Finite Group Databasebeta

← #20255667

Subgroups — #20255667

Order 6016.

374 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#15689841C211yesmaximal, characteristic
2Q8×C22⋊D47C211yesmaximal, characteristic
3#15689472C211yesmaximal, characteristic, complemented
4#15689464C211yesmaximal, characteristic, complemented
5#15689462C211yesmaximal, characteristic, complemented
6#15689406C211yesmaximal, characteristic, complemented
7#15689381C211yesmaximal, characteristic, complemented
8#15689380C211yesmaximal, characteristic, complemented
9#15689332C211yesmaximal, characteristic, complemented
10#15689280C211yesmaximal, characteristic, complemented
11#15689279C211yesmaximal, characteristic, complemented
12#15689215C211yesmaximal, characteristic, complemented
13#15689199C211yesmaximal, characteristic
14#15689130C211yesmaximal, characteristic, complemented
15C47×#419C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Dic188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic
19C2×#10625337C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094022—21no—
23#13094022C2211yescharacteristic
24#13094018—21no—
25#13094017—21no—
26#13094010—21no—
27#13094004C2211yescharacteristic
28#13094003—21no—
29#13094003C2211yescharacteristic
30#13094003C2211yescharacteristic
31#13094000—21no—
32#13094000C2211yescharacteristic
33Q8×Dic47C2211yescharacteristic
34C4×Dic94—21no—
35#13093989C2211yescharacteristic
36C4×C22⋊D47—21no—
37C4×C22⋊D47C2211yescharacteristic
38#13093982C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093956C2211yescharacteristic
41#13093955C2211yescharacteristic
42Dic47⋊C8C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093948C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093947C2211yescharacteristic
48#13093947C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C22×Q8×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic
54#117×C47C2211yescharacteristic
55#103×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#103×C47C2211yescharacteristic
58#103×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×Q8×C47C2311yescharacteristic
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47D411yescharacteristic
67Q8×D47—22no—
68Q8×D47—41no—
69C2×C4×D47—21no—
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—21no—
72C2×Dic94—21no—
73C2×Dic94C2311yescharacteristic
74C2×Dic94C2311yescharacteristic
75M16×C47—41no—
76C2×C8×C47C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C4⋊C4×C47C2311yescharacteristic
79C4⋊C4×C47C2311yescharacteristic
80C22⋊C4×C47—21no—
81C42×C47—21no—
82C22⋊Dic47—21no—
83C22⋊Dic47—21no—
84C22⋊Dic47D411yescharacteristic
85#10625337—22no—
86#10625337—41no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4D411yescharacteristic
91C4⋊Dic47—21no—
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4D411yescharacteristic
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C4×Dic47C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109Dic188—41no—
110#10625324—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47C2×D411yescharacteristic
113Q8×C47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—42no—
117Q8×C47#4112yes—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—42no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—22no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47C2×D411yescharacteristic
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—42no—
138Dic94—21no—
139Dic94—21no—
140Dic94—21no—
141Dic94—21no—
142Dic94—42no—
143Dic94—42no—
144C8×C47—21no—
145C8×C47—21no—
146C47⋊C8—21no—
147C47⋊C8—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47C22×D411yescharacteristic
152C2×D47—21no—
153C2×D47—21no—
154C2×D47—21no—
155C4×C47—22no—
156C4×C47—21no—
157C4×C47—41no—
158C4×C47—41no—
159C4×C47—41no—
160C4×C47C2×#4111yescharacteristic
