Finite Group Databasebeta

← C83×#22886 #35250710

Subgroups — C83×#22886 #35250710

Order 21248.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3002C211yesmaximal, characteristic
2C2×#444×C83C211yesmaximal, characteristic, complemented
3C83×#2933C211yesmaximal, characteristic, complemented
4C22×#104×C83C211yesmaximal, characteristic, complemented
5C83×#2880C211yesmaximal, characteristic, complemented
6C83×#1975C211yesmaximal, characteristic, complemented
7C83×#1938C211yesmaximal, characteristic, complemented
8C83×#1929C211yesmaximal, characteristic, complemented
9C83×#1896C211yesmaximal, characteristic, complemented
10C83×#1876C211yesmaximal, characteristic, complemented
11C83×#1876C211yesmaximal, characteristic, complemented
12C83×#1866C211yesmaximal, characteristic, complemented
13C83×#1855C211yesmaximal, characteristic, complemented
14C83×#1765C211yesmaximal, characteristic, complemented
15C83×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C2×#135×C83C2211yescharacteristic
18C2×#135×C83C2211yescharacteristic
19C2×#131×C83C2211yescharacteristic
20C2×#131×C83C2211yescharacteristic
21C2×#131×C83C2211yescharacteristic, complemented
22C22×M16×C83C2211yescharacteristic
23#525×C83C2211yescharacteristic
24C22×C42×C83C2211yescharacteristic
25#452×C83C411yescharacteristic, complemented
26#452×C83C411yescharacteristic, complemented
27#451×C83C411yescharacteristic, complemented
28#450×C83C411yescharacteristic, complemented
29#449×C83C411yescharacteristic, complemented
30#449×C83C411yescharacteristic, complemented
31#448×C83C411yescharacteristic, complemented
32#447×C83C411yescharacteristic, complemented
33#444×C83—24no—
34#436×C83—21no—
35#435×C83—21no—
36#435×C83—21no—
37C8×D4×C83—21no—
38C2×#108×C83C2211yescharacteristic, complemented
39C2×#108×C83C2211yescharacteristic, complemented
40#424×C83C2211yescharacteristic, complemented
41C2×#104×C83—24no—
42C2×#104×C83C2211yescharacteristic
43C2×#104×C83C2211yescharacteristic
44C2×#104×C83C2211yescharacteristic
45C2×#104×C83C2211yescharacteristic
46C2×#104×C83C2211yescharacteristic, complemented
47C2×#104×C83C2211yescharacteristic, complemented
48#416×C83C2211yescharacteristic
49#416×C83C2211yescharacteristic
50#408×C83—21no—
51#408×C83—21no—
52#408×C83C2211yescharacteristic
53#408×C83C2211yescharacteristic
54#408×C83C2211yescharacteristic, complemented
55#407×C83—21no—
56#407×C83C2211yescharacteristic
57C2×C22⋊C8×C83—21no—
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60#405×C83C2211yescharacteristic, complemented
61C2×#97×C83C2211yescharacteristic, complemented
62C2×#97×C83C2211yescharacteristic, complemented
63#341×C83C2211yescharacteristic, complemented
64#341×C83C2211yescharacteristic, complemented
65#339×C83C2211yescharacteristic, complemented
66#339×C83C2211yescharacteristic, complemented
67#336×C83C2211yescharacteristic, complemented
68#336×C83C2211yescharacteristic, complemented
69C2×#41×C83—21no—
70C2×#41×C83—21no—
71C2×#41×C83—22no—
72C2×#41×C83—22no—
73C2×#41×C83—41no—
74C2×#41×C83—41no—
75C2×#41×C83C2×C411yescharacteristic
76C2×#41×C83C2×C411yescharacteristic
77C2×#41×C83C2311yescharacteristic
