Finite Group Databasebeta

← #35314896

Subgroups — #35314896

Order 21248.

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

normal subgroups only

This group has 436 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#24913161C211yesmaximal, characteristic
2#24907196C211yesmaximal, characteristic
3#24905488C212yesmaximal
4#24905464C212yesmaximal
5C83×#1464C211yesmaximal, characteristic
6C2×#14581784C411yescharacteristic, complemented
7C2×#14581751—21no—
8#19127640C411yescharacteristic, complemented
9#19127637C2211yescharacteristic
10#19127631C411yescharacteristic, complemented
11#19127626C2211yescharacteristic
12#19127596—21no—
13#19127595—21no—
14#19127585—21no—
15#19127574—21no—
16#19127547C411yescharacteristic, complemented
17#19127468—21no—
18#19127468C2212yes—
19C2×#117×C83C2211yescharacteristic
20#432×C83—21no—
21#324×C83—21no—
22#323×C83C2212yes—
23#14581784—41no—
24#14581784—41no—
25#14581751—24no—
26#14581751—42no—
27C2×C4⋊Dic83—41no—
28C2×C4⋊Dic83C2×C411yescharacteristic
29C2×C4⋊Dic83C2×C411yescharacteristic
30C2×Dic83⋊C4—21no—
31C2×Dic83⋊C4—21no—
32C2×Dic83⋊C4—21no—
33C2×Dic83⋊C4—21no—
34C2×C22⋊Dic83—22no—
35C2×C22⋊Dic83—21no—
36C2×C22⋊Dic83—21no—
37C2×C4×Dic83—21no—
38C2×C4×Dic83—41no—
39C83⋊#95—21no—
40C83⋊#95—21no—
41C83⋊#95—21no—
42C83⋊#95—21no—
43C83⋊#95—21no—
44C83⋊#95C2×C411yescharacteristic
45C83⋊#95C2×C411yescharacteristic
46C23×C4×C83D411yescharacteristic
47#117×C83—41no—
48#117×C83—41no—
49C2×C4⋊C4×C83C2×C411yescharacteristic
50C2×C4⋊C4×C83D411yescharacteristic
51C2×C22⋊C4×C83D411yescharacteristic
52C2×C22⋊C4×C83C2311yescharacteristic
53C2×C42×C83C2×C411yescharacteristic
54C2×C42×C83D411yescharacteristic
55C4⋊C8×C83—41no—
56C22⋊C8×C83—22no—
57#97×C83—41no—
58C22×Dic83—21no—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—21no—
62C22×Dic83—42no—
63C4⋊Dic83—44no—
64C4⋊Dic83—41no—
65C4⋊Dic83—41no—
66Dic83⋊C4—42no—
67Dic83⋊C4—42no—
68Dic83⋊C4—41no—
69Dic83⋊C4—41no—
70Dic83⋊C4—42no—
71C22⋊Dic83—24no—
72C22⋊Dic83—42no—
73C22⋊Dic83—41no—
74C22⋊Dic83—42no—
75C22⋊Dic83—41no—
76C4×Dic83—42no—
77C4×Dic83—44no—
78C24×C83C2×D411yescharacteristic
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—22no—
84C22×C4×C83C22⋊C411yescharacteristic
85C22×C4×C83C22⋊C411yescharacteristic
86C22×C4×C83C22⋊C411yescharacteristic
87C22×C4×C83C22⋊C411yescharacteristic
88C22×C4×C83C22×C411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C2×C8×C83—42no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C22⋊C4×C83—41no—
94C22⋊C4×C83—41no—
95C42×C83—21no—
96C42×C83—21no—
97C42×C83—21no—
98C42×C83—21no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—41no—
102C23×C83—41no—
103C23×C83C2×C22⋊C411yescharacteristic
104C23×C83AGL(1,ℤ/8)11yescharacteristic
105C23×C83#13711yescharacteristic
106C2×C4×C83—22no—
107C2×C4×C83—22no—
108C2×C4×C83—22no—
109C2×C4×C83—22no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
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—41no—
119C2×C4×C83—41no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83#9911yescharacteristic
123C2×C4×C83#9911yescharacteristic
124C2×C4×C83#10412yes—
125C2×Dic83—22no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—44no—
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—82no—
139C2×Dic83—82no—
140C8×C83—82no—
141C22×C83—21no—
142C22×C83—21no—
143C22×C83—21no—
144C22×C83—21no—
145C22×C83—41no—
146C22×C83—41no—
147C22×C83—41no—
148C22×C83—41no—
149C22×C83—81no—
150C22×C83C2×#9911yescharacteristic
151C22×C83#41711yescharacteristic
152C22×C83C2×#10411yescharacteristic
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—22no—
156C4×C83—41no—
157C4×C83—41no—
