Finite Group Databasebeta

← #23764242

Subgroups — #23764242

Order 10112.

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

normal subgroups only

This group has 292 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×#14579159C211yesmaximal, characteristic
2#19098586C211yesmaximal, characteristic
3C2×#14579080C211yesmaximal, characteristic
4C2×#14579079C211yesmaximal, characteristic
5C2×#14579079C211yesmaximal, characteristic
6M16×Dic79C211yesmaximal, characteristic
7C2×#101×C79C211yesmaximal, characteristic
8C22×Dic158C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C2×#11929608C2211yescharacteristic
11#14579159—21no—
12#14579159—21no—
13#14579159—22no—
14C2×Dic79⋊C4C414yes—
15C2×C4×Dic79C2211yescharacteristic
16Dic79⋊C8—22no—
17#14579080—22no—
18#14579079—22no—
19#14579079—22no—
20#14579071—21no—
21C8×Dic79—21no—
22C22×Q8×C79C2211yescharacteristic
23C2×M16×C79C2211yescharacteristic
24C2×M16×C79C2211yescharacteristic
25#101×C79—22no—
26C2×Dic158—21no—
27C2×Dic158—21no—
28C2×Dic158—21no—
29C2×Dic158—21no—
30C2×Dic158—21no—
31C2×Dic158—21no—
32C22×Dic79C2×C412yes—
33C22×Dic79C2×C412yes—
34#11929608—21no—
35#11929608—21no—
36#11929608—21no—
37#11929608D412yes—
38C2×C79⋊C8—21no—
39C2×C79⋊C8—21no—
40Dic79⋊C4—24no—
41Dic79⋊C4—24no—
42C4×Dic79D411yescharacteristic
43C4×Dic79D411yescharacteristic
44C4×Dic79D412yes—
45C2×Q8×C79—21no—
46C2×Q8×C79—21no—
47C2×Q8×C79—21no—
48C2×Q8×C79—21no—
49C2×Q8×C79—21no—
50C2×Q8×C79—21no—
51C22×C4×C79C2×C412yes—
52C22×C4×C79C2311yescharacteristic
53M16×C79—21no—
54M16×C79—21no—
55M16×C79—21no—
56M16×C79D412yes—
57C2×C8×C79—21no—
58C2×C8×C79—21no—
59C23×C79C22×C411yescharacteristic
60Q8×C79—41no—
61Q8×C79—41no—
62Q8×C79—41no—
63Q8×C79—41no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2×D411yescharacteristic
70C2×C4×C79C2×D411yescharacteristic
71C2×C4×C79#4111yescharacteristic
72C2×C4×C79#4111yescharacteristic
73C2×Dic79—24no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—22no—
77C2×Dic79C22⋊C412yes—
78C2×Dic79C22⋊C412yes—
79Dic158—41no—
80Dic158—41no—
81Dic158—41no—
82Dic158—41no—
83C8×C79—22no—
84C8×C79—41no—
85C79⋊C8—22no—
86C79⋊C8—41no—
87C22×C79—22no—
88C22×C79C2×C22⋊C411yescharacteristic
89C22×C79C4×D411yescharacteristic
90C22×C79C4×D411yescharacteristic
91C4×C79—42no—
92C4×C79#12111yescharacteristic
93C4×C79#12111yescharacteristic
94C4×C79#12411yescharacteristic
95C4×C79#12711yescharacteristic
96Dic79—22no—
97Dic79—42no—
98Dic79#10114yescomplemented
99C2×C79—21no—
100C2×C79—21no—
101C2×C79#39011yescharacteristic
102C2×C79C2×#10112yes—
103#1966—791nomaximal, Sylow
104C79#196611yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—791no—
106#423—791no—
107C2×#101—791no—
108C2×#101—791no—
109C2×#101—791no—
110C2×#101D7911yescharacteristic
111C4×M16—791no—
112C22×Q8—791no—
113C22×Q8C2×D7911yescharacteristic
114C2×M16—791no—
115C2×M16—791no—
116C2×M16C2×D7911yescharacteristic
117C2×M16C2×D7911yescharacteristic
118C4⋊Q8—1581no—
119C4⋊Q8—1581no—
120C4⋊Q8—1582no—
121C2×C4⋊C4—794no—
122C2×C42—791no—
123C4⋊C8—1582no—
124#101—22no—
125#101—1582no—
126#101—1582no—
127#101—1582no—
128#97—1581no—
129C4×C8—1581no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—1581no—
137C2×Q8—1581no—
138C2×Q8—1581no—
139C2×Q8—1581no—
140C2×Q8—1581no—
141C2×Q8—1581no—
142C22×C4—792no—
143C22×C4—792no—
144C22×C4C4×D7912yes—
145C22×C4C22×D7911yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—792no—
150M16—1581no—
151M16—1581no—
152M16—1581no—
153M16C22⋊D7912yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—1581no—
157C2×C8—1581no—
158C4⋊C4—1584no—
159C4⋊C4—1584no—
160C42—791no—
161C42—791no—
162C42—792no—
163C23C2×C4×D7911yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—3161no—
169Q8—3161no—
170Q8—3161no—
171Q8—3161no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—792no—
176C2×C4—792no—
177C2×C4—1582no—
178C2×C4—1582no—
179C2×C4—1582no—
180C2×C4—1584no—
181C2×C4D4×D7911yescharacteristic
182C2×C4D4×D7911yescharacteristic
183C2×C4D4×D7911yescharacteristic
184C2×C4C2×C22⋊D7911yescharacteristic
185C2×C4#1192962311yescharacteristic
186C2×C4#1192962411yescharacteristic
187C8—22no—
188C8—41no—
189C8—3161no—
190C8—1582no—
191C22—22no—
192C22C22⋊C4×D7911yescharacteristic
193C22(C22⋊D79)⋊C411yescharacteristic
194C22C4×C22⋊D7911yescharacteristic
195C4—42no—
196C4—3162no—
197C4—794no—
198C4—1582no—
199C4#1457913311yescharacteristic
200C4#1457913411yescharacteristic
201C4#1457914711yescharacteristic
202C4#1457915711yescharacteristic
203C2—21no—
204C2—21no—
205C2#1909846311yescharacteristic
206C2#101×D7912yes—
subgroupG/H
centerC22C22⋊C4×D79
commutator, prime radicalC23×C79C22×C4
FrattiniC22×C4C22×D79
FittingC2×#101×C79C2
socleC22×C79C2×C22⋊C4
cosocleC22×C4×C79C23
hypercenterC2×#101D79
hypocenterC79#1966
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
98. Dic79#101semidirect
104. C79#1966semidirect