Finite Group Databasebeta

← #20254103

Subgroups — #20254103

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689677C211yesmaximal, characteristic, complemented
2#15689670C211yesmaximal, characteristic
3#15689527C211yesmaximal, characteristic, complemented
4#15689494C211yesmaximal, characteristic, complemented
5#15689472C211yesmaximal, characteristic, complemented
6#15689468C211yesmaximal, characteristic, complemented
7#15689372C211yesmaximal, characteristic, complemented
8#15689370C211yesmaximal, characteristic, complemented
9#15689368C211yesmaximal, characteristic, complemented
10#15689366C211yesmaximal, characteristic, complemented
11#15689225C211yesmaximal, characteristic, complemented
12#15689223C211yesmaximal, characteristic, complemented
13#15689221C211yesmaximal, characteristic, complemented
14#15689075C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625325C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C2×#10625324C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094023C2211yescharacteristic
24#13094022C2211yescharacteristic
25#13094020C2211yescharacteristic
26#13094014—21no—
27#13094010—21no—
28#13094004C2211yescharacteristic
29#13094002—21no—
30#13094000C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093997—21no—
33#13093995C2211yescharacteristic
34C4×Dic94—21no—
35C4×Dic94C2211yescharacteristic
36C4×D188C2211yescharacteristic
37C4×C22⋊D47—21no—
38#13093981—21no—
39C42×D47C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093935C2211yescharacteristic
50C8×Dic47C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65#10625350—44no—
66C2×D188—21no—
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47D411yescharacteristic
70C2×C4×D47D411yescharacteristic
71C2×C4×D47C2311yescharacteristic
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94C2311yescharacteristic
75SD16×C47—22no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47—21no—
79C4⋊C4×C47C2311yescharacteristic
80C4⋊C4×C47C2311yescharacteristic
81C22⋊C4×C47—21no—
82C42×C47—21no—
83C42×C47C2311yescharacteristic
84C22⋊Dic47—21no—
85#10625336—22no—
86#10625335—22no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47C2311yescharacteristic
93C4⋊Dic47C2311yescharacteristic
94Dic47⋊C4—21no—
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100C4×Dic47—21no—
101C4×Dic47D411yescharacteristic
102C4×Dic47D411yescharacteristic
103C4×Dic47C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106#10625325—22no—
107#10625324—22no—
108#10625324—22no—
109C23×C47—21no—
110C22×D47—21no—
111C22×D47C2×D411yescharacteristic
112Q8×C47—21no—
113Q8×C47—21no—
114D4×C47—21no—
115D4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—42no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2×D411yescharacteristic
122C2×C4×C47C2411yescharacteristic
123C22⋊D47—42no—
124C22⋊D47—42no—
125C22⋊D47—42no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47C2×D411yescharacteristic
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132D188—21no—
133D188—21no—
134D188—42no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—22no—
138C4×D47—22no—
139C4×D47—42no—
140Dic94—21no—
141Dic94—21no—
142Dic94—42no—
143Dic94—42no—
144C8×C47—21no—
145C8×C47#4112yescomplemented
146C47⋊C8—21no—
147C47⋊C8#4112yescomplemented
148C22×C47—41no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C22×D411yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C2×D47—41no—
156C2×D47—41no—
157C2×D47—41no—
158C4×C47—21no—
159C4×C47—21no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47C2×#4111yescharacteristic
164C4×C47C2×#4111yescharacteristic
165Dic47—21no—
166Dic47—41no—
167Dic47—41no—
168Dic47—41no—