78C2×#41×C83C2311yescharacteristic
79C2×#41×C83C2311yescharacteristic
80C22×Q8×C83C2×C411yescharacteristic
81C22×D4×C83—21no—
82C22×D4×C83C2×C411yescharacteristic
83C23×C4×C83—21no—
84C23×C4×C83—21no—
85C23×C4×C83C2311yescharacteristic
86#135×C83—22no—
87#135×C83—22no—
88#135×C83—41no—
89#135×C83—41no—
90C2×Q16×C83C2×C411yescharacteristic, complemented
91C2×Q16×C83C2×C411yescharacteristic, complemented
92C2×SD16×C83C2×C411yescharacteristic, complemented
93C2×SD16×C83C2×C411yescharacteristic, complemented
94C2×SD16×C83C2×C411yescharacteristic, complemented
95C2×SD16×C83C2×C411yescharacteristic, complemented
96C2×D8×C83C2×C411yescharacteristic, complemented
97C2×D8×C83C2×C411yescharacteristic, complemented
98#131×C83—22no—
99#131×C83—22no—
100#131×C83—22no—
101#131×C83—41no—
102#131×C83—41no—
103#131×C83—41no—
104C2×M16×C83—21no—
105C2×M16×C83—21no—
106C2×M16×C83—21no—
107C2×M16×C83—21no—
108C2×M16×C83—22no—
109C2×M16×C83—41no—
110C2×M16×C83C2311yescharacteristic
111C2×M16×C83C2311yescharacteristic
112C2×M16×C83C2311yescharacteristic
113C2×M16×C83C2311yescharacteristic
114C22×C8×C83—21no—
115C22×C8×C83—21no—
116C22×C8×C83—21no—
117C22×C8×C83—21no—
118C22×C8×C83C2311yescharacteristic
119C22×C8×C83C2311yescharacteristic
120C22×C8×C83C2311yescharacteristic
121C22×C8×C83C2311yescharacteristic
122#123×C83—21no—
123C22⋊Q8×C83C2×C411yescharacteristic
124C22⋊Q8×C83C2×C411yescharacteristic
125#121×C83C2×C411yescharacteristic
126#121×C83C2×C411yescharacteristic
127#120×C83—21no—
128C4×D4×C83—21no—
129C4×D4×C83—21no—
130#117×C83C2311yescharacteristic
131C2×C42×C83—22no—
132C2×C42×C83—21no—
133C2×C42×C83—41no—
134C2×C42×C83C2311yescharacteristic
135C2×C42×C83C2311yescharacteristic
136#108×C83—22no—
137#108×C83—41no—
138C4⋊C8×C83—21no—
139C4⋊C8×C83—21no—
140#104×C83—22no—
141#104×C83—22no—
142#104×C83—22no—
143#104×C83—22no—
144#104×C83—41no—
145#104×C83D414yescomplemented
146#103×C83C2×C411yescharacteristic, complemented
147#103×C83C2×C411yescharacteristic, complemented
148#103×C83C2×C411yescharacteristic, complemented
149#103×C83C2×C411yescharacteristic, complemented
150#102×C83C2×C411yescharacteristic, complemented
151#102×C83C2×C411yescharacteristic, complemented
152#102×C83C2×C411yescharacteristic, complemented
153#102×C83C2×C411yescharacteristic, complemented
154C22⋊C8×C83—21no—
155C22⋊C8×C83—21no—
156C22⋊C8×C83—21no—
157C22⋊C8×C83—21no—
158C22⋊C8×C83—21no—
159C22⋊C8×C83—21no—
160C22⋊C8×C83—21no—
161C22⋊C8×C83—21no—
162C22⋊C8×C83C2×C411yescharacteristic
163C22⋊C8×C83C2×C411yescharacteristic
164C22⋊C8×C83C2×C411yescharacteristic
165C22⋊C8×C83C2×C411yescharacteristic
166C22⋊C8×C83D411yescharacteristic
167C22⋊C8×C83D411yescharacteristic
168C22⋊C8×C83D411yescharacteristic
169C22⋊C8×C83D411yescharacteristic
170#97×C83—21no—
171#97×C83—22no—
172#97×C83—41no—
173C4×C8×C83—21no—
174C24×C83—21no—
175C24×C83#4111yescharacteristic
176#41×C83—21no—
177#41×C83—21no—
178#41×C83—22no—
179#41×C83—22no—
180#41×C83—21no—
181#41×C83—21no—
182#41×C83—21no—
183#41×C83—21no—
184#41×C83—21no—
185#41×C83—21no—
186#41×C83—21no—
187#41×C83—21no—
188#41×C83—42no—
189#41×C83—42no—
