Finite Group Databasebeta

← #20248305

Subgroups — #20248305

Order 6016.

620 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094002C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3C2×#13093989C211yesmaximal, characteristic, complemented
4C2×(C22⋊D47)⋊C4C211yesmaximal, characteristic
5#15689046C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689045C211yesmaximal, characteristic, complemented
8#15689023C211yesmaximal, characteristic
9#15689023C211yesmaximal, characteristic
10#15689020C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15688992C211yesmaximal, characteristic, complemented
13#15688982C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#396C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C22×C4×D47C2211yescharacteristic
20#13094002—24no—
21#13094001—24no—
22#13093989—24no—
23(C22⋊D47)⋊C4—24no—
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×Dic47⋊C4C2211yescharacteristic
34C2×Dic47⋊C4C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
36C2×C22⋊Dic47C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×(C2×D47)⋊C4C2211yescharacteristic
42C2×C4×Dic47C2211yescharacteristic
43C2×C4×Dic47C2211yescharacteristic
44C2×C4×Dic47C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C2×C4⋊C4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—22no—
64C2×C22⋊D47—22no—
65C2×C22⋊D47Q814yescomplemented
66C22×Dic47—22no—
67C22×Dic47—22no—
68C22×Dic47—22no—
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C22×Dic47C2311yescharacteristic
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—22no—
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94D414yescomplemented
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—41no—
85C22⋊C4×C47—22no—
86C22⋊C4×C47—22no—
87C22⋊C4×C47—41no—
88C22⋊Dic47—22no—
89C22⋊Dic47—41no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—41no—
94(C2×D47)⋊C4—41no—
95C4⋊Dic47—22no—
96C4⋊Dic47—41no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4—22no—
103Dic47⋊C4—22no—
104Dic47⋊C4—22no—
105Dic47⋊C4—22no—
106C4×Dic47—22no—
107C4×Dic47—22no—
108C4×Dic47D414yes—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47C2×Q812yes—
116C23×C47C2411yescharacteristic
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47C2×Q812yes—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47C2×D412yes—
141C2×C4×C47C2×D412yes—
142C22⋊D47—28no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—44no—
158C2×Dic47C2×D412yes—
159C2×Dic47C2×D412yes—
160C2×Dic47C2×D412yes—
161C2×Dic47C2×D412yes—
162C2×Dic47C2×Q812yes—
163C2×Dic47#4112yes—
164C2×Dic47#4112yes—
165C4×D47—44no—
166Dic94—28no—
167C22×C47—22no—
168C22×C47—22no—
169C22×C47—22no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47C22×D411yescharacteristic
175C22×C47C22×D411yescharacteristic
176C22×C47C22×Q811yescharacteristic
177C22×C47C2×#4111yescharacteristic
178C22×C47C2×#4111yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C472−1+411yescharacteristic
181C2×D47—22no—
182C2×D47—22no—
183C2×D47—22no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C4×C47—22no—
189C4×C47—22no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194Dic47—22no—
195Dic47—41no—
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47#12114yes—
200Dic47C22⋊Q814yescomplemented
201#2538—471nomaximal, Sylow
202C2×C47—42no—
203C2×C47C2×#12111yescharacteristic
204C2×C47C2×C22⋊Q811yescharacteristic
205C2×C47#53711yescharacteristic
206C2×C47D4×Q811yescharacteristic
207C2×C47#55011yescharacteristic
208C2×C47#55411yescharacteristic
209C2×C47#55611yescharacteristic
210D47—42no—
211C2×C22⋊Q8—471no—
212C2×C22⋊Q8—471no—
213C2×C4×Q8—471no—
214C2×C4×D4—471no—
215#396—471no—
216#396—471no—
