Finite Group Databasebeta

← #35308495

Subgroups — #35308495

Order 21248.

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

normal subgroups only

This group has 364 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#24907616C211yesmaximal, characteristic
2#24906163C212yesmaximal
3#24905975C212yesmaximal
4#24905333C211yesmaximal, characteristic
5C83×#3249C211yesmaximal, characteristic
6#19127758C2212yes—
7C2×C4⋊(C83⋊C8)C2211yescharacteristic
8C2×Dic83⋊C8—22no—
9#19127547C2211yescharacteristic
10#19127447—22no—
11#19127447—22no—
12#19127438—24no—
13#533×C83C2212yes—
14#477×C83—22no—
15#467×C83—22no—
16#462×C83—22no—
17C2×C4⋊C8×C83C2211yescharacteristic
18C22×C83⋊C8—21no—
19C2×C4×Dic83—21no—
20C4⋊(C83⋊C8)—22no—
21C4⋊(C83⋊C8)—22no—
22Dic83⋊C8—44no—
23C22⋊(C83⋊C8)—22no—
24#14581703—22no—
25C83⋊#95—21no—
26C83⋊#95D412yes—
27C2×Q16×C83—22no—
28C22×C8×C83D412yes—
29C4⋊Q8×C83D412yes—
30C4⋊Q8×C83D412yes—
31#125×C83—22no—
32C22⋊Q8×C83—22no—
33C22⋊Q8×C83—22no—
34C4×Q8×C83—22no—
35C4×Q8×C83—22no—
36#117×C83—22no—
37C2×C42×C83C2311yescharacteristic
38#107×C83—22no—
39C4⋊C8×C83—22no—
40#103×C83—24no—
41C22×Dic83—22no—
42C2×C83⋊C8—42no—
43C2×C83⋊C8—41no—
44C2×C83⋊C8—42no—
45C4×Dic83—22no—
46C4×Dic83—22no—
47C2×Q8×C83—22no—
48C2×Q8×C83—22no—
49C22×C4×C83C2×D411yescharacteristic
50C22×C4×C83C2×D411yescharacteristic
51C22×C4×C83#4111yescharacteristic
52Q16×C83—82no—
53C2×C8×C83—22no—
54C2×C8×C83—42no—
55C4⋊C4×C83—22no—
56C4⋊C4×C83—22no—
57C4⋊C4×C83—22no—
58C4⋊C4×C83—22no—
59C4⋊C4×C83—42no—
60C4⋊C4×C83—42no—
61C22⋊C4×C83—42no—
62C42×C83—42no—
63C42×C83C2×D412yes—
64C42×C83#4112yes—
65C23×C83#12111yescharacteristic
66Q8×C83—42no—
67Q8×C83—42no—
68Q8×C83—82no—
69C2×C4×C83—22no—
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—41no—
73C2×C4×C83—42no—
74C2×C4×C83—42no—
75C2×C4×C83#12011yescharacteristic
76C2×C4×C83#12112yes—
77C2×C4×C83#12312yes—
78C2×C4×C83#12411yescharacteristic
79C2×Dic83—24no—
80C2×Dic83—42no—
81C2×Dic83—42no—
82C8×C83—42no—
83C83⋊C8—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—82no—
93C4×C83—82no—
94C4×C83#45311yescharacteristic
95C4×C83#45611yescharacteristic
96Dic83—44no—
97#10516—831nomaximal, Sylow
98C2×C83—22no—
99C2×C83#203911yescharacteristic
100C2×C83#204711yescharacteristic
101C2×C83#205311yescharacteristic
102#3249D8311yescharacteristic
103#1843—831no—
104#1552—832no—
105#1506—832no—
106#1290—831no—
107C83#1051611yescharacteristic, complemented, Sylow
108#533C2×D8312yes—
109#477—22no—
110#467—22no—
111#462—22no—
112#432—832no—
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—22no—
121C22×C8—1661no—
122C22×C8C22⋊D8312yes—
123C4⋊Q8C22⋊D8312yes—
124C4⋊Q8C22⋊D8312yes—
125#125—22no—
126C22⋊Q8—22no—
127C22⋊Q8—22no—
128C4×Q8—22no—
129C4×Q8—22no—
130#117—22no—
131C2×C42—1661no—
132C2×C42C22×D8311yescharacteristic
133#107—22no—
134C4⋊C8—22no—
135C4⋊C8—3324no—
136C4⋊C8—1662no—
137C4⋊C8—1662no—
138#103—24no—
139C22⋊C8—1662no—
140#97—1662no—
141#95—832no—
142#95—1661no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—1662no—
146C22×C4D4×D8311yescharacteristic
147C22×C4C2×C22⋊D8311yescharacteristic
148C22×C4#1305058911yescharacteristic
149Q16—82no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—3322no—
153C2×C8—3321no—
154C2×C8—3322no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—22no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C22⋊C4—42no—
162C42—42no—
163C42—1662no—
164C42—1662no—
165C42C2×C22⋊D8312yes—
166C42#1305058912yes—
167C23#1458176311yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—82no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—3322no—
178C2×C4—3322no—
179C2×C4—1664no—
180C2×C4#1458176111yescharacteristic
181C2×C4#1458176412yes—
182C2×C4#1458177312yes—
183C2×C4#1458177911yescharacteristic
184C8—42no—
185C8—6642no—
186C8—6641no—
187C22—21no—
188C22—21no—
189C22#1912761511yescharacteristic
190C22#1912797312yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—82no—
195C4—82no—
196C4—3324no—
197C4#1912786911yescharacteristic
198C4#1912788411yescharacteristic
199C2—22no—
200C2#2490868411yescharacteristic
201C2#2490872811yescharacteristic
202C2#2490876611yescharacteristic
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3249C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#3249D83
hypocenterC83#10516
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

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
#249076162
#249061632
#249059752
#249053332
C83×#32492
#1051683