Finite Group Databasebeta

← #20241654

Subgroups — #20241654

Order 6016.

520 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic47⋊C4C211yesmaximal, characteristic
2C2×C47⋊#95C211yesmaximal, characteristic
3C2×C47⋊#95C211yesmaximal, characteristic
4C2×C47⋊#95C211yesmaximal, characteristic
5C2×C47⋊#95C211yesmaximal, characteristic
6C2×C47⋊#95C211yesmaximal, characteristic
7C2×#95×C47C211yesmaximal, characteristic
8C23×Dic47C2211yescharacteristic
9C23×Dic47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C23×Dic47C2211yescharacteristic
12C2×Dic47⋊C4—22no—
13C2×Dic47⋊C4—22no—
14C2×Dic47⋊C4C414yescomplemented
15C47⋊#95—22no—
16C47⋊#95—22no—
17C47⋊#95—22no—
18C47⋊#95—22no—
19C47⋊#95—22no—
20C23×C4×C47C2211yescharacteristic
21C23×C4×C47C2211yescharacteristic
22C23×C4×C47C2211yescharacteristic
23#95×C47—22no—
24C24×C47C2311yescharacteristic
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47—21no—
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47C2×C412yes—
44C22×C4×C47D412yes—
45C22×C4×C47Q812yes—
46C22×Dic47—21no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49C22×Dic47—21no—
50C22×Dic47—21no—
51C22×Dic47—21no—
52C22×Dic47—21no—
53C22×Dic47—21no—
54C22×Dic47—21no—
55C22×Dic47—21no—
56C22×Dic47—21no—
57C22×Dic47—21no—
58C22×Dic47—21no—
59C22×Dic47—21no—
60C22×Dic47—21no—
61C22×Dic47—21no—
62C22×Dic47—21no—
63C22×Dic47—21no—
64C22×Dic47—21no—
65C22×Dic47—21no—
66C22×Dic47—21no—
67C22×Dic47—21no—
68C22×Dic47C2×C412yes—
69C22×Dic47C2×C412yes—
70C22×Dic47D412yes—
71C22×Dic47D412yes—
72C22×Dic47D412yes—
73C22×Dic47Q812yes—
74Dic47⋊C4—28no—
75C23×C47C22×C411yescharacteristic
76C23×C47C2×D411yescharacteristic
77C23×C47C2×D411yescharacteristic
78C23×C47C2×D411yescharacteristic
79C23×C47C2×D411yescharacteristic
80C23×C47C2×Q811yescharacteristic
81C23×C47C2×Q811yescharacteristic
82C23×C47#4111yescharacteristic
83C23×C47#4111yescharacteristic
84C23×C47#4111yescharacteristic
85C23×C47#4111yescharacteristic
86C23×C47#4111yescharacteristic
87C23×C47#4111yescharacteristic
88C23×C47#4111yescharacteristic
89C23×C47#4111yescharacteristic
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—22no—
95C2×C4×C47—22no—
96C2×C4×C47—22no—
97C2×C4×C47—22no—
98C2×C4×C47—22no—
99C2×C4×C47—41no—
100C2×C4×C47—41no—
101C2×C4×C47—41no—
102C2×C4×C47—41no—
103C2×C4×C47—41no—
104C2×C4×C47—41no—
105C2×C4×C47—41no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×Dic47—22no—
112C2×Dic47—22no—
113C2×Dic47—22no—
114C2×Dic47—22no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47—22no—
118C2×Dic47—22no—
119C2×Dic47—22no—
120C2×Dic47—22no—
121C2×Dic47—22no—
122C2×Dic47—22no—
123C2×Dic47—22no—
124C2×Dic47—22no—
125C2×Dic47—22no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47C22⋊C414yes—
139C22×C47C2×C22⋊C411yescharacteristic
140C22×C47#11711yescharacteristic
141C22×C47#11711yescharacteristic
142C22×C47C4×D411yescharacteristic
143C22×C47C4×D411yescharacteristic
144C22×C47C4×Q811yescharacteristic
145C22×C47C4×Q811yescharacteristic
146C22×C47#12111yescharacteristic
147C22×C47#12111yescharacteristic
148C22×C47C22⋊Q811yescharacteristic
149C22×C47C22⋊Q811yescharacteristic
150C22×C47C22⋊Q811yescharacteristic
151C22×C47C22⋊Q811yescharacteristic
152C22×C47C22⋊Q811yescharacteristic
153C22×C47C22⋊Q811yescharacteristic
154C22×C47#12311yescharacteristic
155C22×C47#12311yescharacteristic
156C22×C47#12311yescharacteristic
157C22×C47#12311yescharacteristic
158C22×C47#12311yescharacteristic
159C22×C47#12311yescharacteristic
160C22×C47#12311yescharacteristic
161C22×C47#12311yescharacteristic
162C22×C47#12411yescharacteristic
163C22×C47#12411yescharacteristic
164C22×C47#12511yescharacteristic
165C22×C47#12511yescharacteristic
166C22×C47#12511yescharacteristic
167C22×C47#12511yescharacteristic
168C22×C47#12611yescharacteristic
169C22×C47#12611yescharacteristic
170C22×C47#12611yescharacteristic
171C22×C47#12611yescharacteristic
172C22×C47#12711yescharacteristic
173C22×C47C4⋊Q811yescharacteristic
174C4×C47—42no—
175C4×C47—42no—
176C4×C47—42no—
177Dic47—24no—
178Dic47—42no—
179Dic47—42no—
180Dic47—42no—
181#1445—471nomaximal, Sylow
182C2×C47#38111yescharacteristic
183C2×C47#38711yescharacteristic
184C2×C47#38711yescharacteristic
185C2×C47#38711yescharacteristic
186C2×C47#38711yescharacteristic
