Finite Group Databasebeta

← #23764539

Subgroups — #23764539

Order 10112.

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

normal subgroups only

This group has 290 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
1C2×#14579160C211yesmaximal, characteristic
2C2×#14579085C211yesmaximal, characteristic
3#19098470C211yesmaximal, characteristic
4#19098326C211yesmaximal, characteristic
5#19098325C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7C2×#103×C79C211yesmaximal, characteristic
8C22×Dic158—21no—
9C22×C79⋊C8C2211yescharacteristic
10#14579160—22no—
11#14579160—22no—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×C4⋊Dic79C2211yescharacteristic
14C2×Dic79⋊C4—21no—
15C2×C4×Dic79C2211yescharacteristic
16#14579085—22no—
17C79⋊#95—21no—
18C79⋊#95—21no—
19C22×Q8×C79C2211yescharacteristic
20C22×C8×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22#103×C79—22no—
23C2×Dic158—24no—
24C2×Dic158—42no—
25C2×Dic158—42no—
26C22×Dic79—21no—
27C22×Dic79—21no—
28C22×Dic79D411yescharacteristic
29C22×Dic79D411yescharacteristic
30C2×C79⋊C8—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79D412yes—
37Dic79⋊C4—24no—
38C4×Dic79—21no—
39C4×Dic79—21no—
40C2×Q8×C79—21no—
41C2×Q8×C79—21no—
42C2×Q8×C79—21no—
43C2×Q8×C79—21no—
44C2×Q8×C79—21no—
45C2×Q8×C79Q812yescomplemented
46C22×C4×C79—21no—
47C22×C4×C79—21no—
48C22×C4×C79C2311yescharacteristic
49C2×C8×C79—21no—
50C2×C8×C79—21no—
51C2×C8×C79—21no—
52C4⋊C4×C79—21no—
53C4⋊C4×C79D412yes—
54C23×C79C2×D411yescharacteristic
55Q8×C79—22no—
56Q8×C79—22no—
57Q8×C79—41no—
58Q8×C79—41no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79—41no—
64C2×C4×C79—41no—
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×Q811yescharacteristic
68C2×C4×C79#4111yescharacteristic
69C2×C4×C79#4111yescharacteristic
70C2×C4×C79#4111yescharacteristic
71C2×Dic79—21no—
72C2×Dic79—21no—
73C2×Dic79—21no—
74C2×Dic79—21no—
75C2×Dic79—22no—
76C2×Dic79—41no—
77C2×Dic79—41no—
78C2×Dic79—41no—
79C2×Dic79—41no—
80C2×Dic79—41no—
81C2×Dic79SD1612yes—
82C2×Dic79Q1612yes—
83Dic158—48no—
84C8×C79—41no—
85C79⋊C8—41no—
86C22×C79#12011yescharacteristic
87C22×C79C22⋊Q811yescharacteristic
88C22×C79#12411yescharacteristic
89C22×C79C2×SD1611yescharacteristic
90C22×C79C2×Q1611yescharacteristic
91C22×C79AGL(1,ℤ/8)11yescharacteristic
92C22×C79#13711yescharacteristic
93C4×C79—42no—
94C4×C79—42no—
95C4×C79C22⋊Q811yescharacteristic
96C4×C79C22⋊Q811yescharacteristic
97C4×C79#12411yescharacteristic
98C4×C79#12411yescharacteristic
99Dic79—22no—
100Dic79—22no—
101Dic79—42no—
102Dic79—81no—
103C2×C79#39311yescharacteristic
104C2×C79#45011yescharacteristic
105C2×C79#45111yescharacteristic
106C2×C79#47511yescharacteristic
107C2×C79#47711yescharacteristic
108C2×C79#48711yescharacteristic
109C2×C79#48911yescharacteristic
110#2024—791nomaximal, Sylow
111C79#202411yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—791no—
113C2×#103—791no—
114C2×#103D7911yescharacteristic
115#391—791no—
116#340—791no—
117#340—791no—
118#336—791no—
119C22×Q8—1581no—
120C22×Q8C2×D7911yescharacteristic
121C22×C8—791no—
122C22×C8C2×D7911yescharacteristic
123C4⋊Q8—1582no—
124C4⋊Q8—1582no—
125C2×C4⋊C4—791no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—1581no—
128C2×C4⋊C4C2×D7911yescharacteristic
129C2×C42—791no—
130#103—22no—
131#103—1582no—
132#95—1581no—
133#95—1581no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—3162no—
140C2×Q8—3162no—
141C2×Q8—1584no—
142C2×Q8Dic15812yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—791no—
146C22×C4—791no—
147C22×C4—1581no—
148C22×C4—1581no—
149C22×C4C22×D7911yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1581no—
154C2×C8—1581no—
155C2×C8—1581no—
156C4⋊C4—21no—
157C4⋊C4—792no—
158C4⋊C4—1584no—
159C4⋊C4—1581no—
160C4⋊C4—1581no—
161C4⋊C4—1581no—
162C4⋊C4C22⋊D7912yes—
163C42—1581no—
164C42—1581no—
165C23D4×D7911yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—3168no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3161no—
178C2×C4—3161no—
179C2×C4—3161no—
180C2×C4—3161no—
181C2×C4—3161no—
182C2×C4—792no—
183C2×C4—792no—
184C2×C4—1582no—
185C2×C4—1581no—
186C2×C4—1581no—
187C2×C4—1581no—
188C2×C4—1581no—
189C2×C4D4×D7911yescharacteristic
190C2×C4C2×C22⋊D7911yescharacteristic
191C2×C4C2×Dic15811yescharacteristic
192C2×C4#1192962311yescharacteristic
193C2×C4#1192962311yescharacteristic
194C2×C4#1192962411yescharacteristic
195C8—41no—
196C8—3161no—
197C22#1457912911yescharacteristic
198C22#1457913811yescharacteristic
199C22#1457914711yescharacteristic
200C22SD16×D7911yescharacteristic
201C22Q16×D7911yescharacteristic
202C22#1457918811yescharacteristic
203C22#1457919311yescharacteristic
204C4—42no—
205C4—42no—
206C4—3162no—
207C4—6321no—
208C4—1582no—
209C4—1582no—
210C4#1457913811yescharacteristic
211C4#1457914011yescharacteristic
212C4#1457914711yescharacteristic
213C4#1457914811yescharacteristic
214C2#1909847511yescharacteristic
215C2#1909871211yescharacteristic
216C2#1909871711yescharacteristic
217C2#1909884611yescharacteristic
218C2#1909885611yescharacteristic
219C2#1909891211yescharacteristic
220C2#1909892411yescharacteristic
subgroupG/H
centerC23D4×D79
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
FittingC2×#103×C79C2
socle, prime radicalC23×C79C2×D4
hypercenterC2×#103D79
hypocenterC79#2024
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
45. C2×Q8×C79Q8semidirect
111. C79#2024semidirect
142. C2×Q8Dic158semidirect