Finite Group Databasebeta

← #35315298

Subgroups — #35315298

Order 21248.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913161C211yesmaximal, characteristic
2#24907540C211yesmaximal, characteristic
3#24905488C212yesmaximal
4#24905464C212yesmaximal
5C83×#1458C211yesmaximal, characteristic
6C2×#14581784C411yescharacteristic, complemented
7#19127640C411yescharacteristic, complemented
8#19127637C2211yescharacteristic
9#19127631C411yescharacteristic, complemented
10#19127626C2211yescharacteristic
11#19127596—21no—
12#19127595—21no—
13#19127585—21no—
14#19127574—21no—
15#19127564—21no—
16#19127547C411yescharacteristic, complemented
17#19127468—21no—
18#19127468C2212yes—
19C2×#117×C83C2211yescharacteristic
20#431×C83—21no—
21#324×C83—21no—
22#323×C83C2212yes—
23#14581784—41no—
24#14581784—41no—
25C2×C4⋊Dic83C2×C411yescharacteristic
26C2×C4⋊Dic83C2×C411yescharacteristic
27C2×Dic83⋊C4—21no—
28C2×Dic83⋊C4—21no—
29C2×Dic83⋊C4—21no—
30C2×Dic83⋊C4—21no—
31C2×C22⋊Dic83—21no—
32C2×C22⋊Dic83—21no—
33C2×C22⋊Dic83—22no—
34C2×C4×Dic83—21no—
35C83⋊#95—21no—
36C83⋊#95—21no—
37C83⋊#95—21no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—41no—
41C83⋊#95—41no—
42C83⋊#95C2×C411yescharacteristic
43C83⋊#95C2×C411yescharacteristic
44C23×C4×C83D411yescharacteristic
45#117×C83—41no—
46#117×C83—41no—
47C2×C4⋊C4×C83C2×C411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C22⋊C4×C83D411yescharacteristic
50C2×C22⋊C4×C83C2311yescharacteristic
51C2×C42×C83C2×C411yescharacteristic
52C2×C42×C83D411yescharacteristic
53C4⋊C8×C83—41no—
54C22⋊C8×C83—22no—
55C4×C8×C83—41no—
56C22×Dic83—21no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—42no—
61C4⋊Dic83—41no—
62C4⋊Dic83—41no—
63Dic83⋊C4—42no—
64Dic83⋊C4—42no—
65Dic83⋊C4—42no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68C22⋊Dic83—42no—
69C22⋊Dic83—42no—
70C22⋊Dic83—42no—
71C22⋊Dic83—42no—
72C4×Dic83—42no—
73C24×C83C2×D411yescharacteristic
74C22×C4×C83—22no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83—41no—
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22⋊C411yescharacteristic
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C22×C411yescharacteristic
83C22×C4×C83C2×D411yescharacteristic
84C2×C8×C83—42no—
85C4⋊C4×C83—41no—
86C4⋊C4×C83—41no—
87C22⋊C4×C83—41no—
88C22⋊C4×C83—41no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—41no—
96C23×C83—41no—
97C23×C83C2×C22⋊C411yescharacteristic
98C23×C83#13512yes—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83#9911yescharacteristic
115C2×C4×C83#9911yescharacteristic
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—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—82no—
129C2×Dic83—82no—
130C2×Dic83—82no—
131C8×C83—82no—
132C22×C83—21no—
133C22×C83—21no—
134C22×C83—22no—
135C22×C83—42no—
136C22×C83—41no—
137C22×C83—41no—
138C22×C83—81no—
139C22×C83C2×#9911yescharacteristic
140C22×C83#41611yescharacteristic
141C22×C83#42111yescharacteristic
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—41no—
145C4×C83—41no—
146C4×C83—41no—
147C4×C83—41no—
148C4×C83—41no—
149Dic83—42no—
150Dic83—81no—
151Dic83—81no—
152Dic83—81no—
153Dic83—162no—
154#11846—831nomaximal, Sylow
155C2×C83—21no—
156C2×C83—21no—
157C2×C83—42no—
158C2×C83#151611yescharacteristic
159C2×C83#212311yescharacteristic
