Finite Group Databasebeta

← #35297394

Subgroups — #35297394

Order 21248.

388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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#24916175C211yesmaximal, characteristic
2#24906224C212yesmaximal, complemented
3#24906098C211yesmaximal, characteristic
4#24905373C212yesmaximal, complemented
5C83×#1536C211yesmaximal, characteristic
6C2×#14581799C412yes—
7#19127779—22no—
8D4×C83⋊C8—22no—
9#19127758C2212yes—
10#19127725C2211yescharacteristic
11#19127668C412yes—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127453—22no—
14#19127451—22no—
15#19127441—22no—
16#532×C83C2211yescharacteristic
17#432×C83C2212yes—
18#329×C83—22no—
19#14581799—44no—
20C2×#13050574—22no—
21C2×#13050574C2×C412yes—
22C22×C83⋊C8—22no—
23C22×C83⋊C8C2×C411yescharacteristic
24C22×C83⋊C8C2×C411yescharacteristic
25C4⋊(C83⋊C8)—22no—
26C4⋊(C83⋊C8)—22no—
27C22⋊(C83⋊C8)—24no—
28C22⋊(C83⋊C8)—22no—
29#14581703—22no—
30C4×C83⋊C8D412yes—
31C4×C83⋊C8D412yes—
32C2×#41×C83C2×C412yes—
33C4⋊Q8×C83Q811yescharacteristic
34#127×C83Q811yescharacteristic
35#124×C83D412yes—
36#121×C83—22no—
37C4×D4×C83—22no—
38C2×C42×C83C2311yescharacteristic
39C4⋊C8×C83—22no—
40C22⋊C8×C83—22no—
41#97×C83—22no—
42#13050574—44no—
43#13050574—42no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8—22no—
46C2×C83⋊C8—41no—
47C2×C83⋊C8—44no—
48C2×C83⋊C8—42no—
49C2×C83⋊C8C22⋊C411yescharacteristic
50C2×C83⋊C8C22⋊C412yes—
51C2×C83⋊C8C22⋊C411yescharacteristic
52#41×C83—42no—
53#41×C83—42no—
54C2×Q8×C83C4⋊C412yes—
55C2×D4×C83—22no—
56C2×D4×C83—22no—
57C2×D4×C83C4⋊C412yes—
58C22×C4×C83—22no—
59C22×C4×C83C22×C411yescharacteristic
60C22×C4×C83#4112yes—
61C2×C8×C83—42no—
62C4⋊C4×C83—22no—
63C22⋊C4×C83—24no—
64C42×C83C2×D412yes—
65C42×C83C2×D411yescharacteristic
66C42×C83C2×Q811yescharacteristic
67C23×C83—22no—
68C23×C83#11711yescharacteristic
69Q8×C83—42no—
70D4×C83—42no—
71D4×C83—44no—
72D4×C83—44no—
73C2×C4×C83—21no—
74C2×C4×C83—21no—
75C2×C4×C83—22no—
76C2×C4×C83—42no—
77C2×C4×C83—42no—
78C2×C4×C83—42no—
79C2×C4×C83C2×C22⋊C411yescharacteristic
80C2×C4×C83C2×C4⋊C411yescharacteristic
81C2×C4×C83#12112yes—
82C2×C4×C83C22⋊Q812yes—
83C8×C83—82no—
84C83⋊C8—21no—
85C83⋊C8—22no—
86C83⋊C8—42no—
87C83⋊C8—82no—
88C83⋊C8#10012yes—
89C22×C83—21no—
90C22×C83—22no—
91C22×C83—42no—
92C22×C83—44no—
93C22×C83#38011yescharacteristic
94C4×C83—21no—
95C4×C83—22no—
96C4×C83—22no—
97C4×C83—42no—
98C4×C83C2×#10011yescharacteristic
99C4×C83#41311yescharacteristic
100#8630—831nomaximal, Sylow
101C2×C83—41no—
102C2×C83—82no—
103C2×C83#180011yescharacteristic
104C2×C83#181412yes—
105#2931—831no—
106#1568—832no—
107#1536—831no—
108#1536D8311yescharacteristic
109#1307—832no—
110C83#863011yescharacteristic, complemented, Sylow
111C2×#131—832no—
112#532C2×D8311yescharacteristic
113#436—1662no—
114C8×D4—1662no—
115#432—832no—
116#432C2×D8312yes—
117#423—831no—
118#408—832no—
119C2×C4×C8—831no—
120#335—1662no—
121#334—1662no—
122#329—22no—
123#329—1662no—
124C2×#41C4×D8312yes—
125#131—3324no—
126C2×M16—832no—
127C2×M16—1662no—
128C22×C8—831no—
129C22×C8—831no—
130C22×C8—1662no—
131C4⋊Q8Dic16611yescharacteristic
132#127Dic16611yescharacteristic
133#124C22⋊D8312yes—
134#121—22no—
135C4×D4—22no—
136C2×C42C22×D8311yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—1662no—
139C4⋊C8—1662no—
140C22⋊C8—22no—
141C22⋊C8—1662no—
142C22⋊C8—1664no—
143#97—22no—
144#97—1662no—
145C4×C8—832no—
146C4×C8—832no—
147#41—42no—
148#41—42no—
149C2×Q8Dic83⋊C412yes—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4Dic83⋊C412yes—
153C22×C4—22no—
154C22×C4C2×C4×D8311yescharacteristic
155C22×C4#1305058912yes—
156M16—3324no—
157M16—3322no—
158C2×C8—42no—
159C2×C8—3324no—
160C2×C8—3322no—
161C2×C8—3321no—
162C2×C8—831no—
163C2×C8—832no—
164C2×C8—831no—
165C2×C8—1662no—
166C2×C8—1662no—
167C4⋊C4—22no—
168C22⋊C4—24no—
169C42D4×D8312yes—
170C42C2×C22⋊D8311yescharacteristic
171C42C2×Dic16611yescharacteristic
172C23—22no—
173C23#1458174811yescharacteristic
174Q8—42no—
175D4—42no—
176D4—44no—
177D4—44no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4C22⋊C4×D8311yescharacteristic
185C2×C4C2×Dic83⋊C411yescharacteristic
186C2×C4#1458176412yes—
187C2×C4#1458176912yes—
188C8—82no—
189C8—3322no—
190C8—832no—
191C8—6642no—
192C8—1661no—
193C8—1662no—
194C22—21no—
195C22—22no—
196C22—42no—
197C22—44no—
198C22#1912755911yescharacteristic
199C4—21no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4#100×D8311yescharacteristic
204C4#1912768211yescharacteristic
205C2—41no—
206C2—82no—
207C2#2490745311yescharacteristic
208C2#2490751512yes—
subgroupG/H
centerC22#19127559
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1536C2
socleC22×C83#380
prime radical#532×C83C22
cosocleC2×C42×C83C23
hypercenter#1536D83
hypocenterC83#8630
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

Complements

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

NH ≅ G/Ntype
2. #24906224C2semidirect
4. #24905373C2semidirect
110. C83#8630semidirect

Maximal subgroups

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

subgroupindex
#249161752
#249062242
#249060982
#249053732
C83×#15362
#863083