190#41×C83—41no—
191#41×C83—41no—
192#41×C83—42no—
193#41×C83—42no—
194#41×C83C2×D412yes—
195#41×C83#4112yes—
196C2×Q8×C83—21no—
197C2×Q8×C83—22no—
198C2×Q8×C83—41no—
199C2×Q8×C83C22×C411yescharacteristic
200C2×Q8×C83C22×C411yescharacteristic
201C2×Q8×C83C22×C411yescharacteristic
202C2×D4×C83—21no—
203C2×D4×C83—22no—
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—41no—
212C2×D4×C83—42no—
213C2×D4×C83—42no—
214C2×D4×C83C22×C411yescharacteristic
215C2×D4×C83C22×C411yescharacteristic
216C2×D4×C83C22×C411yescharacteristic
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—42no—
230C22×C4×C83—42no—
231C22×C4×C83—42no—
232C22×C4×C83—42no—
233C22×C4×C83—42no—
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83#4111yescharacteristic
239C22×C4×C83C2411yescharacteristic
240Q16×C83—22no—
241Q16×C83—41no—
242SD16×C83—22no—
243SD16×C83—22no—
244SD16×C83—41no—
245SD16×C83—41no—
246D8×C83—22no—
247D8×C83—41no—
248M16×C83—21no—
249M16×C83—21no—
250M16×C83—21no—
251M16×C83—21no—
252M16×C83—21no—
253M16×C83—21no—
254M16×C83—21no—
255M16×C83—42no—
256M16×C83—42no—
257M16×C83—42no—
258M16×C83—42no—
259M16×C83C2×D412yes—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—21no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83—21no—
271C2×C8×C83—21no—
272C2×C8×C83—42no—
273C2×C8×C83—42no—
274C2×C8×C83—42no—
275C2×C8×C83—42no—
276C2×C8×C83C22×C411yescharacteristic
277C2×C8×C83C22×C411yescharacteristic
278C2×C8×C83C22×C411yescharacteristic
279C2×C8×C83C22×C411yescharacteristic
280C2×C8×C83C2×D411yescharacteristic
281C2×C8×C83C2×D411yescharacteristic
282C2×C8×C83C2×D411yescharacteristic
283C2×C8×C83C2×D411yescharacteristic
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83C22×C411yescharacteristic
287C4⋊C4×C83C22×C411yescharacteristic
288C22⋊C4×C83—21no—
289C22⋊C4×C83—21no—
290C22⋊C4×C83—21no—
291C22⋊C4×C83—21no—
292C22⋊C4×C83—21no—
293C42×C83—21no—
294C42×C83—21no—
295C42×C83—21no—
296C42×C83—21no—
297C42×C83—42no—
298C42×C83C2×D412yes—
299C23×C83—21no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—22no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—41no—
306C23×C83—42no—
307C23×C83—42no—
308C23×C83—81no—
309C23×C83C4×D411yescharacteristic
310C23×C83C4×D411yescharacteristic
311C23×C83C2×#4111yescharacteristic
312Q8×C83—21no—
313Q8×C83—21no—
314Q8×C83—21no—
315Q8×C83—21no—
316Q8×C83—21no—
317Q8×C83—42no—
318Q8×C83C4×D412yes—
319D4×C83—22no—
320D4×C83—22no—
321D4×C83—21no—
322D4×C83—21no—
323D4×C83—21no—
324D4×C83—21no—
325D4×C83—21no—
326D4×C83—42no—
327D4×C83—42no—
328D4×C83—42no—
329D4×C83—41no—
330D4×C83—41no—
331D4×C83—41no—
332D4×C83—41no—
333D4×C83—42no—
334D4×C83—81no—
335D4×C83C4×D412yes—
336C2×C4×C83—21no—
337C2×C4×C83—21no—
338C2×C4×C83—21no—
339C2×C4×C83—21no—
340C2×C4×C83—21no—
341C2×C4×C83—21no—
342C2×C4×C83—21no—
343C2×C4×C83—21no—
344C2×C4×C83—22no—
345C2×C4×C83—21no—
346C2×C4×C83—22no—
347C2×C4×C83—21no—
348C2×C4×C83—21no—
349C2×C4×C83—22no—
350C2×C4×C83—21no—
351C2×C4×C83—21no—
352C2×C4×C83—21no—
353C2×C4×C83—21no—
354C2×C4×C83—22no—
355C2×C4×C83—42no—
356C2×C4×C83—42no—
