Finite Group Databasebeta

← C83×#22623 #35250447

Subgroups — C83×#22623 #35250447

Order 21248.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#428×C83C211yesmaximal, characteristic
2C83×#2347C211yesmaximal, characteristic
3C83×#2345C211yesmaximal, characteristic
4C83×#1944C211yesmaximal, characteristic, complemented
5C83×#1941C211yesmaximal, characteristic, complemented
6C83×#1921C211yesmaximal, characteristic, complemented
7C83×#1920C211yesmaximal, characteristic, complemented
8C83×#1919C211yesmaximal, characteristic, complemented
9C83×#1918C211yesmaximal, characteristic, complemented
10C83×#1825C211yesmaximal, characteristic
11C83×#1823C211yesmaximal, characteristic
12C83×#1809C211yesmaximal, characteristic
13C83×#1776C211yesmaximal, characteristic, complemented
14C4×#107×C83C211yesmaximal, characteristic, complemented
15C83×#1753C211yesmaximal, characteristic
16C22×M16×C83C2211yescharacteristic
17C2×#117×C83C2211yescharacteristic
18C22×C4⋊C4×C83C2211yescharacteristic
19#428×C83C418yescomplemented
20C2×#107×C83C2211yescharacteristic
21C2×#107×C83C2211yescharacteristic
22C2×#107×C83C2211yescharacteristic
23C2×#106×C83C2211yescharacteristic
24C2×#106×C83C2211yescharacteristic
25C2×#106×C83C2211yescharacteristic
26C2×C22⋊C8×C83C2211yescharacteristic
27C2×#97×C83C2211yescharacteristic
28C2×C4×C8×C83C2211yescharacteristic
29#389×C83C2211yescharacteristic
30#389×C83C2211yescharacteristic
31#389×C83C2211yescharacteristic
32#389×C83C2211yescharacteristic
33#388×C83—21no—
34#388×C83—21no—
35#387×C83—21no—
36#387×C83—21no—
37#383×C83—21no—
38#380×C83—21no—
39#380×C83C2211yescharacteristic
40#380×C83C2211yescharacteristic
41C4×C4⋊C4×C83—21no—
42C4×C4⋊C4×C83C2211yescharacteristic
43C4×C4⋊C4×C83C2211yescharacteristic
44C4×C4⋊C4×C83C2211yescharacteristic
45C4×C4⋊C4×C83C2211yescharacteristic
46C4×C22⋊C4×C83—21no—
47C4×C22⋊C4×C83C2211yescharacteristic
48#340×C83C2211yescharacteristic
49#340×C83C2211yescharacteristic
50#340×C83C2211yescharacteristic
51#340×C83C2211yescharacteristic
52#340×C83C2211yescharacteristic
53#340×C83C2211yescharacteristic
54#340×C83C2211yescharacteristic
55#340×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60C23×C4×C83—21no—
61C23×C4×C83C2311yescharacteristic
62C2×M16×C83—22no—
63C2×M16×C83—22no—
64C2×M16×C83C2×C414yes—
65C22×C8×C83C2311yescharacteristic
66C22×C8×C83C2311yescharacteristic
67C22×C8×C83C2311yescharacteristic
68C22×C8×C83C2311yescharacteristic
69#117×C83—22no—
70#117×C83C2×C414yes—
71C2×C4⋊C4×C83—21no—
72C2×C4⋊C4×C83—22no—
73C2×C4⋊C4×C83—21no—
74C2×C4⋊C4×C83—21no—
75C2×C4⋊C4×C83—21no—
76C2×C4⋊C4×C83—21no—
77C2×C4⋊C4×C83C2×C414yes—
78C2×C4⋊C4×C83C2311yescharacteristic
79C2×C4⋊C4×C83C2311yescharacteristic
80C2×C4⋊C4×C83C2311yescharacteristic
81C2×C4⋊C4×C83C2311yescharacteristic
82C2×C4⋊C4×C83C2311yescharacteristic
83C2×C4⋊C4×C83C2311yescharacteristic
84C2×C4⋊C4×C83C2311yescharacteristic
85C2×C4⋊C4×C83C2311yescharacteristic
86C2×C22⋊C4×C83—21no—
87C2×C22⋊C4×C83—21no—
88C2×C22⋊C4×C83—21no—
89C2×C22⋊C4×C83D411yescharacteristic
90C2×C22⋊C4×C83D411yescharacteristic
91C2×C42×C83—21no—
92C2×C42×C83—21no—
93C2×C42×C83—21no—
94C2×C42×C83—21no—
95C2×C42×C83—21no—
96C2×C42×C83C2311yescharacteristic
97C2×C42×C83C2311yescharacteristic
98#107×C83—22no—
