Finite Group Databasebeta

← #35293719

Subgroups — #35293719

Order 21248.

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

normal subgroups only

This group has 322 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#24915454C211yesmaximal, characteristic
2#24909027C211yesmaximal, characteristic
3#24909027C211yesmaximal, characteristic
4#24909026C211yesmaximal, characteristic
5#24905287C211yesmaximal, characteristic
6#24905285C211yesmaximal, characteristic
7C83×#1271C211yesmaximal, characteristic
8#19127641—21no—
9#19127640—21no—
10#19127639—21no—
11#19127599C2211yescharacteristic
12#19127599C2211yescharacteristic
13#19127588—21no—
14#19127587—21no—
15#19127582—21no—
16#19127571C2211yescharacteristic
17#19127464—21no—
18#19127464—21no—
19#19127464—21no—
20#19127464—21no—
21#19127463—21no—
22#19127463—21no—
23#19127456C2211yescharacteristic
24#389×C83C2211yescharacteristic
25#336×C83C2211yescharacteristic
26#336×C83C2211yescharacteristic
27C22×C83⋊C8—21no—
28C2×C4⋊Dic83—21no—
29C2×C4⋊Dic83—21no—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83D411yescharacteristic
32C2×C4⋊Dic83D411yescharacteristic
33C2×C4⋊Dic83D411yescharacteristic
34C2×C4⋊Dic83D411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×Dic83⋊C4—21no—
37C2×C4×Dic83—21no—
38C83⋊#95—21no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C22×C8×C83—21no—
48C22×C8×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C4⋊C4×C83D411yescharacteristic
52C2×C42×C83C2311yescharacteristic
53#95×C83—21no—
54C22×Dic83—21no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C22×Dic83—21no—
58C22×Dic83—41no—
59C2×C83⋊C8—41no—
60C2×C83⋊C8—41no—
61C2×C83⋊C8—41no—
62C4⋊Dic83—21no—
63C4⋊Dic83—21no—
64C4⋊Dic83—21no—
65C4⋊Dic83—21no—
66C4⋊Dic83—41no—
67C4⋊Dic83—41no—
68C4⋊Dic83—42no—
69C4⋊Dic83—42no—
70C4⋊Dic83—42no—
71Dic83⋊C4—41no—
72Dic83⋊C4—41no—
73Dic83⋊C4—41no—
74Dic83⋊C4—41no—
75C4×Dic83—81no—
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C2×C8×C83—41no—
82C2×C8×C83—41no—
83C2×C8×C83—41no—
84C2×C8×C83—41no—
85C2×C8×C83—41no—
86C2×C8×C83—41no—
87C4⋊C4×C83—21no—
88C4⋊C4×C83—21no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C42×C83—41no—
93C23×C83#12011yescharacteristic
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—41no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83#13511yescharacteristic
107C2×C4×C83#13511yescharacteristic
108C2×C4×C83#13511yescharacteristic
109C2×C4×C83#13711yescharacteristic
110C2×C4×C83#13711yescharacteristic
111C2×C4×C83#13711yescharacteristic
112C2×Dic83—41no—
113C2×Dic83—41no—
114C2×Dic83—41no—
115C2×Dic83—41no—
116C2×Dic83—41no—
117C2×Dic83—41no—
118C2×Dic83—41no—
119C2×Dic83—41no—
120C2×Dic83—41no—
121C2×Dic83—41no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—81no—
125C2×Dic83—81no—
126C2×Dic83—81no—
127C8×C83—81no—
128C8×C83—81no—
129C83⋊C8—81no—
130C22×C83#45211yescharacteristic
131C22×C83#45211yescharacteristic
132C22×C83#45211yescharacteristic
133C22×C83#45411yescharacteristic
134C22×C83#45411yescharacteristic
135C22×C83#45411yescharacteristic
136C22×C83#45811yescharacteristic
137C4×C83—21no—
138C4×C83—21no—
139C4×C83—21no—
140C4×C83—21no—
141C4×C83—21no—
142C4×C83—21no—
143C4×C83—81no—
144C4×C83—81no—
145Dic83—81no—
146Dic83—81no—
147Dic83—81no—
148Dic83—81no—
149Dic83—161no—
150#7832—831nomaximal, Sylow
151C2×C83#161511yescharacteristic
152C2×C83#161511yescharacteristic
