
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic, complemented
32C2×#121×C83C2211yescharacteristic, complemented
33C2×#120×C83—21no—
34C2×#120×C83—21no—
35C2×#117×C83C2211yescharacteristic
36#469×C83—24no—
37#466×C83—24no—
38#447×C83—24no—
39C2×#107×C83C2211yescharacteristic, complemented
40C2×#106×C83C2211yescharacteristic, complemented
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic, complemented
48C2×#102×C83C2211yescharacteristic, complemented
49#408×C83—24no—
50C2×C22⋊C8×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic, complemented
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#393×C83—21no—
55#392×C83—21no—
56#392×C83—21no—
57#392×C83—21no—
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic, complemented
60#380×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#340×C83C2211yescharacteristic, complemented
64#340×C83C2211yescharacteristic, complemented
65C25×C83—21no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—41no—
71C2×#41×C83—41no—
72C22×Q8×C83D411yescharacteristic
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83—22no—
78C22×D4×C83—22no—
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83—21no—
83C22×D4×C83—22no—
84C22×D4×C83—22no—
85C22×D4×C83—41no—
86C22×D4×C83—41no—
87C22×D4×C83D411yescharacteristic
88C22×D4×C83D411yescharacteristic
89C22×D4×C83D411yescharacteristic
90C22×D4×C83C2311yescharacteristic
91C22×D4×C83C2311yescharacteristic
92C22×D4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2311yescharacteristic
96C2×D8×C83—22no—
97C2×D8×C83—22no—
98C2×D8×C83—22no—
99C2×D8×C83—22no—
100C2×D8×C83—41no—
101C2×D8×C83—41no—
102C2×M16×C83—22no—
103C2×M16×C83—22no—
104C2×M16×C83—41no—
105C22×C8×C83—22no—
106C22×C8×C83—22no—
107C22×C8×C83—41no—
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2311yescharacteristic
112#127×C83—28no—
113#124×C83—28no—
114#121×C83—22no—
115#121×C83—22no—
116#121×C83—22no—
117#121×C83—22no—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—22no—
123#121×C83—22no—
124#121×C83—41no—
125#121×C83—41no—
126#121×C83D414yescomplemented
127#121×C83D414yescomplemented
128#120×C83—28no—
129#120×C83—28no—
130#117×C83—22no—
131#117×C83—22no—
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C22⋊C4×C83—21no—
138C2×C22⋊C4×C83—21no—
139C2×C22⋊C4×C83—21no—
140C2×C22⋊C4×C83—21no—
141C2×C22⋊C4×C83—21no—
142C2×C22⋊C4×C83—21no—
143C2×C22⋊C4×C83—21no—
144C2×C22⋊C4×C83—21no—
145C2×C22⋊C4×C83—21no—
146C2×C22⋊C4×C83—21no—
147C2×C22⋊C4×C83—21no—
148C2×C42×C83—21no—
149#107×C83—22no—
150#106×C83—22no—
151#102×C83—22no—
152#102×C83—22no—
153#102×C83—22no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—41no—
158#102×C83—41no—
159C22⋊C8×C83—22no—
160C22⋊C8×C83—22no—
161C22⋊C8×C83—22no—
162C22⋊C8×C83D414yescomplemented
163#95×C83—21no—
164#95×C83—21no—
165#95×C83—21no—
166C24×C83—24no—
167C24×C83—21no—
168C24×C83—21no—
169C24×C83—21no—
170C24×C83—42no—
171C24×C83—42no—
172C24×C83—81no—
173C24×C83—81no—
174C24×C83—81no—
175C24×C83—81no—
176C24×C83C2×D411yescharacteristic
177C24×C83C2×D411yescharacteristic
178C24×C83C2×D411yescharacteristic
179#41×C83—44no—
180#41×C83—44no—
181#41×C83—44no—
182#41×C83—44no—
183C2×Q8×C83—22no—
184C2×Q8×C83—22no—
185C2×Q8×C83—41no—
186C2×D4×C83—24no—
187C2×D4×C83—22no—
188C2×D4×C83—22no—
189C2×D4×C83—22no—
