Finite Group Databasebeta

← C2×C83×#1390 #35240396

Subgroups — C2×C83×#1390 #35240396

Order 21248.

1202 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C83C211yesmaximal, characteristic
2C22×#99×C83C211yesmaximal, characteristic
3C2×#386×C83C211yesmaximal, characteristic
4C83×#1390C214yesmaximal, direct product factor
5C23×D4×C83C2211yescharacteristic
6C24×C4×C83C411yescharacteristic, complemented
7C22×M16×C83—21no—
8C22×C22⋊C4×C83—21no—
9C22×C22⋊C4×C83—21no—
10C22×C22⋊C4×C83C411yescharacteristic, complemented
11C2×#100×C83—21no—
12C2×#100×C83—22no—
13C2×#100×C83C414yescomplemented
14C2×#100×C83C2212yes—
15C2×#99×C83—21no—
16C2×#99×C83—22no—
17C2×#99×C83C414yescomplemented
18C2×#99×C83C2212yes—
19#386×C83—21no—
20#386×C83—21no—
21#386×C83C412yescomplemented
22#386×C83C2212yes—
23C2×#95×C83—21no—
24C25×C83C2×C411yescharacteristic
25C25×C83D411yescharacteristic
26C22×D4×C83—42no—
27C22×D4×C83—41no—
28C22×D4×C83—41no—
29C22×D4×C83C2×C411yescharacteristic
30C22×D4×C83C2×C412yes—
31C22×D4×C83C2×C412yes—
32C22×D4×C83D411yescharacteristic
33C22×D4×C83D412yes—
34C22×D4×C83D411yescharacteristic
35C22×D4×C83Q812yes—
36C22×D4×C83C2311yescharacteristic
37C23×C4×C83—21no—
38C23×C4×C83—21no—
39C23×C4×C83—21no—
40C23×C4×C83—44no—
41C23×C4×C83—41no—
42C23×C4×C83—41no—
43C23×C4×C83—41no—
44C23×C4×C83C2×C412yescomplemented
45C23×C4×C83D411yescharacteristic
46C2×M16×C83—24no—
47C2×M16×C83—22no—
48C2×M16×C83—42no—
49C2×M16×C83—41no—
50C22×C8×C83—41no—
51C2×C22⋊C4×C83—24no—
52C2×C22⋊C4×C83—22no—
53C2×C22⋊C4×C83—22no—
54C2×C22⋊C4×C83—21no—
55C2×C22⋊C4×C83—22no—
56C2×C22⋊C4×C83—44no—
57C2×C22⋊C4×C83—41no—
58C2×C22⋊C4×C83—42no—
59C2×C22⋊C4×C83—42no—
60C2×C22⋊C4×C83C2×C412yescomplemented
61#100×C83—24no—
62#100×C83—22no—
63#100×C83C2×C414yescomplemented
64#99×C83—24no—
65#99×C83—22no—
66#99×C83C2×C414yescomplemented
67#95×C83—22no—
68#95×C83—22no—
69C24×C83—22no—
70C24×C83—21no—
71C24×C83—21no—
72C24×C83—21no—
73C24×C83—22no—
74C24×C83—21no—
75C24×C83—42no—
76C24×C83—42no—
77C24×C83—42no—
78C24×C83—42no—
79C24×C83C4212yes—
80C24×C83C22⋊C412yes—
81C24×C83C22⋊C411yescharacteristic
82C24×C83C22⋊C411yescharacteristic
83C24×C83C22⋊C411yescharacteristic
84C24×C83C4⋊C412yes—
85C24×C83C4⋊C412yes—
86C24×C83C22×C411yescharacteristic
87C24×C83C2×D411yescharacteristic
88C2×D4×C83—42no—
89C2×D4×C83—42no—
90C2×D4×C83—42no—
91C2×D4×C83—42no—
92C2×D4×C83—41no—
93C2×D4×C83—41no—
94C2×D4×C83—42no—
95C2×D4×C83—42no—
96C2×D4×C83—41no—
97C2×D4×C83—41no—
98C2×D4×C83—41no—
99C2×D4×C83—41no—
100C2×D4×C83—42no—
101C2×D4×C83—42no—
102C2×D4×C83—41no—
103C2×D4×C83—41no—
104C2×D4×C83C4212yes—
105C2×D4×C83C22⋊C412yes—
106C2×D4×C83C22⋊C412yes—
107C2×D4×C83C4⋊C412yes—
108C2×D4×C83C4⋊C412yes—
109C2×D4×C83C4⋊C412yes—
110C2×D4×C83C22×C411yescharacteristic
111C2×D4×C83C22×C411yescharacteristic
112C2×D4×C83C2×D411yescharacteristic
113C2×D4×C83C2×Q811yescharacteristic
114C22×C4×C83—22no—
115C22×C4×C83—21no—
116C22×C4×C83—21no—
117C22×C4×C83—24no—
118C22×C4×C83—22no—
