Finite Group Databasebeta

← #35313749

Subgroups — #35313749

Order 21248.

296 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 91 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#24916396C211yesmaximal, characteristic
2#24909259C212yesmaximal
3#24905405C211yesmaximal, characteristic
4#24905404C212yesmaximal
5C83×#1323C211yesmaximal, characteristic
6#19128254C411yescharacteristic
7#19127830—22no—
8#19127825—22no—
9#19127727C2211yescharacteristic
10#19127724C411yescharacteristic
11#19127659C411yescharacteristic
12#19127657C411yescharacteristic
13C2×C8×Dic83C2211yescharacteristic
14Dic83⋊C16—22no—
15C22⋊(C83⋊C16)C2212yes—
16C16×Dic83—22no—
17#424×C83C2211yescharacteristic
18C22⋊C16×C83C2212yes—
19C2×#13050574C2×C411yescharacteristic
20C22×C83⋊C8C2×C411yescharacteristic
21#14581791C812yes—
22#14581783C812yes—
23#14581769—22no—
24C4×Dic166—22no—
25#14581751C2×C411yescharacteristic
26C2×C4×Dic83C2×C411yescharacteristic
27C2×C83⋊C16—22no—
28Dic83⋊C8—22no—
29Dic83⋊C8—22no—
30#14581703—21no—
31#14581702—21no—
32C4×C83⋊C8—21no—
33C8×Dic83—21no—
34C8×Dic83D412yes—
35C8×Dic83D412yes—
36C2×M16×C83C2×C411yescharacteristic
37C22×C8×C83C2311yescharacteristic
38#117×C83C2×C411yescharacteristic
39C2×C16×C83—22no—
40C4⋊C8×C83—22no—
41C2×Dic166—22no—
42C22×Dic83M1612yes—
43#13050574—41no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8—21no—
46C2×C83⋊C8C22⋊C411yescharacteristic
47C2×C83⋊C8C22⋊C411yescharacteristic
48C4⋊Dic83—22no—
49C4⋊Dic83C2×C812yes—
50Dic83⋊C4—22no—
51Dic83⋊C4—22no—
52C22⋊Dic83—21no—
53C4×Dic83—21no—
54C4×Dic83C22⋊C412yes—
55C4×Dic83C2×C811yescharacteristic
56C4×Dic83C2×C811yescharacteristic
57C83⋊C16—42no—
58C22×C4×C83C22×C411yescharacteristic
59M16×C83—41no—
60C2×C8×C83—21no—
61C2×C8×C83—41no—
62C2×C8×C83C2×D412yes—
63C4⋊C4×C83C2×C812yes—
64C22⋊C4×C83—21no—
65C42×C83—21no—
66C16×C83—42no—
67C23×C83C2×M1611yescharacteristic
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83—22no—
71C2×C4×C83C2×C22⋊C411yescharacteristic
72C2×C4×C83C22×C811yescharacteristic
73C2×Dic83—24no—
74C2×Dic83—22no—
75C2×Dic83C22⋊C812yes—
76C2×Dic83C22⋊C812yes—
77Dic166—44no—
78C8×C83—22no—
79C8×C83—41no—
80C83⋊C8—21no—
81C83⋊C8—41no—
82C83⋊C8#10112yes—
83C22×C83—22no—
84C22×C83—21no—
85C22×C83C2×C22⋊C811yescharacteristic
86C4×C83—21no—
87C4×C83—42no—
88C4×C83#41011yescharacteristic
89C4×C83C2×#10111yescharacteristic
90Dic83—22no—
91Dic83—42no—
92Dic83#35014yes—
93#11496—831nomaximal, Sylow
94C2×C83—41no—
95C2×C83#146111yescharacteristic
96C2×C83C2×#35012yes—
97#2960—831no—
98#2162—832no—
99#1323—831no—
100#1323—832no—
101#1323D8311yescharacteristic
102C83#1149611yescharacteristic, complemented, Sylow
103#533—831no—
104#446—1662no—
105C8×Q8—1662no—
106#424—831no—
107#424C2×D8311yescharacteristic
108#423—831no—
109#405—831no—
110#405—831no—
111C2×C4×C8—831no—
112C4⋊C16—1662no—
113C22⋊C16—832no—
114C22⋊C16C2×D8312yes—
115C4×C16—1662no—
116C2×M16—831no—
117C2×M16C4×D8311yescharacteristic
118C22×C8—831no—
119C22×C8C22×D8311yescharacteristic
120C4⋊Q8—832no—
121#125—832no—
122C22⋊Q8—1662no—
123C4×Q8—1662no—
124#117—831no—
125#117C4×D8311yescharacteristic
126C2×C42—831no—
127C2×C16—22no—
128C2×C16—1662no—
129C4⋊C8—22no—
130C4⋊C8—1662no—
131C4⋊C8—1662no—
132#97—1661no—
133#97—1661no—
134C4×C8—832no—
135C4×C8—832no—
136C4×C8—1661no—
137C4×C8—1661no—
138C2×Q8—1662no—
139C22×C4—832no—
140C22×C4C2×C4×D8311yescharacteristic
141M16—41no—
142M16—3321no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—831no—
146C2×C8—831no—
147C2×C8—1661no—
148C2×C8—1662no—
149C2×C8D4×D8312yes—
150C4⋊C4—832no—
151C4⋊C4—1662no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4C8×D8312yes—
155C22⋊C4—21no—
156C22⋊C4—1661no—
157C42—21no—
158C42—831no—
159C42—831no—
160C42—832no—
161C42—1661no—
162C16—42no—
163C16—3322no—
164C23M16×D8311yescharacteristic
165Q8—3324no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—832no—
170C2×C4—832no—
171C2×C4—1662no—
172C2×C4—1664no—
173C2×C4C22⋊C4×D8311yescharacteristic
174C2×C4C2×C8×D8311yescharacteristic
175C8—22no—
176C8—41no—
177C8—3321no—
178C8—832no—
179C8—1661no—
180C22—22no—
181C22—21no—
182C22C22⋊C8×D8311yescharacteristic
183C4—21no—
184C4—42no—
185C4—3322no—
186C4—834no—
187C4—1662no—
188C4#1912767311yescharacteristic
189C4#101×D8311yescharacteristic
190C2—41no—
191C2#2490578511yescharacteristic
192C2#350×D8312yes—
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C22×C8
FrattiniC22×C8C22×D83
FittingC83×#1323C2
socleC22×C83C2×C22⋊C8
prime radicalC23×C83C2×M16
cosocleC22×C8×C83C23
hypercenter#1323D83
hypocenterC83#11496
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
102. C83#11496semidirect

Maximal subgroups

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

subgroupindex
#249163962
#249092592
#249054052
#249054042
C83×#13232
#1149683