Finite Group Databasebeta

← #35299366

Subgroups — #35299366

Order 21248.

398 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 95 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#24917811C211yesmaximal, characteristic
2#24916569C211yesmaximal, characteristic, complemented
3#24905933C212yesmaximal
4#24905363C212yesmaximal, complemented
5C83×#1544C211yesmaximal, characteristic, complemented
6#19128251C2211yescharacteristic
7#19128071C412yes—
8#19128067C412yes—
9#19128063—22no—
10#19127832—24no—
11#19127762—22no—
12#19127758C2212yes—
13#19127695—22no—
14C2×#14581703C2211yescharacteristic
15#19127430—24no—
16#533×C83C2211yescharacteristic
17#431×C83C2212yes—
18#332×C83—22no—
19C2×#13050590—21no—
20C22×C83⋊C8—21no—
21#14581792C2×C411yescharacteristic
22#14581789C2×C411yescharacteristic
23#14581780—21no—
24#14581766—22no—
25C4×D332—22no—
26C4⋊(C83⋊C8)—24no—
27C4⋊(C83⋊C8)D414yes—
28#14581715—24no—
29#14581712—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32#14581703—22no—
33#14581703—21no—
34#14581703C2×C412yes—
35C4×C83⋊C8—22no—
36C4⋊Q8×C83D412yes—
37#125×C83C2×C412yes—
38C22⋊Q8×C83—22no—
39C4×Q8×C83—22no—
40#117×C83D412yes—
41C2×C42×C83C2311yescharacteristic
42C4⋊C8×C83—22no—
43C22⋊C8×C83—22no—
44C4×C8×C83—22no—
45#13050590—44no—
46C2×Dic166—21no—
47C2×D332—21no—
48C2×D332—22no—
49C2×C22⋊D83—41no—
50C2×C4×D83—41no—
51C2×C83⋊C8—22no—
52C2×C83⋊C8—24no—
53C2×C83⋊C8—42no—
54C4⋊Dic83—22no—
55(C2×D83)⋊C4—42no—
56C2×Q8×C83—22no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83#4112yes—
59C2×C8×C83—42no—
60C4⋊C4×C83—24no—
61C4⋊C4×C83—22no—
62C4⋊C4×C83C22⋊C414yes—
63C22⋊C4×C83—22no—
64C42×C83—22no—
65C42×C83C22×C411yescharacteristic
66C42×C83C2×D412yes—
67C42×C83C2×D411yescharacteristic
68C23×C83#12311yescharacteristic
69C22×D83—41no—
70Q8×C83—82no—
71C2×C4×C83—22no—
72C2×C4×C83—24no—
73C2×C4×C83—42no—
74C2×C4×C83C2×C22⋊C411yescharacteristic
75C2×C4×C83C4×D412yes—
76C2×C4×C83#12011yescharacteristic
77C2×C4×C83#12112yes—
78C22⋊D83—82no—
79C2×Dic83—41no—
80D332—44no—
81D332—42no—
82C4×D83—82no—
83Dic166—42no—
84C8×C83—82no—
85C83⋊C8—42no—
86C83⋊C8—44no—
87C22×C83—22no—
88C22×C83—21no—
89C22×C83#38611yescharacteristic
90C2×D83—82no—
91C2×D83—81no—
92C4×C83—22no—
93C4×C83—22no—
94C4×C83—21no—
95C4×C83—44no—
96C4×C83#45412yes—
97Dic83—81no—
98#9008—831nomaximal, Sylow
99C2×C83—41no—
100C2×C83#188112yes—
101C2×C83#188811yescharacteristic
102D83—161no—
103#3135—831no—
104#2987—831no—
105#1544D8311yescharacteristic, complemented
106#1496—832no—
107#1302—832no—
108C83#900811yescharacteristic, complemented, Sylow
109#533C2×D8311yescharacteristic
110#532—831no—
111#491—832no—
112#490—832no—
113#489—1662no—
114#446—1664no—
115#433—1662no—
116#432—832no—
117#431C2×D8312yes—
118#416—1662no—
119C2×#97—831no—
120#332—22no—
121D4⋊C8—1664no—
122C2×#41—1661no—
123C22×C8—1661no—
124C4⋊Q8—831no—
125C4⋊Q8C22⋊D8312yes—
126#127—831no—
127#125C4×D8312yes—
128#124—1661no—
129C22⋊Q8—22no—
130#121—1662no—
131C4×Q8—22no—
132C4×D4—1662no—
133#117D33212yes—
134C2×C42C22×D8311yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—834no—
137C4⋊C8—1664no—
138#103—1664no—
139#102—1664no—
140C22⋊C8—22no—
141C22⋊C8—1662no—
142#97—832no—
143#97—1662no—
144#97—1662no—
145#97—1661no—
146C4×C8—22no—
147C4×C8—1662no—
148#41—3324no—
149C2×Q8—22no—
150C2×Q8—1661no—
151C2×D4—3321no—
152C2×D4—1661no—
153C2×D4—1662no—
154C22×C4—3321no—
155C22×C4C2×D33211yescharacteristic
156C22×C4#1305058912yes—
157C2×C8—42no—
158C2×C8—3322no—
159C2×C8—1664no—
160C2×C8—1662no—
161C4⋊C4—22no—
162C4⋊C4—24no—
163C4⋊C4—1662no—
164C4⋊C4(C2×D83)⋊C414yes—
165C22⋊C4—22no—
166C22⋊C4—3322no—
167C42—22no—
168C42C2×C4×D8311yescharacteristic
169C42D4×D8312yes—
170C42C2×C22⋊D8311yescharacteristic
171C23—3321no—
172C23#1458177611yescharacteristic
173Q8—82no—
174Q8—3322no—
175D4—3322no—
176D4—3324no—
177D4—6642no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—3321no—
182C2×C4—6642no—
183C2×C4C2×(C2×D83)⋊C411yescharacteristic
184C2×C4(C22⋊D83)⋊C412yes—
185C2×C4#1458176211yescharacteristic
186C2×C4#1458176412yes—
187C8—82no—
188C8—3322no—
189C8—3324no—
190C22—22no—
191C22—21no—
192C22—6642no—
193C22—6641no—
194C22#1912757811yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—6641no—
200C4#1912787612yes—
201C2—41no—
202C2—13281no—
203C2#2490782312yes—
204C2#2490786411yescharacteristic
subgroupG/H
centerC2×C4#14581762
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1544C2
socleC22×C83#386
prime radical#19128251C22
cosocleC2×C42×C83C23
hypercenter#1544D83
hypocenterC83#9008
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1544

Complements

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

NH ≅ G/Ntype
2. #24916569C2semidirect
4. #24905363C2semidirect
5. C83×#1544C2semidirect
105. #1544D83semidirect
108. C83#9008semidirect

Maximal subgroups

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

subgroupindex
#249178112
#249165692
#249059332
#249053632
C83×#15442
#900883