Finite Group Databasebeta

← #20253683

Subgroups — #20253683

Order 6016.

358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689600C211yesmaximal, characteristic
2#15689461C212yesmaximal
3#15689427C212yesmaximal, complemented
4#15689330C212yesmaximal, complemented
5#15689278C212yesmaximal
6#15689228C212yesmaximal, complemented
7C4×#10625337C212yesmaximal, complemented
8#15689184C211yesmaximal, characteristic
9C47×#541C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C2×#10625337C2212yes—
12C2×#10625337C2212yes—
13C4×Dic94C2212yes—
14C4×Dic94C2212yes—
15#13093989—22no—
16#13093983C2211yescharacteristic
17#13093980—22no—
18#13093957C2212yes—
19#13093955C2212yes—
20C4⋊(C47⋊C8)C2212yes—
21#13093948C2212yes—
22#13093948C2212yes—
23#13093947C2212yes—
24#13093947C2212yes—
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2211yescharacteristic
27C4×C47⋊C8C2211yescharacteristic
28C4⋊Q8×C47C2211yescharacteristic
29#126×C47—22no—
30#125×C47—22no—
31#125×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33C4×Q8×C47C2212yes—
34#117×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C2×Dic94—21no—
39C2×Dic94—24no—
40C2×Dic94C2312yes—
41C4⋊C4×C47—22no—
42C4⋊C4×C47—22no—
43C4⋊C4×C47—22no—
44C4⋊C4×C47—22no—
45C4⋊C4×C47D412yes—
46C4⋊C4×C47C2312yes—
47C22⋊C4×C47—22no—
48C22⋊C4×C47D412yes—
49C42×C47—22no—
50C42×C47C2311yescharacteristic
51C42×C47C2311yescharacteristic
52C22⋊Dic47—21no—
53#10625337—24no—
54#10625337—24no—
55C4⋊Dic47C2312yes—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58C4×Dic47—22no—
59C4×Dic47—22no—
60C4×Dic47—21no—
61C2×C47⋊C8C2312yes—
62C2×C47⋊C8C2312yes—
63C23×C47C2×D411yescharacteristic
64Q8×C47—22no—
65Q8×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—24no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76Dic94—24no—
77Dic94—22no—
78Dic94#4114yes—
79C47⋊C8—22no—
80C47⋊C8—22no—
81C22×C47—21no—
82C22×C47—22no—
83C22×C47C22×D411yescharacteristic
84C4×C47—21no—
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—42no—
88C4×C47—42no—
89C4×C47C2×#4112yes—
90Dic47—24no—
91Dic47—42no—
92#3127—471nomaximal, Sylow
93C2×C47—41no—
94C2×C47#52511yescharacteristic
95C2×C47#57812yes—
96#541D4711yescharacteristic
97#519—471no—
98#485—472no—
99#479—472no—
100#462—472no—
101#451—472no—
102#441—472no—
103C4×Q16—472no—
104#433—471no—
105C47#312711yescharacteristic, complemented, Sylow
106C22×Q8—471no—
107C2×Q16—472no—
108C2×Q16—472no—
109C4⋊Q8C2×D4711yescharacteristic
110#126—22no—
111#125—22no—
112#125C2×D4711yescharacteristic
113C22⋊Q8C2×D4712yes—
114C4×Q8—472no—
115C4×Q8—472no—
116C4×Q8—942no—
117C4×Q8C2×D4712yes—
118#117—471no—
119#117—942no—
120#117C2×D4711yescharacteristic
121#107—472no—
122#106—472no—
123C4⋊C8—472no—
124#103—472no—
125#103—472no—
126#103—472no—
127#103—472no—
128C22⋊C8—472no—
129#97—471no—
130C4×C8—471no—
131C2×Q8—472no—
132C2×Q8—944no—
133C2×Q8—941no—
134C2×Q8C22×D4712yes—
135C22×C4—941no—
136C22×C4C22×D4711yescharacteristic
137Q16—944no—
138Q16—944no—
139C2×C8—472no—
140C2×C8—472no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—472no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4C22⋊D4712yes—
149C4⋊C4C22×D4712yes—
150C22⋊C4—22no—
151C22⋊C4—941no—
152C22⋊C4C22⋊D4712yes—
153C42—22no—
154C42—941no—
155C42—942no—
156C42—942no—
157C42C22×D4711yescharacteristic
158C42C22×D4711yescharacteristic
159C23C2×C22⋊D4711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—474no—
163Q8—944no—
164Q8—942no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—944no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4C2×C22⋊D4712yes—
172C2×C4C2×C22⋊D4712yes—
173C2×C4C2×C22⋊D4711yescharacteristic
174C2×C4C23×D4711yescharacteristic
175C8—942no—
176C8—942no—
177C22—21no—
178C22—22no—
179C22C22×C22⋊D4711yescharacteristic
180C4—21no—
181C4—22no—
182C4—22no—
183C4—42no—
184C4—42no—
185C4—944no—
186C4—1882no—
187C4#41×D4712yes—
188C2—41no—
189C2#1568963011yescharacteristic
190C2#1568993812yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3127
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
3. #15689427C2semidirect
4. #15689330C2semidirect
6. #15689228C2semidirect
7. C4×#10625337C2semidirect
105. C47#3127semidirect