Finite Group Databasebeta

← #20246183

Subgroups — #20246183

Order 6016.

532 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094008C211yesmaximal, characteristic
2#15689023C211yesmaximal, characteristic
3#15689019C211yesmaximal, characteristic, complemented
4#15689016C211yesmaximal, characteristic, complemented
5#15689014C211yesmaximal, characteristic, complemented
6#15689013C211yesmaximal, characteristic, complemented
7#15689008C211yesmaximal, characteristic, complemented
8#15689006C211yesmaximal, characteristic, complemented
9#15688999C211yesmaximal, characteristic
10#15688997C211yesmaximal, characteristic, complemented
11#15688981C211yesmaximal, characteristic, complemented
12C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C23×Dic47C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13094008C418yescomplemented
20C2×C4⋊Dic47C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×(C2×D47)⋊C4C2211yescharacteristic
29C2×(C2×D47)⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×C4×Dic47C2211yescharacteristic
34C2×C4×Dic47C2211yescharacteristic
35C2×C4×Dic47C2211yescharacteristic
36C2×C4×Dic47C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C2×C4⋊C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C42×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52C24×C47C2311yescharacteristic
53C23×D47C2311yescharacteristic
54C22×C4×C47C2311yescharacteristic
55C22×C4×C47C2311yescharacteristic
56C22×C4×C47C2311yescharacteristic
57C22×C4×C47C2311yescharacteristic
58C22×C4×C47C2311yescharacteristic
59C22×C4×C47C2311yescharacteristic
60C2×C22⋊D47—41no—
61C2×C22⋊D47—41no—
62C2×C22⋊D47C2×C414yes—
63C22×Dic47—41no—
64C22×Dic47—41no—
65C22×Dic47C2×C414yescomplemented
66C22×Dic47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C2×C4×D47—22no—
74C2×C4×D47—41no—
75C2×C4×D47—41no—
76C4⋊C4×C47—41no—
77C22⋊C4×C47—22no—
78C22⋊C4×C47—41no—
79C22⋊C4×C47C2×C414yescomplemented
80C42×C47—22no—
81C22⋊Dic47—22no—
82C22⋊Dic47—41no—
83(C2×D47)⋊C4—22no—
84(C2×D47)⋊C4—41no—
85(C2×D47)⋊C4—41no—
86(C2×D47)⋊C4C2×C414yes—
87(C2×D47)⋊C4C2×C414yes—
88C4⋊Dic47—22no—
89C4⋊Dic47C2×C414yescomplemented
90C4⋊Dic47C2×C414yescomplemented
91Dic47⋊C4—41no—
92Dic47⋊C4—41no—
93Dic47⋊C4—41no—
94C4×Dic47—41no—
95C4×Dic47—41no—
96C4×Dic47—41no—
97C4×Dic47—41no—
98C23×C47—21no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47C22×C412yes—
105C23×C47C2411yescharacteristic
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47C22×C412yes—
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—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C22×C412yes—
129C2×C4×C47C22×C412yes—
130C2×C4×C47#4112yes—
131C22⋊D47—44no—
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×Dic47—21no—
149C2×Dic47—44no—
150C2×Dic47C22×C412yes—
151C2×Dic47C22×C412yes—
152C2×Dic47C22×C412yes—
153C2×Dic47#4112yes—
154C4×D47—44no—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47—22no—
158C22×C47—41no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47C23×C411yescharacteristic
163C22×C47C2×#4111yescharacteristic
164C22×C47C2×#4111yescharacteristic
165C22×C47H(5,𝔽2)11yescharacteristic
166C22×C47H(5,𝔽2)11yescharacteristic
167C22×C47H(5,𝔽2)11yescharacteristic
168C22×C472−1+411yescharacteristic
169C2×D47—22no—
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C4×C47—22no—
177C4×C47—22no—
178C4×C47—22no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47—41no—
182Dic47—22no—
183Dic47—22no—
184Dic47—22no—
185Dic47—22no—
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189#2335—471nomaximal, Sylow
190C2×C47—42no—
191C2×C47C4×#4111yescharacteristic
192C2×C47#51811yescharacteristic
193C2×C47#52011yescharacteristic
194C2×C47#53811yescharacteristic
195C2×C47#53911yescharacteristic
196C2×C47#54011yescharacteristic
197C2×C47#54211yescharacteristic
198D47—42no—
199C2×#123—471no—
200#390—471no—
201#389—471no—
