Finite Group Databasebeta

← #35314080

Subgroups — #35314080

Order 21248.

426 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 87 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#24911780C211yesmaximal, characteristic
2#24905804C211yesmaximal, characteristic
3#24905412C214yesmaximal, complemented
4C83×#1459C211yesmaximal, characteristic
5C22×C4⋊Dic83C411yescharacteristic
6#19127758—21no—
7#19127640—21no—
8#19127637—21no—
9#19127599—21no—
10#19127581C412yes—
11#19127573C2212yes—
12#19127561—21no—
13#19127561C411yescharacteristic
14#19127425—21no—
15#19127425C2212yes—
16C2×C4×D4×C83C2211yescharacteristic
17C2×C22⋊C8×C83—21no—
18#324×C83—21no—
19#323×C83C2212yes—
20C23×Dic83C2×C412yes—
21C2×C4⋊Dic83—21no—
22C2×C4⋊Dic83—21no—
23C2×C4⋊Dic83—21no—
24C2×C4⋊Dic83—41no—
25C2×C4⋊Dic83—41no—
26C2×Dic83⋊C4—22no—
27C2×C22⋊Dic83—22no—
28C2×C22⋊Dic83C2×C412yes—
29C4⋊(C83⋊C8)—41no—
30C22⋊(C83⋊C8)—22no—
31#14581703—41no—
32C83⋊#95—21no—
33C83⋊#95—22no—
34C83⋊#95—22no—
35C22×D4×C83C2×C411yescharacteristic
36C23×C4×C83C2×C411yescharacteristic
37C23×C4×C83D411yescharacteristic
38C22×C8×C83—41no—
39C4×D4×C83—41no—
40C4×D4×C83—41no—
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C22⋊C4×C83D411yescharacteristic
43C2×C22⋊C4×C83C2311yescharacteristic
44C2×C42×C83D411yescharacteristic
45C22⋊C8×C83—22no—
46C22⋊C8×C83—41no—
47C22×Dic83—22no—
48C22×Dic83—22no—
49C22×Dic83—42no—
50C22×Dic83—82no—
51C2×C83⋊C8—42no—
52C4⋊Dic83—42no—
53C4⋊Dic83—42no—
54C4⋊Dic83—41no—
55C4⋊Dic83—41no—
56Dic83⋊C4—82no—
57C22⋊Dic83—24no—
58C22⋊Dic83—82no—
59C24×C83C22⋊C411yescharacteristic
60C24×C83C22×C411yescharacteristic
61C2×D4×C83—22no—
62C2×D4×C83—22no—
63C2×D4×C83—41no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83—42no—
69C22×C4×C83—42no—
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C2×D411yescharacteristic
74C22×C4×C83C2×D411yescharacteristic
75C2×C8×C83—42no—
76C2×C8×C83—82no—
77C4⋊C4×C83—41no—
78C22⋊C4×C83—41no—
79C22⋊C4×C83—41no—
80C42×C83—21no—
81C42×C83—21no—
82C23×C83—21no—
83C23×C83—21no—
84C23×C83—21no—
85C23×C83—21no—
86C23×C83—41no—
87C23×C83—41no—
88C23×C83—41no—
89C23×C83—41no—
90C23×C83#10112yes—
91C23×C83C2×C22⋊C411yescharacteristic
92C23×C83#13112yes—
93D4×C83—44no—
94C2×C4×C83—22no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—42no—
102C2×C4×C83—42no—
103C2×C4×C83—42no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—81no—
108C2×C4×C83#9911yescharacteristic
109C2×C4×C83#9911yescharacteristic
110C2×Dic83—42no—
111C2×Dic83—42no—
112C2×Dic83—42no—
113C2×Dic83—42no—
114C2×Dic83—42no—
115C2×Dic83—42no—
116C2×Dic83—84no—
117C8×C83—82no—
118C83⋊C8—82no—
119C22×C83—21no—
120C22×C83—21no—
121C22×C83—22no—
122C22×C83—22no—
123C22×C83—42no—
124C22×C83—42no—
125C22×C83—42no—
126C22×C83—41no—
127C22×C83—41no—
128C22×C83—41no—
129C22×C83—41no—
130C22×C83—81no—
131C22×C83#40811yescharacteristic
132C22×C83C2×#9911yescharacteristic
133C22×C83C2×#10111yescharacteristic
134C4×C83—21no—
135C4×C83—41no—
136C4×C83—41no—
137C4×C83—41no—
138C4×C83—41no—
139C4×C83#35212yes—
140Dic83—82no—
141Dic83—82no—
142#11576—831nomaximal, Sylow
