Finite Group Databasebeta

← #35309118

Subgroups — #35309118

Order 21248.

366 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908398C211yesmaximal, characteristic
2#24907622C211yesmaximal, characteristic
3#24907469C211yesmaximal, characteristic
4#24907465C211yesmaximal, characteristic
5#24905347C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C83×#1296C211yesmaximal, characteristic
8C2×C4×Dic166C2211yescharacteristic
9C2×#14581725—21no—
10C2×#14581725—21no—
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×#14581717—21no—
13C2×#14581715—21no—
14C2×C4×C83⋊C8C2211yescharacteristic
15#19127571C2211yescharacteristic
16#19127464—21no—
17#19127463—21no—
18#19127455—21no—
19#19127455—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22#384×C83C2211yescharacteristic
23C22×Dic166D411yescharacteristic
24C22×C83⋊C8—21no—
25C22×C83⋊C8D411yescharacteristic
26C22×C83⋊C8D411yescharacteristic
27C4×Dic166—21no—
28C4×Dic166—21no—
29C4×Dic166—21no—
30C4×Dic166—21no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83D411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×C4×Dic83—21no—
37#14581725—42no—
38#14581725—42no—
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41#14581717—42no—
42#14581715—42no—
43C4×C83⋊C8—21no—
44C4×C83⋊C8—21no—
45C22×C8×C83—21no—
46C22×C8×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C42×C83C2311yescharacteristic
51C4⋊C8×C83—21no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C2×Dic166—21no—
56C2×Dic166—21no—
57C2×Dic166—21no—
58C2×Dic166—21no—
59C2×Dic166—21no—
60C2×Dic166D812yes—
61C22×Dic83—21no—
62C22×Dic83—21no—
63C22×Dic83—41no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—21no—
66C2×C83⋊C8—21no—
67C2×C83⋊C8—21no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8SD1612yes—
72C2×C83⋊C8Q1612yes—
73C4⋊Dic83—21no—
74C4⋊Dic83—21no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C4⋊Dic83—41no—
78C4⋊Dic83—41no—
79C4⋊Dic83—81no—
80Dic83⋊C4—41no—
81Dic83⋊C4—41no—
82C4×Dic83—41no—
83C4×Dic83—41no—
84C22×C4×C83—41no—
85C22×C4×C83C2×D411yescharacteristic
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83#4111yescharacteristic
88C2×C8×C83—41no—
89C2×C8×C83—41no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C2×C8×C83—41no—
93C2×C8×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—81no—
99C42×C83#4111yescharacteristic
100C42×C83#4111yescharacteristic
101C42×C83#4111yescharacteristic
102C42×C83#4111yescharacteristic
103C23×C83#12111yescharacteristic
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—81no—
107C2×C4×C83—81no—
108C2×C4×C83—81no—
109C2×C4×C83#12311yescharacteristic
110C2×C4×C83#12311yescharacteristic
111C2×C4×C83#12311yescharacteristic
112C2×C4×C83#12411yescharacteristic
113C2×C4×C83#12611yescharacteristic
114C2×C4×C83#12611yescharacteristic
115C2×C4×C83C2×D811yescharacteristic
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83C2×Q1611yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×C4×C83#13711yescharacteristic
122C2×C4×C83#13711yescharacteristic
123C2×Dic83—22no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—81no—
130C2×Dic83—81no—
131C2×Dic83—81no—
132Dic166—22no—
133Dic166—22no—
134Dic166—41no—
135Dic166—41no—
136C8×C83—81no—
137C8×C83—81no—
138C83⋊C8—22no—
139C83⋊C8—22no—
140C83⋊C8—81no—
141C22×C83#39711yescharacteristic
142C22×C83#46011yescharacteristic
143C22×C83#46211yescharacteristic
144C22×C83#46611yescharacteristic
145C22×C83#47011yescharacteristic
146C22×C83#47211yescharacteristic
147C22×C83#47311yescharacteristic
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—161no—
151C4×C83#48011yescharacteristic
152C4×C83#48011yescharacteristic
153C4×C83#48311yescharacteristic
154C4×C83#48411yescharacteristic
155C4×C83#48511yescharacteristic
156C4×C83#48511yescharacteristic
157C4×C83#48711yescharacteristic
158C4×C83#48911yescharacteristic
159Dic83—42no—
160Dic83—81no—
161Dic83—161no—
162#10617—831nomaximal, Sylow
163C2×C83#166811yescharacteristic
