Finite Group Databasebeta

← #20241639

Subgroups — #20241639

Order 6016.

564 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic47⋊C4C211yesmaximal, characteristic
2C22×Dic47⋊C4C211yesmaximal, 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⋊C4—22no—
15C2×Dic47⋊C4—22no—
16C2×Dic47⋊C4—22no—
17C2×Dic47⋊C4C414yescomplemented
18C47⋊#95—22no—
19C47⋊#95—22no—
20C47⋊#95—22no—
21C47⋊#95—22no—
22C23×C4×C47C2211yescharacteristic
23C23×C4×C47C2211yescharacteristic
24C23×C4×C47C2211yescharacteristic
25#95×C47—22no—
26C24×C47C2311yescharacteristic
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×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47C2×C412yes—
46C22×C4×C47D412yes—
47C22×C4×C47Q812yes—
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×Dic47D412yes—
74C22×Dic47Q812yes—
75C22×Dic47Q812yes—
76Dic47⋊C4—28no—
77Dic47⋊C4—28no—
78C23×C47C22×C411yescharacteristic
79C23×C47C2×D411yescharacteristic
80C23×C47C2×D411yescharacteristic
81C23×C47C2×D411yescharacteristic
82C23×C47C2×D411yescharacteristic
83C23×C47C2×D411yescharacteristic
84C23×C47C2×Q811yescharacteristic
85C23×C47C2×Q811yescharacteristic
86C23×C47C2×Q811yescharacteristic
87C23×C47#4111yescharacteristic
88C23×C47#4111yescharacteristic
89C23×C47#4111yescharacteristic
90C23×C47#4111yescharacteristic
91C23×C47#4111yescharacteristic
92C23×C47#4111yescharacteristic
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—22no—
100C2×C4×C47—22no—
101C2×C4×C47—22no—
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×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
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—22no—
127C2×Dic47—22no—
128C2×Dic47—22no—
129C2×Dic47—22no—
130C2×Dic47—22no—
131C2×Dic47—22no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C2×Dic47—41no—
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—41no—
140C2×Dic47C22⋊C414yes—
141C2×Dic47C4⋊C414yescomplemented
142C22×C47C2×C22⋊C411yescharacteristic
143C22×C47C2×C4⋊C411yescharacteristic
144C22×C47#11711yescharacteristic
145C22×C47C4×D411yescharacteristic
146C22×C47C4×D411yescharacteristic
147C22×C47C4×Q811yescharacteristic
148C22×C47C4×Q811yescharacteristic
149C22×C47#12011yescharacteristic
150C22×C47#12111yescharacteristic
151C22×C47#12111yescharacteristic
152C22×C47#12111yescharacteristic
153C22×C47#12111yescharacteristic
154C22×C47#12111yescharacteristic
155C22×C47#12111yescharacteristic
156C22×C47C22⋊Q811yescharacteristic
157C22×C47C22⋊Q811yescharacteristic
158C22×C47C22⋊Q811yescharacteristic
159C22×C47C22⋊Q811yescharacteristic
160C22×C47C22⋊Q811yescharacteristic
161C22×C47C22⋊Q811yescharacteristic
162C22×C47C22⋊Q811yescharacteristic
163C22×C47C22⋊Q811yescharacteristic
164C22×C47#12311yescharacteristic
165C22×C47#12311yescharacteristic
166C22×C47#12311yescharacteristic
167C22×C47#12411yescharacteristic
168C22×C47#12511yescharacteristic
169C22×C47#12511yescharacteristic
170C22×C47#12511yescharacteristic
171C22×C47#12511yescharacteristic
172C22×C47#12611yescharacteristic
173C22×C47#12611yescharacteristic
174C22×C47C4⋊Q811yescharacteristic
175C22×C47C4⋊Q811yescharacteristic
176C22×C47C4⋊Q811yescharacteristic
177C4×C47—42no—
178C4×C47—42no—
179C4×C47—42no—
180Dic47—24no—
181Dic47—24no—
182Dic47—42no—
183Dic47—42no—
184#1441—471nomaximal, Sylow
185C2×C47#38011yescharacteristic
186C2×C47#38611yescharacteristic
187C2×C47#38711yescharacteristic
188C2×C47#38711yescharacteristic
189C2×C47#38911yescharacteristic
190C2×C47#38911yescharacteristic
191C2×C47#39111yescharacteristic
192C2×C47#39411yescharacteristic
193C2×C47#39511yescharacteristic
194C2×C47#39611yescharacteristic
195C2×C47#39611yescharacteristic
196C2×C47#39811yescharacteristic
197C2×C47#39811yescharacteristic
198C2×C47#39811yescharacteristic
199C2×C47#40011yescharacteristic
200C22×C4⋊C4—471no—
201C22×C4⋊C4—471no—
202C2×#95—471no—
203C2×#95—471no—
204C2×#95—471no—
205C2×#95—471no—
206C2×#95D4711yescharacteristic
