Finite Group Databasebeta

← #23764754

Subgroups — #23764754

Order 10112.

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

normal subgroups only

This group has 314 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#19099189C211yesmaximal, characteristic
2#19098438C212yesmaximal
3#19098435C211yesmaximal, characteristic
4#19098329C212yesmaximal
5#342×C79C211yesmaximal, characteristic
6C23×Dic79C2211yescharacteristic
7#14579140—21no—
8#14579140—21no—
9#14579138—22no—
10#14579138—22no—
11C2×C4⋊Dic79—22no—
12C2×Dic79⋊C4—21no—
13C2×C22⋊Dic79C2212yes—
14C2×C22⋊Dic79C2211yescharacteristic
15C79⋊#95—21no—
16C79⋊#95—22no—
17C2×C22⋊C4×C79C2211yescharacteristic
18C2×C22⋊C4×C79C2212yes—
19C2×Dic158—21no—
20C2×Dic158—21no—
21C22×Dic79—21no—
22C22×Dic79—21no—
23C22×Dic79—22no—
24C22×Dic79—42no—
25C22×Dic79D412yes—
26C22×Dic79D412yes—
27C4⋊Dic79—21no—
28C4⋊Dic79—21no—
29C4⋊Dic79—44no—
30Dic79⋊C4—22no—
31Dic79⋊C4—22no—
32Dic79⋊C4—42no—
33C22⋊Dic79—22no—
34C22⋊Dic79—22no—
35C22⋊Dic79—21no—
36C22⋊Dic79Q812yescomplemented
37C24×C79C2311yescharacteristic
38C22×C4×C79—22no—
39C22×C4×C79D411yescharacteristic
40C22×C4×C79D411yescharacteristic
41C22⋊C4×C79—22no—
42C22⋊C4×C79—22no—
43C22⋊C4×C79Q814yescomplemented
44C23×C79—41no—
45C23×C79—41no—
46C23×C79C2×D412yes—
47C23×C79C2×D411yescharacteristic
48C23×C79C2×Q811yescharacteristic
49C23×C79C2×Q812yes—
50C23×C79#4111yescharacteristic
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—24no—
54C2×C4×C79—42no—
55C2×C4×C79—42no—
56C2×C4×C79—41no—
57C2×C4×C79—41no—
58C2×Dic79—22no—
59C2×Dic79—24no—
60C2×Dic79—22no—
61C2×Dic79—22no—
62C2×Dic79—22no—
63C2×Dic79—41no—
64C2×Dic79—41no—
65C2×Dic79—41no—
66C2×Dic79—42no—
67C2×Dic79—41no—
68C2×Dic79—42no—
69C2×Dic79—42no—
70Dic158—81no—
71Dic158—81no—
72C22×C79—22no—
73C22×C79—21no—
74C22×C79—22no—
75C22×C79—21no—
76C22×C79—41no—
77C22×C79—42no—
78C22×C79—41no—
79C22×C79#12011yescharacteristic
80C22×C79C22⋊Q812yes—
81C22×C79C22⋊Q811yescharacteristic
82C22×C79C4⋊Q812yes—
83C22×C79C4⋊Q811yescharacteristic
84C4×C79—44no—
85C4×C79—41no—
86C4×C79—41no—
87Dic79—42no—
88Dic79—42no—
89Dic79—42no—
90Dic79—42no—
91C2×C79—21no—
92C2×C79—22no—
93C2×C79—22no—
94C2×C79—21no—
95C2×C79#39511yescharacteristic
96C2×C79B(4,𝔽2)11yescharacteristic
97C2×C79#45811yescharacteristic
98#2062—791nomaximal, Sylow
99C79#206211yescharacteristic, complemented, Sylow
100#543—791no—
101#385—791no—
102#385—792no—
103#342—792no—
104#342D7911yescharacteristic
105C23×C4—791no—
106C22⋊Q8—1582no—
107C22⋊Q8—1582no—
108C22⋊Q8—1581no—
109C22⋊Q8—1581no—
110C2×C4⋊C4—1582no—
111C2×C4⋊C4—1581no—
112C2×C22⋊C4—791no—
113C2×C22⋊C4—792no—
114C2×C22⋊C4C2×D7911yescharacteristic
115C2×C22⋊C4C2×D7912yes—
116#95—1582no—
117#95—1581no—
118C24C22×D7911yescharacteristic
119C2×Q8—1581no—
120C2×Q8—1581no—
121C22×C4—22no—
122C22×C4—3162no—
123C22×C4—792no—
124C22×C4—792no—
125C22×C4—1582no—
126C22×C4—1581no—
127C22×C4—1581no—
128C22×C4D31611yescharacteristic
129C22×C4D31611yescharacteristic
130C4⋊C4—3162no—
131C4⋊C4—3164no—
132C4⋊C4—1582no—
133C4⋊C4—1582no—
134C4⋊C4—1581no—
135C4⋊C4—1581no—
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—792no—
139C22⋊C4—1582no—
140C22⋊C4—1582no—
141C22⋊C4—1581no—
142C22⋊C4Dic15814yescomplemented
143C23—41no—
144C23—41no—
145C23D4×D7912yes—
146C23C2×D31611yescharacteristic
147C23Q8×D7911yescharacteristic
148C23C2×Dic15812yes—
149C23#1192962311yescharacteristic
150Q8—6321no—
151Q8—6321no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—3161no—
160C2×C4—3162no—
161C2×C4—3161no—
162C2×C4—3161no—
163C2×C4—3161no—
164C2×C4—3162no—
165C2×C4—3162no—
166C2×C4—1584no—
167C2×C4—1582no—
168C2×C4—1582no—
169C2×C4—1582no—
170C2×C4—1582no—
171C22—22no—
172C22—21no—
173C22—22no—
174C22—21no—
175C22—41no—
176C22—42no—
177C22—41no—
178C22#1457913111yescharacteristic
179C22#1457913812yes—
180C22#1457914111yescharacteristic
181C22#1457916012yes—
182C22#1457916111yescharacteristic
183C4—44no—
184C4—41no—
185C4—41no—
186C4—3162no—
187C4—3162no—
188C4—3162no—
189C4—3162no—
190C2—22no—
191C2—21no—
192C2—22no—
193C2—21no—
194C2#1909848411yescharacteristic
195C2#1909875111yescharacteristic
196C2#1909875411yescharacteristic
subgroupG/H
centerC22#14579131
commutator, prime radical, cosocleC24×C79C23
FrattiniC24C22×D79
Fitting#342×C79C2
socleC22×C79#120
hypercenter#342D79
hypocenterC79#2062
LCSG ▷ C24×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
36. C22⋊Dic79Q8semidirect
43. C22⋊C4×C79Q8semidirect
99. C79#2062semidirect
142. C22⋊C4Dic158semidirect