Finite Group Databasebeta

← #23764574

Subgroups — #23764574

Order 10112.

244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 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#19099116C211yesmaximal, characteristic, complemented
2#19098580C211yesmaximal, characteristic
3C2×#14579088C211yesmaximal, characteristic
4#19098333C211yesmaximal, characteristic, complemented
5#19098322C211yesmaximal, characteristic, complemented
6#19098319C211yesmaximal, characteristic, complemented
7#410×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10#14579160—21no—
11#14579152—21no—
12#14579138—22no—
13C4×Dic158—22no—
14#14579120C2211yescharacteristic
15C2×C4×Dic79C2211yescharacteristic
16#14579088—21no—
17#14579088—21no—
18#14579088—22no—
19C2×#41×C79C2211yescharacteristic
20#117×C79C2211yescharacteristic
21#117×C79C2211yescharacteristic
22#99×C79—22no—
23C2×Dic158—22no—
24C22×Dic79—21no—
25#11929608—21no—
26#11929608—21no—
27#11929608—21no—
28#11929608—21no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79—22no—
32C4⋊Dic79—21no—
33Dic79⋊C4—22no—
34Dic79⋊C4—22no—
35C22⋊Dic79—21no—
36C4×Dic79—21no—
37C4×Dic79D411yescharacteristic
38C4×Dic79D411yescharacteristic
39C4×Dic79D412yes—
40#41×C79—21no—
41#41×C79—21no—
42#41×C79—21no—
43#41×C79—21no—
44C2×Q8×C79Q811yescharacteristic, complemented
45C2×D4×C79—21no—
46C2×D4×C79Q811yescharacteristic, complemented
47C22×C4×C79—21no—
48C22×C4×C79C2311yescharacteristic
49C4⋊C4×C79—21no—
50C4⋊C4×C79—21no—
51C22⋊C4×C79—21no—
52C22⋊C4×C79D412yes—
53C42×C79—21no—
54C42×C79—21no—
55C23×C79—21no—
56C23×C79C2×D411yescharacteristic
57Q8×C79—21no—
58Q8×C79—21no—
59D4×C79—21no—
60D4×C79—21no—
61D4×C79—41no—
62D4×C79—41no—
63C2×C4×C79—22no—
64C2×C4×C79—21no—
65C2×C4×C79—41no—
66C2×C4×C79—41no—
67C2×C4×C79—41no—
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×Q811yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×C4×C79#4111yescharacteristic
73C2×C4×C79#4111yescharacteristic
74C2×Dic79—21no—
75C2×Dic79—21no—
76C2×Dic79—22no—
77C2×Dic79—42no—
78Dic158—44no—
79C79⋊C8—41no—
80C79⋊C8—41no—
81C22×C79—41no—
82C22×C79—41no—
83C22×C79—81no—
84C22×C79#12011yescharacteristic
85C22×C79C22⋊Q811yescharacteristic
86C22×C79#12411yescharacteristic
87C4×C79—42no—
88C4×C79—41no—
89C4×C79—81no—
90C4×C79C22⋊Q811yescharacteristic
91C4×C79C22⋊Q811yescharacteristic
92C4×C79#12411yescharacteristic
93C4×C79#12411yescharacteristic
94Dic79—22no—
95Dic79—42no—
96Dic79—41no—
97C2×C79—21no—
98C2×C79—21no—
99C2×C79—21no—
100C2×C79—81no—
101C2×C79#39311yescharacteristic
102#2031—791nomaximal, Sylow
103C79#203111yescharacteristic, complemented, Sylow
104#533—791no—
105#421—791no—
106C2×#104—791no—
107#410D7911yescharacteristic
108#344—791no—
109#339—791no—
110H(3,ℤ/4)—791no—
111C2×#41C2×D7911yescharacteristic
112C2×M16—791no—
113C2×M16—791no—
114C4⋊Q8—1581no—
115#125—1581no—
116C22⋊Q8—1582no—
117C4×Q8—1582no—
118#117—791no—
119#117C2×D7911yescharacteristic
120#117C2×D7911yescharacteristic
121C2×C42—791no—
122#104—1581no—
123#104—1581no—
124#104—1582no—
125#99—22no—
126#41—21no—
127#41—21no—
128#41—21no—
129#41—21no—
130C2×Q8—1582no—
131C2×Q8Dic15811yescharacteristic, complemented
132C2×D4—21no—
133C2×D4Dic15811yescharacteristic, complemented
134C22×C4—21no—
135C22×C4—1581no—
136C22×C4C22×D7911yescharacteristic
137M16—1581no—
138M16—1581no—
139M16—1581no—
140M16—1581no—
141C2×C8—1581no—
142C2×C8—1581no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1582no—
146C4⋊C4—1582no—
147C4⋊C4—1582no—
148C4⋊C4—1581no—
149C22⋊C4—21no—
150C22⋊C4—1581no—
151C22⋊C4C22⋊D7912yes—
152C42—21no—
153C42—21no—
154C42—791no—
155C42—791no—
156C42—792no—
157C42—1581no—
158C23—21no—
159C23C2×C22⋊D7911yescharacteristic
160Q8—21no—
161Q8—21no—
162Q8—3164no—
163D4—21no—
164D4—21no—
165D4—41no—
166D4—41no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3162no—
173C2×C4—1581no—
174C2×C4—1582no—
175C2×C4—1581no—
176C2×C4D4×D7911yescharacteristic
177C2×C4D4×D7911yescharacteristic
178C2×C4C2×Dic15811yescharacteristic
179C2×C4#1192962311yescharacteristic
180C2×C4#1192962311yescharacteristic
181C2×C4#1192962411yescharacteristic
182C8—3161no—
183C8—3161no—
184C22—41no—
185C22—41no—
186C22—81no—
187C22#1457912911yescharacteristic
188C22#1457914011yescharacteristic
189C22#1457914811yescharacteristic
190C4—42no—
191C4—41no—
192C4—81no—
193C4—3161no—
194C4—3162no—
195C4—1582no—
196C4#1457913811yescharacteristic
197C4#1457913811yescharacteristic
198C4#1457914711yescharacteristic
199C4#1457914711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—81no—
204C2#1909847511yescharacteristic
subgroupG/H
centerC4#14579147
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#410×C79C2
socleC2×C79#393
prime radicalC2×#41×C79C22
hypercenter#410D79
hypocenterC79#2031
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #19099116C2semidirect
4. #19098333C2semidirect
5. #19098322C2semidirect
6. #19098319C2semidirect
44. C2×Q8×C79Q8semidirect
46. C2×D4×C79Q8semidirect
103. C79#2031semidirect
131. C2×Q8Dic158semidirect
133. C2×D4Dic158semidirect