Finite Group Databasebeta

← #20243689

Subgroups — #20243689

Order 6016.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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×M16×D47C211yesmaximal, characteristic, complemented
2#15689635C211yesmaximal, characteristic
3C2×#13093952C211yesmaximal, characteristic, complemented
4C2×#13093950C211yesmaximal, characteristic, complemented
5C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×C4×D47C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11C2×#10625324—21no—
12M16×D47—22no—
13M16×D47—22no—
14C2×C8×D47—21no—
15#13094008—21no—
16#13094004C411yescharacteristic, complemented
17#13094004C411yescharacteristic, complemented
18#13093999C411yescharacteristic, complemented
19#13093999C411yescharacteristic, complemented
20#13093994—21no—
21C4×D188—21no—
22C4×D188—21no—
23C2×(C2×D47)⋊C4—21no—
24C2×C4×Dic47C2211yescharacteristic
25#13093952—22no—
26#13093950—22no—
27C47⋊#95—21no—
28C2×M16×C47C2211yescharacteristic
29#117×C47C2211yescharacteristic
30C2×C42×C47C2211yescharacteristic
31C23×D47D411yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37#10625350—21no—
38#10625350—21no—
39#10625350—21no—
40#10625350—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188C2×C411yescharacteristic
44C2×C4×D47—21no—
45C2×C4×D47—21no—
46C2×C4×D47—21no—
47C2×C4×D47—21no—
48C2×C4×D47—21no—
49C2×C4×D47C2×C411yescharacteristic
50C2×C4×D47C2×C411yescharacteristic
51C2×C4×D47D411yescharacteristic
52C2×C4×D47D411yescharacteristic
53C2×Dic94C2×C411yescharacteristic
54M16×C47—21no—
55M16×C47D412yescomplemented
56C2×C8×C47—21no—
57C4⋊C4×C47C2×C411yescharacteristic
58C4⋊C4×C47C2×C411yescharacteristic
59C22⋊C4×C47—21no—
60C42×C47—21no—
61C42×C47—21no—
62C42×C47—21no—
63(C2×D47)⋊C4—24no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—21no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68C4⋊Dic47—21no—
69C4⋊Dic47—21no—
70C4×Dic47—21no—
71C4×Dic47—21no—
72#10625329—21no—
73#10625329D412yescomplemented
74C2×C47⋊C8—21no—
75#10625324—24no—
76C8×D47—24no—
77C23×C47C2×D411yescharacteristic
78C22×D47—21no—
79C22×D47—21no—
80C22×D47—22no—
81C22×D47—21no—
82C22×D47—41no—
83C22×D47C22⋊C411yescharacteristic
84C22×D47C22⋊C411yescharacteristic
85C2×C4×C47—22no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47C22×C411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47#4111yescharacteristic
95C2×C4×C47#4111yescharacteristic
96C22⋊D47—41no—
97C22⋊D47—41no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102C2×Dic47—41no—
103C2×Dic47—41no—
104C2×Dic47C22⋊C411yescharacteristic
105C2×Dic47C22⋊C411yescharacteristic
106D188—21no—
107D188—21no—
108D188—42no—
109D188—42no—
110C4×D47—21no—
111C4×D47—21no—
112C4×D47—21no—
113C4×D47—21no—
114C4×D47—21no—
115C4×D47—21no—
116C4×D47—21no—
117C4×D47—21no—
118C4×D47—41no—
119C4×D47—41no—
120Dic94—21no—
121Dic94—21no—
122C8×C47—22no—
123C47⋊C8—22no—
124C22×C47—21no—
125C22×C47—21no—
126C22×C47C2×C22⋊C411yescharacteristic
127C22×C47#12111yescharacteristic
128C22×C47#12111yescharacteristic
129C2×D47—21no—
130C2×D47—21no—
131C2×D47—21no—
132C2×D47—21no—
133C2×D47—21no—
134C2×D47—42no—
135C2×D47—42no—
136C2×D47—41no—
137C2×D47—41no—
138C2×D47—41no—
139C2×D47#10412yescomplemented
140C4×C47—42no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47C4×D411yescharacteristic
144C4×C47C4×D411yescharacteristic
145C4×C47#12011yescharacteristic
146C4×C47#12311yescharacteristic
147Dic47—21no—
148Dic47—21no—
149Dic47—42no—
150Dic47—41no—
151#1871—471nomaximal, Sylow
152C2×C47—21no—
153C2×C47—21no—
154C2×C47#38611yescharacteristic
