Finite Group Databasebeta

← #23762727

Subgroups — #23762727

Order 10112.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C79⋊#564C211yesmaximal, characteristic
2#19098969C211yesmaximal, characteristic
3#19098931C211yesmaximal, characteristic
4#19098305C211yesmaximal, characteristic
5#19098304C211yesmaximal, characteristic
6#19098304C211yesmaximal, characteristic
7#501×C79C211yesmaximal, characteristic
8#14579153C2211yescharacteristic
9#14579153C2211yescharacteristic
10#14579152—21no—
11#14579152—21no—
12#14579151—21no—
13#14579151—21no—
14#14579151—21no—
15#14579151—21no—
16#14579094—21no—
17#14579092—21no—
18#14579085—21no—
19#14579085—21no—
20#14579072C2211yescharacteristic
21#14579072C2211yescharacteristic
22C4⋊Q8×C79C2211yescharacteristic
23#125×C79C2211yescharacteristic
24#107×C79—21no—
25#106×C79—21no—
26#97×C79C2211yescharacteristic
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C4⋊Dic79D411yescharacteristic
32C4⋊Dic79D411yescharacteristic
33C4⋊Dic79D411yescharacteristic
34C4⋊Dic79D411yescharacteristic
35Dic79⋊C4—21no—
36Dic79⋊C4—21no—
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—21no—
42Dic79⋊C4—21no—
43C4×Dic79—21no—
44C4×Dic79—21no—
45C2×Q8×C79—21no—
46C2×C8×C79—21no—
47C4⋊C4×C79—21no—
48C4⋊C4×C79—21no—
49C4⋊C4×C79—21no—
50C4⋊C4×C79—21no—
51C4⋊C4×C79D411yescharacteristic
52C4⋊C4×C79D411yescharacteristic
53C42×C79C2311yescharacteristic
54Q8×C79—42no—
55C2×C4×C79—21no—
56C2×C4×C79—21no—
57C2×C4×C79—41no—
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C8×C79—22no—
66C79⋊C8—22no—
67C79⋊C8—41no—
68C22×C79#12011yescharacteristic
69C4×C79—21no—
70C4×C79—21no—
71C4×C79—21no—
72C4×C79—41no—
73C4×C79—41no—
74C4×C79—81no—
75Dic79—41no—
76Dic79—41no—
77Dic79—41no—
78Dic79—41no—
79C2×C79#45411yescharacteristic
80C2×C79#45611yescharacteristic
81C2×C79#45611yescharacteristic
82#1663—791nomaximal, Sylow
83C79#166311yescharacteristic, complemented, Sylow
84#564—791no—
85#501—791no—
86#501D7911yescharacteristic
87#491—791no—
88#330—791no—
89#330—791no—
90#330—791no—
91C4⋊Q8C2×D7911yescharacteristic
92#125—791no—
93#125—791no—
94#125—1581no—
95#125—1581no—
96#125—1581no—
97#125—1581no—
98#125—1581no—
99#125—1581no—
100#125C2×D7911yescharacteristic
101#107—21no—
102#107—1581no—
103#106—21no—
104#106—1581no—
105#103—1581no—
106#103—1581no—
107#97—791no—
108#97—791no—
109#97C2×D7911yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—1581no—
113C2×C8—1581no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—791no—
119C4⋊C4—791no—
120C4⋊C4—791no—
121C4⋊C4—791no—
122C4⋊C4—1581no—
123C4⋊C4—1581no—
124C4⋊C4—1581no—
125C4⋊C4—1581no—
126C4⋊C4—1581no—
127C4⋊C4—1581no—
128C4⋊C4—1581no—
129C4⋊C4—1581no—
130C4⋊C4—1581no—
131C4⋊C4—1581no—
132C4⋊C4C22⋊D7911yescharacteristic
133C4⋊C4C22⋊D7911yescharacteristic
134C42—1581no—
135C42—1581no—
136C42C22×D7911yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—1581no—
142C2×C4—1581no—
143C2×C4—1581no—
144C2×C4—1581no—
145C2×C4D4×D7911yescharacteristic
146C2×C4D4×D7911yescharacteristic
147C2×C4C2×C22⋊D7911yescharacteristic
148C8—22no—
149C8—3161no—
150C8—1582no—
151C22#1457912911yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—3161no—
159C4—3161no—
160C4—3161no—
161C4—3161no—
162C2#1909873411yescharacteristic
163C2#1909874411yescharacteristic
164C2#1909874511yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#501×C79C2
socle, prime radicalC22×C79#120
hypercenter#501D79
hypocenterC79#1663
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
83. C79#1663semidirect