207C47#144111yescharacteristic, complemented, Sylow
208C23×C4—471no—
209C23×C4—471no—
210C23×C4—471no—
211C23×C4—471no—
212C23×C4C2×D4711yescharacteristic
213C23×C4C2×D4711yescharacteristic
214C23×C4C2×D4711yescharacteristic
215C2×C4⋊C4—474no—
216C2×C4⋊C4—942no—
217C2×C4⋊C4—942no—
218C2×C4⋊C4—942no—
219C2×C4⋊C4—942no—
220C2×C4⋊C4—942no—
221#95—22no—
222#95—942no—
223#95—942no—
224#95—942no—
225#95—942no—
226C24C22×D4711yescharacteristic
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—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—472no—
248C22×C4—472no—
249C22×C4—472no—
250C22×C4—472no—
251C22×C4—472no—
252C22×C4—472no—
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×C4—941no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—941no—
272C22×C4—941no—
273C22×C4Dic9412yes—
274C22×C4C4×D4712yes—
275C22×C4C22⋊D4712yes—
276C4⋊C4—948no—
277C4⋊C4—948no—
278C23C2×Dic9411yescharacteristic
279C23C2×C4×D4711yescharacteristic
280C23#1062535011yescharacteristic
281C23#1062535011yescharacteristic
282C23#1062535011yescharacteristic
283C23#1062535011yescharacteristic
284C23D4×D4711yescharacteristic
285C23D4×D4711yescharacteristic
286C23D4×D4711yescharacteristic
287C23D4×D4711yescharacteristic
288C23#1062535211yescharacteristic
289C23#1062535211yescharacteristic
290C23Q8×D4711yescharacteristic
291C23Q8×D4711yescharacteristic
292C23C2×C22⋊D4711yescharacteristic
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—474no—
315C2×C4—474no—
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—942no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4—942no—
330C2×C4—942no—
331C2×C4—942no—
332C2×C4—942no—
333C2×C4—942no—
334C2×C4—1881no—
335C2×C4—1881no—
336C2×C4—1881no—
337C2×C4—1881no—
338C2×C4—1881no—
339C2×C4—1881no—
340C2×C4—1881no—
341C2×C4—1881no—
342C22C22⋊C4×D4711yescharacteristic
343C22C4⋊C4×D4711yescharacteristic
344C22#1309398111yescharacteristic
345C22(C22⋊D47)⋊C411yescharacteristic
346C22C4×C22⋊D4711yescharacteristic
347C22#1309398911yescharacteristic
348C22C4×Dic9411yescharacteristic
349C22#1309399211yescharacteristic
350C22#1309399511yescharacteristic
351C22#1309399611yescharacteristic
352C22#1309399711yescharacteristic
353C22#1309399711yescharacteristic
354C22#1309399711yescharacteristic
355C22#1309399711yescharacteristic
356C22#1309400111yescharacteristic
357C22#1309400111yescharacteristic
358C22#1309400211yescharacteristic
359C22#1309400211yescharacteristic
360C22#1309400211yescharacteristic
361C22#1309400211yescharacteristic
362C22#1309400211yescharacteristic
363C22#1309400311yescharacteristic
364C22#1309400611yescharacteristic
365C22#1309400611yescharacteristic
366C22#1309400711yescharacteristic
367C22#1309401011yescharacteristic
368C22#1309401411yescharacteristic
369C22#1309401411yescharacteristic
370C22#1309401411yescharacteristic
371C22#1309401611yescharacteristic
372C22#1309401711yescharacteristic
373C22#1309401811yescharacteristic
374C22#1309402211yescharacteristic
375C22#1309402311yescharacteristic
376C22#1309402311yescharacteristic
377C4—42no—
378C4—42no—
379C4—42no—
380C4—944no—
381C4—944no—
382C4—1882no—
383C4—1882no—
384C2#1568898211yescharacteristic
385C2#1568899911yescharacteristic
386C2#1568900511yescharacteristic
387C2#1568900711yescharacteristic
388C2#1568901811yescharacteristic
389C2#1568902011yescharacteristic
390C2#1568902711yescharacteristic
391C2#1568903811yescharacteristic
392C2#1568904311yescharacteristic
393C2#1568904611yescharacteristic
394C2#1568904711yescharacteristic
395C2#1568905411yescharacteristic
396C2#1568905711yescharacteristic
397C2#1568905711yescharacteristic
398C2#1568906411yescharacteristic
subgroupG/H
center, FrattiniC24C22×D47
commutatorC23×C47C22×C4
FittingC2×#95×C47C2
socleC24×C47C23
hypercenterC2×#95D47
hypocenterC47#1441
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
17. C2×Dic47⋊C4C4semidirect
141. C2×Dic47C4⋊C4semidirect
207. C47#1441semidirect