Finite Group Databasebeta

← #23761949

Subgroups — #23761949

Order 10112.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#19099115C211yesmaximal, characteristic
2#19098617C211yesmaximal, characteristic
3#19098430C211yesmaximal, characteristic
4#19098301C211yesmaximal, characteristic
5#19098300C211yesmaximal, characteristic
6#19098299C211yesmaximal, characteristic
7#328×C79C211yesmaximal, characteristic
8#14579160C411yescharacteristic, complemented
9#14579159C411yescharacteristic, complemented
10#14579151—21no—
11#14579140C2211yescharacteristic
12#14579138—21no—
13Q8×Dic79C411yescharacteristic, complemented
14#14579126—21no—
15#14579126C411yescharacteristic, complemented
16#14579117—21no—
17C2×C4×Dic79C2211yescharacteristic
18Dic79⋊C8—21no—
19C22⋊(C79⋊C8)C2211yescharacteristic
20#14579071—21no—
21C79⋊#95—21no—
22C79⋊#95—21no—
23C79⋊#95C2211yescharacteristic
24C22⋊Q8×C79C2211yescharacteristic
25C22⋊C8×C79C2211yescharacteristic
26#95×C79C2211yescharacteristic
27C2×Dic158—21no—
28C2×Dic158C2×C411yescharacteristic
29C22×Dic79—21no—
30C22×Dic79D411yescharacteristic
31C22×Dic79D411yescharacteristic
32C2×C79⋊C8—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79C2×C411yescharacteristic
35Dic79⋊C4—21no—
36Dic79⋊C4—21no—
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40C22⋊Dic79—21no—
41C4×Dic79—21no—
42C4×Dic79—21no—
43C4×Dic79C2×C411yescharacteristic
44C4×Dic79C2×C411yescharacteristic
45C4×Dic79D411yescharacteristic
46C4×Dic79D411yescharacteristic
47C2×Q8×C79C2×C411yescharacteristic
48C22×C4×C79—21no—
49C22×C4×C79C2311yescharacteristic
50C2×C8×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79C2×C411yescharacteristic
53C22⋊C4×C79—21no—
54C23×C79C2×D411yescharacteristic
55Q8×C79—41no—
56C2×C4×C79—21no—
57C2×C4×C79—21no—
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×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—41no—
69C2×Dic79—41no—
70C2×Dic79—41no—
71C2×Dic79—41no—
72C2×Dic79C22⋊C411yescharacteristic
73C2×Dic79C22⋊C411yescharacteristic
74C2×Dic79C22⋊C411yescharacteristic
75C2×Dic79C22⋊C411yescharacteristic
76Dic158—42no—
77Dic158—41no—
78C8×C79—41no—
79C79⋊C8—41no—
80C22×C79—21no—
81C22×C79—21no—
82C22×C79C2×C22⋊C411yescharacteristic
83C22×C79#13711yescharacteristic
84C22×C79#13711yescharacteristic
85C4×C79—21no—
86C4×C79—21no—
87C4×C79—41no—
88C4×C79—41no—
89C4×C79—81no—
90Dic79—21no—
91Dic79—21no—
92Dic79—21no—
93Dic79—21no—
94Dic79—41no—
95Dic79—41no—
96Dic79—81no—
97C2×C79—21no—
98C2×C79—21no—
99C2×C79#41011yescharacteristic
100C2×C79#41911yescharacteristic
101C2×C79#42111yescharacteristic
102#1515—791nomaximal, Sylow
103C79#151511yescharacteristic, complemented, Sylow
104#533—791no—
105#432—791no—
106#383—791no—
107#328—791no—
108#328—791no—
109#328—791no—
110#328D7911yescharacteristic
111C4⋊Q8—791no—
112C4⋊Q8—791no—
113#125—1581no—
114C22⋊Q8—791no—
115C22⋊Q8—1581no—
116C22⋊Q8C2×D7911yescharacteristic
117C4×Q8—791no—
118C4×Q8—791no—
119C4×Q8—1581no—
120#117—1581no—
121C2×C42—791no—
122C4⋊C8—1581no—
123C22⋊C8—791no—
124C22⋊C8C2×D7911yescharacteristic
125#97—1581no—
126#95—791no—
127#95—1581no—
128#95—1581no—
129#95C2×D7911yescharacteristic
130C2×Q8—791no—
131C2×Q8—1581no—
132C2×Q8C4×D7911yescharacteristic
133C22×C4—21no—
134C22×C4—791no—
135C22×C4—791no—
136C22×C4—1581no—
137C22×C4C22×D7911yescharacteristic
138C2×C8—21no—
139C2×C8—1581no—
140C4⋊C4—21no—
141C4⋊C4—791no—
142C4⋊C4—1581no—
143C4⋊C4—1581no—
144C4⋊C4—1581no—
145C4⋊C4—1581no—
146C4⋊C4—1581no—
147C4⋊C4—1581no—
148C4⋊C4C4×D7911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—1581no—
151C42—791no—
152C42—791no—
153C42—791no—
154C42—791no—
155C42—1581no—
156C42—1581no—
157C23D4×D7911yescharacteristic
158Q8—41no—
159Q8—3161no—
160Q8—3162no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—3161no—
168C2×C4—3161no—
169C2×C4—3161no—
170C2×C4—3161no—
171C2×C4—791no—
172C2×C4—791no—
173C2×C4—791no—
174C2×C4—791no—
175C2×C4—1581no—
176C2×C4—1581no—
177C2×C4—1581no—
178C2×C4—1581no—
179C2×C4C2×C4×D7911yescharacteristic
180C2×C4D4×D7911yescharacteristic
181C8—41no—
182C8—3161no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D7911yescharacteristic
186C22#1457919011yescharacteristic
187C22#1457919311yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—3161no—
194C4—3161no—
195C4—6321no—
196C4—1581no—
197C4—1581no—
198C4—1581no—
199C4—1581no—
200C2—21no—
201C2—21no—
202C2#1909853511yescharacteristic
203C2#1909857011yescharacteristic
204C2#1909857811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#328×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC23×C79C2×D4
cosocleC22×C4×C79C23
hypercenter#328D79
hypocenterC79#1515
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14579160C4semidirect
9. #14579159C4semidirect
13. Q8×Dic79C4semidirect
15. #14579126C4semidirect
103. C79#1515semidirect