Finite Group Databasebeta

← C83×#25179 #35253003

Subgroups — C83×#25179 #35253003

Order 21248.

1206 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C83C211yesmaximal, characteristic, complemented
2C2×#449×C83C211yesmaximal, characteristic, complemented
3C2×#449×C83C211yesmaximal, characteristic, complemented
4C2×#440×C83C211yesmaximal, characteristic, complemented
5C83×#2428C211yesmaximal, characteristic, complemented
6C83×#2341C211yesmaximal, characteristic, complemented
7C83×#2067C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2033C211yesmaximal, characteristic, complemented
10C83×#2011C211yesmaximal, characteristic, complemented
11C83×#1972C211yesmaximal, characteristic, complemented
12C83×#1924C211yesmaximal, characteristic, complemented
13C83×#1880C211yesmaximal, characteristic, complemented
14C83×#1879C211yesmaximal, characteristic, complemented
15C83×#1865C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×SD16×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C2×#127×C83C2211yescharacteristic
22C2×#121×C83—21no—
23C2×#121×C83C2211yescharacteristic
24C2×#121×C83C2211yescharacteristic
25C2×C4×Q8×C83C2211yescharacteristic
26C2×C4×Q8×C83C2211yescharacteristic
27C2×C4×D4×C83C2211yescharacteristic
28#460×C83—24no—
29#449×C83—24no—
30#449×C83—24no—
31#440×C83—24no—
32C2×#107×C83C2211yescharacteristic
33C2×#106×C83C2211yescharacteristic
34C2×C4⋊C8×C83C2211yescharacteristic
35C2×#103×C83C2211yescharacteristic
36C2×#103×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic
41C2×#102×C83C2211yescharacteristic
42C2×#102×C83C2211yescharacteristic
43C2×C22⋊C8×C83C2211yescharacteristic
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×#97×C83C2211yescharacteristic
46#394×C83—21no—
47#392×C83—21no—
48#390×C83—21no—
49#390×C83—21no—
50#390×C83C2211yescharacteristic
51#390×C83C2211yescharacteristic
52#390×C83C2211yescharacteristic
53#389×C83C2211yescharacteristic
54#386×C83—21no—
55#380×C83—21no—
56#380×C83C2211yescharacteristic
57C4×C22⋊C4×C83—21no—
58C4×C22⋊C4×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C2×#41×C83—22no—
64C2×#41×C83—22no—
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—41no—
68C2×#41×C83—41no—
69C22×Q8×C83C2311yescharacteristic
70C22×D4×C83—21no—
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83C2311yescharacteristic
76C22×D4×C83C2311yescharacteristic
77C22×D4×C83C2311yescharacteristic
78C23×C4×C83—21no—
79C23×C4×C83—21no—
80C23×C4×C83C2311yescharacteristic
81C2×SD16×C83—22no—
82C2×SD16×C83—22no—
83C2×SD16×C83—22no—
84C2×SD16×C83—22no—
85C2×SD16×C83—22no—
86C2×SD16×C83D414yescomplemented
87C2×D8×C83—22no—
88C2×D8×C83—22no—
89C2×D8×C83—22no—
90C2×D8×C83—22no—
91C2×D8×C83—41no—
92C2×D8×C83—41no—
93C22×C8×C83C2311yescharacteristic
94C22×C8×C83C2311yescharacteristic
95C22×C8×C83C2311yescharacteristic
96C22×C8×C83C2311yescharacteristic
97#127×C83—22no—
98#127×C83—41no—
99#121×C83—22no—
100#121×C83—22no—
101#121×C83—44no—
102#121×C83—41no—
103#121×C83—41no—
104C4×Q8×C83—22no—
105C4×Q8×C83—22no—
106C4×Q8×C83—41no—
107C4×Q8×C83—41no—
108C4×D4×C83—22no—
109C4×D4×C83—41no—
110C2×C4⋊C4×C83—21no—
111C2×C4⋊C4×C83—21no—
112C2×C4⋊C4×C83—21no—
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—21no—
120C2×C22⋊C4×C83—21no—
121C2×C22⋊C4×C83—21no—
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×C83D411yescharacteristic
128C2×C22⋊C4×C83D411yescharacteristic
129C2×C42×C83—21no—
130C2×C42×C83—21no—
131C2×C42×C83C2311yescharacteristic
132C2×C42×C83C2311yescharacteristic
133#107×C83—22no—
134#106×C83—41no—
135C4⋊C8×C83—22no—
136#103×C83—22no—
137#103×C83D414yescomplemented
138#102×C83—22no—
139#102×C83—22no—
140#102×C83—22no—
141#102×C83—22no—
142#102×C83—22no—
143#102×C83—41no—
144C22⋊C8×C83—22no—
145C22⋊C8×C83—22no—
146#97×C83—22no—
147#95×C83—21no—
148#95×C83—21no—
149#95×C83D411yescharacteristic
