Finite Group Databasebeta

← #20255730

Subgroups — #20255730

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689774C211yesmaximal, characteristic, complemented
2#15689773C211yesmaximal, characteristic, complemented
3#15689527C211yesmaximal, characteristic, complemented
4#15689438C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689435C211yesmaximal, characteristic, complemented
7#15689402C211yesmaximal, characteristic, complemented
8#15689401C211yesmaximal, characteristic, complemented
9#15689358C211yesmaximal, characteristic, complemented
10#15689357C211yesmaximal, characteristic, complemented
11#15689203C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
13C2×#13093957C211yesmaximal, characteristic, complemented
14#107×D47C211yesmaximal, characteristic, complemented
15C47×#480C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625352—21no—
18C2×#10625334C2211yescharacteristic
19C22×C47⋊C8C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094009—21no—
24#13094007—21no—
25#13094006—21no—
26#13094005—21no—
27#13094002—21no—
28#13094001—21no—
29#13093999C2211yescharacteristic
30#13093998C2211yescharacteristic
31#13093995C2211yescharacteristic
32D4×Dic47C2211yescharacteristic
33#13093986C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093957C2211yescharacteristic
44#13093957C2211yescharacteristic
45Dic47⋊C8C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093946C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52#121×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×D4×C47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47D411yescharacteristic
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625352—44no—
69#10625350—44no—
70C2×D188—21no—
71C2×D188C2311yescharacteristic
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47—21no—
75C2×C4×D47C2311yescharacteristic
76C2×Dic94—21no—
77C2×Dic94—21no—
78C2×C8×C47C2311yescharacteristic
79C2×C8×C47C2311yescharacteristic
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C22⋊Dic47—21no—
86C22⋊Dic47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625334—22no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96C4⋊Dic47C2311yescharacteristic
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4D411yescharacteristic
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8—22no—
104C2×C47⋊C8C2311yescharacteristic
105C2×C47⋊C8C2311yescharacteristic
106C8×D47—22no—
107C23×C47—21no—
108C23×C47C2×D411yescharacteristic
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111D4×C47—21no—
112D4×C47—21no—
113D4×C47—42no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—42no—
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—42no—
123C22⋊D47—42no—
124C22⋊D47D814yescomplemented
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—42no—
129C2×Dic47—42no—
130C2×Dic47C2×D411yescharacteristic
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—21no—
134D188—21no—
135D188—42no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—42no—
139C4×D47—42no—
140C4×D47—42no—
141Dic94—42no—
142Dic94—42no—
143C8×C47—21no—
144C8×C47—21no—
145C47⋊C8—21no—
146C47⋊C8#4112yescomplemented
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47—41no—
152C22×C47C2×D812yes—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47—41no—
157C2×D47—41no—
158C2×D47—41no—
159C2×D47C2×D812yes—
160C4×C47—21no—
161C4×C47—41no—
162C4×C47—41no—
163C4×C47—41no—
164C4×C47C2×#4111yescharacteristic
165C4×C472−1+411yescharacteristic
166Dic47—21no—
167Dic47—21no—
168Dic47—41no—
169Dic47—41no—
170Dic47—41no—
171Dic47C2×D812yes—
172#3334—471nomaximal, Sylow
173C2×C47—22no—
174C2×C47—81no—
175C2×C47#54711yescharacteristic
176C2×C47C22×D811yescharacteristic
177C2×C47#57811yescharacteristic
178D47—22no—
179D47—81no—
180#547—471no—
181#547—471no—
182#500—471no—
183#480—471no—
184#480—471no—
185#480—471no—
186#480D4711yescharacteristic, complemented
187#474—471no—
188#474—471no—
189#466—471no—
190#466—471no—
191C4×D8—471no—
192C8×D4—471no—
193C2×#107—471no—
194C2×#107—471no—
195C47#333411yescharacteristic, complemented, Sylow
196C2×#41—941no—
197C2×#41—941no—
198C2×D8—471no—
199C22×C8—471no—
200C22×C8—471no—
201C4⋊Q8—471no—
202C4⋊Q8—471no—
203#123—941no—
204#123—941no—
205#123—941no—
206#123—941no—
207C22⋊Q8—941no—
208C22⋊Q8—941no—
209#121—471no—
210#121—471no—
211#121—471no—
212#121C2×D4711yescharacteristic
213C4×D4—471no—
214C4×D4—471no—
215C4×D4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4C2×D4711yescharacteristic
220#107—471no—
221#107—471no—
222#107—471no—
223#107—471no—
224#107—471no—
225#107—471no—
226#107—471no—
227#107C2×D4711yescharacteristic
228#107C2×D4711yescharacteristic
229C4⋊C8—471no—
230#102—471no—
231#102—471no—
232#102—471no—
233#102—471no—
234#102C2×D4711yescharacteristic
235#102C2×D4711yescharacteristic
236C22⋊C8—471no—
237C22⋊C8C2×D4711yescharacteristic
238C4×C8—471no—
239#41—1884no—
240#41—1884no—
241C2×Q8—941no—
242C2×Q8—941no—
243C2×D4—21no—
244C2×D4—471no—
245C2×D4—471no—
246C2×D4—941no—
247C2×D4—941no—
248C2×D4—941no—
249C2×D4C22×D4711yescharacteristic
250C22×C4—21no—
251C22×C4—471no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258D8—942no—
259C2×C8—471no—
260C2×C8—471no—
261C2×C8—942no—
262C2×C8—942no—
263C2×C8C22×D4711yescharacteristic
264C2×C8C22×D4711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—471no—
269C4⋊C4—471no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4C22×D4711yescharacteristic
276C4⋊C4C22×D4711yescharacteristic
277C4⋊C4C22×D4711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—471no—
280C22⋊C4—471no—
281C22⋊C4—941no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C42—471no—
287C23—21no—
288C23—471no—
289C23—941no—
290C23D4×D4711yescharacteristic
291Q8—1882no—
292Q8—1882no—
293D4—21no—
294D4—21no—
295D4—42no—
296D4—474no—
297D4—941no—
298D4—941no—
299D4—1882no—
300D4—1882no—
301D4—1882no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—1882no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4—1882no—
320C2×C4—1882no—
321C2×C4D4×D4711yescharacteristic
322C2×C4C23×D4711yescharacteristic
323C8—21no—
324C8—21no—
325C8—472no—
326C8—941no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—472no—
333C22—941no—
334C22—941no—
335C22—1881no—
336C22—1881no—
337C22—1881no—
338C22D8×D4712yes—
339C22C2×D4×D4711yescharacteristic
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—472no—
345C4—941no—
346C4—941no—
347C4—1881no—
348C4—1881no—
349C4—1881no—
350C4#41×D4711yescharacteristic
351C4#1309407111yescharacteristic
352C2—22no—
353C2—81no—
354C2—942no—
355C2—3761no—
356C2#1568977111yescharacteristic
357C2C2×D8×D4711yescharacteristic
358C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3334
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #15689774C2semidirect
2. #15689773C2semidirect
3. #15689527C2semidirect
4. #15689438C2semidirect
5. #15689437C2semidirect
6. #15689435C2semidirect
7. #15689402C2semidirect
8. #15689401C2semidirect
9. #15689358C2semidirect
10. #15689357C2semidirect
11. #15689203C2semidirect
12. (C22⋊D47)⋊C8C2semidirect
13. C2×#13093957C2semidirect
14. #107×D47C2semidirect
15. C47×#480C2semidirect
124. C22⋊D47D8semidirect
146. C47⋊C8#41semidirect
186. #480D47semidirect
195. C47#3334semidirect