187C2×C47#39011yescharacteristic
188C2×C47#39111yescharacteristic
189C2×C47#39711yescharacteristic
190C2×C47#39711yescharacteristic
191C2×C47#39811yescharacteristic
192C2×C47#39811yescharacteristic
193C2×C47#39911yescharacteristic
194C2×C47#39911yescharacteristic
195C2×C47#40011yescharacteristic
196C2×C47#40011yescharacteristic
197C22×C4⋊C4—471no—
198C2×#95—471no—
199C2×#95—471no—
200C2×#95—471no—
201C2×#95—471no—
202C2×#95—471no—
203C2×#95D4711yescharacteristic
204C47#144511yescharacteristic, complemented, Sylow
205C23×C4—471no—
206C23×C4—471no—
207C23×C4—471no—
208C23×C4—471no—
209C23×C4C2×D4711yescharacteristic
210C23×C4C2×D4711yescharacteristic
211C23×C4C2×D4711yescharacteristic
212C2×C4⋊C4—474no—
213C2×C4⋊C4—942no—
214C2×C4⋊C4—942no—
215#95—22no—
216#95—942no—
217#95—942no—
218#95—942no—
219#95—942no—
220#95—942no—
221C24C22×D4711yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—472no—
241C22×C4—472no—
242C22×C4—472no—
243C22×C4—472no—
244C22×C4—472no—
245C22×C4—472no—
246C22×C4—941no—
247C22×C4—941no—
248C22×C4—941no—
249C22×C4—941no—
250C22×C4—941no—
251C22×C4—941no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4Dic9412yes—
269C22×C4C4×D4712yes—
270C22×C4C22⋊D4712yes—
271C4⋊C4—948no—
272C23C2×Dic9411yescharacteristic
273C23C2×C4×D4711yescharacteristic
274C23#1062535011yescharacteristic
275C23#1062535011yescharacteristic
276C23#1062535011yescharacteristic
277C23#1062535011yescharacteristic
278C23D4×D4711yescharacteristic
279C23D4×D4711yescharacteristic
280C23D4×D4711yescharacteristic
281C23#1062535211yescharacteristic
282C23#1062535211yescharacteristic
283C23#1062535211yescharacteristic
284C23Q8×D4711yescharacteristic
285C23#1062535411yescharacteristic
286C23C2×C22⋊D4711yescharacteristic
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—474no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—942no—
315C2×C4—942no—
316C2×C4—942no—
317C2×C4—942no—
318C2×C4—942no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—942no—
322C2×C4—942no—
323C2×C4—942no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C2×C4—1881no—
331C2×C4—1881no—
332C2×C4—1881no—
333C2×C4—1881no—
334C2×C4—1881no—
335C2×C4—1881no—
336C22C22⋊C4×D4711yescharacteristic
337C22#1309398111yescharacteristic
338C22#1309398211yescharacteristic
339C22(C22⋊D47)⋊C411yescharacteristic
340C22C4×C22⋊D4711yescharacteristic
341C22#1309398911yescharacteristic
342C22C4×Dic9411yescharacteristic
343C22#1309399611yescharacteristic
344C22#1309399711yescharacteristic
345C22#1309400011yescharacteristic
346C22#1309400111yescharacteristic
347C22#1309400111yescharacteristic
348C22#1309400211yescharacteristic
349C22#1309400211yescharacteristic
350C22#1309400311yescharacteristic
351C22#1309400511yescharacteristic
352C22#1309400611yescharacteristic
353C22#1309400611yescharacteristic
354C22#1309400611yescharacteristic
355C22#1309400711yescharacteristic
356C22#1309400911yescharacteristic
357C22#1309400911yescharacteristic
358C22#1309400911yescharacteristic
359C22#1309401011yescharacteristic
360C22#1309401011yescharacteristic
361C22#1309401411yescharacteristic
362C22#1309401411yescharacteristic
363C22#1309401511yescharacteristic
364C22#1309401611yescharacteristic
365C22#1309401711yescharacteristic
366C22#1309401711yescharacteristic
367C22#1309401811yescharacteristic
368C22#1309401911yescharacteristic
369C22#1309402011yescharacteristic
370C22#1309402311yescharacteristic
371C4—42no—
372C4—42no—
373C4—42no—
374C4—944no—
375C4—1882no—
376C4—1882no—
377C4—1882no—
378C2#1568898511yescharacteristic
379C2#1568900411yescharacteristic
380C2#1568900511yescharacteristic
381C2#1568900711yescharacteristic
382C2#1568901011yescharacteristic
383C2#1568902311yescharacteristic
384C2#1568902711yescharacteristic
385C2#1568905111yescharacteristic
386C2#1568905211yescharacteristic
387C2#1568905611yescharacteristic
388C2#1568905711yescharacteristic
389C2#1568905811yescharacteristic
390C2#1568905911yescharacteristic
391C2#1568906411yescharacteristic
392C2#1568906511yescharacteristic
subgroupG/H
center, FrattiniC24C22×D47
commutatorC23×C47C22×C4
FittingC2×#95×C47C2
socleC24×C47C23
hypercenterC2×#95D47
hypocenterC47#1445
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
14. C2×Dic47⋊C4C4semidirect
204. C47#1445semidirect