Finite Group Databasebeta

← #23764182

Subgroups — #23764182

Order 10112.

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

normal subgroups only

This group has 196 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×#14579096C211yesmaximal, characteristic
2#19098606C211yesmaximal, characteristic
3C2×#14579094C211yesmaximal, characteristic
4#19098519C211yesmaximal, characteristic
5#19098332C211yesmaximal, characteristic
6#19098331C211yesmaximal, characteristic
7#428×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C22×C79⋊C8C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12#14579096C414yescomplemented
13#14579094—21no—
14#14579094—21no—
15#14579094—21no—
16#14579092—21no—
17#14579072—21no—
18C4×C79⋊C8—21no—
19C2×M16×C79C2211yescharacteristic
20#117×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22#107×C79—21no—
23#106×C79—21no—
24C22×Dic79—21no—
25#11929608—21no—
26#11929608—21no—
27#11929608C2×C412yes—
28#11929608Q812yes—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C2×C79⋊C8C2×C412yes—
32C2×C79⋊C8D411yescharacteristic
33C2×C79⋊C8D411yescharacteristic
34C2×C79⋊C8Q812yes—
35C4⋊Dic79—21no—
36C4⋊Dic79—21no—
37C22×C4×C79—21no—
38C22×C4×C79C2311yescharacteristic
39M16×C79—21no—
40M16×C79C2×C412yes—
41C2×C8×C79—21no—
42C4⋊C4×C79—21no—
43C4⋊C4×C79—21no—
44C4⋊C4×C79D411yescharacteristic
45C4⋊C4×C79D411yescharacteristic
46C22⋊C4×C79—21no—
47C42×C79—21no—
48C23×C79#4111yescharacteristic
49C2×C4×C79—21no—
50C2×C4×C79—21no—
51C2×C4×C79—41no—
52C2×C4×C79—81no—
53C2×C4×C79C22×C411yescharacteristic
54C2×C4×C79C2×D411yescharacteristic
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79C2×Q811yescharacteristic
57C2×C4×C79C2×Q811yescharacteristic
58C2×C4×C79#4111yescharacteristic
59C2×Dic79—41no—
60C2×Dic79—81no—
61C8×C79—22no—
62C79⋊C8—22no—
63C79⋊C8—22no—
64C79⋊C8C4⋊C412yes—
65C79⋊C8C4⋊C412yes—
66C22×C79—21no—
67C22×C79—21no—
68C22×C79C4×Q811yescharacteristic
69C22×C79#12111yescharacteristic
70C22×C79#12511yescharacteristic
71C4×C79—41no—
72C4×C79—41no—
73C4×C79—81no—
74C4×C79C2×C4⋊C411yescharacteristic
75C4×C79C4×D411yescharacteristic
76C4×C79C22⋊Q811yescharacteristic
77C4×C79C4⋊Q811yescharacteristic
78Dic79—81no—
79C2×C79—21no—
80C2×C79—21no—
81C2×C79#38911yescharacteristic
82C2×C79#47211yescharacteristic
83C2×C79#47311yescharacteristic
84#1952—791nomaximal, Sylow
85C79#195211yescharacteristic, complemented, Sylow
86C2×#108—791no—
87#428—791no—
88#428D7911yescharacteristic
89C2×#107—791no—
90#405—791no—
91#343—791no—
92#343—791no—
93C2×M16—791no—
94C2×M16—791no—
95C2×M16C2×D7911yescharacteristic
96C22×C8—791no—
97#117C2×D7911yescharacteristic
98C2×C4⋊C4—791no—
99C2×C4⋊C4C2×D7911yescharacteristic
100#108—794no—
101#107—21no—
102#107—1581no—
103#107—1581no—
104#107—1581no—
105#106—21no—
106#106—1581no—
107#97—1581no—
108C4×C8—1581no—
109C22×C4—21no—
110C22×C4—1581no—
111C22×C4C22×D7911yescharacteristic
112M16—21no—
113M16—792no—
114M16—792no—
115M16—1581no—
116M16—1581no—
117M16C4×D7912yes—
118C2×C8—21no—
119C2×C8—792no—
120C2×C8—791no—
121C2×C8—791no—
122C2×C8—792no—
123C2×C8—1581no—
124C2×C8—1581no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—1581no—
128C4⋊C4—1581no—
129C4⋊C4C22⋊D7911yescharacteristic
130C4⋊C4C22⋊D7911yescharacteristic
131C22⋊C4—21no—
132C42—21no—
133C23#1192962311yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—3161no—
139C2×C4—6321no—
140C2×C4C2×C4×D7911yescharacteristic
141C2×C4D4×D7911yescharacteristic
142C2×C4C2×C22⋊D7911yescharacteristic
143C2×C4Q8×D7911yescharacteristic
144C2×C4Q8×D7911yescharacteristic
145C2×C4#1192962411yescharacteristic
146C8—22no—
147C8—792no—
148C8—792no—
149C8—1582no—
150C8—1582no—
151C22—21no—
152C22—21no—
153C22#1457912611yescharacteristic
154C22#1457913311yescharacteristic
155C22#1457915111yescharacteristic
156C4—41no—
157C4—41no—
158C4—81no—
159C4—6321no—
160C4C4⋊C4×D7911yescharacteristic
161C4C4×C22⋊D7911yescharacteristic
162C4#1457913911yescharacteristic
163C4#1457915911yescharacteristic
164C2—21no—
165C2—21no—
166C2#1909845811yescharacteristic
167C2#1909883111yescharacteristic
168C2#1909883611yescharacteristic
subgroupG/H
centerC22#14579133
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#428×C79C2
socleC22×C79#121
prime radicalC23×C79#41
cosocleC22×C4×C79C23
hypercenter#428D79
hypocenterC79#1952
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
12. #14579096C4semidirect
85. C79#1952semidirect