Finite Group Databasebeta

← #35404379

Subgroups — #35404379

Order 21248.

1382 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 251 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
1C2×#19128175C211yesmaximal, characteristic
2#24916098C212yesmaximal, complemented
3#24907546C211yesmaximal, characteristic, complemented
4#24907454C214yesmaximal, complemented
5#24907383C212yesmaximal
6#24907254C214yesmaximal, complemented
7C83×#1822C211yesmaximal, characteristic, complemented
8C23×D332C2211yescharacteristic
9#19128175—28no—
10C2×C4×D332C414yes—
11C2×#14581754C2212yes—
12C2×#14581754C2212yes—
13C2×#14581751C2211yescharacteristic
14C2×C22⋊C4×D83C414yes—
15#19127759—28no—
16#19127724C2214yescomplemented
17C2×#14581708C2218yes—
18#19127665C2212yes—
19M16×Dic83C2214yescomplemented
20#19127470C2214yescomplemented
21C2×#117×C83C2211yescharacteristic
22#407×C83C2212yes—
23#343×C83C2214yescomplemented
24C24×D83C2×C412yes—
25C22×D332—28no—
26C22×D332—24no—
27C22×D332C2×C412yes—
28C22×D332C2312yes—
29C22×C4×D83C2×C414yes—
30C22×C4×D83C2×C414yes—
31C2×#13050574C2314yes—
32C4×D332—216no—
33#14581754—28no—
34#14581754—28no—
35#14581751D418yes—
36C2×C4⋊Dic83C2×C412yes—
37C2×C22⋊Dic83C2×C412yes—
38C2×(C2×D83)⋊C4C2×C414yes—
39C2×(C2×D83)⋊C4C2×C414yes—
40C22⋊C4×D83—216no—
41C2×C4×Dic83C2311yescharacteristic
42C2×C4×Dic83C2311yescharacteristic
43Dic83⋊C8—28no—
44#14581708—216no—
45C22⋊(C83⋊C8)—24no—
46#14581702—24no—
47C8×Dic83—24no—
48C23×C4×C83C2311yescharacteristic
49C2×M16×C83C2314yes—
50#117×C83—24no—
51C2×C4⋊C4×C83C2312yes—
52C2×C22⋊C4×C83C2×C412yes—
53C2×C42×C83C2×C412yes—
54C22⋊C8×C83—24no—
55C23×D83—24no—
56C23×D83—28no—
57C23×D83—84no—
58C23×D83C22×C414yes—
59C2×D332—232no—
60C2×D332—28no—
61C2×D332—24no—
62C2×D332—24no—
63C2×D332—24no—
64C2×D332#4118yes—
65C22×Dic83C22×C412yes—
66C22×Dic83C22×C412yes—
67C2×C4×D83—28no—
68C2×C4×D83—28no—
69C2×C4×D83—84no—
70C2×C4×D83—84no—
71#13050574—28no—
72C2×C83⋊C8—24no—
73C4⋊Dic83C22⋊C418yes—
74C22⋊Dic83C22⋊C418yes—
75(C2×D83)⋊C4—28no—
76(C2×D83)⋊C4—28no—
77C4×Dic83C2×D414yes—
78C4×Dic83C2×D414yes—
79C24×C83C22×C411yescharacteristic
80C22×C4×C83—24no—
81C22×C4×C83C22×C411yescharacteristic
82C22×C4×C83C22×C414yes—
83C22×C4×C83C2×D414yes—
84C22×C4×C83C2411yescharacteristic
85M16×C83—28no—
86C2×C8×C83—24no—
87C4⋊C4×C83—24no—
88C22⋊C4×C83—24no—
89C42×C83—24no—
90C23×C83—22no—
91C23×C83—42no—
92C23×C83C2×C22⋊C412yes—
93C23×C83C23×C411yescharacteristic
94C22×D83—24no—
95C22×D83—24no—
96C22×D83—216no—
97C22×D83—44no—
98C22×D83—44no—
99C22×D83—88no—
100C22×D83—816no—
101C22×D83#11718yes—
102C2×C4×C83—22no—
103C2×C4×C83—28no—
104C2×C4×C83—24no—
105C2×C4×C83—44no—
106C2×C4×C83C2×C22⋊C412yes—
107C2×C4×C83C22×D412yes—
108C2×C4×C83C2×#4114yes—
109C2×Dic83—42no—
110C2×Dic83—42no—
111C2×Dic83C2×C22⋊C414yes—
112C2×Dic83C2×C22⋊C414yes—
113D332—216no—
114D332—216no—
115C4×D83—88no—
116C4×D83—88no—
117C8×C83—44no—
118C83⋊C8—44no—
119C22×C83—22no—
120C22×C83—24no—
121C22×C83—22no—
122C22×C83—44no—
123C22×C83C22×C22⋊C411yescharacteristic
124C22×C83C2×#11712yes—
125C2×D83—28no—
126C2×D83—48no—
127C2×D83—44no—
128C2×D83—44no—
129C2×D83—48no—
130C2×D83—816no—
131C4×C83—22no—
132C4×C83—44no—
133C4×C83#52514yes—
134Dic83—24no—
135Dic83—24no—
136#20729—831nomaximal, Sylow
137C2×C83—22no—
138C2×C83—42no—
139C2×C83#228011yescharacteristic
140C2×C83#288812yes—
