Finite Group Databasebeta

← #35315592

Subgroups — #35315592

Order 21248.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#24918121C211yesmaximal, characteristic
2#24909277C211yesmaximal, characteristic
3#24909066C211yesmaximal, characteristic
4#24905498C211yesmaximal, characteristic, complemented
5#24905497C211yesmaximal, characteristic, complemented
6#24905497C211yesmaximal, characteristic, complemented
7C83×#1356C211yesmaximal, characteristic, complemented
8#19128314C411yescharacteristic
9#19128312C411yescharacteristic
10M32×D83—21no—
11#19128100C411yescharacteristic
12#19128080C411yescharacteristic
13#19128070C2211yescharacteristic
14#19127958—21no—
15#19127941—21no—
16#19127805—21no—
17#19127793—21no—
18#19127658C2211yescharacteristic
19#19127521—21no—
20#19127482—21no—
21#19127479C2211yescharacteristic
22#19127479C2211yescharacteristic
23#19127478—21no—
24#491×C83C2211yescharacteristic
25#347×C83C2211yescharacteristic
26#347×C83C2211yescharacteristic
27C2×#13050580—21no—
28C2×#13050580—21no—
29C2×#13050573D411yescharacteristic
30C2×C8×D83D411yescharacteristic
31#14581792C2×C411yescharacteristic
32#14581787—41no—
33#14581787—41no—
34#14581784C2×C411yescharacteristic
35#14581783—41no—
36#14581782—41no—
37#14581772—21no—
38#14581768—21no—
39Q8×Dic83—21no—
40#14581757—21no—
41#14581749C2×C411yescharacteristic
42#14581732—21no—
43#14581732—21no—
44#14581731—22no—
45C16×D83—22no—
46#14581725—21no—
47#14581723—21no—
48#14581717—21no—
49#14581717—21no—
50#14581702D411yescharacteristic
51C4×C83⋊C8C2×C411yescharacteristic
52C8×Dic83D411yescharacteristic
53C4⋊Q8×C83C2×C411yescharacteristic
54#125×C83C2×C411yescharacteristic
55M32×C83—21no—
56M32×C83—21no—
57#103×C83—21no—
58#103×C83—21no—
59#97×C83C2311yescharacteristic
60C2×Dic166—21no—
61C2×C4×D83C22⋊C411yescharacteristic
62#13050580—42no—
63#13050580—41no—
64#13050580—41no—
65#13050573—41no—
66C2×C83⋊C8C22⋊C411yescharacteristic
67C2×C83⋊C8C22⋊C411yescharacteristic
68C8×D83—21no—
69C8×D83—21no—
70C4⋊Dic83—21no—
71C4⋊Dic83—41no—
72C4⋊Dic83—41no—
73C4⋊Dic83—41no—
74Dic83⋊C4—21no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77Dic83⋊C4—41no—
78(C2×D83)⋊C4—21no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81C4×Dic83—41no—
82C4×Dic83—41no—
83C4×Dic83C22⋊C411yescharacteristic
84C83⋊C16—22no—
85C83⋊C16—41no—
86C2×Q8×C83—21no—
87C2×C8×C83C2×D411yescharacteristic
88C2×C8×C83C2×D411yescharacteristic
89C4⋊C4×C83—21no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C42×C83C22×C411yescharacteristic
93C16×C83—22no—
94C16×C83—41no—
95C22×D83#10011yescharacteristic
96Q8×C83—41no—
97Q8×C83—41no—
98C2×C4×C83—21no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83C2×C22⋊C411yescharacteristic
102C2×Dic83—21no—
103C2×Dic83—41no—
104C2×Dic83—41no—
105C2×Dic83#10011yescharacteristic
106C4×D83—21no—
107C4×D83—21no—
108Dic166—41no—
109Dic166—41no—
110C8×C83—21no—
111C8×C83—21no—
112C83⋊C8—21no—
113C83⋊C8#10411yescharacteristic
114C83⋊C8#10411yescharacteristic
115C22×C83C2×#10011yescharacteristic
116C2×D83—21no—
117C2×D83—41no—
118C4×C83—41no—
119C4×C83—81no—
120C4×C83—81no—