99#107×C83C2×C414yes—
100#107×C83C2×C414yes—
101#106×C83—22no—
102#106×C83C2×C414yes—
103#106×C83C2×C414yes—
104C22⋊C8×C83—22no—
105#97×C83—22no—
106C4×C8×C83—22no—
107#95×C83—21no—
108#95×C83—21no—
109#95×C83—21no—
110#95×C83—21no—
111#95×C83—21no—
112#95×C83—21no—
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83D411yescharacteristic
118#95×C83D411yescharacteristic
119C24×C83C2×D411yescharacteristic
120C22×C4×C83—21no—
121C22×C4×C83—21no—
122C22×C4×C83—21no—
123C22×C4×C83—21no—
124C22×C4×C83—21no—
125C22×C4×C83—21no—
126C22×C4×C83—21no—
127C22×C4×C83—21no—
128C22×C4×C83—24no—
129C22×C4×C83—21no—
130C22×C4×C83—21no—
131C22×C4×C83—21no—
132C22×C4×C83—21no—
133C22×C4×C83—81no—
134C22×C4×C83—81no—
135C22×C4×C83C22×C412yes—
136C22×C4×C83C2×D411yescharacteristic
137C22×C4×C83C2×D411yescharacteristic
138C22×C4×C83C2×D411yescharacteristic
139C22×C4×C83C2×D411yescharacteristic
140C22×C4×C83C2×D411yescharacteristic
141C22×C4×C83#4112yes—
142C22×C4×C83C2411yescharacteristic
143M16×C83—28no—
144C2×C8×C83—21no—
145C2×C8×C83—21no—
146C2×C8×C83—21no—
147C2×C8×C83—21no—
148C2×C8×C83—21no—
149C2×C8×C83—21no—
150C2×C8×C83—21no—
151C2×C8×C83—21no—
152C2×C8×C83C22×C412yes—
153C2×C8×C83C22×C412yes—
154C2×C8×C83#4112yes—
155C2×C8×C83#4112yes—
156C4⋊C4×C83—24no—
157C4⋊C4×C83—21no—
158C4⋊C4×C83—21no—
159C4⋊C4×C83—21no—
160C4⋊C4×C83—21no—
161C4⋊C4×C83—21no—
162C4⋊C4×C83—21no—
163C4⋊C4×C83—21no—
164C4⋊C4×C83—21no—
165C4⋊C4×C83—21no—
166C4⋊C4×C83—21no—
167C4⋊C4×C83—21no—
168C4⋊C4×C83—21no—
169C4⋊C4×C83—42no—
170C4⋊C4×C83—42no—
171C4⋊C4×C83—81no—
172C4⋊C4×C83—81no—
173C4⋊C4×C83C22×C412yes—
174C4⋊C4×C83C22×C412yes—
175C4⋊C4×C83C22×C412yes—
176C4⋊C4×C83C22×C412yes—
177C22⋊C4×C83—24no—
178C22⋊C4×C83—22no—
179C22⋊C4×C83—41no—
180C22⋊C4×C83—42no—
181C22⋊C4×C83—81no—
182C42×C83—24no—
183C42×C83—21no—
184C42×C83—21no—
185C42×C83—21no—
186C42×C83—21no—
187C42×C83—81no—
188C42×C83—81no—
189C42×C83—81no—
190C42×C83—81no—
191C23×C83—21no—
192C23×C83—21no—
193C23×C83—21no—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83—21no—
197C23×C83C4×D412yes—
198C23×C83C22×D411yescharacteristic
199C2×C4×C83—21no—
200C2×C4×C83—21no—
201C2×C4×C83—21no—
202C2×C4×C83—21no—
203C2×C4×C83—22no—
204C2×C4×C83—22no—
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—22no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—84no—
241C2×C4×C83C4×D412yes—
242C2×C4×C83#13712yes—
243C2×C4×C83C23×C411yescharacteristic
244C2×C4×C83C2×#4111yescharacteristic
245C2×C4×C83C2×#4111yescharacteristic
246C2×C4×C83C2×#4111yescharacteristic
247C2×C4×C832−1+411yescharacteristic
248C2×C4×C832−1+411yescharacteristic
249C8×C83—22no—
250C8×C83—41no—
251C8×C83—41no—
252C8×C83#11714yes—
253C22×C83—22no—
254C22×C83—22no—
255C22×C83—22no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83C2×C4×D411yescharacteristic
261C22×C83#54711yescharacteristic
262C22×C83#54711yescharacteristic
263C22×C83C2×#13711yescharacteristic
264C22×C83#57511yescharacteristic
265C22×C83#57611yescharacteristic
266C22×C83#57711yescharacteristic
267C4×C83—22no—
268C4×C83—22no—
269C4×C83—41no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—42no—
273C4×C83—42no—
274C4×C83—42no—
275C4×C83—42no—
276C4×C83—81no—
277C4×C83—81no—
278C4×C83—81no—
279C4×C83—81no—
280C4×C83C2×#11711yescharacteristic