357C2×C4×C83—42no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—48no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83C4×D411yescharacteristic
368C2×C4×C83C4×D411yescharacteristic
369C2×C4×C83C23×C411yescharacteristic
370C2×C4×C83C22×D411yescharacteristic
371C2×C4×C83C22×D411yescharacteristic
372C2×C4×C83C2×#4111yescharacteristic
373C2×C4×C83H(5,𝔽2)11yescharacteristic
374C2×C4×C83H(5,𝔽2)11yescharacteristic
375C8×C83—21no—
376C8×C83—21no—
377C8×C83—21no—
378C8×C83—21no—
379C8×C83—21no—
380C8×C83—21no—
381C8×C83—22no—
382C8×C83—21no—
383C8×C83—21no—
384C8×C83—41no—
385C8×C83—41no—
386C8×C83—41no—
387C22×C83—21no—
388C22×C83—21no—
389C22×C83—21no—
390C22×C83—21no—
391C22×C83—21no—
392C22×C83—22no—
393C22×C83—21no—
394C22×C83—21no—
395C22×C83—42no—
396C22×C83—42no—
397C22×C83—41no—
398C22×C83—41no—
399C22×C83—41no—
400C22×C83—41no—
401C22×C83—41no—
402C22×C83—41no—
403C22×C83—41no—
404C22×C83—41no—
405C22×C83—84no—
406C22×C83#44412yescomplemented
407C22×C83C2×C4×D411yescharacteristic
408C22×C83#54611yescharacteristic
409C22×C83#55111yescharacteristic
410C4×C83—21no—
411C4×C83—21no—
412C4×C83—22no—
413C4×C83—42no—
414C4×C83—42no—
415C4×C83—41no—
416C4×C83—41no—
417C4×C83—41no—
418C4×C83—41no—
419C4×C83C2×C4×D411yescharacteristic
420C4×C83#51811yescharacteristic
421C4×C83D4211yescharacteristic
422C4×C83#54611yescharacteristic
423#22886C8311yesmaximal, characteristic, direct product factor, Sylow
424C2×C83—21no—
425C2×C83—22no—
426C2×C83—21no—
427C2×C83—41no—
428C2×C83—42no—
429C2×C83—81no—
430C2×C83—81no—
431C2×C83#235811yescharacteristic
432C2×C83C2×#44411yescharacteristic
433C2×C83#295611yescharacteristic
434#3002C2×C8311yescharacteristic
435C2×#444C2×C8311yescharacteristic, complemented
436#2933C2×C8311yescharacteristic, complemented
437C22×#104C2×C8311yescharacteristic, complemented
438#2880C2×C8311yescharacteristic, complemented
439#1975C2×C8311yescharacteristic, complemented
440#1938C2×C8311yescharacteristic, complemented
441#1929C2×C8311yescharacteristic, complemented
442#1896C2×C8311yescharacteristic, complemented
443#1876C2×C8311yescharacteristic, complemented
444#1876C2×C8311yescharacteristic, complemented
445#1866C2×C8311yescharacteristic, complemented
446#1855C2×C8311yescharacteristic, complemented
447#1765C2×C8311yescharacteristic, complemented
448#1749C2×C8311yescharacteristic, complemented
449C83#2288611yescharacteristic, direct product factor, Sylow
450C22×#41C22×C8311yescharacteristic
451C2×#135C22×C8311yescharacteristic
452C2×#135C22×C8311yescharacteristic
453C2×#131C22×C8311yescharacteristic
454C2×#131C22×C8311yescharacteristic
455C2×#131C22×C8311yescharacteristic, complemented
456C22×M16C22×C8311yescharacteristic
457#525C22×C8311yescharacteristic
458C22×C42C22×C8311yescharacteristic
459#452C4×C8311yescharacteristic, complemented
460#452C4×C8311yescharacteristic, complemented
461#451C4×C8311yescharacteristic, complemented
462#450C4×C8311yescharacteristic, complemented
463#449C4×C8311yescharacteristic, complemented
464#449C4×C8311yescharacteristic, complemented
465#448C4×C8311yescharacteristic, complemented
466#447C4×C8311yescharacteristic, complemented
