Finite Group Databasebeta

← #35302541

Subgroups — #35302541

Order 21248.

372 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908179C211yesmaximal, characteristic
2C4×#14581726C211yesmaximal, characteristic
3#24907328C211yesmaximal, characteristic
4#24905302C211yesmaximal, characteristic
5#24905302C211yesmaximal, characteristic
6C83⋊#1273C211yesmaximal, characteristic
7C83×#1277C211yesmaximal, characteristic
8C2×#14581726C411yescharacteristic
9C2×#14581726C411yescharacteristic
10C2×Dic83⋊C8—21no—
11C2×C4×C83⋊C8C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13C2×C8×Dic83—21no—
14C4×C4⋊Dic83C2211yescharacteristic
15C4×C4⋊Dic83C2211yescharacteristic
16#19127464C411yescharacteristic
17#19127464C411yescharacteristic
18#19127455—21no—
19#19127455—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4×C8×C83C2211yescharacteristic
23C22×C83⋊C8—21no—
24C22×C83⋊C8D411yescharacteristic
25C22×C83⋊C8D411yescharacteristic
26C2×C4⋊Dic83C2×C411yescharacteristic
27C2×C4⋊Dic83C2×C411yescharacteristic
28C2×C4⋊Dic83C2×C411yescharacteristic
29C2×C4⋊Dic83C2×C411yescharacteristic
30C2×C4×Dic83—21no—
31C2×C4×Dic83—21no—
32#14581726—22no—
33#14581726C814yescomplemented
34Dic83⋊C8—42no—
35C4×C83⋊C8—21no—
36C4×C83⋊C8—21no—
37C4×C83⋊C8—21no—
38C4×C83⋊C8—21no—
39C8×Dic83—42no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C22×C8×C83—21no—
43C22×C8×C83—21no—
44C22×C8×C83C2×C411yescharacteristic
45C22×C8×C83C2×C411yescharacteristic
46C2×C42×C83C2311yescharacteristic
47C4⋊C8×C83—21no—
48C4⋊C8×C83—21no—
49C4⋊C8×C83—21no—
50C4⋊C8×C83Q812yes—
51C4×C8×C83—21no—
52C4×C8×C83—21no—
53C22×Dic83—21no—
54C22×Dic83—21no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—22no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8Q1612yes—
66C4⋊Dic83—21no—
67C4⋊Dic83—21no—
68C4⋊Dic83—21no—
69C4⋊Dic83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83C2×C812yes—
72C4⋊Dic83C2×C812yes—
73C4⋊Dic83M1612yes—
74C4×Dic83—41no—
75C4×Dic83—41no—
76C4×Dic83—41no—
77C4×Dic83—41no—
78C22×C4×C83C22×C411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83—22no—
85C2×C8×C83—21no—
86C2×C8×C83—21no—
87C2×C8×C83—41no—
88C2×C8×C83—41no—
89C2×C8×C83—41no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C2×C8×C83C2×C812yes—
93C42×C83C2×Q811yescharacteristic
94C42×C83#4111yescharacteristic
95C42×C83#4111yescharacteristic
96C42×C83#4111yescharacteristic
97C23×C83C4×D411yescharacteristic
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83#11711yescharacteristic
101C2×C4×C83C4×Q811yescharacteristic
102C2×C4×C83C22⋊Q811yescharacteristic
103C2×C4×C83#12311yescharacteristic
104C2×C4×C83#12511yescharacteristic
105C2×C4×C83#12611yescharacteristic
106C2×C4×C83C22×C811yescharacteristic
107C2×C4×C83C2×M1611yescharacteristic
108C2×C4×C83#13111yescharacteristic
109C2×C4×C83#13111yescharacteristic
110C2×C4×C83C2×Q1611yescharacteristic
111C2×C4×C83#13511yescharacteristic
112C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
114C2×Dic83—22no—
115C2×Dic83—22no—
116C2×Dic83—22no—
117C2×Dic83—41no—
118C2×Dic83—41no—
119C2×Dic83—41no—
120C2×Dic83—41no—
121C2×Dic83—41no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C8×C83—22no—
127C8×C83—41no—
128C8×C83—42no—
129C8×C83—81no—
130C83⋊C8—22no—
131C83⋊C8—42no—
132C83⋊C8—41no—
133C22×C83#38711yescharacteristic
134C22×C83C8×D411yescharacteristic
135C22×C83#43511yescharacteristic
136C22×C83C4×Q1611yescharacteristic
137C22×C83#44211yescharacteristic
138C22×C83#44311yescharacteristic
139C22×C83#44411yescharacteristic
140C4×C83—21no—
141C4×C83—21no—
142C4×C83#43111yescharacteristic
143C4×C83#43311yescharacteristic
144C4×C83C8×Q811yescharacteristic
145C4×C83#44611yescharacteristic
146C4×C83#47711yescharacteristic
147C4×C83#47811yescharacteristic
148C4×C83#48211yescharacteristic
149C4×C83#48411yescharacteristic
150Dic83—42no—
151Dic83—42no—
152Dic83—42no—
153Dic83—81no—
154#9536—831nomaximal, Sylow
155C2×C83C8×Q1611yescharacteristic
156C2×C83#158011yescharacteristic
157C2×C83#158411yescharacteristic
158C2×C83#158611yescharacteristic
159C2×C83#191611yescharacteristic