281C4×C83#51911yescharacteristic
282C4×C83#55211yescharacteristic
283C4×C83#55211yescharacteristic
284#22623C8311yesmaximal, characteristic, direct product factor, Sylow
285C2×C83—42no—
286C2×C83#234411yescharacteristic
287C2×C83C4×#13711yescharacteristic
288C2×C83#294611yescharacteristic
289C2×C83#334611yescharacteristic
290C2×C83#335011yescharacteristic
291C2×C83#335511yescharacteristic
292C2×C83#335611yescharacteristic
293C2×#428C2×C8311yescharacteristic
294#2347C2×C8311yescharacteristic
295#2345C2×C8311yescharacteristic
296#1944C2×C8311yescharacteristic, complemented
297#1941C2×C8311yescharacteristic, complemented
298#1921C2×C8311yescharacteristic, complemented
299#1920C2×C8311yescharacteristic, complemented
300#1919C2×C8311yescharacteristic, complemented
301#1918C2×C8311yescharacteristic, complemented
302#1825C2×C8311yescharacteristic
303#1823C2×C8311yescharacteristic
304#1809C2×C8311yescharacteristic
305#1776C2×C8311yescharacteristic, complemented
306C4×#107C2×C8311yescharacteristic, complemented
307#1753C2×C8311yescharacteristic
308C83#2262311yescharacteristic, direct product factor, Sylow
309C22×M16C22×C8311yescharacteristic
310C2×#117C22×C8311yescharacteristic
311C22×C4⋊C4C22×C8311yescharacteristic
312#428C4×C8318yescomplemented
313C2×#107C22×C8311yescharacteristic
314C2×#107C22×C8311yescharacteristic
315C2×#107C22×C8311yescharacteristic
316C2×#106C22×C8311yescharacteristic
317C2×#106C22×C8311yescharacteristic
318C2×#106C22×C8311yescharacteristic
319C2×C22⋊C8C22×C8311yescharacteristic
320C2×#97C22×C8311yescharacteristic
321C2×C4×C8C22×C8311yescharacteristic
322#389C22×C8311yescharacteristic
323#389C22×C8311yescharacteristic
324#389C22×C8311yescharacteristic
325#389C22×C8311yescharacteristic
326#388—21no—
327#388—21no—
328#387—21no—
329#387—21no—
330#383—21no—
331#380—21no—
332#380C22×C8311yescharacteristic
333#380C22×C8311yescharacteristic
334C4×C4⋊C4—21no—
335C4×C4⋊C4C22×C8311yescharacteristic
336C4×C4⋊C4C22×C8311yescharacteristic
337C4×C4⋊C4C22×C8311yescharacteristic
338C4×C4⋊C4C22×C8311yescharacteristic
339C4×C22⋊C4—21no—
340C4×C22⋊C4C22×C8311yescharacteristic
341#340C22×C8311yescharacteristic
342#340C22×C8311yescharacteristic
343#340C22×C8311yescharacteristic
344#340C22×C8311yescharacteristic
345#340C22×C8311yescharacteristic
346#340C22×C8311yescharacteristic
347#340C22×C8311yescharacteristic
348#340C22×C8311yescharacteristic
349#340C22×C8311yescharacteristic
350#340C22×C8311yescharacteristic
351#336C22×C8311yescharacteristic
352#336C22×C8311yescharacteristic
353C23×C4—21no—
354C23×C4C23×C8311yescharacteristic
355C2×M16—22no—
356C2×M16—22no—
357C2×M16C2×C4×C8314yes—
358C22×C8C23×C8311yescharacteristic
359C22×C8C23×C8311yescharacteristic
360C22×C8C23×C8311yescharacteristic
361C22×C8C23×C8311yescharacteristic
362#117—22no—
363#117C2×C4×C8314yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C2×C4×C8314yes—
371C2×C4⋊C4C23×C8311yescharacteristic
372C2×C4⋊C4C23×C8311yescharacteristic
373C2×C4⋊C4C23×C8311yescharacteristic
374C2×C4⋊C4C23×C8311yescharacteristic
375C2×C4⋊C4C23×C8311yescharacteristic
376C2×C4⋊C4C23×C8311yescharacteristic
377C2×C4⋊C4C23×C8311yescharacteristic
378C2×C4⋊C4C23×C8311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4D4×C8311yescharacteristic
