Finite Group Databasebeta

← #20251007

Subgroups — #20251007

Order 6016.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47⋊#401C211yesmaximal, characteristic, complemented
2#15689063C211yesmaximal, characteristic, complemented
3#15689052C211yesmaximal, characteristic, complemented
4#15689039C211yesmaximal, characteristic, complemented
5#15689038C211yesmaximal, characteristic, complemented
6#15689031C211yesmaximal, characteristic
7#15689016C211yesmaximal, characteristic, complemented
8#15689012C211yesmaximal, characteristic, complemented
9#15689011C211yesmaximal, characteristic, complemented
10#15689003C211yesmaximal, characteristic, complemented
11#15689002C211yesmaximal, characteristic, complemented
12#15689000C211yesmaximal, characteristic, complemented
13#15688996C211yesmaximal, characteristic, complemented
14#15688981C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19C2×C4⋊Dic47C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×Dic47⋊C4C2211yescharacteristic
23C2×C22⋊Dic47C2211yescharacteristic
24C2×C22⋊Dic47C2211yescharacteristic
25C2×C22⋊Dic47C2211yescharacteristic
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
34C47⋊#95C2211yescharacteristic
35C47⋊#95C2211yescharacteristic
36C47⋊#95C2211yescharacteristic
37C47⋊#95C2211yescharacteristic
38C47⋊#95C2211yescharacteristic
39C47⋊#95C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C22×D4×C47C2211yescharacteristic
45C23×C4×C47C2211yescharacteristic
46C2×C22⋊C4×C47C2211yescharacteristic
47C2×C22⋊C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49#95×C47C2211yescharacteristic
50#95×C47C2211yescharacteristic
51C24×C47C2311yescharacteristic
52C24×C47C2311yescharacteristic
53C23×D47C2311yescharacteristic
54C2×D4×C47—22no—
55C2×D4×C47—22no—
56C2×D4×C47—41no—
57C22×C4×C47—41no—
58C22×C4×C47—41no—
59C22×C4×C47—41no—
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—22no—
66C2×C22⋊D47—22no—
67C2×C22⋊D47—41no—
68C2×C22⋊D47—41no—
69C2×C22⋊D47—41no—
70C2×C22⋊D47—41no—
71C22×Dic47—22no—
72C22×Dic47—41no—
73C22×Dic47—41no—
74C22×Dic47C2311yescharacteristic
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22⋊C4×C47—22no—
82C22⋊C4×C47—41no—
83C22⋊C4×C47—41no—
84C22⋊Dic47—22no—
85C22⋊Dic47—22no—
86C22⋊Dic47—41no—
87C22⋊Dic47—41no—
88C22⋊Dic47—41no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—41no—
91(C2×D47)⋊C4—41no—
92(C2×D47)⋊C4—41no—
93(C2×D47)⋊C4—41no—
94C4⋊Dic47—41no—
95Dic47⋊C4—41no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—41no—
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—21no—
102C23×C47—21no—
103C23×C47—21no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47#4112yes—
112C23×C47#4112yes—
113C23×C47C2411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121D4×C47—44no—
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×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—44no—
138C22⋊D47—44no—
139C22⋊D47—44no—
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—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—21no—
156C2×Dic47—21no—
157C2×Dic47—21no—
158C2×Dic47—21no—
159C2×Dic47—21no—
160C2×Dic47—44no—
161C2×Dic47#4112yes—
162C22×C47—22no—
163C22×C47—22no—
164C22×C47—22no—
165C22×C47—22no—
166C22×C47—22no—
167C22×C47—22no—
168C22×C47—41no—
169C22×C47—41no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47—41no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47C2×#4111yescharacteristic
177C22×C47C2×#4111yescharacteristic
178C22×C47C2×#4111yescharacteristic
179C22×C47H(5,𝔽2)11yescharacteristic
180C22×C47H(5,𝔽2)11yescharacteristic
181C22×C47H(5,𝔽2)11yescharacteristic
182C22×C47H(5,𝔽2)11yescharacteristic
183C2×D47—41no—
184C2×D47—41no—
185C2×D47—41no—
186C2×D47—41no—
187C2×D47—41no—
188C2×D47—41no—
189C2×D47—41no—
190C4×C47—41no—
191C4×C47—41no—
192C4×C47—41no—
193C4×C47—41no—
194C4×C47—41no—
195Dic47—22no—
196Dic47—41no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200Dic47—41no—
201Dic47—41no—
