Finite Group Databasebeta

← #23763640

Subgroups — #23763640

Order 10112.

262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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#19098611C211yesmaximal, characteristic, complemented
2#19098586C211yesmaximal, characteristic, complemented
3#19098580C211yesmaximal, characteristic
4C2×#14579088C211yesmaximal, characteristic
5#19098334C211yesmaximal, characteristic, complemented
6#19098324C211yesmaximal, characteristic, complemented
7#568×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10#14579120C2211yescharacteristic
11C2×C4×Dic79C2211yescharacteristic
12#14579096—22no—
13Dic79⋊C8—22no—
14#14579088—22no—
15#14579088C412yescomplemented
16#14579088C412yescomplemented
17C2×#41×C79C2211yescharacteristic
18#131×C79—22no—
19#131×C79—22no—
20C2×M16×C79—22no—
21C2×M16×C79C2211yescharacteristic
22C2×M16×C79C2211yescharacteristic
23C22×Dic79—21no—
24#11929608—21no—
25#11929608—21no—
26#11929608—21no—
27#11929608C2×C412yes—
28C2×C79⋊C8—21no—
29C2×C79⋊C8—21no—
30C4⋊Dic79—21no—
31C22⋊Dic79—21no—
32C4×Dic79—21no—
33C4×Dic79—21no—
34C4×Dic79C2×C411yescharacteristic
35C4×Dic79C2×C411yescharacteristic
36#41×C79—21no—
37#41×C79—21no—
38#41×C79C2×C412yes—
39#41×C79D412yes—
40C2×Q8×C79Q811yescharacteristic
41C2×D4×C79—21no—
42C2×D4×C79Q811yescharacteristic
43C22×C4×C79—21no—
44C22×C4×C79C2311yescharacteristic
45M16×C79—24no—
46M16×C79—21no—
47M16×C79—21no—
48M16×C79—21no—
49M16×C79D412yes—
50C2×C8×C79—24no—
51C2×C8×C79—21no—
52C2×C8×C79D412yes—
53C23×C79—21no—
54C23×C79#4111yescharacteristic
55Q8×C79—21no—
56Q8×C79C4⋊C412yes—
57D4×C79—22no—
58D4×C79—22no—
59D4×C79—21no—
60D4×C79C4⋊C412yes—
61C2×C4×C79—21no—
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79C22×C411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×Q811yescharacteristic
69C2×C4×C79#4111yescharacteristic
70C2×Dic79—21no—
71C2×Dic79—21no—
72C2×Dic79—42no—
73C2×Dic79—41no—
74C8×C79—22no—
75C8×C79—22no—
76C79⋊C8—22no—
77C79⋊C8—41no—
78C22×C79—22no—
79C22×C79—41no—
80C22×C79—81no—
81C22×C79C4×D411yescharacteristic
82C22×C79C22⋊Q811yescharacteristic
83C22×C79#12311yescharacteristic
84C4×C79—22no—
85C4×C79C2×C4⋊C411yescharacteristic
86C4×C79C4×D411yescharacteristic
87C4×C79#12011yescharacteristic
88C4×C79C22⋊Q811yescharacteristic
89Dic79—22no—
90Dic79—41no—
91Dic79—81no—
92C2×C79—21no—
93C2×C79—21no—
94C2×C79—21no—
95C2×C79—42no—
96C2×C79#38511yescharacteristic
97#1861—791nomaximal, Sylow
98C79#186111yescharacteristic, complemented, Sylow
99#568D7911yescharacteristic
100#430—791no—
101#423—791no—
102#421—791no—
103C2×#104—791no—
104#344—791no—
105#339—791no—
106C2×#41C2×D7911yescharacteristic
107#131—22no—
108#131—22no—
109C2×M16—22no—
110C2×M16—791no—
111C2×M16—791no—
112C2×M16C2×D7911yescharacteristic
113C2×M16C2×D7911yescharacteristic
114#117—791no—
115C2×C42—791no—
116#108—1582no—
117C4⋊C8—1582no—
118#104—792no—
119#104—792no—
120#104—1582no—
121#41—21no—
122#41—21no—
123#41C4×D7912yes—
124#41C22⋊D7912yes—
125C2×Q8Dic15811yescharacteristic
126C2×D4—21no—
127C2×D4Dic15811yescharacteristic
128C22×C4—21no—
129C22×C4—1581no—
130C22×C4C22×D7911yescharacteristic
131M16—24no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—792no—
136M16—1581no—
137M16—1581no—
138M16—1581no—
139M16C22⋊D7912yes—
140C2×C8—24no—
141C2×C8—21no—
142C2×C8—1581no—
143C2×C8—1581no—
144C2×C8C22⋊D7912yes—
145C4⋊C4—1581no—
146C22⋊C4—1581no—
147C42—791no—
148C42—791no—
149C42—1581no—
150C42—1581no—
151C23—21no—
152C23#1192962411yescharacteristic
153Q8—21no—
154Q8Dic79⋊C412yes—
155D4—22no—
156D4—22no—
157D4—21no—
158D4Dic79⋊C412yes—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—3162no—
163C2×C4—3161no—
164C2×C4—1581no—
165C2×C4—1581no—
166C2×C4C2×C4×D7911yescharacteristic
167C2×C4C2×C22⋊D7911yescharacteristic
168C2×C4C2×C22⋊D7911yescharacteristic
169C2×C4C2×C22⋊D7911yescharacteristic
170C2×C4C2×Dic15811yescharacteristic
171C2×C4#1192962411yescharacteristic
172C8—22no—
173C8—22no—
174C8—3161no—
175C8—1582no—
176C22—22no—
177C22—41no—
178C22—81no—
179C22C4×C22⋊D7911yescharacteristic
180C22#1457914011yescharacteristic
181C22#1457914411yescharacteristic
182C4—22no—
183C4—3161no—
184C4—6321no—
185C4—1582no—
186C4C2×Dic79⋊C411yescharacteristic
187C4C4×C22⋊D7911yescharacteristic
188C4#1457913011yescharacteristic
189C4#1457914011yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—42no—
194C2#1909843611yescharacteristic
subgroupG/H
centerC4#14579130
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#568×C79C2
socleC2×C79#385
prime radicalC2×#41×C79C22
cosocleC22×C4×C79C23
hypercenter#568D79
hypocenterC79#1861
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
1. #19098611C2semidirect
2. #19098586C2semidirect
5. #19098334C2semidirect
6. #19098324C2semidirect
15. #14579088C4semidirect
16. #14579088C4semidirect
98. C79#1861semidirect