Finite Group Databasebeta

← #35315885

Subgroups — #35315885

Order 21248.

350 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 85 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#24918043C211yesmaximal, characteristic
2C4⋊C16×D83C211yesmaximal, characteristic, complemented
3#24906225C211yesmaximal, characteristic, complemented
4#24905521C211yesmaximal, characteristic, complemented
5#24905510C211yesmaximal, characteristic, complemented
6#24905508C211yesmaximal, characteristic, complemented
7C83×#1365C211yesmaximal, characteristic, complemented
8#19128252—21no—
9C2×C16×D83—21no—
10#19128078C2211yescharacteristic
11#19128049—21no—
12#19127938—21no—
13#19127938C412yes—
14#19127783—21no—
15#19127783C412yes—
16#19127757—21no—
17C4×C8×D83C2211yescharacteristic
18C4⋊(C83⋊C16)C2211yescharacteristic
19Dic83⋊C16—21no—
20#19127454C2211yescharacteristic
21#19127451—21no—
22#500×C83C2211yescharacteristic
23C4⋊C16×C83C2211yescharacteristic
24#335×C83C2211yescharacteristic
25C2×#13050591—41no—
26C2×D664—21no—
27C2×D664C2×C412yes—
28C2×C8×D83C2×C411yescharacteristic
29C2×C8×D83D411yescharacteristic
30#14581789—21no—
31#14581781—41no—
32#14581767—22no—
33#14581767—41no—
34#14581754—22no—
35#14581754—41no—
36C42×D83D411yescharacteristic
37C2×C83⋊C16—21no—
38C16×D83—42no—
39C4⋊(C83⋊C8)—21no—
40#14581712—22no—
41#14581712—22no—
42(C2×D83)⋊C8—41no—
43#14581702—41no—
44C4×C83⋊C8D411yescharacteristic
45C8×Dic83C2×C411yescharacteristic
46C8×Dic83D411yescharacteristic
47C4⋊Q8×C83—21no—
48C2×C16×C83—21no—
49#107×C83—21no—
50#107×C83C2×C412yes—
51C4⋊C8×C83—21no—
52C4×C8×C83C2311yescharacteristic
53#13050591—84no—
54C2×D332—22no—
55C2×D332—42no—
56C2×D332—41no—
57C2×D332—41no—
58C2×C4×D83—42no—
59C2×C4×D83C22⋊C411yescharacteristic
60C2×C4×D83D811yescharacteristic
61C2×C4×D83SD1611yescharacteristic
62D664—42no—
63D664—41no—
64D664—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8C22⋊C411yescharacteristic
67C2×C83⋊C8C22⋊C411yescharacteristic
68C8×D83—21no—
69C8×D83—21no—
70C8×D83—41no—
71(C2×D83)⋊C4—42no—
72(C2×D83)⋊C4—42no—
73C4×Dic83C22⋊C411yescharacteristic
74C4×Dic83D811yescharacteristic
75C4×Dic83SD1611yescharacteristic
76C83⋊C16—41no—
77C2×Q8×C83—41no—
78C2×C8×C83—41no—
79C2×C8×C83C22×C411yescharacteristic
80C2×C8×C83C2×D411yescharacteristic
81C4⋊C4×C83—22no—
82C4⋊C4×C83—41no—
83C42×C83C2×D411yescharacteristic
84C16×C83—41no—
85C22×D83—42no—
86C22×D83#10211yescharacteristic
87Q8×C83—82no—
88C2×C4×C83—42no—
89C2×C4×C83C2×C22⋊C411yescharacteristic
90C2×C4×C83C2×D811yescharacteristic
91C2×C4×C83C2×SD1611yescharacteristic
92C2×Dic83#10211yescharacteristic
93C2×Dic83#10211yescharacteristic
94C2×Dic83#10211yescharacteristic
95D332—42no—
96D332—42no—
97D332—82no—
98D332—84no—
99D332—81no—
100D332—81no—
101C4×D83—22no—
102C4×D83—21no—
103C4×D83—21no—
104C4×D83—21no—
105C4×D83—21no—
106C4×D83—84no—
107C8×C83—21no—
108C8×C83—81no—
109C8×C83AGL(1,ℤ/8)11yescharacteristic
110C8×C83#13711yescharacteristic
111C83⋊C8—21no—
112C83⋊C8—21no—
113C83⋊C8—81no—
114C22×C83C2×#10211yescharacteristic
115C2×D83—21no—
116C2×D83—21no—
117C2×D83—82no—
118C2×D83—82no—
119C2×D83—82no—
120C2×D83#36112yes—
121C4×C83—21no—
122C4×C83—82no—
123C4×C83#41311yescharacteristic
124C4×C83#41711yescharacteristic
125C4×C83#50811yescharacteristic
126C4×C83#50811yescharacteristic
127Dic83—21no—
128Dic83—21no—
