Finite Group Databasebeta

← C83×#10539 #35238363

Subgroups — C83×#10539 #35238363

Order 21248.

490 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C83C211yesmaximal, characteristic
2C83×#1987C211yesmaximal, characteristic, complemented
3C83×#1982C211yesmaximal, characteristic
4C83×#1939C211yesmaximal, characteristic, complemented
5C2×#333×C83C211yesmaximal, characteristic, complemented
6C2×#331×C83C211yesmaximal, characteristic
7C83×#1277C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C83C2211yescharacteristic
9C2×#127×C83C2211yescharacteristic
10#486×C83—22no—
11#486×C83—22no—
12C2×C4⋊C8×C83—21no—
13C2×C4⋊C8×C83C2211yescharacteristic
14C2×C4⋊C8×C83C2211yescharacteristic
15C2×C4⋊C8×C83C2211yescharacteristic
16C2×#102×C83—21no—
17C2×#102×C83—21no—
18C2×#102×C83—21no—
19C2×#102×C83—21no—
20C2×C4×C8×C83C2211yescharacteristic
21C4×C4⋊C4×C83C2211yescharacteristic
22#340×C83—21no—
23#340×C83—21no—
24#336×C83—21no—
25#333×C83—22no—
26#331×C83—22no—
27C22×Q8×C83—21no—
28C22×D4×C83—21no—
29C22×D4×C83—21no—
30C22×D4×C83—21no—
31C22×C8×C83—21no—
32C22×C8×C83—21no—
33C22×C8×C83—21no—
34C22×C8×C83D411yescharacteristic
35C22×C8×C83D411yescharacteristic
36C4⋊Q8×C83—21no—
37C4⋊Q8×C83—21no—
38C4⋊Q8×C83—21no—
39C4⋊Q8×C83D412yes—
40#127×C83—21no—
41#127×C83—21no—
42#127×C83—21no—
43#127×C83D412yes—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83—21no—
49C2×C42×C83C2311yescharacteristic
50C4⋊C8×C83—21no—
51C4⋊C8×C83—21no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C4⋊C8×C83—21no—
56C4⋊C8×C83—42no—
57#102×C83—24no—
58#102×C83—24no—
59#102×C83—42no—
60#102×C83—42no—
61C4×C8×C83—21no—
62C4×C8×C83—21no—
63#95×C83—21no—
64C24×C83—41no—
65C2×Q8×C83—22no—
66C2×Q8×C83—41no—
67C2×Q8×C83—81no—
68C2×Q8×C83—81no—
69C2×D4×C83—22no—
70C2×D4×C83—22no—
71C2×D4×C83—22no—
72C2×D4×C83—41no—
73C2×D4×C83—41no—
74C2×D4×C83—41no—
75C2×D4×C83—41no—
76C2×D4×C83—41no—
77C2×D4×C83—41no—
78C2×D4×C83—41no—
79C2×D4×C83—41no—
80C2×D4×C83—41no—
81C2×D4×C83—41no—
82C2×D4×C83—41no—
83C2×D4×C83—81no—
84C2×D4×C83—81no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—41no—
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83#4111yescharacteristic
91C2×C8×C83—21no—
92C2×C8×C83—21no—
93C2×C8×C83—21no—
94C2×C8×C83—21no—
95C2×C8×C83—21no—
96C2×C8×C83—21no—
97C2×C8×C83—41no—
98C2×C8×C83—41no—
99C2×C8×C83—41no—
100C2×C8×C83—41no—
101C2×C8×C83—41no—
102C2×C8×C83—41no—
103C2×C8×C83—41no—
104C2×C8×C83—41no—
105C2×C8×C83—41no—
106C4⋊C4×C83—21no—
107C4⋊C4×C83—22no—
108C4⋊C4×C83—22no—
109C4⋊C4×C83—21no—
110C4⋊C4×C83—21no—
111C4⋊C4×C83—41no—
112C4⋊C4×C83—41no—
113C4⋊C4×C83SD1612yes—
114C42×C83—41no—
115C42×C83—41no—
116C42×C83C2×D411yescharacteristic
117C42×C83C2×D411yescharacteristic
118C42×C83#4111yescharacteristic
119C42×C83#4111yescharacteristic
120C23×C83—42no—
121C23×C83—81no—
122C23×C83—81no—
123C23×C83—81no—
124C23×C83—81no—
125C23×C83—81no—
126C23×C83—81no—
127C23×C83#12111yescharacteristic
128Q8×C83—82no—
129Q8×C83—82no—
130D4×C83—42no—
131D4×C83—42no—
132D4×C83—42no—
133D4×C83—42no—
134D4×C83—82no—
135D4×C83—82no—
