Finite Group Databasebeta

← #23764174

Subgroups — #23764174

Order 10112.

200 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14579097C211yesmaximal, characteristic
2C2×#14579096C211yesmaximal, characteristic
3#19098586C211yesmaximal, characteristic
4C2×Dic79⋊C8C211yesmaximal, characteristic
5M16×Dic79C211yesmaximal, characteristic
6#19098327C211yesmaximal, characteristic
7#341×C79C211yesmaximal, characteristic
8C2×#11929608C2211yescharacteristic
9C2×#11929608C2211yescharacteristic
10C22×C79⋊C8C2211yescharacteristic
11C2×C4×Dic79C2211yescharacteristic
12#14579097—22no—
13#14579096—22no—
14Dic79⋊C8—21no—
15Dic79⋊C8—21no—
16Dic79⋊C8C412yes—
17Dic79⋊C8C412yes—
18#14579071—21no—
19C8×Dic79—21no—
20C2×M16×C79C2211yescharacteristic
21C2×M16×C79C2211yescharacteristic
22C22×C8×C79C2211yescharacteristic
23C22×Dic79Q811yescharacteristic
24C22×Dic79Q811yescharacteristic
25#11929608—21no—
26#11929608—21no—
27#11929608—21no—
28#11929608D412yes—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C2×C79⋊C8—21no—
32C2×C79⋊C8—21no—
33C2×C79⋊C8C2×C412yes—
34C4×Dic79C2×C411yescharacteristic
35C4×Dic79C2×C411yescharacteristic
36C4×Dic79D411yescharacteristic
37C4×Dic79D411yescharacteristic
38C22×C4×C79C2311yescharacteristic
39M16×C79—21no—
40M16×C79—21no—
41M16×C79—21no—
42M16×C79Q812yes—
43C2×C8×C79—21no—
44C2×C8×C79—21no—
45C2×C8×C79—21no—
46C2×C8×C79—21no—
47C2×C8×C79C2×C412yes—
48C23×C79C2×Q811yescharacteristic
49C2×C4×C79C22×C411yescharacteristic
50C2×C4×C79C2×D411yescharacteristic
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2×Q811yescharacteristic
53C2×C4×C79#4111yescharacteristic
54C2×C4×C79#4111yescharacteristic
55C2×Dic79—22no—
56C2×Dic79—41no—
57C2×Dic79C4⋊C411yescharacteristic
58C2×Dic79C4⋊C411yescharacteristic
59C2×Dic79C4⋊C411yescharacteristic
60C2×Dic79C4⋊C411yescharacteristic
61C8×C79—22no—
62C8×C79—22no—
63C8×C79—41no—
64C79⋊C8—22no—
65C79⋊C8—22no—
66C79⋊C8—41no—
67C22×C79—21no—
68C22×C79—21no—
69C22×C79C2×C4⋊C411yescharacteristic
70C22×C79#12511yescharacteristic
71C22×C79C4⋊Q811yescharacteristic
72C4×C79C4×D411yescharacteristic
73C4×C79C4×Q811yescharacteristic
74C4×C79#12111yescharacteristic
75C4×C79C22⋊Q811yescharacteristic
76Dic79—21no—
77Dic79—21no—
78Dic79—21no—
79Dic79#10812yescomplemented
80C2×C79—21no—
81C2×C79—21no—
82C2×C79#38911yescharacteristic
83C2×C79C2×#10811yescharacteristic
84C2×C79#43011yescharacteristic
85#1950—791nomaximal, Sylow
86C79#195011yescharacteristic, complemented, Sylow
87C2×#108—791no—
88C2×#108—791no—
89#423—791no—
90C2×C4⋊C8—791no—
91C4×M16—791no—
92#341—791no—
93#341D7911yescharacteristic
94C2×M16—791no—
95C2×M16—791no—
96C2×M16C2×D7911yescharacteristic
97C2×M16C2×D7911yescharacteristic
98C22×C8—791no—
99C22×C8C2×D7911yescharacteristic
100C2×C42—791no—
101#108—1582no—
102#108—1582no—
103C4⋊C8—792no—
104C4⋊C8—792no—
105C4⋊C8—1581no—
106C4⋊C8—1581no—
107#97—1581no—
108C4×C8—1581no—
109C22×C4—791no—
110C22×C4—791no—
111C22×C4C22×D7911yescharacteristic
112M16—21no—
113M16—21no—
114M16—21no—
115M16—792no—
116M16—1581no—
117M16—1581no—
118M16—1581no—
119M16Dic15812yes—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—792no—
125C2×C8—1581no—
126C2×C8—1581no—
127C2×C8—1581no—
128C2×C8—1581no—
129C2×C8C4×D7912yes—
130C42—791no—
131C42—791no—
132C42—791no—
133C42—791no—
134C23Q8×D7911yescharacteristic
135C2×C4—3161no—
136C2×C4—791no—
137C2×C4—791no—
138C2×C4—791no—
139C2×C4—791no—
140C2×C4—1582no—
141C2×C4C2×C4×D7911yescharacteristic
142C2×C4D4×D7911yescharacteristic
143C2×C4D4×D7911yescharacteristic
144C2×C4C2×Dic15811yescharacteristic
145C2×C4#1192962311yescharacteristic
146C2×C4#1192962411yescharacteristic
147C8—22no—
148C8—22no—
149C8—41no—
150C8—3161no—
151C8—1582no—
152C8—1582no—
153C22—21no—
154C22—21no—
155C22C4⋊C4×D7911yescharacteristic
156C22#1457915111yescharacteristic
157C22#1457916011yescharacteristic
158C4—792no—
159C4—1581no—
160C4—1581no—
161C4—1581no—
162C4(C22⋊D79)⋊C411yescharacteristic
163C4C4×Dic15811yescharacteristic
164C4#1457913411yescharacteristic
165C4#1457913811yescharacteristic
166C2—21no—
167C2—21no—
168C2#1909846011yescharacteristic
169C2#108×D7911yescharacteristic
170C2#1909861011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#341×C79C2
socleC22×C79C2×C4⋊C4
prime radicalC23×C79C2×Q8
cosocleC22×C4×C79C23
hypercenter#341D79
hypocenterC79#1950
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
79. Dic79#108semidirect
86. C79#1950semidirect