Finite Group Databasebeta

← #35308499

Subgroups — #35308499

Order 21248.

364 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 77 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#24918808C211yesmaximal, characteristic
2#24907616C211yesmaximal, characteristic
3#24906164C212yesmaximal
4#24905976C212yesmaximal
5C83×#1290C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127997—22no—
8#19127942—22no—
9#19127912—22no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×Dic83⋊C8—22no—
12#19127547C2211yescharacteristic
13#19127448—22no—
14#19127446—22no—
15#19127439—24no—
16#432×C83C2212yes—
17C2×C4⋊C8×C83C2211yescharacteristic
18C2×Dic332—22no—
19C22×C83⋊C8—21no—
20#14581792D412yes—
21#14581792D412yes—
22#14581784—22no—
23#14581771—22no—
24#14581771—22no—
25C4×Dic166—22no—
26C4×Dic166—22no—
27#14581751—22no—
28C2×C4×Dic83—21no—
29#14581726—22no—
30C4⋊(C83⋊C8)—22no—
31Dic83⋊C8—44no—
32#14581717—24no—
33C83⋊#95—21no—
34C83⋊#95D412yes—
35C22×C8×C83D412yes—
36C2×C42×C83C2311yescharacteristic
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C22⋊C8×C83—22no—
40#97×C83—22no—
41C2×Dic166—22no—
42C2×Dic166—22no—
43C22×Dic83—22no—
44Dic332—82no—
45C2×C83⋊C8—42no—
46C2×C83⋊C8—41no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51Dic83⋊C4—42no—
52Dic83⋊C4—42no—
53C22⋊Dic83—42no—
54C4×Dic83—22no—
55C4×Dic83—22no—
56C4×Dic83—42no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83#4111yescharacteristic
60C2×C8×C83—22no—
61C2×C8×C83—42no—
62C2×C8×C83—42no—
63C42×C83C2×D412yes—
64C42×C83#4112yes—
65C23×C83#12111yescharacteristic
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—41no—
70C2×C4×C83#12011yescharacteristic
71C2×C4×C83#12112yes—
72C2×C4×C83#12312yes—
73C2×C4×C83#12411yescharacteristic
74C2×Dic83—24no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C2×Dic83—42no—
79Dic166—42no—
80Dic166—42no—
81Dic166—82no—
82C8×C83—42no—
83C8×C83—82no—
84C83⋊C8—81no—
85C22×C83—21no—
86C22×C83—21no—
87C22×C83#39411yescharacteristic
88C22×C83#47312yes—
89C4×C83—22no—
90C4×C83—21no—
91C4×C83—22no—
92C4×C83#45311yescharacteristic
93C4×C83#45611yescharacteristic
94Dic83—44no—
95Dic83—82no—
96Dic83—82no—
97#10516—831nomaximal, Sylow
98C2×C83—22no—
99C2×C83#203911yescharacteristic
100C2×C83#204711yescharacteristic
101C2×C83#205311yescharacteristic
102#3249—831no—
103#1843—831no—
104#1552—832no—
105#1506—832no—
106#1290D8311yescharacteristic
107C83#1051611yescharacteristic, complemented, Sylow
108#533—832no—
109#477—1662no—
110#467—1662no—
111#462—1662no—
112#432C2×D8312yes—
113C2×C4⋊C8—831no—
114C2×C4⋊C8—1662no—
115C2×C4⋊C8C2×D8311yescharacteristic
116#376—831no—
117#332—1662no—
118#332—1662no—
119#328—1664no—
120C2×Q16—1662no—
121C22×C8—1661no—
122C22×C8D33212yes—
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×C42—1661no—
132C2×C42C22×D8311yescharacteristic
133#107—1662no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—3324no—
137C4⋊C8—1662no—
138#103—1664no—
139C22⋊C8—22no—
140#97—22no—
141#95—832no—
142#95—1661no—
143C2×Q8—1662no—
144C2×Q8—1662no—
145C22×C4—1662no—
146C22×C4D4×D8311yescharacteristic
147C22×C4C2×D33211yescharacteristic
148C22×C4#1305059111yescharacteristic
149Q16—6642no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—3322no—
154C2×C8—3321no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C4⋊C4—1662no—
160C4⋊C4—1662no—
161C22⋊C4—3322no—
162C42—3322no—
163C42—1662no—
164C42—1662no—
165C42D4×D8312yes—
166C42#1305059012yes—
167C23#1458176711yescharacteristic
168Q8—3322no—
169Q8—3322no—
170Q8—6642no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—3322no—
176C2×C4—3322no—
177C2×C4—3322no—
178C2×C4—3322no—
179C2×C4—1664no—
180C2×C4#1458176211yescharacteristic
181C2×C4#1458176512yes—
182C2×C4#1458177712yes—
183C2×C4#1458178011yescharacteristic
184C8—42no—
185C8—82no—
186C8—6641no—
187C22—21no—
188C22—21no—
189C22#1912761911yescharacteristic
190C22#1912797712yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—3324no—
195C4—6642no—
196C4—6642no—
197C4#1912787111yescharacteristic
198C4#1912788611yescharacteristic
199C2—22no—
200C2#2490868811yescharacteristic
201C2#2490873211yescharacteristic
202C2#2490877011yescharacteristic
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1290C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1290D83
hypocenterC83#10516
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
107. C83#10516semidirect

Maximal subgroups

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

subgroupindex
#249188082
#249076162
#249061642
#249059762
C83×#12902
#1051683