Finite Group Databasebeta

← #35293267

Subgroups — #35293267

Order 21248.

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

normal subgroups only

This group has 416 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#24908791C211yesmaximal, characteristic
2#24908791C211yesmaximal, characteristic
3#24908709C211yesmaximal, characteristic
4#24905286C211yesmaximal, characteristic
5#24905286C211yesmaximal, characteristic
6#24905286C211yesmaximal, characteristic
7C83×#2726C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×#14581725—21no—
10C2×#14581725—21no—
11C2×#14581715—21no—
12C2×#14581715—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×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#14581725—42no—
36#14581715—42no—
37#14581715—42no—
38#125×C83—42no—
39#125×C83—42no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—21no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C4⋊C4×C83D411yescharacteristic
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C4⋊C4×C83D411yescharacteristic
52C2×C4⋊C4×C83D411yescharacteristic
53C2×C42×C83—21no—
54C2×C42×C83C2311yescharacteristic
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61C2×Dic166—22no—
62C2×Dic166—41no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C2×Dic166—41no—
66C2×Dic166—41no—
67C22×Dic83—41no—
68C2×C83⋊C8—22no—
69C2×C83⋊C8—22no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8—41no—
75C2×C83⋊C8—41no—
76C2×C83⋊C8—41no—
77C4⋊Dic83—22no—
78C4⋊Dic83—22no—
79C4⋊Dic83—41no—
80C4⋊Dic83—41no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
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—42no—
98C4⋊C4×C83—42no—
99C4⋊C4×C83—42no—
100C4⋊C4×C83—41no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—41no—
103C4⋊C4×C83—41no—
104C4⋊C4×C83—41no—
105C4⋊C4×C83—41no—
106C4⋊C4×C83—81no—
107C4⋊C4×C83D812yes—
108C4⋊C4×C83Q1612yes—
109C42×C83—41no—
110C42×C83—42no—
111C23×C83#12011yescharacteristic
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—22no—
119C2×C4×C83—22no—
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—41no—
131C2×C4×C83—41no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83C2×D811yescharacteristic
137C2×C4×C83C2×Q1611yescharacteristic
138C2×C4×C83#13511yescharacteristic
139C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C83#13711yescharacteristic
141C2×C4×C83#13711yescharacteristic
142C2×Dic83—42no—
143C2×Dic83—81no—
144C2×Dic83—81no—
145Dic166—42no—
146Dic166—42no—
147Dic166—81no—
148Dic166—81no—
149C83⋊C8—42no—
150C83⋊C8—42no—
151C83⋊C8—81no—
152C22×C83#44711yescharacteristic
153C22×C83#45111yescharacteristic
154C22×C83#45211yescharacteristic
155C22×C83#45411yescharacteristic
156C22×C83#45611yescharacteristic
157C22×C83#45611yescharacteristic
158C22×C83B(4,𝔽2)11yescharacteristic
159C4×C83—21no—
160C4×C83—21no—
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—42no—
166C4×C83—42no—
167C4×C83—81no—
168C4×C83—81no—
169C4×C83—81no—
170C4×C83—81no—
171Dic83—82no—
172#7763—831nomaximal, Sylow
173C2×C83#159811yescharacteristic
174C2×C83#160311yescharacteristic
175C2×C83#160511yescharacteristic
176C2×C83#163611yescharacteristic
177C2×C83#164711yescharacteristic
178C2×C83#164911yescharacteristic
179C2×C83#166311yescharacteristic
180#2726D8311yescharacteristic
181#2057—831no—
182#2057—831no—
183#2043—831no—
184#1271—831no—
185#1271—831no—
186#1271—831no—
187C83#776311yescharacteristic, complemented, Sylow
188C2×C4⋊Q8—831no—
189C2×#125—21no—
190C2×#107—1661no—
191C2×#107—1661no—
192C2×#103—1661no—
193C2×#103—1661no—
194#398—21no—
195#398—21no—
196#398—21no—
197#389—21no—
198#389C2×D8311yescharacteristic
199#389C2×D8311yescharacteristic
200#389C2×D8311yescharacteristic
201#387—21no—
202#340—1661no—
203#340—1661no—
204#336—831no—
205#336—831no—
206#336—831no—
207C22×Q8—1661no—
208C22×C8—1661no—
209C22×C8—1661no—
210C22×C8—1661no—
211C4⋊Q8—3322no—
212#125—42no—
213#125—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—1661no—
222C2×C4⋊C4—1661no—
223C2×C4⋊C4C22⋊D8311yescharacteristic
224C2×C4⋊C4C22⋊D8311yescharacteristic
225C2×C4⋊C4C22⋊D8311yescharacteristic
226C2×C4⋊C4C22⋊D8311yescharacteristic
227C2×C4⋊C4C22⋊D8311yescharacteristic
228C2×C4⋊C4C22⋊D8311yescharacteristic
229C2×C42—21no—
230C2×C42C22×D8311yescharacteristic
231#107—3322no—
232#107—3322no—
233#103—3322no—
234#103—3322no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×Q8—3321no—
242C2×Q8—3321no—
243C2×Q8—3321no—
244C2×Q8—3321no—
245C2×Q8—3321no—
246C2×Q8—1662no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—3321no—
254C22×C4C2×C22⋊D8311yescharacteristic
255C22×C4C2×C22⋊D8311yescharacteristic
256C22×C4C2×C22⋊D8311yescharacteristic
257C2×C8—3321no—
258C2×C8—3321no—
259C2×C8—3321no—
260C2×C8—3321no—
261C2×C8—3321no—
262C2×C8—3321no—
263C2×C8—3321no—
264C2×C8—1662no—
265C2×C8—1662no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—3321no—
284C4⋊C4—3321no—
285C4⋊C4—1662no—
286C4⋊C4—1662no—
287C4⋊C4#1305057512yes—
288C4⋊C4#1305058012yes—
289C42—41no—
290C42—42no—
291C23#1458176111yescharacteristic
292Q8—3322no—
293Q8—3322no—
294Q8—6641no—
295Q8—6641no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—3322no—
321C2×C4—6641no—
322C2×C4—6641no—
323C2×C4C2×#1305057511yescharacteristic
324C2×C4C2×#1305058011yescharacteristic
325C2×C4#1458181211yescharacteristic
326C2×C4#1458181811yescharacteristic
327C2×C4#1458182211yescharacteristic
328C2×C4#1458182311yescharacteristic
329C8—3322no—
330C8—3322no—
331C8—6641no—
332C22#1912783511yescharacteristic
333C22#1912785711yescharacteristic
334C22#1912786311yescharacteristic
335C22#1912787411yescharacteristic
336C22#1912788411yescharacteristic
337C22#1912788411yescharacteristic
338C22#1912788811yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—6642no—
352C2#2490639811yescharacteristic
353C2#2490642611yescharacteristic
354C2#2490643711yescharacteristic
355C2#2490662111yescharacteristic
356C2#2490669811yescharacteristic
357C2#2490671211yescharacteristic
358C2#2490679111yescharacteristic
subgroupG/H
centerC23#14581761
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2726C2
socle, prime radicalC23×C83#120
hypercenter#2726D83
hypocenterC83#7763
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
187. C83#7763semidirect

Maximal subgroups

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

subgroupindex
#249087912
#249087092
#249052862
C83×#27262
#776383