Finite Group Databasebeta

← #20243934

Subgroups — #20243934

Order 6016.

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

normal subgroups only

This group has 340 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, complemented
2#15689692C211yesmaximal, characteristic
3#15689105C211yesmaximal, characteristic, complemented
4C2×#13093940C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688893C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×D188C2211yescharacteristic
10#13094032—22no—
11#13094030—22no—
12C2×#10625329C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14M16×D47—22no—
15#13094021—21no—
16#13094012—21no—
17#13093999—22no—
18#13093994C414yes—
19#13093942—21no—
20#13093940—21no—
21#13093940—22no—
22#13093940—22no—
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C23×D47C2×C412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47C2×C412yes—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32#10625350—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188—21no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—24no—
40C2×D188D411yescharacteristic
41C2×C4×D47D412yes—
42C2×Dic94D411yescharacteristic
43M16×C47—21no—
44M16×C47—21no—
45M16×C47—21no—
46M16×C47D412yescomplemented
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C4⋊C4×C47—21no—
50C22⋊C4×C47C2×C412yes—
51C42×C47—21no—
52(C2×D47)⋊C4—24no—
53#10625329—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329D412yescomplemented
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59#10625324—24no—
60C8×D47—24no—
61C23×C47C22×C411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—82no—
66C22×D47C22⋊C412yes—
67C2×C4×C47—22no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C22⋊D47—22no—
75C22⋊D47—22no—
76C2×Dic47C22⋊C412yes—
77D188—21no—
78D188—21no—
79D188—41no—
80D188—41no—
81D188—41no—
82D188—41no—
83D188—84no—
84C4×D47—22no—
85C4×D47—22no—
86Dic94—21no—
87Dic94—21no—
88C8×C47—22no—
89C8×C47—41no—
90C47⋊C8—22no—
91C47⋊C8—41no—
92C22×C47—41no—
93C22×C47C2×C22⋊C411yescharacteristic
94C22×C47C4×D411yescharacteristic
95C22×C47C4×D411yescharacteristic
96C2×D47—22no—
97C2×D47—42no—
98C2×D47—44no—
99C2×D47—42no—
100C2×D47—82no—
101C2×D47—82no—
102C4×C47—42no—
103C4×C47#12011yescharacteristic
104C4×C47#12111yescharacteristic
105C4×C47#12111yescharacteristic
106C4×C47#12311yescharacteristic
107Dic47—22no—
108#1914—471nomaximal, Sylow
109C2×C47—21no—
110C2×C47—21no—
111C2×C47—21no—
112C2×C47#38611yescharacteristic
113D47—42no—
114D47—82no—
115#568—471no—
116#535—471no—
117#413—471no—
118C2×#100—471no—
119C2×#100—471no—
120#344—471no—
121#344D4711yescharacteristic, complemented
122C47#191411yescharacteristic, complemented, Sylow
123C2×#41—471no—
124C22×D4—471no—
125#131—942no—
126#131—942no—
127C2×M16—471no—
128C2×M16—471no—
129C2×M16—942no—
130C2×M16C2×D4711yescharacteristic
131C2×M16C2×D4711yescharacteristic
132#127—941no—
133#124—941no—
134#121—942no—
135#120—474no—
136#117C2×D4711yescharacteristic
137#101—941no—
138#100—942no—
139#100—941no—
140#100—942no—
141C24—472no—
142#41—941no—
143#41—941no—
144#41—941no—
145#41—941no—
146C2×Q8—471no—
147C2×D4—472no—
148C2×D4—471no—
149C2×D4—944no—
150C2×D4—941no—
151C2×D4—941no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4—941no—
155C2×D4—941no—
156C22×C4—472no—
157C22×C4C22×D4711yescharacteristic
158M16—21no—
159M16—21no—
160M16—21no—
161M16—472no—
162M16—944no—
163M16—941no—
164M16—941no—
165M16—941no—
166M16D18812yescomplemented
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—944no—
170C2×C8—941no—
171C2×C8—941no—
172C4⋊C4—21no—
173C22⋊C4—944no—
174C22⋊C4C4×D4712yes—
175C42—21no—
176C23—472no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23—3762no—
181C23C2×C4×D4711yescharacteristic
182Q8—941no—
183Q8—941no—
184D4—942no—
185D4—942no—
186D4—941no—
187D4—941no—
188D4—3764no—
189D4—1881no—
190D4—1881no—
191D4—1881no—
192D4—1881no—
193C2×C4—22no—
194C2×C4—472no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4C2×D18811yescharacteristic
198C2×C4#1062535011yescharacteristic
199C2×C4D4×D4711yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4#1062535411yescharacteristic
203C8—22no—
204C8—41no—
205C8—942no—
206C8—1881no—
207C22—41no—
208C22—942no—
209C22—3762no—
210C22—3762no—
211C22—1884no—
212C22—1882no—
213C22—1882no—
214C22C22⋊C4×D4711yescharacteristic
215C22#1309398611yescharacteristic
216C22C4×D18811yescharacteristic
217C4—42no—
218C4—942no—
219C4#1309399411yescharacteristic
220C4#1309399711yescharacteristic
221C4#1309399911yescharacteristic
222C4#1309400911yescharacteristic
223C2—21no—
224C2—21no—
225C2—21no—
226C2—3762no—
227C2—1882no—
228C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1914
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
1. #15689889C2semidirect
3. #15689105C2semidirect
4. C2×#13093940C2semidirect
5. C2×#13093940C2semidirect
6. #15688893C2semidirect
7. C47×#344C2semidirect
46. M16×C47D4semidirect
56. #10625329D4semidirect
121. #344D47semidirect
122. C47#1914semidirect
166. M16D188semidirect