Finite Group Databasebeta

← #24906637

Subgroups — #24906637

Order 10624.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#19128421C211yesmaximal, characteristic
2#19128052C211yesmaximal, characteristic, complemented
3#19127997C211yesmaximal, characteristic, complemented
4#19127991C211yesmaximal, characteristic
5#19127446C211yesmaximal, characteristic, complemented
6#19127433C211yesmaximal, characteristic, complemented
7D4⋊C8×C83C211yesmaximal, characteristic
8#14581792C2211yescharacteristic
9#14581792C2211yescharacteristic
10#14581785—22no—
11#14581779—21no—
12#14581771—21no—
13C4×Dic166C2211yescharacteristic
14#14581757—21no—
15#14581751—21no—
16#14581726—21no—
17#14581723—21no—
18C4⋊(C83⋊C8)C2211yescharacteristic
19#14581717—21no—
20#14581717—22no—
21#14581713—21no—
22C4×D4×C83C2211yescharacteristic
23C4⋊C8×C83C2211yescharacteristic
24C4×C8×C83C2211yescharacteristic
25C2×Dic166—21no—
26C2×Dic166—21no—
27C2×Dic166D411yescharacteristic
28C2×C83⋊C8—21no—
29C4⋊Dic83—21no—
30C4⋊Dic83—21no—
31C4⋊Dic83—21no—
32C4⋊Dic83D412yes—
33C4⋊Dic83D411yescharacteristic
34Dic83⋊C4—22no—
35Dic83⋊C4—21no—
36C22⋊Dic83—22no—
37C22⋊Dic83—22no—
38C4×Dic83—22no—
39C4×Dic83—21no—
40C2×D4×C83D411yescharacteristic
41C22×C4×C83—21no—
42C2×C8×C83—21no—
43C2×C8×C83—21no—
44C4⋊C4×C83D411yescharacteristic
45C22⋊C4×C83—21no—
46C42×C83C2311yescharacteristic
47C23×C83—21no—
48D4×C83—21no—
49D4×C83—21no—
50C2×C4×C83—21no—
51C2×C4×C83—41no—
52C2×C4×C83—41no—
53C2×C4×C83C2×D411yescharacteristic
54C2×C4×C83C2×D411yescharacteristic
55C2×C4×C83C2×D411yescharacteristic
56C2×Dic83—21no—
57C2×Dic83—21no—
58C2×Dic83—22no—
59C2×Dic83—41no—
60Dic166—21no—
61Dic166—21no—
62Dic166—41no—
63Dic166—41no—
64Dic166—42no—
65C8×C83—41no—
66C8×C83—41no—
67C83⋊C8—41no—
68C22×C83—41no—
69C22×C83—41no—
70C22×C83—41no—
71C22×C83#12011yescharacteristic
72C4×C83—21no—
73C4×C83—41no—
74C4×C83#13511yescharacteristic
75C4×C83#13511yescharacteristic
76C4×C83#13711yescharacteristic
77C4×C83#13711yescharacteristic
78Dic83—41no—
79Dic83—42no—
80Dic83—41no—
81Dic83—81no—
82C2×C83—81no—
83C2×C83#45211yescharacteristic
84C2×C83#45211yescharacteristic
85C2×C83#45411yescharacteristic
86#1638—831nomaximal, Sylow
87C83#163811yescharacteristic, complemented, Sylow
88#556—831no—
89#487—831no—
90#477—831no—
91#476—831no—
92#332—831no—
93Q8⋊C8—831no—
94D4⋊C8D8311yescharacteristic
95C4⋊Q8—831no—
96C4⋊Q8—831no—
97#126—1662no—
98#124—1661no—
99C22⋊Q8—1661no—
100C4×Q8—831no—
101C4×Q8—1661no—
102C4×D4C2×D8311yescharacteristic
103#117—1661no—
104#107—1661no—
105#106—1661no—
106C4⋊C8—831no—
107C4⋊C8C2×D8311yescharacteristic
108#103—1662no—
109#103—1661no—
110#102—1661no—
111C4×C8C2×D8311yescharacteristic
112C2×Q8—831no—
113C2×Q8—1661no—
114C2×Q8—1661no—
115C2×D4D33211yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—1661no—
120C4⋊C4—832no—
121C4⋊C4—831no—
122C4⋊C4—1662no—
123C4⋊C4—1661no—
124C4⋊C4—1661no—
125C4⋊C4—1661no—
126C4⋊C4—1661no—
127C4⋊C4D33211yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—1662no—
130C22⋊C4—1662no—
131C42—1662no—
132C42—1661no—
133C42C22×D8311yescharacteristic
134C23—21no—
135Q8—3322no—
136Q8—3321no—
137Q8—3321no—
138Q8—1661no—
139Q8—1661no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—3321no—
146C2×C4—1661no—
147C2×C4—1662no—
148C2×C4—1661no—
149C2×C4D4×D8311yescharacteristic
150C2×C4D4×D8311yescharacteristic
151C2×C4C2×D33211yescharacteristic
152C8—41no—
153C8—41no—
154C8—3321no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1458176211yescharacteristic
159C4—21no—
160C4—41no—
161C4—3321no—
162C4—3322no—
163C4—3321no—
164C4—6641no—
165C4#1458181111yescharacteristic
166C4#1458181411yescharacteristic
167C4#1458182111yescharacteristic
168C4#1458182511yescharacteristic
169C2—81no—
170C2#1912786411yescharacteristic
171C2#1912786511yescharacteristic
172C2#1912787511yescharacteristic
subgroupG/H
centerC22#14581762
commutator, cosocleC42×C83C23
FrattiniC42C22×D83
FittingD4⋊C8×C83C2
socleC22×C83#120
prime radicalC2×D4×C83D4
hypercenterD4⋊C8D83
hypocenterC83#1638
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #19128052C2semidirect
3. #19127997C2semidirect
5. #19127446C2semidirect
6. #19127433C2semidirect
87. C83#1638semidirect

Maximal subgroups

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

subgroupindex
#191284212
#191280522
#191279972
#191279912
#191274462
#191274332
D4⋊C8×C832
#163883