467#444—24no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C8311yescharacteristic, complemented
473C2×#108C22×C8311yescharacteristic, complemented
474#424C22×C8311yescharacteristic, complemented
475C2×#104—24no—
476C2×#104C22×C8311yescharacteristic
477C2×#104C22×C8311yescharacteristic
478C2×#104C22×C8311yescharacteristic
479C2×#104C22×C8311yescharacteristic
480C2×#104C22×C8311yescharacteristic, complemented
481C2×#104C22×C8311yescharacteristic, complemented
482#416C22×C8311yescharacteristic
483#416C22×C8311yescharacteristic
484#408—21no—
485#408—21no—
486#408C22×C8311yescharacteristic
487#408C22×C8311yescharacteristic
488#408C22×C8311yescharacteristic, complemented
489#407—21no—
490#407C22×C8311yescharacteristic
491C2×C22⋊C8—21no—
492C2×C22⋊C8C22×C8311yescharacteristic
493C2×C22⋊C8C22×C8311yescharacteristic
494#405C22×C8311yescharacteristic, complemented
495C2×#97C22×C8311yescharacteristic, complemented
496C2×#97C22×C8311yescharacteristic, complemented
497#341C22×C8311yescharacteristic, complemented
498#341C22×C8311yescharacteristic, complemented
499#339C22×C8311yescharacteristic, complemented
500#339C22×C8311yescharacteristic, complemented
501#336C22×C8311yescharacteristic, complemented
502#336C22×C8311yescharacteristic, complemented
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C8311yescharacteristic
510C2×#41C2×C4×C8311yescharacteristic
511C2×#41C23×C8311yescharacteristic
512C2×#41C23×C8311yescharacteristic
513C2×#41C23×C8311yescharacteristic
514C22×Q8C2×C4×C8311yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C8311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C8311yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C8311yescharacteristic, complemented
525C2×Q16C2×C4×C8311yescharacteristic, complemented
526C2×SD16C2×C4×C8311yescharacteristic, complemented
527C2×SD16C2×C4×C8311yescharacteristic, complemented
528C2×SD16C2×C4×C8311yescharacteristic, complemented
529C2×SD16C2×C4×C8311yescharacteristic, complemented
530C2×D8C2×C4×C8311yescharacteristic, complemented
531C2×D8C2×C4×C8311yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C8311yescharacteristic
545C2×M16C23×C8311yescharacteristic
546C2×M16C23×C8311yescharacteristic
547C2×M16C23×C8311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C8311yescharacteristic
553C22×C8C23×C8311yescharacteristic
554C22×C8C23×C8311yescharacteristic
555C22×C8C23×C8311yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C8311yescharacteristic
558C22⋊Q8C2×C4×C8311yescharacteristic
559#121C2×C4×C8311yescharacteristic
560#121C2×C4×C8311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C8311yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C8311yescharacteristic
569C2×C42C23×C8311yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C8314yescomplemented
580#103C2×C4×C8311yescharacteristic, complemented
581#103C2×C4×C8311yescharacteristic, complemented
582#103C2×C4×C8311yescharacteristic, complemented
583#103C2×C4×C8311yescharacteristic, complemented
584#102C2×C4×C8311yescharacteristic, complemented
585#102C2×C4×C8311yescharacteristic, complemented
586#102C2×C4×C8311yescharacteristic, complemented
