Finite Group Databasebeta

← #20253408

Subgroups — #20253408

Order 6016.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689657C211yesmaximal, characteristic, complemented
2C4×#10625350C211yesmaximal, characteristic, complemented
3#15689465C211yesmaximal, characteristic, complemented
4#15689448C211yesmaximal, characteristic, complemented
5#15689431C211yesmaximal, characteristic, complemented
6#15689424C211yesmaximal, characteristic, complemented
7#15689346C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689287C211yesmaximal, characteristic, complemented
10#15689270C211yesmaximal, characteristic
11C4×Dic188C211yesmaximal, characteristic, complemented
12C4×#10625325C211yesmaximal, characteristic, complemented
13C4×#10625325C211yesmaximal, characteristic, complemented
14C4×D376C211yesmaximal, characteristic, complemented
15C47×#431C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625325C2211yescharacteristic
19C2×#10625325C2211yescharacteristic
20C2×D376C2211yescharacteristic
21#13094018—21no—
22#13094016C2211yescharacteristic
23#13094012C2211yescharacteristic
24#13094007—21no—
25#13094003C2211yescharacteristic
26#13093998C2211yescharacteristic
27C4×Dic94C2211yescharacteristic
28C4×Dic94C2211yescharacteristic
29C4×Dic94C2211yescharacteristic
30C4×D188C2211yescharacteristic
31C4×D188C2211yescharacteristic
32C4×D188C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47—21no—
35C4×C22⋊D47—21no—
36#13093983C2211yescharacteristic
37#13093981—21no—
38#13093981—21no—
39C42×D47—21no—
40#13093958C2211yescharacteristic
41#13093958C2211yescharacteristic
42#13093956C2211yescharacteristic
43#13093956C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093949C2211yescharacteristic
47#13093949C2211yescharacteristic
48#13093946C2211yescharacteristic
49#13093946C2211yescharacteristic
50#13093946C2211yescharacteristic
51#13093946C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic
53C4⋊C8×C47C2211yescharacteristic
54C4⋊C8×C47C2211yescharacteristic
55C22⋊C8×C47C2211yescharacteristic
56C22⋊C8×C47C2211yescharacteristic
57C4×C8×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic
59C22×C4×C47D411yescharacteristic
60C22×C4×C47D411yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64#10625350—22no—
65#10625350—22no—
66C2×D188C2311yescharacteristic
67C2×D188C2311yescharacteristic
68C2×C4×D47—21no—
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×Dic94C2311yescharacteristic
73C2×Dic94C2311yescharacteristic
74C2×C8×C47C2311yescharacteristic
75C2×C8×C47C2311yescharacteristic
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C42×C47D411yescharacteristic
79C42×C47D411yescharacteristic
80C42×C47C2311yescharacteristic
81C42×C47C2311yescharacteristic
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90C4⋊Dic47C2311yescharacteristic
91C4⋊Dic47C2311yescharacteristic
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×Dic47—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104Dic188—22no—
105D376—22no—
106#10625325—22no—
107#10625325—22no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C22×D47—21no—
111C2×C4×C47—22no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—41no—
115C2×C4×C47C2×D411yescharacteristic
116C2×C4×C47C2×D411yescharacteristic
117C2×C4×C47C2×D411yescharacteristic
118C2×C4×C47C2×D411yescharacteristic
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2411yescharacteristic
121C22⋊D47—24no—
122C22⋊D47—42no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129D188—21no—
130D188—21no—
131D188—21no—
132D188#4112yes—
133C4×D47—24no—
134C4×D47—42no—
135C4×D47—42no—
136C4×D47—42no—
137Dic94—21no—
138Dic94—21no—
139Dic94—21no—
140Dic94#4112yes—
141C8×C47—21no—
142C8×C47—21no—
143C8×C47—21no—
144C8×C47—21no—
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—21no—
148C22×C47C22×D411yescharacteristic
149C2×D47—22no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C2×D47—41no—
