Finite Group Databasebeta

← #20244567

Subgroups — #20244567

Order 6016.

368 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13093957C211yesmaximal, characteristic, complemented
2C2×#13093945C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
5#15688983C211yesmaximal, characteristic, complemented
6#15688885C211yesmaximal, characteristic, complemented
7C2×#121×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×C22⋊Dic47—21no—
13#13093957—22no—
14#13093945—22no—
15#13093945—22no—
16C22⋊(C47⋊C8)—22no—
17C47⋊#95—21no—
18C22×D4×C47—21no—
19C22×D4×C47C2211yescharacteristic
20C23×C4×C47C2211yescharacteristic
21#121×C47—22no—
22#121×C47—22no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—21no—
25C24×C47—21no—
26C24×C47D411yescharacteristic
27C2×D4×C47—24no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—42no—
34C2×D4×C47—42no—
35C2×D4×C47D412yes—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47—21no—
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C22×Dic47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47D412yes—
49C22⋊C4×C47—24no—
50C22⋊Dic47—42no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8D412yescomplemented
61C23×C47—21no—
62C23×C47—21no—
63C23×C47—21no—
64C23×C47—21no—
65C23×C47—21no—
66C23×C47—21no—
67C23×C47—22no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47—41no—
72C23×C47—41no—
73C23×C47—41no—
74C23×C47D812yes—
75C23×C47C2×D411yescharacteristic
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—48no—
79D4×C47—41no—
80D4×C47—41no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47—41no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47#4111yescharacteristic
95C2×C4×C47#4111yescharacteristic
96C2×C4×C47#4111yescharacteristic
97C2×Dic47—41no—
98C2×Dic47—41no—
99C2×Dic47—41no—
100C2×Dic47—41no—
101C2×Dic47—41no—
102C2×Dic47—41no—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—22no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47—41no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—81no—
116C22×C47—81no—
117C22×C47—81no—
118C22×C47—81no—
119C22×C47#12011yescharacteristic
120C22×C47#12111yescharacteristic
121C22×C47#12311yescharacteristic
122C22×C47C2×D811yescharacteristic
123C22×C47#13511yescharacteristic
124C22×C47AGL(1,ℤ/8)11yescharacteristic
125C22×C47#13711yescharacteristic
126C4×C47—41no—
127C4×C47—42no—
128C4×C47#12111yescharacteristic
129C4×C47#12111yescharacteristic
130C4×C47#12311yescharacteristic
131C4×C47#12411yescharacteristic
132Dic47—81no—
133Dic47—81no—
134#2033—471nomaximal, Sylow
135C2×C47—42no—
136C2×C47—82no—
137C2×C47#39411yescharacteristic
138C2×C47#44711yescharacteristic
139C2×C47#45211yescharacteristic
140C2×C47#46611yescharacteristic
141C2×C47#46811yescharacteristic
142C2×C47#48011yescharacteristic
143C2×C47#48211yescharacteristic
144C2×#121D4711yescharacteristic
145C2×#107—471no—
146C2×#102—471no—
147C2×#102—471no—
148C2×C22⋊C8—471no—
149#380—471no—
150#340—471no—
151C47#203311yescharacteristic, complemented, Sylow
152C22×D4—21no—
153C22×D4C2×D4711yescharacteristic
154C23×C4C2×D4711yescharacteristic
155C22×C8—471no—
156C22×C8—471no—
157#121—22no—
158#121—22no—
159C2×C4⋊C4—471no—
160C2×C4⋊C4—471no—
161C2×C4⋊C4C2×D4711yescharacteristic
162C2×C22⋊C4—21no—
163C2×C22⋊C4—941no—
164#107—942no—
165#102—942no—
166#102—942no—
167C22⋊C8—942no—
168#95—941no—
169C24—21no—
170C24C22⋊D4711yescharacteristic
171C2×D4—24no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—42no—
178C2×D4—42no—
179C2×D4C22⋊D4712yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—941no—
188C22×C4—941no—
189C22×C4C22⋊D4711yescharacteristic
190C22×C4C22×D4711yescharacteristic
191C2×C8—472no—
192C2×C8—941no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8—941no—
197C4⋊C4—21no—
198C4⋊C4—941no—
199C4⋊C4—941no—
200C4⋊C4—941no—
201C4⋊C4—941no—
202C4⋊C4C22⋊D4712yes—
203C22⋊C4—24no—
204C22⋊C4—1882no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23#1062533412yes—
219C23C2×C22⋊D4711yescharacteristic
220D4—22no—
221D4—22no—
222D4—48no—
223D4—41no—
224D4—41no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—1881no—
236C2×C4—1881no—
237C2×C4—1881no—
238C2×C4—1881no—
239C2×C4—1881no—
240C2×C4—1881no—
241C2×C4D4×D4711yescharacteristic
242C2×C4#1062535211yescharacteristic
243C2×C4#1062535211yescharacteristic
244C2×C4#1062535211yescharacteristic
245C2×C4C2×C22⋊D4711yescharacteristic
246C2×C4C2×C22⋊D4711yescharacteristic
247C8—942no—
248C8—1881no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22#1309399311yescharacteristic
264C22#1309399611yescharacteristic
265C22#1309400511yescharacteristic
266C22C2×#1062533411yescharacteristic
267C22#1309404411yescharacteristic
268C22#1309405011yescharacteristic
269C22#1309405411yescharacteristic
270C4—42no—
271C4—41no—
272C4—3761no—
273C4—3761no—
274C4#1309399511yescharacteristic
275C4#1309399611yescharacteristic
276C4#1309400511yescharacteristic
277C4#1309401111yescharacteristic
278C2—42no—
279C2—82no—
280C2#1568903711yescharacteristic
281C2#1568925711yescharacteristic
282C2#1568928511yescharacteristic
283C2#1568935711yescharacteristic
284C2#1568936711yescharacteristic
285C2#1568943411yescharacteristic
286C2#1568944411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#121×C47C2
socleC23×C47C2×D4
hypercenterC2×#121D47
hypocenterC47#2033
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13093957C2semidirect
2. C2×#13093945C2semidirect
3. C2×#13093945C2semidirect
4. C2×C22⋊(C47⋊C8)C2semidirect
5. #15688983C2semidirect
6. #15688885C2semidirect
60. C2×C47⋊C8D4semidirect
151. C47#2033semidirect