Finite Group Databasebeta

← #20242414

Subgroups — #20242414

Order 6016.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#15689748C211yesmaximal, characteristic
2#15689459C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689060C211yesmaximal, characteristic
5#15688859C211yesmaximal, characteristic, complemented
6#15688846C211yesmaximal, characteristic
7C47×#328C211yesmaximal, characteristic, complemented
8#13094004—21no—
9#13094003C2211yescharacteristic
10#13094002—21no—
11#13094002—21no—
12#13094001—21no—
13#13094000—21no—
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×(C2×D47)⋊C4—21no—
17C2×(C2×D47)⋊C4C2211yescharacteristic
18C22⋊C4×D47—21no—
19#13093958—21no—
20#13093957—21no—
21#13093949—21no—
22#13093948—21no—
23C22⋊(C47⋊C8)C2211yescharacteristic
24C22⋊Q8×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C2×Q8×C47D411yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C2×C4×D47—21no—
34C2×C4×D47—21no—
35C2×Dic94—21no—
36C2×Dic94D411yescharacteristic
37C2×C8×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C22⋊C4×C47—21no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—42no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—42no—
51C4⋊Dic47D411yescharacteristic
52Dic47⋊C4—21no—
53Dic47⋊C4—21no—
54Dic47⋊C4—21no—
55C2×C47⋊C8—21no—
56C23×C47C2×D411yescharacteristic
57C22×D47—21no—
58C22×D47—21no—
59C22×D47—41no—
60C22×D47—41no—
61C22×D47Q1612yes—
62Q8×C47—41no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C4×D47—81no—
79C4×D47—81no—
80Dic94—41no—
81Dic94—81no—
82C8×C47—41no—
83C47⋊C8—41no—
84C22×C47—21no—
85C22×C47—21no—
86C22×C47#12011yescharacteristic
87C22×C47C2×Q1611yescharacteristic
88C22×C47#13711yescharacteristic
89C2×D47—22no—
90C2×D47—41no—
91C2×D47—41no—
92C2×D47—42no—
93C2×D47—81no—
94C4×C47—21no—
95C4×C47—21no—
96C4×C47—42no—
97C4×C47—41no—
98C4×C47—41no—
99Dic47—41no—
100Dic47—41no—
101Dic47—41no—
102Dic47—81no—
103#1614—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47#45111yescharacteristic
107C2×C47#45311yescharacteristic
108C2×C47#45811yescharacteristic
109D47—42no—
110#543—471no—
111#484—471no—
112#484—471no—
113#399—471no—
114#328—471no—
115#328D4711yescharacteristic, complemented
116#323—471no—
117C47#161411yescharacteristic, complemented, Sylow
118C22⋊Q8—471no—
119C22⋊Q8—941no—
120C22⋊Q8—941no—
121C22⋊Q8—941no—
122C22⋊Q8—941no—
123C22⋊Q8—941no—
124C22⋊Q8C2×D4711yescharacteristic
125C2×C4⋊C4—471no—
126C2×C4⋊C4—941no—
127C2×C22⋊C4—471no—
128C2×C22⋊C4—941no—
129C2×C22⋊C4—941no—
130#107—941no—
131#107—941no—
132#103—941no—
133#103—941no—
134C22⋊C8—471no—
135C22⋊C8C2×D4711yescharacteristic
136#95C2×D4711yescharacteristic
137C24—471no—
138C2×Q8—471no—
139C2×Q8—941no—
140C2×Q8D18811yescharacteristic
141C22×C4—21no—
142C22×C4—471no—
143C22×C4—941no—
144C22×C4—941no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147C2×C8—21no—
148C2×C8—941no—
149C4⋊C4—21no—
150C4⋊C4—471no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C4⋊C4—941no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4—1882no—
158C4⋊C4D18811yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—941no—
164C22⋊C4—941no—
165C22⋊C4—1882no—
166C23—472no—
167C23—941no—
168C23—941no—
169C23—1881no—
170C23—1881no—
171C23D4×D4711yescharacteristic
172Q8—41no—
173Q8—3761no—
174Q8—1881no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—3761no—
185C2×C4—3761no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4C2×D18811yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C8—41no—
193C8—1881no—
194C22—21no—
195C22—21no—
196C22—942no—
197C22—3761no—
198C22—1882no—
199C22—1881no—
200C22—1881no—
201C22#1309399411yescharacteristic
202C22Q16×D4711yescharacteristic
203C22#1309405311yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—3761no—
210C4—1881no—
211C4—1881no—
212C4—1881no—
213C2—21no—
214C2—21no—
215C2—1882no—
216C2#1568928011yescharacteristic
217C2#1568929211yescharacteristic
218C2#1568931411yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47#120
hypercenter#328D47
hypocenterC47#1614
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #15689459C2semidirect
3. #15689456C2semidirect
5. #15688859C2semidirect
7. C47×#328C2semidirect
115. #328D47semidirect
117. C47#1614semidirect