Finite Group Databasebeta

← #23762443

Subgroups — #23762443

Order 10112.

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

normal subgroups only

This group has 202 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#19098899C211yesmaximal, characteristic
3#19098896C211yesmaximal, characteristic
4#19098503C211yesmaximal, 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⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2211yescharacteristic
17#14579095—21no—
18#14579094—21no—
19#14579086—21no—
20#14579085—21no—
21C22⋊(C79⋊C8)C2211yescharacteristic
22C79⋊#95—21no—
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⋊Dic79D411yescharacteristic
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—21no—
42Dic79⋊C4—21no—
43Dic79⋊C4—21no—
44C22⋊Dic79—21no—
45C4×Dic79—21no—
46C4×Dic79—21no—
47C2×Q8×C79D411yescharacteristic
48C22×C4×C79—21no—
49C22×C4×C79C2311yescharacteristic
50C2×C8×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79D411yescharacteristic
53C22⋊C4×C79—21no—
54C23×C79C2×D411yescharacteristic
55Q8×C79—41no—
56C2×C4×C79—21no—
57C2×C4×C79—21no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79C2×D411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—41no—
70C2×Dic79—42no—
71C2×Dic79—41no—
72C2×Dic79Q1612yes—
73Dic158—41no—
74Dic158—81no—
75C8×C79—41no—
76C79⋊C8—41no—
77C22×C79—21no—
78C22×C79—21no—
79C22×C79#12011yescharacteristic
80C22×C79C2×Q1611yescharacteristic
81C22×C79#13711yescharacteristic
82C4×C79—21no—
83C4×C79—21no—
84C4×C79—41no—
85C4×C79—41no—
86C4×C79—81no—
87Dic79—22no—
88Dic79—41no—
89Dic79—41no—
90Dic79—41no—
91Dic79—81no—
92C2×C79—21no—
93C2×C79—21no—
94C2×C79#45111yescharacteristic
95C2×C79#45411yescharacteristic
96C2×C79#45811yescharacteristic
97#1617—791nomaximal, Sylow
98C79#161711yescharacteristic, complemented, Sylow
99#544—791no—
100#484—791no—
101#484—791no—
102#400—791no—
103#328—791no—
104#328D7911yescharacteristic
105#324—791no—
106C4⋊Q8—1581no—
107C4⋊Q8—1581no—
108#125—1581no—
109#125—1581no—
110C22⋊Q8—791no—
111C22⋊Q8—1581no—
112C22⋊Q8C2×D7911yescharacteristic
113#117—1581no—
114C2×C4⋊C4—791no—
115C2×C4⋊C4—791no—
116#107—1581no—
117#107—1581no—
118#103—1581no—
119#103—1581no—
120C22⋊C8—791no—
121C22⋊C8C2×D7911yescharacteristic
122#95—1581no—
123#95—1581no—
124#95C2×D7911yescharacteristic
125C2×Q8—791no—
126C2×Q8—1581no—
127C2×Q8D31611yescharacteristic
128C22×C4—21no—
129C22×C4—791no—
130C22×C4—791no—
131C22×C4—1581no—
132C22×C4C22×D7911yescharacteristic
133C2×C8—21no—
134C2×C8—1581no—
135C4⋊C4—21no—
136C4⋊C4—791no—
137C4⋊C4—1581no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C4⋊C4—1581no—
144C4⋊C4—1581no—
145C4⋊C4—1581no—
146C4⋊C4—1581no—
147C4⋊C4D31611yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1581no—
150C42—1581no—
151C42—1581no—
152C23D4×D7911yescharacteristic
153Q8—41no—
154Q8—3161no—
155Q8—6321no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3161no—
163C2×C4—3162no—
164C2×C4—3161no—
165C2×C4—792no—
166C2×C4—1581no—
167C2×C4—1581no—
168C2×C4—1581no—
169C2×C4—1581no—
170C2×C4—1581no—
171C2×C4D4×D7911yescharacteristic
172C2×C4C2×D31611yescharacteristic
173C8—41no—
174C8—3161no—
175C22—21no—
176C22—21no—
177C22#1457913111yescharacteristic
178C22Q16×D7911yescharacteristic
179C22#1457919011yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3161no—
186C4—3161no—
187C4—3161no—
188C4—6321no—
189C4—1582no—
190C2—21no—
191C2—21no—
192C2#1909872011yescharacteristic
193C2#1909873711yescharacteristic
194C2#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#1617
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
98. C79#1617semidirect