202#388—471no—
203#388—471no—
204#388—471no—
205#388D4711yescharacteristic, complemented
206#387—471no—
207#387—471no—
208#386—471no—
209#385—471no—
210#380—471no—
211C4×C4⋊C4—471no—
212C4×C22⋊C4—471no—
213C4×C22⋊C4—471no—
214C47#233511yescharacteristic, complemented, Sylow
215C22×D4—471no—
216C23×C4—471no—
217C23×C4—471no—
218#123—478no—
219C2×C4⋊C4—471no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4C2×D4711yescharacteristic
226C2×C22⋊C4—471no—
227C2×C22⋊C4—471no—
228C2×C22⋊C4—471no—
229C2×C22⋊C4—471no—
230C2×C22⋊C4—471no—
231C2×C22⋊C4—471no—
232C2×C22⋊C4—471no—
233C2×C22⋊C4C2×D4711yescharacteristic
234C2×C22⋊C4C2×D4711yescharacteristic
235C2×C22⋊C4C2×D4711yescharacteristic
236C2×C42—471no—
237C2×C42—471no—
238C2×C42—471no—
239C2×C42—471no—
240C2×C42C2×D4711yescharacteristic
241#95—471no—
242#95—471no—
243#95—471no—
244#95—471no—
245#95—471no—
246#95—471no—
247#95—471no—
248#95—471no—
249#95C2×D4711yescharacteristic
250#95C2×D4711yescharacteristic
251C24—471no—
252C24C22×D4711yescharacteristic
253C2×D4—474no—
254C2×D4—1881no—
255C2×D4—1881no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—474no—
261C22×C4—471no—
262C22×C4—471no—
263C22×C4—471no—
264C22×C4—942no—
265C22×C4—1881no—
266C22×C4—1881no—
267C22×C4—1881no—
268C22×C4—1881no—
269C22×C4C22×D4711yescharacteristic
270C22×C4C22×D4711yescharacteristic
271C22×C4C22×D4711yescharacteristic
272C22×C4C22×D4711yescharacteristic
273C22×C4C22×D4711yescharacteristic
274C22×C4C22×D4711yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—474no—
277C4⋊C4—474no—
278C4⋊C4—942no—
279C4⋊C4—1881no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—474no—
285C22⋊C4—474no—
286C22⋊C4—942no—
287C22⋊C4—942no—
288C22⋊C4—1881no—
289C22⋊C4—1881no—
290C22⋊C4—1881no—
291C22⋊C4C4×D4714yescomplemented
292C42—22no—
293C42—1881no—
294C42—1881no—
295C42—1881no—
296C42—1881no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—472no—
304C23—941no—
305C23—941no—
306C23—941no—
307C23—941no—
308C23—941no—
309C23—941no—
310C23C2×C4×D4712yes—
311C23C23×D4711yescharacteristic
312D4—1884no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—472no—
329C2×C4—472no—
330C2×C4—472no—
331C2×C4—472no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—941no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—1884no—
350C2×C4—1884no—
351C2×C4C2×C4×D4712yes—
352C2×C4C2×C4×D4712yes—
353C2×C4#1062535212yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—942no—
362C22—942no—
363C22—942no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22C22×C4×D4711yescharacteristic
369C22#41×D4711yescharacteristic
370C22C2×#1062535211yescharacteristic
371C22#1309406911yescharacteristic
372C22#1309407011yescharacteristic
373C22#1309407011yescharacteristic
374C22#1309407111yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—942no—
382C4—942no—
383C4—942no—
384C4—942no—
385C4—1881no—
386C4—1881no—
387C4—1881no—
388C2—42no—
389C2—1882no—
390C2C4×#1062535211yescharacteristic
391C2#1568959711yescharacteristic
392C2#1568960211yescharacteristic
393C2#1568970711yescharacteristic
394C2#1568971711yescharacteristic
395C2#1568972611yescharacteristic
396C2#1568973911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#388C2
socleC23×C47C24
hypercenter#388D47
hypocenterC47#2335
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
3. #15689019C2semidirect
4. #15689016C2semidirect
5. #15689014C2semidirect
6. #15689013C2semidirect
7. #15689008C2semidirect
8. #15689006C2semidirect
10. #15688997C2semidirect
11. #15688981C2semidirect
12. C4×C4⋊Dic47C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. #15688970C2semidirect
15. C47×#388C2semidirect
19. #13094008C4semidirect
65. C22×Dic47C2×C4semidirect
79. C22⋊C4×C47C2×C4semidirect
89. C4⋊Dic47C2×C4semidirect
90. C4⋊Dic47C2×C4semidirect
205. #388D47semidirect
214. C47#2335semidirect
291. C22⋊C4C4×D47semidirect