190C2×D4×C83—22no—
191C2×D4×C83—24no—
192C2×D4×C83—24no—
193C2×D4×C83—24no—
194C2×D4×C83—24no—
195C2×D4×C83—22no—
196C2×D4×C83—22no—
197C2×D4×C83—21no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—21no—
208C2×D4×C83—21no—
209C2×D4×C83—21no—
210C2×D4×C83—21no—
211C2×D4×C83—21no—
212C2×D4×C83—21no—
213C2×D4×C83—44no—
214C2×D4×C83—44no—
215C2×D4×C83—44no—
216C2×D4×C83—44no—
217C2×D4×C83—41no—
218C2×D4×C83—41no—
219C2×D4×C83—41no—
220C2×D4×C83—42no—
221C2×D4×C83—42no—
222C2×D4×C83—42no—
223C2×D4×C83—42no—
224C2×D4×C83—42no—
225C2×D4×C83—81no—
226C2×D4×C83—81no—
227C2×D4×C83—81no—
228C2×D4×C83—81no—
229C2×D4×C83—81no—
230C2×D4×C83—81no—
231C2×D4×C83—81no—
232C2×D4×C83—81no—
233C2×D4×C83—81no—
234C2×D4×C83—81no—
235C2×D4×C83—81no—
236C2×D4×C83—81no—
237C2×D4×C83—81no—
238C2×D4×C83—81no—
239C2×D4×C83C2×D412yes—
240C2×D4×C83C2×D412yes—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83C2×D411yescharacteristic
261C22×C4×C83C2×D411yescharacteristic
262C22×C4×C83C2×D412yes—
263C22×C4×C83C2×D412yes—
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D412yes—
266C22×C4×C83#4112yes—
267C22×C4×C83C2411yescharacteristic
268D8×C83—44no—
269D8×C83—44no—
270M16×C83—44no—
271C2×C8×C83—21no—
272C2×C8×C83—21no—
273C2×C8×C83—21no—
274C2×C8×C83—21no—
275C2×C8×C83—21no—
276C2×C8×C83—21no—
277C2×C8×C83—21no—
278C2×C8×C83—21no—
279C2×C8×C83—21no—
280C2×C8×C83—21no—
281C2×C8×C83—44no—
282C2×C8×C83C2×D412yes—
283C2×C8×C83C2×D412yes—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83—21no—
291C4⋊C4×C83—21no—
292C4⋊C4×C83C2×D412yes—
293C4⋊C4×C83C2×D412yes—
294C22⋊C4×C83—24no—
295C22⋊C4×C83—24no—
296C22⋊C4×C83—24no—
297C22⋊C4×C83—24no—
298C22⋊C4×C83—24no—
299C22⋊C4×C83—42no—
300C22⋊C4×C83—42no—
301C22⋊C4×C83—42no—
302C22⋊C4×C83—81no—
303C22⋊C4×C83—81no—
304C22⋊C4×C83—81no—
305C42×C83—24no—
306C23×C83—21no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—21no—
314C23×C83—21no—
315C23×C83—21no—
316C23×C83—21no—
317C23×C83—21no—
318C23×C83—22no—
319C23×C83—22no—
320C23×C83—21no—
321C23×C83—21no—
322C23×C83—21no—
323C23×C83—21no—
324C23×C83—21no—
325C23×C83—21no—
326C23×C83—21no—
327C23×C83—48no—
328C23×C83—41no—
329C23×C83—41no—
330C23×C83—41no—
331C23×C83—41no—
332C23×C83—41no—
333C23×C83—41no—
334C23×C83—41no—
335C23×C83—41no—
336C23×C83—41no—
337C23×C83—41no—
338C23×C83—41no—
339C23×C83—41no—
340C23×C83—41no—
341C23×C83—41no—
342C23×C83—41no—
343C23×C83—41no—
344C23×C83—41no—
345C23×C83—41no—
346C23×C83—41no—
347C23×C83—84no—
348C23×C83—84no—
349C23×C83—84no—
350C23×C83—84no—
351C23×C83—84no—
352C23×C83—84no—
353C23×C83#12012yes—
354C23×C83#12112yes—
355C23×C83C22×D411yescharacteristic
356Q8×C83—44no—
357D4×C83—22no—
358D4×C83—22no—
359D4×C83—22no—
360D4×C83—22no—
361D4×C83—44no—
362D4×C83—44no—
363D4×C83—48no—
364D4×C83—44no—
365D4×C83—41no—
366D4×C83—41no—
367D4×C83—41no—
368D4×C83—41no—
369D4×C83—41no—
370D4×C83—41no—
371D4×C83—41no—
372D4×C83—41no—
373D4×C83—84no—
374D4×C83—84no—
375D4×C83—84no—
376D4×C83—84no—
377D4×C83—84no—
378D4×C83—84no—
379D4×C83—84no—
380C2×C4×C83—21no—
381C2×C4×C83—21no—
382C2×C4×C83—21no—
383C2×C4×C83—21no—
384C2×C4×C83—22no—
385C2×C4×C83—22no—
386C2×C4×C83—22no—
387C2×C4×C83—22no—
388C2×C4×C83—22no—
389C2×C4×C83—22no—
390C2×C4×C83—22no—
391C2×C4×C83—22no—
392C2×C4×C83—22no—
393C2×C4×C83—22no—
394C2×C4×C83—21no—
