Finite Group Databasebeta

← #20241649

Subgroups — #20241649

Order 6016.

476 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47⋊#95C211yesmaximal, 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
12C47⋊#95—22no—
13C47⋊#95—22no—
14C47⋊#95—22no—
15C47⋊#95—22no—
16C47⋊#95—22no—
17C47⋊#95C414yescomplemented
18C23×C4×C47C2211yescharacteristic
19C23×C4×C47C2211yescharacteristic
20C23×C4×C47C2211yescharacteristic
21#95×C47—22no—
22C24×C47C2311yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47—21no—
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×C47C2×C412yes—
42C22×C4×C47D412yes—
43C22×C4×C47Q812yes—
44C22×Dic47—21no—
45C22×Dic47—21no—
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—
72C23×C47C22×C411yescharacteristic
73C23×C47C2×D411yescharacteristic
74C23×C47C2×D411yescharacteristic
75C23×C47C2×D411yescharacteristic
76C23×C47C2×Q811yescharacteristic
77C23×C47#4111yescharacteristic
78C23×C47#4111yescharacteristic
79C23×C47#4111yescharacteristic
80C23×C47#4111yescharacteristic
81C23×C47#4111yescharacteristic
82C23×C47#4111yescharacteristic
83C23×C47#4111yescharacteristic
84C23×C47#4111yescharacteristic
85C23×C47#4111yescharacteristic
86C23×C47#4111yescharacteristic
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
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—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
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×Dic47—22no—
109C2×Dic47—22no—
110C2×Dic47—22no—
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—41no—
121C2×Dic47—41no—
122C2×Dic47—41no—
123C2×Dic47—41no—
124C2×Dic47—41no—
125C2×Dic47—41no—
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—
136C22×C47#11711yescharacteristic
137C22×C47#11711yescharacteristic
138C22×C47#11711yescharacteristic
139C22×C47C4×D411yescharacteristic
140C22×C47C4×D411yescharacteristic
141C22×C47C4×D411yescharacteristic
142C22×C47C4×Q811yescharacteristic
143C22×C47#12111yescharacteristic
144C22×C47#12111yescharacteristic
145C22×C47#12111yescharacteristic
146C22×C47C22⋊Q811yescharacteristic
147C22×C47C22⋊Q811yescharacteristic
148C22×C47C22⋊Q811yescharacteristic
149C22×C47#12311yescharacteristic
150C22×C47#12311yescharacteristic
151C22×C47#12311yescharacteristic
152C22×C47#12311yescharacteristic
153C22×C47#12311yescharacteristic
154C22×C47#12311yescharacteristic
155C22×C47#12411yescharacteristic
156C22×C47#12411yescharacteristic
157C22×C47#12411yescharacteristic
158C22×C47#12511yescharacteristic
159C22×C47#12511yescharacteristic
160C22×C47#12511yescharacteristic
161C22×C47#12611yescharacteristic
162C22×C47#12611yescharacteristic
163C22×C47#12611yescharacteristic
164C22×C47#12611yescharacteristic
165C22×C47#12611yescharacteristic
166C22×C47#12611yescharacteristic
167C22×C47#12611yescharacteristic
168C22×C47#12611yescharacteristic
169C22×C47#12611yescharacteristic
170C22×C47#12611yescharacteristic
171C4×C47—42no—
172C4×C47—42no—
173C4×C47—42no—
174Dic47—42no—
175Dic47—42no—
176Dic47—42no—
177Dic47—42no—
178#1443—471nomaximal, Sylow
179C2×C47#38311yescharacteristic
180C2×C47#38711yescharacteristic
181C2×C47#38711yescharacteristic
182C2×C47#38711yescharacteristic
183C2×C47#38811yescharacteristic
184C2×C47#38811yescharacteristic
185C2×C47#38811yescharacteristic
186C2×C47#39611yescharacteristic
187C2×C47#39711yescharacteristic
188C2×C47#39711yescharacteristic
189C2×C47#39711yescharacteristic
190C2×C47#40011yescharacteristic
191C2×C47#40011yescharacteristic
192C2×C47#40011yescharacteristic
193C2×C47#40111yescharacteristic
194C2×#95—471no—
195C2×#95—471no—
196C2×#95—471no—
197C2×#95—471no—
198C2×#95—471no—
199C2×#95—471no—
200C2×#95D4711yescharacteristic
201C47#144311yescharacteristic, complemented, Sylow
