Finite Group Databasebeta

← #35313498

Subgroups — #35313498

Order 21248.

526 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 93 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#24910048C211yesmaximal, characteristic
2#24905774C212yesmaximal
3#24905393C211yesmaximal, characteristic
4#24905392C212yesmaximal
5C83×#1317C211yesmaximal, characteristic
6C23×Dic166C411yescharacteristic
7C2×#14581748C411yescharacteristic
8C2×#14581748C2211yescharacteristic
9#19127751—22no—
10#19127605—22no—
11#19127605—22no—
12#19127564C411yescharacteristic
13#19127562C411yescharacteristic
14#19127562C2211yescharacteristic
15#19127426—22no—
16#19127425C2212yes—
17#381×C83C2211yescharacteristic
18#323×C83C2212yes—
19C22×Dic166—21no—
20C22×Dic166—21no—
21C22×Dic166—22no—
22C22×Dic166—42no—
23C22×Dic166—42no—
24C22×Dic166C814yescomplemented
25C23×Dic83C2×C411yescharacteristic
26C23×Dic83C2×C411yescharacteristic
27#14581748—42no—
28#14581748—42no—
29C2×Dic83⋊C4—21no—
30C2×Dic83⋊C4D412yes—
31C2×C22⋊Dic83C2×C411yescharacteristic
32C2×C22⋊Dic83C2×C411yescharacteristic
33C2×C4×Dic83—21no—
34C2×C4×Dic83D412yes—
35Dic83⋊C8—42no—
36C22⋊(C83⋊C8)—22no—
37C8×Dic83—42no—
38C83⋊#95—22no—
39C83⋊#95—22no—
40C83⋊#95—22no—
41C23×C4×C83C2×C411yescharacteristic
42C2×C22⋊C4×C83C2×C411yescharacteristic
43C2×C22⋊C4×C83C2311yescharacteristic
44C22⋊C8×C83—22no—
45#95×C83—22no—
46C2×Dic166—24no—
47C2×Dic166—24no—
48C2×Dic166—42no—
49C2×Dic166—42no—
50C2×Dic166—48no—
51C2×Dic166—42no—
52C2×Dic166—42no—
53C2×Dic166—48no—
54C22×Dic83—22no—
55C22×Dic83—22no—
56C22×Dic83—21no—
57C22×Dic83—21no—
58C22×Dic83—21no—
59C22×Dic83—41no—
60C22×Dic83—41no—
61C22×Dic83C22⋊C411yescharacteristic
62C22×Dic83C22⋊C412yes—
63C22×Dic83C22⋊C411yescharacteristic
64C22×Dic83C2×C812yes—
65C22×Dic83C2×C812yes—
66C22×Dic83M1612yes—
67C2×C83⋊C8—42no—
68Dic83⋊C4—42no—
69Dic83⋊C4—42no—
70C22⋊Dic83—41no—
71C22⋊Dic83—41no—
72C4×Dic83—22no—
73C4×Dic83—22no—
74C4×Dic83—42no—
75C24×C83C22×C411yescharacteristic
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—41no—
80C22×C4×C83—41no—
81C22×C4×C83C2×C812yes—
82C22×C4×C83C2×D412yes—
83C2×C8×C83—42no—
84C22⋊C4×C83—41no—
85C22⋊C4×C83—41no—
86C23×C83—21no—
87C23×C83—21no—
88C23×C83—42no—
89C23×C83C2×C22⋊C411yescharacteristic
90C23×C83C22×C811yescharacteristic
91C23×C83C2×M1611yescharacteristic
92C2×C4×C83—22no—
93C2×C4×C83—22no—
94C2×C4×C83—42no—
95C2×C4×C83—41no—
96C2×C4×C83—41no—
97C2×C4×C83—42no—
98C2×C4×C83—42no—
99C2×C4×C83—42no—
100C2×C4×C83—41no—
101C2×Dic83—21no—
102C2×Dic83—21no—
103C2×Dic83—24no—
104C2×Dic83—24no—
105C2×Dic83—22no—
106C2×Dic83—22no—
107C2×Dic83—42no—
108C2×Dic83—41no—
109C2×Dic83—41no—
110C2×Dic83—42no—
111C2×Dic83—42no—
112C2×Dic83—42no—
113C2×Dic83—41no—
114C2×Dic83C22⋊C812yes—
115C2×Dic83C22⋊C812yes—
116C2×Dic83#9912yes—
117C2×Dic83#10012yes—
118Dic166—48no—
119Dic166—48no—
120C8×C83—82no—
121C83⋊C8—82no—
122C22×C83—22no—
123C22×C83—21no—
124C22×C83—21no—
125C22×C83—41no—
126C22×C83—41no—
127C22×C83—42no—
128C22×C83—42no—
129C22×C83C2×C22⋊C811yescharacteristic
130C22×C83C2×#9911yescharacteristic
131C22×C83C2×#10011yescharacteristic
132C4×C83—42no—
133C4×C83—42no—
134C4×C83—81no—
135Dic83—22no—