160C2×C83#192111yescharacteristic
161C2×C83#192211yescharacteristic
162#1939—831no—
163C4×#107—831no—
164C8×C4⋊C4—831no—
165#1279—831no—
166#1279—831no—
167#1277D8311yescharacteristic
168#1273—831no—
169C83#953611yescharacteristic, complemented, Sylow
170C2×#107—831no—
171C2×#107—831no—
172C2×C4⋊C8—1661no—
173C2×C4⋊C8C2×D8311yescharacteristic
174C2×C4⋊C8C2×D8311yescharacteristic
175C2×C4×C8—831no—
176C2×C4×C8—831no—
177C2×C4×C8—1661no—
178C2×C4×C8C2×D8311yescharacteristic
179C4×C4⋊C4—831no—
180C4×C4⋊C4—831no—
181#340—831no—
182#340—831no—
183#336—1661no—
184#336—1661no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—831no—
188C22×C8—831no—
189C22×C8—1661no—
190C22×C8C4×D8311yescharacteristic
191C22×C8C4×D8311yescharacteristic
192C2×C4⋊C4—831no—
193C2×C4⋊C4—831no—
194C2×C4⋊C4—831no—
195C2×C4⋊C4—831no—
196C2×C42—1661no—
197C2×C42—1661no—
198C2×C42C22×D8311yescharacteristic
199#107—834no—
200#107—1662no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—3322no—
205C4⋊C8Dic16612yes—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—3322no—
209C4×C8—1661no—
210C4×C8—1661no—
211C4×C8—1661no—
212C4×C8—1661no—
213#95—1661no—
214#95—1661no—
215C22×C4—1661no—
216C22×C4—1661no—
217C22×C4—1661no—
218C22×C4—1661no—
219C22×C4C2×C4×D8311yescharacteristic
220C22×C4D4×D8311yescharacteristic
221C22×C4#1305059111yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—832no—
236C2×C8—1662no—
237C2×C8—1661no—
238C2×C8—1661no—
239C2×C8—1661no—
240C2×C8—1661no—
241C2×C8—1661no—
242C2×C8C8×D8312yes—
243C4⋊C4—832no—
244C4⋊C4—832no—
245C4⋊C4—832no—
246C4⋊C4—1661no—
247C4⋊C4—1661no—
248C4⋊C4—1661no—
249C4⋊C4—1661no—
250C4⋊C4—1661no—
251C42—3321no—
252C42—3321no—
253C42—3321no—
254C42—3321no—
255C42C2×Dic16611yescharacteristic
256C42#1305058911yescharacteristic
257C42#1305058911yescharacteristic
258C42#1305059011yescharacteristic
259C23#1458175411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—3321no—
263C2×C4—3321no—
264C2×C4—3321no—
265C2×C4—3321no—
266C2×C4—3321no—
267C2×C4—3321no—
268C2×C4—3321no—
269C2×C4—3321no—
270C2×C4—3321no—
271C2×C4—1662no—
272C2×C4—1662no—
273C2×C4—1662no—
274C2×C4#1458174811yescharacteristic
275C2×C4C4×Dic16611yescharacteristic
276C2×C4#1458176911yescharacteristic
277C2×C4#1458177411yescharacteristic
278C2×C4#1458178311yescharacteristic
279C2×C4#1458178711yescharacteristic
280C2×C4C2×C8×D8311yescharacteristic
281C2×C4M16×D8311yescharacteristic
282C2×C4#1458179811yescharacteristic
283C2×C4#1458180011yescharacteristic
284C2×C4Q16×D8311yescharacteristic
285C2×C4#1458181111yescharacteristic
286C2×C4#1458181911yescharacteristic
287C2×C4#1458181911yescharacteristic
288C8—22no—
289C8—42no—
290C8—41no—
291C8—81no—
292C8—3322no—
293C8—3321no—
294C8—1662no—
295C22#1912758411yescharacteristic
296C22#1912776611yescharacteristic
297C22#1912777111yescharacteristic
298C22#1912779511yescharacteristic
299C22#1912781211yescharacteristic
300C22#1912781711yescharacteristic
301C22#1912782211yescharacteristic
302C4—21no—
303C4—21no—
304C4—3322no—
305C4—3322no—
306C4—3322no—
307C4—6641no—
308C4#1912775111yescharacteristic
309C4#1912775911yescharacteristic
310C4C8×Dic16611yescharacteristic
311C4#1912782911yescharacteristic
312C4#1912799411yescharacteristic
313C4#1912799911yescharacteristic
314C4#1912802311yescharacteristic
315C4#1912803511yescharacteristic
316C2#2490626911yescharacteristic
317C2#2490628611yescharacteristic
318C2#2490631211yescharacteristic
319C2#2490632611yescharacteristic
320C2#2490801911yescharacteristic
321C2#2490805411yescharacteristic
322C2#2490806111yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC2×C4×C83C22×C8
FrattiniC2×C42C22×D83
FittingC83×#1277C2
socle, prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenter#1277D83
hypocenterC83#9536
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
33. #14581726C8semidirect
169. C83#9536semidirect

Maximal subgroups

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

subgroupindex
#249081792
C4×#145817262
#249073282
#249053022
C83⋊#12732
C83×#12772
#953683