Finite Group Databasebeta

← #20255257

Subgroups — #20255257

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
2Q8×C22⋊D47C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689457C211yesmaximal, characteristic, complemented
6#15689416C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689361C211yesmaximal, characteristic, complemented
9#15689331C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11Q16×Dic47C211yesmaximal, characteristic, complemented
12(C22⋊D47)⋊C8C211yesmaximal, characteristic
13C2×#13093948C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#451C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×#10625337C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19C2×C8×D47C2211yescharacteristic
20#13094023C2211yescharacteristic
21#13094022—21no—
22#13094022C2211yescharacteristic
23#13094014—21no—
24#13094004—21no—
25#13094003—21no—
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13094000—21no—
29#13094000C2211yescharacteristic
30#13094000C2211yescharacteristic
31Q8×Dic47C2211yescharacteristic
32Q8×Dic47C2211yescharacteristic
33C4×C22⋊D47—21no—
34C4×C22⋊D47C2211yescharacteristic
35(C22⋊D47)⋊C4—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic
38#13093958C2211yescharacteristic
39#13093958C2211yescharacteristic
40#13093957C2211yescharacteristic
41Dic47⋊C8C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093948C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×Q16×C47C2211yescharacteristic
54C2×Q16×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C2×Q8×C47C2311yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47D411yescharacteristic
68C22×Dic47—21no—
69Q8×D47—22no—
70Q8×D47—41no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77Q16×C47—22no—
78Q16×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85C22⋊Dic47D411yescharacteristic
86#10625337—41no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4D411yescharacteristic
90C4⋊Dic47—21no—
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95C4⋊Dic47C2311yescharacteristic
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4D411yescharacteristic
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8—41no—
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—
117Q8×C47—21no—
118Q8×C47—42no—
119Q8×C47#4112yes—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—42no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2411yescharacteristic
129C22⋊D47Q1614yescomplemented
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—81no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138C4×D47—21no—
139C4×D47—21no—
140C4×D47—42no—
141C4×D47—81no—
142Dic94—21no—
143Dic94—21no—
144Dic94—42no—
145Dic94—81no—
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—22no—
158C4×C47—21no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47—41no—
162C4×C47C2×#4111yescharacteristic
163C4×C47H(5,𝔽2)11yescharacteristic
164Dic47—21no—
165Dic47—21no—
166Dic47—41no—
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#467—471no—
185#462—471no—
186#451—471no—
187#451D4711yescharacteristic, complemented
188C4×Q16—471no—
189C8×D4—471no—
190C2×#103—471no—
191C2×#103—471no—
192C47#329911yescharacteristic, complemented, Sylow
193C22×Q8—471no—
194C22×Q8C2×D4711yescharacteristic
195C2×Q16—471no—
196C2×Q16C2×D4711yescharacteristic
197C2×Q16C2×D4711yescharacteristic
198C22×C8—471no—
199C22×C8—471no—
200C4⋊Q8—471no—
201C4⋊Q8—471no—
202C4⋊Q8—941no—
203#125—941no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206C22⋊Q8—471no—
207C22⋊Q8—941no—
208C22⋊Q8—941no—
209C22⋊Q8—941no—
210C22⋊Q8—941no—
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#107—471no—
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⋊C8C2×D4711yescharacteristic
235C4×C8—471no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—471no—
240C2×Q8—941no—
241C2×Q8—941no—
242C2×Q8—942no—
243C2×Q8—1881no—
244C2×Q8C22×D4711yescharacteristic
245C2×Q8C22×D4711yescharacteristic
246C2×Q8C22×D4711yescharacteristic
247C2×D4—471no—
248C22×C4—21no—
249C22×C4—471no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4C22×D4711yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—1881no—
257C2×C8—471no—
258C2×C8—471no—
259C2×C8—1881no—
260C2×C8—1881no—
261C2×C8C22×D4711yescharacteristic
262C2×C8C22×D4711yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—471no—
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⋊C4—941no—
278C4⋊C4C22×D4711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—471no—
281C22⋊C4—471no—
282C22⋊C4—941no—
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—21no—
295Q8—42no—
296Q8—941no—
297Q8—941no—
298Q8—3761no—
299Q8—1882no—
300Q8#1062535212yes—
301D4—474no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—471no—
310C2×C4—471no—
311C2×C4—471no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—3761no—
319C2×C4—3761no—
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—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—472no—
340C4—941no—
341C4—941no—
342C4—1881no—
343C4—1881no—
344C4—1881no—
345C4—1881no—
346C4C2×#1062535211yescharacteristic
347C4#1309406911yescharacteristic
348C2—22no—
349C2—942no—
350C2#1568976011yescharacteristic
351C2C2×Q16×D4711yescharacteristic
352C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47#3299
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #15689472C2semidirect
4. #15689459C2semidirect
5. #15689457C2semidirect
6. #15689416C2semidirect
7. #15689362C2semidirect
8. #15689361C2semidirect
9. #15689331C2semidirect
10. #15689277C2semidirect
11. Q16×Dic47C2semidirect
13. C2×#13093948C2semidirect
14. #103×D47C2semidirect
15. C47×#451C2semidirect
129. C22⋊D47Q16semidirect
187. #451D47semidirect
192. C47#3299semidirect