Finite Group Databasebeta

← #23763567

Subgroups — #23763567

Order 10112.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×#14579094C211yesmaximal, characteristic
2C2×#14579093C211yesmaximal, characteristic
3C2×#14579092C211yesmaximal, characteristic
4C2×#14579071C211yesmaximal, characteristic
5#19098432C211yesmaximal, characteristic
6#19098428C211yesmaximal, characteristic
7C2×#107×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C2×C4⋊Dic79C2211yescharacteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×Dic79⋊C4—22no—
12C2×C4×Dic79C2211yescharacteristic
13#14579094—22no—
14#14579093—22no—
15#14579092—22no—
16#14579071C414yescomplemented
17C79⋊#95—22no—
18C22×C8×C79C2211yescharacteristic
19C2×C4⋊C4×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21#107×C79—22no—
22C22×Dic79—21no—
23C22×Dic79—21no—
24C22×Dic79D412yes—
25C2×C79⋊C8C2×C412yes—
26C2×C79⋊C8D412yes—
27C2×C79⋊C8Q812yes—
28C4⋊Dic79—21no—
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C4⋊Dic79—21no—
32Dic79⋊C4—44no—
33C4×Dic79C2×C412yes—
34C4×Dic79Q812yes—
35C22×C4×C79—21no—
36C22×C4×C79—21no—
37C22×C4×C79C2311yescharacteristic
38C2×C8×C79C2×C412yes—
39C2×C8×C79D412yes—
40C2×C8×C79Q812yes—
41C4⋊C4×C79—21no—
42C4⋊C4×C79—21no—
43C4⋊C4×C79—21no—
44C4⋊C4×C79—21no—
45C23×C79C2×D411yescharacteristic
46C2×C4×C79—41no—
47C2×C4×C79—41no—
48C2×C4×C79—42no—
49C2×C4×C79—42no—
50C2×C4×C79C22×C411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2×D411yescharacteristic
53C2×C4×C79C2×Q811yescharacteristic
54C2×C4×C79C2×Q811yescharacteristic
55C2×C4×C79C2×Q811yescharacteristic
56C2×Dic79—22no—
57C2×Dic79—22no—
58C2×Dic79—41no—
59C2×Dic79—41no—
60C2×Dic79—42no—
61C2×Dic79—42no—
62C2×Dic79C4⋊C414yes—
63C8×C79C4⋊C414yescomplemented
64C79⋊C8C4⋊C414yescomplemented
65C22×C79C2×C4⋊C411yescharacteristic
66C22×C79#12711yescharacteristic
67C22×C79C4⋊Q811yescharacteristic
68C22×C79AGL(1,ℤ/8)12yes—
69C22×C79#13712yes—
70C4×C79—81no—
71C4×C79—81no—
72C4×C79C2×C4⋊C411yescharacteristic
73C4×C79C2×C4⋊C411yescharacteristic
74C4×C79C4⋊Q811yescharacteristic
75C4×C79C4⋊Q811yescharacteristic
76Dic79—24no—
77Dic79—81no—
78Dic79—81no—
79C2×C79#38411yescharacteristic
80C2×C79#42812yes—
81C2×C79#49611yescharacteristic
82C2×C79#49711yescharacteristic
83C2×C79#50112yes—
84#1847—791nomaximal, Sylow
85C79#184711yescharacteristic, complemented, Sylow
86C2×#107—791no—
87C2×#107D7911yescharacteristic
88C2×#106—791no—
89C2×#106—791no—
90C2×#97—791no—
91#384—791no—
92#382—791no—
93C22×C8—791no—
94C22×C8C2×D7911yescharacteristic
95C2×C4⋊C4—791no—
96C2×C4⋊C4—791no—
97C2×C4⋊C4—1582no—
98C2×C4⋊C4C2×D7911yescharacteristic
99C2×C4⋊C4C2×D7911yescharacteristic
100C2×C42—791no—
101#107—22no—
102#107—1582no—
103#106—1582no—
104#106—1582no—
105#97—794no—
106#95—1582no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—792no—
110C22×C4—1581no—
111C22×C4—1581no—
112C22×C4C22×D7911yescharacteristic
113C2×C8—792no—
114C2×C8—792no—
115C2×C8—792no—
116C2×C8Dic15812yes—
117C2×C8C4×D7912yes—
118C2×C8C22⋊D7912yes—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—3164no—
124C4⋊C4—1581no—
125C4⋊C4—1581no—
126C4⋊C4—1581no—
127C4⋊C4—1581no—
128C42—792no—
129C42—792no—
130C23D4×D7911yescharacteristic
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—3161no—
136C2×C4—3161no—
137C2×C4—3162no—
138C2×C4—3162no—
139C2×C4—794no—
140C2×C4—1582no—
141C2×C4—1582no—
142C2×C4C2×C4×D7911yescharacteristic
143C2×C4D4×D7911yescharacteristic
144C2×C4C2×C22⋊D7911yescharacteristic
145C2×C4Q8×D7911yescharacteristic
146C2×C4Q8×D7911yescharacteristic
147C2×C4C2×Dic15811yescharacteristic
148C8—794no—
149C8Dic79⋊C414yescomplemented
150C22C4⋊C4×D7911yescharacteristic
151C22#1457915711yescharacteristic
152C22#1457916011yescharacteristic
153C22#1457918512yes—
154C22#1457919312yes—
155C4—81no—
156C4—81no—
157C4—6321no—
158C4—6321no—
159C4—1584no—
160C4C4⋊C4×D7911yescharacteristic
161C4C2×Dic79⋊C411yescharacteristic
162C4#1457915911yescharacteristic
163C4#1457916011yescharacteristic
164C2#1909843211yescharacteristic
165C2#1909860412yes—
166C2#1909895111yescharacteristic
167C2#1909895611yescharacteristic
168C2#1909897112yes—
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#107×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenterC2×#107D79
hypocenterC79#1847
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
16. #14579071C4semidirect
63. C8×C79C4⋊C4semidirect
64. C79⋊C8C4⋊C4semidirect
85. C79#1847semidirect
149. C8Dic79⋊C4semidirect