395C2×C4×C83—21no—
396C2×C4×C83—21no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83—41no—
400C2×C4×C83—41no—
401C2×C4×C83—41no—
402C2×C4×C83—41no—
403C2×C4×C83—41no—
404C2×C4×C83—41no—
405C2×C4×C83—41no—
406C2×C4×C83—41no—
407C2×C4×C83—41no—
408C2×C4×C83—41no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83—41no—
412C2×C4×C83—41no—
413C2×C4×C83—41no—
414C2×C4×C83#12012yes—
415C2×C4×C83#12112yes—
416C2×C4×C83C22×D411yescharacteristic
417C2×C4×C83C22×D411yescharacteristic
418C2×C4×C83C22×D411yescharacteristic
419C2×C4×C83C2×#4111yescharacteristic
420C2×C4×C83H(5,𝔽2)11yescharacteristic
421C2×C4×C83H(5,𝔽2)11yescharacteristic
422C8×C83—22no—
423C8×C83—22no—
424C8×C83—41no—
425C8×C83—41no—
426C22×C83—22no—
427C22×C83—22no—
428C22×C83—22no—
429C22×C83—22no—
430C22×C83—22no—
431C22×C83—22no—
432C22×C83—41no—
433C22×C83—41no—
434C22×C83—41no—
435C22×C83—41no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—41no—
439C22×C83—41no—
440C22×C83—41no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—41no—
444C22×C83—41no—
445C22×C83—41no—
446C22×C83—42no—
447C22×C83—42no—
448C22×C83—41no—
449C22×C83—42no—
450C22×C83—42no—
451C22×C83—41no—
452C22×C83—41no—
453C22×C83—816no—
454C22×C83—81no—
455C22×C83—81no—
456C22×C83—81no—
457C22×C83—81no—
458C22×C83—81no—
459C22×C83—81no—
460C22×C83—81no—
461C22×C83—81no—
462C22×C83—81no—
463C22×C83—81no—
464C22×C83—81no—
465C22×C83—81no—
466C22×C83—81no—
467C22×C83—81no—
468C22×C83—81no—
469C22×C83C2×#12011yescharacteristic
470C22×C83C2×#12111yescharacteristic
471C22×C83#53411yescharacteristic
472C22×C83#57611yescharacteristic
473C22×C83#57611yescharacteristic
474C22×C83#57611yescharacteristic
475C22×C83#57711yescharacteristic
476C4×C83—22no—
477C4×C83—22no—
478C4×C83—41no—
479C4×C83—42no—
480C4×C83—42no—
481C4×C83—81no—
482C4×C83—81no—
483C4×C83—81no—
484C4×C83D4211yescharacteristic
485C4×C83D4211yescharacteristic
486C4×C83#54611yescharacteristic
487C4×C83#54611yescharacteristic
488#24390C8311yesmaximal, characteristic, direct product factor, Sylow
489C2×C83—42no—
490C2×C83—42no—
491C2×C83—81no—
492C2×C83—82no—
493C2×C83—82no—
494C2×C83—161no—
495C2×C83#241011yescharacteristic
496C2×C83#300811yescharacteristic
497C2×C83#301211yescharacteristic
498C2×C83#305811yescharacteristic
499C2×C83#306211yescharacteristic
500C2×C83#319811yescharacteristic
501C2×C83#319911yescharacteristic
502C2×#535C2×C8311yescharacteristic, complemented
503C2×#469C2×C8311yescharacteristic, complemented
504C2×#466C2×C8311yescharacteristic, complemented
505C2×#447C2×C8311yescharacteristic, complemented
506C2×#408C2×C8311yescharacteristic, complemented
507#2615C2×C8311yescharacteristic, complemented
508#2034C2×C8311yescharacteristic, complemented
509#2033C2×C8311yescharacteristic, complemented
510#1999C2×C8311yescharacteristic, complemented
511#1999C2×C8311yescharacteristic, complemented
512#1895C2×C8311yescharacteristic, complemented
513#1893C2×C8311yescharacteristic, complemented
514#1875C2×C8311yescharacteristic, complemented
515#1854C2×C8311yescharacteristic, complemented
516#1786C2×C8311yescharacteristic, complemented
517C83#2439011yescharacteristic, direct product factor, Sylow
518C22×#41C22×C8311yescharacteristic
519C23×D4C22×C8311yescharacteristic
520C22×D8C22×C8311yescharacteristic
