Finite Group Databasebeta

← #35298079

Subgroups — #35298079

Order 21248.

342 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24907614C211yesmaximal, characteristic
2#24907579C211yesmaximal, characteristic
3#24907208C211yesmaximal, characteristic
4#24905298C211yesmaximal, characteristic
5#24905297C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C83×#1277C211yesmaximal, characteristic
8C2×C4⋊(C83⋊C8)C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×Dic83⋊C8—21no—
11C2×Dic83⋊C8—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13C42×Dic83C2211yescharacteristic
14#19127455—21no—
15#19127455—21no—
16#19127455C411yescharacteristic
17#19127455C411yescharacteristic
18#19127455C411yescharacteristic
19#19127455C411yescharacteristic
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22C2×C4×C8×C83C2211yescharacteristic
23C22×C83⋊C8—21no—
24C22×C83⋊C8—21no—
25C22×C83⋊C8C2×C411yescharacteristic
26C22×C83⋊C8C2×C411yescharacteristic
27C2×C4×Dic83C2×C411yescharacteristic
28C2×C4×Dic83C2×C411yescharacteristic
29C2×C4×Dic83D411yescharacteristic
30C2×C4×Dic83D411yescharacteristic
31C2×C4×Dic83Q811yescharacteristic
32C2×C4×Dic83Q811yescharacteristic
33C4⋊(C83⋊C8)—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37Dic83⋊C8—42no—
38Dic83⋊C8—42no—
39C4×C83⋊C8—21no—
40C4×C83⋊C8—21no—
41C22×C8×C83—21no—
42C22×C8×C83—21no—
43C22×C8×C83C2×C411yescharacteristic
44C22×C8×C83C2×C411yescharacteristic
45C2×C42×C83C2311yescharacteristic
46C4⋊C8×C83—21no—
47C4⋊C8×C83—21no—
48C4⋊C8×C83—21no—
49C4⋊C8×C83—21no—
50C4×C8×C83—21no—
51C4×C8×C83—21no—
52C22×Dic83C4⋊C411yescharacteristic
53C22×Dic83C4⋊C411yescharacteristic
54C22×Dic83C4⋊C411yescharacteristic
55C22×Dic83C4⋊C411yescharacteristic
56C2×C83⋊C8—21no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—21no—
61C2×C83⋊C8—21no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C4×Dic83—21no—
69C4×Dic83—21no—
70C4×Dic83—21no—
71C4×Dic83—21no—
72C4×Dic83—21no—
73C4×Dic83—21no—
74C4×Dic83—21no—
75C4×Dic83—21no—
76C4×Dic83—22no—
77C4×Dic83—22no—
78C22×C4×C83C22×C411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83C2×Q811yescharacteristic
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83—21no—
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×C83—41no—
93C42×C83#4111yescharacteristic
94C42×C83#4111yescharacteristic
95C42×C83#4111yescharacteristic
96C42×C83#4111yescharacteristic
97C23×C83C2×C4⋊C411yescharacteristic
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83#11711yescharacteristic
101C2×C4×C83#11711yescharacteristic
102C2×C4×C83#12411yescharacteristic
103C2×C4×C83#12411yescharacteristic
104C2×C4×C83#12511yescharacteristic
105C2×C4×C83#12511yescharacteristic
106C2×C4×C83#13111yescharacteristic
107C2×C4×C83#13111yescharacteristic
108C2×C4×C83#13111yescharacteristic
109C2×C4×C83#13111yescharacteristic
110C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C83#13711yescharacteristic
113C2×C4×C83#13711yescharacteristic
114C2×Dic83—21no—
115C2×Dic83—21no—
116C2×Dic83—21no—
117C2×Dic83—21no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83#10812yes—
125C2×Dic83#10812yes—
126C8×C83—41no—
127C8×C83—41no—
128C8×C83—81no—
129C8×C83—81no—
130C83⋊C8—41no—
131C83⋊C8—41no—
132C83⋊C8—81no—
133C83⋊C8—81no—
134C22×C83#38211yescharacteristic
135C22×C83#42411yescharacteristic
136C22×C83#42411yescharacteristic
137C22×C83#42811yescharacteristic
138C22×C83#42811yescharacteristic
139C22×C83C2×#10811yescharacteristic
140C22×C83C2×#10811yescharacteristic
141C4×C83—21no—
142C4×C83—21no—
143C4×C83#43311yescharacteristic
144C4×C83#43311yescharacteristic
145C4×C83#43311yescharacteristic
146C4×C83#43311yescharacteristic
147C4×C83#48911yescharacteristic
148C4×C83#48911yescharacteristic
149C4×C83#49011yescharacteristic
150C4×C83#49111yescharacteristic
151Dic83—22no—
152Dic83—22no—
153Dic83—41no—
154Dic83—41no—
155#8789—831nomaximal, Sylow
156C2×C83#157311yescharacteristic
157C2×C83#157311yescharacteristic
158C2×C83#157411yescharacteristic
159C2×C83#157411yescharacteristic
