Finite Group Databasebeta

← #23762552

Subgroups — #23762552

Order 10112.

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

normal subgroups only

This group has 234 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#19099216C211yesmaximal, characteristic
2#19098915C211yesmaximal, characteristic, complemented
3#19098854C211yesmaximal, characteristic, complemented
4#19098854C211yesmaximal, characteristic, complemented
5#19098290C211yesmaximal, characteristic, complemented
6#19098290C211yesmaximal, characteristic, complemented
7#332×C79C211yesmaximal, characteristic, complemented
8C2×#11929625—21no—
9#14579161C2211yescharacteristic
10#14579146—22no—
11#14579137—21no—
12#14579136—21no—
13C4×D316C2211yescharacteristic
14C4×D316C2211yescharacteristic
15C4⋊C4×D79—21no—
16#14579093—21no—
17#14579093—21no—
18#14579084—22no—
19#14579083—21no—
20#14579083—21no—
21C4×C79⋊C8C2211yescharacteristic
22C4⋊Q8×C79C2211yescharacteristic
23C4⋊C8×C79C2211yescharacteristic
24C4⋊C8×C79C2211yescharacteristic
25#11929625—42no—
26#11929625—42no—
27C2×Dic158—21no—
28C2×D316—22no—
29C2×D316D411yescharacteristic
30C2×D316D411yescharacteristic
31C2×C4×D79—22no—
32C2×C4×D79—21no—
33C2×C4×D79—21no—
34C2×C79⋊C8—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79—21no—
37C4⋊Dic79D411yescharacteristic
38C4⋊Dic79D411yescharacteristic
39Dic79⋊C4—22no—
40(C2×D79)⋊C4—22no—
41(C2×D79)⋊C4—21no—
42(C2×D79)⋊C4—21no—
43C2×Q8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C4⋊C4×C79—21no—
47C4⋊C4×C79D412yes—
48C42×C79C2311yescharacteristic
49C22×D79—21no—
50C22×D79—21no—
51Q8×C79—41no—
52Q8×C79—41no—
53C2×C4×C79—22no—
54C2×C4×C79C2×D411yescharacteristic
55C2×C4×C79C2×D411yescharacteristic
56C2×C4×C79C2×D411yescharacteristic
57C2×Dic79—21no—
58C2×Dic79—21no—
59C2×Dic79—41no—
60D316—21no—
61D316—21no—
62D316—21no—
63D316—44no—
64D316SD1612yes—
65C4×D79—44no—
66C4×D79—41no—
67C4×D79—41no—
68C4×D79—41no—
69C4×D79—41no—
70Dic158—42no—
71C8×C79—41no—
72C8×C79—41no—
73C79⋊C8—41no—
74C22×C79#12011yescharacteristic
75C2×D79—22no—
76C2×D79—41no—
77C2×D79—41no—
78C2×D79—41no—
79C2×D79—41no—
80C2×D79—41no—
81C4×C79—21no—
82C4×C79—42no—
83C4×C79C2×SD1611yescharacteristic
84C4×C79#13511yescharacteristic
85C4×C79AGL(1,ℤ/8)11yescharacteristic
86C4×C79#13711yescharacteristic
87Dic79—41no—
88Dic79—41no—
89Dic79—81no—
90C2×C79#45011yescharacteristic
91C2×C79#45211yescharacteristic
92C2×C79#45411yescharacteristic
93D79—42no—
94D79—81no—
95#1635—791nomaximal, Sylow
96C79#163511yescharacteristic, complemented, Sylow
97#547—791no—
98#487—791no—
99#476—791no—
100#476—791no—
101#332D7911yescharacteristic, complemented
102D4⋊C8—791no—
103D4⋊C8—791no—
104C2×#41—1581no—
105C4⋊Q8—791no—
106C4⋊Q8C2×D7911yescharacteristic
107#123—1582no—
108C22⋊Q8—1581no—
109#121—1581no—
110C4×D4—791no—
111C4×D4—791no—
112C2×C4⋊C4—1581no—
113#106—1581no—
114#106—1581no—
115C4⋊C8C2×D7911yescharacteristic
116C4⋊C8C2×D7911yescharacteristic
117#103—1582no—
118#102—1581no—
119#102—1581no—
120C4×C8—791no—
121#41—3162no—
122#41—3162no—
123C2×Q8—21no—
124C2×Q8—1581no—
125C2×D4—791no—
126C2×D4—791no—
127C2×D4—1582no—
128C22×C4—1582no—
129C22×C4—1581no—
130C22×C4—1581no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—1581no—
134C4⋊C4—21no—
135C4⋊C4—791no—
136C4⋊C4—791no—
137C4⋊C4—1582no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4D31612yes—
141C22⋊C4—1582no—
142C22⋊C4—1581no—
143C22⋊C4—1581no—
144C42C22×D7911yescharacteristic
145C23—1581no—
146C23—1581no—
147Q8—41no—
148Q8—41no—
149Q8—3162no—
150D4—3164no—
151D4—792no—
152D4—1581no—
153D4—1581no—
154D4—1581no—
155C2×C4—22no—
156C2×C4—3164no—
157C2×C4—3161no—
158C2×C4—3161no—
159C2×C4—3161no—
160C2×C4—3161no—
161C2×C4—3161no—
162C2×C4—1581no—
163C2×C4—1581no—
164C2×C4D4×D7911yescharacteristic
165C2×C4D4×D7911yescharacteristic
166C2×C4C2×D31611yescharacteristic
167C8—41no—
168C8—41no—
169C8—3161no—
170C22—3161no—
171C22—3161no—
172C22—3161no—
173C22—3161no—
174C22—3161no—
175C22—1582no—
176C22#1457913111yescharacteristic
177C4—21no—
178C4—42no—
179C4—3161no—
180C4—3161no—
181C4—6321no—
182C4SD16×D7911yescharacteristic
183C4#1457918211yescharacteristic
184C4#1457918511yescharacteristic
185C4#1457919311yescharacteristic
186C2—3162no—
187C2—6321no—
188C2#1909871511yescharacteristic
189C2#1909872811yescharacteristic
190C2#1909873811yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#332×C79C2
socleC22×C79#120
prime radical#19099216C2
hypercenter#332D79
hypocenterC79#1635
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #19098915C2semidirect
3. #19098854C2semidirect
4. #19098854C2semidirect
5. #19098290C2semidirect
6. #19098290C2semidirect
7. #332×C79C2semidirect
96. C79#1635semidirect
101. #332D79semidirect