Finite Group Databasebeta

← #20247064

Subgroups — #20247064

Order 6016.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094003C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic
3#15689065C211yesmaximal, characteristic, complemented
4#15689057C211yesmaximal, characteristic, complemented
5#15689055C211yesmaximal, characteristic, complemented
6#15689044C211yesmaximal, characteristic, complemented
7#15689027C211yesmaximal, characteristic, complemented
8#15689020C211yesmaximal, characteristic, complemented
9#15689010C211yesmaximal, characteristic, complemented
10#15689006C211yesmaximal, characteristic, complemented
11#15688996C211yesmaximal, characteristic
12#15688996C211yesmaximal, characteristic
13#15688986C211yesmaximal, characteristic
14#15688983C211yesmaximal, characteristic
15C2×#95×C47C211yesmaximal, characteristic
16C22×Dic94C2211yescharacteristic
17#13094003—24no—
18#13093983—24no—
19C2×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C23×C4×C47C2211yescharacteristic
47C23×C4×C47C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—41no—
61C22×C4×C47—41no—
62C22×C4×C47Q814yescomplemented
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C2×Dic94—22no—
78C2×Dic94—22no—
79C2×Dic94—41no—
80C22⋊Dic47—22no—
81C22⋊Dic47—22no—
82C22⋊Dic47—22no—
83C22⋊Dic47D414yes—
84C4⋊Dic47—22no—
85C4⋊Dic47—22no—
86C4⋊Dic47—22no—
87C4⋊Dic47—22no—
88C4⋊Dic47—41no—
89Dic47⋊C4—22no—
90Dic47⋊C4—22no—
91Dic47⋊C4—22no—
92Dic47⋊C4—22no—
93Dic47⋊C4—41no—
94Dic47⋊C4—41no—
95C4×Dic47—22no—
96C4×Dic47—22no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47C2×D412yes—
102C23×C47C2×Q812yes—
103C23×C47#4112yes—
104C23×C47C2411yescharacteristic
105C2×C4×C47—28no—
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×C47—44no—
121C2×C4×C47—44no—
122C2×C4×C47C2×Q812yes—
123C2×C4×C47C2×Q812yes—
124C2×C4×C47#4112yes—
125C2×C4×C47#4112yes—
126C2×Dic47—21no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
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×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47C2×D412yes—
149C2×Dic47C2×D412yes—
150Dic94—44no—
151C22×C47—22no—
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—22no—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47C22⋊Q814yes—
158C22×C47C22×D411yescharacteristic
159C22×C47C22×Q811yescharacteristic
160C22×C47C2×#4111yescharacteristic
161C22×C47C2×#4111yescharacteristic
162C22×C47C2×#4111yescharacteristic
163C22×C47H(5,𝔽2)11yescharacteristic
164C22×C472−1+411yescharacteristic
165C4×C47—22no—
166C4×C47—22no—
167C4×C47—22no—
168C4×C47—22no—
169C4×C47—41no—
170C4×C47—41no—
171Dic47—22no—
172Dic47—22no—
173Dic47—41no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179#2438—471nomaximal, Sylow
180C2×C47—24no—
181C2×C47C2×C22⋊Q811yescharacteristic
182C2×C47#53311yescharacteristic
183C2×C47#54411yescharacteristic
184C2×C47#54611yescharacteristic
185C2×C47#54711yescharacteristic
186C2×C47#55111yescharacteristic
187C2×C47#55211yescharacteristic
188C2×C22⋊Q8—471no—
189C2×#117—471no—
190#400—471no—
191#398—471no—
192#398—471no—
193#395—471no—
194#391—471no—
195#389—471no—
196#387—471no—
197#387—471no—
198#385—471no—
199#385—471no—
200#381—471no—
201#380—471no—
202C2×#95D4711yescharacteristic
203C47#243811yescharacteristic, complemented, Sylow
204C22×Q8—471no—
205C23×C4C2×D4711yescharacteristic
206C23×C4C2×D4711yescharacteristic
207C23×C4C2×D4711yescharacteristic
208C22⋊Q8—944no—
209#117—944no—
210C2×C4⋊C4—471no—
211C2×C4⋊C4—471no—
212C2×C4⋊C4—471no—
213C2×C4⋊C4—471no—
214C2×C4⋊C4—471no—
215C2×C4⋊C4—471no—
216C2×C4⋊C4—471no—
217C2×C4⋊C4—471no—
218C2×C4⋊C4—471no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C22⋊C4—471no—
222C2×C22⋊C4—471no—
223C2×C22⋊C4—471no—
224C2×C22⋊C4—471no—
225C2×C42—471no—
226C2×C42—471no—
227#95—471no—
228#95—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#95C2×D4711yescharacteristic
238#95C2×D4711yescharacteristic
239#95C2×D4711yescharacteristic
240#95C2×D4711yescharacteristic
241C24C22×D4711yescharacteristic
242C2×Q8—942no—
243C2×Q8—942no—
244C2×Q8—1881no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—471no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—471no—
261C22×C4Dic9414yescomplemented
262C22×C4C22×D4711yescharacteristic
263C22×C4C22×D4711yescharacteristic
264C22×C4C22×D4711yescharacteristic
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267C22×C4C22×D4711yescharacteristic
268C4⋊C4—942no—
269C4⋊C4—942no—
270C4⋊C4—942no—
271C4⋊C4—942no—
272C4⋊C4—942no—
273C4⋊C4—942no—
274C4⋊C4—942no—
275C4⋊C4—942no—
276C4⋊C4—1881no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C22⋊C4—474no—
280C22⋊C4—942no—
281C22⋊C4—942no—
282C22⋊C4—942no—
283C42—942no—
284C42—942no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×Dic9412yes—
290C23D4×D4712yes—
291C23#1062535212yes—
292C23C23×D4711yescharacteristic
293Q8—1884no—
294C2×C4—28no—
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—21no—
308C2×C4—21no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—472no—
312C2×C4—472no—
313C2×C4—941no—
314C2×C4—941no—
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×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4C2×Dic9412yes—
336C2×C4C2×Dic9412yes—
337C2×C4#1062535012yes—
338C2×C4#1062535012yes—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22#1309400114yes—
346C22C2×D4×D4711yescharacteristic
347C22C22×Dic9411yescharacteristic
348C22C2×#1062535211yescharacteristic
349C22C2×#1062535011yescharacteristic
350C22C2×#1062535011yescharacteristic
351C22#1309406911yescharacteristic
352C22#1309407211yescharacteristic
353C4—22no—
354C4—22no—
355C4—22no—
356C4—22no—
357C4—41no—
358C4—41no—
359C4—942no—
360C4—942no—
361C4—1881no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4—1881no—
367C2—24no—
368C2C2×#1309400111yescharacteristic
369C2#1568968011yescharacteristic
370C2#1568975411yescharacteristic
371C2#1568976311yescharacteristic
372C2#1568977411yescharacteristic
373C2#1568979911yescharacteristic
374C2#1568980811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#95×C47C2
hypercenterC2×#95D47
hypocenterC47#2438
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #15689065C2semidirect
4. #15689057C2semidirect
5. #15689055C2semidirect
6. #15689044C2semidirect
7. #15689027C2semidirect
8. #15689020C2semidirect
9. #15689010C2semidirect
10. #15689006C2semidirect
62. C22×C4×C47Q8semidirect
203. C47#2438semidirect
261. C22×C4Dic94semidirect