Finite Group Databasebeta

← #35302076

Subgroups — #35302076

Order 21248.

424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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#24916548C211yesmaximal, characteristic
2#24912650C211yesmaximal, characteristic
3#24906089C212yesmaximal
4#24905320C212yesmaximal
5C83×#1467C211yesmaximal, characteristic
6C2×#14581784C2211yescharacteristic
7#19127832—24no—
8#19127758—21no—
9#19127758C2212yes—
10#19127754—21no—
11#19127634—21no—
12#19127634—21no—
13#19127608C411yescharacteristic
14#19127608C411yescharacteristic
15#19127585—21no—
16#19127585—21no—
17#19127570C411yescharacteristic
18#19127566C411yescharacteristic
19C4×C4⋊Dic83C2211yescharacteristic
20#19127442—24no—
21C2×C4×Q8×C83C2211yescharacteristic
22#432×C83C2212yes—
23#324×C83—21no—
24#324×C83—21no—
25#14581784—22no—
26#14581784—22no—
27C2×C4⋊Dic83—21no—
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×C4×Dic83C2×C411yescharacteristic
35C2×C4×Dic83C2×C411yescharacteristic
36C4⋊(C83⋊C8)—22no—
37C4⋊(C83⋊C8)—22no—
38C4⋊(C83⋊C8)—22no—
39C22⋊(C83⋊C8)—22no—
40#14581703—22no—
41#14581703D414yes—
42C4×C83⋊C8—22no—
43C83⋊#95—21no—
44C83⋊#95—21no—
45C83⋊#95—21no—
46C83⋊#95—21no—
47C83⋊#95—21no—
48C83⋊#95—21no—
49C83⋊#95—21no—
50C22×Q8×C83C2×C411yescharacteristic
51C4×Q8×C83—22no—
52C4×Q8×C83—22no—
53C2×C4⋊C4×C83C2×C411yescharacteristic
54C2×C4⋊C4×C83D411yescharacteristic
55C2×C4⋊C4×C83D411yescharacteristic
56C2×C42×C83D411yescharacteristic
57C2×C42×C83D411yescharacteristic
58C2×C42×C83C2311yescharacteristic
59C4⋊C8×C83—22no—
60C22⋊C8×C83—22no—
61#97×C83—22no—
62C22×Dic83—21no—
63C22×Dic83—21no—
64C22×Dic83—21no—
65C22×Dic83—21no—
66C2×C83⋊C8—24no—
67C4⋊Dic83—22no—
68C4⋊Dic83—22no—
69C4⋊Dic83—42no—
70Dic83⋊C4—42no—
71Dic83⋊C4—42no—
72Dic83⋊C4—41no—
73Dic83⋊C4—42no—
74Dic83⋊C4—41no—
75C4×Dic83—41no—
76C4×Dic83—41no—
77C2×Q8×C83—22no—
78C2×Q8×C83—22no—
79C2×Q8×C83—41no—
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C22⋊C411yescharacteristic
83C22×C4×C83C22⋊C411yescharacteristic
84C22×C4×C83C22×C411yescharacteristic
85C22×C4×C83C2×D411yescharacteristic
86C22×C4×C83C2×D411yescharacteristic
87C2×C8×C83—42no—
88C4⋊C4×C83—22no—
89C4⋊C4×C83—22no—
90C4⋊C4×C83—22no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—21no—
94C42×C83—21no—
95C42×C83C2×D412yes—
96C42×C83#4112yes—
97C23×C83C2×C22⋊C411yescharacteristic
98Q8×C83—44no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83#10112yes—
113C2×C4×C83C4×D412yes—
114C2×C4×C83#12011yescharacteristic
115C2×C4×C83#12112yes—
116C2×C4×C83#12311yescharacteristic
117C2×Dic83—22no—
118C2×Dic83—41no—
119C2×Dic83—41no—
120C2×Dic83—41no—
121C2×Dic83—41no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—42no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C8×C83—82no—
129C83⋊C8—44no—
130C22×C83—21no—
131C22×C83—21no—
132C22×C83#38611yescharacteristic
133C22×C83C2×#10111yescharacteristic
134C22×C83#41311yescharacteristic
135C4×C83—22no—
136C4×C83—22no—
137C4×C83—22no—
138C4×C83—21no—
139C4×C83—21no—
140C4×C83—41no—
141C4×C83—41no—
142C4×C83—41no—
143Dic83—42no—
144Dic83—81no—
145Dic83—81no—
146Dic83—81no—
147#9450—831nomaximal, Sylow
148C2×C83—21no—
149C2×C83—21no—
150C2×C83#188411yescharacteristic