143C2×C83—21no—
144C2×C83—21no—
145C2×C83—42no—
146C2×C83—42no—
147C2×C83#147211yescharacteristic
148C2×C83C2×#35211yescharacteristic
149C2×C83#212211yescharacteristic
150#2487—831no—
151#1466—831no—
152#1459D8311yescharacteristic
153#1326—834no—
154C83#1157611yescharacteristic, complemented, Sylow
155C2×C4×D4C2×D8311yescharacteristic
156C22×C4⋊C4—831no—
157#432—1661no—
158C2×C22⋊C8—21no—
159#400—1661no—
160#399—1661no—
161#389—1661no—
162#386—832no—
163#385—832no—
164#380—831no—
165#380—1661no—
166#324—21no—
167#323—832no—
168#323—1661no—
169#323C2×D8312yes—
170C22×D4C4×D8311yescharacteristic
171C23×C4—832no—
172C23×C4C4×D8311yescharacteristic
173C23×C4C22⋊D8311yescharacteristic
174C22×C8—41no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—3321no—
178C2×C4⋊C4—3321no—
179C2×C4⋊C4—1661no—
180C2×C4⋊C4—1661no—
181C2×C4⋊C4—1661no—
182C2×C4⋊C4—1662no—
183C2×C4⋊C4C22⋊D8311yescharacteristic
184C2×C22⋊C4—832no—
185C2×C22⋊C4—1662no—
186C2×C22⋊C4D33211yescharacteristic
187C2×C22⋊C4C22×D8311yescharacteristic
188C2×C42D33211yescharacteristic
189C4⋊C8—3321no—
190C22⋊C8—22no—
191C22⋊C8—41no—
192C22⋊C8—1662no—
193#97—3321no—
194#95—1661no—
195#95—1662no—
196#95—1662no—
197C24(C2×D83)⋊C411yescharacteristic
198C24C2×C4×D8311yescharacteristic
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—3322no—
209C22×C4—6642no—
210C22×C4—1662no—
211C22×C4—1662no—
212C22×C4(C2×D83)⋊C411yescharacteristic
213C22×C4(C2×D83)⋊C411yescharacteristic
214C22×C4(C2×D83)⋊C411yescharacteristic
215C22×C4C2×C22⋊D8311yescharacteristic
216C22×C4C2×D33211yescharacteristic
217C2×C8—42no—
218C2×C8—82no—
219C2×C8—3322no—
220C4⋊C4—41no—
221C4⋊C4—3322no—
222C4⋊C4—3322no—
223C4⋊C4—3321no—
224C4⋊C4—3321no—
225C4⋊C4—6642no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—6642no—
229C22⋊C4—1664no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23#1458171012yes—
241C23C2×(C2×D83)⋊C411yescharacteristic
242C23#1458179812yes—
243D4—44no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—3322no—
259C2×C4—3322no—
260C2×C4—3322no—
261C2×C4—3322no—
262C2×C4—3322no—
263C2×C4—3322no—
264C2×C4—6644no—
265C2×C4#1458170611yescharacteristic
266C2×C4#1458170611yescharacteristic
267C8—82no—
268C8—6642no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22#1912766711yescharacteristic
282C22C2×#1458170611yescharacteristic
283C22C2×#1458171011yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—6642no—
290C4—6642no—
291C4#1912749012yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—42no—
296C2#2490582611yescharacteristic
297C2C2×#1912749011yescharacteristic
298C2#2490911411yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC24×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1459C2
socleC22×C83C2×#99
prime radicalC22×D4×C83C2×C4
cosocleC2×C22⋊C4×C83C23
hypercenter#1459D83
hypocenterC83#11576
LCSG ▷ C24×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #24905412C2semidirect
154. C83#11576semidirect

Maximal subgroups

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

subgroupindex
#249117802
#249058042
#249054122
C83×#14592
#1157683