155C2×C47C2×#10411yescharacteristic
156C2×C47#42111yescharacteristic
157D47—22no—
158D47—41no—
159D47—81no—
160C22×M16—471no—
161#525—471no—
162C2×#104—471no—
163C2×#104—471no—
164C4×C22⋊C4—471no—
165#339—471no—
166#339D4711yescharacteristic, complemented
167C47#187111yescharacteristic, complemented, Sylow
168C2×#41—471no—
169C23×C4—471no—
170C2×M16—471no—
171C2×M16—941no—
172C2×M16—942no—
173C2×M16—942no—
174C2×M16C2×D4711yescharacteristic
175C22×C8—941no—
176#123—941no—
177C22⋊Q8—471no—
178C22⋊Q8—471no—
179#121—471no—
180#121—471no—
181#120—941no—
182C4×D4—941no—
183C4×D4—941no—
184#117C2×D4711yescharacteristic
185C2×C22⋊C4—941no—
186C2×C42—471no—
187C2×C42C2×D4711yescharacteristic
188#104—942no—
189#104—942no—
190#95—941no—
191C24—471no—
192#41—941no—
193#41—941no—
194#41—941no—
195#41—941no—
196C2×Q8—471no—
197C2×D4—471no—
198C2×D4—941no—
199C2×D4—941no—
200C2×D4—941no—
201C22×C4—21no—
202C22×C4—471no—
203C22×C4—471no—
204C22×C4—471no—
205C22×C4—471no—
206C22×C4—471no—
207C22×C4—941no—
208C22×C4—941no—
209C22×C4—941no—
210C22×C4—941no—
211C22×C4—941no—
212C22×C4—941no—
213C22×C4C22×D4711yescharacteristic
214M16—21no—
215M16—472no—
216M16—944no—
217M16—941no—
218M16D18812yescomplemented
219C2×C8—21no—
220C2×C8—944no—
221C2×C8—941no—
222C4⋊C4—941no—
223C4⋊C4—941no—
224C4⋊C4C4×D4711yescharacteristic
225C4⋊C4C4×D4711yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—941no—
228C22⋊C4—941no—
229C22⋊C4—941no—
230C22⋊C4—941no—
231C22⋊C4—944no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—941no—
236C42—941no—
237C23—471no—
238C23—471no—
239C23—942no—
240C23—941no—
241C23—941no—
242C23—941no—
243C23—1881no—
244C23D4×D4711yescharacteristic
245Q8—941no—
246Q8—941no—
247D4—941no—
248D4—941no—
249D4—1882no—
250D4—1882no—
251D4—1881no—
252D4—1881no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—471no—
259C2×C4—471no—
260C2×C4—941no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—941no—
264C2×C4—941no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—941no—
268C2×C4—941no—
269C2×C4—941no—
270C2×C4—942no—
271C2×C4—941no—
272C2×C4—1881no—
273C2×C4—1881no—
274C2×C4—1881no—
275C2×C4—1881no—
276C2×C4C2×C4×D4711yescharacteristic
277C2×C4C2×D18811yescharacteristic
278C2×C4#1062535011yescharacteristic
279C2×C4D4×D4711yescharacteristic
280C2×C4D4×D4711yescharacteristic
281C2×C4#1062535411yescharacteristic
282C8—22no—
283C8—942no—
284C22—21no—
285C22—21no—
286C22—472no—
287C22—941no—
288C22—941no—
289C22—941no—
290C22—941no—
291C22—941no—
292C22—1882no—
293C22—1882no—
294C22—1881no—
295C22—1881no—
296C22—1881no—
297C22C22⋊C4×D4711yescharacteristic
298C22#1309399711yescharacteristic
299C22#1309399911yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—941no—
304C4—941no—
305C4—1882no—
306C4—1881no—
307C4#1309398611yescharacteristic
308C4C4×D18811yescharacteristic
309C4#1309399411yescharacteristic
310C4#1309400911yescharacteristic
311C2—21no—
312C2—21no—
313C2—942no—
314C2—3761no—
315C2—1881no—
316C2#1568900111yescharacteristic
317C2#104×D4711yescharacteristic
318C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1871
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D47C2semidirect
3. C2×#13093952C2semidirect
4. C2×#13093950C2semidirect
5. C4×(C2×D47)⋊C4C2semidirect
6. #15688882C2semidirect
7. C47×#339C2semidirect
16. #13094004C4semidirect
17. #13094004C4semidirect
18. #13093999C4semidirect
19. #13093999C4semidirect
55. M16×C47D4semidirect
73. #10625329D4semidirect
139. C2×D47#104semidirect
166. #339D47semidirect
167. C47#1871semidirect
218. M16D188semidirect