Finite Group Databasebeta

← #35293505

Subgroups — #35293505

Order 21248.

374 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 85 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#24914415C211yesmaximal, characteristic
2#24909020C211yesmaximal, characteristic
3#24908935C211yesmaximal, characteristic
4#24905287C211yesmaximal, characteristic
5#24905287C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2084C211yesmaximal, characteristic
8C2×#14581782—21no—
9C2×#14581725—21no—
10#19127633—21no—
11#19127631—21no—
12#19127631—21no—
13#19127600—21no—
14#19127599C2211yescharacteristic
15#19127599C2211yescharacteristic
16#19127586—21no—
17#19127463—21no—
18#19127463—21no—
19#19127463—21no—
20#19127456C2211yescharacteristic
21#19127456C2211yescharacteristic
22C2×#106×C83—21no—
23#389×C83C2211yescharacteristic
24#384×C83C2211yescharacteristic
25#340×C83—21no—
26#336×C83C2211yescharacteristic
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29#14581782—42no—
30#14581782—42no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83D411yescharacteristic
34C2×C4⋊Dic83D411yescharacteristic
35C2×C4⋊Dic83D411yescharacteristic
36C2×C4⋊Dic83D411yescharacteristic
37C2×Dic83⋊C4—21no—
38C2×Dic83⋊C4—21no—
39C2×Dic83⋊C4—21no—
40C2×Dic83⋊C4—21no—
41C2×C4×Dic83—21no—
42#14581725—42no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—21no—
48C22×C8×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C4⋊C4×C83—21no—
53C2×C4⋊C4×C83D411yescharacteristic
54C2×C4⋊C4×C83D411yescharacteristic
55C2×C42×C83C2311yescharacteristic
56#106×C83—42no—
57#95×C83—21no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C2×C83⋊C8—22no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C4⋊Dic83—21no—
69C4⋊Dic83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83—42no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74C4⋊Dic83—81no—
75C4⋊Dic83SD1612yes—
76Dic83⋊C4—42no—
77Dic83⋊C4—42no—
78Dic83⋊C4—41no—
79Dic83⋊C4—41no—
80Dic83⋊C4—41no—
81Dic83⋊C4—41no—
82C4×Dic83—42no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—41no—
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C2×C8×C83—22no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C4⋊C4×C83—21no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—42no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—41no—
97C4⋊C4×C83—41no—
98C4⋊C4×C83—41no—
99C4⋊C4×C83—41no—
100C4⋊C4×C83—41no—
101C4⋊C4×C83D812yes—
102C42×C83—41no—
103C23×C83#12011yescharacteristic
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—22no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—81no—
117C2×C4×C83—81no—
118C2×C4×C83—81no—
119C2×C4×C83C2×D811yescharacteristic
120C2×C4×C83C2×SD1611yescharacteristic
121C2×C4×C83#13511yescharacteristic
122C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×C4×C83#13711yescharacteristic
125C2×Dic83—22no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130C2×Dic83—41no—
131C2×Dic83—41no—
132C2×Dic83—41no—
133C2×Dic83—41no—
134C2×Dic83—41no—
135C2×Dic83—41no—
136C2×Dic83—41no—
137C8×C83—42no—
138C83⋊C8—42no—
139C83⋊C8—81no—
140C22×C83#44711yescharacteristic
141C22×C83#44811yescharacteristic
142C22×C83#45211yescharacteristic
143C22×C83#45411yescharacteristic
144C22×C83#45611yescharacteristic
145C22×C83#45611yescharacteristic
146C22×C83#45811yescharacteristic
147C4×C83—21no—
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—42no—
154C4×C83—81no—
155C4×C83—161no—
156Dic83—42no—
157Dic83—81no—
158Dic83—81no—
159Dic83—81no—
160#7798—831nomaximal, Sylow
161C2×C83#161011yescharacteristic