136D4×C83—81no—
137D4×C83—81no—
138D4×C83—81no—
139D4×C83—81no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—22no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—42no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—81no—
150C2×C4×C83—81no—
151C2×C4×C83#12011yescharacteristic
152C2×C4×C83#12111yescharacteristic
153C2×C4×C83#12111yescharacteristic
154C2×C4×C83#12311yescharacteristic
155C2×C4×C83#12311yescharacteristic
156C2×C4×C83#12411yescharacteristic
157C2×C4×C83C2×SD1611yescharacteristic
158C2×C4×C83#13511yescharacteristic
159C2×C4×C83#13511yescharacteristic
160C2×C4×C83#13511yescharacteristic
161C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C83#13711yescharacteristic
164C2×C4×C83#13711yescharacteristic
165C8×C83—41no—
166C8×C83—41no—
167C8×C83—81no—
168C8×C83—81no—
169C8×C83—81no—
170C22×C83—82no—
171C22×C83—82no—
172C22×C83—82no—
173C22×C83—161no—
174C22×C83—161no—
175C22×C83—161no—
176C22×C83—161no—
177C22×C83#39411yescharacteristic
178C22×C83#46311yescharacteristic
179C22×C83#46411yescharacteristic
180C22×C83#46511yescharacteristic
181C22×C83#46811yescharacteristic
182C22×C83#47211yescharacteristic
183C22×C83#47211yescharacteristic
184C4×C83—21no—
185C4×C83—21no—
186C4×C83—42no—
187C4×C83—81no—
188C4×C83—82no—
189C4×C83#44911yescharacteristic
190C4×C83#45211yescharacteristic
191C4×C83#46011yescharacteristic
192C4×C83#46111yescharacteristic
193C4×C83#46311yescharacteristic
194C4×C83#46411yescharacteristic
195C4×C83#48811yescharacteristic
196C4×C83#48911yescharacteristic
197#10539C8311yesmaximal, characteristic, direct product factor, Sylow
198C2×C83—162no—
199C2×C83#167711yescharacteristic
200C2×C83#167811yescharacteristic
201C2×C83#169711yescharacteristic
202C2×C83#169811yescharacteristic
203C2×C83#204211yescharacteristic
204C2×C83#204511yescharacteristic
205C2×C83#205511yescharacteristic
206C2×#486C2×C8311yescharacteristic
207#1987C2×C8311yescharacteristic, complemented
208#1982C2×C8311yescharacteristic
209#1939C2×C8311yescharacteristic, complemented
210C2×#333C2×C8311yescharacteristic, complemented
211C2×#331C2×C8311yescharacteristic
212#1277C2×C8311yescharacteristic, complemented
213C83#1053911yescharacteristic, direct product factor, Sylow
214C2×C4⋊Q8C22×C8311yescharacteristic
215C2×#127C22×C8311yescharacteristic
216#486—22no—
217#486—22no—
218C2×C4⋊C8—21no—
219C2×C4⋊C8C22×C8311yescharacteristic
220C2×C4⋊C8C22×C8311yescharacteristic
221C2×C4⋊C8C22×C8311yescharacteristic
222C2×#102—21no—
223C2×#102—21no—
224C2×#102—21no—
225C2×#102—21no—
226C2×C4×C8C22×C8311yescharacteristic
227C4×C4⋊C4C22×C8311yescharacteristic
228#340—21no—
229#340—21no—
230#336—21no—
231#333—22no—
232#331—22no—
233C22×Q8—21no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8D4×C8311yescharacteristic
241C22×C8D4×C8311yescharacteristic
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8D4×C8312yes—
246#127—21no—
247#127—21no—
248#127—21no—
249#127D4×C8312yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C8311yescharacteristic
253C2×C4⋊C4D4×C8311yescharacteristic
254C2×C42—21no—
