Finite Group Databasebeta

← #23762409

Subgroups — #23762409

Order 10112.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#19099192C211yesmaximal, characteristic
2#19098894C211yesmaximal, characteristic
3#19098891C211yesmaximal, characteristic
4#19098495C211yesmaximal, characteristic
5#19098299C211yesmaximal, characteristic
6#19098288C211yesmaximal, characteristic
7#328×C79C211yesmaximal, characteristic
8#14579160—21no—
9#14579159—21no—
10#14579151—21no—
11#14579151—21no—
12#14579140C2211yescharacteristic
13#14579138—21no—
14#14579117—21no—
15C2×C4⋊Dic79—21no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18#14579093—21no—
19#14579092—21no—
20#14579086—21no—
21#14579085—21no—
22C22⋊(C79⋊C8)C2211yescharacteristic
23C79⋊#95—21no—
24C22⋊Q8×C79C2211yescharacteristic
25C22⋊C8×C79C2211yescharacteristic
26#95×C79C2211yescharacteristic
27C2×Dic158—21no—
28C2×Dic158D411yescharacteristic
29C22×Dic79—21no—
30C22×Dic79D411yescharacteristic
31C22×Dic79D411yescharacteristic
32C2×C79⋊C8—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79—42no—
37C4⋊Dic79D411yescharacteristic
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—21no—
42Dic79⋊C4—21no—
43Dic79⋊C4—21no—
44Dic79⋊C4—21no—
45C22⋊Dic79—21no—
46C4×Dic79—21no—
47C4×Dic79—21no—
48C2×Q8×C79D411yescharacteristic
49C22×C4×C79—21no—
50C22×C4×C79C2311yescharacteristic
51C2×C8×C79—21no—
52C4⋊C4×C79—21no—
53C4⋊C4×C79D411yescharacteristic
54C22⋊C4×C79—21no—
55C23×C79C2×D411yescharacteristic
56Q8×C79—41no—
57C2×C4×C79—22no—
58C2×C4×C79—21no—
59C2×C4×C79—21no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79—41no—
71C2×Dic79—41no—
72C2×Dic79—41no—
73C2×Dic79—41no—
74C2×Dic79SD1612yes—
75Dic158—41no—
76Dic158—81no—
77C8×C79—41no—
78C79⋊C8—41no—
79C22×C79—21no—
80C22×C79—21no—
81C22×C79#12011yescharacteristic
82C22×C79C2×SD1611yescharacteristic
83C22×C79#13711yescharacteristic
84C4×C79—21no—
85C4×C79—21no—
86C4×C79—42no—
87C4×C79—41no—
88C4×C79—41no—
89Dic79—22no—
90Dic79—41no—
91Dic79—41no—
92Dic79—41no—
93Dic79—81no—
94C2×C79—21no—
95C2×C79—21no—
96C2×C79#44811yescharacteristic
97C2×C79#45611yescharacteristic
98C2×C79#45811yescharacteristic
99#1611—791nomaximal, Sylow
100C79#161111yescharacteristic, complemented, Sylow
101#544—791no—
102#483—791no—
103#483—791no—
104#398—791no—
105#328—791no—
106#328D7911yescharacteristic
107#324—791no—
108C4⋊Q8—1581no—
109C4⋊Q8—1581no—
110#125—1581no—
111#125—1581no—
112C22⋊Q8—791no—
113C22⋊Q8—1581no—
114C22⋊Q8C2×D7911yescharacteristic
115#117—1581no—
116C2×C4⋊C4—791no—
117C2×C4⋊C4—791no—
118C2×C4⋊C4—1581no—
119#106—1581no—
120#106—1581no—
121#103—1581no—
122#103—1581no—
123C22⋊C8—791no—
124C22⋊C8C2×D7911yescharacteristic
125#95—1581no—
126#95C2×D7911yescharacteristic
127C2×Q8—791no—
128C2×Q8—1581no—
129C2×Q8D31611yescharacteristic
130C22×C4—21no—
131C22×C4—791no—
132C22×C4—791no—
133C22×C4—1581no—
134C22×C4C22×D7911yescharacteristic
135C2×C8—21no—
136C2×C8—1581no—
137C4⋊C4—21no—
138C4⋊C4—3162no—
139C4⋊C4—791no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C4⋊C4—1581no—
144C4⋊C4—1581no—
145C4⋊C4—1581no—
146C4⋊C4—1581no—
147C4⋊C4—1581no—
148C4⋊C4—1581no—
149C4⋊C4—1581no—
150C4⋊C4D31611yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1581no—
153C42—1581no—
154C42—1581no—
155C23D4×D7911yescharacteristic
156Q8—41no—
157Q8—3161no—
158Q8—6321no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3161no—
166C2×C4—3161no—
167C2×C4—3161no—
168C2×C4—3161no—
169C2×C4—792no—
170C2×C4—1581no—
171C2×C4—1581no—
172C2×C4—1581no—
173C2×C4—1581no—
174C2×C4—1581no—
175C2×C4D4×D7911yescharacteristic
176C2×C4C2×D31611yescharacteristic
177C8—41no—
178C8—3161no—
179C22—21no—
180C22—21no—
181C22#1457913111yescharacteristic
182C22SD16×D7911yescharacteristic
183C22#1457919311yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—3161no—
190C4—3161no—
191C4—3161no—
192C4—6321no—
193C4—1582no—
194C2—21no—
195C2—21no—
196C2#1909870311yescharacteristic
197C2#1909874711yescharacteristic
198C2#1909875411yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#328×C79C2
socleC22×C79#120
prime radicalC23×C79C2×D4
hypercenter#328D79
hypocenterC79#1611
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
100. C79#1611semidirect