Finite Group Databasebeta

← #20244775

Subgroups — #20244775

Order 6016.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#13093958C211yesmaximal, characteristic, complemented
2C2×#13093946C211yesmaximal, characteristic
3C2×#13093946C211yesmaximal, characteristic
4#15689025C211yesmaximal, characteristic
5#15689021C211yesmaximal, characteristic, complemented
6#15688886C211yesmaximal, characteristic, complemented
7C2×C4⋊C8×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×C4⋊Dic47C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14C2×(C2×D47)⋊C4—21no—
15#13093958—22no—
16#13093946—22no—
17#13093946—22no—
18C47⋊#95—21no—
19C22×C8×C47C2211yescharacteristic
20C22×C8×C47C2211yescharacteristic
21C2×C42×C47C2211yescharacteristic
22C4⋊C8×C47—22no—
23C23×D47—21no—
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C22×Dic47—21no—
28C22×Dic47—21no—
29C22×Dic47—21no—
30C2×D188—21no—
31C2×D188—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188Q812yes—
36C2×C8×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41C2×C8×C47D412yes—
42C42×C47—21no—
43C42×C47—21no—
44(C2×D47)⋊C4—42no—
45(C2×D47)⋊C4—42no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47D412yes—
52Dic47⋊C4—42no—
53C23×C47C2×D411yescharacteristic
54C22×D47—22no—
55C22×D47—41no—
56C22×D47—41no—
57C22×D47—41no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47—41no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47D812yes—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×Q811yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—41no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82D188—22no—
83D188—22no—
84D188—41no—
85D188—41no—
86C8×C47—22no—
87C8×C47—41no—
88C22×C47#12111yescharacteristic
89C22×C47#12111yescharacteristic
90C22×C47C22⋊Q811yescharacteristic
91C22×C47C2×D811yescharacteristic
92C22×C47#13511yescharacteristic
93C22×C47AGL(1,ℤ/8)11yescharacteristic
94C22×C47#13711yescharacteristic
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47—81no—
99C2×D47—81no—
100C2×D47—81no—
101C2×D47—81no—
102C4×C47—22no—
103C4×C47—41no—
104C4×C47#12111yescharacteristic
105C4×C47C22⋊Q811yescharacteristic
106C4×C47C22⋊Q811yescharacteristic
107C4×C47#12611yescharacteristic
108Dic47—42no—
109Dic47—81no—
110Dic47—81no—
111#2067—471nomaximal, Sylow
112C2×C47#39611yescharacteristic
113C2×C47#45911yescharacteristic
114C2×C47#46411yescharacteristic
115C2×C47#46611yescharacteristic
116C2×C47#46811yescharacteristic
117C2×C47#47411yescharacteristic
118C2×C47#47811yescharacteristic
119D47—82no—
120C2×#107—471no—
121C2×C4⋊C8D4711yescharacteristic, complemented
122C2×#102—471no—
123C2×#102—471no—
124#390—471no—
125#389—471no—
126#340—471no—
127C47#206711yescharacteristic, complemented, Sylow
128C22×D4—471no—
129C22×C8C2×D4711yescharacteristic
130C22×C8C2×D4711yescharacteristic
131C2×C4⋊C4—471no—
132C2×C4⋊C4—471no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4—941no—
135C2×C22⋊C4—941no—
136C2×C22⋊C4—941no—
137C2×C42C2×D4711yescharacteristic
138#107—942no—
139C4⋊C8—22no—
140#102—942no—
141#102—942no—
142#95—941no—
143C24—941no—
144C2×D4—472no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C22×C4—941no—
151C22×C4—941no—
152C22×C4—941no—
153C22×C4D18811yescharacteristic
154C22×C4D18811yescharacteristic
155C22×C4C22×D4711yescharacteristic
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8C22⋊D4712yes—
162C4⋊C4—472no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—1882no—
169C22⋊C4—1882no—
170C22⋊C4—1882no—
171C42—21no—
172C42—21no—
173C23—942no—
174C23—1881no—
175C23—1881no—
176C23—1881no—
177C23—1881no—
178C23—1881no—
179C23—1881no—
180C23C2×D18811yescharacteristic
181D4—942no—
182D4—942no—
183D4—1881no—
184D4—1881no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—942no—
191C2×C4—1881no—
192C2×C4—1881no—
193C2×C4—1881no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4D37612yes—
200C2×C4#1062535011yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4#1062535211yescharacteristic
203C2×C4Q8×D4711yescharacteristic
204C2×C4#1062535411yescharacteristic
205C2×C4C2×C22⋊D4711yescharacteristic
206C8—22no—
207C8—41no—
208C22—3761no—
209C22—3761no—
210C22—3761no—
211C22—3761no—
212C22—1882no—
213C22—1882no—
214C22—1882no—
215C22#1309399811yescharacteristic
216C22#1309399911yescharacteristic
217C22#1309400411yescharacteristic
218C22C2×D37611yescharacteristic
219C22#1309404611yescharacteristic
220C22#1309405211yescharacteristic
221C22#1309405711yescharacteristic
222C4—22no—
223C4—41no—
224C4—3761no—
225C4—3761no—
226C4—1882no—
227C4#1309399611yescharacteristic
228C4#1309400011yescharacteristic
229C4#1309400211yescharacteristic
230C4#1309401911yescharacteristic
231C2—3762no—
232C2#1568904511yescharacteristic
233C2#1568931911yescharacteristic
234C2#1568934611yescharacteristic
235C2#1568935911yescharacteristic
236C2#1568936911yescharacteristic
237C2#1568940411yescharacteristic
238C2#1568942411yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×C4⋊C8×C47C2
socleC23×C47C2×D4
hypercenterC2×C4⋊C8D47
hypocenterC47#2067
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#13093958C2semidirect
5. #15689021C2semidirect
6. #15688886C2semidirect
7. C2×C4⋊C8×C47C2semidirect
121. C2×C4⋊C8D47semidirect
127. C47#2067semidirect