Finite Group Databasebeta

← #23762425

Subgroups — #23762425

Order 10112.

236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 57 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#19098896C212yesmaximal, complemented
2#19098499C211yesmaximal, characteristic
3#19098300C212yesmaximal, complemented
4#19098287C211yesmaximal, characteristic
5#543×C79C211yesmaximal, characteristic
6C2×C4⋊Dic79C2211yescharacteristic
7C2×Dic79⋊C4—21no—
8C2×C22⋊Dic79—21no—
9#14579094—22no—
10#14579085—22no—
11C22⋊(C79⋊C8)C2212yes—
12C79⋊#95C2211yescharacteristic
13C22⋊Q8×C79—22no—
14C22⋊Q8×C79—21no—
15C22⋊Q8×C79—22no—
16C22⋊Q8×C79C2212yes—
17C2×C22⋊C4×C79—21no—
18C2×C22⋊C4×C79C2211yescharacteristic
19C22×Dic79—21no—
20C22×Dic79—21no—
21C2×C79⋊C8—22no—
22C4⋊Dic79—22no—
23Dic79⋊C4—42no—
24C22⋊Dic79—42no—
25C24×C79D411yescharacteristic
26C2×Q8×C79—21no—
27C2×Q8×C79D412yes—
28C22×C4×C79—21no—
29C22×C4×C79—21no—
30C22×C4×C79D411yescharacteristic
31C22×C4×C79C2311yescharacteristic
32C4⋊C4×C79—21no—
33C4⋊C4×C79—22no—
34C4⋊C4×C79—22no—
35C4⋊C4×C79D412yes—
36C22⋊C4×C79—22no—
37C22⋊C4×C79—22no—
38C22⋊C4×C79—22no—
39C23×C79—21no—
40C23×C79—21no—
41C23×C79—41no—
42C23×C79—41no—
43C23×C79Q1612yes—
44C23×C79C2×D411yescharacteristic
45Q8×C79—42no—
46Q8×C79—81no—
47C2×C4×C79—22no—
48C2×C4×C79—21no—
49C2×C4×C79—22no—
50C2×C4×C79—41no—
51C2×C4×C79—41no—
52C2×C4×C79—81no—
53C2×C4×C79—81no—
54C2×C4×C79C2×D412yes—
55C2×Dic79—22no—
56C2×Dic79—41no—
57C2×Dic79—41no—
58C2×Dic79—41no—
59C2×Dic79—41no—
60C2×Dic79—41no—
61C79⋊C8—42no—
62C22×C79—21no—
63C22×C79—21no—
64C22×C79—22no—
65C22×C79—42no—
66C22×C79—41no—
67C22×C79—41no—
68C22×C79—81no—
69C22×C79#12011yescharacteristic
70C22×C79C2×Q1611yescharacteristic
71C22×C79#13711yescharacteristic
72C4×C79—22no—
73C4×C79—41no—
74C4×C79—42no—
75C4×C79—42no—
76Dic79—42no—
77Dic79—81no—
78C2×C79—21no—
79C2×C79—21no—
80C2×C79—42no—
81C2×C79#45111yescharacteristic
82C2×C79#45311yescharacteristic
83C2×C79#45811yescharacteristic
84#1614—791nomaximal, Sylow
85C79#161411yescharacteristic, complemented, Sylow
86#543D7911yescharacteristic
87#484—792no—
88#399—791no—
89#328—792no—
90#323—791no—
91C22⋊Q8—22no—
92C22⋊Q8—21no—
93C22⋊Q8—22no—
94C22⋊Q8C2×D7912yes—
95C2×C4⋊C4—791no—
96C2×C4⋊C4—1581no—
97C2×C22⋊C4—21no—
98C2×C22⋊C4—1581no—
99C2×C22⋊C4C2×D7911yescharacteristic
100#107—1582no—
101#103—1582no—
102C22⋊C8—792no—
103#95—791no—
104C24C22⋊D7911yescharacteristic
105C2×Q8—21no—
106C2×Q8C22⋊D7912yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—1581no—
110C22×C4—1581no—
111C22×C4C22⋊D7911yescharacteristic
112C22×C4C22×D7911yescharacteristic
113C2×C8—1582no—
114C4⋊C4—21no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—3162no—
118C4⋊C4—1582no—
119C4⋊C4C22⋊D7912yes—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C22⋊C4—3162no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1192961412yes—
129C23C2×C22⋊D7911yescharacteristic
130Q8—42no—
131Q8—81no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—81no—
138C2×C4—81no—
139C2×C4—3161no—
140C2×C4—3161no—
141C2×C4—3161no—
142C2×C4—3161no—
143C2×C4—3161no—
144C2×C4—1582no—
145C2×C4C2×C22⋊D7912yes—
146C8—3162no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1457913011yescharacteristic
155C22C2×#1192961411yescharacteristic
156C22#1457919211yescharacteristic
157C4—22no—
158C4—41no—
159C4—42no—
160C4—42no—
161C4—3162no—
162C4—6321no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1909871911yescharacteristic
167C2#1909873111yescharacteristic
168C2#1909875311yescharacteristic
subgroupG/H
centerC22#14579130
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#543×C79C2
socleC22×C79#120
prime radicalC24×C79D4
hypercenter#543D79
hypocenterC79#1614
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #19098896C2semidirect
3. #19098300C2semidirect
85. C79#1614semidirect