Finite Group Databasebeta

← #23762018

Subgroups — #23762018

Order 10112.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#19099097C211yesmaximal, characteristic
2#19098620C211yesmaximal, characteristic, complemented
3#19098304C212yesmaximal, complemented
4#19098302C212yesmaximal, complemented
5C2×#97×C79C211yesmaximal, characteristic, complemented
6#14579155—21no—
7#14579153C2211yescharacteristic
8#14579149C2211yescharacteristic
9#14579144—21no—
10#14579140C411yescharacteristic
11#14579135C411yescharacteristic
12C4×Dic158C411yescharacteristic
13C4×D316C411yescharacteristic
14C4×C22⋊D79—21no—
15#14579118—21no—
16C4⋊(C79⋊C8)—21no—
17C22⋊(C79⋊C8)—21no—
18#14579072C2212yes—
19C22×C8×C79—21no—
20C2×C42×C79C2211yescharacteristic
21#97×C79—21no—
22#97×C79C2212yes—
23C2×Dic158C2×C411yescharacteristic
24C2×D316C2×C411yescharacteristic
25C2×C22⋊D79—21no—
26C2×C4×D79—21no—
27C2×C79⋊C8—22no—
28C4⋊Dic79C2×C411yescharacteristic
29C4⋊Dic79C2×C411yescharacteristic
30Dic79⋊C4—21no—
31Dic79⋊C4—21no—
32Dic79⋊C4—21no—
33Dic79⋊C4—21no—
34C22⋊Dic79—21no—
35(C2×D79)⋊C4—21no—
36(C2×D79)⋊C4—21no—
37(C2×D79)⋊C4—21no—
38(C2×D79)⋊C4—21no—
39C4×Dic79—21no—
40C22×C4×C79C2×C411yescharacteristic
41C22×C4×C79D411yescharacteristic
42C22×C4×C79D411yescharacteristic
43C2×C8×C79—24no—
44C2×C8×C79—22no—
45C42×C79C2×C411yescharacteristic
46C42×C79D411yescharacteristic
47C42×C79D411yescharacteristic
48C42×C79C2311yescharacteristic
49C23×C79C22⋊C411yescharacteristic
50C22×D79—21no—
51C2×C4×C79—22no—
52C2×C4×C79—41no—
53C2×C4×C79—41no—
54C2×C4×C79C22⋊C411yescharacteristic
55C2×C4×C79C22⋊C411yescharacteristic
56C2×C4×C79C22⋊C411yescharacteristic
57C2×C4×C79C22×C411yescharacteristic
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C22⋊D79—42no—
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64D316—41no—
65C4×D79—42no—
66Dic158—41no—
67C8×C79—24no—
68C79⋊C8—42no—
69C22×C79—21no—
70C22×C79—21no—
71C22×C79#10412yes—
72C22×C79C2×C22⋊C411yescharacteristic
73C2×D79—41no—
74C2×D79—41no—
75C2×D79—41no—
76C4×C79—21no—
77C4×C79—21no—
78C4×C79—21no—
79C4×C79—21no—
80C4×C79—21no—
81C4×C79—21no—
82Dic79—41no—
83Dic79—41no—
84Dic79—41no—
85C2×C79—22no—
86C2×C79#41311yescharacteristic
87C2×C79C2×#10411yescharacteristic
88C2×C79#42111yescharacteristic
89D79—81no—
90#1532—791nomaximal, Sylow
91C79#153211yescharacteristic, complemented, Sylow
92#529—791no—
93#432—791no—
94C2×#97D7911yescharacteristic, complemented
95#330—792no—
96#329—792no—
97C22×C8—21no—
98#126—1581no—
99#125—791no—
100#124—791no—
101#123—1581no—
102C22⋊Q8—791no—
103#121—791no—
104C4×Q8—791no—
105C4×D4—791no—
106C4×D4—1581no—
107#117—1581no—
108C2×C42C2×D7911yescharacteristic
109C4⋊C8—1581no—
110C22⋊C8—1581no—
111#97—21no—
112#97—792no—
113#97C2×D7912yes—
114C2×Q8—791no—
115C2×D4—791no—
116C2×D4—1581no—
117C22×C4—1581no—
118C22×C4C4×D7911yescharacteristic
119C22×C4D31611yescharacteristic
120C22×C4C22⋊D7911yescharacteristic
121C2×C8—24no—
122C2×C8—22no—
123C2×C8—1582no—
124C4⋊C4—791no—
125C4⋊C4—791no—
126C4⋊C4—1581no—
127C4⋊C4—1581no—
128C4⋊C4—1581no—
129C4⋊C4—1581no—
130C22⋊C4—1581no—
131C22⋊C4—1581no—
132C22⋊C4—1581no—
133C22⋊C4—1581no—
134C22⋊C4—1581no—
135C42—1581no—
136C42C4×D7911yescharacteristic
137C42D31611yescharacteristic
138C42C22⋊D7911yescharacteristic
139C42C22×D7911yescharacteristic
140C23—1581no—
141C23(C2×D79)⋊C411yescharacteristic
142Q8—3161no—
143D4—3161no—
144D4—3162no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3162no—
149C2×C4—1581no—
150C2×C4—1581no—
151C2×C4—1581no—
152C2×C4(C2×D79)⋊C411yescharacteristic
153C2×C4(C2×D79)⋊C411yescharacteristic
154C2×C4(C2×D79)⋊C411yescharacteristic
155C2×C4C2×C4×D7911yescharacteristic
156C2×C4C2×C22⋊D7911yescharacteristic
157C2×C4C2×D31611yescharacteristic
158C8—24no—
159C8—3162no—
160C22—21no—
161C22—21no—
162C22—3161no—
163C22—3161no—
164C22—3161no—
165C22#1457908912yes—
166C22C2×(C2×D79)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—3161no—
174C4—3161no—
175C4—3161no—
176C2—22no—
177C2—6321no—
178C2#1909854511yescharacteristic
179C2C2×#1457908911yescharacteristic
180C2#1909857911yescharacteristic
subgroupG/H
centerC22C2×(C2×D79)⋊C4
commutatorC2×C4×C79C22×C4
FrattiniC42C22×D79
FittingC2×#97×C79C2
socleC22×C79C2×C22⋊C4
prime radical#14579135C4
cosocleC42×C79C23
hypercenterC2×#97D79
hypocenterC79#1532
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #19098620C2semidirect
3. #19098304C2semidirect
4. #19098302C2semidirect
5. C2×#97×C79C2semidirect
91. C79#1532semidirect
94. C2×#97D79semidirect