Finite Group Databasebeta

← #20243939

Subgroups — #20243939

Order 6016.

308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic
2#15689699C211yesmaximal, characteristic
3#15689105C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic, complemented
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15688893C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10#13094032—22no—
11#13094030—22no—
12C2×#10625329C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14M16×D47—22no—
15#13094024—21no—
16#13094012—21no—
17#13094008C414yes—
18#13094004—22no—
19#13093942—21no—
20#13093942—22no—
21#13093942—22no—
22#13093940—21no—
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47C2×C412yes—
28C22×Dic47C2×C412yes—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32#10625350—21no—
33C2×D188D411yescharacteristic
34C2×C4×D47D412yes—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94D411yescharacteristic
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47—21no—
49C22⋊C4×C47C2×C412yes—
50C42×C47—21no—
51(C2×D47)⋊C4—24no—
52C4⋊Dic47—24no—
53#10625329—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329D412yes—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59#10625324—24no—
60C8×D47—24no—
61C23×C47C22×C411yescharacteristic
62C22×D47C22⋊C412yes—
63C2×C4×C47—22no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C22⋊D47—22no—
71C22⋊D47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47C22⋊C412yes—
76D188—21no—
77D188—21no—
78C4×D47—22no—
79C4×D47—22no—
80Dic94—21no—
81Dic94—21no—
82Dic94—41no—
83Dic94—41no—
84Dic94—41no—
85Dic94—41no—
86C8×C47—22no—
87C8×C47—41no—
88C47⋊C8—22no—
89C47⋊C8—41no—
90C22×C47—41no—
91C22×C47C2×C22⋊C411yescharacteristic
92C22×C47C4×D411yescharacteristic
93C22×C47C4×D411yescharacteristic
94C2×D47—22no—
95C2×D47—42no—
96C4×C47—42no—
97C4×C47#12011yescharacteristic
98C4×C47#12111yescharacteristic
99C4×C47#12111yescharacteristic
100C4×C47#12311yescharacteristic
101Dic47—22no—
102Dic47—42no—
103#1915—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47—21no—
107C2×C47#38611yescharacteristic
108D47—42no—
109#568—471no—
110#536—471no—
111#413—471no—
112C2×#101—471no—
113C2×#101—471no—
114#344—471no—
115#344D4711yescharacteristic, complemented
116C47#191511yescharacteristic, complemented, Sylow
117C2×#41—471no—
118C22×Q8—471no—
119#131—942no—
120#131—942no—
121C2×M16—471no—
122C2×M16—471no—
123C2×M16—942no—
124C2×M16C2×D4711yescharacteristic
125C2×M16C2×D4711yescharacteristic
126C4⋊Q8—941no—
127#124—941no—
128#123—474no—
129C22⋊Q8—942no—
130#117C2×D4711yescharacteristic
131#101—942no—
132#101—941no—
133#101—942no—
134#100—941no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—471no—
140C2×Q8—941no—
141C2×Q8—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C2×Q8—941no—
145C2×Q8—941no—
146C2×D4—472no—
147C2×D4—471no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4C22×D4711yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—472no—
155M16—944no—
156M16—941no—
157M16—941no—
158M16—941no—
159M16D18812yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—944no—
163C2×C8—941no—
164C2×C8—941no—
165C4⋊C4—21no—
166C4⋊C4—944no—
167C22⋊C4—944no—
168C22⋊C4C4×D4712yes—
169C42—21no—
170C23—472no—
171C23C2×C4×D4711yescharacteristic
172Q8—941no—
173Q8—941no—
174Q8—1881no—
175Q8—1881no—
176Q8—1881no—
177Q8—1881no—
178D4—942no—
179D4—942no—
180D4—941no—
181D4—941no—
182C2×C4—22no—
183C2×C4—472no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4C2×D18811yescharacteristic
190C2×C4#1062535011yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4#1062535411yescharacteristic
195C8—22no—
196C8—41no—
197C8—942no—
198C8—1881no—
199C22—41no—
200C22—942no—
201C22—1882no—
202C22C22⋊C4×D4711yescharacteristic
203C22#1309398611yescharacteristic
204C22C4×D18811yescharacteristic
205C4—42no—
206C4—942no—
207C4—1882no—
208C4#1309399411yescharacteristic
209C4#1309399711yescharacteristic
210C4#1309399911yescharacteristic
211C4#1309400911yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—1882no—
216C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1915
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. C2×#13093942C2semidirect
5. C2×#13093942C2semidirect
6. #15688893C2semidirect
7. C47×#344C2semidirect
115. #344D47semidirect
116. C47#1915semidirect