Finite Group Databasebeta

← C83×#9519 #35237343

Subgroups — C83×#9519 #35237343

Order 21248.

644 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3004C211yesmaximal, characteristic
2C83×#2976C211yesmaximal, characteristic
3C83×#1787C211yesmaximal, characteristic, complemented
4C83×#1784C211yesmaximal, characteristic, complemented
5C83×#1513C211yesmaximal, characteristic
6C83×#1305C211yesmaximal, characteristic, complemented
7C83×#1293C211yesmaximal, characteristic, complemented
8C23×Q8×C83C2211yescharacteristic
9C2×#137×C83—21no—
10#525×C83C2211yescharacteristic
11#451×C83—21no—
12#451×C83C412yescomplemented
13#448×C83—21no—
14#448×C83C412yescomplemented
15#436×C83—21no—
16#435×C83—21no—
17#435×C83—21no—
18C8×D4×C83—21no—
19#433×C83—21no—
20#419×C83—21no—
21C2×#103×C83—21no—
22C2×#103×C83—21no—
23C2×#101×C83—21no—
24C2×#101×C83—21no—
25#408×C83—21no—
26#407×C83C2211yescharacteristic
27#407×C83C2211yescharacteristic
28#407×C83C2211yescharacteristic
29C2×C22⋊C8×C83C2211yescharacteristic
30#380×C83C2211yescharacteristic
31#328×C83—21no—
32#327×C83—21no—
33C2×#41×C83D411yescharacteristic
34C22×Q8×C83—21no—
35C22×Q8×C83—21no—
36C22×Q8×C83—21no—
37C22×Q8×C83—21no—
38C22×Q8×C83—21no—
39C22×Q8×C83—42no—
40C22×Q8×C83—42no—
41C22×Q8×C83C2×C412yes—
42C23×C4×C83—21no—
43C23×C4×C83C2311yescharacteristic
44#137×C83—42no—
45#137×C83—42no—
46C2×Q16×C83—22no—
47C2×SD16×C83—22no—
48C2×M16×C83—21no—
49C2×M16×C83—21no—
50C2×M16×C83—21no—
51C2×M16×C83D411yescharacteristic
52C2×M16×C83D411yescharacteristic
53C22×C8×C83—21no—
54C22×C8×C83D411yescharacteristic
55C22×C8×C83D411yescharacteristic
56#123×C83—21no—
57C22⋊Q8×C83C2×C411yescharacteristic
58C22⋊Q8×C83D411yescharacteristic
59#121×C83C2×C411yescharacteristic
60#121×C83D411yescharacteristic
61#120×C83—21no—
62C4×D4×C83—21no—
63C4×D4×C83—21no—
64#117×C83D411yescharacteristic
65C2×C4⋊C4×C83—21no—
66C2×C22⋊C4×C83—21no—
67C4⋊C8×C83—21no—
68C4⋊C8×C83—21no—
69#103×C83—22no—
70#103×C83—22no—
71#103×C83—42no—
72#103×C83—42no—
73#101×C83—42no—
74#101×C83—42no—
75C22⋊C8×C83—21no—
76C22⋊C8×C83—21no—
77C22⋊C8×C83—21no—
78C22⋊C8×C83—21no—
79C22⋊C8×C83—21no—
80C22⋊C8×C83—21no—
81C22⋊C8×C83—21no—
82C22⋊C8×C83—21no—
83C22⋊C8×C83—21no—
84C22⋊C8×C83C2×C412yes—
85#97×C83—21no—
86C4×C8×C83—21no—
87#95×C83—21no—
88C24×C83#4111yescharacteristic
89#41×C83—41no—
90#41×C83—41no—
91C2×Q8×C83—22no—
92C2×Q8×C83—22no—
93C2×Q8×C83—22no—
94C2×Q8×C83—22no—
95C2×Q8×C83—22no—
96C2×Q8×C83—22no—
97C2×Q8×C83—22no—
98C2×Q8×C83—22no—
99C2×Q8×C83—44no—
100C2×Q8×C83—41no—
101C2×Q8×C83—41no—
102C2×Q8×C83—41no—
103C2×Q8×C83—41no—
104C2×Q8×C83—41no—
105C2×Q8×C83—41no—
106C2×Q8×C83—44no—
107C2×Q8×C83—44no—
108C2×Q8×C83—41no—
109C2×Q8×C83—41no—
110C2×Q8×C83C22⋊C411yescharacteristic
111C2×D4×C83—21no—
112C2×D4×C83—21no—
113C2×D4×C83—21no—
114C2×D4×C83C22⋊C411yescharacteristic
115C22×C4×C83—22no—
116C22×C4×C83—21no—
117C22×C4×C83—41no—
118C22×C4×C83—41no—
119C22×C4×C83—44no—
120C22×C4×C83—41no—
121C22×C4×C83—41no—
122C22×C4×C83—41no—
123C22×C4×C83C22×C411yescharacteristic
124C22×C4×C83C2×D411yescharacteristic
125C22×C4×C83C2×D411yescharacteristic
126C22×C4×C83C2×D411yescharacteristic
127C22×C4×C83C2×D411yescharacteristic
128C22×C4×C83#4111yescharacteristic
129Q16×C83—44no—
130SD16×C83—44no—
131M16×C83—41no—
132M16×C83—41no—
133M16×C83—41no—
134M16×C83—41no—
135M16×C83—41no—
136M16×C83—41no—
137M16×C83—81no—
138C2×C8×C83—22no—
139C2×C8×C83—21no—
140C2×C8×C83—21no—