119C22×C4×C83—22no—
120C22×C4×C83—44no—
121C22×C4×C83—44no—
122C22×C4×C83—42no—
123C22×C4×C83—42no—
124C22×C4×C83—48no—
125C22×C4×C83—44no—
126C22×C4×C83—41no—
127C22×C4×C83—41no—
128C22×C4×C83—42no—
129C22×C4×C83—44no—
130C22×C4×C83—44no—
131C22×C4×C83—42no—
132C22×C4×C83—42no—
133C22×C4×C83—42no—
134C22×C4×C83—42no—
135C22×C4×C83—82no—
136C22×C4×C83—82no—
137C22×C4×C83C22⋊C411yescharacteristic
138C22×C4×C83C22⋊C412yes—
139C22×C4×C83C4⋊C412yes—
140C22×C4×C83C2×D411yescharacteristic
141M16×C83—24no—
142M16×C83—44no—
143M16×C83—42no—
144C2×C8×C83—44no—
145C2×C8×C83—42no—
146C22⋊C4×C83—24no—
147C22⋊C4×C83—44no—
148C22⋊C4×C83—44no—
149C22⋊C4×C83—44no—
150C22⋊C4×C83—42no—
151C22⋊C4×C83—42no—
152C22⋊C4×C83—42no—
153C23×C83—22no—
154C23×C83—22no—
155C23×C83—22no—
156C23×C83—22no—
157C23×C83—22no—
158C23×C83—22no—
159C23×C83—22no—
160C23×C83—22no—
161C23×C83—21no—
162C23×C83—21no—
163C23×C83—21no—
164C23×C83—21no—
165C23×C83—21no—
166C23×C83—21no—
167C23×C83—22no—
168C23×C83—22no—
169C23×C83—21no—
170C23×C83—21no—
171C23×C83—41no—
172C23×C83—41no—
173C23×C83—44no—
174C23×C83—41no—
175C23×C83—44no—
176C23×C83—41no—
177C23×C83—42no—
178C23×C83—42no—
179C23×C83—48no—
180C23×C83—41no—
181C23×C83—41no—
182C23×C83—41no—
183C23×C83—44no—
184C23×C83—44no—
185C23×C83—41no—
186C23×C83—42no—
187C23×C83—42no—
188C23×C83—42no—
189C23×C83—42no—
190C23×C83—81no—
191C23×C83—81no—
192C23×C83—84no—
193C23×C83#9512yes—
194C23×C83#9512yes—
195C23×C83#9512yes—
196C23×C83#9911yescharacteristic
197C23×C83#9912yes—
198C23×C83#9911yescharacteristic
199C23×C83C2×C4211yescharacteristic
200C23×C83C2×C22⋊C411yescharacteristic
201C23×C83C2×C22⋊C411yescharacteristic
202C23×C83C2×C4⋊C411yescharacteristic
203C23×C83C2×C4⋊C411yescharacteristic
204D4×C83—42no—
205D4×C83—42no—
206D4×C83—42no—
207D4×C83—42no—
208D4×C83—42no—
209D4×C83—42no—
210D4×C83—41no—
211D4×C83—41no—
212D4×C83—41no—
213D4×C83—41no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—24no—
223C2×C4×C83—42no—
224C2×C4×C83—44no—
225C2×C4×C83—48no—
226C2×C4×C83—44no—
227C2×C4×C83—44no—
228C2×C4×C83—42no—
229C2×C4×C83—44no—
230C2×C4×C83—44no—
231C2×C4×C83—42no—
232C2×C4×C83—42no—
233C2×C4×C83—42no—
234C2×C4×C83—84no—
235C2×C4×C83—82no—
236C2×C4×C83—82no—
237C2×C4×C83—88no—
238C2×C4×C83#9512yes—
239C2×C4×C83C2×C22⋊C411yescharacteristic
240C2×C4×C83C2×C4⋊C411yescharacteristic
241C8×C83—44no—
242C22×C83—21no—
243C22×C83—21no—
244C22×C83—21no—
245C22×C83—21no—
246C22×C83—24no—
247C22×C83—24no—
248C22×C83—21no—
249C22×C83—22no—
250C22×C83—22no—
251C22×C83—21no—
252C22×C83—21no—
253C22×C83—21no—
254C22×C83—42no—
255C22×C83—42no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—42no—
261C22×C83—42no—
262C22×C83—44no—
263C22×C83—44no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83—41no—
272C22×C83—44no—
273C22×C83—44no—
274C22×C83—44no—
275C22×C83—44no—
276C22×C83—81no—
277C22×C83—81no—
278C22×C83—82no—
279C22×C83—82no—
280C22×C83#34212yes—
281C22×C83#34212yes—