162C2×C83#161111yescharacteristic
163C2×C83#161511yescharacteristic
164C2×C83#162711yescharacteristic
165C2×C83#164711yescharacteristic
166C2×C83#165311yescharacteristic
167C2×C83#166311yescharacteristic
168#2726—831no—
169#2099—831no—
170#2084D8311yescharacteristic
171#2083—831no—
172#1271—831no—
173#1271—831no—
174#1271—831no—
175C83#779811yescharacteristic, complemented, Sylow
176C2×#125—1661no—
177C2×#107—1661no—
178C2×#106—21no—
179#398—1661no—
180#398—1661no—
181#398—1661no—
182#389—831no—
183#389—831no—
184#389—1661no—
185#389C2×D8311yescharacteristic
186#387—1661no—
187#384C2×D8311yescharacteristic
188#340—21no—
189#340—1661no—
190#340—1661no—
191#340—1661no—
192#336—831no—
193#336—831no—
194#336C2×D8311yescharacteristic
195C22×C8—21no—
196C22×C8—1661no—
197C22×C8—1661no—
198#125—3322no—
199#125—3322no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—831no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4—1661no—
211C2×C4⋊C4—1661no—
212C2×C4⋊C4—1661no—
213C2×C4⋊C4—1661no—
214C2×C4⋊C4C22⋊D8311yescharacteristic
215C2×C4⋊C4C22⋊D8311yescharacteristic
216C2×C42—1661no—
217C2×C42C22×D8311yescharacteristic
218#107—3322no—
219#106—42no—
220#95—21no—
221#95—1661no—
222#95—1661no—
223#95—1661no—
224#95—1661no—
225#95—1661no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—1661no—
230C22×C4—1661no—
231C22×C4—1661no—
232C22×C4—1661no—
233C22×C4D4×D8311yescharacteristic
234C22×C4D4×D8311yescharacteristic
235C22×C4C2×C22⋊D8311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—3321no—
240C2×C8—3321no—
241C2×C8—3321no—
242C2×C8—3321no—
243C2×C8—3321no—
244C2×C8—1662no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—42no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—3321no—
255C4⋊C4—3321no—
256C4⋊C4—3322no—
257C4⋊C4—3322no—
258C4⋊C4—3322no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—3321no—
262C4⋊C4—3321no—
263C4⋊C4—832no—
264C4⋊C4—6641no—
265C4⋊C4—1661no—
266C4⋊C4—1661no—
267C4⋊C4—1661no—
268C4⋊C4#1305057512yes—
269C42—41no—
270C42—3322no—
271C23#1458176011yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—3321no—
288C2×C4—3321no—
289C2×C4—3321no—
290C2×C4—3321no—
291C2×C4—3321no—
292C2×C4—3321no—
293C2×C4—3321no—
294C2×C4—3321no—
295C2×C4—3321no—
296C2×C4—3321no—
297C2×C4—3321no—
298C2×C4—1662no—
299C2×C4C2×#1305057511yescharacteristic
300C2×C4SD16×D8311yescharacteristic
301C2×C4#1458181311yescharacteristic
302C2×C4#1458181711yescharacteristic
303C2×C4#1458182111yescharacteristic
304C2×C4#1458182111yescharacteristic
305C8—42no—
306C8—3322no—
307C8—6641no—
308C22#1912783411yescharacteristic
309C22#1912783811yescharacteristic
310C22#1912786011yescharacteristic
311C22#1912787211yescharacteristic
312C22#1912788211yescharacteristic
313C22#1912788311yescharacteristic
314C22#1912789011yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—161no—
324C4—3322no—
325C4—6641no—
326C4—6641no—
327C4—6641no—
328C2#2490646511yescharacteristic
329C2#2490646911yescharacteristic
330C2#2490649111yescharacteristic
331C2#2490656411yescharacteristic
332C2#2490669611yescharacteristic
333C2#2490673711yescharacteristic
334C2#2490679011yescharacteristic
subgroupG/H
centerC23#14581760
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2084C2
socle, prime radicalC23×C83#120
hypercenter#2084D83
hypocenterC83#7798
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
175. C83#7798semidirect

Maximal subgroups

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

subgroupindex
#249144152
#249090202
#249089352
#249052872
#249052862
C83×#20842
#779883