169Dic47AGL(1,ℤ/8)12yes—
170Dic47#13712yes—
171#3182—471nomaximal, Sylow
172C2×C47—81no—
173C2×C47#53211yescharacteristic
174C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C47C2×#13711yescharacteristic
176D47—41no—
177D47—81no—
178#533—471no—
179#532—471no—
180#500—471no—
181#492—471no—
182#487—471no—
183#486—471no—
184#468—471no—
185#468—471no—
186#468—471no—
187#468—471no—
188#440—471no—
189#440—471no—
190#440—471no—
191#440D4711yescharacteristic, complemented
192C4×M16—471no—
193C47#318211yescharacteristic, complemented, Sylow
194C2×#41—941no—
195C2×SD16—471no—
196C2×SD16—471no—
197C2×SD16—471no—
198C2×SD16C2×D4711yescharacteristic
199C2×M16—471no—
200C2×M16—471no—
201C4⋊Q8—471no—
202C4⋊Q8—471no—
203C4⋊Q8—471no—
204#127—471no—
205#125—941no—
206#124—941no—
207C22⋊Q8—471no—
208C22⋊Q8—471no—
209C22⋊Q8—941no—
210#121—471no—
211#121—471no—
212#121—941no—
213C4×Q8—471no—
214C4×Q8—941no—
215C4×Q8C2×D4711yescharacteristic
216C4×D4—471no—
217C4×D4—941no—
218C4×D4C2×D4711yescharacteristic
219#117—941no—
220C2×C42—471no—
221#107—471no—
222#107—471no—
223#107—471no—
224#107C2×D4711yescharacteristic
225#103—471no—
226#103—471no—
227#103—471no—
228#103C2×D4711yescharacteristic
229#102—471no—
230#102—471no—
231#102—471no—
232#102C2×D4711yescharacteristic
233#97—471no—
234#97C2×D4711yescharacteristic
235C4×C8—471no—
236C4×C8—471no—
237#41—1884no—
238C2×Q8—471no—
239C2×Q8—941no—
240C2×Q8—941no—
241C2×Q8C22×D4711yescharacteristic
242C2×D4—471no—
243C2×D4—941no—
244C2×D4—941no—
245C2×D4—941no—
246C2×D4—941no—
247C2×D4C22×D4711yescharacteristic
248C22×C4—21no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—941no—
253SD16—22no—
254SD16—942no—
255SD16—942no—
256SD16—942no—
257M16—942no—
258M16—942no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8C22×D4711yescharacteristic
262C2×C8C22×D4711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—471no—
265C4⋊C4—471no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4C22×D4711yescharacteristic
274C4⋊C4C22×D4711yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C42—21no—
282C42—471no—
283C42—471no—
284C42—471no—
285C42—941no—
286C42C22×D4711yescharacteristic
287C23—21no—
288C23—471no—
289C23—941no—
290Q8—21no—
291Q8—21no—
292Q8—941no—
293Q8—941no—
294Q8—1882no—
295Q8—1882no—
296D4—21no—
297D4—21no—
298D4—941no—
299D4—941no—
300D4—1882no—
301D4—1882no—
302D4—1882no—
303D4—1882no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—1882no—
319C2×C4D4×D4711yescharacteristic
320C2×C4D4×D4711yescharacteristic
321C2×C4C23×D4711yescharacteristic
322C8—21no—
323C8—472no—
324C8—941no—
325C8#1062535012yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—941no—
330C22—941no—
331C22—941no—
332C22—1881no—
333C22—1881no—
334C22—1881no—
335C22C2×D4×D4711yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—472no—
342C4—472no—
343C4—941no—
344C4—1881no—
345C4—1881no—
346C4—1881no—
347C4#41×D4711yescharacteristic
348C4C2×#1062535011yescharacteristic
349C2—81no—
350C2—3761no—
351C2—1881no—
352C2#1568967011yescharacteristic
353C2AGL(1,ℤ/8)×D4711yescharacteristic
354C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3182
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689677C2semidirect
3. #15689527C2semidirect
4. #15689494C2semidirect
5. #15689472C2semidirect
6. #15689468C2semidirect
7. #15689372C2semidirect
8. #15689370C2semidirect
9. #15689368C2semidirect
10. #15689366C2semidirect
11. #15689225C2semidirect
12. #15689223C2semidirect
13. #15689221C2semidirect
14. #15689075C2semidirect
15. C47×#440C2semidirect
145. C8×C47#41semidirect
147. C47⋊C8#41semidirect
191. #440D47semidirect
193. C47#3182semidirect
325. C8#10625350semidirect