Finite Group Databasebeta

← #35313953

Subgroups — #35313953

Order 21248.

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

normal subgroups only

This group has 380 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#24911746C211yesmaximal, characteristic
2#24905797C211yesmaximal, characteristic
3#24905412C212yesmaximal
4#24905392C212yesmaximal
5C83×#1458C211yesmaximal, characteristic
6C22×Dic83⋊C4C411yescharacteristic
7#19127758—21no—
8#19127639—21no—
9#19127632—21no—
10#19127585—21no—
11#19127585—21no—
12#19127573C411yescharacteristic
13#19127573C2211yescharacteristic
14#19127564C411yescharacteristic
15#19127562C411yescharacteristic
16#19127562C2211yescharacteristic
17#19127427—21no—
18#19127425C2212yes—
19C2×#117×C83C2211yescharacteristic
20#431×C83—21no—
21#324×C83—21no—
22#323×C83C2212yes—
23C23×Dic83C2×C411yescharacteristic
24C23×Dic83C2×C411yescharacteristic
25C2×Dic83⋊C4—21no—
26C2×Dic83⋊C4—21no—
27C2×Dic83⋊C4—21no—
28C2×Dic83⋊C4—21no—
29C2×Dic83⋊C4—41no—
30C2×Dic83⋊C4—41no—
31C2×C22⋊Dic83C2×C411yescharacteristic
32C2×C22⋊Dic83C2×C411yescharacteristic
33C4⋊(C83⋊C8)—41no—
34C22⋊(C83⋊C8)—22no—
35#14581703—41no—
36C83⋊#95—21no—
37C83⋊#95—21no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C23×C4×C83C2×C411yescharacteristic
45#117×C83—41no—
46#117×C83—41no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C22⋊C4×C83C2×C411yescharacteristic
50C2×C22⋊C4×C83C2311yescharacteristic
51C2×C42×C83D411yescharacteristic
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—22no—
61C22×Dic83—42no—
62C22×Dic83—41no—
63C22×Dic83—41no—
64C22×Dic83—41no—
65C2×C83⋊C8—42no—
66Dic83⋊C4—42no—
67Dic83⋊C4—42no—
68Dic83⋊C4—42no—
69Dic83⋊C4—41no—
70Dic83⋊C4—41no—
71C22⋊Dic83—22no—
72C22⋊Dic83—41no—
73C24×C83C22×C411yescharacteristic
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×C83C2×D411yescharacteristic
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#13112yes—
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—42no—
119C2×Dic83—41no—
120C2×Dic83—42no—
121C2×Dic83—41no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130C2×Dic83—82no—
131C8×C83—82no—
132C83⋊C8—82no—
133C22×C83—21no—
134C22×C83—21no—
135C22×C83—22no—
136C22×C83—42no—
137C22×C83—42no—
138C22×C83—41no—
139C22×C83—41no—
140C22×C83#40811yescharacteristic
141C22×C83C2×#9911yescharacteristic
142C22×C83#41311yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—41no—
146C4×C83—41no—
147C4×C83—41no—
148C4×C83—41no—
149C4×C83—41no—
150Dic83—42no—
151Dic83—81no—
152Dic83—81no—
153Dic83—81no—
154#11548—831nomaximal, Sylow
155C2×C83—21no—
156C2×C83—21no—
157C2×C83—42no—
158C2×C83#146811yescharacteristic
159C2×C83#212011yescharacteristic
160C2×C83#212311yescharacteristic
161#2484—831no—
162#1464—831no—
163#1458D8311yescharacteristic
164#1326—832no—
165#1317—832no—
166C83#1154811yescharacteristic, complemented, Sylow
167C2×#117C2×D8311yescharacteristic
168C22×C4⋊C4—831no—
169#432—1661no—
170#431—21no—
171#400—1661no—
172#398—1661no—
173#387—1661no—
174#387—1661no—
175#385—831no—
176#385—831no—
177#381—831no—
178#381—831no—
179#381—831no—
180#324—21no—
181#324—1661no—
182#323—832no—
183#323C2×D8312yes—
184C23×C4—831no—
185C23×C4—831no—
186C23×C4C4×D8311yescharacteristic
187#117—41no—
188#117—41no—
189C2×C4⋊C4—3321no—
190C2×C4⋊C4—3321no—
191C2×C4⋊C4—1661no—
192C2×C4⋊C4—1661no—
193C2×C4⋊C4—1661no—
194C2×C4⋊C4—1661no—
195C2×C4⋊C4D33211yescharacteristic
196C2×C4⋊C4C22⋊D8311yescharacteristic
197C2×C22⋊C4—831no—
198C2×C22⋊C4—831no—
199C2×C22⋊C4C4×D8311yescharacteristic
200C2×C22⋊C4C22×D8311yescharacteristic
201C2×C42D33211yescharacteristic
202C2×C42C22⋊D8311yescharacteristic
203C4⋊C8—41no—
204C4⋊C8—3321no—
205C22⋊C8—22no—
206C22⋊C8—1662no—
207#97—3321no—
208C4×C8—41no—
209#95—1661no—
210#95—1661no—
211#95—1661no—
212#95—1661no—
213#95—1661no—
214#95—1661no—
215#95—1661no—
216#95—1661no—
217C24C2×C4×D8311yescharacteristic
218C22×C4—22no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—3321no—
223C22×C4—3322no—
224C22×C4—3321no—
225C22×C4—3321no—
226C22×C4—1661no—
227C22×C4—1661no—
228C22×C4—1661no—
229C22×C4—1661no—
230C22×C4—1662no—
231C22×C4(C2×D83)⋊C411yescharacteristic
232C22×C4(C2×D83)⋊C411yescharacteristic
233C22×C4(C2×D83)⋊C411yescharacteristic
234C22×C4(C2×D83)⋊C411yescharacteristic
235C22×C4C2×C22⋊D8311yescharacteristic
236C22×C4C2×D33211yescharacteristic
237C2×C8—42no—
238C2×C8—3322no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—3322no—
242C4⋊C4—3322no—
243C4⋊C4—3322no—
244C4⋊C4—3321no—
245C4⋊C4—3321no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—3321no—
249C22⋊C4—1662no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23C2×(C2×D83)⋊C411yescharacteristic
259C23#1458179812yes—
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—3322no—
277C2×C4—3321no—
278C2×C4—3322no—
279C2×C4—3321no—
280C2×C4—3321no—
281C2×C4—3321no—
282C2×C4—3321no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—3321no—
288C2×C4—6642no—
289C2×C4—1662no—
290C2×C4#1458170611yescharacteristic
291C2×C4#1458170611yescharacteristic
292C8—82no—
293C8—6642no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22#1912766711yescharacteristic
302C22C2×#1458170611yescharacteristic
303C22#1912768311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—3322no—
312C4—6641no—
313C4—6641no—
314C4—6641no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#2490580911yescharacteristic
319C2#2490910511yescharacteristic
320C2#2490911611yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutator, prime radicalC24×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1458C2
socleC22×C83C2×#99
cosocleC2×C22⋊C4×C83C23
hypercenter#1458D83
hypocenterC83#11548
LCSG ▷ C24×C83 ▷ C22×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
166. C83#11548semidirect

Maximal subgroups

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

subgroupindex
#249117462
#249057972
#249054122
#249053922
C83×#14582
#1154883