Finite Group Databasebeta

← #23764387

Subgroups — #23764387

Order 10112.

260 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14579160C211yesmaximal, characteristic
2#19098586C211yesmaximal, characteristic
3M16×Dic79C211yesmaximal, characteristic
4#19098332C211yesmaximal, characteristic
5#19098331C211yesmaximal, characteristic
6#19098331C211yesmaximal, characteristic
7#343×C79C211yesmaximal, characteristic
8C22×Dic158C412yes—
9C2×#11929608C2211yescharacteristic
10C2×#11929608C2211yescharacteristic
11#14579160—21no—
12#14579160—21no—
13#14579160—21no—
14#14579160—21no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C412yes—
17C2×C4×Dic79C2211yescharacteristic
18Dic79⋊C8—21no—
19Dic79⋊C8—21no—
20#14579071—21no—
21C8×Dic79—21no—
22C2×M16×C79C2211yescharacteristic
23C2×M16×C79C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25C2×Dic158—22no—
26C2×Dic158—22no—
27C2×Dic158—44no—
28C22×Dic79C2×C411yescharacteristic
29C22×Dic79C2×C411yescharacteristic
30C22×Dic79C2×C412yes—
31#11929608—21no—
32#11929608—21no—
33#11929608—21no—
34#11929608Q812yescomplemented
35C2×C79⋊C8—21no—
36C2×C79⋊C8—21no—
37C4⋊Dic79—21no—
38C4⋊Dic79—21no—
39Dic79⋊C4—22no—
40Dic79⋊C4—22no—
41C4×Dic79D411yescharacteristic
42C4×Dic79D411yescharacteristic
43C4×Dic79D411yescharacteristic
44C4×Dic79D411yescharacteristic
45C22×C4×C79C2×C412yes—
46C22×C4×C79C2311yescharacteristic
47M16×C79—21no—
48M16×C79—21no—
49M16×C79—21no—
50M16×C79Q812yescomplemented
51C2×C8×C79—21no—
52C2×C8×C79—21no—
53C4⋊C4×C79—21no—
54C4⋊C4×C79—21no—
55C23×C79C22×C411yescharacteristic
56C2×C4×C79—22no—
57C2×C4×C79—42no—
58C2×C4×C79C2×D411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×Q811yescharacteristic
61C2×C4×C79C2×Q811yescharacteristic
62C2×C4×C79#4111yescharacteristic
63C2×C4×C79#4111yescharacteristic
64C2×Dic79—22no—
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—42no—
68C2×Dic79C22⋊C411yescharacteristic
69C2×Dic79C22⋊C411yescharacteristic
70C2×Dic79C22⋊C411yescharacteristic
71C2×Dic79C22⋊C411yescharacteristic
72Dic158—44no—
73Dic158—44no—
74C8×C79—22no—
75C8×C79—41no—
76C79⋊C8—22no—
77C79⋊C8—41no—
78C22×C79—21no—
79C22×C79—21no—
80C22×C79C2×C22⋊C411yescharacteristic
81C22×C79C4×Q811yescharacteristic
82C22×C79C4×Q811yescharacteristic
83C4×C79—42no—
84C4×C79C22⋊Q811yescharacteristic
85C4×C79C22⋊Q811yescharacteristic
86C4×C79#12411yescharacteristic
87C4×C79C4⋊Q811yescharacteristic
88Dic79—21no—
89Dic79—21no—
90Dic79—42no—
91Dic79#10012yes—
92Dic79#10112yes—
93C2×C79—21no—
94C2×C79—21no—
95C2×C79#39111yescharacteristic
96C2×C79C2×#10011yescharacteristic
97C2×C79C2×#10111yescharacteristic
98#1997—791nomaximal, Sylow
99C79#199711yescharacteristic, complemented, Sylow
100C2×C4⋊Q8—791no—
101#423—791no—
102C4×M16—791no—
103#343—791no—
104#343—791no—
105#343—791no—
106#343D7911yescharacteristic
107C22×Q8—792no—
108C2×M16—791no—
109C2×M16—791no—
110C2×M16C2×D7911yescharacteristic
111C2×M16C2×D7911yescharacteristic
112C4⋊Q8—1581no—
113C4⋊Q8—1581no—
114C4⋊Q8—1581no—
115C4⋊Q8—1581no—
116C2×C4⋊C4—791no—
117C2×C4⋊C4—792no—
118C2×C4⋊C4C2×D7911yescharacteristic
119C2×C42—791no—
120C4⋊C8—1581no—
121C4⋊C8—1581no—
122#97—1581no—
123C4×C8—1581no—
124C2×Q8—3164no—
125C2×Q8—1582no—
126C2×Q8—1582no—
127C22×C4—792no—
128C22×C4—791no—
129C22×C4—791no—
130C22×C4C4×D7912yes—
131C22×C4C22×D7911yescharacteristic
132M16—21no—
133M16—21no—
134M16—21no—
135M16—792no—
136M16—1581no—
137M16—1581no—
138M16—1581no—
139M16Dic15812yescomplemented
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—1581no—
143C2×C8—1581no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—1582no—
147C4⋊C4—1582no—
148C4⋊C4—1581no—
149C4⋊C4—1581no—
150C42—791no—
151C42—791no—
152C42—791no—
153C42—791no—
154C23C2×C4×D7911yescharacteristic
155Q8—3164no—
156Q8—3164no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—3162no—
160C2×C4—791no—
161C2×C4—791no—
162C2×C4—791no—
163C2×C4—791no—
164C2×C4—1582no—
165C2×C4—1582no—
166C2×C4—1582no—
167C2×C4D4×D7911yescharacteristic
168C2×C4D4×D7911yescharacteristic
169C2×C4Q8×D7911yescharacteristic
170C2×C4C2×Dic15811yescharacteristic
171C2×C4#1192962311yescharacteristic
172C2×C4#1192962411yescharacteristic
173C8—22no—
174C8—41no—
175C8—3161no—
176C8—1582no—
177C22—21no—
178C22—21no—
179C22C22⋊C4×D7911yescharacteristic
180C22#1457912611yescharacteristic
181C22C4×Dic15811yescharacteristic
182C4—42no—
183C4—3162no—
184C4—792no—
185C4—792no—
186C4—1581no—
187C4—1581no—
188C4#1457913811yescharacteristic
189C4#1457913911yescharacteristic
190C4#1457914711yescharacteristic
191C4#1457916011yescharacteristic
192C2—21no—
193C2—21no—
194C2#1909846711yescharacteristic
195C2#100×D7911yescharacteristic
196C2#101×D7911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D79
commutator, prime radicalC23×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#343×C79C2
socleC22×C79C2×C22⋊C4
cosocleC22×C4×C79C23
hypercenter#343D79
hypocenterC79#1997
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
34. #11929608Q8semidirect
50. M16×C79Q8semidirect
99. C79#1997semidirect
139. M16Dic158semidirect