255C2×C42C23×C8311yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—42no—
263#102—24no—
264#102—24no—
265#102—42no—
266#102—42no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270C24—41no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—81no—
274C2×Q8—81no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—81no—
290C2×D4—81no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C8311yescharacteristic
295C22×C4C2×D4×C8311yescharacteristic
296C22×C4#41×C8311yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4SD16×C8312yes—
320C42—41no—
321C42—41no—
322C42C2×D4×C8311yescharacteristic
323C42C2×D4×C8311yescharacteristic
324C42#41×C8311yescharacteristic
325C42#41×C8311yescharacteristic
326C23—42no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23#121×C8311yescharacteristic
334Q8—82no—
335Q8—82no—
336D4—42no—
337D4—42no—
338D4—42no—
339D4—42no—
340D4—82no—
341D4—82no—
342D4—81no—
343D4—81no—
344D4—81no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4#120×C8311yescharacteristic
358C2×C4#121×C8311yescharacteristic
359C2×C4#121×C8311yescharacteristic
360C2×C4#123×C8311yescharacteristic
361C2×C4#123×C8311yescharacteristic
362C2×C4#124×C8311yescharacteristic
363C2×C4C2×SD16×C8311yescharacteristic
364C2×C4#135×C8311yescharacteristic
365C2×C4#135×C8311yescharacteristic
366C2×C4#135×C8311yescharacteristic
367C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
368C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
369C2×C4#137×C8311yescharacteristic
370C2×C4#137×C8311yescharacteristic
371C8—41no—
372C8—41no—
373C8—81no—
374C8—81no—
375C8—81no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22—161no—
380C22—161no—
381C22—161no—
382C22—161no—
383C22#394×C8311yescharacteristic
384C22#463×C8311yescharacteristic
385C22#464×C8311yescharacteristic
386C22#465×C8311yescharacteristic
387C22#468×C8311yescharacteristic
388C22#472×C8311yescharacteristic
389C22#472×C8311yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—82no—
394C4—81no—
395C4#449×C8311yescharacteristic
396C4#452×C8311yescharacteristic
397C4#460×C8311yescharacteristic
398C4#461×C8311yescharacteristic
399C4#463×C8311yescharacteristic
400C4#464×C8311yescharacteristic
401C4#488×C8311yescharacteristic
402C4#489×C8311yescharacteristic
403C2—162no—
404C2C83×#167711yescharacteristic
405C2C83×#167811yescharacteristic
406C2C83×#169711yescharacteristic
407C2C83×#169811yescharacteristic
408C2C83×#204211yescharacteristic
409C2C83×#204511yescharacteristic
410C2C83×#205511yescharacteristic
subgroupG/H
center, socleC23×C83#121
commutator, Frattini, cosocleC2×C42C23×C83
prime radicalC2×#127×C83C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#1987C2semidirect
4. C83×#1939C2semidirect
5. C2×#333×C83C2semidirect
7. C83×#1277C2semidirect
197. #10539C83direct (N × H)
207. #1987C2×C83semidirect
209. #1939C2×C83semidirect
210. C2×#333C2×C83semidirect
212. #1277C2×C83semidirect
213. C83#10539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#486×C832
C83×#19872
C83×#19822
C83×#19392
C2×#333×C832
C2×#331×C832
C83×#12772
#1053983