282C22×C83AΣL(1,𝔽16)12yes—
283C22×C83#35212yes—
284C22×C83C2×#9511yescharacteristic
285C22×C83C2×#9911yescharacteristic
286C22×C83C2×#9911yescharacteristic
287C4×C83—21no—
288C4×C83—22no—
289C4×C83—21no—
290C4×C83—44no—
291C4×C83—82no—
292C4×C83—84no—
293C2×#1390C8311yesmaximal, characteristic, direct product factor, Sylow
294C2×C83—21no—
295C2×C83—21no—
296C2×C83—22no—
297C2×C83—41no—
298C2×C83—42no—
299C2×C83—41no—
300C2×C83—41no—
301C2×C83—42no—
302C2×C83—41no—
303C2×C83#139014yesdirect product factor
304C2×C83C2×#34211yescharacteristic
305C2×C83C2×AΣL(1,𝔽16)11yescharacteristic
306C2×C83C2×#35211yescharacteristic
307C22×#100C2×C8311yescharacteristic
308C22×#99C2×C8311yescharacteristic
309C2×#386C2×C8311yescharacteristic
310#1390C2×C8314yesdirect product factor
311C83C2×#139011yescharacteristic, direct product factor, Sylow
312C23×D4C22×C8311yescharacteristic
313C24×C4C4×C8311yescharacteristic, complemented
314C22×M16—21no—
315C22×C22⋊C4—21no—
316C22×C22⋊C4—21no—
317C22×C22⋊C4C4×C8311yescharacteristic, complemented
318C2×#100—21no—
319C2×#100—22no—
320C2×#100C4×C8314yescomplemented
321C2×#100C22×C8312yes—
322C2×#99—21no—
323C2×#99—22no—
324C2×#99C4×C8314yescomplemented
325C2×#99C22×C8312yes—
326#386—21no—
327#386—21no—
328#386C4×C8312yescomplemented
329#386C22×C8312yes—
330C2×#95—21no—
331C25C2×C4×C8311yescharacteristic
332C25D4×C8311yescharacteristic
333C22×D4—41no—
334C22×D4—42no—
335C22×D4—41no—
336C22×D4C2×C4×C8311yescharacteristic
337C22×D4C2×C4×C8312yes—
338C22×D4C2×C4×C8312yes—
339C22×D4D4×C8311yescharacteristic
340C22×D4D4×C8312yes—
341C22×D4D4×C8311yescharacteristic
342C22×D4Q8×C8312yes—
343C22×D4C23×C8311yescharacteristic
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—21no—
347C23×C4—44no—
348C23×C4—41no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C8312yescomplemented
352C23×C4D4×C8311yescharacteristic
353C2×M16—24no—
354C2×M16—22no—
355C2×M16—42no—
356C2×M16—41no—
357C22×C8—41no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4C2×C4×C8312yescomplemented
368#100—24no—
369#100—22no—
370#100C2×C4×C8314yescomplemented
371#99—24no—
372#99—22no—
373#99C2×C4×C8314yescomplemented
374#95—22no—
375#95—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—21no—
382C24—42no—
383C24—42no—
384C24—42no—
385C24—42no—
386C24C42×C8312yes—
387C24C22⋊C4×C8311yescharacteristic
388C24C22⋊C4×C8312yes—
389C24C22⋊C4×C8311yescharacteristic
390C24C22⋊C4×C8311yescharacteristic
391C24C4⋊C4×C8312yes—
392C24C4⋊C4×C8312yes—
393C24C22×C4×C8311yescharacteristic
394C24C2×D4×C8311yescharacteristic
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4C42×C8312yes—
412C2×D4C22⋊C4×C8312yes—
413C2×D4C22⋊C4×C8312yes—
414C2×D4C4⋊C4×C8312yes—
415C2×D4C4⋊C4×C8312yes—
416C2×D4C4⋊C4×C8312yes—
417C2×D4C22×C4×C8311yescharacteristic
418C2×D4C22×C4×C8311yescharacteristic
419C2×D4C2×D4×C8311yescharacteristic
420C2×D4C2×Q8×C8311yescharacteristic
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—82no—
443C22×C4—82no—
