Finite Group Databasebeta

← #24918669

Subgroups — #24918669

Order 10624.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#19128258C211yesmaximal, characteristic
2#19128111C212yesmaximal, complemented
3#19128071C212yesmaximal, complemented
4#19128036C212yesmaximal
5#19128031C212yesmaximal
6#19128005C214yesmaximal, complemented
7#19127758C211yesmaximal, characteristic
8C2×#125×C83C211yesmaximal, characteristic
9#14581792C2211yescharacteristic
10#14581792C2211yescharacteristic
11#14581784—21no—
12#14581771—21no—
13#14581771C2212yes—
14C4×Dic166—21no—
15C4×Dic166C2212yes—
16#14581751—21no—
17#14581725C2214yes—
18#14581723C2214yes—
19C4⋊(C83⋊C8)C2212yes—
20#14581715C2214yes—
21#14581715C2214yes—
22C22⋊(C83⋊C8)C2212yes—
23#14581703C2212yes—
24#125×C83—21no—
25#125×C83—21no—
26#125×C83C2212yes—
27#125×C83C2212yes—
28C2×C4⋊C4×C83—21no—
29C2×C4⋊C4×C83—21no—
30C2×C4⋊C4×C83C2211yescharacteristic
31C2×C4⋊C4×C83C2211yescharacteristic
32C2×C42×C83C2211yescharacteristic
33C2×Dic166—21no—
34C2×Dic166C2312yes—
35C2×C83⋊C8C2314yes—
36C4⋊Dic83—21no—
37C4⋊Dic83—21no—
38C4⋊Dic83—21no—
39C4⋊Dic83C2312yes—
40Dic83⋊C4—22no—
41Dic83⋊C4—22no—
42C22⋊Dic83—22no—
43C4×Dic83—22no—
44C22×C4×C83—21no—
45C22×C4×C83—21no—
46C22×C4×C83D411yescharacteristic
47C22×C4×C83D411yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C4⋊C4×C83—22no—
50C4⋊C4×C83—22no—
51C4⋊C4×C83—22no—
52C4⋊C4×C83—22no—
53C4⋊C4×C83—21no—
54C4⋊C4×C83—21no—
55C4⋊C4×C83C2312yes—
56C4⋊C4×C83C2312yes—
57C42×C83D411yescharacteristic
58C42×C83D411yescharacteristic
59C42×C83C2311yescharacteristic
60C42×C83C2311yescharacteristic
61C23×C83C2×D411yescharacteristic
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—41no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83C2×D411yescharacteristic
70C2×C4×C83C2×D411yescharacteristic
71C2×C4×C83C2×D411yescharacteristic
72C2×C4×C83C2×D411yescharacteristic
73C2×C4×C83C2×D411yescharacteristic
74C2×C4×C83C2411yescharacteristic
75C2×Dic83—22no—
76C2×Dic83—22no—
77Dic166—24no—
78Dic166—42no—
79C83⋊C8—24no—
80C22×C83—21no—
81C22×C83—21no—
82C22×C83#13712yes—
83C22×C83C22×D411yescharacteristic
84C4×C83—21no—
85C4×C83—21no—
86C4×C83—21no—
87C4×C83—21no—
88C4×C83—21no—
89C4×C83—42no—
90C4×C83—42no—
91C4×C832−1+412yes—
92Dic83—42no—
93Dic83—42no—
94C2×C83—22no—
95C2×C83#53611yescharacteristic
96C2×C83C2×#13711yescharacteristic
97C2×C83#57511yescharacteristic
98#3236—831nomaximal, Sylow
99C83#323611yescharacteristic, complemented, Sylow
100#533—831no—
101C2×#125D8311yescharacteristic
102#501—832no—
103#491—832no—
104#484—832no—
105#483—832no—
106#479—834no—
107#432—831no—
108C4⋊Q8—831no—
109C4⋊Q8—831no—
110#125—21no—
111#125—21no—
112#125—1661no—
113#125C2×D8312yes—
114#125C2×D8312yes—
115C22⋊Q8—832no—
116C22⋊Q8—1661no—
117C4×Q8—832no—
118C4×Q8—1661no—
119#117—1661no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D8311yescharacteristic
123C2×C4⋊C4C2×D8311yescharacteristic
124C2×C42C2×D8311yescharacteristic
125#107—834no—
126#106—834no—
127C4⋊C8—832no—
128#103—834no—
129#103—834no—
130C22⋊C8—832no—
131#97—832no—
132C2×Q8—832no—
133C2×Q8—1661no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D8311yescharacteristic
137C22×C4C22⋊D8311yescharacteristic
138C22×C4C22×D8311yescharacteristic
139C2×C8—834no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—832no—
147C4⋊C4—1661no—
148C4⋊C4—1661no—
149C4⋊C4—1662no—
150C4⋊C4—1662no—
151C4⋊C4—1661no—
152C4⋊C4C22×D8312yes—
153C4⋊C4C22×D8312yes—
154C22⋊C4—1662no—
155C42—1662no—
156C42C22⋊D8311yescharacteristic
157C42C22⋊D8311yescharacteristic
158C42C22×D8311yescharacteristic
159C42C22×D8311yescharacteristic
160C23C2×C22⋊D8311yescharacteristic
161Q8—3322no—
162Q8—1664no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—1662no—
171C2×C4—1662no—
172C2×C4C2×C22⋊D8311yescharacteristic
173C2×C4C2×C22⋊D8311yescharacteristic
174C2×C4C2×C22⋊D8311yescharacteristic
175C2×C4C2×C22⋊D8311yescharacteristic
176C2×C4C2×C22⋊D8311yescharacteristic
177C2×C4C23×D8311yescharacteristic
178C8—1664no—
179C22—21no—
180C22—21no—
181C22#1458182212yes—
182C22C22×C22⋊D8311yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—3322no—
191C4—3322no—
192C4#1458184012yes—
193C2—22no—
194C2#1912827511yescharacteristic
195C2C2×#1458182211yescharacteristic
196C2#1912849911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#125×C83C2
socleC22×C83C22×D4
prime radicalC23×C83C2×D4
hypercenterC2×#125D83
hypocenterC83#3236
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #19128111C2semidirect
3. #19128071C2semidirect
6. #19128005C2semidirect
99. C83#3236semidirect

Maximal subgroups

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

subgroupindex
#191282582
#191281112
#191280712
#191280362
#191280312
#191280052
#191277582
C2×#125×C832
#323683