Finite Group Databasebeta

← #20243414

Subgroups — #20243414

Order 6016.

336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C22×C8×D47C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic, complemented
3#15688980C212yesmaximal
4#15688885C212yesmaximal, complemented
5C2×#107×C47C211yesmaximal, characteristic, complemented
6C22×C4×D47C2211yescharacteristic
7C22×C47⋊C8C2211yescharacteristic
8C2×C8×D47—22no—
9C2×C8×D47—22no—
10C2×C8×D47C414yescomplemented
11C2×C4⋊Dic47C2212yes—
12C2×(C2×D47)⋊C4—22no—
13#13093958—22no—
14C47⋊#95—22no—
15C22×C8×C47C2211yescharacteristic
16C2×C4⋊C4×C47C2212yes—
17#107×C47—22no—
18C23×D47D411yescharacteristic
19C22×C4×C47—22no—
20C22×C4×C47C2311yescharacteristic
21C22×Dic47—22no—
22C22×Dic47D411yescharacteristic
23C2×C4×D47—21no—
24C2×C4×D47—21no—
25C2×C4×D47—21no—
26C2×C4×D47—21no—
27C2×C4×D47C2×C412yes—
28C2×C4×D47Q812yes—
29C2×C8×C47C2×C412yes—
30C2×C8×C47D412yes—
31C2×C8×C47D412yes—
32C4⋊C4×C47—22no—
33C4⋊C4×C47—22no—
34(C2×D47)⋊C4—44no—
35C4⋊Dic47—22no—
36C4⋊Dic47—22no—
37C2×C47⋊C8—21no—
38C2×C47⋊C8—21no—
39C2×C47⋊C8C2×C412yes—
40C8×D47—28no—
41C23×C47C2×D411yescharacteristic
42C22×D47—21no—
43C22×D47—21no—
44C22×D47—21no—
45C22×D47—21no—
46C22×D47C4⋊C412yes—
47C22×D47D812yes—
48C22×D47Q1612yes—
49C2×C4×C47—42no—
50C2×C4×C47—42no—
51C2×C4×C47—42no—
52C2×C4×C47C22×C411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×Q811yescharacteristic
56C2×C4×C47#4111yescharacteristic
57C2×C4×C47#4111yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—42no—
61C2×Dic47—42no—
62C2×Dic47—42no—
63C2×Dic47C4⋊C412yes—
64C4×D47—22no—
65C4×D47—22no—
66C4×D47—22no—
67C4×D47—22no—
68C8×C47C22⋊C414yescomplemented
69C47⋊C8—22no—
70C22×C47C2×C4⋊C411yescharacteristic
71C22×C47#12111yescharacteristic
72C22×C47#12111yescharacteristic
73C22×C47C2×D811yescharacteristic
74C22×C47C2×Q1611yescharacteristic
75C22×C47#13511yescharacteristic
76C22×C47#13511yescharacteristic
77C2×D47—22no—
78C2×D47—22no—
79C2×D47—22no—
80C2×D47—22no—
81C2×D47—22no—
82C2×D47—22no—
83C2×D47#10714yescomplemented
84C4×C47—82no—
85C4×C47C2×C22⋊C411yescharacteristic
86C4×C47#11711yescharacteristic
87C4×C47C22⋊Q811yescharacteristic
88C4×C47C22⋊Q811yescharacteristic
89Dic47—22no—
90Dic47—82no—
91#1808—471nomaximal, Sylow
92C2×C47#38011yescharacteristic
93C2×C47C2×#10711yescharacteristic
94C2×C47#42711yescharacteristic
95C2×C47#46611yescharacteristic
96C2×C47#46611yescharacteristic
97C2×C47#46711yescharacteristic
98C2×C47#46711yescharacteristic
99D47—24no—
100C23×C8—471no—
101C2×#107—471no—
102C2×#107D4711yescharacteristic, complemented
103#380—472no—
104#340—472no—
105C47#180811yescharacteristic, complemented, Sylow
106C23×C4—471no—
107C22×C8—471no—
108C22×C8—474no—
109C22×C8—942no—
110C22×C8—942no—
111C22×C8C2×D4711yescharacteristic
112C2×C4⋊C4—472no—
113C2×C4⋊C4C2×D4712yes—
114C2×C22⋊C4—942no—
115#107—22no—
116#107—942no—
117#95—942no—
118C24—471no—
119C22×C4—22no—
120C22×C4—471no—
121C22×C4—472no—
122C22×C4—472no—
123C22×C4—941no—
124C22×C4—941no—
125C22×C4—941no—
126C22×C4—941no—
127C22×C4—942no—
128C22×C4C22×D4711yescharacteristic
129C2×C8—472no—
130C2×C8—941no—
131C2×C8—941no—
132C2×C8—948no—
133C2×C8C4×D4712yes—
134C2×C8D18812yes—
135C2×C8C22⋊D4712yes—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—942no—
139C4⋊C4—942no—
140C22⋊C4—1884no—
141C23—472no—
142C23—472no—
143C23—472no—
144C23—941no—
145C23—941no—
146C23—941no—
147C23—941no—
148C23D4×D4711yescharacteristic
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—472no—
153C2×C4—941no—
154C2×C4—941no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—942no—
158C2×C4—942no—
159C2×C4—1882no—
160C2×C4—1882no—
161C2×C4—1882no—
162C2×C4C2×C4×D4711yescharacteristic
163C2×C4C2×D18811yescharacteristic
164C2×C4#1062535211yescharacteristic
165C2×C4Q8×D4711yescharacteristic
166C2×C4#1062535411yescharacteristic
167C2×C4C2×C22⋊D4711yescharacteristic
168C8—942no—
169C8(C2×D47)⋊C414yescomplemented
170C22—474no—
171C22—942no—
172C22—942no—
173C22—942no—
174C22—942no—
175C22—942no—
176C22—942no—
177C22C4⋊C4×D4711yescharacteristic
178C22#1309399511yescharacteristic
179C22#1309399911yescharacteristic
180C22D8×D4711yescharacteristic
181C22Q16×D4711yescharacteristic
182C22#1309404311yescharacteristic
183C22#1309404711yescharacteristic
184C4—82no—
185C4—942no—
186C4—3762no—
187C4C2×(C2×D47)⋊C411yescharacteristic
188C4#1309398211yescharacteristic
189C4#1309400011yescharacteristic
190C4#1309400411yescharacteristic
191C2—944no—
192C2#1568898011yescharacteristic
193C2#107×D4711yescharacteristic
194C2#1568916011yescharacteristic
195C2#1568935611yescharacteristic
196C2#1568936011yescharacteristic
197C2#1568936111yescharacteristic
198C2#1568936511yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#107×C47C2
socleC23×C47C2×D4
hypercenterC2×#107D47
hypocenterC47#1808
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#13093958C2semidirect
4. #15688885C2semidirect
5. C2×#107×C47C2semidirect
10. C2×C8×D47C4semidirect
68. C8×C47C22⋊C4semidirect
83. C2×D47#107semidirect
102. C2×#107D47semidirect
105. C47#1808semidirect
169. C8(C2×D47)⋊C4semidirect