Finite Group Databasebeta

← #23764293

Subgroups — #23764293

Order 10112.

292 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#14579183C211yesmaximal, characteristic
2C2×#14579097C211yesmaximal, characteristic, complemented
3C2×#14579089C212yesmaximal, complemented
4#19098529C212yesmaximal, complemented
5C2×#97×C79C211yesmaximal, characteristic, complemented
6C2×#11929624C2212yes—
7#14579183—22no—
8#14579183—22no—
9C2×Dic316C411yescharacteristic, complemented
10C2×#11929613C412yescomplemented
11C2×D632C411yescharacteristic, complemented
12C2×#11929608C2212yes—
13#14579097—22no—
14#14579089—24no—
15(C2×D79)⋊C8—24no—
16C22×C8×C79C2211yescharacteristic
17C22×C8×C79C2211yescharacteristic
18C2×C42×C79C2211yescharacteristic
19#97×C79—22no—
20#11929624—22no—
21#11929624—22no—
22#11929624—22no—
23#11929624—22no—
24C2×Dic158C2×C412yes—
25C2×D316C2×C412yes—
26C2×C22⋊D79—22no—
27C2×C4×D79—22no—
28Dic316—22no—
29#11929613—24no—
30D632—22no—
31#11929608—22no—
32#11929608—22no—
33C2×C79⋊C8—22no—
34C22×C4×C79—21no—
35C22×C4×C79C2311yescharacteristic
36C2×C8×C79—21no—
37C2×C8×C79—21no—
38C2×C8×C79C2×C411yescharacteristic
39C2×C8×C79C2×C411yescharacteristic
40C2×C8×C79D412yes—
41C2×C8×C79D412yes—
42C2×C8×C79D412yes—
43C42×C79—21no—
44C42×C79D412yes—
45C23×C79#4111yescharacteristic
46C22×D79—22no—
47C2×C4×C79—22no—
48C2×C4×C79—42no—
49C2×C4×C79C22×C411yescharacteristic
50C2×C4×C79C2×D411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2×D411yescharacteristic
53C2×C4×C79C2×D411yescharacteristic
54C2×C4×C79#4111yescharacteristic
55C22⋊D79—42no—
56C22⋊D79—42no—
57C2×Dic79—22no—
58D316—22no—
59D316—22no—
60C4×D79—42no—
61C4×D79—42no—
62Dic158—22no—
63Dic158—22no—
64C8×C79—22no—
65C8×C79C22⋊C412yes—
66C8×C79C22⋊C412yes—
67C79⋊C8—42no—
68C22×C79—22no—
69C22×C79C4×D411yescharacteristic
70C22×C79#12111yescharacteristic
71C22×C79#12411yescharacteristic
72C2×D79—42no—
73C2×D79—44no—
74C4×C79—42no—
75C4×C79C2×C22⋊C411yescharacteristic
76C4×C79C4×D411yescharacteristic
77C4×C79#12111yescharacteristic
78C4×C79#12711yescharacteristic
79Dic79—42no—
80C2×C79—21no—
81C2×C79—21no—
82C2×C79#39011yescharacteristic
83C2×C79#44412yes—
84D79—82no—
85#1975—791nomaximal, Sylow
86C79#197511yescharacteristic, complemented, Sylow
87C2×#135—791no—
88C2×#108—791no—
89C2×#104—792no—
90#408—792no—
91C2×#97D7911yescharacteristic, complemented
92C2×#41—792no—
93#135—1582no—
94#135—1582no—
95C2×Q16—791no—
96C2×SD16—792no—
97C2×D8—791no—
98C2×M16—792no—
99C22×C8C2×D7911yescharacteristic
100C22×C8C2×D7911yescharacteristic
101C2×C42C2×D7911yescharacteristic
102#108—1582no—
103#104—1584no—
104C22⋊C8—1584no—
105#97—22no—
106#41—1582no—
107#41—1582no—
108#41—1582no—
109#41—1582no—
110C2×Q8—792no—
111C2×D4—792no—
112C2×D4—1582no—
113C22×C4—21no—
114C22×C4—1582no—
115C22×C4C22×D7911yescharacteristic
116Q16—1582no—
117SD16—1584no—
118D8—1582no—
119M16—1582no—
120M16—1582no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—1582no—
124C2×C8C4×D7911yescharacteristic
125C2×C8C4×D7911yescharacteristic
126C2×C8D31612yes—
127C2×C8D31612yes—
128C2×C8C22⋊D7912yes—
129C42—21no—
130C42D31612yes—
131C23—1582no—
132C23#1192962411yescharacteristic
133Q8—1582no—
134Q8—1582no—
135D4—3162no—
136D4—3162no—
137D4—1582no—
138D4—1582no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—3162no—
142C2×C4—3162no—
143C2×C4—1582no—
144C2×C4C2×C4×D7911yescharacteristic
145C2×C4C2×C22⋊D7911yescharacteristic
146C2×C4C2×D31611yescharacteristic
147C2×C4C2×D31611yescharacteristic
148C2×C4C2×D31611yescharacteristic
149C2×C4#1192962411yescharacteristic
150C8—22no—
151C8—3162no—
152C8(C2×D79)⋊C412yes—
153C8(C2×D79)⋊C412yes—
154C22—22no—
155C22—3164no—
156C22—3162no—
157C22C4×D31611yescharacteristic
158C22#1457913511yescharacteristic
159C22#1457914911yescharacteristic
160C4—42no—
161C4—3162no—
162C4C2×(C2×D79)⋊C411yescharacteristic
163C4C4×D31611yescharacteristic
164C4#1457913511yescharacteristic
165C4#1457915811yescharacteristic
166C2—21no—
167C2—21no—
168C2—6322no—
169C2#1909846511yescharacteristic
170C2#1909868612yes—
subgroupG/H
centerC2×C4C2×D316
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#97×C79C2
socleC22×C79C4×D4
prime radicalC2×#14579183C2
cosocleC22×C4×C79C23
hypercenterC2×#97D79
hypocenterC79#1975
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#14579097C2semidirect
3. C2×#14579089C2semidirect
4. #19098529C2semidirect
5. C2×#97×C79C2semidirect
9. C2×Dic316C4semidirect
10. C2×#11929613C4semidirect
11. C2×D632C4semidirect
86. C79#1975semidirect
91. C2×#97D79semidirect