Finite Group Databasebeta

← C83×#9928 #35237752

Subgroups — C83×#9928 #35237752

Order 21248.

778 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C83C211yesmaximal, characteristic, complemented
2C83×#2626C211yesmaximal, characteristic
3C2×#399×C83C211yesmaximal, characteristic
4C83×#1824C211yesmaximal, characteristic, complemented
5C2×#328×C83C211yesmaximal, characteristic, complemented
6C2×#323×C83C211yesmaximal, characteristic
7C83×#1294C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C83C2211yescharacteristic
9C22×C4⋊C4×C83—21no—
10C22×C4⋊C4×C83C2211yescharacteristic
11C22×C22⋊C4×C83—21no—
12C22×C22⋊C4×C83C2211yescharacteristic
13#484×C83—22no—
14#484×C83—22no—
15C2×#107×C83—21no—
16C2×#103×C83—21no—
17C2×C22⋊C8×C83C2211yescharacteristic
18C2×C22⋊C8×C83C2211yescharacteristic
19#399×C83—21no—
20#399×C83—22no—
21#399×C83—22no—
22#396×C83—22no—
23#393×C83—21no—
24#385×C83—21no—
25#380×C83C2211yescharacteristic
26#379×C83—21no—
27C2×#95×C83C2211yescharacteristic
28#340×C83—22no—
29#328×C83—22no—
30#323×C83—22no—
31C25×C83D411yescharacteristic
32C22×Q8×C83D411yescharacteristic
33C23×C4×C83—21no—
34C23×C4×C83—21no—
35C23×C4×C83D411yescharacteristic
36C23×C4×C83C2311yescharacteristic
37C22×C8×C83—21no—
38C22×C8×C83—21no—
39C22⋊Q8×C83—21no—
40C22⋊Q8×C83—21no—
41C22⋊Q8×C83—21no—
42C22⋊Q8×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—24no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—22no—
51C2×C4⋊C4×C83—44no—
52C2×C4⋊C4×C83D412yes—
53C2×C4⋊C4×C83D411yescharacteristic
54C2×C4⋊C4×C83D412yes—
55C2×C22⋊C4×C83—24no—
56C2×C22⋊C4×C83—21no—
57C2×C22⋊C4×C83—21no—
58C2×C22⋊C4×C83—21no—
59C2×C22⋊C4×C83—21no—
60C2×C22⋊C4×C83—21no—
61C2×C22⋊C4×C83—21no—
62C2×C22⋊C4×C83—21no—
63C2×C22⋊C4×C83—21no—
64C2×C22⋊C4×C83—22no—
65C2×C22⋊C4×C83—22no—
66C2×C22⋊C4×C83—44no—
67#107×C83—24no—
68#103×C83—24no—
69C22⋊C8×C83—21no—
70C22⋊C8×C83—21no—
71C22⋊C8×C83—21no—
72C22⋊C8×C83D412yes—
73#95×C83—22no—
74#95×C83—21no—
75#95×C83—21no—
76#95×C83D412yes—
77C24×C83—21no—
78C24×C83—21no—
79C24×C83—21no—
80C24×C83—21no—
81C24×C83—21no—
82C24×C83—21no—
83C24×C83—42no—
84C24×C83—42no—
85C24×C83Q1612yes—
86C24×C83C2×D411yescharacteristic
87C2×Q8×C83—21no—
88C2×Q8×C83—21no—
89C2×Q8×C83—42no—
90C22×C4×C83—24no—
91C22×C4×C83—22no—
92C22×C4×C83—21no—
93C22×C4×C83—22no—
94C22×C4×C83—22no—
95C22×C4×C83—21no—
96C22×C4×C83—21no—
97C22×C4×C83—21no—
98C22×C4×C83—21no—
99C22×C4×C83—42no—
100C22×C4×C83—42no—
101C22×C4×C83—41no—
102C22×C4×C83—41no—
103C22×C4×C83—42no—
104C22×C4×C83—42no—
105C22×C4×C83—42no—
106C22×C4×C83—41no—
107C22×C4×C83—41no—
108C22×C4×C83C2×D411yescharacteristic
109C22×C4×C83C2×D411yescharacteristic
110C22×C4×C83C2×D411yescharacteristic
111C22×C4×C83C2×D411yescharacteristic
112C22×C4×C83C2×D411yescharacteristic
113C22×C4×C83#4111yescharacteristic
114C2×C8×C83—22no—
115C2×C8×C83—42no—
116C2×C8×C83—42no—
117C2×C8×C83—41no—
118C4⋊C4×C83—22no—
119C4⋊C4×C83—21no—
120C4⋊C4×C83—22no—
121C4⋊C4×C83—21no—
122C4⋊C4×C83—42no—
123C4⋊C4×C83—48no—
124C4⋊C4×C83—41no—
125C4⋊C4×C83—41no—
126C4⋊C4×C83—41no—
127C4⋊C4×C83—41no—
128C4⋊C4×C83—82no—
129C22⋊C4×C83—48no—
130C22⋊C4×C83—41no—
131C22⋊C4×C83—41no—
132C22⋊C4×C83—41no—
133C22⋊C4×C83—41no—
134C22⋊C4×C83—41no—
135C22⋊C4×C83—41no—
136C22⋊C4×C83—41no—
