Finite Group Databasebeta

← #20246663

Subgroups — #20246663

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093989C211yesmaximal, characteristic, complemented
2C2×#13093980C211yesmaximal, characteristic
3#15689064C211yesmaximal, characteristic, complemented
4#15689059C211yesmaximal, characteristic
5#15689056C211yesmaximal, characteristic, complemented
6#15689053C211yesmaximal, characteristic, complemented
7#15689046C211yesmaximal, characteristic
8#15689043C211yesmaximal, characteristic, complemented
9#15689035C211yesmaximal, characteristic
10C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
12#15688974C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic
14C22⋊C4×Dic47C211yesmaximal, characteristic
15C47×#396C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18#13093989—24no—
19#13093980—24no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C4×Dic47C2211yescharacteristic
32C2×C4×Dic47C2211yescharacteristic
33C2×C4×Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C2×C4⋊C4×C47C2211yescharacteristic
47C2×C4⋊C4×C47C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×Dic47—22no—
61C22×Dic47—22no—
62C22×Dic47Q814yescomplemented
63C22×Dic47C2311yescharacteristic
64C22×Dic47C2311yescharacteristic
65C22×Dic47C2311yescharacteristic
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C2×Dic94—22no—
72C2×Dic94—22no—
73C2×Dic94—22no—
74C4⋊C4×C47—22no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—22no—
77C22⋊C4×C47—22no—
78C22⋊C4×C47—22no—
79C22⋊C4×C47—22no—
80C22⋊Dic47—22no—
81C22⋊Dic47—22no—
82C22⋊Dic47—22no—
83C4⋊Dic47—22no—
84C4⋊Dic47—22no—
85Dic47⋊C4—22no—
86Dic47⋊C4—22no—
87Dic47⋊C4—22no—
88Dic47⋊C4—22no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91C4×Dic47—22no—
92C4×Dic47—22no—
93C4×Dic47—22no—
94C4×Dic47—22no—
95C4×Dic47—22no—
96C4×Dic47D414yes—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47C2×Q812yes—
104C23×C47C2411yescharacteristic
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—21no—
114C2×C4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47C2×D412yes—
121C2×C4×C47#4112yes—
122C2×C4×C47#4112yes—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—28no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47C2×D412yes—
142C2×Dic47C2×D412yes—
143C2×Dic47C2×Q812yes—
144C2×Dic47C2×Q812yes—
145C2×Dic47#4112yes—
146C2×Dic47#4112yes—
147C2×Dic47#4112yes—
148Dic94—28no—
149C22×C47—22no—
150C22×C47—22no—
151C22×C47—22no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47C22×D411yescharacteristic
157C22×C47C22×Q811yescharacteristic
158C22×C47C2×#4111yescharacteristic
159C22×C47C2×#4111yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47C2×#4111yescharacteristic
162C22×C47C2×#4111yescharacteristic
163C4×C47—22no—
164C4×C47—22no—
165C4×C47—22no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169Dic47—22no—
170Dic47—22no—
171Dic47—22no—
172Dic47—22no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47C22⋊Q814yes—
177#2396—471nomaximal, Sylow
178C2×C47—42no—
179C2×C47C2×C22⋊Q811yescharacteristic
180C2×C47#52511yescharacteristic
181C2×C47#52911yescharacteristic
182C2×C47#52911yescharacteristic
183C2×C47#53211yescharacteristic
184C2×C47#53311yescharacteristic
185C2×C47#53311yescharacteristic
186C2×C4×Q8—471no—
187C2×#117—471no—
188#400—471no—
189#399—471no—
190#398—471no—
191#398—471no—
192#396—471no—
193#396D4711yescharacteristic
194#395—471no—
195#393—471no—
196C4×C4⋊C4—471no—
197C4×C4⋊C4—471no—
198C4×C4⋊C4—471no—
199C4×C22⋊C4—471no—
200C4×C22⋊C4—471no—
201C47#239611yescharacteristic, complemented, Sylow
202C22×Q8—471no—
203C23×C4—471no—
204C4×Q8—944no—
205#117—944no—
206C2×C4⋊C4—471no—
207C2×C4⋊C4—471no—
208C2×C4⋊C4—471no—
209C2×C4⋊C4—471no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4C2×D4711yescharacteristic
215C2×C4⋊C4C2×D4711yescharacteristic
216C2×C4⋊C4C2×D4711yescharacteristic
217C2×C22⋊C4—471no—
218C2×C22⋊C4—471no—
219C2×C22⋊C4—471no—
220C2×C22⋊C4C2×D4711yescharacteristic
221C2×C22⋊C4C2×D4711yescharacteristic
222C2×C22⋊C4C2×D4711yescharacteristic
223C2×C42—471no—
224C2×C42—471no—
225C2×C42—471no—
226C2×C42—471no—
227C2×C42—471no—
228C2×C42—471no—
229#95—471no—
230#95—471no—
231#95—471no—
232#95—471no—
233#95—471no—
234#95—471no—
235#95—471no—
236#95—471no—
237#95—471no—
238#95C2×D4711yescharacteristic
239C24C22×D4711yescharacteristic
240C2×Q8—942no—
241C2×Q8—942no—
242C2×Q8—942no—
243C22×C4—471no—
244C22×C4—474no—
245C22×C4—471no—
246C22×C4—471no—
247C22×C4—471no—
248C22×C4—471no—
249C22×C4—471no—
250C22×C4—471no—
251C22×C4—471no—
252C22×C4—942no—
253C22×C4—942no—
254C22×C4C22×D4711yescharacteristic
255C22×C4C22×D4711yescharacteristic
256C22×C4C22×D4711yescharacteristic
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259C22×C4C22×D4711yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—942no—
264C4⋊C4—942no—
265C4⋊C4—942no—
266C4⋊C4—942no—
267C4⋊C4—942no—
268C4⋊C4—942no—
269C4⋊C4—942no—
270C4⋊C4—942no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—942no—
275C22⋊C4—942no—
276C22⋊C4—942no—
277C42—474no—
278C42—942no—
279C42—942no—
280C42—942no—
281C42—942no—
282C42—942no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23Q8×D4712yes—
290C23C23×D4711yescharacteristic
291Q8—948no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—472no—
308C2×C4—472no—
309C2×C4—472no—
310C2×C4—472no—
311C2×C4—472no—
312C2×C4—472no—
313C2×C4—472no—
314C2×C4—948no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—941no—
332C2×C4D4×D4712yes—
333C2×C4#1062535212yes—
334C2×C4#1062535212yes—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C2×D4×D4711yescharacteristic
343C22C2×Q8×D4711yescharacteristic
344C22#41×D4711yescharacteristic
345C22#41×D4711yescharacteristic
346C22#41×D4711yescharacteristic
347C22C2×#1062535211yescharacteristic
348C22C2×#1062535211yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—474no—
356C4—942no—
357C4—942no—
358C4—942no—
359C4—942no—
360C4—1881no—
361C4—1881no—
362C4—1881no—
363C2—42no—
364C2C22⋊Q8×D4711yescharacteristic
365C2#1568963311yescharacteristic
366C2#1568965411yescharacteristic
367C2#1568965611yescharacteristic
368C2#1568966811yescharacteristic
369C2#1568967511yescharacteristic
370C2#1568967511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2396
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13093989C2semidirect
3. #15689064C2semidirect
5. #15689056C2semidirect
6. #15689053C2semidirect
8. #15689043C2semidirect
10. C4⋊C4×Dic47C2semidirect
11. C4⋊C4×Dic47C2semidirect
12. #15688974C2semidirect
62. C22×Dic47Q8semidirect
201. C47#2396semidirect