141D83—48no—
142C2×#518—831no—
143#2921—832no—
144#1822—831no—
145#1822D8311yescharacteristic, complemented
146#1800—834no—
147#1783—832no—
148C4×#100—834no—
149C83#2072911yescharacteristic, complemented, Sylow
150C23×D4—831no—
151#518—1668no—
152C2×C4×D4—832no—
153C2×C4×D4—832no—
154C2×C4×D4—834no—
155C2×#117—831no—
156C2×#117C2×D8311yescharacteristic
157C22×C22⋊C4—834no—
158#433—1668no—
159#423—834no—
160C2×#100—838no—
161#407—832no—
162#407C2×D8312yes—
163C4×M16—834no—
164#343—834no—
165#343C2×D8314yescomplemented
166C25—832no—
167C22×D4—832no—
168C22×D4—832no—
169C22×D4—1668no—
170C22×D4—1664no—
171C23×C4—834no—
172C23×C4—834no—
173C23×C4C22×D8311yescharacteristic
174C2×M16—834no—
175C2×M16C22×D8314yes—
176C4×D4—16616no—
177C4×D4—1668no—
178C4×D4—1668no—
179#117—24no—
180#117—838no—
181C2×C4⋊C4—832no—
182C2×C4⋊C4C22×D8312yes—
183C2×C22⋊C4—832no—
184C2×C22⋊C4—834no—
185C2×C22⋊C4—834no—
186C2×C22⋊C4—16616no—
187C2×C22⋊C4C4×D8312yes—
188C2×C42—831no—
189C2×C42—831no—
190C2×C42C4×D8312yes—
191C4⋊C8—1668no—
192#100—16616no—
193C22⋊C8—24no—
194C22⋊C8—1664no—
195#97—1664no—
196C4×C8—1664no—
197C24—834no—
198C24—6644no—
199C24—1668no—
200C24—1664no—
201C24C2×C4×D8311yescharacteristic
202C2×D4—838no—
203C2×D4—1668no—
204C2×D4—16632no—
205C2×D4—1664no—
206C2×D4—1664no—
207C2×D4—1664no—
208C22×C4—24no—
209C22×C4—832no—
210C22×C4—832no—
211C22×C4—6644no—
212C22×C4—6644no—
213C22×C4—1668no—
214C22×C4—1668no—
215C22×C4C2×C4×D8311yescharacteristic
216C22×C4C2×C4×D8314yes—
217C22×C4D4×D8314yes—
218C22×C4C23×D8311yescharacteristic
219M16—28no—
220M16—1668no—
221C2×C8—24no—
222C2×C8—1664no—
223C4⋊C4—24no—
224C4⋊C4—838no—
225C22⋊C4—24no—
226C22⋊C4—838no—
227C22⋊C4—1668no—
228C22⋊C4—1668no—
229C42—24no—
230C42—834no—
231C42—834no—
232C23—22no—
233C23—42no—
234C23—3324no—
235C23—3324no—
236C23—838no—
237C23—6648no—
238C23—66416no—
239C23—16616no—
240C23—1664no—
241C23—1664no—
242C23C22⋊C4×D8312yes—
243C23C22×C4×D8311yescharacteristic
244D4—16616no—
245D4—16616no—
246C2×C4—22no—
247C2×C4—28no—
248C2×C4—24no—
249C2×C4—44no—
250C2×C4—3322no—
251C2×C4—3322no—
252C2×C4—834no—
253C2×C4—834no—
254C2×C4—6648no—
255C2×C4—6648no—
256C2×C4C22⋊C4×D8312yes—
257C2×C4C2×D4×D8312yes—
258C2×C4#41×D8314yes—
259C8—44no—
260C8—3324no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—44no—
265C22—3328no—
266C22—3328no—
267C22—3324no—
268C22—3324no—
269C22—66416no—
270C22—1668no—
271C22C2×C22⋊C4×D8311yescharacteristic
272C22#117×D8312yes—
273C4—22no—
274C4—44no—
275C4—1664no—
276C4—1664no—
277C4#1912820914yes—
278C2—22no—
279C2—42no—
280C2—3328no—
281C2#2490984311yescharacteristic
282C2#2491594012yes—
subgroupG/H
centerC22C2×C22⋊C4×D83
commutatorC23×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1822C2
socleC22×C83C22×C22⋊C4
prime radicalC23×D332C22
cosocleC22×C4×C83C24
hypercenter#1822D83
hypocenterC83#20729
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. #24916098C2semidirect
3. #24907546C2semidirect
4. #24907454C2semidirect
6. #24907254C2semidirect
7. C83×#1822C2semidirect
16. #19127724C22semidirect
19. M16×Dic83C22semidirect
20. #19127470C22semidirect
23. #343×C83C22semidirect
145. #1822D83semidirect
149. C83#20729semidirect
165. #343C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191281752
#249160982
#249075462
#249074542
#249073832
#249072542
C83×#18222
#2072983