137C22⋊C4×C83—41no—
138C22⋊C4×C83—82no—
139C22⋊C4×C83—82no—
140C23×C83—22no—
141C23×C83—22no—
142C23×C83—22no—
143C23×C83—22no—
144C23×C83—22no—
145C23×C83—44no—
146C23×C83—42no—
147C23×C83—44no—
148C23×C83—42no—
149C23×C83—41no—
150C23×C83—41no—
151C23×C83—41no—
152C23×C83—42no—
153C23×C83—42no—
154C23×C83—41no—
155C23×C83—82no—
156C23×C83—82no—
157C23×C83—81no—
158C23×C83—81no—
159C23×C83#12011yescharacteristic
160C23×C83#12011yescharacteristic
161C23×C83#12111yescharacteristic
162C23×C83C2×Q1611yescharacteristic
163C23×C83#13511yescharacteristic
164C23×C83#13711yescharacteristic
165C23×C83#13711yescharacteristic
166Q8×C83—42no—
167Q8×C83—81no—
168C2×C4×C83—22no—
169C2×C4×C83—22no—
170C2×C4×C83—24no—
171C2×C4×C83—41no—
172C2×C4×C83—41no—
173C2×C4×C83—41no—
174C2×C4×C83—41no—
175C2×C4×C83—44no—
176C2×C4×C83—44no—
177C2×C4×C83—42no—
178C2×C4×C83—42no—
179C2×C4×C83—42no—
180C2×C4×C83—42no—
181C2×C4×C83—42no—
182C2×C4×C83—41no—
183C2×C4×C83—41no—
184C2×C4×C83—41no—
185C2×C4×C83—42no—
186C2×C4×C83—42no—
187C2×C4×C83—42no—
188C2×C4×C83—42no—
189C2×C4×C83—42no—
190C2×C4×C83—42no—
191C2×C4×C83—42no—
192C2×C4×C83—82no—
193C2×C4×C83—82no—
194C2×C4×C83—81no—
195C2×C4×C83#12011yescharacteristic
196C2×C4×C83#12111yescharacteristic
197C2×C4×C83#12111yescharacteristic
198C2×C4×C83#12711yescharacteristic
199C8×C83—42no—
200C8×C83—81no—
201C22×C83—22no—
202C22×C83—22no—
203C22×C83—22no—
204C22×C83—22no—
205C22×C83—21no—
206C22×C83—21no—
207C22×C83—21no—
208C22×C83—21no—
209C22×C83—44no—
210C22×C83—44no—
211C22×C83—42no—
212C22×C83—82no—
213C22×C83—82no—
214C22×C83—82no—
215C22×C83—82no—
216C22×C83—81no—
217C22×C83—81no—
218C22×C83#39211yescharacteristic
219C22×C83#45111yescharacteristic
220C22×C83#45111yescharacteristic
221C22×C83#45211yescharacteristic
222C22×C83#45211yescharacteristic
223C22×C83#45312yes—
224C22×C83#45812yes—
225C22×C83#46711yescharacteristic
226C22×C83#47011yescharacteristic
227C4×C83—21no—
228C4×C83—21no—
229C4×C83—21no—
230C4×C83—21no—
231C4×C83—44no—
232C4×C83—82no—
233C4×C83—81no—
234C4×C83—81no—
235C4×C83—82no—
236C4×C83—81no—
237#9928C8311yesmaximal, characteristic, direct product factor, Sylow
238C2×C83—21no—
239C2×C83—21no—
240C2×C83—21no—
241C2×C83—21no—
242C2×C83—82no—
243C2×C83#161412yes—
244C2×C83#161812yes—
245C2×C83#200111yescharacteristic
246C2×C83#200211yescharacteristic
247C2×C83#202211yescharacteristic
248C2×#484C2×C8311yescharacteristic, complemented
249#2626C2×C8311yescharacteristic
250C2×#399C2×C8311yescharacteristic
251#1824C2×C8311yescharacteristic, complemented
252C2×#328C2×C8311yescharacteristic, complemented
253C2×#323C2×C8311yescharacteristic
254#1294C2×C8311yescharacteristic, complemented
255C83#992811yescharacteristic, direct product factor, Sylow
256C2×C22⋊Q8C22×C8311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4C22×C8311yescharacteristic
259C22×C22⋊C4—21no—
260C22×C22⋊C4C22×C8311yescharacteristic
261#484—22no—
262#484—22no—
263C2×#107—21no—
264C2×#103—21no—
265C2×C22⋊C8C22×C8311yescharacteristic
266C2×C22⋊C8C22×C8311yescharacteristic
267#399—21no—
268#399—22no—
269#399—22no—
270#396—22no—
271#393—21no—
272#385—21no—
273#380C22×C8311yescharacteristic
274#379—21no—
275C2×#95C22×C8311yescharacteristic
276#340—22no—
277#328—22no—
278#323—22no—
