Finite Group Databasebeta

← #23764375

Subgroups — #23764375

Order 10112.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#19099116C211yesmaximal, characteristic
2#19098586C211yesmaximal, characteristic
3C42×Dic79C211yesmaximal, characteristic
4#19098324C211yesmaximal, characteristic
5#19098323C211yesmaximal, characteristic
6#19098322C211yesmaximal, characteristic
7#339×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9#14579160C412yescomplemented
10#14579152C412yescomplemented
11#14579138—22no—
12C4×Dic158—22no—
13#14579120C2211yescharacteristic
14C2×C4×Dic79—22no—
15C2×C4×Dic79C2211yescharacteristic
16C2×C4×Dic79C2211yescharacteristic
17Dic79⋊C8—22no—
18C2×M16×C79C2211yescharacteristic
19#117×C79C2211yescharacteristic
20C2×C42×C79C2211yescharacteristic
21C2×Dic158—22no—
22C22×Dic79—21no—
23C22×Dic79D412yes—
24#11929608—21no—
25#11929608—21no—
26C2×C79⋊C8—21no—
27C4⋊Dic79—22no—
28C4⋊Dic79C2×C412yes—
29Dic79⋊C4—22no—
30Dic79⋊C4—22no—
31C22⋊Dic79—21no—
32C4×Dic79—28no—
33C4×Dic79—21no—
34C4×Dic79—21no—
35C4×Dic79C2×C411yescharacteristic
36C4×Dic79C2×C411yescharacteristic
37C4×Dic79D412yes—
38C4×Dic79Q812yescomplemented
39C22×C4×C79—21no—
40C22×C4×C79C2311yescharacteristic
41M16×C79—21no—
42M16×C79—21no—
43C2×C8×C79—21no—
44C4⋊C4×C79C2×C412yes—
45C22⋊C4×C79—21no—
46C42×C79—21no—
47C42×C79—21no—
48C42×C79Q812yescomplemented
49C23×C79C2×D411yescharacteristic
50C2×C4×C79—24no—
51C2×C4×C79—22no—
52C2×C4×C79—22no—
53C2×C4×C79C22×C411yescharacteristic
54C2×C4×C79C2×D411yescharacteristic
55C2×C4×C79C2×Q811yescharacteristic
56C2×C4×C79C2×Q811yescharacteristic
57C2×C4×C79#4111yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×Dic79—24no—
60C2×Dic79—22no—
61C2×Dic79—24no—
62C2×Dic79—22no—
63C2×Dic79C22⋊C412yes—
64C2×Dic79C22⋊C412yes—
65Dic158—44no—
66C8×C79—41no—
67C79⋊C8—41no—
68C22×C79—22no—
69C22×C79C2×C22⋊C411yescharacteristic
70C22×C79C22⋊Q811yescharacteristic
71C22×C79C22⋊Q811yescharacteristic
72C4×C79—24no—
73C4×C79—42no—
74C4×C79C4×Q811yescharacteristic
75C4×C79C4×Q811yescharacteristic
76C4×C79#12411yescharacteristic
77C4×C79C4⋊Q811yescharacteristic
78Dic79—24no—
79Dic79—22no—
80Dic79—42no—
81Dic79#10414yes—
82C2×C79—21no—
83C2×C79—21no—
84C2×C79#39111yescharacteristic
85C2×C79C2×#10412yes—
86#1994—791nomaximal, Sylow
87C79#199411yescharacteristic, complemented, Sylow
88#533—791no—
89#423—791no—
90C43—791no—
91#339—791no—
92#339—791no—
93#339—791no—
94#339D7911yescharacteristic
95C2×M16—791no—
96C2×M16C2×D7911yescharacteristic
97C4⋊Q8—792no—
98#125—792no—
99C22⋊Q8—1582no—
100C4×Q8—1582no—
101#117—791no—
102#117C2×D7911yescharacteristic
103C2×C42—791no—
104C2×C42—791no—
105C2×C42—1582no—
106C2×C42C2×D7911yescharacteristic
107C4⋊C8—1582no—
108C2×Q8—1582no—
109C22×C4—21no—
110C22×C4—792no—
111C22×C4—1581no—
112C22×C4C22×D7911yescharacteristic
113M16—21no—
114M16—21no—
115M16—1581no—
116M16—1581no—
117C2×C8—21no—
118C2×C8—1581no—
119C4⋊C4—792no—
120C4⋊C4—1582no—
121C4⋊C4—1582no—
122C4⋊C4—1582no—
123C4⋊C4C4×D7912yes—
124C22⋊C4—21no—
125C22⋊C4—1581no—
126C42—21no—
127C42—21no—
128C42—791no—
129C42—791no—
130C42—792no—
131C42—792no—
132C42—1588no—
133C42—1581no—
134C42—1581no—
135C42Dic15812yescomplemented
136C23D4×D7911yescharacteristic
137Q8—3164no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—792no—
142C2×C4—792no—
143C2×C4—1582no—
144C2×C4—1584no—
145C2×C4—1584no—
146C2×C4—1582no—
147C2×C4C2×C4×D7911yescharacteristic
148C2×C4D4×D7911yescharacteristic
149C2×C4Q8×D7911yescharacteristic
150C2×C4C2×Dic15811yescharacteristic
151C2×C4#1192962311yescharacteristic
152C2×C4#1192962411yescharacteristic
153C8—41no—
154C8—3161no—
155C22—22no—
156C22C22⋊C4×D7911yescharacteristic
157C22#1457913811yescharacteristic
158C22#1457913911yescharacteristic
159C4—24no—
160C4—42no—
161C4—3162no—
162C4—794no—
163C4—1584no—
164C4—1582no—
165C4#1457912611yescharacteristic
166C4C4×Dic15811yescharacteristic
167C4#1457914711yescharacteristic
168C4#1457916011yescharacteristic
169C2—21no—
170C2—21no—
171C2#1909846711yescharacteristic
172C2#104×D7912yes—
subgroupG/H
centerC2×C4D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#339×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#339D79
hypocenterC79#1994
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14579160C4semidirect
10. #14579152C4semidirect
38. C4×Dic79Q8semidirect
48. C42×C79Q8semidirect
87. C79#1994semidirect
135. C42Dic158semidirect