150#95×C83D411yescharacteristic
151C24×C83—21no—
152C24×C83—21no—
153C24×C83—21no—
154C24×C83C2×D411yescharacteristic
155#41×C83—44no—
156#41×C83—44no—
157#41×C83—44no—
158#41×C83—44no—
159C2×Q8×C83—21no—
160C2×Q8×C83—21no—
161C2×Q8×C83—21no—
162C2×Q8×C83C2×D412yes—
163C2×Q8×C83C2×D412yes—
164C2×Q8×C83#4112yes—
165C2×D4×C83—24no—
166C2×D4×C83—21no—
167C2×D4×C83—21no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—21no—
174C2×D4×C83—21no—
175C2×D4×C83—21no—
176C2×D4×C83—21no—
177C2×D4×C83—21no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—42no—
183C2×D4×C83—42no—
184C2×D4×C83—42no—
185C2×D4×C83—42no—
186C2×D4×C83—42no—
187C2×D4×C83—42no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—42no—
191C2×D4×C83—42no—
192C2×D4×C83—81no—
193C2×D4×C83—81no—
194C2×D4×C83—81no—
195C2×D4×C83—81no—
196C2×D4×C83C2×D412yes—
197C2×D4×C83#4112yes—
198C22×C4×C83—21no—
199C22×C4×C83—24no—
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—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—42no—
211C22×C4×C83—42no—
212C22×C4×C83—42no—
213C22×C4×C83—42no—
214C22×C4×C83—81no—
215C22×C4×C83C2×D411yescharacteristic
216C22×C4×C83C2×D411yescharacteristic
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2×D411yescharacteristic
219C22×C4×C83C2×D411yescharacteristic
220C22×C4×C83C2411yescharacteristic
221SD16×C83—28no—
222SD16×C83—44no—
223D8×C83—44no—
224D8×C83—44no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—21no—
231C2×C8×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83—21no—
234C2×C8×C83—21no—
235C2×C8×C83C2×D412yes—
236C2×C8×C83C2×D412yes—
237C4⋊C4×C83—21no—
238C4⋊C4×C83—21no—
239C4⋊C4×C83—21no—
240C4⋊C4×C83—21no—
241C4⋊C4×C83—21no—
242C4⋊C4×C83—21no—
243C4⋊C4×C83—21no—
244C4⋊C4×C83—42no—
245C4⋊C4×C83—42no—
246C4⋊C4×C83—42no—
247C4⋊C4×C83C2×D412yes—
248C22⋊C4×C83—22no—
249C22⋊C4×C83—41no—
250C22⋊C4×C83—42no—
251C22⋊C4×C83—42no—
252C22⋊C4×C83—42no—
253C22⋊C4×C83—42no—
254C22⋊C4×C83—42no—
255C22⋊C4×C83—42no—
256C22⋊C4×C83—81no—
257C22⋊C4×C83—81no—
258C22⋊C4×C83—81no—
259C22⋊C4×C83—81no—
260C42×C83—21no—
261C42×C83—21no—
262C42×C83—21no—
263C42×C83—21no—
264C42×C83—42no—
265C42×C83—42no—
266C23×C83—21no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—21no—
270C23×C83—21no—
271C23×C83—21no—
272C23×C83—21no—
273C23×C83—21no—
274C23×C83—21no—
275C23×C83—41no—
276C23×C83—41no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83C22×D411yescharacteristic
295Q8×C83—22no—
296Q8×C83—22no—
297Q8×C83—22no—
298Q8×C83#12114yescomplemented
299D4×C83—22no—
300D4×C83—22no—
301D4×C83—22no—
302D4×C83—22no—
303D4×C83—48no—
304D4×C83—41no—
305D4×C83—41no—
306D4×C83—41no—
307D4×C83—41no—
308D4×C83—41no—
309D4×C83—41no—
310D4×C83—41no—
311D4×C83—41no—
312D4×C83—84no—
313D4×C83—84no—
314D4×C83—84no—
315D4×C83—84no—
316C2×C4×C83—22no—
317C2×C4×C83—21no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—21no—
324C2×C4×C83—21no—
325C2×C4×C83—22no—
326C2×C4×C83—21no—
327C2×C4×C83—21no—
328C2×C4×C83—21no—
329C2×C4×C83—21no—
330C2×C4×C83—21no—
331C2×C4×C83—21no—
332C2×C4×C83—21no—
333C2×C4×C83—21no—
334C2×C4×C83—48no—
335C2×C4×C83—41no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
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—84no—
351C2×C4×C83AGL(1,ℤ/8)12yes—
352C2×C4×C83C22×D411yescharacteristic
353C2×C4×C83C22×D411yescharacteristic
354C2×C4×C83C2×#4111yescharacteristic
355C2×C4×C83C2×#4111yescharacteristic
356C2×C4×C83H(5,𝔽2)11yescharacteristic
357C2×C4×C83H(5,𝔽2)11yescharacteristic
358C8×C83—22no—
359C8×C83—22no—
360C8×C83—41no—
361C8×C83—41no—
362C22×C83—41no—
363C22×C83—42no—
364C22×C83—41no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—41no—
368C22×C83—42no—
369C22×C83—41no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—41no—
373C22×C83—41no—
374C22×C83—41no—
375C22×C83—81no—
376C22×C83—81no—