129Dic83—21no—
130#11982—831nomaximal, Sylow
131C2×C83#154711yescharacteristic
132C2×C83#213811yescharacteristic
133C2×C83C2×#36111yescharacteristic
134D83—22no—
135D83—162no—
136#3169—831no—
137C2×C4⋊C16—831no—
138#1568—831no—
139#1365—831no—
140#1365D8311yescharacteristic, complemented
141#1361—831no—
142#1361—831no—
143C83#1198211yescharacteristic, complemented, Sylow
144#532—1661no—
145C22×C16—1661no—
146#500C2×D8311yescharacteristic
147#493—831no—
148#486—1661no—
149#466—832no—
150#466—1661no—
151C4×D8—832no—
152C4×D8—1661no—
153#432—1661no—
154C2×C4×C8—831no—
155C4⋊C16—831no—
156C4⋊C16—1661no—
157C4⋊C16C2×D8311yescharacteristic
158#335—831no—
159#335C2×D8311yescharacteristic
160#334—1661no—
161C2×#41—3321no—
162C2×D8—832no—
163C2×D8—1661no—
164C22×C8—831no—
165C22×C8—831no—
166C4⋊Q8—21no—
167#127—1661no—
168#124—3321no—
169#121—3321no—
170#121—1662no—
171C4×D4—3321no—
172C4×D4—1662no—
173C2×C42—831no—
174C2×C16—21no—
175C2×C16—3322no—
176C2×C16—1661no—
177#107—21no—
178#107C4×D8312yes—
179C4⋊C8—21no—
180C4⋊C8—1661no—
181#102—1662no—
182#102—1662no—
183C22⋊C8—3321no—
184#97—3321no—
185C4×C8—831no—
186C4×C8—831no—
187C4×C8—831no—
188C4×C8C22×D8311yescharacteristic
189#41—6644no—
190C2×Q8—41no—
191C2×D4—3322no—
192C2×D4—3321no—
193C2×D4—3321no—
194C2×D4—1662no—
195C22×C4—3322no—
196C22×C4—831no—
197C22×C4—831no—
198C22×C4—831no—
199D8—3322no—
200D8—3321no—
201D8—3321no—
202C2×C8—41no—
203C2×C8—3321no—
204C2×C8—3321no—
205C2×C8—831no—
206C2×C8—831no—
207C2×C8—1661no—
208C2×C8—1661no—
209C2×C8C2×C4×D8311yescharacteristic
210C2×C8D4×D8311yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—41no—
213C22⋊C4—3322no—
214C22⋊C4—3322no—
215C42—831no—
216C42—831no—
217C42—831no—
218C42D4×D8311yescharacteristic
219C16—41no—
220C16—3321no—
221C23—3322no—
222C23—831no—
223Q8—82no—
224D4—3322no—
225D4—3322no—
226D4—6642no—
227D4—6644no—
228D4—6641no—
229D4—6641no—
230C2×C4—42no—
231C2×C4—831no—
232C2×C4—831no—
233C2×C4—831no—
234C2×C4—6644no—
235C2×C4—1662no—
236C2×C4—1661no—
237C2×C4—1661no—
238C2×C4—1661no—
239C2×C4—1661no—
240C2×C4C22⋊C4×D8311yescharacteristic
241C2×C4D8×D8311yescharacteristic
242C2×C4SD16×D8311yescharacteristic
243C8—21no—
244C8—81no—
245C8—6641no—
246C8—1661no—
247C8—1661no—
248C8#1458181911yescharacteristic
249C8#1458182411yescharacteristic
250C22—832no—
251C22—6642no—
252C22—6642no—
253C22—6642no—
254C22—1661no—
255C22—1661no—
256C22#102×D8311yescharacteristic
257C4—21no—
258C4—82no—
259C4—1661no—
260C4—1661no—
261C4—1661no—
262C4#1912768411yescharacteristic
263C4#1912770111yescharacteristic
264C4#1912813211yescharacteristic
265C4#1912813411yescharacteristic
266C2—13282no—
267C2—1662no—
268C2#2490613911yescharacteristic
269C2#2490916911yescharacteristic
270C2#361×D8311yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1365C2
socleC22×C83C2×#102
prime radical#24918043C2
cosocleC4×C8×C83C23
hypercenter#1365D83
hypocenterC83#11982
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
2. C4⋊C16×D83C2semidirect
3. #24906225C2semidirect
4. #24905521C2semidirect
5. #24905510C2semidirect
6. #24905508C2semidirect
7. C83×#1365C2semidirect
140. #1365D83semidirect
143. C83#11982semidirect

Maximal subgroups

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

subgroupindex
#249180432
C4⋊C16×D832
#249062252
#249055212
#249055102
#249055082
C83×#13652
#1198283