587#102C2×C4×C8311yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C8311yescharacteristic
597C22⋊C8C2×C4×C8311yescharacteristic
598C22⋊C8C2×C4×C8311yescharacteristic
599C22⋊C8C2×C4×C8311yescharacteristic
600C22⋊C8D4×C8311yescharacteristic
601C22⋊C8D4×C8311yescharacteristic
602C22⋊C8D4×C8311yescharacteristic
603C22⋊C8D4×C8311yescharacteristic
604#97—21no—
605#97—22no—
606#97—41no—
607C4×C8—21no—
608C24—21no—
609C24#41×C8311yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C8312yes—
629#41#41×C8312yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C8311yescharacteristic
634C2×Q8C22×C4×C8311yescharacteristic
635C2×Q8C22×C4×C8311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C8311yescharacteristic
649C2×D4C22×C4×C8311yescharacteristic
650C2×D4C22×C4×C8311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C8311yescharacteristic
669C22×C4C22×C4×C8311yescharacteristic
670C22×C4C2×D4×C8311yescharacteristic
671C22×C4C2×D4×C8311yescharacteristic
672C22×C4#41×C8311yescharacteristic
673C22×C4C24×C8311yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C8312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C8311yescharacteristic
711C2×C8C22×C4×C8311yescharacteristic
712C2×C8C22×C4×C8311yescharacteristic
713C2×C8C22×C4×C8311yescharacteristic
714C2×C8C2×D4×C8311yescharacteristic
715C2×C8C2×D4×C8311yescharacteristic
716C2×C8C2×D4×C8311yescharacteristic
717C2×C8C2×D4×C8311yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C8311yescharacteristic
721C4⋊C4C22×C4×C8311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C8312yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C8311yescharacteristic
744C23C4×D4×C8311yescharacteristic
745C23C2×#41×C8311yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C8312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—81no—
769D4C4×D4×C8312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C8311yescharacteristic
802C2×C4C4×D4×C8311yescharacteristic
803C2×C4C23×C4×C8311yescharacteristic
804C2×C4C22×D4×C8311yescharacteristic
805C2×C4C22×D4×C8311yescharacteristic
806C2×C4C2×#41×C8311yescharacteristic
807C2×C4H(5,𝔽2)×C8311yescharacteristic
808C2×C4H(5,𝔽2)×C8311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#444×C8312yescomplemented
841C22C2×C4×D4×C8311yescharacteristic
842C22#546×C8311yescharacteristic
843C22#551×C8311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C8311yescharacteristic
854C4#518×C8311yescharacteristic
855C4D42×C8311yescharacteristic
856C4#546×C8311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2C83×#235811yescharacteristic
865C2C2×#444×C8311yescharacteristic
866C2C83×#295611yescharacteristic
subgroupG/H
centerC2×C4×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
socleC22×C83C2×C4×D4
prime radicalC83×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C83 ◁ C2×C22⋊C8×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#444×C83C2semidirect
3. C83×#2933C2semidirect
4. C22×#104×C83C2semidirect
5. C83×#2880C2semidirect
6. C83×#1975C2semidirect
7. C83×#1938C2semidirect
8. C83×#1929C2semidirect
9. C83×#1896C2semidirect
10. C83×#1876C2semidirect
11. C83×#1876C2semidirect