383C2×C22⋊C4D4×C8311yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C8311yescharacteristic
390C2×C42C23×C8311yescharacteristic
391#107—22no—
392#107C2×C4×C8314yes—
393#107C2×C4×C8314yes—
394#106—22no—
395#106C2×C4×C8314yes—
396#106C2×C4×C8314yes—
397C22⋊C8—22no—
398#97—22no—
399C4×C8—22no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95D4×C8311yescharacteristic
411#95D4×C8311yescharacteristic
412C24C2×D4×C8311yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4C22×C4×C8312yes—
429C22×C4C2×D4×C8311yescharacteristic
430C22×C4C2×D4×C8311yescharacteristic
431C22×C4C2×D4×C8311yescharacteristic
432C22×C4C2×D4×C8311yescharacteristic
433C22×C4C2×D4×C8311yescharacteristic
434C22×C4#41×C8312yes—
435C22×C4C24×C8311yescharacteristic
436M16—28no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8C22×C4×C8312yes—
446C2×C8C22×C4×C8312yes—
447C2×C8#41×C8312yes—
448C2×C8#41×C8312yes—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4C22×C4×C8312yes—
467C4⋊C4C22×C4×C8312yes—
468C4⋊C4C22×C4×C8312yes—
469C4⋊C4C22×C4×C8312yes—
470C22⋊C4—24no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—81no—
481C42—81no—
482C42—81no—
483C42—81no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23C4×D4×C8312yes—
491C23C22×D4×C8311yescharacteristic
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4C4×D4×C8312yes—
535C2×C4#137×C8312yes—
536C2×C4C23×C4×C8311yescharacteristic
537C2×C4C2×#41×C8311yescharacteristic
538C2×C4C2×#41×C8311yescharacteristic
539C2×C4C2×#41×C8311yescharacteristic
540C2×C42−1+4×C8311yescharacteristic
541C2×C42−1+4×C8311yescharacteristic
542C8—22no—
543C8—41no—
544C8—41no—
545C8#117×C8314yes—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22C2×C4×D4×C8311yescharacteristic
554C22#547×C8311yescharacteristic
555C22#547×C8311yescharacteristic
556C22C2×#137×C8311yescharacteristic
557C22#575×C8311yescharacteristic
558C22#576×C8311yescharacteristic
559C22#577×C8311yescharacteristic
560C4—22no—
561C4—22no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4C2×#117×C8311yescharacteristic
574C4#519×C8311yescharacteristic
575C4#552×C8311yescharacteristic
576C4#552×C8311yescharacteristic
577C2—42no—
578C2C83×#234411yescharacteristic
579C2C4×#137×C8311yescharacteristic
580C2C83×#294611yescharacteristic
581C2C83×#334611yescharacteristic
582C2C83×#335011yescharacteristic
583C2C83×#335511yescharacteristic
584C2C83×#335611yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC24×C83C2×D4
LCSG ▷ C2×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
4. C83×#1944C2semidirect
5. C83×#1941C2semidirect
6. C83×#1921C2semidirect
7. C83×#1920C2semidirect
8. C83×#1919C2semidirect
9. C83×#1918C2semidirect
13. C83×#1776C2semidirect
14. C4×#107×C83C2semidirect
19. #428×C83C4semidirect
284. #22623C83direct (N × H)
296. #1944C2×C83semidirect
297. #1941C2×C83semidirect
298. #1921C2×C83semidirect
299. #1920C2×C83semidirect
300. #1919C2×C83semidirect
301. #1918C2×C83semidirect
305. #1776C2×C83semidirect
306. C4×#107C2×C83semidirect
308. C83#22623direct (N × H)
312. #428C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#428×C832
C83×#23472
C83×#23452
C83×#19442
C83×#19412
C83×#19212
C83×#19202
C83×#19192
C83×#19182
C83×#18252
C83×#18232
C83×#18092
C83×#17762
C4×#107×C832
C83×#17532
#2262383