161C4×C47H(5,𝔽2)11yescharacteristic
162Dic47—21no—
163Dic47—21no—
164Dic47—41no—
165Dic47—41no—
166Dic47—41no—
167Dic47—41no—
168Dic47#13712yes—
169#3328—471nomaximal, Sylow
170C2×C47—41no—
171C2×C47#54611yescharacteristic
172C2×C47C2×#13711yescharacteristic
173C2×C47#57811yescharacteristic
174D47—41no—
175#556—471no—
176D4×Q8—471no—
177#487—471no—
178#485—471no—
179#485—471no—
180#475—471no—
181#470—471no—
182#470—471no—
183#462—471no—
184#451—471no—
185#451—471no—
186C4×Q16—471no—
187#436—471no—
188#419—471no—
189#419D4711yescharacteristic, complemented
190C47#332811yescharacteristic, complemented, Sylow
191C22×Q8—471no—
192C22×Q8C2×D4711yescharacteristic
193C2×Q16—471no—
194C2×Q16—471no—
195C2×Q16—471no—
196C2×M16—471no—
197C2×M16C2×D4711yescharacteristic
198C4⋊Q8—471no—
199C4⋊Q8—471no—
200C4⋊Q8—941no—
201#126—941no—
202#126—941no—
203#124—941no—
204C22⋊Q8—471no—
205C22⋊Q8—471no—
206C22⋊Q8—471no—
207C22⋊Q8—471no—
208C22⋊Q8—941no—
209C22⋊Q8—941no—
210C4×Q8—471no—
211C4×Q8—471no—
212C4×Q8—941no—
213C4×D4—471no—
214C4×D4—941no—
215#117—471no—
216#117C2×D4711yescharacteristic
217#107—471no—
218#106—471no—
219#106—471no—
220C4⋊C8—471no—
221#103—471no—
222#103—471no—
223#103—471no—
224#103—471no—
225#103—471no—
226#103—471no—
227#103C2×D4711yescharacteristic
228#103C2×D4711yescharacteristic
229#103C2×D4711yescharacteristic
230#103C2×D4711yescharacteristic
231C22⋊C8—471no—
232C22⋊C8—471no—
233C4×C8—471no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—41no—
237C2×Q8—471no—
238C2×Q8—471no—
239C2×Q8—941no—
240C2×Q8—941no—
241C2×Q8—942no—
242C2×Q8—1881no—
243C2×Q8C22×D4711yescharacteristic
244C2×Q8C22×D4711yescharacteristic
245C2×D4—471no—
246C22×C4—21no—
247C22×C4—471no—
248C22×C4—941no—
249C22×C4C22×D4711yescharacteristic
250Q16—942no—
251Q16—1881no—
252Q16—1881no—
253M16—41no—
254M16—1881no—
255C2×C8—471no—
256C2×C8—471no—
257C2×C8C22×D4711yescharacteristic
258C2×C8C22×D4711yescharacteristic
259C4⋊C4—471no—
260C4⋊C4—471no—
261C4⋊C4—471no—
262C4⋊C4—941no—
263C4⋊C4—941no—
264C4⋊C4—941no—
265C4⋊C4—941no—
266C4⋊C4—941no—
267C4⋊C4—941no—
268C4⋊C4—941no—
269C4⋊C4—941no—
270C4⋊C4—941no—
271C4⋊C4C22×D4711yescharacteristic
272C4⋊C4C22×D4711yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—471no—
275C22⋊C4—471no—
276C22⋊C4—941no—
277C22⋊C4—941no—
278C22⋊C4—941no—
279C22⋊C4—941no—
280C22⋊C4—941no—
281C42—21no—
282C42—471no—
283C42—941no—
284C42—941no—
285C42—941no—
286C23—471no—
287C23D4×D4711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—42no—
292Q8—941no—
293Q8—941no—
294Q8—941no—
295Q8—941no—
296Q8—1882no—
297Q8—1882no—
298Q8#1062535012yes—
299D4—942no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—471no—
308C2×C4—471no—
309C2×C4—471no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—1882no—
317C2×C4D4×D4711yescharacteristic
318C2×C4C23×D4711yescharacteristic
319C8—21no—
320C8—21no—
321C8—941no—
322C8—941no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—941no—
327C22—941no—
328C22—941no—
329C22C2×D4×D4711yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—472no—
336C4—941no—
337C4—941no—
338C4—1881no—
339C4—1881no—
340C4—1881no—
341C4—1881no—
342C4C2×#1062535011yescharacteristic
343C4#1309406911yescharacteristic
344C2—41no—
345C2—1881no—
346C2#1568976311yescharacteristic
347C2#137×D4711yescharacteristic
348C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3328
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #15689472C2semidirect
4. #15689464C2semidirect
5. #15689462C2semidirect
6. #15689406C2semidirect
7. #15689381C2semidirect
8. #15689380C2semidirect
9. #15689332C2semidirect
10. #15689280C2semidirect
11. #15689279C2semidirect
12. #15689215C2semidirect
14. #15689130C2semidirect
15. C47×#419C2semidirect
189. #419D47semidirect
190. C47#3328semidirect