Finite Group Databasebeta

← #23764804

Subgroups — #23764804

Order 10112.

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

normal subgroups only

This group has 274 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
1C2×#14579081C212yesmaximal
2#19098465C211yesmaximal, characteristic
3#19098325C212yesmaximal, complemented
4#19098318C211yesmaximal, characteristic, complemented
5#384×C79C211yesmaximal, characteristic, complemented
6C22×D316C2211yescharacteristic
7C22×C79⋊C8C2212yes—
8C2×C4⋊Dic79C2211yescharacteristic
9C2×(C2×D79)⋊C4—21no—
10C2×(C2×D79)⋊C4—21no—
11#14579081—24no—
12C2×C4⋊C4×C79—21no—
13C2×C4⋊C4×C79—21no—
14C2×C4⋊C4×C79C2212yes—
15C2×C42×C79C2211yescharacteristic
16C23×D79—21no—
17C2×D316—21no—
18C2×D316—22no—
19C2×D316—22no—
20C2×D316D412yes—
21C22×Dic79—21no—
22C2×C79⋊C8—22no—
23C2×C79⋊C8—22no—
24C2×C79⋊C8—22no—
25C4⋊Dic79—22no—
26(C2×D79)⋊C4—42no—
27(C2×D79)⋊C4—42no—
28C22×C4×C79—22no—
29C22×C4×C79D411yescharacteristic
30C22×C4×C79D411yescharacteristic
31C22×C4×C79C2311yescharacteristic
32C4⋊C4×C79—22no—
33C4⋊C4×C79—22no—
34C4⋊C4×C79—42no—
35C4⋊C4×C79—42no—
36C42×C79—22no—
37C23×C79C2×D411yescharacteristic
38C22×D79—22no—
39C22×D79—41no—
40C22×D79—41no—
41C22×D79—41no—
42C22×D79—41no—
43C22×D79—41no—
44C22×D79—41no—
45C2×C4×C79—21no—
46C2×C4×C79—21no—
47C2×C4×C79—21no—
48C2×C4×C79—21no—
49C2×C4×C79—42no—
50C2×C4×C79—42no—
51C2×C4×C79—42no—
52C2×C4×C79D812yes—
53C2×C4×C79SD1612yes—
54C2×C4×C79C2×D411yescharacteristic
55C2×C4×C79#4111yescharacteristic
56C2×C4×C79#4112yes—
57C2×C4×C79#4112yes—
58C2×Dic79—41no—
59C2×Dic79—41no—
60C2×Dic79—41no—
61D316—24no—
62D316—42no—
63C79⋊C8—42no—
64C22×C79#12111yescharacteristic
65C22×C79#12311yescharacteristic
66C22×C79#12411yescharacteristic
67C22×C79C2×D811yescharacteristic
68C22×C79C2×SD1611yescharacteristic
69C22×C79AGL(1,ℤ/8)11yescharacteristic
70C22×C79#13711yescharacteristic
71C2×D79—42no—
72C2×D79—42no—
73C2×D79—42no—
74C2×D79—81no—
75C2×D79—81no—
76C2×D79—81no—
77C2×D79—81no—
78C4×C79—22no—
79C4×C79—22no—
80C4×C79—82no—
81C4×C79#12312yes—
82C4×C79#12612yes—
83Dic79—81no—
84C2×C79#39711yescharacteristic
85C2×C79#45911yescharacteristic
86C2×C79#46111yescharacteristic
87C2×C79#48011yescharacteristic
88C2×C79#48111yescharacteristic
89C2×C79#48611yescharacteristic
90C2×C79#48911yescharacteristic
91D79—82no—
92#2071—791nomaximal, Sylow
93C79#207111yescharacteristic, complemented, Sylow
94C2×#102—792no—
95#390—791no—
96#384D7911yescharacteristic, complemented
97#340—792no—
98#336—791no—
99C22×D4—791no—
100C22×C8—792no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—791no—
104C2×C4⋊C4C2×D7912yes—
105C2×C22⋊C4—1581no—
106C2×C22⋊C4—1581no—
107C2×C42C2×D7911yescharacteristic
108#102—1584no—
109C24—1581no—
110C2×D4—792no—
111C2×D4—1581no—
112C2×D4—1582no—
113C2×D4—1582no—
114C22×C4—22no—
115C22×C4—1581no—
116C22×C4C22⋊D7911yescharacteristic
117C22×C4C22⋊D7911yescharacteristic
118C22×C4C22×D7911yescharacteristic
119C2×C8—1582no—
120C2×C8—1582no—
121C2×C8—1582no—
122C4⋊C4—22no—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—1582no—
127C22⋊C4—3162no—
128C22⋊C4—3162no—
129C42—22no—
130C23—3161no—
131C23—3161no—
132C23—3161no—
133C23—3161no—
134C23—3161no—
135C23—3161no—
136C23—1582no—
137C23C2×C22⋊D7911yescharacteristic
138D4—3162no—
139D4—1584no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—3161no—
148C2×C4—3161no—
149C2×C4—3161no—
150C2×C4#1192960912yes—
151C2×C4#1192961112yes—
152C2×C4D4×D7911yescharacteristic
153C2×C4#1192962311yescharacteristic
154C2×C4#1192962412yes—
155C2×C4#1192962512yes—
156C8—3162no—
157C22—3162no—
158C22—3162no—
159C22—3162no—
160C22—6321no—
161C22—6321no—
162C22—6321no—
163C22—6321no—
164C22#1457913211yescharacteristic
165C22#1457914411yescharacteristic
166C22#1457915011yescharacteristic
167C22C2×#1192960911yescharacteristic
168C22C2×#1192961111yescharacteristic
169C22#1457918711yescharacteristic
170C22#1457919211yescharacteristic
171C4—22no—
172C4—22no—
173C4—82no—
174C4—6321no—
175C4#1457914612yes—
176C4#1457915612yes—
177C2—6322no—
178C2#1909848911yescharacteristic
179C2#1909875511yescharacteristic
180C2#1909876511yescharacteristic
181C2#1909887611yescharacteristic
182C2#1909888111yescharacteristic
183C2#1909891111yescharacteristic
184C2#1909892511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#384×C79C2
socleC23×C79C2×D4
prime radicalC22×D316C22
hypercenter#384D79
hypocenterC79#2071
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #19098325C2semidirect
4. #19098318C2semidirect
5. #384×C79C2semidirect
93. C79#2071semidirect
96. #384D79semidirect