202#2778—471nomaximal, Sylow
203C2×C47—42no—
204C2×C47—42no—
205C2×C47#53811yescharacteristic
206C2×C47#53811yescharacteristic
207C2×C47#53811yescharacteristic
208C2×C47#55111yescharacteristic
209C2×C47#55311yescharacteristic
210C2×C47#55311yescharacteristic
211C2×C47#56011yescharacteristic
212D47—81no—
213#401—471no—
214#400—471no—
215#397—471no—
216#394—471no—
217#394—471no—
218#392—471no—
219#388—471no—
220#388—471no—
221#388—471no—
222#386—471no—
223#386—471no—
224#386—471no—
225#386D4711yescharacteristic, complemented
226#385—471no—
227#380—471no—
228C47#277811yescharacteristic, complemented, Sylow
229C22×D4—471no—
230C22×D4—471no—
231C22×D4C2×D4711yescharacteristic
232C23×C4—471no—
233C23×C4C2×D4711yescharacteristic
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C22⋊C4—471no—
239C2×C22⋊C4—471no—
240C2×C22⋊C4—471no—
241C2×C22⋊C4—471no—
242C2×C22⋊C4—471no—
243C2×C22⋊C4—471no—
244C2×C22⋊C4—471no—
245C2×C22⋊C4—471no—
246C2×C22⋊C4—471no—
247C2×C22⋊C4—471no—
248C2×C22⋊C4C2×D4711yescharacteristic
249C2×C22⋊C4C2×D4711yescharacteristic
250C2×C22⋊C4C2×D4711yescharacteristic
251C2×C42—471no—
252#95—471no—
253#95—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259#95—471no—
260#95—471no—
261#95—471no—
262#95C2×D4711yescharacteristic
263#95C2×D4711yescharacteristic
264C24—471no—
265C24C22×D4711yescharacteristic
266C24C22×D4711yescharacteristic
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—41no—
270C2×D4—942no—
271C2×D4—942no—
272C2×D4—1881no—
273C2×D4—1881no—
274C2×D4—1881no—
275C2×D4—1881no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—471no—
280C22×C4—471no—
281C22×C4—471no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—471no—
285C22×C4—471no—
286C22×C4—942no—
287C22×C4—1881no—
288C22×C4—1881no—
289C22×C4C22×D4711yescharacteristic
290C22×C4C22×D4711yescharacteristic
291C22×C4C22×D4711yescharacteristic
292C22×C4C22×D4711yescharacteristic
293C22×C4C22×D4711yescharacteristic
294C4⋊C4—1881no—
295C4⋊C4—1881no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—1881no—
305C22⋊C4—1881no—
306C22⋊C4—1881no—
307C22⋊C4—1881no—
308C22⋊C4—1881no—
309C22⋊C4—1881no—
310C22⋊C4—1881no—
311C42—1881no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—941no—
325C23—941no—
326C23—941no—
327C23—941no—
328C23—941no—
329C23—941no—
330C23—941no—
331C23#1062535012yes—
332C23#1062535212yes—
333C23C23×D4711yescharacteristic
334D4—44no—
335D4—1884no—
336D4—1884no—
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—44no—
353C2×C4—472no—
354C2×C4—941no—
355C2×C4—941no—
356C2×C4—941no—
357C2×C4—941no—
358C2×C4—941no—
359C2×C4—941no—
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—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—1881no—
390C22—1881no—
391C22—1881no—
392C22—1881no—
393C22—1881no—
394C22—1881no—
395C22—1881no—
396C22#41×D4711yescharacteristic
397C22C2×#1062535211yescharacteristic
398C22C2×#1062535011yescharacteristic
399C22#1309406911yescharacteristic
400C22#1309406911yescharacteristic
401C22#1309406911yescharacteristic
402C22#1309407011yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—942no—
409C4—1881no—
410C4—1881no—
411C4—1881no—
412C4—1881no—
413C4—1881no—
414C4—1881no—
415C2—42no—
416C2—42no—
417C2—3761no—
418C2#1568970611yescharacteristic
419C2#1568970911yescharacteristic
420C2#1568971011yescharacteristic
421C2#1568979911yescharacteristic
422C2#1568981611yescharacteristic
423C2#1568982211yescharacteristic
424C2#1568986211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2778
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C47⋊#401C2semidirect
2. #15689063C2semidirect
3. #15689052C2semidirect
4. #15689039C2semidirect
5. #15689038C2semidirect
7. #15689016C2semidirect
8. #15689012C2semidirect
9. #15689011C2semidirect
10. #15689003C2semidirect
11. #15689002C2semidirect
12. #15689000C2semidirect
13. #15688996C2semidirect
14. #15688981C2semidirect
15. C47×#386C2semidirect
225. #386D47semidirect
228. C47#2778semidirect