Finite Group Databasebeta

← #20243752

Subgroups — #20243752

Order 6016.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689890C211yesmaximal, characteristic, complemented
2#15689140C211yesmaximal, characteristic, complemented
3#15689119C211yesmaximal, characteristic, complemented
4#15689090C211yesmaximal, characteristic, complemented
5#15688895C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#575C211yesmaximal, characteristic
8#13094031—22no—
9#13094031—22no—
10C2×#10625329—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14#13093983C2211yescharacteristic
15#13093951—22no—
16#13093948—21no—
17#13093945—21no—
18C22⋊(C47⋊C8)—22no—
19C2×#41×C47C2211yescharacteristic
20C2×#41×C47C2211yescharacteristic
21#137×C47—21no—
22#137×C47C412yescomplemented
23AGL(1,ℤ/8)×C47—21no—
24AGL(1,ℤ/8)×C47C412yescomplemented
25#135×C47—22no—
26C2×M16×C47C2211yescharacteristic
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32#41×C47—21no—
33#41×C47C2×C412yes—
34#41×C47D412yes—
35C2×Q8×C47C2×C411yescharacteristic
36C2×Q8×C47D411yescharacteristic
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47C2×C411yescharacteristic
40C2×D4×C47D411yescharacteristic
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44Q16×C47—22no—
45SD16×C47—22no—
46SD16×C47—22no—
47D8×C47—22no—
48M16×C47—21no—
49M16×C47C2×C412yes—
50C2×C8×C47—21no—
51C22⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4×Dic47—21no—
54#10625329—24no—
55#10625329—21no—
56#10625329—21no—
57#10625329—21no—
58#10625329D412yes—
59C2×C47⋊C8—24no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8D412yes—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47#4111yescharacteristic
68Q8×C47—21no—
69Q8×C47—21no—
70Q8×C47—21no—
71Q8×C47C22⋊C412yes—
72D4×C47—22no—
73D4×C47—22no—
74D4×C47—21no—
75D4×C47—21no—
76D4×C47—21no—
77D4×C47—41no—
78D4×C47—41no—
79D4×C47C22⋊C412yes—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47C22×C411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C2×Dic47—41no—
93C8×C47—22no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C47⋊C8—41no—
97C22×C47—22no—
98C22×C47—41no—
99C22×C47—42no—
100C22×C47—41no—
101C22×C47—81no—
102C22×C47C4×D411yescharacteristic
103C22×C47#12111yescharacteristic
104C22×C47#12311yescharacteristic
105C4×C47—22no—
106C4×C47—41no—
107C4×C47C2×C22⋊C411yescharacteristic
108C4×C47C4×D411yescharacteristic
109C4×C47#12011yescharacteristic
110C4×C47#12111yescharacteristic
111Dic47—81no—
112#1881—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—42no—
117C2×C47—81no—
118C2×C47#38611yescharacteristic
119#575D4711yescharacteristic
120#568—471no—
121#421—471no—
122#416—471no—
123#408—471no—
124#344—471no—
125#341—471no—
126C47#188111yescharacteristic, complemented, Sylow
127C2×#41C2×D4711yescharacteristic
128C2×#41C2×D4711yescharacteristic
129#137—21no—
130#137Dic4712yescomplemented
131AGL(1,ℤ/8)—21no—
132AGL(1,ℤ/8)Dic4712yescomplemented
133#135—22no—
134#131—942no—
135#131—942no—
136C2×M16—471no—
137C2×M16—471no—
138C2×M16—942no—
139C2×M16C2×D4711yescharacteristic
140C22×C8—471no—
141#117—471no—
142#104—942no—
143#103—941no—
144#102—941no—
145C22⋊C8—942no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152#41C2×Dic4712yes—
153#41C22⋊D4712yes—
154C2×Q8C2×Dic4711yescharacteristic
155C2×Q8C22⋊D4711yescharacteristic
156C2×D4—21no—
157C2×D4—21no—
158C2×D4C2×Dic4711yescharacteristic
159C2×D4C22⋊D4711yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4C22×D4711yescharacteristic
163Q16—22no—
164SD16—22no—
165SD16—22no—
166D8—22no—
167M16—21no—
168M16—472no—
169M16—944no—
170M16—941no—
171M16—941no—
172M16—941no—
173M16C2×Dic4712yes—
174C2×C8—21no—
175C2×C8—472no—
176C2×C8—944no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C2×C8—941no—
181C4⋊C4—941no—
182C22⋊C4—941no—
183C42—941no—
184C23—21no—
185C23—21no—
186C23#1062535211yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—21no—
190Q8C22⋊Dic4712yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—21no—
195D4—21no—
196D4—41no—
197D4—41no—
198D4C22⋊Dic4712yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—1881no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4#1062535211yescharacteristic
209C2×C4C22×Dic4711yescharacteristic
210C2×C4C2×C22⋊D4711yescharacteristic
211C2×C4C2×C22⋊D4711yescharacteristic
212C8—22no—
213C8—942no—
214C8—942no—
215C8—1881no—
216C22—22no—
217C22—41no—
218C22—42no—
219C22—41no—
220C22—81no—
221C22D4×Dic4711yescharacteristic
222C22#1309399611yescharacteristic
223C22#1309400511yescharacteristic
224C4—22no—
225C4—41no—
226C4—3761no—
227C4C2×C22⋊Dic4711yescharacteristic
228C4D4×Dic4711yescharacteristic
229C4#1309399211yescharacteristic
230C4#1309399611yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—81no—
236C2#1568900311yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#575C2
socleC2×C47#386
hypercenter#575D47
hypocenterC47#1881
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #15689890C2semidirect
2. #15689140C2semidirect
3. #15689119C2semidirect
4. #15689090C2semidirect
5. #15688895C2semidirect
6. #15688887C2semidirect
22. #137×C47C4semidirect
24. AGL(1,ℤ/8)×C47C4semidirect
126. C47#1881semidirect
130. #137Dic47semidirect
132. AGL(1,ℤ/8)Dic47semidirect