164C2×C83#167411yescharacteristic
165C2×C83#169011yescharacteristic
166C2×C83#169611yescharacteristic
167C2×C83#207211yescharacteristic
168C2×C83#207511yescharacteristic
169C2×C83#207811yescharacteristic
170#1984—831no—
171#1845—831no—
172#1803—831no—
173#1803—831no—
174#1296—831no—
175#1296D8311yescharacteristic
176#1277—831no—
177C83#1061711yescharacteristic, complemented, Sylow
178C2×C4×Q8—831no—
179C2×#107—1661no—
180C2×#107—1661no—
181C2×C4⋊C8—831no—
182C2×C4⋊C8C2×D8311yescharacteristic
183C2×C4⋊C8C2×D8311yescharacteristic
184C2×#103—1661no—
185C2×#103—1661no—
186C2×C4×C8—831no—
187#384—831no—
188#384C2×D8311yescharacteristic
189#340—1661no—
190#340—1661no—
191#336—1661no—
192#336—1661no—
193C22×Q8—831no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—831no—
197C22×C8—831no—
198C22×C8—1661no—
199C4×Q8—1661no—
200C4×Q8—1661no—
201C4×Q8—1661no—
202C4×Q8—1661no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4—1661no—
211C2×C42—1661no—
212C2×C42C22×D8311yescharacteristic
213#107—3322no—
214#107—3322no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—1661no—
220C4⋊C8—1661no—
221#103—3322no—
222#103—3322no—
223C4×C8—1661no—
224C4×C8—1661no—
225C2×Q8—832no—
226C2×Q8—1661no—
227C2×Q8—1661no—
228C2×Q8—1661no—
229C2×Q8—1661no—
230C2×Q8—1661no—
231C22×C4—41no—
232C22×C4—3321no—
233C22×C4—1661no—
234C22×C4—1661no—
235C22×C4D4×D8311yescharacteristic
236C22×C4D4×D8311yescharacteristic
237C22×C4#1305059011yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—3321no—
245C2×C8—3321no—
246C2×C8—3321no—
247C2×C8—832no—
248C2×C8—832no—
249C2×C8—1661no—
250C2×C8—1661no—
251C2×C8—1661no—
252C2×C8—1661no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—3321no—
262C4⋊C4—3321no—
263C4⋊C4—3321no—
264C4⋊C4—6641no—
265C4⋊C4—1661no—
266C4⋊C4—1661no—
267C42—3321no—
268C42—3321no—
269C42#1305058911yescharacteristic
270C42#1305059011yescharacteristic
271C42#1305059011yescharacteristic
272C42#1305059111yescharacteristic
273C23#1458176511yescharacteristic
274Q8—3321no—
275Q8—3321no—
276Q8—1662no—
277Q8—1662no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4—6641no—
289C2×C4—6641no—
290C2×C4—6641no—
291C2×C4—1662no—
292C2×C4#1458177411yescharacteristic
293C2×C4#1458177711yescharacteristic
294C2×C4#1458177711yescharacteristic
295C2×C4#1458177811yescharacteristic
296C2×C4#1458178611yescharacteristic
297C2×C4#1458178711yescharacteristic
298C2×C4D8×D8311yescharacteristic
299C2×C4SD16×D8311yescharacteristic
300C2×C4Q16×D8311yescharacteristic
301C2×C4#1458181311yescharacteristic
302C2×C4#1458181611yescharacteristic
303C2×C4#1458182111yescharacteristic
304C2×C4#1458182111yescharacteristic
305C2×C4#1458182411yescharacteristic
306C8—81no—
307C8—81no—
308C8—6641no—
309C8—1662no—
310C8—1662no—
311C22#1912763011yescharacteristic
312C22#1912790011yescharacteristic
313C22#1912791011yescharacteristic
314C22#1912793611yescharacteristic
315C22#1912795811yescharacteristic
316C22#1912797011yescharacteristic
317C22#1912797511yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—13281no—
322C4—3322no—
323C4—6641no—
324C4#1912801311yescharacteristic
325C4#1912801611yescharacteristic
326C4#1912803311yescharacteristic
327C4#1912803811yescharacteristic
328C4#1912804011yescharacteristic
329C4#1912804511yescharacteristic
330C4#1912805011yescharacteristic
331C4#1912805911yescharacteristic
332C2#2490682211yescharacteristic
333C2#2490685611yescharacteristic
334C2#2490695611yescharacteristic
335C2#2490699011yescharacteristic
336C2#2490887511yescharacteristic
337C2#2490889011yescharacteristic
338C2#2490890711yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socle, prime radicalC23×C83#121
hypercenter#1296D83
hypocenterC83#10617
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
177. C83#10617semidirect

Maximal subgroups

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

subgroupindex
#249083982
#249076222
#249074692
#249074652
#249053472
#249052972
C83×#12962
#1061783