Finite Group Databasebeta

← #23764002

Subgroups — #23764002

Order 10112.

186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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#19098599C211yesmaximal, characteristic
2#19098590C211yesmaximal, characteristic
3#19098521C211yesmaximal, characteristic
4#19098327C211yesmaximal, characteristic
5#19098323C211yesmaximal, characteristic
6#19098318C211yesmaximal, characteristic
7#339×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C22×C79⋊C8C2211yescharacteristic
11#14579120C2211yescharacteristic
12#14579094C411yescharacteristic, complemented
13#14579094C411yescharacteristic, complemented
14#14579092C411yescharacteristic, complemented
15#14579092C411yescharacteristic, complemented
16C4⋊(C79⋊C8)—21no—
17C4⋊(C79⋊C8)—21no—
18#14579071—21no—
19C8×Dic79—21no—
20C2×M16×C79C2211yescharacteristic
21#117×C79C2211yescharacteristic
22C2×C42×C79C2211yescharacteristic
23#11929608—21no—
24#11929608—21no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8C2×C411yescharacteristic
31C2×C79⋊C8C2×C411yescharacteristic
32C2×C79⋊C8D411yescharacteristic
33C2×C79⋊C8D411yescharacteristic
34C4⋊Dic79C2×C411yescharacteristic
35C4⋊Dic79C2×C411yescharacteristic
36C22⋊Dic79—21no—
37C4×Dic79—21no—
38C22×C4×C79—21no—
39C22×C4×C79C2311yescharacteristic
40M16×C79—21no—
41M16×C79Q812yes—
42C2×C8×C79—21no—
43C4⋊C4×C79C2×C411yescharacteristic
44C4⋊C4×C79C2×C411yescharacteristic
45C22⋊C4×C79—21no—
46C42×C79—21no—
47C42×C79—21no—
48C42×C79—21no—
49C23×C79#4111yescharacteristic
50C2×C4×C79—22no—
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79C22×C411yescharacteristic
56C2×C4×C79C2×D411yescharacteristic
57C2×C4×C79C2×Q811yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×C4×C79#4111yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C8×C79—22no—
64C79⋊C8—21no—
65C79⋊C8—21no—
66C79⋊C8—21no—
67C79⋊C8—21no—
68C79⋊C8—41no—
69C22×C79—21no—
70C22×C79—21no—
71C22×C79C4×D411yescharacteristic
72C22×C79#12511yescharacteristic
73C22×C79#12611yescharacteristic
74C4×C79—42no—
75C4×C79—41no—
76C4×C79—41no—
77C4×C79#11711yescharacteristic
78C4×C79C4×Q811yescharacteristic
79C4×C79C22⋊Q811yescharacteristic
80C4×C79#12311yescharacteristic
81Dic79—41no—
82Dic79—41no—
83C2×C79—21no—
84C2×C79—21no—
85C2×C79#38711yescharacteristic
86C2×C79#44311yescharacteristic
87C2×C79#44411yescharacteristic
88#1922—791nomaximal, Sylow
89C79#192211yescharacteristic, complemented, Sylow
90#427—791no—
91#424—791no—
92#405—791no—
93#341—791no—
94#339—791no—
95#339D7911yescharacteristic
96#336—791no—
97C2×M16—791no—
98C2×M16C2×D7911yescharacteristic
99C22×C8—791no—
100C22×C8—791no—
101#117—791no—
102#117C2×D7911yescharacteristic
103C2×C42C2×D7911yescharacteristic
104#107—791no—
105#107—791no—
106#106—791no—
107#106—791no—
108C4⋊C8—1581no—
109C4⋊C8—1581no—
110#97—1581no—
111C4×C8—1581no—
112C22×C4—21no—
113C22×C4C22×D7911yescharacteristic
114M16—21no—
115M16—1581no—
116M16—1581no—
117M16Dic15812yes—
118C2×C8—21no—
119C2×C8—791no—
120C2×C8—791no—
121C2×C8—791no—
122C2×C8—791no—
123C2×C8—1581no—
124C2×C8—1581no—
125C2×C8—1581no—
126C2×C8—1581no—
127C2×C8—1581no—
128C4⋊C4—791no—
129C4⋊C4—791no—
130C4⋊C4C4×D7911yescharacteristic
131C4⋊C4C4×D7911yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—1581no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—1581no—
138C23#1192962311yescharacteristic
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—1581no—
145C2×C4—1581no—
146C2×C4C2×C4×D7911yescharacteristic
147C2×C4D4×D7911yescharacteristic
148C2×C4C2×Dic15811yescharacteristic
149C2×C4#1192962311yescharacteristic
150C2×C4#1192962411yescharacteristic
151C2×C4#1192962511yescharacteristic
152C8—22no—
153C8—3161no—
154C8—1581no—
155C8—1581no—
156C8—1581no—
157C8—1581no—
158C22—21no—
159C22—21no—
160C22(C22⋊D79)⋊C411yescharacteristic
161C22#1457915211yescharacteristic
162C22#1457915411yescharacteristic
163C4—42no—
164C4—41no—
165C4—41no—
166C4—3161no—
167C4—3161no—
168C4#1457911911yescharacteristic
169C4C4×Dic15811yescharacteristic
170C4#1457913811yescharacteristic
171C4#1457914611yescharacteristic
172C2—21no—
173C2—21no—
174C2#1909845011yescharacteristic
175C2#1909867711yescharacteristic
176C2#1909868211yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#339×C79C2
socleC22×C79C4×D4
prime radicalC23×C79#41
cosocleC22×C4×C79C23
hypercenter#339D79
hypocenterC79#1922
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
12. #14579094C4semidirect
13. #14579094C4semidirect
14. #14579092C4semidirect
15. #14579092C4semidirect
89. C79#1922semidirect