Finite Group Databasebeta

← #23763261

Subgroups — #23763261

Order 10112.

296 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 149 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×Dic79⋊C8C211yesmaximal, characteristic
2C2×C4×C79⋊C8C211yesmaximal, characteristic
3C2×C8×Dic79C211yesmaximal, characteristic
4C2×C8×Dic79C211yesmaximal, characteristic
5C4×Dic79⋊C4C211yesmaximal, characteristic
6#19098317C211yesmaximal, characteristic
7#336×C79C211yesmaximal, characteristic
8C22×C79⋊C8C2211yescharacteristic
9C22×C79⋊C8C2211yescharacteristic
10C2×Dic79⋊C4C412yes—
11C2×C4×Dic79C2211yescharacteristic
12C2×C4×Dic79C2211yescharacteristic
13Dic79⋊C8C414yescomplemented
14C4×C79⋊C8—22no—
15C8×Dic79—22no—
16C8×Dic79C414yescomplemented
17C79⋊#95C412yes—
18C22×C8×C79C2211yescharacteristic
19C22×C8×C79C2211yescharacteristic
20C2×C42×C79C2211yescharacteristic
21C22×Dic79C2×C411yescharacteristic
22C22×Dic79C2×C412yes—
23C22×Dic79C2×C411yescharacteristic
24C2×C79⋊C8—21no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8C2×C412yes—
27C2×C79⋊C8C2×C412yes—
28C2×C79⋊C8D412yes—
29C2×C79⋊C8Q812yes—
30Dic79⋊C4C818yescomplemented
31C4×Dic79—21no—
32C4×Dic79—21no—
33C4×Dic79C2×C412yes—
34C4×Dic79C2×C412yes—
35C22×C4×C79C2×C412yes—
36C22×C4×C79C2311yescharacteristic
37C2×C8×C79—21no—
38C2×C8×C79—21no—
39C2×C8×C79—21no—
40C2×C8×C79—21no—
41C2×C8×C79C2×C412yes—
42C2×C8×C79C2×C412yes—
43C42×C79—21no—
44C42×C79—21no—
45C23×C79C22×C411yescharacteristic
46C2×C4×C79—22no—
47C2×C4×C79—22no—
48C2×C4×C79C2×C814yes—
49C2×C4×C79C22×C411yescharacteristic
50C2×C4×C79C22×C411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2×Q811yescharacteristic
53C2×C4×C79#4111yescharacteristic
54C2×C4×C79#4111yescharacteristic
55C2×Dic79—22no—
56C2×Dic79—22no—
57C2×Dic79—22no—
58C2×Dic79C4212yes—
59C2×Dic79C4212yes—
60C2×Dic79C2×C814yes—
61C2×Dic79C2×C814yes—
62C8×C79—22no—
63C8×C79—22no—
64C79⋊C8—22no—
65C79⋊C8C4⋊C414yescomplemented
66C22×C79C2×C4211yescharacteristic
67C22×C79C4×D411yescharacteristic
68C22×C79C4×Q811yescharacteristic
69C22×C79C22×C812yes—
70C22×C79#13112yes—
71C4×C79—24no—
72C4×C79C2×C4⋊C411yescharacteristic
73C4×C79#11711yescharacteristic
74C4×C79C4×D411yescharacteristic
75C4×C79C4×Q811yescharacteristic
76Dic79—22no—
77Dic79—24no—
78Dic79C4×C814yescomplemented
79C2×C79C4×C4⋊C411yescharacteristic
80C2×C79C2×C4×C811yescharacteristic
81C2×C79#40511yescharacteristic
82C2×C79C8×D412yes—
83C2×C79C8×Q812yes—
84C8×C4⋊C4—791nomaximal, Sylow
85C79C8×C4⋊C411yescharacteristic, complemented, Sylow
86C2×C4⋊C8—791no—
87C2×C4×C8—791no—
88C2×C4×C8—791no—
89C2×C4×C8—791no—
90C4×C4⋊C4—791no—
91#336—791no—
92#336D7911yescharacteristic
93C22×C8—791no—
94C22×C8—791no—
95C22×C8C2×D7911yescharacteristic
96C22×C8C2×D7911yescharacteristic
97C2×C4⋊C4—792no—
98C2×C42—791no—
99C2×C42—791no—
100C2×C42C2×D7911yescharacteristic
101C4⋊C8—794no—
102C4×C8—794no—
103C4×C8—1582no—
104C4×C8—1582no—
105#95—792no—
106C22×C4—791no—
107C22×C4—791no—
108C22×C4—792no—
109C22×C4C4×D7912yes—
110C22×C4C22×D7911yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—792no—
116C2×C8—792no—
117C2×C8—792no—
118C2×C8—792no—
119C2×C8—1581no—
120C2×C8—1581no—
121C2×C8C4×D7912yes—
122C2×C8C4×D7912yes—
123C4⋊C4—798no—
124C42—21no—
125C42—21no—
126C42—792no—
127C42—792no—
128C42—1581no—
129C42—1581no—
130C23C2×C4×D7911yescharacteristic
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—792no—
134C2×C4—794no—
135C2×C4—792no—
136C2×C4—794no—
137C2×C4—1582no—
138C2×C4—1582no—
139C2×C4—1582no—
140C2×C4C8×D7914yes—
141C2×C4C2×C4×D7911yescharacteristic
142C2×C4C2×C4×D7911yescharacteristic
143C2×C4D4×D7911yescharacteristic
144C2×C4Q8×D7911yescharacteristic
145C2×C4#1192962311yescharacteristic
146C2×C4#1192962311yescharacteristic
147C8—22no—
148C8—22no—
149C8—794no—
150C8—1582no—
151C22C42×D7911yescharacteristic
152C22(C22⋊D79)⋊C411yescharacteristic
153C22#1457912611yescharacteristic
154C22C2×C8×D7912yes—
155C22#1457916912yes—
156C4—24no—
157C4—794no—
158C4—1584no—
159C4—1582no—
160C4C4⋊C4×D7911yescharacteristic
161C4#1457911711yescharacteristic
162C4(C22⋊D79)⋊C411yescharacteristic
163C4#1457912611yescharacteristic
164C2#1909841411yescharacteristic
165C2C4×C8×D7911yescharacteristic
166C2#1909852011yescharacteristic
167C2(C22⋊D79)⋊C812yes—
168C2#1909868712yes—
subgroupG/H
center, FrattiniC22×C4C22×D79
commutatorC2×C79C2×C4×C8
Fitting#336×C79C2
socle, prime radicalC23×C79C22×C4
cosocleC22×C4×C79C23
hypercenter#336D79
hypocenterC79C8×C4⋊C4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
13. Dic79⋊C8C4semidirect
16. C8×Dic79C4semidirect
30. Dic79⋊C4C8semidirect
65. C79⋊C8C4⋊C4semidirect
78. Dic79C4×C8semidirect
85. C79C8×C4⋊C4semidirect