202C23×C4—471no—
203C23×C4—471no—
204C23×C4—471no—
205C23×C4—471no—
206C23×C4C2×D4711yescharacteristic
207C23×C4C2×D4711yescharacteristic
208C23×C4C2×D4711yescharacteristic
209#95—22no—
210#95—474no—
211#95—942no—
212#95—942no—
213#95—942no—
214#95—942no—
215#95—942no—
216C24C22×D4711yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
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—472no—
236C22×C4—472no—
237C22×C4—472no—
238C22×C4—472no—
239C22×C4—941no—
240C22×C4—941no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4—941no—
245C22×C4—941no—
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×C4Dic9412yes—
264C22×C4C4×D4712yes—
265C22×C4C22⋊D4712yes—
266C23C2×Dic9411yescharacteristic
267C23C2×C4×D4711yescharacteristic
268C23#1062535011yescharacteristic
269C23#1062535011yescharacteristic
270C23#1062535011yescharacteristic
271C23#1062535011yescharacteristic
272C23D4×D4711yescharacteristic
273C23D4×D4711yescharacteristic
274C23#1062535211yescharacteristic
275C23#1062535211yescharacteristic
276C23#1062535211yescharacteristic
277C23#1062535211yescharacteristic
278C23#1062535411yescharacteristic
279C23#1062535411yescharacteristic
280C23C2×C22⋊D4711yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—942no—
303C2×C4—942no—
304C2×C4—942no—
305C2×C4—942no—
306C2×C4—942no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—942no—
310C2×C4—942no—
311C2×C4—942no—
312C2×C4—942no—
313C2×C4—942no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1881no—
321C2×C4—1881no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4—1881no—
329C2×C4—1881no—
330C22#1309398011yescharacteristic
331C22#1309398111yescharacteristic
332C22#1309398211yescharacteristic
333C22(C22⋊D47)⋊C411yescharacteristic
334C22C4×C22⋊D4711yescharacteristic
335C22#1309398611yescharacteristic
336C22C4×Dic9411yescharacteristic
337C22#1309399511yescharacteristic
338C22#1309399611yescharacteristic
339C22#1309399711yescharacteristic
340C22#1309400111yescharacteristic
341C22#1309400111yescharacteristic
342C22#1309400311yescharacteristic
343C22#1309400511yescharacteristic
344C22#1309400611yescharacteristic
345C22#1309400711yescharacteristic
346C22#1309400911yescharacteristic
347C22#1309400911yescharacteristic
348C22#1309400911yescharacteristic
349C22#1309401011yescharacteristic
350C22#1309401011yescharacteristic
351C22#1309401311yescharacteristic
352C22#1309401511yescharacteristic
353C22#1309401511yescharacteristic
354C22#1309401611yescharacteristic
355C22#1309401711yescharacteristic
356C22#1309401711yescharacteristic
357C22#1309401711yescharacteristic
358C22#1309401711yescharacteristic
359C22#1309401811yescharacteristic
360C22#1309401911yescharacteristic
361C22#1309401911yescharacteristic
362C22#1309401911yescharacteristic
363C22#1309401911yescharacteristic
364C22#1309401911yescharacteristic
365C4—42no—
366C4—42no—
367C4—42no—
368C4—1882no—
369C4—1882no—
370C4—1882no—
371C4—1882no—
372C2#1568899011yescharacteristic
373C2#1568900611yescharacteristic
374C2#1568900711yescharacteristic
375C2#1568901011yescharacteristic
376C2#1568901111yescharacteristic
377C2#1568901211yescharacteristic
378C2#1568901311yescharacteristic
379C2#1568904611yescharacteristic
380C2#1568904911yescharacteristic
381C2#1568905111yescharacteristic
382C2#1568905211yescharacteristic
383C2#1568906211yescharacteristic
384C2#1568906511yescharacteristic
385C2#1568906511yescharacteristic
386C2C47⋊#40111yescharacteristic
subgroupG/H
center, FrattiniC24C22×D47
commutatorC23×C47C22×C4
FittingC2×#95×C47C2
socleC24×C47C23
hypercenterC2×#95D47
hypocenterC47#1443
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. C47⋊#95C4semidirect
201. C47#1443semidirect