Finite Group Databasebeta

← #35302565

Subgroups — #35302565

Order 21248.

356 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#24908182C211yesmaximal, characteristic
2#24907332C211yesmaximal, characteristic
3#24905304C211yesmaximal, characteristic
4#24905304C211yesmaximal, characteristic
5#24905298C211yesmaximal, characteristic
6C83⋊#1273C211yesmaximal, characteristic
7C4×#106×C83C211yesmaximal, characteristic
8C2×C4⋊(C83⋊C8)—21no—
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×#14581703—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13C2×C4×C83⋊C8C2211yescharacteristic
14#19127456—21no—
15#19127456—21no—
16C2×#106×C83C411yescharacteristic
17C2×#106×C83C411yescharacteristic
18C2×C4×C8×C83C2211yescharacteristic
19C4×C4⋊C4×C83C2211yescharacteristic
20C4×C4⋊C4×C83C2211yescharacteristic
21#340×C83C411yescharacteristic
22#340×C83C411yescharacteristic
23C22×C83⋊C8—21no—
24C22×C83⋊C8—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8D411yescharacteristic
27C22×C83⋊C8D411yescharacteristic
28C4⋊(C83⋊C8)—21no—
29C4⋊(C83⋊C8)—21no—
30C4⋊(C83⋊C8)—21no—
31C4⋊(C83⋊C8)—42no—
32C4⋊(C83⋊C8)Q812yes—
33#14581703—42no—
34C4×C83⋊C8—21no—
35C4×C83⋊C8—21no—
36C4×C83⋊C8—21no—
37C4×C83⋊C8—21no—
38C22×C8×C83C2×C411yescharacteristic
39C22×C8×C83C2×C411yescharacteristic
40C2×C4⋊C4×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83C2×C411yescharacteristic
43C2×C4⋊C4×C83C2×C411yescharacteristic
44C2×C42×C83—21no—
45C2×C42×C83—21no—
46C2×C42×C83C2311yescharacteristic
47#106×C83—22no—
48#106×C83—22no—
49C4×C8×C83—21no—
50C4×C8×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53C2×C83⋊C8—21no—
54C2×C83⋊C8—21no—
55C2×C83⋊C8—22no—
56C2×C83⋊C8—22no—
57C2×C83⋊C8—21no—
58C2×C83⋊C8—21no—
59C2×C83⋊C8—21no—
60C2×C83⋊C8—41no—
61C2×C83⋊C8—41no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8SD1612yes—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83C22×C411yescharacteristic
73C22×C4×C83C2×D411yescharacteristic
74C22×C4×C83#4111yescharacteristic
75C2×C8×C83—21no—
76C2×C8×C83—21no—
77C2×C8×C83—21no—
78C2×C8×C83—21no—
79C2×C8×C83—21no—
80C2×C8×C83M1612yes—
81C4⋊C4×C83—21no—
82C4⋊C4×C83—21no—
83C4⋊C4×C83—21no—
84C4⋊C4×C83—21no—
85C4⋊C4×C83—21no—
86C4⋊C4×C83—21no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83M1612yes—
89C42×C83—41no—
90C42×C83—41no—
91C42×C83—41no—
92C42×C83—41no—
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—22no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83#11711yescharacteristic
113C2×C4×C83C4×Q811yescharacteristic
114C2×C4×C83C22⋊Q811yescharacteristic
115C2×C4×C83#12311yescharacteristic
116C2×C4×C83#12511yescharacteristic
117C2×C4×C83#12611yescharacteristic
118C2×C4×C83C2×M1611yescharacteristic
119C2×C4×C83C2×M1611yescharacteristic
120C2×C4×C83#13111yescharacteristic
121C2×C4×C83#13111yescharacteristic
122C2×C4×C83C2×SD1611yescharacteristic
123C2×C4×C83#13511yescharacteristic
124C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C83#13711yescharacteristic
126C8×C83—22no—
127C8×C83—41no—
128C83⋊C8—22no—
129C83⋊C8—42no—
130C83⋊C8—42no—
131C83⋊C8—41no—
132C83⋊C8—81no—
133C22×C83#38711yescharacteristic
134C22×C83#43511yescharacteristic
135C22×C83#43611yescharacteristic
136C22×C83C4×SD1611yescharacteristic
137C22×C83#44011yescharacteristic
138C22×C83#44311yescharacteristic
139C22×C83#44411yescharacteristic
140C4×C83—21no—
141C4×C83—21no—
142C4×C83—42no—
143C4×C83—81no—
144C4×C83—81no—
145C4×C83—81no—
146C4×C83#43211yescharacteristic
147C4×C83#43311yescharacteristic
148C4×C83#44611yescharacteristic
149C4×C83#44611yescharacteristic
150C4×C83#47611yescharacteristic
151C4×C83#47911yescharacteristic
152C4×C83#48211yescharacteristic
153C4×C83#48311yescharacteristic
154#9539—831nomaximal, Sylow
155C2×C83#158311yescharacteristic
156C2×C83#158511yescharacteristic
157C2×C83#159011yescharacteristic
158C2×C83#159211yescharacteristic
159C2×C83#191711yescharacteristic
160C2×C83#192011yescharacteristic
