Finite Group Databasebeta

← #35308601

Subgroups — #35308601

Order 21248.

358 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 81 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#24918857C211yesmaximal, characteristic
2#24907634C211yesmaximal, characteristic
3#24906200C212yesmaximal
4#24905917C212yesmaximal
5C83×#1309C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127987—22no—
8#19127959—22no—
9#19127912—22no—
10C2×#14581727—22no—
11#19127725C2211yescharacteristic
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127448—22no—
14#19127446—22no—
15#19127431—24no—
16#423×C83C2212yes—
17#423×C83C2211yescharacteristic
18C2×Dic332—22no—
19C2×#13050574—21no—
20C22×C83⋊C8—21no—
21#14581792D412yes—
22#14581792D412yes—
23#14581784—22no—
24#14581771—22no—
25#14581771—22no—
26C4×Dic166—22no—
27C4×Dic166—22no—
28#14581751—22no—
29#14581727—44no—
30#14581724—22no—
31C4⋊(C83⋊C8)—22no—
32#14581717—24no—
33C4×C83⋊C8—21no—
34C4×C83⋊C8D412yes—
35C2×M16×C83—22no—
36C2×M16×C83D412yes—
37C2×C42×C83C2311yescharacteristic
38C4⋊C8×C83—22no—
39C4⋊C8×C83—22no—
40C4⋊C8×C83—22no—
41C2×Dic166—22no—
42C2×Dic166—22no—
43Dic332—82no—
44#13050574—42no—
45C2×C83⋊C8—22no—
46C2×C83⋊C8—22no—
47C2×C83⋊C8—22no—
48C2×C83⋊C8—41no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52C4⋊Dic83—22no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55C22⋊Dic83—42no—
56C4×Dic83—42no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83#4112yes—
59M16×C83—42no—
60M16×C83—82no—
61C2×C8×C83—22no—
62C2×C8×C83—42no—
63C42×C83C2×D412yes—
64C42×C83C2×D411yescharacteristic
65C42×C83#4111yescharacteristic
66C23×C83#12411yescharacteristic
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83#12011yescharacteristic
72C2×C4×C83#12112yes—
73C2×C4×C83#12111yescharacteristic
74C2×C4×C83#12312yes—
75C2×Dic83—42no—
76C2×Dic83—42no—
77Dic166—42no—
78Dic166—42no—
79Dic166—42no—
80Dic166—42no—
81C8×C83—42no—
82C8×C83—82no—
83C83⋊C8—24no—
84C83⋊C8—81no—
85C22×C83—22no—
86C22×C83—21no—
87C22×C83#39411yescharacteristic
88C4×C83—22no—
89C4×C83—21no—
90C4×C83#45311yescharacteristic
91C4×C83#45611yescharacteristic
92C4×C83#47112yes—
93C4×C83#47312yes—
94Dic83—82no—
95Dic83—82no—
96#10534—831nomaximal, Sylow
97C2×C83—41no—
98C2×C83#203911yescharacteristic
99C2×C83#205212yes—
100#3255—831no—
101#1848—831no—
102#1561—832no—
103#1493—832no—
104#1309D8311yescharacteristic
105C83#1053411yescharacteristic, complemented, Sylow
106#533—832no—
107#475—1662no—
108#470—1662no—
109#462—1662no—
110C2×#108—1662no—
111#423—831no—
112#423C2×D8312yes—
113#423C2×D8311yescharacteristic
114C2×C4×C8—831no—
115#332—1662no—
116#332—1662no—
117Q8⋊C8—1664no—
118C2×Q16—1662no—
119C2×M16—22no—
120C2×M16—1661no—
121C2×M16D33212yes—
122C22×C8—1661no—
123C4⋊Q8—832no—
124C4⋊Q8—832no—
125#125—1662no—
126C22⋊Q8—1662no—
127C22⋊Q8—1662no—
128C4×Q8—1662no—
129C4×Q8—1662no—
130#117—1662no—
131C2×C42C22×D8311yescharacteristic
132#108—3324no—
133#106—1662no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—1662no—
138#103—1664no—
139C4×C8—832no—
140C4×C8—1661no—
141C2×Q8—1662no—
142C2×Q8—1662no—
143C22×C4C2×D33211yescharacteristic
144C22×C4#1305059012yes—
145Q16—6642no—
146M16—42no—
147M16—82no—
148M16—3322no—
149C2×C8—22no—
150C2×C8—42no—
151C2×C8—3321no—
152C2×C8—1662no—
153C2×C8—1662no—
154C2×C8—1662no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C4⋊C4—1662no—
160C4⋊C4—1662no—
161C22⋊C4—3322no—
162C42—3322no—
163C42D4×D8312yes—
164C42D4×D8311yescharacteristic
165C42#1305059111yescharacteristic
166C23#1458178011yescharacteristic
167Q8—3322no—
168Q8—3322no—
169Q8—3322no—
170Q8—3322no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—3322no—
176C2×C4—3322no—
177C2×C4#1458176211yescharacteristic
178C2×C4#1458176512yes—
179C2×C4#1458176711yescharacteristic
180C2×C4#1458177712yes—
181C8—42no—
182C8—82no—
183C8—6641no—
184C8—1664no—
185C22—21no—
186C22—22no—
187C22#1912761911yescharacteristic
188C4—21no—
189C4—22no—
190C4—6642no—
191C4—6642no—
192C4#1912787111yescharacteristic
193C4#1912788611yescharacteristic
194C4#1912796312yes—
195C4#1912797512yes—
196C2—41no—
197C2#2490868811yescharacteristic
198C2#2490876512yes—
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1309C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#1309D83
hypocenterC83#10534
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
105. C83#10534semidirect

Maximal subgroups

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

subgroupindex
#249188572
#249076342
#249062002
#249059172
C83×#13092
#1053483