141C2×C8×C83—21no—
142C2×C8×C83—21no—
143C2×C8×C83—41no—
144C2×C8×C83—41no—
145C2×C8×C83—41no—
146C2×C8×C83—81no—
147C4⋊C4×C83—21no—
148C4⋊C4×C83—21no—
149C4⋊C4×C83—41no—
150C4⋊C4×C83—41no—
151C4⋊C4×C83C22⋊C411yescharacteristic
152C4⋊C4×C83C22⋊C411yescharacteristic
153C22⋊C4×C83—21no—
154C22⋊C4×C83—21no—
155C22⋊C4×C83—21no—
156C22⋊C4×C83—21no—
157C22⋊C4×C83—21no—
158C22⋊C4×C83—81no—
159C42×C83—21no—
160C23×C83—21no—
161C23×C83—21no—
162C23×C83—21no—
163C23×C83—41no—
164C23×C83—41no—
165C23×C83C4×D411yescharacteristic
166C23×C83#12111yescharacteristic
167C23×C83#12311yescharacteristic
168Q8×C83—24no—
169Q8×C83—24no—
170Q8×C83—41no—
171Q8×C83—42no—
172Q8×C83—42no—
173Q8×C83—42no—
174Q8×C83—42no—
175Q8×C83—42no—
176Q8×C83—42no—
177D4×C83—41no—
178D4×C83—41no—
179D4×C83—41no—
180D4×C83—81no—
181D4×C83—81no—
182C2×C4×C83—21no—
183C2×C4×C83—21no—
184C2×C4×C83—21no—
185C2×C4×C83—21no—
186C2×C4×C83—21no—
187C2×C4×C83—21no—
188C2×C4×C83—24no—
189C2×C4×C83—21no—
190C2×C4×C83—21no—
191C2×C4×C83—21no—
192C2×C4×C83—41no—
193C2×C4×C83—41no—
194C2×C4×C83—41no—
195C2×C4×C83—42no—
196C2×C4×C83—42no—
197C2×C4×C83—42no—
198C2×C4×C83—42no—
199C2×C4×C83—42no—
200C2×C4×C83—42no—
201C2×C4×C83—41no—
202C2×C4×C83—41no—
203C2×C4×C83—81no—
204C2×C4×C83—81no—
205C2×C4×C83—81no—
206C2×C4×C83C2×C22⋊C411yescharacteristic
207C2×C4×C83C4×D411yescharacteristic
208C2×C4×C83#12011yescharacteristic
209C2×C4×C83#12111yescharacteristic
210C8×C83—42no—
211C8×C83—41no—
212C8×C83—41no—
213C8×C83—41no—
214C8×C83—41no—
215C8×C83—81no—
216C22×C83—21no—
217C22×C83—21no—
218C22×C83—21no—
219C22×C83—21no—
220C22×C83—21no—
221C22×C83—21no—
222C22×C83—21no—
223C22×C83—21no—
224C22×C83—42no—
225C22×C83—42no—
226C22×C83—41no—
227C22×C83—41no—
228C22×C83—41no—
229C22×C83#38611yescharacteristic
230C22×C83#47111yescharacteristic
231C22×C83#47311yescharacteristic
232C4×C83—21no—
233C4×C83—21no—
234C4×C83—21no—
235C4×C83—44no—
236C4×C83—41no—
237C4×C83—41no—
238C4×C83—41no—
239C4×C83—161no—
240C4×C83B(4,𝔽2)11yescharacteristic
241C4×C83B(4,𝔽2)11yescharacteristic
242#9519C8311yesmaximal, characteristic, direct product factor, Sylow
243C2×C83—21no—
244C2×C83—21no—
245C2×C83—41no—
246C2×C83—41no—
247C2×C83—81no—
248C2×C83#188911yescharacteristic
249C2×C83#190211yescharacteristic
250C2×C83#190811yescharacteristic
251#3004C2×C8311yescharacteristic
252#2976C2×C8311yescharacteristic
253#1787C2×C8311yescharacteristic, complemented
254#1784C2×C8311yescharacteristic, complemented
255#1513C2×C8311yescharacteristic
256#1305C2×C8311yescharacteristic, complemented
257#1293C2×C8311yescharacteristic, complemented
258C83#951911yescharacteristic, direct product factor, Sylow
259C23×Q8C22×C8311yescharacteristic
260C2×#137—21no—
261#525C22×C8311yescharacteristic
262#451—21no—
263#451C4×C8312yescomplemented
264#448—21no—
265#448C4×C8312yescomplemented
266#436—21no—
267#435—21no—
268#435—21no—
269C8×D4—21no—
270#433—21no—
271#419—21no—
272C2×#103—21no—
273C2×#103—21no—
274C2×#101—21no—
275C2×#101—21no—
276#408—21no—
277#407C22×C8311yescharacteristic
278#407C22×C8311yescharacteristic
279#407C22×C8311yescharacteristic
280C2×C22⋊C8C22×C8311yescharacteristic
281#380C22×C8311yescharacteristic
282#328—21no—
283#327—21no—
284C2×#41D4×C8311yescharacteristic
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—42no—
291C22×Q8—42no—
292C22×Q8C2×C4×C8312yes—
293C23×C4—21no—
294C23×C4C23×C8311yescharacteristic
295#137—42no—
296#137—42no—
297C2×Q16—22no—
