Finite Group Databasebeta

← #35308498

Subgroups — #35308498

Order 21248.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#24906161C212yesmaximal
3#24905974C212yesmaximal
4#24905333C211yesmaximal, characteristic
5C83×#1843C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127997—22no—
8#19127942—22no—
9#19127912—22no—
10#19127758C2212yes—
11#19127448—22no—
12#19127446—22no—
13#19127437—24no—
14C2×C4⋊C8×C83—22no—
15C2×C4⋊C8×C83C2211yescharacteristic
16C2×C4⋊C8×C83C2211yescharacteristic
17#376×C83C2211yescharacteristic
18C2×Dic332—22no—
19#14581792D412yes—
20#14581792D412yes—
21#14581784—22no—
22#14581771—22no—
23#14581771—22no—
24C4×Dic166—22no—
25C4×Dic166—22no—
26#14581751—22no—
27#14581726—22no—
28C4⋊(C83⋊C8)—22no—
29#14581717—24no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32C22×C8×C83—21no—
33C22×C8×C83D412yes—
34C2×C42×C83—21no—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C4⋊C8×C83—44no—
39#95×C83—21no—
40#95×C83D412yes—
41C2×Dic166—22no—
42C2×Dic166—22no—
43Dic332—82no—
44C2×C83⋊C8—42no—
45C4⋊Dic83—22no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49Dic83⋊C4—42no—
50Dic83⋊C4—42no—
51C22⋊Dic83—42no—
52C4×Dic83—42no—
53C22×C4×C83—22no—
54C22×C4×C83C2×D411yescharacteristic
55C22×C4×C83C2×D411yescharacteristic
56C22×C4×C83#4111yescharacteristic
57C2×C8×C83—22no—
58C2×C8×C83—42no—
59C2×C8×C83—42no—
60C2×C8×C83—41no—
61C42×C83—22no—
62C42×C83—22no—
63C42×C83C2×D412yes—
64C42×C83#4112yes—
65C23×C83#12111yescharacteristic
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—21no—
69C2×C4×C83—24no—
70C2×C4×C83—41no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83#12011yescharacteristic
74C2×C4×C83#12112yes—
75C2×C4×C83#12312yes—
76C2×C4×C83#12411yescharacteristic
77C2×Dic83—42no—
78C2×Dic83—42no—
79Dic166—42no—
80Dic166—42no—
81Dic166—82no—
82C8×C83—42no—
83C8×C83—81no—
84C83⋊C8—82no—
85C22×C83—21no—
86C22×C83—21no—
87C22×C83#39411yescharacteristic
88C22×C83#47312yes—
89C4×C83—22no—
90C4×C83—21no—
91C4×C83—22no—
92C4×C83—44no—
93C4×C83#45311yescharacteristic
94C4×C83#45611yescharacteristic
95Dic83—82no—
96Dic83—82no—
97#10516—831nomaximal, Sylow
98C2×C83—22no—
99C2×C83#203911yescharacteristic
100C2×C83#204711yescharacteristic
101C2×C83#205311yescharacteristic
102#3249—831no—
103#1843D8311yescharacteristic
104#1552—832no—
105#1506—832no—
106#1290—831no—
107C83#1051611yescharacteristic, complemented, Sylow
108#533—832no—
109#477—1662no—
110#467—1662no—
111#462—1662no—
112#432—832no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8C2×D8311yescharacteristic
115C2×C4⋊C8C2×D8311yescharacteristic
116#376C2×D8311yescharacteristic
117#332—1662no—
118#332—1662no—
119#328—1664no—
120C2×Q16—1662no—
121C22×C8—21no—
122C22×C8C22⋊D8312yes—
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—21no—
132C2×C42C22×D8311yescharacteristic
133#107—1662no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—1662no—
138#103—1664no—
139C22⋊C8—1662no—
140#97—1662no—
141#95—21no—
142#95D33212yes—
143C2×Q8—1662no—
144C2×Q8—1662no—
145C22×C4—22no—
146C22×C4C2×C22⋊D8311yescharacteristic
147C22×C4C2×D33211yescharacteristic
148C22×C4#1305059011yescharacteristic
149Q16—6642no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—3322no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C4⋊C4—1662no—
160C4⋊C4—1662no—
161C22⋊C4—3322no—
162C42—22no—
163C42—22no—
164C42—3322no—
165C42D4×D8312yes—
166C42#1305059112yes—
167C23#1458176611yescharacteristic
168Q8—3322no—
169Q8—3322no—
170Q8—6642no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—3322no—
179C2×C4—3322no—
180C2×C4#1458176011yescharacteristic
181C2×C4#1458176712yes—
182C2×C4#1458177712yes—
183C2×C4#1458178111yescharacteristic
184C8—42no—
185C8—81no—
186C8—6642no—
187C22—21no—
188C22—21no—
189C22#1912761811yescharacteristic
190C22#1912797612yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—6642no—
196C4—6642no—
197C4#1912786811yescharacteristic
198C4#1912788311yescharacteristic
199C2—22no—
200C2#2490868711yescharacteristic
201C2#2490873111yescharacteristic
202C2#2490876911yescharacteristic
subgroupG/H
centerC22#19127618
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1843C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1843D83
hypocenterC83#10516
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

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
#249061612
#249059742
#249053332
C83×#18432
#1051683