161C2×C83#192211yescharacteristic
162#1939—831no—
163C4×#106D8311yescharacteristic
164#1770—831no—
165#1279—831no—
166#1279—831no—
167#1277—831no—
168#1273—831no—
169C83#953911yescharacteristic, complemented, Sylow
170C2×#106Dic8311yescharacteristic
171C2×#106Dic8311yescharacteristic
172C2×C4⋊C8—831no—
173C2×C4⋊C8—831no—
174C2×C4⋊C8—1661no—
175C2×#97—1661no—
176C2×C4×C8—831no—
177C2×C4×C8—831no—
178C2×C4×C8C2×D8311yescharacteristic
179C4×C4⋊C4C2×D8311yescharacteristic
180C4×C4⋊C4C2×D8311yescharacteristic
181#340Dic8311yescharacteristic
182#340Dic8311yescharacteristic
183#336—1661no—
184#336—1661no—
185C22×C8—831no—
186C22×C8—831no—
187C22×C8—1661no—
188C22×C8—1661no—
189C22×C8—1661no—
190C22×C8C2×Dic8311yescharacteristic
191C22×C8C2×Dic8311yescharacteristic
192C2×C4⋊C4C2×Dic8311yescharacteristic
193C2×C4⋊C4C2×Dic8311yescharacteristic
194C2×C4⋊C4C2×Dic8311yescharacteristic
195C2×C4⋊C4C2×Dic8311yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C22×D8311yescharacteristic
199#106—22no—
200#106—22no—
201C4⋊C8—3322no—
202C4⋊C8—832no—
203C4⋊C8—1661no—
204C4⋊C8—1661no—
205C4⋊C8—1661no—
206#97—3322no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—1661no—
210C4×C8—1661no—
211C4×C8—1661no—
212C4×C8—1661no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22×Dic8311yescharacteristic
220C22×C4D4×D8311yescharacteristic
221C22×C4#1305058911yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—3321no—
228C2×C8—3321no—
229C2×C8—3321no—
230C2×C8—3321no—
231C2×C8—3321no—
232C2×C8—3321no—
233C2×C8—3321no—
234C2×C8—832no—
235C2×C8—1662no—
236C2×C8—1662no—
237C2×C8—1661no—
238C2×C8—1661no—
239C2×C8—1661no—
240C2×C8—1661no—
241C2×C8—1661no—
242C2×C8#1305057412yes—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4#1305057412yes—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42Q8×D8311yescharacteristic
256C42#1305059011yescharacteristic
257C42#1305059011yescharacteristic
258C42#1305059111yescharacteristic
259C23D4×Dic8311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4#1458175111yescharacteristic
275C2×C4Q8×Dic8311yescharacteristic
276C2×C4#1458177011yescharacteristic
277C2×C4#1458177711yescharacteristic
278C2×C4#1458178211yescharacteristic
279C2×C4#1458178711yescharacteristic
280C2×C4C2×#1305057411yescharacteristic
281C2×C4C2×#1305057411yescharacteristic
282C2×C4#1458179911yescharacteristic
283C2×C4#1458179911yescharacteristic
284C2×C4SD16×D8311yescharacteristic
285C2×C4#1458181311yescharacteristic
286C2×C4#1458181911yescharacteristic
287C2×C4#1458182111yescharacteristic
288C8—22no—
289C8—41no—
290C8—3322no—
291C8—3322no—
292C8—3321no—
293C8—6641no—
294C8—1662no—
295C22#1912758711yescharacteristic
296C22#1912777311yescharacteristic
297C22#1912777911yescharacteristic
298C22SD16×Dic8311yescharacteristic
299C22#1912780211yescharacteristic
300C22#1912781811yescharacteristic
301C22#1912782311yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4#1912775811yescharacteristic
309C4#1912776211yescharacteristic
310C4#1912783211yescharacteristic
311C4#1912783211yescharacteristic
312C4#1912799011yescharacteristic
313C4#1912801111yescharacteristic
314C4#1912802711yescharacteristic
315C4#1912803311yescharacteristic
316C2#2490630711yescharacteristic
317C2#2490632111yescharacteristic
318C2#2490635411yescharacteristic
319C2#2490636611yescharacteristic
320C2#2490802911yescharacteristic
321C2#2490805011yescharacteristic
322C2#2490806411yescharacteristic
subgroupG/H
centerC22×C4D4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC4×#106×C83C2
socle, prime radicalC23×C83C4×D4
cosocleC2×C42×C83C23
hypercenterC4×#106D83
hypocenterC83#9539
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

Complements

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

NH ≅ G/Ntype
169. C83#9539semidirect

Maximal subgroups

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

subgroupindex
#249081822
#249073322
#249053042
#249052982
C83⋊#12732
C4×#106×C832
#953983