377C22×C83—81no—
378C22×C83—81no—
379C22×C83—81no—
380C22×C83—81no—
381C22×C83—81no—
382C22×C83—81no—
383C22×C83—81no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83—81no—
389C22×C83—81no—
390C22×C83#52511yescharacteristic
391C22×C83D4211yescharacteristic
392C22×C83D4211yescharacteristic
393C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C83#57511yescharacteristic
395C22×C83#57611yescharacteristic
396C22×C83#57711yescharacteristic
397C4×C83—24no—
398C4×C83—22no—
399C4×C83—41no—
400C4×C83—41no—
401C4×C83—41no—
402C4×C83—41no—
403C4×C83—42no—
404C4×C83—81no—
405C4×C83—81no—
406C4×C83—81no—
407C4×C83C2×#12111yescharacteristic
408C4×C83#53811yescharacteristic
409C4×C83#54611yescharacteristic
410C4×C83#54611yescharacteristic
411#25179C8311yesmaximal, characteristic, direct product factor, Sylow
412C2×C83—81no—
413C2×C83—82no—
414C2×C83—82no—
415C2×C83—161no—
416C2×C83#242411yescharacteristic
417C2×C83#311511yescharacteristic
418C2×C83#311911yescharacteristic
419C2×C83#326511yescharacteristic
420C2×C83#326811yescharacteristic
421C2×C83#327111yescharacteristic
422C2×C83#327411yescharacteristic
423C2×#460C2×C8311yescharacteristic, complemented
424C2×#449C2×C8311yescharacteristic, complemented
425C2×#449C2×C8311yescharacteristic, complemented
426C2×#440C2×C8311yescharacteristic, complemented
427#2428C2×C8311yescharacteristic, complemented
428#2341C2×C8311yescharacteristic, complemented
429#2067C2×C8311yescharacteristic, complemented
430#2034C2×C8311yescharacteristic, complemented
431#2033C2×C8311yescharacteristic, complemented
432#2011C2×C8311yescharacteristic, complemented
433#1972C2×C8311yescharacteristic, complemented
434#1924C2×C8311yescharacteristic, complemented
435#1880C2×C8311yescharacteristic, complemented
436#1879C2×C8311yescharacteristic, complemented
437#1865C2×C8311yescharacteristic, complemented
438C83#2517911yescharacteristic, direct product factor, Sylow
439C22×#41C22×C8311yescharacteristic
440C22×SD16C22×C8311yescharacteristic
441C22×SD16C22×C8311yescharacteristic
442C22×D8C22×C8311yescharacteristic
443C22×D8C22×C8311yescharacteristic
444C2×#127C22×C8311yescharacteristic
445C2×#121—21no—
446C2×#121C22×C8311yescharacteristic
447C2×#121C22×C8311yescharacteristic
448C2×C4×Q8C22×C8311yescharacteristic
449C2×C4×Q8C22×C8311yescharacteristic
450C2×C4×D4C22×C8311yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454#440—24no—
455C2×#107C22×C8311yescharacteristic
456C2×#106C22×C8311yescharacteristic
457C2×C4⋊C8C22×C8311yescharacteristic
458C2×#103C22×C8311yescharacteristic
459C2×#103C22×C8311yescharacteristic
460C2×#102C22×C8311yescharacteristic
461C2×#102C22×C8311yescharacteristic
462C2×#102C22×C8311yescharacteristic
463C2×#102C22×C8311yescharacteristic
464C2×#102C22×C8311yescharacteristic
465C2×#102C22×C8311yescharacteristic
466C2×C22⋊C8C22×C8311yescharacteristic
467C2×C22⋊C8C22×C8311yescharacteristic
468C2×#97C22×C8311yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C8311yescharacteristic
474#390C22×C8311yescharacteristic
475#390C22×C8311yescharacteristic
476#389C22×C8311yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C8311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C8311yescharacteristic
482#340C22×C8311yescharacteristic
483#340C22×C8311yescharacteristic
484#336C22×C8311yescharacteristic
485#336C22×C8311yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C8311yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C8311yescharacteristic
499C22×D4C23×C8311yescharacteristic
500C22×D4C23×C8311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C8311yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C8314yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C8311yescharacteristic
517C22×C8C23×C8311yescharacteristic
518C22×C8C23×C8311yescharacteristic
