Finite Group Databasebeta

← #23764356

Subgroups — #23764356

Order 10112.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14579152C211yesmaximal, characteristic
2C2×Dic79⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic79C211yesmaximal, characteristic
4#19098326C211yesmaximal, characteristic
5#19098325C211yesmaximal, characteristic
6#19098325C211yesmaximal, characteristic
7#340×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9#14579152—22no—
10#14579152C414yescomplemented
11C2×C4⋊Dic79—21no—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×C4⋊Dic79C2211yescharacteristic
14C2×Dic79⋊C4—21no—
15C2×C4×Dic79—21no—
16C2×C4×Dic79C2211yescharacteristic
17Dic79⋊C8—22no—
18C79⋊#95—21no—
19C22×C8×C79C2211yescharacteristic
20C2×C4⋊C4×C79C2211yescharacteristic
21C2×C4⋊C4×C79C2211yescharacteristic
22C22×Dic79—21no—
23C22×Dic79—21no—
24C22×Dic79D411yescharacteristic
25C22×Dic79D411yescharacteristic
26C2×C79⋊C8—21no—
27C2×C79⋊C8—21no—
28C2×C79⋊C8—21no—
29C4⋊Dic79—24no—
30C4⋊Dic79—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79C2×C412yes—
33C4⋊Dic79Q812yes—
34Dic79⋊C4—24no—
35C4×Dic79—42no—
36C4×Dic79C2×C412yes—
37C4×Dic79D412yes—
38C22×C4×C79—21no—
39C22×C4×C79—21no—
40C22×C4×C79C2311yescharacteristic
41C2×C8×C79—21no—
42C2×C8×C79—21no—
43C2×C8×C79—21no—
44C4⋊C4×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79C2×C412yes—
47C4⋊C4×C79Q812yes—
48C23×C79C2×D411yescharacteristic
49C2×C4×C79—22no—
50C2×C4×C79—22no—
51C2×C4×C79—41no—
52C2×C4×C79—41no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79C22×C411yescharacteristic
56C2×C4×C79C2×D411yescharacteristic
57C2×C4×C79C2×Q811yescharacteristic
58C2×C4×C79C2×Q811yescharacteristic
59C2×C4×C79#4111yescharacteristic
60C2×C4×C79#4111yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79—21no—
64C2×Dic79—21no—
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—41no—
68C2×Dic79—41no—
69C2×Dic79—41no—
70C2×Dic79—41no—
71C2×Dic79C22⋊C412yes—
72C2×Dic79C22⋊C412yes—
73C8×C79—41no—
74C79⋊C8—41no—
75C22×C79C2×C22⋊C411yescharacteristic
76C22×C79C22⋊Q811yescharacteristic
77C22×C79C22⋊Q811yescharacteristic
78C22×C79#13511yescharacteristic
79C22×C79#13511yescharacteristic
80C22×C79AGL(1,ℤ/8)11yescharacteristic
81C22×C79#13711yescharacteristic
82C4×C79—42no—
83C4×C79—42no—
84C4×C79C4×Q811yescharacteristic
85C4×C79C4×Q811yescharacteristic
86C4×C79#12411yescharacteristic
87C4×C79C4⋊Q811yescharacteristic
88Dic79—22no—
89Dic79—22no—
90Dic79—42no—
91Dic79—42no—
92C2×C79#39111yescharacteristic
93C2×C79#41611yescharacteristic
94C2×C79#41711yescharacteristic
95C2×C79#47811yescharacteristic
96C2×C79#47811yescharacteristic
97C2×C79#47911yescharacteristic
98C2×C79#47911yescharacteristic
99#1989—791nomaximal, Sylow
100C79#198911yescharacteristic, complemented, Sylow
101C2×#125—791no—
102C2×C4⋊C8—791no—
103C4×C4⋊C4—791no—
104#340—791no—
105#340—791no—
106#340—791no—
107#340D7911yescharacteristic
108C22×C8—791no—
109C22×C8C2×D7911yescharacteristic
110#125—794no—
111#125—1582no—
112C2×C4⋊C4—791no—
113C2×C4⋊C4—791no—
114C2×C4⋊C4—1581no—
115C2×C4⋊C4—1581no—
116C2×C4⋊C4C2×D7911yescharacteristic
117C2×C4⋊C4C2×D7911yescharacteristic
118C2×C42—791no—
119C2×C42—1581no—
120C4⋊C8—1582no—
121#95—1581no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—791no—
125C22×C4—791no—
126C22×C4—1581no—
127C22×C4—1581no—
128C22×C4C22×D7911yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1581no—
133C2×C8—1581no—
134C2×C8—1581no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—792no—
138C4⋊C4—792no—
139C4⋊C4—1584no—
140C4⋊C4—1584no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C4⋊C4Dic15812yes—
144C4⋊C4C4×D7912yes—
145C42—3162no—
146C42—792no—
147C42—792no—
148C23D4×D7911yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3161no—
156C2×C4—3161no—
157C2×C4—3161no—
158C2×C4—3161no—
159C2×C4—792no—
160C2×C4—792no—
161C2×C4—1582no—
162C2×C4—1582no—
163C2×C4—1581no—
164C2×C4—1581no—
165C2×C4—1581no—
166C2×C4—1581no—
167C2×C4C2×C4×D7911yescharacteristic
168C2×C4D4×D7911yescharacteristic
169C2×C4Q8×D7911yescharacteristic
170C2×C4C2×Dic15811yescharacteristic
171C2×C4#1192962311yescharacteristic
172C2×C4#1192962411yescharacteristic
173C8—41no—
174C8—3161no—
175C22C22⋊C4×D7911yescharacteristic
176C22#1457913811yescharacteristic
177C22#1457913911yescharacteristic
178C22#1457918011yescharacteristic
179C22#1457918211yescharacteristic
180C22#1457918811yescharacteristic
181C22#1457919311yescharacteristic
182C4—42no—
183C4—42no—
184C4—3162no—
185C4—3162no—
186C4—1582no—
187C4—1582no—
188C4#1457912611yescharacteristic
189C4C4×Dic15811yescharacteristic
190C4#1457914711yescharacteristic
191C4#1457916011yescharacteristic
192C2#1909846711yescharacteristic
193C2#1909855611yescharacteristic
194C2#1909856311yescharacteristic
195C2#1909886111yescharacteristic
196C2#1909886211yescharacteristic
197C2#1909886811yescharacteristic
198C2#1909886911yescharacteristic
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#1989
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
10. #14579152C4semidirect
100. C79#1989semidirect