521C22×D8C22×C8311yescharacteristic
522C22×M16C22×C8311yescharacteristic, complemented
523C23×C8C22×C8311yescharacteristic, complemented
524#535—24no—
525#535—24no—
526C2×#127—21no—
527C2×#124—21no—
528C2×#121C22×C8311yescharacteristic
529C2×#121C22×C8311yescharacteristic
530C2×#121C22×C8311yescharacteristic
531C2×#121C22×C8311yescharacteristic
532C2×#121C22×C8311yescharacteristic
533C2×#121C22×C8311yescharacteristic, complemented
534C2×#121C22×C8311yescharacteristic, complemented
535C2×#120—21no—
536C2×#120—21no—
537C2×#117C22×C8311yescharacteristic
538#469—24no—
539#466—24no—
540#447—24no—
541C2×#107C22×C8311yescharacteristic, complemented
542C2×#106C22×C8311yescharacteristic, complemented
543C2×#102C22×C8311yescharacteristic
544C2×#102C22×C8311yescharacteristic
545C2×#102C22×C8311yescharacteristic
546C2×#102C22×C8311yescharacteristic
547C2×#102C22×C8311yescharacteristic
548C2×#102C22×C8311yescharacteristic
549C2×#102C22×C8311yescharacteristic, complemented
550C2×#102C22×C8311yescharacteristic, complemented
551#408—24no—
552C2×C22⋊C8C22×C8311yescharacteristic
553C2×C22⋊C8C22×C8311yescharacteristic
554C2×C22⋊C8C22×C8311yescharacteristic, complemented
555C2×C22⋊C8C22×C8311yescharacteristic, complemented
556#393—21no—
557#392—21no—
558#392—21no—
559#392—21no—
560#380C22×C8311yescharacteristic
561#380C22×C8311yescharacteristic, complemented
562#380C22×C8311yescharacteristic, complemented
563#340C22×C8311yescharacteristic, complemented
564#340C22×C8311yescharacteristic, complemented
565#340C22×C8311yescharacteristic, complemented
566#340C22×C8311yescharacteristic, complemented
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C8311yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C8311yescharacteristic
590C22×D4D4×C8311yescharacteristic
591C22×D4D4×C8311yescharacteristic
592C22×D4C23×C8311yescharacteristic
593C22×D4C23×C8311yescharacteristic
594C22×D4C23×C8311yescharacteristic
595C23×C4C23×C8311yescharacteristic
596C23×C4C23×C8311yescharacteristic
597C23×C4C23×C8311yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C8311yescharacteristic
611C22×C8C23×C8311yescharacteristic
612C22×C8C23×C8311yescharacteristic
613C22×C8C23×C8311yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C8314yescomplemented
629#121D4×C8314yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C8311yescharacteristic
635C2×C4⋊C4C23×C8311yescharacteristic
636C2×C4⋊C4C23×C8311yescharacteristic
637C2×C4⋊C4C23×C8311yescharacteristic
638C2×C4⋊C4C23×C8311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C8314yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C8311yescharacteristic
679C24C2×D4×C8311yescharacteristic
680C24C2×D4×C8311yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C8312yes—
742C2×D4C2×D4×C8312yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C8311yescharacteristic
763C22×C4C2×D4×C8311yescharacteristic
764C22×C4C2×D4×C8312yes—
765C22×C4C2×D4×C8312yes—
766C22×C4C2×D4×C8311yescharacteristic
767C22×C4C2×D4×C8312yes—
768C22×C4#41×C8312yes—
769C22×C4C24×C8311yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C8312yes—
785C2×C8C2×D4×C8312yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C8312yes—
795C4⋊C4C2×D4×C8312yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C8312yes—
856C23#121×C8312yes—
