Finite Group Databasebeta

← #35315922

Subgroups — #35315922

Order 21248.

292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 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#24918113C211yesmaximal, characteristic
2#24909229C211yesmaximal, characteristic, complemented
3#24905523C212yesmaximal, complemented
4#24905499C212yesmaximal, complemented
5C83×#2166C211yesmaximal, characteristic, complemented
6#19128306C412yes—
7C2×#14581732—21no—
8#19128103C2211yescharacteristic
9#19128078C2211yescharacteristic
10#19128066C412yes—
11#19127954—21no—
12#19127937—21no—
13#19127814—21no—
14C4×D664—21no—
15#19127522—21no—
16#19127522C2212yes—
17#405×C83C2211yescharacteristic
18#364×C83C2212yes—
19#349×C83—21no—
20#347×C83—21no—
21C2×D664—21no—
22C2×D664—21no—
23#14581789C2×C412yes—
24#14581784C2×C412yes—
25#14581777—42no—
26#14581766—22no—
27#14581765—42no—
28C4×D332—22no—
29#14581732—22no—
30#14581732—41no—
31C2×C83⋊C16—41no—
32#14581726—21no—
33#14581724—21no—
34#14581714—22no—
35#14581714—22no—
36C2×M16×C83D411yescharacteristic
37C22×C8×C83D411yescharacteristic
38#117×C83C2×C411yescharacteristic
39M32×C83—22no—
40#97×C83C2×C411yescharacteristic
41#97×C83D411yescharacteristic
42C4×C8×C83D411yescharacteristic
43C4×C8×C83C2311yescharacteristic
44C2×D332—22no—
45C2×D332—42no—
46C2×C22⋊D83—42no—
47C2×C4×D83—42no—
48D664—42no—
49D664—41no—
50D664—41no—
51C4⋊Dic83—22no—
52Dic83⋊C4—42no—
53(C2×D83)⋊C4—42no—
54(C2×D83)⋊C4—42no—
55C83⋊C16—42no—
56C22×C4×C83C22⋊C411yescharacteristic
57M16×C83—22no—
58C2×C8×C83—21no—
59C2×C8×C83—21no—
60C2×C8×C83C22⋊C411yescharacteristic
61C2×C8×C83C22⋊C411yescharacteristic
62C2×C8×C83C2×D411yescharacteristic
63C2×C8×C83C2×D411yescharacteristic
64C4⋊C4×C83—21no—
65C22⋊C4×C83—21no—
66C42×C83C22⋊C411yescharacteristic
67C42×C83C22×C411yescharacteristic
68C16×C83—42no—
69C23×C83#10011yescharacteristic
70C22×D83—42no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—21no—
74C2×C4×C83—21no—
75C2×C4×C83#10011yescharacteristic
76C2×C4×C83C2×C22⋊C411yescharacteristic
77C22⋊D83—162no—
78C2×Dic83—42no—
79D332—42no—
80D332—42no—
81D332—162no—
82C4×D83—162no—
83C8×C83—21no—
84C8×C83—21no—
85C8×C83#13512yes—
86C8×C83AGL(1,ℤ/8)11yescharacteristic
87C8×C83#13711yescharacteristic
88C22×C83—21no—
89C22×C83—41no—
90C22×C83C2×#10011yescharacteristic
91C2×D83—82no—
92C2×D83—82no—
93C2×D83—82no—
94C4×C83—21no—
95C4×C83—41no—
96C4×C83—41no—
97C4×C83#41611yescharacteristic
98C4×C83#41711yescharacteristic
99Dic83—82no—
100#11989—831nomaximal, Sylow
101C2×C83—21no—
102C2×C83—41no—
103C2×C83#155111yescharacteristic
104D83—162no—
105#3176—831no—
106#2166D8311yescharacteristic, complemented
107#2153—831no—
108#1366—832no—
109#1357—832no—
110C83#1198911yescharacteristic, complemented, Sylow
111#540—832no—
112C2×M32—1661no—
113#499—831no—
114#493—831no—
115#490—832no—
116#469—1661no—
117#466—1661no—
118#442—1661no—
119C4×D8—1661no—
120#405C2×D8311yescharacteristic
121#364—832no—
122#364—1661no—
123#364C2×D8312yes—
124#349—21no—
125#347—21no—
126C2×D8—1661no—
127C2×D8—1661no—
128C2×M16C22⋊D8311yescharacteristic
129C22×C8D33211yescharacteristic
130#127—832no—
131#125—832no—
132#123—3322no—
133#121—3322no—
134#121—1662no—
135C4×D4—1662no—
136#117C4×D8311yescharacteristic
137M32—22no—
138M32—3321no—
139M32—1662no—
140C2×C16—3321no—
141#107—1661no—
142#106—1661no—
143#102—1662no—
144#102—1662no—
145#97C4×D8311yescharacteristic
146#97C22⋊D8311yescharacteristic
147C4×C8D33211yescharacteristic
148C4×C8C22×D8311yescharacteristic
149C2×D4—3322no—
150C2×D4—3322no—
151C2×D4—1662no—
152C22×C4—3322no—
153C22×C4(C2×D83)⋊C411yescharacteristic
154D8—3322no—
155D8—3321no—
156D8—3321no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8(C2×D83)⋊C411yescharacteristic
161C2×C8(C2×D83)⋊C411yescharacteristic
162C2×C8C2×C22⋊D8311yescharacteristic
163C2×C8C2×D33211yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—3322no—
166C4⋊C4—1662no—
167C22⋊C4—21no—
168C22⋊C4—3322no—
169C22⋊C4—3322no—
170C42(C2×D83)⋊C411yescharacteristic
171C42C2×C4×D8311yescharacteristic
172C16—42no—
173C16—3322no—
174C23—3322no—
175C23#1458170811yescharacteristic
176D4—13282no—
177D4—13282no—
178D4—3322no—
179D4—3322no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—13282no—
185C2×C4—3322no—
186C2×C4#1458170811yescharacteristic
187C2×C4C2×(C2×D83)⋊C411yescharacteristic
188C8—21no—
189C8—21no—
190C8#1458181212yes—
191C8#1458182011yescharacteristic
192C8#1458182511yescharacteristic
193C22—21no—
194C22—41no—
195C22—6642no—
196C22—6642no—
197C22—6642no—
198C22C2×#1458170811yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—6642no—
203C4#1912769511yescharacteristic
204C4#1912770311yescharacteristic
205C2—21no—
206C2—41no—
207C2—13282no—
208C2#2490615911yescharacteristic
subgroupG/H
centerC2#24906159
commutatorC42×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#2166C2
socleC2×C83#1551
prime radical#24918113C2
cosocleC4×C8×C83C23
hypercenter#2166D83
hypocenterC83#11989
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #24909229C2semidirect
3. #24905523C2semidirect
4. #24905499C2semidirect
5. C83×#2166C2semidirect
106. #2166D83semidirect
110. C83#11989semidirect

Maximal subgroups

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

subgroupindex
#249181132
#249092292
#249055232
#249054992
C83×#21662
#1198983