Finite Group Databasebeta

← #20244595

Subgroups — #20244595

Order 6016.

326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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#15689166C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic, complemented
3#15689124C211yesmaximal, characteristic, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5#15689026C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#535C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C22⋊Dic47—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093957—21no—
14#13093955—21no—
15#13093951—22no—
16#13093948—21no—
17#13093945—21no—
18#13093941—22no—
19C2×#41×C47C2211yescharacteristic
20C22×D4×C47C2211yescharacteristic
21#127×C47—21no—
22#124×C47—21no—
23#121×C47—21no—
24#121×C47—21no—
25#120×C47—22no—
26#117×C47C2211yescharacteristic
27C24×C47D412yes—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32C2×Q8×C47D411yescharacteristic
33C2×D4×C47—21no—
34C2×D4×C47—22no—
35C2×D4×C47—22no—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47—21no—
41C2×D4×C47—21no—
42C2×D4×C47D411yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C4⋊C4×C47D411yescharacteristic
48C4⋊C4×C47D411yescharacteristic
49C22⋊C4×C47—22no—
50C22⋊C4×C47—22no—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53C22⋊Dic47—44no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4×Dic47—21no—
57C4×Dic47—21no—
58#10625329—21no—
59#10625329—21no—
60#10625329—21no—
61#10625329D412yescomplemented
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C23×C47—22no—
65C23×C47—21no—
66C23×C47—22no—
67C23×C47—22no—
68C23×C47—42no—
69C23×C47—42no—
70C23×C47C2×D411yescharacteristic
71Q8×C47—21no—
72Q8×C47—21no—
73D4×C47—21no—
74D4×C47—21no—
75D4×C47—41no—
76D4×C47—41no—
77D4×C47—41no—
78D4×C47—41no—
79D4×C47—41no—
80D4×C47—41no—
81D4×C47—82no—
82D4×C47—82no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C2×C4×C47#4111yescharacteristic
94C2×Dic47—22no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97C2×Dic47—42no—
98C2×Dic47—41no—
99C47⋊C8—22no—
100C47⋊C8—41no—
101C22×C47—21no—
102C22×C47—21no—
103C22×C47—44no—
104C22×C47—41no—
105C22×C47—42no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47—41no—
109C22×C47—42no—
110C22×C47—82no—
111C22×C47#12011yescharacteristic
112C22×C47#12111yescharacteristic
113C22×C47#12311yescharacteristic
114C4×C47—41no—
115C4×C47—41no—
116C4×C47—41no—
117C4×C47#12111yescharacteristic
118C4×C47#12111yescharacteristic
119C4×C47#12311yescharacteristic
120C4×C47#12411yescharacteristic
121Dic47—42no—
122Dic47—81no—
123#2037—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—81no—
127C2×C47—82no—
128C2×C47#39411yescharacteristic
129C2×C47#45311yescharacteristic
130C2×C47#45511yescharacteristic
131#535D4711yescharacteristic
132#428—471no—
133C2×#104—471no—
134#417—471no—
135C2×#100—471no—
136#390—471no—
137#339—471no—
138C47#203711yescharacteristic, complemented, Sylow
139C2×#41C2×D4711yescharacteristic
140C22×D4C2×D4711yescharacteristic
141C2×M16—471no—
142C2×M16—471no—
143#127—21no—
144#124—21no—
145#121—21no—
146#121—21no—
147#120—22no—
148#117C2×D4711yescharacteristic
149C2×C4⋊C4—471no—
150C2×C22⋊C4—942no—
151C2×C42—471no—
152#107—941no—
153#106—941no—
154#104—942no—
155#103—941no—
156#102—941no—
157#100—942no—
158C24C22⋊D4712yes—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163C2×Q8C22⋊D4711yescharacteristic
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4C22⋊D4711yescharacteristic
174C22×C4—21no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178M16—472no—
179M16—941no—
180M16—941no—
181M16—941no—
182C2×C8—941no—
183C2×C8—941no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4C22⋊D4711yescharacteristic
187C4⋊C4C22⋊D4711yescharacteristic
188C22⋊C4—22no—
189C22⋊C4—22no—
190C22⋊C4—21no—
191C22⋊C4—1884no—
192C42—21no—
193C42—941no—
194C42—941no—
195C23—22no—
196C23—21no—
197C23—22no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23C2×C22⋊D4711yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—82no—
213D4—82no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—942no—
220C2×C4—1882no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4—1881no—
224C2×C4D4×D4711yescharacteristic
225C2×C4#1062535211yescharacteristic
226C2×C4#1062535211yescharacteristic
227C2×C4#1062535211yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C8—942no—
231C8—1881no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—41no—
236C22—42no—
237C22—41no—
238C22—42no—
239C22—41no—
240C22—42no—
241C22—82no—
242C22#1309399311yescharacteristic
243C22#1309399611yescharacteristic
244C22#1309400511yescharacteristic
245C4—41no—
246C4—41no—
247C4—41no—
248C4—3761no—
249C4—1882no—
250C4#1309399511yescharacteristic
251C4#1309399611yescharacteristic
252C4#1309400511yescharacteristic
253C4#1309401111yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—81no—
258C2#1568903711yescharacteristic
259C2#1568929111yescharacteristic
260C2#1568930111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#535C2
socleC22×C47#120
hypercenter#535D47
hypocenterC47#2037
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #15689166C2semidirect
2. C2×#13093951C2semidirect
3. #15689124C2semidirect
4. C2×#13093941C2semidirect
5. #15689026C2semidirect
6. #15688882C2semidirect
61. #10625329D4semidirect
138. C47#2037semidirect