Finite Group Databasebeta

← #20243937

Subgroups — #20243937

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#15689697C211yesmaximal, characteristic
3#15689105C211yesmaximal, characteristic
4C2×#13093943C211yesmaximal, characteristic, complemented
5#15688895C211yesmaximal, characteristic, complemented
6#15688894C211yesmaximal, characteristic, complemented
7C2×#101×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13M16×D47—22no—
14#13094022—21no—
15#13094013—21no—
16#13094007C414yes—
17#13094000—22no—
18#13093983C2211yescharacteristic
19#13093943—22no—
20#13093942—21no—
21#13093940—21no—
22C22×Q8×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25#101×C47—22no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C22×C4×C47C2×C412yes—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47C2×C412yes—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39C2×D188D411yescharacteristic
40C2×C4×D47D412yes—
41C2×Dic94D411yescharacteristic
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C22⋊Dic47C2×C412yes—
49(C2×D47)⋊C4—24no—
50C4⋊Dic47—21no—
51Dic47⋊C4—24no—
52C4×Dic47—21no—
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—
63Q8×C47—41no—
64Q8×C47—41no—
65Q8×C47—41no—
66Q8×C47—41no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C22⋊D47—22no—
77C22⋊D47—22no—
78C2×Dic47—22no—
79C2×Dic47C22⋊C412yes—
80D188—21no—
81D188—21no—
82C4×D47—22no—
83C4×D47—22no—
84Dic94—21no—
85Dic94—21no—
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×#101D4711yescharacteristic, complemented
114#344—471no—
115#344—471no—
116C47#191511yescharacteristic, complemented, Sylow
117C2×#41—471no—
118C22×Q8C2×D4711yescharacteristic
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#117—471no—
131#101—22no—
132#101—941no—
133#101—942no—
134#100—941no—
135#41—941no—
136#41—941no—
137#41—941no—
138#41—941no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—21no—
145C2×Q8—471no—
146C2×D4—472no—
147C2×D4—471no—
148C22×C4—472no—
149C22×C4C4×D4712yes—
150C22×C4C22×D4711yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—472no—
155M16—944no—
156M16—941no—
157M16—941no—
158M16—941no—
159M16C22⋊D4712yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—944no—
163C2×C8—941no—
164C2×C8—941no—
165C4⋊C4—944no—
166C4⋊C4—941no—
167C22⋊C4—472no—
168C22⋊C4—944no—
169C42—941no—
170C23—472no—
171C23C2×C4×D4711yescharacteristic
172Q8—41no—
173Q8—41no—
174Q8—41no—
175Q8—41no—
176Q8—941no—
177Q8—941no—
178D4—942no—
179D4—942no—
180D4—941no—
181D4—941no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—472no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4#1062535011yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C2×C4D4×D4711yescharacteristic
193C2×C4#1062535211yescharacteristic
194C2×C4C2×C22⋊D4711yescharacteristic
195C8—22no—
196C8—41no—
197C8—942no—
198C8—1881no—
199C22—41no—
200C22—942no—
201C22—1882no—
202C22C22⋊C4×D4711yescharacteristic
203C22(C22⋊D47)⋊C411yescharacteristic
204C22C4×C22⋊D4711yescharacteristic
205C4—42no—
206C4—942no—
207C4—1882no—
208C4#1309399211yescharacteristic
209C4#1309399511yescharacteristic
210C4#1309399711yescharacteristic
211C4#1309400611yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—1882no—
216C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#101×C47C2
socleC2×C47#386
hypercenterC2×#101D47
hypocenterC47#1915
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
4. C2×#13093943C2semidirect
5. #15688895C2semidirect
6. #15688894C2semidirect
7. C2×#101×C47C2semidirect
113. C2×#101D47semidirect
116. C47#1915semidirect