Finite Group Databasebeta

← #23762528

Subgroups — #23762528

Order 10112.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#19099233C211yesmaximal, characteristic
2#19098935C211yesmaximal, characteristic, complemented
3#19098859C211yesmaximal, characteristic, complemented
4#19098854C211yesmaximal, characteristic, complemented
5#19098293C211yesmaximal, characteristic, complemented
6#19098290C211yesmaximal, characteristic, complemented
7#331×C79C211yesmaximal, characteristic, complemented
8C2×#11929623—21no—
9C2×#11929612—22no—
10#14579161C2211yescharacteristic
11#14579157—21no—
12#14579133—22no—
13#14579132—21no—
14C4×Dic158C2211yescharacteristic
15C4×D316C2211yescharacteristic
16D4×Dic79—21no—
17#14579095—21no—
18#14579093—21no—
19#14579086—21no—
20#14579083—21no—
21C4×C79⋊C8C2211yescharacteristic
22#127×C79C2211yescharacteristic
23C4⋊C8×C79C2211yescharacteristic
24C4⋊C8×C79C2211yescharacteristic
25#11929623—42no—
26#11929623—42no—
27C2×Dic158—21no—
28C2×Dic158D411yescharacteristic
29C2×D316D411yescharacteristic
30C2×C22⋊D79—22no—
31C2×C22⋊D79—22no—
32C22×Dic79—22no—
33C2×C4×D79—21no—
34#11929612—44no—
35C2×C79⋊C8—21no—
36C4⋊Dic79—21no—
37C4⋊Dic79—21no—
38C4⋊Dic79D411yescharacteristic
39C4⋊Dic79D411yescharacteristic
40Dic79⋊C4—21no—
41C22⋊Dic79—22no—
42(C2×D79)⋊C4—21no—
43C4×Dic79—21no—
44C2×D4×C79—21no—
45C2×D4×C79—21no—
46C2×D4×C79D412yes—
47C2×C8×C79—21no—
48C2×C8×C79—21no—
49C42×C79C2311yescharacteristic
50C23×C79—22no—
51C22×D79—21no—
52D4×C79—42no—
53D4×C79—41no—
54D4×C79—41no—
55D4×C79—41no—
56D4×C79—41no—
57C2×C4×C79C2×D411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C22⋊D79—44no—
61C22⋊D79—82no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C2×Dic79—44no—
66C2×Dic79—41no—
67D316—21no—
68D316—21no—
69C4×D79—41no—
70C4×D79—41no—
71Dic158—21no—
72Dic158—42no—
73Dic158SD1612yescomplemented
74C8×C79—41no—
75C8×C79—41no—
76C79⋊C8—22no—
77C22×C79—42no—
78C22×C79—42no—
79C22×C79—42no—
80C22×C79#12011yescharacteristic
81C2×D79—41no—
82C2×D79—41no—
83C2×D79—41no—
84C4×C79—21no—
85C4×C79C2×SD1611yescharacteristic
86C4×C79#13511yescharacteristic
87C4×C79AGL(1,ℤ/8)11yescharacteristic
88C4×C79#13711yescharacteristic
89Dic79—22no—
90Dic79—41no—
91Dic79—41no—
92Dic79—81no—
93C2×C79—82no—
94C2×C79#45011yescharacteristic
95C2×C79#45211yescharacteristic
96C2×C79#45311yescharacteristic
97D79—81no—
98#1631—791nomaximal, Sylow
99C79#163111yescharacteristic, complemented, Sylow
100#550—791no—
101#492—791no—
102#477—791no—
103#476—791no—
104#331D7911yescharacteristic, complemented
105Q8⋊C8—791no—
106D4⋊C8—791no—
107C2×#41—1581no—
108C2×SD16—1582no—
109C4⋊Q8—791no—
110#127—1581no—
111#127C2×D7911yescharacteristic
112#121—1581no—
113#121—1582no—
114C4×Q8—791no—
115C4×D4—791no—
116C4×D4—1581no—
117#107—1581no—
118#106—1581no—
119C4⋊C8C2×D7911yescharacteristic
120C4⋊C8C2×D7911yescharacteristic
121#103—1581no—
122#102—1581no—
123C4×C8—791no—
124#41—3162no—
125#41—3162no—
126C2×Q8—791no—
127C2×Q8—1581no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—791no—
131C2×D4—1582no—
132C2×D4—1582no—
133C2×D4D31612yes—
134C22×C4—1582no—
135C22×C4—1581no—
136SD16—3164no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—1581no—
140C4⋊C4—791no—
141C4⋊C4—791no—
142C4⋊C4—1581no—
143C4⋊C4—1581no—
144C4⋊C4—1581no—
145C22⋊C4—1582no—
146C22⋊C4—1581no—
147C42—1581no—
148C42C22×D7911yescharacteristic
149C23—22no—
150C23—1581no—
151Q8—3162no—
152Q8—792no—
153Q8—1581no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—3164no—
160D4—6322no—
161D4—1581no—
162D4—1581no—
163C2×C4—3164no—
164C2×C4—3161no—
165C2×C4—3161no—
166C2×C4—3161no—
167C2×C4—1581no—
168C2×C4—1581no—
169C2×C4—1581no—
170C2×C4D4×D7911yescharacteristic
171C2×C4D4×D7911yescharacteristic
172C2×C4C2×D31611yescharacteristic
173C8—41no—
174C8—41no—
175C8—1582no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—3161no—
180C22—3161no—
181C22—3161no—
182C22#1457913111yescharacteristic
183C4—21no—
184C4—3161no—
185C4—3161no—
186C4—6321no—
187C4—1582no—
188C4SD16×D7911yescharacteristic
189C4#1457918011yescharacteristic
190C4#1457918511yescharacteristic
191C4#1457919011yescharacteristic
192C2—82no—
193C2—6321no—
194C2#1909871511yescharacteristic
195C2#1909872611yescharacteristic
196C2#1909873311yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#331×C79C2
socleC22×C79#120
prime radical#19099233C2
hypercenter#331D79
hypocenterC79#1631
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #19098935C2semidirect
3. #19098859C2semidirect
4. #19098854C2semidirect
5. #19098293C2semidirect
6. #19098290C2semidirect
7. #331×C79C2semidirect
73. Dic158SD16semidirect
99. C79#1631semidirect
104. #331D79semidirect