Finite Group Databasebeta

← #23763404

Subgroups — #23763404

Order 10112.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14579126C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic
3C2×#14579086C211yesmaximal, characteristic
4C2×#14579084C211yesmaximal, characteristic
5#19098432C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic
7#340×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10#14579126—22no—
11#14579126C414yescomplemented
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4—21no—
14C2×Dic79⋊C4—21no—
15C2×Dic79⋊C4—21no—
16C2×C4×Dic79—21no—
17C2×C4×Dic79C2211yescharacteristic
18Dic79⋊C8—22no—
19#14579086—22no—
20#14579084—22no—
21C22×C8×C79C2211yescharacteristic
22C2×C4⋊C4×C79C2211yescharacteristic
23C2×C4⋊C4×C79C2211yescharacteristic
24C2×Dic158—21no—
25C2×Dic158—21no—
26C2×Dic158—21no—
27C2×Dic158C2×C412yes—
28C2×Dic158D412yes—
29C2×Dic158Q812yes—
30C22×Dic79—21no—
31C22×Dic79—21no—
32C22×Dic79D411yescharacteristic
33C22×Dic79D411yescharacteristic
34C2×C79⋊C8—21no—
35C2×C79⋊C8—21no—
36C2×C79⋊C8—21no—
37C4⋊Dic79—21no—
38C4⋊Dic79—21no—
39Dic79⋊C4—24no—
40Dic79⋊C4—42no—
41Dic79⋊C4—42no—
42C4×Dic79—24no—
43C4×Dic79C2×C412yes—
44C4×Dic79D412yes—
45C22×C4×C79—21no—
46C22×C4×C79—21no—
47C22×C4×C79C2311yescharacteristic
48C2×C8×C79—21no—
49C2×C8×C79—21no—
50C2×C8×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79—21no—
53C4⋊C4×C79—21no—
54C4⋊C4×C79C2×C412yes—
55C23×C79C2×D411yescharacteristic
56C2×C4×C79—22no—
57C2×C4×C79—41no—
58C2×C4×C79—41no—
59C2×C4×C79—41no—
60C2×C4×C79—41no—
61C2×C4×C79—41no—
62C2×C4×C79C22×C411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×Q811yescharacteristic
66C2×C4×C79#4111yescharacteristic
67C2×C4×C79#4111yescharacteristic
68C2×Dic79—22no—
69C2×Dic79—22no—
70C2×Dic79—22no—
71C2×Dic79—21no—
72C2×Dic79—21no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76C2×Dic79C22⋊C412yes—
77C2×Dic79C22⋊C412yes—
78C2×Dic79SD1612yes—
79C2×Dic79Q1612yes—
80Dic158—22no—
81Dic158—22no—
82Dic158—22no—
83Dic158C4⋊C414yescomplemented
84C8×C79—41no—
85C79⋊C8—41no—
86C22×C79C2×C22⋊C411yescharacteristic
87C22×C79#12111yescharacteristic
88C22×C79C22⋊Q811yescharacteristic
89C22×C79C2×SD1611yescharacteristic
90C22×C79C2×Q1611yescharacteristic
91C22×C79AGL(1,ℤ/8)11yescharacteristic
92C22×C79#13711yescharacteristic
93C4×C79—42no—
94C4×C79—81no—
95C4×C79C2×C4⋊C411yescharacteristic
96C4×C79#11711yescharacteristic
97C4×C79#12111yescharacteristic
98C4×C79C22⋊Q811yescharacteristic
99Dic79—24no—
100Dic79—22no—
101Dic79—81no—
102Dic79#10314yescomplemented
103C2×C79#38011yescharacteristic
104C2×C79C2×#10311yescharacteristic
105C2×C79#41711yescharacteristic
106C2×C79#46011yescharacteristic
107C2×C79#46211yescharacteristic
108C2×C79#47511yescharacteristic
109C2×C79#47711yescharacteristic
110#1803—791nomaximal, Sylow
111C79#180311yescharacteristic, complemented, Sylow
112C2×C4×Q8—791no—
113C2×C4⋊C8—791no—
114C2×#103—791no—
115C2×#103—791no—
116#384—791no—
117#340—791no—
118#340D7911yescharacteristic
119C22×Q8—791no—
120C22×C8—791no—
121C22×C8C2×D7911yescharacteristic
122C4×Q8—794no—
123C4×Q8—1582no—
124C2×C4⋊C4—791no—
125C2×C4⋊C4—1581no—
126C2×C4⋊C4—1581no—
127C2×C4⋊C4—1581no—
128C2×C4⋊C4C2×D7911yescharacteristic
129C2×C4⋊C4C2×D7911yescharacteristic
130C2×C42—791no—
131C2×C42—1581no—
132C4⋊C8—1582no—
133#103—1582no—
134#103—1582no—
135C2×Q8—792no—
136C2×Q8—792no—
137C2×Q8—792no—
138C2×Q8—1581no—
139C2×Q8—1581no—
140C2×Q8—1581no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—791no—
144C22×C4—791no—
145C22×C4—1581no—
146C22×C4—1581no—
147C22×C4C22×D7911yescharacteristic
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—1581no—
152C2×C8—1581no—
153C2×C8—1581no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—3162no—
158C4⋊C4—3162no—
159C4⋊C4—1584no—
160C4⋊C4—1581no—
161C4⋊C4—1581no—
162C4⋊C4C4×D7912yes—
163C42—792no—
164C42—792no—
165C42—1584no—
166C23D4×D7911yescharacteristic
167Q8—794no—
168Q8—1582no—
169Q8—1582no—
170Q8—1582no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3161no—
178C2×C4—3161no—
179C2×C4—3161no—
180C2×C4—792no—
181C2×C4—792no—
182C2×C4—792no—
183C2×C4—792no—
184C2×C4—1582no—
185C2×C4—1582no—
186C2×C4—1582no—
187C2×C4—1581no—
188C2×C4—1581no—
189C2×C4C2×C4×D7911yescharacteristic
190C2×C4D4×D7911yescharacteristic
191C2×C4D4×D7911yescharacteristic
192C2×C4Q8×D7911yescharacteristic
193C2×C4#1192962411yescharacteristic
194C2×C4#1192962411yescharacteristic
195C8—41no—
196C8—3161no—
197C22C22⋊C4×D7911yescharacteristic
198C22#1457913411yescharacteristic
199C22#1457913911yescharacteristic
200C22SD16×D7911yescharacteristic
201C22Q16×D7911yescharacteristic
202C22#1457918511yescharacteristic
203C22#1457919011yescharacteristic
204C4—42no—
205C4—81no—
206C4—794no—
207C4—6321no—
208C4—1584no—
209C4—1582no—
210C4C4⋊C4×D7911yescharacteristic
211C4#1457911811yescharacteristic
212C4#1457913411yescharacteristic
213C4#1457913911yescharacteristic
214C2#1909842211yescharacteristic
215C2#103×D7911yescharacteristic
216C2#1909856111yescharacteristic
217C2#1909876211yescharacteristic
218C2#1909877211yescharacteristic
219C2#1909884711yescharacteristic
220C2#1909885711yescharacteristic
subgroupG/H
centerC23D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#340×C79C2
socle, prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#340D79
hypocenterC79#1803
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #14579126C4semidirect
83. Dic158C4⋊C4semidirect
102. Dic79#103semidirect
111. C79#1803semidirect