Finite Group Databasebeta

← #20244576

Subgroups — #20244576

Order 6016.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13093995C211yesmaximal, characteristic
2C2×#13093956C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
5#15688980C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×C22⋊D47—21no—
9C22×C4×D47C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13093995—22no—
12#13093995—22no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C22⋊Dic47—21no—
16C2×(C2×D47)⋊C4—21no—
17#13093956—22no—
18#13093945—22no—
19(C2×D47)⋊C8—22no—
20C47⋊#95—21no—
21C22×D4×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#102×C47—22no—
25C24×C47—21no—
26C23×D47D411yescharacteristic
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47D412yes—
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—24no—
36C2×C22⋊D47—42no—
37C2×C22⋊D47—42no—
38C22×Dic47—21no—
39C22×Dic47—21no—
40C22×Dic47D411yescharacteristic
41C2×C4×D47—21no—
42C2×C4×D47—21no—
43C2×C4×D47—21no—
44C2×C4×D47—21no—
45C2×C4×D47—21no—
46C2×C4×D47—21no—
47C2×C8×C47—21no—
48C2×C8×C47—21no—
49C2×C8×C47D412yescomplemented
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C22⋊Dic47—24no—
53(C2×D47)⋊C4—42no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47D412yes—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C23×C47—22no—
62C23×C47—41no—
63C23×C47—41no—
64C23×C47—41no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47C2×D411yescharacteristic
69C22×D47—21no—
70C22×D47—21no—
71C22×D47—21no—
72C22×D47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47SD1612yes—
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—41no—
79D4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C22⋊D47—48no—
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—21no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97C2×Dic47—41no—
98C2×Dic47—41no—
99C4×D47—41no—
100C4×D47—41no—
101C4×D47—41no—
102C4×D47—41no—
103C8×C47—22no—
104C47⋊C8—41no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47—81no—
109C22×C47—81no—
110C22×C47—81no—
111C22×C47—81no—
112C22×C47#12011yescharacteristic
113C22×C47#12111yescharacteristic
114C22×C47#12311yescharacteristic
115C22×C47C2×SD1611yescharacteristic
116C22×C47#13511yescharacteristic
117C22×C47AGL(1,ℤ/8)11yescharacteristic
118C22×C47AGL(1,ℤ/8)11yescharacteristic
119C2×D47—22no—
120C2×D47—22no—
121C2×D47—22no—
122C2×D47—41no—
123C2×D47—41no—
124C2×D47—41no—
125C2×D47—41no—
126C4×C47—81no—
127C4×C47#12111yescharacteristic
128C4×C47#12111yescharacteristic
129C4×C47#12311yescharacteristic
130C4×C47#12411yescharacteristic
131Dic47—41no—
132Dic47—42no—
133Dic47—81no—
134#2034—471nomaximal, Sylow
135C2×C47—82no—
136C2×C47#39411yescharacteristic
137C2×C47#44911yescharacteristic
138C2×C47#45011yescharacteristic
139C2×C47#46511yescharacteristic
140C2×C47#46911yescharacteristic
141C2×C47#48111yescharacteristic
142C2×C47#48211yescharacteristic
143D47—42no—
144C2×#121—471no—
145C2×#106—471no—
146C2×#102—471no—
147C2×#102D4711yescharacteristic, complemented
148C2×C22⋊C8—471no—
149#380—471no—
150#340—471no—
151C47#203411yescharacteristic, complemented, Sylow
152C22×D4—941no—
153C22×D4C2×D4711yescharacteristic
154C23×C4—471no—
155C22×C8—471no—
156C22×C8C2×D4711yescharacteristic
157#121—942no—
158#121—942no—
159C2×C4⋊C4—471no—
160C2×C4⋊C4—471no—
161C2×C4⋊C4C2×D4711yescharacteristic
162C2×C22⋊C4—941no—
163C2×C22⋊C4—941no—
164#106—942no—
165#102—22no—
166#102—942no—
167C22⋊C8—942no—
168#95—941no—
169C24—21no—
170C24—471no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—944no—
177C2×D4—1882no—
178C2×D4—1882no—
179C2×D4D18812yes—
180C22×C4—21no—
181C22×C4—471no—
182C22×C4—941no—
183C22×C4—941no—
184C22×C4—941no—
185C22×C4—941no—
186C22×C4—941no—
187C22×C4—941no—
188C22×C4—941no—
189C22×C4—941no—
190C22×C4C22×D4711yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8C22⋊D4712yescomplemented
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—472no—
200C4⋊C4—941no—
201C4⋊C4—941no—
202C4⋊C4—941no—
203C22⋊C4—944no—
204C22⋊C4—1882no—
205C23—22no—
206C23—41no—
207C23—41no—
208C23—41no—
209C23—41no—
210C23—41no—
211C23—41no—
212C23—472no—
213C23—941no—
214C23—941no—
215C23—941no—
216C23—941no—
217C23—941no—
218C23—941no—
219C23D4×D4711yescharacteristic
220D4—22no—
221D4—22no—
222D4—41no—
223D4—41no—
224D4—1888no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—941no—
229C2×C4—942no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—1881no—
233C2×C4—1881no—
234C2×C4—1881no—
235C2×C4—1881no—
236C2×C4—1881no—
237C2×C4—1881no—
238C2×C4—1881no—
239C2×C4—1881no—
240C2×C4—1881no—
241C2×C4C2×D18811yescharacteristic
242C2×C4#1062535011yescharacteristic
243C2×C4D4×D4711yescharacteristic
244C2×C4#1062535211yescharacteristic
245C2×C4#1062535211yescharacteristic
246C2×C4C2×C22⋊D4711yescharacteristic
247C8—22no—
248C8—1881no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—81no—
253C22—81no—
254C22—81no—
255C22—81no—
256C22—942no—
257C22—942no—
258C22—942no—
259C22—1881no—
260C22—1881no—
261C22—1881no—
262C22—1881no—
263C22#1309399411yescharacteristic
264C22#1309399511yescharacteristic
265C22#1309400611yescharacteristic
266C22SD16×D4711yescharacteristic
267C22#1309404511yescharacteristic
268C22#1309404811yescharacteristic
269C22#1309404811yescharacteristic
270C4—81no—
271C4—3761no—
272C4—1882no—
273C4—1881no—
274C4#1309399611yescharacteristic
275C4#1309399811yescharacteristic
276C4#1309400811yescharacteristic
277C4#1309401011yescharacteristic
278C2—82no—
279C2—1882no—
280C2#1568903911yescharacteristic
281C2#1568926911yescharacteristic
282C2#1568927511yescharacteristic
283C2#1568934911yescharacteristic
284C2#1568937311yescharacteristic
285C2#1568944011yescharacteristic
286C2#1568944611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2034
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13093956C2semidirect
3. C2×#13093945C2semidirect
4. C2×(C2×D47)⋊C8C2semidirect
5. #15688980C2semidirect
6. #15688885C2semidirect
7. C2×#102×C47C2semidirect
49. C2×C8×C47D4semidirect
147. C2×#102D47semidirect
151. C47#2034semidirect
196. C2×C8C22⋊D47semidirect