Finite Group Databasebeta

← #35298036

Subgroups — #35298036

Order 21248.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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#24910403C211yesmaximal, characteristic
2#24905801C211yesmaximal, characteristic
3#24905349C212yesmaximal, complemented
4#24905316C212yesmaximal, complemented
5C4×#99×C83C211yesmaximal, characteristic
6#19127665C2212yes—
7#19127594—21no—
8#19127587—21no—
9#19127581—21no—
10#19127569C411yescharacteristic, complemented
11#19127564C2211yescharacteristic
12#19127561C411yescharacteristic, complemented
13C22⋊C4×Dic83—21no—
14C4×C22⋊Dic83C2211yescharacteristic
15#19127547C411yescharacteristic, complemented
16C2×C83⋊#95C411yescharacteristic, complemented
17#19127427—21no—
18#19127425—21no—
19C2×C4×D4×C83C2211yescharacteristic
20C2×#99×C83—21no—
21C4×C22⋊C4×C83C2212yes—
22#342×C83—21no—
23C23×Dic83—21no—
24C2×#13050574—22no—
25C2×C4⋊Dic83—21no—
26C2×C22⋊Dic83—21no—
27C2×C22⋊Dic83—21no—
28C2×C22⋊Dic83—21no—
29C2×C4×Dic83—21no—
30C2×C4×Dic83—21no—
31C22⋊(C83⋊C8)—22no—
32C22⋊(C83⋊C8)—22no—
33C83⋊#95—21no—
34C83⋊#95—21no—
35C83⋊#95—21no—
36C83⋊#95—21no—
37C83⋊#95—21no—
38C83⋊#95C2×C411yescharacteristic
39C83⋊#95C2×C411yescharacteristic
40C83⋊#95C2×C411yescharacteristic
41C83⋊#95C2×C411yescharacteristic
42C22×D4×C83D411yescharacteristic
43C23×C4×C83C2×C411yescharacteristic
44C23×C4×C83C2311yescharacteristic
45C4×D4×C83—22no—
46C4×D4×C83—22no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C22⋊C4×C83—22no—
49C2×C22⋊C4×C83D411yescharacteristic
50C2×C22⋊C4×C83D411yescharacteristic
51C2×C42×C83—22no—
52C2×C42×C83C2×C411yescharacteristic
53#99×C83—24no—
54#95×C83—22no—
55C22×Dic83—21no—
56C22×Dic83—21no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—42no—
60C22×Dic83—42no—
61C22×Dic83—81no—
62#13050574—82no—
63C2×C83⋊C8—42no—
64C4⋊Dic83—81no—
65C22⋊Dic83—42no—
66C22⋊Dic83—42no—
67C22⋊Dic83—81no—
68C4×Dic83—42no—
69C4×Dic83—81no—
70C24×C83C22⋊C411yescharacteristic
71C24×C83C2×D411yescharacteristic
72C2×D4×C83—22no—
73C2×D4×C83—22no—
74C2×D4×C83—41no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83—42no—
78C22×C4×C83—81no—
79C22×C4×C83—81no—
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C22⋊C411yescharacteristic
83C22×C4×C83C22×C411yescharacteristic
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83#4112yes—
86C22×C4×C83#4112yes—
87C4⋊C4×C83—22no—
88C22⋊C4×C83—22no—
89C22⋊C4×C83—22no—
90C22⋊C4×C83—24no—
91C22⋊C4×C83—42no—
92C42×C83—21no—
93C42×C83—21no—
94C42×C83—82no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83—21no—
98C23×C83—21no—
99C23×C83—41no—
100C23×C83—41no—
101C23×C83—41no—
102C23×C83—41no—
103C23×C83#10412yes—
104C23×C83C2×C22⋊C411yescharacteristic
105C23×C83#12312yes—
106D4×C83—44no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—42no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—42no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—44no—
119C2×C4×C83—81no—
120C2×C4×C83—81no—
121C2×C4×C83—82no—
122C2×C4×C83—82no—
123C2×C4×C83#11711yescharacteristic
124C2×C4×C83#11711yescharacteristic
125C2×C4×C83#12312yes—
126C2×Dic83—22no—
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—
137C2×Dic83—41no—
138C2×Dic83—84no—
139C83⋊C8—82no—
140C22×C83—21no—
141C22×C83—21no—
142C22×C83—22no—
143C22×C83—22no—
144C22×C83—22no—
145C22×C83—22no—
146C22×C83—42no—
147C22×C83—42no—
148C22×C83—41no—
149C22×C83—41no—
150C22×C83—81no—
151C22×C83—81no—
152C22×C83#38111yescharacteristic
153C22×C83C2×#10411yescharacteristic
154C22×C83#42111yescharacteristic
155C4×C83—22no—
156C4×C83—21no—
157C4×C83—21no—
158C4×C83—41no—
159C4×C83—41no—
160C4×C83—41no—
161C4×C83—84no—