154C2×D47—41no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47#13512yes—
160C4×C47C2×#4111yescharacteristic
161C4×C47C2×#4111yescharacteristic
162Dic47—22no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168#3102—471nomaximal, Sylow
169C2×C47—41no—
170C2×C47#52511yescharacteristic
171C2×C47C2×#13511yescharacteristic
172C2×C47#57511yescharacteristic
173D47—42no—
174D47—81no—
175#529—471no—
176C4×#41—471no—
177#485—471no—
178#482—471no—
179#479—471no—
180#478—471no—
181#464—471no—
182#463—471no—
183#452—471no—
184#449—471no—
185C4×Q16—471no—
186C4×SD16—471no—
187C4×SD16—471no—
188C4×D8—471no—
189#431D4711yescharacteristic, complemented
190C47#310211yescharacteristic, complemented, Sylow
191C2×#41—471no—
192C2×Q16—471no—
193C2×SD16—471no—
194C2×SD16—471no—
195C2×D8—471no—
196#126—941no—
197#125—471no—
198#124—471no—
199#123—941no—
200C22⋊Q8—471no—
201#121—471no—
202C4×Q8—471no—
203C4×Q8—471no—
204C4×Q8—471no—
205C4×D4—471no—
206C4×D4—471no—
207C4×D4—471no—
208C4×D4—941no—
209C4×D4—941no—
210C4×D4—941no—
211#117—471no—
212#117—941no—
213#117—941no—
214C2×C42—941no—
215C2×C42C2×D4711yescharacteristic
216#107—471no—
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8C2×D4711yescharacteristic
221C4⋊C8C2×D4711yescharacteristic
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#102—471no—
227#102—471no—
228#102—471no—
229#102—471no—
230C22⋊C8C2×D4711yescharacteristic
231C22⋊C8C2×D4711yescharacteristic
232C4×C8C2×D4711yescharacteristic
233C4×C8C2×D4711yescharacteristic
234#41—942no—
235#41—942no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×D4—471no—
239C2×D4—471no—
240C2×D4—941no—
241C2×D4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
246C22×C4D18811yescharacteristic
247C22×C4D18811yescharacteristic
248C22×C4C22×D4711yescharacteristic
249Q16—942no—
250SD16—942no—
251SD16—942no—
252D8—942no—
253C2×C8C22×D4711yescharacteristic
254C2×C8C22×D4711yescharacteristic
255C2×C8C22×D4711yescharacteristic
256C2×C8C22×D4711yescharacteristic
257C4⋊C4—471no—
258C4⋊C4—471no—
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C22⋊C4—941no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C42—941no—
276C42—941no—
277C42—941no—
278C42—941no—
279C42D18811yescharacteristic
280C42D18811yescharacteristic
281C42C22×D4711yescharacteristic
282C42C22×D4711yescharacteristic
283C23—941no—
284C23—941no—
285C23C2×D18811yescharacteristic
286Q8—472no—
287Q8—941no—
288Q8—941no—
289Q8—941no—
290D4—472no—
291D4—944no—
292D4—941no—
293D4—941no—
294D4—941no—
295D4—1882no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—944no—
301C2×C4—941no—
302C2×C4—941no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—1882no—
308C2×C4—1882no—
309C2×C4—1882no—
310C2×C4C2×D18811yescharacteristic
311C2×C4C2×D18811yescharacteristic
312C2×C4C2×D18811yescharacteristic
313C2×C4C2×D18811yescharacteristic
314C2×C4C2×D18811yescharacteristic
315C2×C4C23×D4711yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—942no—
324C22—1881no—
325C22—1881no—
326C22—1881no—
327C22—1881no—
328C22—1881no—
329C22C22×D18811yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—942no—
335C4—1881no—
336C4—1881no—
337C4—1881no—
338C4—1881no—
339C4—1881no—
340C4#1309404612yes—
341C4#41×D4711yescharacteristic
342C4#41×D4711yescharacteristic
343C2—41no—
344C2—3761no—
345C2—1882no—
346C2#1568963511yescharacteristic
347C2C2×#1309404611yescharacteristic
348C2#1568992311yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#431C2
socleC22×C47C22×D4
hypercenter#431D47
hypocenterC47#3102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #15689657C2semidirect
2. C4×#10625350C2semidirect
3. #15689465C2semidirect
4. #15689448C2semidirect
5. #15689431C2semidirect
6. #15689424C2semidirect
7. #15689346C2semidirect
8. #15689339C2semidirect
9. #15689287C2semidirect
11. C4×Dic188C2semidirect
12. C4×#10625325C2semidirect
13. C4×#10625325C2semidirect
14. C4×D376C2semidirect
15. C47×#431C2semidirect
189. #431D47semidirect
190. C47#3102semidirect