Finite Group Databasebeta

← #20255259

Subgroups — #20255259

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689831C211yesmaximal, characteristic
2#15689786C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689456C211yesmaximal, characteristic, complemented
6#15689417C211yesmaximal, characteristic, complemented
7#15689363C211yesmaximal, characteristic, complemented
8#15689331C211yesmaximal, characteristic, complemented
9#15689278C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11#15689215C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic
13C2×#13093949C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#467C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023—21no—
22#13094023C2211yescharacteristic
23#13094022C2211yescharacteristic
24#13094014—21no—
25#13094004—21no—
26#13094004C2211yescharacteristic
27#13094002—21no—
28#13094001—21no—
29#13094001—21no—
30#13094000C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32#13093989C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34(C22⋊D47)⋊C4—21no—
35(C22⋊D47)⋊C4—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093957C2211yescharacteristic
39#13093957C2211yescharacteristic
40Dic47⋊C8C2211yescharacteristic
41#13093949C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×Q16×C47C2211yescharacteristic
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C2×C22⋊D47D411yescharacteristic
63C22×Dic47—21no—
64C22×Dic47—21no—
65Q8×D47—22no—
66Q8×D47—41no—
67C2×C4×D47—21no—
68C2×C4×D47—21no—
69C2×C4×D47C2311yescharacteristic
70C2×Dic94—22no—
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94—21no—
74C2×Dic94—41no—
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77Q16×C47—41no—
78C2×C8×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625337—22no—
89#10625337—41no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4D411yescharacteristic
93C4⋊Dic47—21no—
94C4⋊Dic47—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47C2311yescharacteristic
97C4⋊Dic47C2311yescharacteristic
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47Q1614yescomplemented
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—42no—
131C2×Dic47—81no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—42no—
138C4×D47—81no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—42no—
143Dic94—42no—
144Dic94—81no—
145Dic94#4112yes—
146C8×C47—21no—
147C8×C47—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47C2×Q1612yes—
153C22×C47C22×D411yescharacteristic
154C2×D47—21no—
155C2×D47—21no—
156C2×D47C2×Q1612yes—
157C4×C47—21no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47C2×#4111yescharacteristic
163C4×C47H(5,𝔽2)11yescharacteristic
164Dic47—22no—
165Dic47—21no—
166Dic47—21no—
167Dic47—41no—
168Dic47—41no—
169Dic47—41no—
170Dic47C2×Q1612yes—
171#3299—471nomaximal, Sylow
172C2×C47—22no—
173C2×C47#54611yescharacteristic
174C2×C47C22×Q1611yescharacteristic
175C2×C47#57711yescharacteristic
176D47—22no—
177#554—471no—
178D4×Q8—471no—
179#487—471no—
180#484—471no—
181#484—471no—
182#477—471no—
183#467—471no—
184#467D4711yescharacteristic, complemented
185#462—471no—
186#451—471no—
187#451—471no—
188C4×Q16—471no—
189C8×D4—471no—
190C2×#103—471no—
191C2×#103—471no—
192C47#329911yescharacteristic, complemented, Sylow
193C22×Q8—471no—
194C22×Q8—471no—
195C2×Q16—471no—
196C2×Q16—471no—
197C2×Q16C2×D4711yescharacteristic
198C22×C8—471no—
199C22×C8C2×D4711yescharacteristic
200C4⋊Q8—471no—
201C4⋊Q8—471no—
202C4⋊Q8—941no—
203#125—941no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206C22⋊Q8—941no—
207C22⋊Q8—941no—
208C22⋊Q8—941no—
209C22⋊Q8—941no—
210C22⋊Q8C2×D4711yescharacteristic
211C22⋊Q8C2×D4711yescharacteristic
212C4×Q8—471no—
213C4×Q8—471no—
214C4×D4—471no—
215C4×D4—941no—
216C4×D4—941no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219#107—471no—
220#107—471no—
221#107C2×D4711yescharacteristic
222C4⋊C8—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103C2×D4711yescharacteristic
232#103C2×D4711yescharacteristic
233C22⋊C8—471no—
234C22⋊C8—471no—
235C4×C8—471no—
236C2×Q8—471no—
237C2×Q8—471no—
238C2×Q8—941no—
239C2×Q8—941no—
240C2×Q8—942no—
241C2×Q8—941no—
242C2×Q8—942no—
243C2×Q8—1881no—
244C2×Q8—1881no—
245C2×Q8C22×D4711yescharacteristic
246C2×Q8C22×D4711yescharacteristic
247C2×D4—471no—
248C22×C4—471no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4C22×D4711yescharacteristic
254Q16—41no—
255Q16—942no—
256Q16—1881no—
257C2×C8—41no—
258C2×C8—471no—
259C2×C8—471no—
260C2×C8—1881no—
261C2×C8C22×D4711yescharacteristic
262C2×C8C22×D4711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—471no—
266C4⋊C4—471no—
267C4⋊C4—471no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4—941no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4C22×D4711yescharacteristic
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—471no—
282C22⋊C4—471no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C42—471no—
286C42—941no—
287C42—941no—
288C23—471no—
289C23D4×D4711yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—472no—
295Q8—941no—
296Q8—941no—
297Q8—941no—
298Q8—3761no—
299Q8—1882no—
300Q8—1882no—
301D4—474no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
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—941no—
317C2×C4—3761no—
318C2×C4—3761no—
319C2×C4—1882no—
320C2×C4—1882no—
321C2×C4D4×D4711yescharacteristic
322C2×C4C23×D4711yescharacteristic
323C8—21no—
324C8—21no—
325C8—941no—
326C8—941no—
327C22—21no—
328C22—21no—
329C22—472no—
330C22—941no—
331C22—941no—
332C22Q16×D4712yes—
333C22C2×D4×D4711yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—472no—
340C4—941no—
341C4—942no—
342C4—941no—
343C4—1881no—
344C4—1881no—
345C4—1881no—
346C4#41×D4711yescharacteristic
347C4#1309406911yescharacteristic
348C2—22no—
349C2—942no—
350C2#1568976211yescharacteristic
351C2C2×Q16×D4711yescharacteristic
352C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3299
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. #15689472C2semidirect
4. #15689460C2semidirect
5. #15689456C2semidirect
6. #15689417C2semidirect
7. #15689363C2semidirect
8. #15689331C2semidirect
9. #15689278C2semidirect
10. #15689277C2semidirect
11. #15689215C2semidirect
13. C2×#13093949C2semidirect
14. #103×D47C2semidirect
15. C47×#467C2semidirect
125. C22⋊D47Q16semidirect
184. #467D47semidirect
192. C47#3299semidirect