162Dic83—42no—
163Dic83—81no—
164Dic83—81no—
165Dic83—81no—
166#8777—831nomaximal, Sylow
167C2×C83—21no—
168C2×C83—21no—
169C2×C83—42no—
170C2×C83—42no—
171C2×C83#182611yescharacteristic
172C2×C83#182711yescharacteristic
173C2×C83#182811yescharacteristic
174#2353—831no—
175C4×#99D8311yescharacteristic
176#1465—831no—
177#1297—832no—
178#1284—832no—
179C83#877711yescharacteristic, complemented, Sylow
180C2×C4×D4C2×D8311yescharacteristic
181C2×#99—21no—
182#407—832no—
183#388—1661no—
184#387—1661no—
185#386—1661no—
186#383—831no—
187#381—831no—
188#380—831no—
189C4×C22⋊C4—831no—
190C4×C22⋊C4—1661no—
191C4×C22⋊C4C2×D8312yes—
192#376—831no—
193C2×#95—831no—
194#342—21no—
195#324—1661no—
196#323—1661no—
197C22×D4C22⋊D8311yescharacteristic
198C23×C4—1661no—
199C23×C4C4×D8311yescharacteristic
200C23×C4C22×D8311yescharacteristic
201C2×M16—1662no—
202C4×D4—22no—
203C4×D4—22no—
204C2×C4⋊C4—1661no—
205C2×C4⋊C4D33211yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—1661no—
208C2×C22⋊C4—1661no—
209C2×C22⋊C4—1661no—
210C2×C22⋊C4D33211yescharacteristic
211C2×C22⋊C4C22⋊D8311yescharacteristic
212C2×C42—22no—
213C2×C42—1661no—
214C2×C42—1661no—
215C2×C42C4×D8311yescharacteristic
216#99—24no—
217C22⋊C8—1662no—
218C22⋊C8—1662no—
219#95—22no—
220#95—831no—
221#95—831no—
222#95—831no—
223#95—831no—
224#95—1661no—
225#95—1661no—
226#95—1661no—
227#95—1661no—
228#95—1661no—
229C24(C2×D83)⋊C411yescharacteristic
230C24C2×C22⋊D8311yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—81no—
238C22×C4—81no—
239C22×C4—3322no—
240C22×C4—3322no—
241C22×C4—6641no—
242C22×C4—1661no—
243C22×C4—1661no—
244C22×C4—1661no—
245C22×C4—1661no—
246C22×C4(C2×D83)⋊C411yescharacteristic
247C22×C4(C2×D83)⋊C411yescharacteristic
248C22×C4(C2×D83)⋊C411yescharacteristic
249C22×C4C2×C4×D8311yescharacteristic
250C22×C4C2×D33211yescharacteristic
251C22×C4#1305058912yes—
252C22×C4#1305058912yes—
253M16—6642no—
254C2×C8—3322no—
255C4⋊C4—22no—
256C4⋊C4—6641no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—42no—
261C22⋊C4—3322no—
262C22⋊C4—3322no—
263C22⋊C4—6641no—
264C42—21no—
265C42—21no—
266C42—82no—
267C42—3322no—
268C42—6641no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#1458172012yes—
278C23C2×(C2×D83)⋊C411yescharacteristic
279C23#1458177312yes—
280D4—44no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—3321no—
298C2×C4—3321no—
299C2×C4—3321no—
300C2×C4—3321no—
301C2×C4—3321no—
302C2×C4—3321no—
303C2×C4—3321no—
304C2×C4—3321no—
305C2×C4—3321no—
306C2×C4—3321no—
307C2×C4—3321no—
308C2×C4—6644no—
309C2×C4—1662no—
310C2×C4#1458174811yescharacteristic
311C2×C4#1458174811yescharacteristic
312C2×C4#1458177612yes—
313C8—6642no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1912756211yescharacteristic
327C22C2×#1458172011yescharacteristic
328C22#1912771911yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—84no—
336C4—3322no—
337C4—6641no—
338C4—6641no—
339C4—6641no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#2490756311yescharacteristic
345C2#2490756411yescharacteristic
346C2#2490756911yescharacteristic
subgroupG/H
centerC22#19127562
commutatorC22×C4×C83C22×C4
FrattiniC23×C4C22×D83
FittingC4×#99×C83C2
socleC22×C83#381
prime radicalC22×D4×C83D4
cosocleC23×C4×C83C23
hypercenterC4×#99D83
hypocenterC83#8777
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #24905349C2semidirect
4. #24905316C2semidirect
10. #19127569C4semidirect
12. #19127561C4semidirect
15. #19127547C4semidirect
16. C2×C83⋊#95C4semidirect
179. C83#8777semidirect

Maximal subgroups

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

subgroupindex
#249104032
#249058012
#249053492
#249053162
C4×#99×C832
#877783