Finite Group Databasebeta

← #35315591

Subgroups — #35315591

Order 21248.

296 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 75 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#24909068C211yesmaximal, characteristic, complemented
3#24905495C214yesmaximal, complemented
4C83×#2166C211yesmaximal, characteristic, complemented
5#19128306C412yes—
6C2×#14581732—21no—
7#19128103C411yescharacteristic
8#19128078C411yescharacteristic
9#19128066C2212yes—
10#19127954—21no—
11#19127937—21no—
12#19127814—21no—
13C4×D664—21no—
14#19127479—21no—
15#19127479C2212yes—
16#405×C83C2211yescharacteristic
17#364×C83—21no—
18#349×C83—21no—
19#347×C83C2212yes—
20C2×D664—21no—
21C2×D664—21no—
22#14581789C2×C412yes—
23#14581784C2×C412yes—
24#14581777—42no—
25#14581766—22no—
26#14581765—42no—
27C4×D332—22no—
28#14581732—22no—
29#14581732—22no—
30C2×C83⋊C16—22no—
31#14581726—21no—
32#14581724—21no—
33#14581714—22no—
34#14581714—22no—
35C2×M16×C83D411yescharacteristic
36C22×C8×C83D411yescharacteristic
37#117×C83C2×C411yescharacteristic
38M32×C83—22no—
39#97×C83D411yescharacteristic
40#97×C83C2311yescharacteristic
41C4×C8×C83C2×C411yescharacteristic
42C4×C8×C83D411yescharacteristic
43C2×D332—22no—
44C2×D332—42no—
45C2×C22⋊D83—42no—
46C2×C4×D83—42no—
47D664—42no—
48D664—41no—
49D664—41no—
50C4⋊Dic83—22no—
51Dic83⋊C4—42no—
52(C2×D83)⋊C4—42no—
53(C2×D83)⋊C4—42no—
54C83⋊C16—24no—
55C22×C4×C83C22⋊C411yescharacteristic
56M16×C83—41no—
57C2×C8×C83—21no—
58C2×C8×C83—21no—
59C2×C8×C83C22⋊C411yescharacteristic
60C2×C8×C83C22⋊C411yescharacteristic
61C2×C8×C83C2×D411yescharacteristic
62C2×C8×C83C2×D411yescharacteristic
63C4⋊C4×C83—21no—
64C22⋊C4×C83—21no—
65C42×C83C22⋊C411yescharacteristic
66C42×C83C22×C411yescharacteristic
67C16×C83—42no—
68C23×C83#10011yescharacteristic
69C22×D83—42no—
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—21no—
74C2×C4×C83#10011yescharacteristic
75C2×C4×C83C2×C22⋊C411yescharacteristic
76C22⋊D83—162no—
77C2×Dic83—42no—
78D332—42no—
79D332—42no—
80D332—162no—
81C4×D83—162no—
82C8×C83—21no—
83C8×C83—21no—
84C8×C83—21no—
85C8×C83#10411yescharacteristic
86C8×C83#10411yescharacteristic
87C22×C83—21no—
88C22×C83—41no—
89C22×C83C2×#10011yescharacteristic
90C2×D83—82no—
91C2×D83—82no—
92C2×D83—82no—
93C4×C83—21no—
94C4×C83—41no—
95C4×C83—41no—
96C4×C83C2×#10411yescharacteristic
97C4×C83#42111yescharacteristic
98Dic83—82no—
99#11913—831nomaximal, Sylow
100C2×C83—21no—
101C2×C83—41no—
102C2×C83#153011yescharacteristic
103D83—162no—
104#3176—831no—
105#2166D8311yescharacteristic, complemented
106#2110—831no—
107#1355—834no—
108C83#1191311yescharacteristic, complemented, Sylow
109#540—832no—
110C2×M32—1661no—
111#499—831no—
112#493—831no—
113#490—832no—
114#469—1661no—
115#466—1661no—
116#442—1661no—
117C4×D8—1661no—
118#405C2×D8311yescharacteristic
119#364—21no—
120#349—21no—
121#347—832no—
122#347—1661no—
123#347C2×D8312yes—
124C2×D8—1661no—
125C2×D8—1661no—
126C2×M16C22⋊D8311yescharacteristic
127C22×C8D33211yescharacteristic
128#127—832no—
129#125—832no—
130#123—3322no—
131#121—3322no—
132#121—1662no—
133C4×D4—1662no—
134#117C4×D8311yescharacteristic
135M32—22no—
136M32—1662no—
137M32—1662no—
138C2×C16—1662no—
139#107—1661no—
140#106—1661no—
141#102—1662no—
142#102—1662no—
143#97D33211yescharacteristic
144#97C22×D8311yescharacteristic
145C4×C8C4×D8311yescharacteristic
146C4×C8C22⋊D8311yescharacteristic
147C2×D4—3322no—
148C2×D4—3322no—
149C2×D4—1662no—
150C22×C4—3322no—
151C22×C4(C2×D83)⋊C411yescharacteristic
152D8—3322no—
153D8—3321no—
154D8—3321no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8(C2×D83)⋊C411yescharacteristic
159C2×C8(C2×D83)⋊C411yescharacteristic
160C2×C8C2×C22⋊D8311yescharacteristic
161C2×C8C2×D33211yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—3322no—
164C4⋊C4—1662no—
165C22⋊C4—21no—
166C22⋊C4—3322no—
167C22⋊C4—3322no—
168C42(C2×D83)⋊C411yescharacteristic
169C42C2×C4×D8311yescharacteristic
170C16—42no—
171C16—1664no—
172C23—3322no—
173C23#1458170811yescharacteristic
174D4—13282no—
175D4—13282no—
176D4—3322no—
177D4—3322no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—13282no—
183C2×C4—3322no—
184C2×C4#1458170811yescharacteristic
185C2×C4C2×(C2×D83)⋊C411yescharacteristic
186C8—21no—
187C8—21no—
188C8—21no—
189C8#1458171811yescharacteristic
190C8#1458171811yescharacteristic
191C22—21no—
192C22—41no—
193C22—6642no—
194C22—6642no—
195C22—6642no—
196C22C2×#1458170811yescharacteristic
197C4—21no—
198C4—41no—
199C4—41no—
200C4—6642no—
201C4C2×#1458171811yescharacteristic
202C4#1912771911yescharacteristic
203C2—21no—
204C2—41no—
205C2—13282no—
206C2#2490607511yescharacteristic
subgroupG/H
centerC2#24906075
commutatorC42×C83C22×C4
Frattini#97C22×D83
FittingC83×#2166C2
socleC2×C83#1530
prime radical#24918113C2
cosocle#97×C83C23
hypercenter#2166D83
hypocenterC83#11913
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. #24909068C2semidirect
3. #24905495C2semidirect
4. C83×#2166C2semidirect
105. #2166D83semidirect
108. C83#11913semidirect

Maximal subgroups

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

subgroupindex
#249181132
#249090682
#249054952
C83×#21662
#1191383