Finite Group Databasebeta

← #35293691

Subgroups — #35293691

Order 21248.

358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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#24909026C211yesmaximal, characteristic
2#24909026C211yesmaximal, characteristic
3#24909026C211yesmaximal, characteristic
4#24905286C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2726C211yesmaximal, characteristic
8#19127571C2211yescharacteristic
9#19127463—21no—
10#19127463—21no—
11#19127463—21no—
12#19127463—21no—
13#19127463—21no—
14#19127463—21no—
15#19127456C2211yescharacteristic
16#19127456C2211yescharacteristic
17#19127456C2211yescharacteristic
18C2×#125×C83—21no—
19#398×C83—21no—
20#398×C83—21no—
21#398×C83—21no—
22#389×C83—21no—
23#389×C83C2211yescharacteristic
24#389×C83C2211yescharacteristic
25#389×C83C2211yescharacteristic
26#387×C83—21no—
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29C22×C83⋊C8—21no—
30C2×C4⋊Dic83—21no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33#125×C83—42no—
34#125×C83—42no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—21no—
42C2×C4⋊C4×C83D411yescharacteristic
43C2×C4⋊C4×C83D411yescharacteristic
44C2×C4⋊C4×C83D411yescharacteristic
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83—21no—
49C2×C42×C83C2311yescharacteristic
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56C22×Dic83—41no—
57C2×C83⋊C8—41no—
58C2×C83⋊C8—41no—
59C2×C83⋊C8—41no—
60C2×C83⋊C8—41no—
61C2×C83⋊C8—41no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C4⋊Dic83—42no—
67C4⋊Dic83—42no—
68C4⋊Dic83—42no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83C2×D411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C4⋊C4×C83—21no—
79C4⋊C4×C83—21no—
80C4⋊C4×C83—21no—
81C4⋊C4×C83—21no—
82C4⋊C4×C83—41no—
83C4⋊C4×C83—41no—
84C4⋊C4×C83—41no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—42no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—81no—
95C4⋊C4×C83SD1612yes—
96C4⋊C4×C83Q1612yes—
97C42×C83—41no—
98C42×C83—42no—
99C23×C83#12011yescharacteristic
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—22no—
107C2×C4×C83—22no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—41no—
124C2×C4×C83C2×SD1611yescharacteristic
125C2×C4×C83C2×Q1611yescharacteristic
126C2×C4×C83#13511yescharacteristic
127C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C83#13711yescharacteristic
129C2×C4×C83#13711yescharacteristic
130C2×Dic83—81no—
131C2×Dic83—81no—
132C2×Dic83—81no—
133C83⋊C8—81no—
134C83⋊C8—81no—
135C83⋊C8—81no—
136C22×C83#45011yescharacteristic
137C22×C83#45111yescharacteristic
138C22×C83#45211yescharacteristic
139C22×C83#45411yescharacteristic
140C22×C83#45411yescharacteristic
141C22×C83#45411yescharacteristic
142C22×C83#45811yescharacteristic
143C4×C83—21no—
144C4×C83—21no—
145C4×C83—21no—
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—21no—
149C4×C83—42no—
150C4×C83—42no—
151C4×C83—81no—
152C4×C83—81no—
153C4×C83—81no—
154C4×C83—81no—
155Dic83—161no—
156#7827—831nomaximal, Sylow
157C2×C83#161511yescharacteristic
158C2×C83#161611yescharacteristic
159C2×C83#161711yescharacteristic
160C2×C83#163511yescharacteristic
161C2×C83#163611yescharacteristic
162C2×C83#163711yescharacteristic
163C2×C83#165811yescharacteristic
164#2726D8311yescharacteristic
165#2100—831no—
166#2100—831no—
167#2100—831no—
168#1271—831no—
169#1271—831no—
170#1271—831no—
171C83#782711yescharacteristic, complemented, Sylow
172C2×#125—21no—
173#398—21no—
174#398—21no—
175#398—21no—
176#389—21no—
177#389C2×D8311yescharacteristic
178#389C2×D8311yescharacteristic
179#389C2×D8311yescharacteristic
180#387—21no—
181#384—831no—
182#340—1661no—
183#340—1661no—
184#340—1661no—
185#340—1661no—
186#340—1661no—
187#340—1661no—
188#336—831no—
189#336—831no—
190#336—831no—
191C22×C8—1661no—
192C22×C8—1661no—
193C22×C8—1661no—
194#125—42no—
195#125—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—1661no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4—1661no—
206C2×C4⋊C4C22⋊D8311yescharacteristic
207C2×C4⋊C4C22⋊D8311yescharacteristic
208C2×C4⋊C4C22⋊D8311yescharacteristic
209C2×C4⋊C4C22⋊D8311yescharacteristic
210C2×C4⋊C4C22⋊D8311yescharacteristic
211C2×C4⋊C4C22⋊D8311yescharacteristic
212C2×C42—21no—
213C2×C42C22×D8311yescharacteristic
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—3321no—
227C22×C4C2×C22⋊D8311yescharacteristic
228C22×C4C2×C22⋊D8311yescharacteristic
229C22×C4C2×C22⋊D8311yescharacteristic
230C2×C8—3321no—
231C2×C8—3321no—
232C2×C8—3321no—
233C2×C8—3321no—
234C2×C8—3321no—
235C2×C8—3321no—
236C2×C8—3321no—
237C2×C8—3321no—
238C2×C8—3321no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—3322no—
257C4⋊C4—3322no—
258C4⋊C4—3322no—
259C4⋊C4#1305057812yes—
260C4⋊C4#1305058012yes—
261C42—41no—
262C42—42no—
263C23#1458176111yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—6641no—
289C2×C4—6641no—
290C2×C4—6641no—
291C2×C4C2×#1305057811yescharacteristic
292C2×C4C2×#1305058011yescharacteristic
293C2×C4#1458181211yescharacteristic
294C2×C4#1458181811yescharacteristic
295C2×C4#1458182211yescharacteristic
296C2×C4#1458182311yescharacteristic
297C8—6641no—
298C8—6641no—
299C8—6641no—
300C22#1912785211yescharacteristic
301C22#1912785711yescharacteristic
302C22#1912786311yescharacteristic
303C22#1912787411yescharacteristic
304C22#1912787411yescharacteristic
305C22#1912787411yescharacteristic
306C22#1912789111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—42no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—13281no—
320C2#2490649411yescharacteristic
321C2#2490650011yescharacteristic
322C2#2490650511yescharacteristic
323C2#2490661411yescharacteristic
324C2#2490662111yescharacteristic
325C2#2490662811yescharacteristic
326C2#2490676511yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2726C2
socle, prime radicalC23×C83#120
hypercenter#2726D83
hypocenterC83#7827
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2726

Complements

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

NH ≅ G/Ntype
171. C83#7827semidirect

Maximal subgroups

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

subgroupindex
#249090262
#249052862
C83×#27262
#782783