121C4×C83C2×#10411yescharacteristic
122C4×C83#42111yescharacteristic
123Dic83—21no—
124Dic83—41no—
125Dic83—81no—
126Dic83—81no—
127#11914—831nomaximal, Sylow
128C2×C83—21no—
129C2×C83#153011yescharacteristic
130D83—41no—
131#3177—831no—
132#2166—831no—
133#2110—831no—
134#1356—831no—
135#1356—831no—
136#1356—831no—
137#1356D8311yescharacteristic, complemented
138C83#1191411yescharacteristic, complemented, Sylow
139#541—831no—
140#541—831no—
141C2×M32—1661no—
142#499—831no—
143#494—831no—
144#491—831no—
145#491C2×D8311yescharacteristic
146#470—1661no—
147#467—1661no—
148#441—1661no—
149C4×Q16—1661no—
150#405—831no—
151#364—1661no—
152#349—1661no—
153#347—831no—
154#347—831no—
155#347—1661no—
156#347C2×D8311yescharacteristic
157#347C2×D8311yescharacteristic
158C2×Q16—1661no—
159C2×Q16—1661no—
160C2×M16—831no—
161C22×C8—831no—
162C4⋊Q8—831no—
163C4⋊Q8C4×D8311yescharacteristic
164#126—3321no—
165#126—3321no—
166#125—3321no—
167#125—3321no—
168#125—831no—
169#125C4×D8311yescharacteristic
170C22⋊Q8—1661no—
171C22⋊Q8—1661no—
172C4×Q8—1661no—
173C4×Q8—1661no—
174#117—831no—
175M32—21no—
176M32—21no—
177M32—1662no—
178M32—1661no—
179M32—1661no—
180C2×C16—1662no—
181#107—1661no—
182#106—1661no—
183#103—21no—
184#103—21no—
185#103—1661no—
186#103—1661no—
187#97—831no—
188#97C22×D8311yescharacteristic
189C4×C8—831no—
190C4×C8—831no—
191C2×Q8—21no—
192C2×Q8—1661no—
193C22×C4—831no—
194Q16—3321no—
195Q16—3321no—
196Q16—3322no—
197M16—3321no—
198C2×C8—831no—
199C2×C8—831no—
200C2×C8—1661no—
201C2×C8—1661no—
202C2×C8D4×D8311yescharacteristic
203C2×C8D4×D8311yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—3321no—
208C4⋊C4—3321no—
209C4⋊C4—3321no—
210C4⋊C4—3321no—
211C4⋊C4—3321no—
212C4⋊C4—3321no—
213C4⋊C4—1661no—
214C4⋊C4—1661no—
215C22⋊C4—3321no—
216C22⋊C4—3321no—
217C22⋊C4—1661no—
218C42—3321no—
219C42—3321no—
220C42—831no—
221C42C2×C4×D8311yescharacteristic
222C16—22no—
223C16—41no—
224C16—3321no—
225C16—1662no—
226C23—831no—
227Q8—41no—
228Q8—41no—
229Q8—3321no—
230Q8—3321no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—3321no—
235C2×C4—3321no—
236C2×C4—831no—
237C2×C4—1661no—
238C2×C4—1661no—
239C2×C4—1661no—
240C2×C4C22⋊C4×D8311yescharacteristic
241C8—21no—
242C8—21no—
243C8—831no—
244C8—831no—
245C8—1661no—
246C22—3321no—
247C22—1661no—
248C22#100×D8311yescharacteristic
249C4—41no—
250C4—81no—
251C4—81no—
252C4—3321no—
253C4—6641no—
254C4—6641no—
255C4—1661no—
256C4#104×D8311yescharacteristic
257C4#1912771611yescharacteristic
258C2—21no—
259C2—3321no—
260C2#2490607211yescharacteristic
subgroupG/H
centerC2#24906072
commutatorC42×C83C22×C4
Frattini#97C22×D83
FittingC83×#1356C2
socleC2×C83#1530
prime radicalC22×D83#100
cosocle#97×C83C23
hypercenter#1356D83
hypocenterC83#11914
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
4. #24905498C2semidirect
5. #24905497C2semidirect
6. #24905497C2semidirect
7. C83×#1356C2semidirect
137. #1356D83semidirect
138. C83#11914semidirect

Maximal subgroups

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

subgroupindex
#249181212
#249092772
#249090662
#249054982
#249054972
C83×#13562
#1191483