279C25D4×C8311yescharacteristic
280C22×Q8D4×C8311yescharacteristic
281C23×C4—21no—
282C23×C4—21no—
283C23×C4D4×C8311yescharacteristic
284C23×C4C23×C8311yescharacteristic
285C22×C8—21no—
286C22×C8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4D4×C8312yes—
301C2×C4⋊C4D4×C8311yescharacteristic
302C2×C4⋊C4D4×C8312yes—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—44no—
315#107—24no—
316#103—24no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8D4×C8312yes—
321#95—22no—
322#95—21no—
323#95—21no—
324#95D4×C8312yes—
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—42no—
332C24—42no—
333C24Q16×C8312yes—
334C24C2×D4×C8311yescharacteristic
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—42no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4C2×D4×C8311yescharacteristic
357C22×C4C2×D4×C8311yescharacteristic
358C22×C4C2×D4×C8311yescharacteristic
359C22×C4C2×D4×C8311yescharacteristic
360C22×C4C2×D4×C8311yescharacteristic
361C22×C4#41×C8311yescharacteristic
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—41no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—42no—
371C4⋊C4—48no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—82no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—82no—
387C22⋊C4—82no—
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—44no—
394C23—42no—
395C23—42no—
396C23—44no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—42no—
402C23—42no—
403C23—82no—
404C23—81no—
405C23—81no—
406C23—82no—
407C23#120×C8311yescharacteristic
408C23#120×C8311yescharacteristic
409C23#121×C8311yescharacteristic
410C23C2×Q16×C8311yescharacteristic
411C23#135×C8311yescharacteristic
412C23#137×C8311yescharacteristic
413C23#137×C8311yescharacteristic
414Q8—42no—
415Q8—81no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4#120×C8311yescharacteristic
444C2×C4#121×C8311yescharacteristic
445C2×C4#121×C8311yescharacteristic
446C2×C4#127×C8311yescharacteristic
447C8—42no—
448C8—81no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—44no—
458C22—42no—
459C22—44no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—81no—
464C22—81no—
465C22—82no—
466C22#392×C8311yescharacteristic
467C22#451×C8311yescharacteristic
468C22#451×C8311yescharacteristic
469C22#452×C8311yescharacteristic
470C22#452×C8311yescharacteristic
471C22#453×C8312yes—
472C22#458×C8312yes—
473C22#467×C8311yescharacteristic
474C22#470×C8311yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—44no—
480C4—81no—
481C4—82no—
482C4—81no—
483C4—81no—
484C4—82no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—82no—
490C2C83×#161412yes—
491C2C83×#161812yes—
492C2C83×#200111yescharacteristic
493C2C83×#200211yescharacteristic
494C2C83×#202211yescharacteristic
subgroupG/H
center, socleC23×C83#120
commutator, Frattini, cosocleC23×C4C23×C83
prime radicalC25×C83D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#484×C83C2semidirect
4. C83×#1824C2semidirect
5. C2×#328×C83C2semidirect
7. C83×#1294C2semidirect
237. #9928C83direct (N × H)
248. C2×#484C2×C83semidirect
251. #1824C2×C83semidirect
252. C2×#328C2×C83semidirect
254. #1294C2×C83semidirect
255. C83#9928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#484×C832
C83×#26262
C2×#399×C832
C83×#18242
C2×#328×C832
C2×#323×C832
C83×#12942
#992883