217#396—471no—
218#396D4711yescharacteristic, complemented
219#390—471no—
220#390—471no—
221#389—471no—
222#389—471no—
223#384—471no—
224#380—471no—
225#380—471no—
226C47#253811yescharacteristic, complemented, Sylow
227C22×Q8—471no—
228C22×D4—471no—
229C23×C4—471no—
230C23×C4—471no—
231C22⋊Q8—944no—
232C22⋊Q8—944no—
233C4×Q8—944no—
234C4×D4—944no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4—471no—
239C2×C4⋊C4—471no—
240C2×C4⋊C4—471no—
241C2×C4⋊C4—471no—
242C2×C4⋊C4—471no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4C2×D4711yescharacteristic
247C2×C4⋊C4C2×D4711yescharacteristic
248C2×C4⋊C4C2×D4711yescharacteristic
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4C2×D4711yescharacteristic
257C2×C22⋊C4C2×D4711yescharacteristic
258C2×C22⋊C4C2×D4711yescharacteristic
259C2×C42—471no—
260C2×C42—471no—
261C2×C42—471no—
262#95—471no—
263#95—471no—
264#95—471no—
265#95C2×D4711yescharacteristic
266C24—471no—
267C24C22×D4711yescharacteristic
268C2×Q8—474no—
269C2×Q8—942no—
270C2×Q8—942no—
271C2×D4—474no—
272C2×D4—942no—
273C2×D4—942no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—942no—
282C22×C4—942no—
283C22×C4—942no—
284C22×C4—942no—
285C22×C4—942no—
286C22×C4—942no—
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291C22×C4C22×D4711yescharacteristic
292C22×C4C22×D4711yescharacteristic
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—942no—
299C4⋊C4—942no—
300C4⋊C4—942no—
301C4⋊C4—942no—
302C4⋊C4—942no—
303C4⋊C4—942no—
304C4⋊C4—942no—
305C4⋊C4—942no—
306C4⋊C4—1881no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—41no—
310C22⋊C4—942no—
311C22⋊C4—942no—
312C22⋊C4—942no—
313C22⋊C4—942no—
314C22⋊C4—1881no—
315C22⋊C4—1881no—
316C22⋊C4—1881no—
317C42—474no—
318C42—942no—
319C42—942no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—472no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23—941no—
332C23—941no—
333C23Q8×D4712yes—
334C23C23×D4711yescharacteristic
335Q8—948no—
336D4—948no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—472no—
354C2×C4—472no—
355C2×C4—472no—
356C2×C4—472no—
357C2×C4—472no—
358C2×C4—472no—
359C2×C4—472no—
360C2×C4—941no—
361C2×C4—941no—
362C2×C4—941no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—941no—
372C2×C4—941no—
373C2×C4—941no—
374C2×C4—1884no—
375C2×C4—1884no—
376C2×C4D4×D4712yes—
377C2×C4D4×D4712yes—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—942no—
386C22—942no—
387C22—942no—
388C22—1881no—
389C22—1881no—
390C22—1881no—
391C22—1881no—
392C22C2×D4×D4711yescharacteristic
393C22C2×D4×D4711yescharacteristic
394C22C2×Q8×D4711yescharacteristic
395C22#41×D4711yescharacteristic
396C22#41×D4711yescharacteristic
397C22#1309406911yescharacteristic
398C22#1309407111yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—474no—
406C4—474no—
407C4—942no—
408C4—1881no—
409C4—1881no—
410C4—1881no—
411C4—1881no—
412C2—42no—
413C2—1882no—
414C2#121×D4711yescharacteristic
415C2C22⋊Q8×D4711yescharacteristic
416C2#1568970011yescharacteristic
417C2#1568978611yescharacteristic
418C2#1568979111yescharacteristic
419C2#1568982711yescharacteristic
420C2#1568984011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2538
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13094002C2semidirect
2. C2×#13094001C2semidirect
3. C2×#13093989C2semidirect
5. #15689046C2semidirect
6. #15689045C2semidirect
7. #15689045C2semidirect
10. #15689020C2semidirect
11. #15689018C2semidirect
12. #15688992C2semidirect
13. #15688982C2semidirect
14. #15688981C2semidirect
15. C47×#396C2semidirect
65. C2×C22⋊D47Q8semidirect
81. C2×Dic94D4semidirect
200. Dic47C22⋊Q8semidirect
218. #396D47semidirect
226. C47#2538semidirect