151C2×C83#190111yescharacteristic
152C2×C83#191211yescharacteristic
153#2983—831no—
154#2565—831no—
155#1534—832no—
156#1467D8311yescharacteristic
157#1285—832no—
158C83#945011yescharacteristic, complemented, Sylow
159C2×#125—831no—
160C2×C4×Q8C2×D8311yescharacteristic
161#446—1664no—
162#432—832no—
163#432—1661no—
164#432C2×D8312yes—
165#431—1661no—
166#398—1661no—
167#398—1661no—
168#391—831no—
169#391—831no—
170#387—1661no—
171#387—1661no—
172#384—831no—
173#382—831no—
174C4×C4⋊C4—831no—
175#330—1664no—
176#324—21no—
177#324—21no—
178C22×Q8C4×D8311yescharacteristic
179#125—1662no—
180#125—1662no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—831no—
184C2×C4⋊C4—831no—
185C2×C4⋊C4—1661no—
186C2×C4⋊C4—1661no—
187C2×C4⋊C4—1661no—
188C2×C4⋊C4—1661no—
189C2×C4⋊C4—1661no—
190C2×C4⋊C4C4×D8311yescharacteristic
191C2×C4⋊C4C22⋊D8311yescharacteristic
192C2×C4⋊C4C22⋊D8311yescharacteristic
193C2×C42—831no—
194C2×C42—831no—
195C2×C42D33211yescharacteristic
196C2×C42D33211yescharacteristic
197C2×C42C22×D8311yescharacteristic
198C4⋊C8—22no—
199C4⋊C8—1662no—
200C4⋊C8—1662no—
201C4⋊C8—1662no—
202C22⋊C8—22no—
203C22⋊C8—1662no—
204#97—22no—
205#97—834no—
206#97—1662no—
207C4×C8—1662no—
208#95—1661no—
209#95—1661no—
210#95—1661no—
211#95—1661no—
212#95—1661no—
213#95—1661no—
214#95—1661no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—1661no—
219C22×C4—1661no—
220C22×C4—1661no—
221C22×C4—1661no—
222C22×C4(C2×D83)⋊C411yescharacteristic
223C22×C4(C2×D83)⋊C411yescharacteristic
224C22×C4(C2×D83)⋊C411yescharacteristic
225C22×C4(C2×D83)⋊C411yescharacteristic
226C22×C4C2×C4×D8311yescharacteristic
227C22×C4C2×C22⋊D8311yescharacteristic
228C22×C4C2×D33211yescharacteristic
229C2×C8—42no—
230C2×C8—1664no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—3322no—
235C4⋊C4—3322no—
236C4⋊C4—3322no—
237C4⋊C4—3321no—
238C4⋊C4—3322no—
239C4⋊C4—3321no—
240C4⋊C4—1662no—
241C4⋊C4—1662no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—3321no—
247C42—3321no—
248C42D4×D8312yes—
249C42#1305058912yes—
250C23C2×(C2×D83)⋊C411yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3321no—
266C2×C4—3321no—
267C2×C4—3321no—
268C2×C4—3321no—
269C2×C4—3321no—
270C2×C4—3321no—
271C2×C4—3322no—
272C2×C4—3321no—
273C2×C4—3321no—
274C2×C4—3321no—
275C2×C4—1662no—
276C2×C4#1458171012yes—
277C2×C4(C22⋊D83)⋊C412yes—
278C2×C4#1458176211yescharacteristic
279C2×C4#1458176412yes—
280C2×C4#1458177611yescharacteristic
281C8—82no—
282C8—3324no—
283C22—21no—
284C22—21no—
285C22#1912757811yescharacteristic
286C22C2×#1458171011yescharacteristic
287C22#1912768311yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—3322no—
297C4—6641no—
298C4—6641no—
299C4—6641no—
300C2—21no—
301C2—21no—
302C2#2490784411yescharacteristic
303C2#2490792911yescharacteristic
304C2#2490799811yescharacteristic
subgroupG/H
centerC22#19127578
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1467C2
socleC22×C83#386
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1467D83
hypocenterC83#9450
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
158. C83#9450semidirect

Maximal subgroups

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

subgroupindex
#249165482
#249126502
#249060892
#249053202
C83×#14672
#945083