519C22×C8C23×C8311yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C8311yescharacteristic
537C2×C4⋊C4C23×C8311yescharacteristic
538C2×C4⋊C4C23×C8311yescharacteristic
539C2×C4⋊C4C23×C8311yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C8311yescharacteristic
551C2×C22⋊C4D4×C8311yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C8311yescharacteristic
555C2×C42C23×C8311yescharacteristic
556#107—22no—
557#106—41no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C8314yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569#97—22no—
570#95—21no—
571#95—21no—
572#95D4×C8311yescharacteristic
573#95D4×C8311yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C8311yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C8312yes—
586C2×Q8C2×D4×C8312yes—
587C2×Q8#41×C8312yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C8312yes—
620C2×D4#41×C8312yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C8311yescharacteristic
639C22×C4C2×D4×C8311yescharacteristic
640C22×C4C2×D4×C8311yescharacteristic
641C22×C4C2×D4×C8311yescharacteristic
642C22×C4C2×D4×C8311yescharacteristic
643C22×C4C24×C8311yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C8312yes—
659C2×C8C2×D4×C8312yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C8312yes—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C8311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C8314yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—48no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4AGL(1,ℤ/8)×C8312yes—
775C2×C4C22×D4×C8311yescharacteristic
776C2×C4C22×D4×C8311yescharacteristic
777C2×C4C2×#41×C8311yescharacteristic
778C2×C4C2×#41×C8311yescharacteristic
779C2×C4H(5,𝔽2)×C8311yescharacteristic
780C2×C4H(5,𝔽2)×C8311yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—42no—
787C22—41no—
788C22—42no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C8311yescharacteristic
814C22D42×C8311yescharacteristic
815C22D42×C8311yescharacteristic
816C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
817C22#575×C8311yescharacteristic
818C22#576×C8311yescharacteristic
819C22#577×C8311yescharacteristic
820C4—24no—
821C4—22no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C8311yescharacteristic
831C4#538×C8311yescharacteristic
832C4#546×C8311yescharacteristic
833C4#546×C8311yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C83×#242411yescharacteristic
839C2C83×#311511yescharacteristic
840C2C83×#311911yescharacteristic
841C2C83×#326511yescharacteristic
842C2C83×#326811yescharacteristic
843C2C83×#327111yescharacteristic
844C2C83×#327411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#460×C83C2semidirect
2. C2×#449×C83C2semidirect
3. C2×#449×C83C2semidirect
4. C2×#440×C83C2semidirect
5. C83×#2428C2semidirect
6. C83×#2341C2semidirect
7. C83×#2067C2semidirect
8. C83×#2034C2semidirect
9. C83×#2033C2semidirect
10. C83×#2011C2semidirect
11. C83×#1972C2semidirect
12. C83×#1924C2semidirect
13. C83×#1880C2semidirect
14. C83×#1879C2semidirect
15. C83×#1865C2semidirect
86. C2×SD16×C83D4semidirect
137. #103×C83D4semidirect
298. Q8×C83#121semidirect
411. #25179C83direct (N × H)
423. C2×#460C2×C83semidirect
424. C2×#449C2×C83semidirect
425. C2×#449C2×C83semidirect
426. C2×#440C2×C83semidirect
427. #2428C2×C83semidirect
428. #2341C2×C83semidirect
429. #2067C2×C83semidirect
430. #2034C2×C83semidirect
431. #2033C2×C83semidirect
432. #2011C2×C83semidirect
433. #1972C2×C83semidirect
434. #1924C2×C83semidirect
435. #1880C2×C83semidirect
436. #1879C2×C83semidirect
437. #1865C2×C83semidirect
438. C83#25179direct (N × H)
509. C2×SD16D4×C83semidirect
560. #103D4×C83semidirect
721. Q8#121×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C832
C2×#449×C832
C2×#440×C832
C83×#24282
C83×#23412
C83×#20672
C83×#20342
C83×#20332
C83×#20112
C83×#19722
C83×#19242
C83×#18802
C83×#18792
C83×#18652
#2517983