158C4×C83—41no—
159C4×C83—41no—
160Dic83—42no—
161Dic83—81no—
162Dic83—84no—
163Dic83—81no—
164Dic83—81no—
165#11760—831nomaximal, Sylow
166C2×C83—21no—
167C2×C83—21no—
168C2×C83—41no—
169C2×C83—41no—
170C2×C83#150411yescharacteristic
171C2×C83#212311yescharacteristic
172C2×C83#212611yescharacteristic
173#2611—831no—
174#1740—831no—
175#1464D8311yescharacteristic
176#1352—832no—
177#1344—832no—
178C83#1176011yescharacteristic, complemented, Sylow
179C2×#125—831no—
180C2×#117—1661no—
181C2×#117C2×D8311yescharacteristic
182#432—21no—
183#400—831no—
184#399—831no—
185#398—831no—
186#397—831no—
187#389—1661no—
188#388—1661no—
189#387—1661no—
190#385—1661no—
191#376—831no—
192#342—832no—
193#342—1661no—
194#324—21no—
195#323C2×D8312yes—
196C23×C4D33211yescharacteristic
197#125—3321no—
198#125—3321no—
199#117—41no—
200#117—41no—
201#117—3322no—
202#117—1664no—
203C2×C4⋊C4—3321no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4—1661no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4C4×D8311yescharacteristic
211C2×C4⋊C4C22⋊D8311yescharacteristic
212C2×C22⋊C4—1661no—
213C2×C22⋊C4—1661no—
214C2×C22⋊C4—1662no—
215C2×C22⋊C4D33211yescharacteristic
216C2×C22⋊C4C22×D8311yescharacteristic
217C2×C42—3321no—
218C2×C42—1661no—
219C2×C42C4×D8311yescharacteristic
220C2×C42C22⋊D8311yescharacteristic
221C4⋊C8—41no—
222C22⋊C8—22no—
223#97—41no—
224#95—831no—
225#95—831no—
226#95—1661no—
227#95—1661no—
228#95—1661no—
229#95—1661no—
230#95—1661no—
231C24C2×D33211yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—3322no—
238C22×C4—1661no—
239C22×C4—1661no—
240C22×C4—1661no—
241C22×C4—1661no—
242C22×C4(C2×D83)⋊C411yescharacteristic
243C22×C4(C2×D83)⋊C411yescharacteristic
244C22×C4(C2×D83)⋊C411yescharacteristic
245C22×C4(C2×D83)⋊C411yescharacteristic
246C22×C4C2×C4×D8311yescharacteristic
247C22×C4C2×C22⋊D8311yescharacteristic
248C2×C8—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—3321no—
252C4⋊C4—3321no—
253C4⋊C4—3324no—
254C4⋊C4—3322no—
255C4⋊C4—3322no—
256C4⋊C4—3321no—
257C4⋊C4—3321no—
258C4⋊C4—3322no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—3322no—
262C22⋊C4—3321no—
263C22⋊C4—3321no—
264C22⋊C4—3322no—
265C22⋊C4—1664no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—3324no—
271C42—3322no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×(C2×D83)⋊C411yescharacteristic
277C23#1458182011yescharacteristic
278C23#1458182511yescharacteristic
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—3321no—
296C2×C4—3321no—
297C2×C4—3324no—
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—6642no—
308C2×C4—6642no—
309C2×C4—1662no—
310C2×C4#1458170611yescharacteristic
311C2×C4#1458170611yescharacteristic
312C2×C4#1458171812yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22C2×#1458170611yescharacteristic
324C22#1912770311yescharacteristic
325C22C2×#1458171811yescharacteristic
326C4—21no—
327C4—21no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3322no—
334C4—6641no—
335C4—6644no—
336C4—6641no—
337C4—6641no—
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2#2490596811yescharacteristic
343C2#2490911811yescharacteristic
344C2#2490912611yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1464C2
socleC22×C83C2×#99
prime radicalC24×C83C2×D4
cosocleC2×C22⋊C4×C83C23
hypercenter#1464D83
hypocenterC83#11760
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
6. C2×#14581784C4semidirect
8. #19127640C4semidirect
10. #19127631C4semidirect
16. #19127547C4semidirect
178. C83#11760semidirect

Maximal subgroups

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

subgroupindex
#249131612
#249071962
#249054882
#249054642
C83×#14642
#1176083