Finite Group Databasebeta

← #23773530

Subgroups — #23773530

Order 10112.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#19099120C211yesmaximal, characteristic
2#19098893C212yesmaximal
3#19098848C212yesmaximal, complemented
4#19098773C212yesmaximal, complemented
5#19098719C212yesmaximal
6#19098668C214yesmaximal, complemented
7#19098620C211yesmaximal, characteristic
8C2×C4×Q8×C79C211yesmaximal, characteristic
9C2×#11929614C2214yes—
10#14579161C2211yescharacteristic
11#14579161C2211yescharacteristic
12#14579153—21no—
13#14579140—21no—
14#14579140C2212yes—
15C4×Dic158—21no—
16C4×Dic158C2212yes—
17#14579120—21no—
18#14579092C2214yes—
19C4⋊(C79⋊C8)C2212yes—
20#14579085C2214yes—
21#14579084C2214yes—
22C22⋊(C79⋊C8)C2212yes—
23#14579072C2212yes—
24C22×Q8×C79C2211yescharacteristic
25C4×Q8×C79—21no—
26C4×Q8×C79—21no—
27C4×Q8×C79C2212yes—
28C4×Q8×C79C2212yes—
29C2×C4⋊C4×C79—21no—
30C2×C4⋊C4×C79C2211yescharacteristic
31C2×C42×C79—21no—
32C2×C42×C79C2211yescharacteristic
33C2×Dic158—21no—
34C2×Dic158C2312yes—
35#11929614—28no—
36C2×C79⋊C8C2314yes—
37C4⋊Dic79—21no—
38C4⋊Dic79—21no—
39C4⋊Dic79—21no—
40C4⋊Dic79C2312yes—
41Dic79⋊C4—22no—
42Dic79⋊C4—22no—
43C22⋊Dic79—22no—
44C4×Dic79—22no—
45C2×Q8×C79—24no—
46C2×Q8×C79—21no—
47C2×Q8×C79C2312yes—
48C22×C4×C79—21no—
49C22×C4×C79—21no—
50C22×C4×C79D411yescharacteristic
51C22×C4×C79D411yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—22no—
54C4⋊C4×C79—22no—
55C4⋊C4×C79—21no—
56C4⋊C4×C79C2312yes—
57C42×C79—22no—
58C42×C79—22no—
59C42×C79D411yescharacteristic
60C42×C79D411yescharacteristic
61C42×C79C2311yescharacteristic
62C42×C79C2311yescharacteristic
63C23×C79C2×D411yescharacteristic
64Q8×C79—24no—
65Q8×C79—22no—
66Q8×C79#4114yes—
67C2×C4×C79—24no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—42no—
74C2×C4×C79C2×D411yescharacteristic
75C2×C4×C79C2×D411yescharacteristic
76C2×C4×C79C2×D411yescharacteristic
77C2×C4×C79C2×D411yescharacteristic
78C2×C4×C79C2×D411yescharacteristic
79C2×C4×C79C2411yescharacteristic
80C2×Dic79—22no—
81C2×Dic79—22no—
82Dic158—24no—
83Dic158—42no—
84C79⋊C8—24no—
85C22×C79—21no—
86C22×C79—21no—
87C22×C79#13712yes—
88C22×C79C22×D411yescharacteristic
89C4×C79—24no—
90C4×C79—21no—
91C4×C79—21no—
92C4×C79—21no—
93C4×C79—21no—
94C4×C79—42no—
95C4×C79#13712yes—
96C4×C79C2×#4112yes—
97Dic79—42no—
98Dic79—42no—
99C2×C79—22no—
100C2×C79#52511yescharacteristic
101C2×C79C2×#13711yescharacteristic
102C2×C79C2×#13711yescharacteristic
103#3113—791nomaximal, Sylow
104C79#311311yescharacteristic, complemented, Sylow
105#533—791no—
106C2×C4×Q8D7911yescharacteristic
107#483—792no—
108#475—792no—
109#462—792no—
110#451—792no—
111#441—794no—
112#432—791no—
113C22×Q8C2×D7911yescharacteristic
114C2×Q16—794no—
115C4⋊Q8—791no—
116C4⋊Q8—791no—
117#125—1581no—
118C22⋊Q8—792no—
119C22⋊Q8—1581no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—792no—
123C4×Q8—1581no—
124C4×Q8C2×D7912yes—
125C4×Q8C2×D7912yes—
126#117—1581no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D7911yescharacteristic
129C2×C42—21no—
130C2×C42C2×D7911yescharacteristic
131#106—794no—
132C4⋊C8—792no—
133#103—794no—
134#103—794no—
135C22⋊C8—792no—
136#97—792no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—792no—
140C2×Q8—1581no—
141C2×Q8C22×D7912yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D7911yescharacteristic
145C22×C4C22⋊D7911yescharacteristic
146C22×C4C22×D7911yescharacteristic
147Q16—1588no—
148C2×C8—794no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—792no—
153C4⋊C4—1582no—
154C4⋊C4—1582no—
155C4⋊C4—1581no—
156C4⋊C4—1581no—
157C4⋊C4—1581no—
158C4⋊C4C22×D7912yes—
159C22⋊C4—1582no—
160C42—22no—
161C42—22no—
162C42—1582no—
163C42C22⋊D7911yescharacteristic
164C42C22⋊D7911yescharacteristic
165C42C22×D7911yescharacteristic
166C42C22×D7911yescharacteristic
167C23C2×C22⋊D7911yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—3162no—
171Q8—1584no—
172Q8#1192962414yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—1582no—
181C2×C4—1582no—
182C2×C4C2×C22⋊D7911yescharacteristic
183C2×C4C2×C22⋊D7911yescharacteristic
184C2×C4C2×C22⋊D7911yescharacteristic
185C2×C4C2×C22⋊D7911yescharacteristic
186C2×C4C2×C22⋊D7911yescharacteristic
187C2×C4C23×D7911yescharacteristic
188C8—1584no—
189C22—21no—
190C22—21no—
191C22#1457919112yes—
192C22C22×C22⋊D7911yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—3162no—
200C4—3162no—
201C4#1457919212yes—
202C4C2×#1192962412yes—
203C2—22no—
204C2#1909907411yescharacteristic
205C2C2×#1457919111yescharacteristic
206C2C2×#1457919211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×C4×Q8×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenterC2×C4×Q8D79
hypocenterC79#3113
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #19098848C2semidirect
4. #19098773C2semidirect
6. #19098668C2semidirect
104. C79#3113semidirect