444C22×C4C22⋊C4×C8311yescharacteristic
445C22×C4C22⋊C4×C8312yes—
446C22×C4C4⋊C4×C8312yes—
447C22×C4C2×D4×C8311yescharacteristic
448M16—24no—
449M16—44no—
450M16—42no—
451C2×C8—44no—
452C2×C8—42no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—44no—
456C22⋊C4—44no—
457C22⋊C4—42no—
458C22⋊C4—42no—
459C22⋊C4—42no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—41no—
479C23—41no—
480C23—44no—
481C23—41no—
482C23—44no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—44no—
491C23—44no—
492C23—41no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—81no—
498C23—81no—
499C23—84no—
500C23#95×C8312yes—
501C23#95×C8312yes—
502C23#95×C8312yes—
503C23#99×C8311yescharacteristic
504C23#99×C8312yes—
505C23#99×C8311yescharacteristic
506C23C2×C42×C8311yescharacteristic
507C23C2×C22⋊C4×C8311yescharacteristic
508C23C2×C22⋊C4×C8311yescharacteristic
509C23C2×C4⋊C4×C8311yescharacteristic
510C23C2×C4⋊C4×C8311yescharacteristic
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—48no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—88no—
545C2×C4#95×C8312yes—
546C2×C4C2×C22⋊C4×C8311yescharacteristic
547C2×C4C2×C4⋊C4×C8311yescharacteristic
548C8—44no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—24no—
554C22—24no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—44no—
570C22—44no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—81no—
584C22—81no—
585C22—82no—
586C22—82no—
587C22#342×C8312yes—
588C22#342×C8312yes—
589C22AΣL(1,𝔽16)×C8312yes—
590C22#352×C8312yes—
591C22C2×#95×C8311yescharacteristic
592C22C2×#99×C8311yescharacteristic
593C22C2×#99×C8311yescharacteristic
594C4—21no—
595C4—22no—
596C4—21no—
597C4—44no—
598C4—82no—
599C4—84no—
600C2—21no—
601C2—21no—
602C2—22no—
603C2—41no—
604C2—42no—
605C2—41no—
606C2—41no—
607C2—42no—
608C2—41no—
609C2C83×#139014yesdirect product factor
610C2C2×#342×C8311yescharacteristic
611C2C2×AΣL(1,𝔽16)×C8311yescharacteristic
612C2C2×#352×C8311yescharacteristic
subgroupG/H
center, socleC23×C83#99
commutatorC23C2×C42×C83
Frattini, cosocleC22×D4C23×C83
prime radicalC23×D4×C83C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C24×C83 ◁ C23×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1390C2direct (N × H)
6. C24×C4×C83C4semidirect
10. C22×C22⋊C4×C83C4semidirect
13. C2×#100×C83C4semidirect
17. C2×#99×C83C4semidirect
21. #386×C83C4semidirect
44. C23×C4×C83C2×C4semidirect
60. C2×C22⋊C4×C83C2×C4semidirect
63. #100×C83C2×C4semidirect
66. #99×C83C2×C4semidirect
293. C2×#1390C83direct (N × H)
303. C2×C83#1390direct (N × H)
310. #1390C2×C83direct (N × H)
311. C83C2×#1390direct (N × H)
313. C24×C4C4×C83semidirect
317. C22×C22⋊C4C4×C83semidirect
320. C2×#100C4×C83semidirect
324. C2×#99C4×C83semidirect
328. #386C4×C83semidirect
351. C23×C4C2×C4×C83semidirect
367. C2×C22⋊C4C2×C4×C83semidirect
370. #100C2×C4×C83semidirect
373. #99C2×C4×C83semidirect
609. C2C83×#1390direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#100×C832
C22×#99×C832
C2×#386×C832
C83×#13902
C2×#139083