Finite Group Databasebeta

← #35315880

Subgroups — #35315880

Order 21248.

358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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#24906220C211yesmaximal, characteristic, complemented
4#24905518C211yesmaximal, characteristic, complemented
5#24905510C211yesmaximal, characteristic, complemented
6#24905508C211yesmaximal, characteristic, complemented
7C83×#1364C211yesmaximal, 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#19127723—21no—
17C4×C8×D83C2211yescharacteristic
18C4⋊(C83⋊C16)C2211yescharacteristic
19Dic83⋊C16—21no—
20#19127454C2211yescharacteristic
21#19127453—21no—
22#500×C83C2211yescharacteristic
23C4⋊C16×C83C2211yescharacteristic
24#335×C83C2211yescharacteristic
25C2×#13050591—41no—
26C2×D664—21no—
27C2×D664C2×C412yes—
28C2×#13050573—41no—
29C2×C8×D83C2×C411yescharacteristic
30C2×C8×D83D411yescharacteristic
31#14581789—21no—
32#14581781—41no—
33#14581767—22no—
34#14581767—41no—
35#14581754—22no—
36#14581754—41no—
37C42×D83D411yescharacteristic
38C2×C83⋊C16—21no—
39C16×D83—42no—
40C4⋊(C83⋊C8)—21no—
41Dic83⋊C8—41no—
42#14581712—22no—
43#14581712—22no—
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—82no—
54#13050591—82no—
55C2×D332—22no—
56C2×D332—42no—
57C2×D332—41no—
58C2×D332—41no—
59C2×C4×D83—42no—
60C2×C4×D83C22⋊C411yescharacteristic
61C2×C4×D83D811yescharacteristic
62C2×C4×D83SD1611yescharacteristic
63D664—42no—
64D664—41no—
65D664—41no—
66#13050573—82no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8C22⋊C411yescharacteristic
69C2×C83⋊C8C22⋊C411yescharacteristic
70C8×D83—21no—
71C8×D83—21no—
72C8×D83—41no—
73(C2×D83)⋊C4—42no—
74(C2×D83)⋊C4—42no—
75C4×Dic83C22⋊C411yescharacteristic
76C4×Dic83D811yescharacteristic
77C4×Dic83SD1611yescharacteristic
78C83⋊C16—41no—
79C2×Q8×C83—41no—
80C2×C8×C83—41no—
81C2×C8×C83C22×C411yescharacteristic
82C2×C8×C83C2×D411yescharacteristic
83C4⋊C4×C83—22no—
84C4⋊C4×C83—41no—
85C42×C83C2×D411yescharacteristic
86C16×C83—41no—
87C22×D83—42no—
88C22×D83#10211yescharacteristic
89Q8×C83—81no—
90Q8×C83—81no—
91C2×C4×C83—42no—
92C2×C4×C83C2×C22⋊C411yescharacteristic
93C2×C4×C83C2×D811yescharacteristic
94C2×C4×C83C2×SD1611yescharacteristic
95C2×Dic83#10211yescharacteristic
96C2×Dic83#10211yescharacteristic
97C2×Dic83#10211yescharacteristic
98D332—42no—
99D332—42no—
100D332—82no—
101D332—84no—
102D332—81no—
103D332—81no—
104C4×D83—21no—
105C4×D83—21no—
106C4×D83—41no—
107C4×D83—84no—
108C4×D83D1612yes—
109C4×D83SD3212yes—
110C8×C83—21no—
111C8×C83—81no—
112C8×C83AGL(1,ℤ/8)11yescharacteristic
113C8×C83#13711yescharacteristic
114C83⋊C8—21no—
115C83⋊C8—21no—
116C83⋊C8—81no—
117C22×C83C2×#10211yescharacteristic
118C2×D83—21no—
119C2×D83—21no—
120C2×D83—82no—
121C2×D83—82no—
122C2×D83—82no—
123C2×D83#35712yes—
124C4×C83—21no—
125C4×C83—82no—
126C4×C83#41311yescharacteristic
127C4×C83#41711yescharacteristic
128C4×C83C2×D1611yescharacteristic
129C4×C83C2×SD3211yescharacteristic
130Dic83—21no—
131Dic83—21no—
132Dic83#35712yes—
133#11981—831nomaximal, Sylow
134C2×C83#154711yescharacteristic
135C2×C83C2×#35711yescharacteristic
136C2×C83#214811yescharacteristic
137D83—22no—
138D83—162no—
139#3169—831no—
140C2×C4⋊C16—831no—
141#1567—831no—
142#1364—831no—