160C2×C83#212611yescharacteristic
161#2611—831no—
162#1820—831no—
163#1458D8311yescharacteristic
164#1352—832no—
165#1344—832no—
166C83#1184611yescharacteristic, complemented, Sylow
167C2×#125—831no—
168C2×#117C2×D8311yescharacteristic
169#431—21no—
170#400—831no—
171#399—831no—
172#398—831no—
173#397—831no—
174#389—1661no—
175#388—1661no—
176#387—1661no—
177#385—1661no—
178#381—1661no—
179#376—831no—
180#342—832no—
181#342—1661no—
182#324—21no—
183#323C2×D8312yes—
184C23×C4D33211yescharacteristic
185#125—3321no—
186#125—3321no—
187#117—41no—
188#117—41no—
189C2×C4⋊C4—831no—
190C2×C4⋊C4—831no—
191C2×C4⋊C4—1661no—
192C2×C4⋊C4—1661no—
193C2×C4⋊C4—1661no—
194C2×C4⋊C4—1661no—
195C2×C4⋊C4C4×D8311yescharacteristic
196C2×C4⋊C4C22⋊D8311yescharacteristic
197C2×C22⋊C4—1662no—
198C2×C22⋊C4—1661no—
199C2×C22⋊C4—1661no—
200C2×C22⋊C4D33211yescharacteristic
201C2×C22⋊C4C22×D8311yescharacteristic
202C2×C42—1661no—
203C2×C42C4×D8311yescharacteristic
204C2×C42C22⋊D8311yescharacteristic
205C4⋊C8—41no—
206C22⋊C8—22no—
207C4×C8—41no—
208#95—3321no—
209#95—3321no—
210#95—831no—
211#95—831no—
212#95—1661no—
213#95—1661no—
214#95—1661no—
215#95—1661no—
216#95—1661no—
217C24C2×D33211yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—3322no—
223C22×C4—1661no—
224C22×C4—1661no—
225C22×C4—1661no—
226C22×C4—1661no—
227C22×C4(C2×D83)⋊C411yescharacteristic
228C22×C4(C2×D83)⋊C411yescharacteristic
229C22×C4(C2×D83)⋊C411yescharacteristic
230C22×C4(C2×D83)⋊C411yescharacteristic
231C22×C4C2×C4×D8311yescharacteristic
232C22×C4C2×C22⋊D8311yescharacteristic
233C2×C8—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—3321no—
237C4⋊C4—3321no—
238C4⋊C4—3322no—
239C4⋊C4—3322no—
240C4⋊C4—3322no—
241C4⋊C4—3321no—
242C4⋊C4—3321no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—3322no—
246C22⋊C4—3322no—
247C22⋊C4—3322no—
248C22⋊C4—3322no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—3322no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×(C2×D83)⋊C411yescharacteristic
259C23#1458181412yes—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—3321no—
276C2×C4—3321no—
277C2×C4—3321no—
278C2×C4—3321no—
279C2×C4—3321no—
280C2×C4—3321no—
281C2×C4—3321no—
282C2×C4—3321no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—6642no—
287C2×C4—6642no—
288C2×C4—6642no—
289C2×C4—1662no—
290C2×C4#1458170611yescharacteristic
291C2×C4#1458170611yescharacteristic
292C8—82no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#1458170611yescharacteristic
301C22#1912769811yescharacteristic
302C22#1912771711yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—13282no—
311C4—3322no—
312C4—6641no—
313C4—6641no—
314C4—6641no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#2490602011yescharacteristic
319C2#2490911811yescharacteristic
320C2#2490912611yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1458C2
socleC22×C83C2×#99
prime radicalC24×C83C2×D4
cosocleC2×C22⋊C4×C83C23
hypercenter#1458D83
hypocenterC83#11846
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
6. C2×#14581784C4semidirect
7. #19127640C4semidirect
9. #19127631C4semidirect
16. #19127547C4semidirect
166. C83#11846semidirect

Maximal subgroups

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

subgroupindex
#249131612
#249075402
#249054882
#249054642
C83×#14582
#1184683