Finite Group Databasebeta

← #24907855

Subgroups — #24907855

Order 10624.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14581792C211yesmaximal, characteristic
2#19128178C211yesmaximal, characteristic
3#19127711C211yesmaximal, characteristic
4#19127709C211yesmaximal, characteristic
5C2×#14581710C211yesmaximal, characteristic
6#19127461C211yesmaximal, characteristic
7#339×C83C211yesmaximal, characteristic
8C22×Dic166C2211yescharacteristic
9C22×Dic166C2211yescharacteristic
10C2×#13050574C2211yescharacteristic
11#14581792—22no—
12#14581792C414yescomplemented
13C4×Dic166—22no—
14#14581757—22no—
15#14581751C2211yescharacteristic
16#14581748—22no—
17C2×C4⋊Dic83—22no—
18#14581717—22no—
19#14581715—22no—
20#14581710—22no—
21C2×M16×C83C2211yescharacteristic
22#117×C83C2211yescharacteristic
23C2×C42×C83C2211yescharacteristic
24C2×Dic166—21no—
25C2×Dic166—21no—
26C2×Dic166—21no—
27C2×Dic166—21no—
28C2×Dic166—21no—
29C2×Dic166—21no—
30C2×Dic166—21no—
31C2×Dic166—21no—
32C2×Dic166—21no—
33C2×Dic166C2×C412yes—
34C2×Dic166C2×C412yes—
35C2×Dic166D412yes—
36C22×Dic83—21no—
37C22×Dic83D412yes—
38#13050574—21no—
39#13050574—21no—
40C2×C83⋊C8—21no—
41C4⋊Dic83—28no—
42C4⋊Dic83D412yes—
43Dic83⋊C4—24no—
44C22⋊Dic83—21no—
45C4×Dic83—24no—
46C4×Dic83—21no—
47C22×C4×C83—21no—
48C22×C4×C83C2311yescharacteristic
49M16×C83—21no—
50M16×C83—21no—
51C2×C8×C83—21no—
52C4⋊C4×C83D412yes—
53C22⋊C4×C83—21no—
54C42×C83—21no—
55C42×C83—21no—
56C42×C83C2×C412yes—
57C23×C83C2×D411yescharacteristic
58C2×C4×C83—24no—
59C2×C4×C83—22no—
60C2×C4×C83—22no—
61C2×C4×C83C22×C411yescharacteristic
62C2×C4×C83C2×D411yescharacteristic
63C2×C4×C83C2×D411yescharacteristic
64C2×C4×C83C2×D411yescharacteristic
65C2×C4×C83#4111yescharacteristic
66C2×C4×C83#4111yescharacteristic
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—41no—
72C2×Dic83—41no—
73C2×Dic83C22⋊C414yes—
74Dic166—22no—
75Dic166—22no—
76Dic166—22no—
77Dic166—22no—
78Dic166—22no—
79Dic166—22no—
80Dic166—41no—
81Dic166—41no—
82C8×C83—41no—
83C83⋊C8—41no—
84C22×C83—22no—
85C22×C83C2×C22⋊C411yescharacteristic
86C22×C83#12011yescharacteristic
87C22×C83#12311yescharacteristic
88C4×C83—24no—
89C4×C83—42no—
90C4×C83C4×D411yescharacteristic
91C4×C83C4×D411yescharacteristic
92C4×C83#12111yescharacteristic
93C4×C83#12111yescharacteristic
94Dic83—24no—
95Dic83—42no—
96Dic83—42no—
97C2×C83—21no—
98C2×C83—21no—
99C2×C83#38611yescharacteristic
100C2×C83#45612yes—
101#1886—831nomaximal, Sylow
102C83#188611yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—831no—
104#519—831no—
105#419—831no—
106#419—831no—
107C2×#101—831no—
108#339—831no—
109#339D8311yescharacteristic
110C22×Q8—831no—
111C22×Q8—831no—
112C2×M16—831no—
113C2×M16C2×D8311yescharacteristic
114C4⋊Q8—834no—
115C4⋊Q8—1662no—
116C4×Q8—1662no—
117C4×Q8—1662no—
118#117—831no—
119#117—1662no—
120#117C2×D8311yescharacteristic
121C2×C4⋊C4—1662no—
122C2×C42C2×D8311yescharacteristic
123#103—1662no—
124#103—1662no—
125#101—1662no—
126C2×Q8—832no—
127C2×Q8—832no—
128C2×Q8—832no—
129C2×Q8—1661no—
130C2×Q8—1661no—
131C2×Q8—1661no—
132C2×Q8—1661no—
133C2×Q8—1661no—
134C2×Q8—1661no—
135C2×Q8—1661no—
136C2×Q8—1661no—
137C2×Q8—1661no—
138C22×C4—21no—
139C22×C4—832no—
140C22×C4—1661no—
141C22×C4C22×D8311yescharacteristic
142M16—21no—
143M16—21no—
144M16—1661no—
145M16—1661no—
146C2×C8—21no—
147C2×C8—1661no—
148C4⋊C4—832no—
149C4⋊C4—1668no—
150C4⋊C4—1664no—
151C4⋊C4D33212yes—
152C22⋊C4—21no—
153C22⋊C4—1661no—
154C42—21no—
155C42—21no—
156C42—1664no—
157C42—1661no—
158C42C4×D8312yes—
159C23D4×D8311yescharacteristic
160Q8—3321no—
161Q8—3321no—
162Q8—1662no—
163Q8—1662no—
164Q8—1662no—
165Q8—1662no—
166Q8—1662no—
167Q8—1662no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—3321no—
172C2×C4—3321no—
173C2×C4—834no—
174C2×C4—1662no—
175C2×C4—1662no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4C2×C4×D8311yescharacteristic
179C2×C4D4×D8311yescharacteristic
180C2×C4D4×D8311yescharacteristic
181C2×C4C2×D33211yescharacteristic
182C2×C4#1305059011yescharacteristic
183C2×C4#1305059111yescharacteristic
184C8—41no—
185C8—3321no—
186C22—22no—
187C22C22⋊C4×D8311yescharacteristic
188C22#1458176211yescharacteristic
189C22#1458177711yescharacteristic
190C4—24no—
191C4—42no—
192C4—3322no—
193C4—3322no—
194C4—1664no—
195C4#1458175411yescharacteristic
196C4C4×D33211yescharacteristic
197C4#1458176511yescharacteristic
198C4#1458176711yescharacteristic
199C2—21no—
200C2—21no—
201C2#1912757911yescharacteristic
202C2#1912788512yes—
subgroupG/H
centerC22#14581762
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#339×C83C2
socleC22×C83#120
prime radicalC23×C83C2×D4
cosocleC22×C4×C83C23
hypercenter#339D83
hypocenterC83#1886
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #14581792C4semidirect
102. C83#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#145817922
#191281782
#191277112
#191277092
C2×#145817102
#191274612
#339×C832
#188683