153C2×C83#161511yescharacteristic
154C2×C83#163811yescharacteristic
155C2×C83#163811yescharacteristic
156C2×C83#163811yescharacteristic
157C2×C83#165811yescharacteristic
158#2810—831no—
159#2100—831no—
160#2100—831no—
161#2100—831no—
162#1271—831no—
163#1271—831no—
164#1271D8311yescharacteristic
165C83#783211yescharacteristic, complemented, Sylow
166#400—1661no—
167#400—1661no—
168#400—1661no—
169#389—831no—
170#389—831no—
171#389C2×D8311yescharacteristic
172#387—1661no—
173#387—1661no—
174#387—1661no—
175#384—831no—
176#340—1661no—
177#340—1661no—
178#340—1661no—
179#340—1661no—
180#340—1661no—
181#340—1661no—
182#336—831no—
183#336C2×D8311yescharacteristic
184#336C2×D8311yescharacteristic
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—1661no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—831no—
190C2×C4⋊C4—831no—
191C2×C4⋊C4—831no—
192C2×C4⋊C4—831no—
193C2×C4⋊C4—1661no—
194C2×C4⋊C4—1661no—
195C2×C4⋊C4—1661no—
196C2×C4⋊C4—1661no—
197C2×C4⋊C4—1661no—
198C2×C4⋊C4D33211yescharacteristic
199C2×C4⋊C4D33211yescharacteristic
200C2×C42—1661no—
201C2×C42C22×D8311yescharacteristic
202#95—21no—
203#95—1661no—
204#95—1661no—
205#95—1661no—
206#95—1661no—
207#95—1661no—
208#95—1661no—
209#95—1661no—
210#95—1661no—
211#95—1661no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—3321no—
215C22×C4—1661no—
216C22×C4—1661no—
217C22×C4—1661no—
218C22×C4—1661no—
219C22×C4D4×D8311yescharacteristic
220C22×C4D4×D8311yescharacteristic
221C22×C4C2×D33211yescharacteristic
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—3321no—
229C2×C8—3321no—
230C2×C8—3321no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
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—
243C4⋊C4—3321no—
244C4⋊C4—3321no—
245C4⋊C4—1661no—
246C4⋊C4—1661no—
247C4⋊C4—1661no—
248C4⋊C4—1661no—
249C42—41no—
250C42—6641no—
251C23#1458176211yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—3321no—
265C2×C4—3321no—
266C2×C4—3321no—
267C2×C4—3321no—
268C2×C4—3321no—
269C2×C4—3321no—
270C2×C4—3321no—
271C2×C4—3321no—
272C2×C4—3321no—
273C2×C4—3321no—
274C2×C4—3321no—
275C2×C4—3321no—
276C2×C4—6641no—
277C2×C4—6641no—
278C2×C4—6641no—
279C2×C4#1458181111yescharacteristic
280C2×C4#1458181311yescharacteristic
281C2×C4#1458181411yescharacteristic
282C2×C4#1458182111yescharacteristic
283C2×C4#1458182411yescharacteristic
284C2×C4#1458182511yescharacteristic
285C8—81no—
286C8—81no—
287C8—6641no—
288C22#1912786411yescharacteristic
289C22#1912786511yescharacteristic
290C22#1912786611yescharacteristic
291C22#1912787511yescharacteristic
292C22#1912787511yescharacteristic
293C22#1912787611yescharacteristic
294C22#1912789211yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—13281no—
304C4—6641no—
305C4—6641no—
306C4—6641no—
307C4—6641no—
308C2#2490649511yescharacteristic
309C2#2490649611yescharacteristic
310C2#2490649711yescharacteristic
311C2#2490663611yescharacteristic
312C2#2490663711yescharacteristic
313C2#2490663811yescharacteristic
314C2#2490676611yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1271C2
socle, prime radicalC23×C83#120
hypercenter#1271D83
hypocenterC83#7832
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
165. C83#7832semidirect

Maximal subgroups

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

subgroupindex
#249154542
#249090272
#249090262
#249052872
#249052852
C83×#12712
#783283