12. C83×#1866C2semidirect
13. C83×#1855C2semidirect
14. C83×#1765C2semidirect
15. C83×#1749C2semidirect
21. C2×#131×C83C22semidirect
25. #452×C83C4semidirect
26. #452×C83C4semidirect
27. #451×C83C4semidirect
28. #450×C83C4semidirect
29. #449×C83C4semidirect
30. #449×C83C4semidirect
31. #448×C83C4semidirect
32. #447×C83C4semidirect
38. C2×#108×C83C22semidirect
39. C2×#108×C83C22semidirect
40. #424×C83C22semidirect
46. C2×#104×C83C22semidirect
47. C2×#104×C83C22semidirect
54. #408×C83C22semidirect
60. #405×C83C22semidirect
61. C2×#97×C83C22semidirect
62. C2×#97×C83C22semidirect
63. #341×C83C22semidirect
64. #341×C83C22semidirect
65. #339×C83C22semidirect
66. #339×C83C22semidirect
67. #336×C83C22semidirect
68. #336×C83C22semidirect
90. C2×Q16×C83C2×C4semidirect
91. C2×Q16×C83C2×C4semidirect
92. C2×SD16×C83C2×C4semidirect
93. C2×SD16×C83C2×C4semidirect
94. C2×SD16×C83C2×C4semidirect
95. C2×SD16×C83C2×C4semidirect
96. C2×D8×C83C2×C4semidirect
97. C2×D8×C83C2×C4semidirect
145. #104×C83D4semidirect
146. #103×C83C2×C4semidirect
147. #103×C83C2×C4semidirect
148. #103×C83C2×C4semidirect
149. #103×C83C2×C4semidirect
150. #102×C83C2×C4semidirect
151. #102×C83C2×C4semidirect
152. #102×C83C2×C4semidirect
153. #102×C83C2×C4semidirect
406. C22×C83#444semidirect
423. #22886C83direct (N × H)
435. C2×#444C2×C83semidirect
436. #2933C2×C83semidirect
437. C22×#104C2×C83semidirect
438. #2880C2×C83semidirect
439. #1975C2×C83semidirect
440. #1938C2×C83semidirect
441. #1929C2×C83semidirect
442. #1896C2×C83semidirect
443. #1876C2×C83semidirect
444. #1876C2×C83semidirect
445. #1866C2×C83semidirect
446. #1855C2×C83semidirect
447. #1765C2×C83semidirect
448. #1749C2×C83semidirect
449. C83#22886direct (N × H)
455. C2×#131C22×C83semidirect
459. #452C4×C83semidirect
460. #452C4×C83semidirect
461. #451C4×C83semidirect
462. #450C4×C83semidirect
463. #449C4×C83semidirect
464. #449C4×C83semidirect
465. #448C4×C83semidirect
466. #447C4×C83semidirect
472. C2×#108C22×C83semidirect
473. C2×#108C22×C83semidirect
474. #424C22×C83semidirect
480. C2×#104C22×C83semidirect
481. C2×#104C22×C83semidirect
488. #408C22×C83semidirect
494. #405C22×C83semidirect
495. C2×#97C22×C83semidirect
496. C2×#97C22×C83semidirect
497. #341C22×C83semidirect
498. #341C22×C83semidirect
499. #339C22×C83semidirect
500. #339C22×C83semidirect
501. #336C22×C83semidirect
502. #336C22×C83semidirect
524. C2×Q16C2×C4×C83semidirect
525. C2×Q16C2×C4×C83semidirect
526. C2×SD16C2×C4×C83semidirect
527. C2×SD16C2×C4×C83semidirect
528. C2×SD16C2×C4×C83semidirect
529. C2×SD16C2×C4×C83semidirect
530. C2×D8C2×C4×C83semidirect
531. C2×D8C2×C4×C83semidirect
579. #104D4×C83semidirect
580. #103C2×C4×C83semidirect
581. #103C2×C4×C83semidirect
582. #103C2×C4×C83semidirect
583. #103C2×C4×C83semidirect
584. #102C2×C4×C83semidirect
585. #102C2×C4×C83semidirect
586. #102C2×C4×C83semidirect
587. #102C2×C4×C83semidirect
840. C22#444×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30022
C2×#444×C832
C83×#29332
C22×#104×C832
C83×#28802
C83×#19752
C83×#19382
C83×#19292
C83×#18962
C83×#18762
C83×#18662
C83×#18552
C83×#17652
C83×#17492
#2288683