Finite Group Databasebeta

← #35293351

Subgroups — #35293351

Order 21248.

380 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 83 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#24908796C211yesmaximal, characteristic
2#24908791C211yesmaximal, characteristic
3#24908709C211yesmaximal, characteristic
4#24905286C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2810C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581725—21no—
10C2×#14581723—21no—
11C2×#14581715—21no—
12C2×#14581715—21no—
13#19127463—21no—
14#19127463—21no—
15#19127456C2211yescharacteristic
16#19127456C2211yescharacteristic
17#19127456C2211yescharacteristic
18#400×C83—21no—
19#400×C83—21no—
20#400×C83—21no—
21#389×C83C2211yescharacteristic
22#389×C83C2211yescharacteristic
23#389×C83C2211yescharacteristic
24#387×C83—21no—
25#387×C83—21no—
26#387×C83—21no—
27C22×Dic166—21no—
28C22×C83⋊C8—21no—
29C22×C83⋊C8—21no—
30C22×C83⋊C8—21no—
31#14581792—42no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34#14581725—42no—
35#14581723—42no—
36#14581715—42no—
37#14581715—42no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83—21no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C4⋊C4×C83D411yescharacteristic
43C2×C4⋊C4×C83D411yescharacteristic
44C2×C4⋊C4×C83D411yescharacteristic
45C2×C4⋊C4×C83D411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C42×C83—21no—
48C2×C42×C83C2311yescharacteristic
49#95×C83—21no—
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59C2×Dic166—22no—
60C2×Dic166—41no—
61C2×Dic166—41no—
62C2×Dic166—41no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C22×Dic83—41no—
66C2×C83⋊C8—22no—
67C2×C83⋊C8—22no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8—41no—
75C4⋊Dic83—22no—
76C4⋊Dic83—22no—
77C4⋊Dic83—41no—
78C4⋊Dic83—41no—
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83C2×D411yescharacteristic
86C22×C4×C83C2×D411yescharacteristic
87C22×C4×C83C2×D411yescharacteristic
88C4⋊C4×C83—21no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83—21no—
93C4⋊C4×C83—21no—
94C4⋊C4×C83—41no—
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×C83—41no—
102C4⋊C4×C83—41no—
103C42×C83—41no—
104C42×C83—81no—
105C23×C83#12011yescharacteristic
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
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×C83—41no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83#13511yescharacteristic
131C2×C4×C83#13511yescharacteristic
132C2×C4×C83#13511yescharacteristic
133C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C83#13711yescharacteristic
135C2×C4×C83#13711yescharacteristic
136C2×Dic83—42no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139Dic166—42no—
140Dic166—42no—
141Dic166—81no—
142Dic166—81no—
143C83⋊C8—42no—
144C83⋊C8—42no—
145C83⋊C8—81no—
146C22×C83#44911yescharacteristic
147C22×C83#45211yescharacteristic
148C22×C83#45211yescharacteristic
149C22×C83#45411yescharacteristic
150C22×C83#45611yescharacteristic
151C22×C83#45611yescharacteristic
152C22×C83B(4,𝔽2)11yescharacteristic
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—21no—
156C4×C83—21no—
157C4×C83—21no—
158C4×C83—21no—
159C4×C83—81no—
160C4×C83—81no—
161C4×C83—81no—
162C4×C83—81no—
163C4×C83—81no—
164C4×C83—81no—
165Dic83—82no—
166#7775—831nomaximal, Sylow
167C2×C83#159711yescharacteristic
168C2×C83#160311yescharacteristic
169C2×C83#160311yescharacteristic
170C2×C83#163811yescharacteristic
171C2×C83#165011yescharacteristic
172C2×C83#165211yescharacteristic
173C2×C83#166311yescharacteristic
174#2810D8311yescharacteristic
175#2058—831no—
176#2057—831no—
177#2043—831no—
178#1271—831no—
179#1271—831no—
180#1271—831no—
181C83#777511yescharacteristic, complemented, Sylow
182C2×C4⋊Q8—831no—
183C2×#107—1661no—
184C2×#106—1661no—
185C2×#103—1661no—
186C2×#103—1661no—
187#400—21no—
188#400—21no—
189#400—21no—
190#389C2×D8311yescharacteristic
191#389C2×D8311yescharacteristic
192#389C2×D8311yescharacteristic
193#387—21no—
194#387—21no—
195#387—21no—
196#340—1661no—
197#340—1661no—
198#336—831no—
199#336—831no—
200#336—831no—
201C22×Q8—1661no—
202C22×C8—1661no—
203C22×C8—1661no—
204C22×C8—1661no—
205C4⋊Q8—3322no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4—1661no—
211C2×C4⋊C4C22⋊D8311yescharacteristic
212C2×C4⋊C4C22⋊D8311yescharacteristic
213C2×C4⋊C4C22⋊D8311yescharacteristic
214C2×C4⋊C4C22⋊D8311yescharacteristic
215C2×C4⋊C4C22⋊D8311yescharacteristic
216C2×C4⋊C4C22⋊D8311yescharacteristic
217C2×C42—21no—
218C2×C42C22×D8311yescharacteristic
219#107—3322no—
220#106—3322no—
221#103—3322no—
222#103—3322no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233C2×Q8—3321no—
234C2×Q8—3321no—
235C2×Q8—3321no—
236C2×Q8—3321no—
237C2×Q8—3321no—
238C2×Q8—1662no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—3321no—
246C22×C4C2×C22⋊D8311yescharacteristic
247C22×C4C2×C22⋊D8311yescharacteristic
248C22×C4C2×C22⋊D8311yescharacteristic
249C2×C8—3321no—
250C2×C8—3321no—
251C2×C8—3321no—
252C2×C8—3321no—
253C2×C8—3321no—
254C2×C8—3321no—
255C2×C8—3321no—
256C2×C8—1662no—
257C2×C8—1662no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C4⋊C4—1662no—
276C4⋊C4—1662no—
277C42—41no—
278C42—81no—
279C23#1458176111yescharacteristic
280Q8—3322no—
281Q8—3322no—
282Q8—6641no—
283Q8—6641no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—3322no—
309C2×C4—6641no—
310C2×C4—6641no—
311C2×C4#1458181211yescharacteristic
312C2×C4#1458181211yescharacteristic
313C2×C4#1458181211yescharacteristic
314C2×C4#1458181711yescharacteristic
315C2×C4#1458182211yescharacteristic
316C2×C4#1458182211yescharacteristic
317C8—3322no—
318C8—3322no—
319C8—6641no—
320C22#1912784611yescharacteristic
321C22#1912786311yescharacteristic
322C22#1912786311yescharacteristic
323C22#1912787411yescharacteristic
324C22#1912788411yescharacteristic
325C22#1912788411yescharacteristic
326C22#1912788811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—6642no—
340C2#2490639211yescharacteristic
341C2#2490642611yescharacteristic
342C2#2490642611yescharacteristic
343C2#2490663511yescharacteristic
344C2#2490671911yescharacteristic
345C2#2490673311yescharacteristic
346C2#2490679111yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2810C2
socle, prime radicalC23×C83#120
hypercenter#2810D83
hypocenterC83#7775
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2810

Complements

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

NH ≅ G/Ntype
181. C83#7775semidirect

Maximal subgroups

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

subgroupindex
#249087962
#249087912
#249087092
#249052862
C83×#28102
#777583