Finite Group Databasebeta

← #23762601

Subgroups — #23762601

Order 10112.

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

normal subgroups only

This group has 250 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#19098909C211yesmaximal, characteristic, complemented
3#19098849C211yesmaximal, characteristic, complemented
4#19098769C211yesmaximal, characteristic, complemented
5#19098293C211yesmaximal, characteristic, complemented
6#19098290C211yesmaximal, characteristic, complemented
7#331×C79C211yesmaximal, characteristic, complemented
8C2×#11929623—21no—
9C2×#11929613—21no—
10#14579161C2211yescharacteristic
11#14579157—21no—
12#14579133—22no—
13#14579132—21no—
14C4×Dic158C2211yescharacteristic
15C4×D316C2211yescharacteristic
16D4×Dic79—21no—
17#14579093—21no—
18#14579086—21no—
19#14579086—21no—
20#14579082—22no—
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#11929613—42no—
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—41no—
73Dic158—41no—
74Dic158SD1612yescomplemented
75C8×C79—41no—
76C8×C79—41no—
77C79⋊C8—41no—
78C22×C79—42no—
79C22×C79—42no—
80C22×C79—42no—
81C22×C79#12011yescharacteristic
82C2×D79—41no—
83C2×D79—41no—
84C2×D79—41no—
85C4×C79—21no—
86C4×C79C2×SD1611yescharacteristic
87C4×C79#13511yescharacteristic
88C4×C79AGL(1,ℤ/8)11yescharacteristic
89C4×C79AGL(1,ℤ/8)11yescharacteristic
90Dic79—22no—
91Dic79—41no—
92Dic79—41no—
93Dic79—81no—
94C2×C79—82no—
95C2×C79#44911yescharacteristic
96C2×C79#45011yescharacteristic
97C2×C79#45511yescharacteristic
98D79—81no—
99#1642—791nomaximal, Sylow
100C79#164211yescharacteristic, complemented, Sylow
101#550—791no—
102#486—791no—
103#475—791no—
104#461—791no—
105#331D7911yescharacteristic, complemented
106Q8⋊C8—791no—
107D4⋊C8—791no—
108C2×#41—1581no—
109C2×SD16—1581no—
110C4⋊Q8—791no—
111#127—1581no—
112#127C2×D7911yescharacteristic
113#121—1581no—
114#121—1582no—
115C4×Q8—791no—
116C4×D4—791no—
117C4×D4—1581no—
118#106—1581no—
119C4⋊C8C2×D7911yescharacteristic
120C4⋊C8C2×D7911yescharacteristic
121#103—1581no—
122#103—1581no—
123#102—1582no—
124C4×C8—791no—
125#41—3162no—
126#41—3162no—
127C2×Q8—791no—
128C2×Q8—1581no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—791no—
132C2×D4—1582no—
133C2×D4—1582no—
134C2×D4D31612yes—
135C22×C4—1582no—
136C22×C4—1581no—
137SD16—3162no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—1581no—
141C4⋊C4—791no—
142C4⋊C4—791no—
143C4⋊C4—1581no—
144C4⋊C4—1581no—
145C4⋊C4—1581no—
146C22⋊C4—1582no—
147C22⋊C4—1581no—
148C42—1581no—
149C42C22×D7911yescharacteristic
150C23—22no—
151C23—1581no—
152Q8—3161no—
153Q8—3161no—
154Q8—792no—
155Q8—1581no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—3164no—
162D4—6322no—
163D4—1581no—
164D4—1581no—
165C2×C4—3164no—
166C2×C4—3161no—
167C2×C4—3161no—
168C2×C4—3161no—
169C2×C4—1581no—
170C2×C4—1581no—
171C2×C4—1581no—
172C2×C4D4×D7911yescharacteristic
173C2×C4D4×D7911yescharacteristic
174C2×C4C2×D31611yescharacteristic
175C8—41no—
176C8—41no—
177C8—3161no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—3161no—
182C22—3161no—
183C22—3161no—
184C22#1457913111yescharacteristic
185C4—21no—
186C4—3161no—
187C4—3161no—
188C4—6321no—
189C4—1582no—
190C4SD16×D7911yescharacteristic
191C4#1457918211yescharacteristic
192C4#1457918511yescharacteristic
193C4#1457918511yescharacteristic
194C2—82no—
195C2—6321no—
196C2#1909870911yescharacteristic
197C2#1909871511yescharacteristic
198C2#1909874311yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#331×C79C2
socleC22×C79#120
prime radical#19099233C2
hypercenter#331D79
hypocenterC79#1642
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. #19098909C2semidirect
3. #19098849C2semidirect
4. #19098769C2semidirect
5. #19098293C2semidirect
6. #19098290C2semidirect
7. #331×C79C2semidirect
74. Dic158SD16semidirect
100. C79#1642semidirect
105. #331D79semidirect