160C2×C83#183211yescharacteristic
161C2×C83#183611yescharacteristic
162C2×C83#183711yescharacteristic
163#1842—831no—
164#1831—831no—
165#1744—831no—
166#1277—831no—
167#1277—831no—
168#1277—831no—
169#1277D8311yescharacteristic
170C83#878911yescharacteristic, complemented, Sylow
171C2×C4⋊C8—831no—
172C2×C4⋊C8—831no—
173C2×C4⋊C8—1661no—
174C2×C4⋊C8—1661no—
175C2×C4⋊C8C2×D8311yescharacteristic
176C2×C4⋊C8C2×D8311yescharacteristic
177C2×C4×C8—831no—
178C2×C4×C8C2×D8311yescharacteristic
179C43—831no—
180#336—831no—
181#336—831no—
182#336—831no—
183#336—831no—
184#336—1661no—
185#336—1661no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—831no—
189C22×C8—831no—
190C22×C8—1661no—
191C22×C8—1661no—
192C22×C8C4×D8311yescharacteristic
193C22×C8C4×D8311yescharacteristic
194C2×C42—831no—
195C2×C42—831no—
196C2×C42—831no—
197C2×C42—831no—
198C2×C42—831no—
199C2×C42—831no—
200C2×C42C22×D8311yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—3322no—
206C4⋊C8—3322no—
207C4⋊C8—1661no—
208C4⋊C8—1661no—
209C4⋊C8—1661no—
210C4⋊C8—1661no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—1661no—
214C4×C8—1661no—
215C22×C4—831no—
216C22×C4—831no—
217C22×C4—831no—
218C22×C4—831no—
219C22×C4C2×C4×D8311yescharacteristic
220C22×C4D4×D8311yescharacteristic
221C22×C4Q8×D8311yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
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—41no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—3321no—
239C2×C8—3321no—
240C2×C8—1661no—
241C2×C8—1661no—
242C2×C8—1661no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C42—1662no—
247C42—1662no—
248C42—1661no—
249C42—1661no—
250C42—1661no—
251C42—1661no—
252C42—1661no—
253C42—1661no—
254C42—1661no—
255C42—1661no—
256C42#1305058911yescharacteristic
257C42#1305058911yescharacteristic
258C42#1305059011yescharacteristic
259C42#1305059011yescharacteristic
260C23C4⋊C4×D8311yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—832no—
264C2×C4—832no—
265C2×C4—1661no—
266C2×C4—1661no—
267C2×C4—1661no—
268C2×C4—1661no—
269C2×C4—1661no—
270C2×C4—1661no—
271C2×C4—1661no—
272C2×C4—1661no—
273C2×C4—1661no—
274C2×C4—1661no—
275C2×C4#1458174811yescharacteristic
276C2×C4#1458174911yescharacteristic
277C2×C4#1458177811yescharacteristic
278C2×C4#1458177811yescharacteristic
279C2×C4#1458178211yescharacteristic
280C2×C4#1458178211yescharacteristic
281C2×C4#1458179811yescharacteristic
282C2×C4#1458179811yescharacteristic
283C2×C4#1458180011yescharacteristic
284C2×C4#1458180011yescharacteristic
285C2×C4#1458181611yescharacteristic
286C2×C4#1458181911yescharacteristic
287C2×C4#1458182111yescharacteristic
288C2×C4#1458182411yescharacteristic
289C8—41no—
290C8—41no—
291C8—81no—
292C8—81no—
293C8—3321no—
294C8—3321no—
295C8—6641no—
296C8—6641no—
297C22#1912756511yescharacteristic
298C22#1912772611yescharacteristic
299C22#1912772611yescharacteristic
300C22#1912774011yescharacteristic
301C22#1912774211yescharacteristic
302C22#108×D8311yescharacteristic
303C22#108×D8311yescharacteristic
304C4—21no—
305C4—21no—
306C4—3321no—
307C4—3321no—
308C4—1662no—
309C4—1662no—
310C4#1912775911yescharacteristic
311C4#1912775911yescharacteristic
312C4#1912776011yescharacteristic
313C4#1912776311yescharacteristic
314C4#1912805911yescharacteristic
315C4#1912806211yescharacteristic
316C4#1912806411yescharacteristic
317C4#1912806811yescharacteristic
318C2#2490624511yescharacteristic
319C2#2490624711yescharacteristic
320C2#2490625011yescharacteristic
321C2#2490625311yescharacteristic
322C2#2490758111yescharacteristic
323C2#2490759511yescharacteristic
324C2#2490759911yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1277C2
socle, prime radicalC23×C83C2×C4⋊C4
cosocleC2×C42×C83C23
hypercenter#1277D83
hypocenterC83#8789
LCSG ▷ C22×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
170. C83#8789semidirect

Maximal subgroups

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

subgroupindex
#249076142
#249075792
#249072082
#249052982
#249052972
C83×#12772
#878983