857C23C22×D4×C8311yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C8312yes—
917C2×C4#121×C8312yes—
918C2×C4C22×D4×C8311yescharacteristic
919C2×C4C22×D4×C8311yescharacteristic
920C2×C4C22×D4×C8311yescharacteristic
921C2×C4C2×#41×C8311yescharacteristic
922C2×C4H(5,𝔽2)×C8311yescharacteristic
923C2×C4H(5,𝔽2)×C8311yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—42no—
954C22—42no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C8311yescharacteristic
972C22C2×#121×C8311yescharacteristic
973C22#534×C8311yescharacteristic
974C22#576×C8311yescharacteristic
975C22#576×C8311yescharacteristic
976C22#576×C8311yescharacteristic
977C22#577×C8311yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C8311yescharacteristic
987C4D42×C8311yescharacteristic
988C4#546×C8311yescharacteristic
989C4#546×C8311yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2C83×#241011yescharacteristic
997C2C83×#300811yescharacteristic
998C2C83×#301211yescharacteristic
999C2C83×#305811yescharacteristic
1000C2C83×#306211yescharacteristic
1001C2C83×#319811yescharacteristic
1002C2C83×#319911yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
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
1. C2×#535×C83C2semidirect
2. C2×#469×C83C2semidirect
3. C2×#466×C83C2semidirect
4. C2×#447×C83C2semidirect
5. C2×#408×C83C2semidirect
6. C83×#2615C2semidirect
7. C83×#2034C2semidirect
8. C83×#2033C2semidirect
9. C83×#1999C2semidirect
10. C83×#1999C2semidirect
11. C83×#1895C2semidirect
12. C83×#1893C2semidirect
13. C83×#1875C2semidirect
14. C83×#1854C2semidirect
15. C83×#1786C2semidirect
20. C22×M16×C83C22semidirect
21. C23×C8×C83C22semidirect
31. C2×#121×C83C22semidirect
32. C2×#121×C83C22semidirect
39. C2×#107×C83C22semidirect
40. C2×#106×C83C22semidirect
47. C2×#102×C83C22semidirect
48. C2×#102×C83C22semidirect
52. C2×C22⋊C8×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
59. #380×C83C22semidirect
60. #380×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #340×C83C22semidirect
64. #340×C83C22semidirect
126. #121×C83D4semidirect
127. #121×C83D4semidirect
162. C22⋊C8×C83D4semidirect
488. #24390C83direct (N × H)
502. C2×#535C2×C83semidirect
503. C2×#469C2×C83semidirect
504. C2×#466C2×C83semidirect
505. C2×#447C2×C83semidirect
506. C2×#408C2×C83semidirect
507. #2615C2×C83semidirect
508. #2034C2×C83semidirect
509. #2033C2×C83semidirect
510. #1999C2×C83semidirect
511. #1999C2×C83semidirect
512. #1895C2×C83semidirect
513. #1893C2×C83semidirect
514. #1875C2×C83semidirect
515. #1854C2×C83semidirect
516. #1786C2×C83semidirect
517. C83#24390direct (N × H)
522. C22×M16C22×C83semidirect
523. C23×C8C22×C83semidirect
533. C2×#121C22×C83semidirect
534. C2×#121C22×C83semidirect
541. C2×#107C22×C83semidirect
542. C2×#106C22×C83semidirect
549. C2×#102C22×C83semidirect
550. C2×#102C22×C83semidirect
554. C2×C22⋊C8C22×C83semidirect
555. C2×C22⋊C8C22×C83semidirect
561. #380C22×C83semidirect
562. #380C22×C83semidirect
563. #340C22×C83semidirect
564. #340C22×C83semidirect
565. #340C22×C83semidirect
566. #340C22×C83semidirect
628. #121D4×C83semidirect
629. #121D4×C83semidirect
664. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C832
C2×#469×C832
C2×#466×C832
C2×#447×C832
C2×#408×C832
C83×#26152
C83×#20342
C83×#20332
C83×#19992
C83×#18952
C83×#18932
C83×#18752
C83×#18542
C83×#17862
#2439083