298C2×SD16—22no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—21no—
302C2×M16D4×C8311yescharacteristic
303C2×M16D4×C8311yescharacteristic
304C22×C8—21no—
305C22×C8D4×C8311yescharacteristic
306C22×C8D4×C8311yescharacteristic
307#123—21no—
308C22⋊Q8C2×C4×C8311yescharacteristic
309C22⋊Q8D4×C8311yescharacteristic
310#121C2×C4×C8311yescharacteristic
311#121D4×C8311yescharacteristic
312#120—21no—
313C4×D4—21no—
314C4×D4—21no—
315#117D4×C8311yescharacteristic
316C2×C4⋊C4—21no—
317C2×C22⋊C4—21no—
318C4⋊C8—21no—
319C4⋊C8—21no—
320#103—22no—
321#103—22no—
322#103—42no—
323#103—42no—
324#101—42no—
325#101—42no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335C22⋊C8C2×C4×C8312yes—
336#97—21no—
337C4×C8—21no—
338#95—21no—
339C24#41×C8311yescharacteristic
340#41—41no—
341#41—41no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—44no—
351C2×Q8—41no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×Q8C22⋊C4×C8311yescharacteristic
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4C22⋊C4×C8311yescharacteristic
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—44no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4C22×C4×C8311yescharacteristic
375C22×C4C2×D4×C8311yescharacteristic
376C22×C4C2×D4×C8311yescharacteristic
377C22×C4C2×D4×C8311yescharacteristic
378C22×C4C2×D4×C8311yescharacteristic
379C22×C4#41×C8311yescharacteristic
380Q16—44no—
381SD16—44no—
382M16—41no—
383M16—41no—
384M16—41no—
385M16—41no—
386M16—41no—
387M16—41no—
388M16—81no—
389C2×C8—22no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—81no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4C22⋊C4×C8311yescharacteristic
403C4⋊C4C22⋊C4×C8311yescharacteristic
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—81no—
410C42—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—41no—
415C23—41no—
416C23C4×D4×C8311yescharacteristic
417C23#121×C8311yescharacteristic
418C23#123×C8311yescharacteristic
419Q8—24no—
420Q8—24no—
421Q8—41no—
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426Q8—42no—
427Q8—42no—
428D4—41no—
429D4—41no—
430D4—41no—
431D4—81no—
432D4—81no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4C2×C22⋊C4×C8311yescharacteristic
458C2×C4C4×D4×C8311yescharacteristic
459C2×C4#120×C8311yescharacteristic
460C2×C4#121×C8311yescharacteristic
461C8—42no—
462C8—41no—
463C8—41no—
464C8—41no—
465C8—41no—
466C8—81no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22#386×C8311yescharacteristic
481C22#471×C8311yescharacteristic
482C22#473×C8311yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—44no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—161no—
491C4B(4,𝔽2)×C8311yescharacteristic
492C4B(4,𝔽2)×C8311yescharacteristic
493C2—21no—
494C2—21no—
495C2—41no—
496C2—41no—
497C2—81no—
498C2C83×#188911yescharacteristic
499C2C83×#190211yescharacteristic
500C2C83×#190811yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radical#525×C83C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#1787C2semidirect
4. C83×#1784C2semidirect
6. C83×#1305C2semidirect
7. C83×#1293C2semidirect
12. #451×C83C4semidirect
14. #448×C83C4semidirect
242. #9519C83direct (N × H)
253. #1787C2×C83semidirect
254. #1784C2×C83semidirect
256. #1305C2×C83semidirect
257. #1293C2×C83semidirect
258. C83#9519direct (N × H)
263. #451C4×C83semidirect
265. #448C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30042
C83×#29762
C83×#17872
C83×#17842
C83×#15132
C83×#13052
C83×#12932
#951983