143#1364D8311yescharacteristic, complemented
144#1361—831no—
145#1361—831no—
146C83#1198111yescharacteristic, complemented, Sylow
147#532—1661no—
148C22×C16—1661no—
149#500C2×D8311yescharacteristic
150#493—831no—
151#486—1661no—
152#466—832no—
153#466—1661no—
154C4×D8—832no—
155C4×D8—1661no—
156#423—1661no—
157C2×C4×C8—831no—
158C4⋊C16—831no—
159C4⋊C16—1661no—
160C4⋊C16C2×D8311yescharacteristic
161#335—831no—
162#335—1661no—
163#335C2×D8311yescharacteristic
164C2×#41—3321no—
165C2×D8—832no—
166C2×D8—1661no—
167C2×M16—3321no—
168C22×C8—831no—
169C22×C8—831no—
170C4⋊Q8—21no—
171#127—1661no—
172#124—3321no—
173#121—3321no—
174#121—1662no—
175C4×D4—3321no—
176C4×D4—1662no—
177C2×C42—831no—
178C2×C16—21no—
179C2×C16—3322no—
180C2×C16—1661no—
181#107—21no—
182#107C4×D8312yes—
183C4⋊C8—21no—
184C4⋊C8—3321no—
185C4⋊C8—1661no—
186#102—1662no—
187#102—1662no—
188C4×C8—831no—
189C4×C8—831no—
190C4×C8—831no—
191C4×C8C22×D8311yescharacteristic
192#41—6642no—
193#41—6642no—
194C2×Q8—41no—
195C2×D4—3322no—
196C2×D4—3321no—
197C2×D4—3321no—
198C2×D4—1662no—
199C22×C4—3322no—
200C22×C4—831no—
201C22×C4—831no—
202C22×C4—831no—
203D8—3322no—
204D8—3321no—
205D8—3321no—
206M16—6642no—
207C2×C8—41no—
208C2×C8—3321no—
209C2×C8—3321no—
210C2×C8—831no—
211C2×C8—831no—
212C2×C8—1661no—
213C2×C8—1661no—
214C2×C8C2×C4×D8311yescharacteristic
215C2×C8D4×D8311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—41no—
218C22⋊C4—3322no—
219C22⋊C4—3322no—
220C42—831no—
221C42—831no—
222C42—831no—
223C42D4×D8311yescharacteristic
224C16—41no—
225C16—3321no—
226C23—3322no—
227C23—831no—
228Q8—81no—
229Q8—81no—
230D4—3322no—
231D4—3322no—
232D4—6642no—
233D4—6644no—
234D4—6641no—
235D4—6641no—
236C2×C4—42no—
237C2×C4—3321no—
238C2×C4—831no—
239C2×C4—832no—
240C2×C4—832no—
241C2×C4—831no—
242C2×C4—831no—
243C2×C4—6644no—
244C2×C4—1661no—
245C2×C4—1661no—
246C2×C4C22⋊C4×D8311yescharacteristic
247C2×C4D8×D8311yescharacteristic
248C2×C4SD16×D8311yescharacteristic
249C8—21no—
250C8—81no—
251C8—6641no—
252C8—1661no—
253C8—1661no—
254C8#1458181911yescharacteristic
255C8#1458182411yescharacteristic
256C22—832no—
257C22—6642no—
258C22—6642no—
259C22—6642no—
260C22—1661no—
261C22—1661no—
262C22#102×D8311yescharacteristic
263C4—21no—
264C4—82no—
265C4—832no—
266C4—1661no—
267C4—1661no—
268C4#1912768411yescharacteristic
269C4#1912770111yescharacteristic
270C4D16×D8311yescharacteristic
271C4SD32×D8311yescharacteristic
272C2—13282no—
273C2—1662no—
274C2#2490613911yescharacteristic
275C2#357×D8311yescharacteristic
276C2#2490921111yescharacteristic
subgroupG/H
centerC22#102×D83
commutatorC2×C8×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#1364C2
socleC22×C83C2×#102
prime radical#24918043C2
cosocleC4×C8×C83C23
hypercenter#1364D83
hypocenterC83#11981
LCSG ▷ C2×C8×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
2. C4⋊C16×D83C2semidirect
3. #24906220C2semidirect
4. #24905518C2semidirect
5. #24905510C2semidirect
6. #24905508C2semidirect
7. C83×#1364C2semidirect
143. #1364D83semidirect
146. C83#11981semidirect

Maximal subgroups

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

subgroupindex
#249180432
C4⋊C16×D832
#249062202
#249055182
#249055102
#249055082
C83×#13642
#1198183