136Dic83—42no—
137Dic83—42no—
138Dic83—81no—
139Dic83#32314yes—
140#11428—831nomaximal, Sylow
141C2×C83—21no—
142C2×C83—21no—
143C2×C83—41no—
144C2×C83—41no—
145C2×C83C2×#32311yescharacteristic
146C2×C83#212312yes—
147#2310—831no—
148#1458—832no—
149#1317—831no—
150#1317—832no—
151#1317D8311yescharacteristic
152C83#1142811yescharacteristic, complemented, Sylow
153C23×Q8—831no—
154C2×#117—831no—
155C2×#117—831no—
156#431—1662no—
157#391—1662no—
158#391—1662no—
159#381—831no—
160#381—831no—
161#381—831no—
162#381C2×D8311yescharacteristic
163#324—1662no—
164#323—832no—
165#323C2×D8312yes—
166C22×Q8—3322no—
167C22×Q8—3322no—
168C22×Q8—834no—
169C22×Q8—1662no—
170C22×Q8—1661no—
171C22×Q8—1661no—
172C23×C4—831no—
173C23×C4—831no—
174C23×C4C4×D8311yescharacteristic
175#117—3322no—
176#117—3322no—
177C2×C4⋊C4—832no—
178C2×C4⋊C4—1661no—
179C2×C22⋊C4—831no—
180C2×C22⋊C4—831no—
181C2×C22⋊C4C4×D8311yescharacteristic
182C2×C22⋊C4C22×D8311yescharacteristic
183C2×C42—832no—
184C2×C42—1661no—
185C4⋊C8—3322no—
186C22⋊C8—22no—
187C22⋊C8—1662no—
188C4×C8—3322no—
189#95—22no—
190#95—1662no—
191#95—1662no—
192#95—1662no—
193C24C2×C4×D8311yescharacteristic
194C2×Q8—3322no—
195C2×Q8—3322no—
196C2×Q8—3328no—
197C2×Q8—3328no—
198C2×Q8—3322no—
199C2×Q8—3322no—
200C2×Q8—1664no—
201C2×Q8—1664no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—3321no—
208C22×C4—3321no—
209C22×C4—832no—
210C22×C4—832no—
211C22×C4—831no—
212C22×C4—832no—
213C22×C4—832no—
214C22×C4—831no—
215C22×C4—1661no—
216C22×C4—1661no—
217C22×C4—1661no—
218C22×C4—1662no—
219C22×C4—1662no—
220C22×C4C8×D8312yes—
221C22×C4D4×D8312yes—
222C2×C8—42no—
223C2×C8—3322no—
224C4⋊C4—3322no—
225C4⋊C4—3322no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—3321no—
229C22⋊C4—3321no—
230C42—3322no—
231C42—1662no—
232C42—1662no—
233C23—21no—
234C23—21no—
235C23—42no—
236C23C22⋊C4×D8311yescharacteristic
237C23C2×C8×D8311yescharacteristic
238C23M16×D8311yescharacteristic
239Q8—3328no—
240Q8—3328no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—3322no—
251C2×C4—3321no—
252C2×C4—3321no—
253C2×C4—3322no—
254C2×C4—3322no—
255C2×C4—3322no—
256C2×C4—3321no—
257C2×C4—832no—
258C2×C4—832no—
259C2×C4—832no—
260C2×C4—832no—
261C2×C4—1662no—
262C2×C4—1662no—
263C2×C4—1664no—
264C2×C4—1664no—
265C2×C4—1661no—
266C2×C4—1661no—
267C8—82no—
268C8—6642no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22C22⋊C8×D8311yescharacteristic
277C22#99×D8311yescharacteristic
278C22#100×D8311yescharacteristic
279C4—42no—
280C4—42no—
281C4—81no—
282C4—3322no—
283C4—3322no—
284C4—834no—
285C4—6641no—
286C4—1662no—
287C2—21no—
288C2—21no—
289C2—41no—
290C2—41no—
291C2#323×D8311yescharacteristic
292C2#2490911512yes—
subgroupG/H
centerC22#99×D83
commutatorC23×C83C22×C8
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1317C2
socleC22×C83C2×#99
prime radicalC24×C83C22×C4
cosocleC2×C22⋊C4×C83C23
hypercenter#1317D83
hypocenterC83#11428
LCSG ▷ C23×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
24. C22×Dic166C8semidirect
152. C83#11428semidirect

Maximal subgroups

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

subgroupindex
#249100482
#249057742
#249053932
#249053922
C83×#13172
#1142883