Finite Group Databasebeta

← #20247496

Subgroups — #20247496

Order 6016.

582 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094008C211yesmaximal, characteristic, complemented
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689059C211yesmaximal, characteristic, complemented
4#15689050C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689031C211yesmaximal, characteristic
7#15689023C211yesmaximal, characteristic, complemented
8#15689023C211yesmaximal, characteristic, complemented
9#15689012C211yesmaximal, characteristic, complemented
10#15689010C211yesmaximal, characteristic, complemented
11#15689008C211yesmaximal, characteristic, complemented
12#15689003C211yesmaximal, characteristic, complemented
13#15689002C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D47C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C23×Dic47C2211yescharacteristic
19#13094008—24no—
20#13093983—24no—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×C4×Dic47C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C47⋊#95C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C22×D4×C47C2211yescharacteristic
47C23×C4×C47C2211yescharacteristic
48C2×C22⋊C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51#95×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53C24×C47C2311yescharacteristic
54C24×C47C2311yescharacteristic
55C23×D47C2311yescharacteristic
56C2×D4×C47—22no—
57C2×D4×C47—22no—
58C2×D4×C47—41no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—22no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—22no—
68C2×C22⋊D47—22no—
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—41no—
72C2×C22⋊D47—41no—
73C22×Dic47—22no—
74C22×Dic47—22no—
75C22×Dic47—41no—
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C22×Dic47C2311yescharacteristic
83C22⋊C4×C47—22no—
84C22⋊C4×C47—22no—
85C22⋊C4×C47—41no—
86C22⋊Dic47—22no—
87C22⋊Dic47—22no—
88C22⋊Dic47—22no—
89C22⋊Dic47—41no—
90C22⋊Dic47—41no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4—41no—
96C4⋊Dic47—22no—
97C4⋊Dic47—22no—
98C4⋊Dic47D414yescomplemented
99Dic47⋊C4—22no—
100Dic47⋊C4—41no—
101Dic47⋊C4—41no—
102C4×Dic47—22no—
103C4×Dic47—22no—
104C4×Dic47—41no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—21no—
110C23×C47—21no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47#4112yes—
118C23×C47#4112yes—
119C23×C47C2411yescharacteristic
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—21no—
125C22×D47—21no—
126C22×D47—21no—
127D4×C47—44no—
128C2×C4×C47—28no—
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—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D412yes—
143C2×C4×C47#4112yes—
144C22⋊D47—44no—
145C22⋊D47—44no—
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—21no—
161C2×Dic47—21no—
162C2×Dic47—21no—
163C2×Dic47—21no—
164C2×Dic47—44no—
165C2×Dic47C2×D412yes—
166C2×Dic47C2×D412yes—
167C2×Dic47#4112yes—
168C22×C47—22no—
169C22×C47—22no—
170C22×C47—22no—
171C22×C47—22no—
172C22×C47—22no—
173C22×C47—22no—
174C22×C47—41no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47C22×D411yescharacteristic
183C22×C47C2×#4111yescharacteristic
184C22×C47C2×#4111yescharacteristic
185C22×C47C2×#4111yescharacteristic
186C22×C47C2×#4111yescharacteristic
187C22×C47H(5,𝔽2)11yescharacteristic
188C22×C47H(5,𝔽2)11yescharacteristic
189C2×D47—41no—
190C2×D47—41no—
191C2×D47—41no—
192C2×D47—41no—
193C2×D47—41no—
194C2×D47—41no—
195C2×D47—41no—
196C4×C47—22no—
197C4×C47—22no—
198C4×C47—41no—
199C4×C47—41no—
200C4×C47—41no—
201Dic47—22no—
202Dic47—22no—
203Dic47—22no—
204Dic47—41no—
205Dic47—41no—
206Dic47—41no—
207Dic47—41no—
208#2471—471nomaximal, Sylow
209C2×C47—42no—
210C2×C47—42no—
211C2×C47#52511yescharacteristic
212C2×C47#52911yescharacteristic
213C2×C47#54011yescharacteristic
214C2×C47#54611yescharacteristic
215C2×C47#55011yescharacteristic
216C2×C47#55111yescharacteristic
217C2×C47#55111yescharacteristic
218D47—81no—
219C2×#123—471no—
220C2×#117—471no—
221#399—471no—
222#397—471no—
223#396—471no—
224#392—471no—
225#390—471no—
226#390—471no—
227#388—471no—
228#387—471no—
229#387—471no—
230#386—471no—
231#386—471no—
232#386D4711yescharacteristic, complemented
233C4×C22⋊C4—471no—
234C47#247111yescharacteristic, complemented, Sylow
235C22×D4—471no—
236C22×D4—471no—
237C22×D4C2×D4711yescharacteristic
238C23×C4—471no—
239C23×C4C2×D4711yescharacteristic
240#123—944no—
241#117—944no—
242C2×C4⋊C4—471no—
243C2×C4⋊C4—471no—
244C2×C4⋊C4—471no—
245C2×C4⋊C4—471no—
246C2×C4⋊C4—471no—
247C2×C4⋊C4—471no—
248C2×C22⋊C4—471no—
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C22⋊C4—471no—
253C2×C22⋊C4—471no—
254C2×C22⋊C4—471no—
255C2×C22⋊C4—471no—
256C2×C22⋊C4—471no—
257C2×C22⋊C4—471no—
258C2×C22⋊C4C2×D4711yescharacteristic
259C2×C22⋊C4C2×D4711yescharacteristic
260C2×C22⋊C4C2×D4711yescharacteristic
261C2×C42—471no—
262C2×C42—471no—
263C2×C42—471no—
264#95—471no—
265#95—471no—
266#95—471no—
267#95—471no—
268#95—471no—
269#95—471no—
270#95C2×D4711yescharacteristic
271#95C2×D4711yescharacteristic
272C24—471no—
273C24C22×D4711yescharacteristic
274C24C22×D4711yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—942no—
279C2×D4—942no—
280C2×D4—942no—
281C2×D4—942no—
282C2×D4—1881no—
283C2×D4—1881no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—471no—
288C22×C4—471no—
289C22×C4—471no—
290C22×C4—471no—
291C22×C4—471no—
292C22×C4—471no—
293C22×C4—471no—
294C22×C4—942no—
295C22×C4—942no—
296C22×C4—1881no—
297C22×C4C22×D4711yescharacteristic
298C22×C4C22×D4711yescharacteristic
299C22×C4C22×D4711yescharacteristic
300C22×C4C22×D4711yescharacteristic
301C22×C4C22×D4711yescharacteristic
302C4⋊C4—474no—
303C4⋊C4—942no—
304C4⋊C4—942no—
305C4⋊C4—942no—
306C4⋊C4—1881no—
307C4⋊C4—1881no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—41no—
311C22⋊C4—942no—
312C22⋊C4—942no—
313C22⋊C4—942no—
314C22⋊C4—942no—
315C22⋊C4—942no—
316C22⋊C4—942no—
317C22⋊C4—1881no—
318C22⋊C4—1881no—
319C22⋊C4—1881no—
320C22⋊C4—1881no—
321C42—942no—
322C42—942no—
323C42—1881no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—941no—
337C23—941no—
338C23—941no—
339C23—941no—
340C23—941no—
341C23—941no—
342C23—941no—
343C23#1062535012yes—
344C23#1062535212yes—
345C23C23×D4711yescharacteristic
346D4—44no—
347D4—1884no—
348D4—1884no—
349C2×C4—28no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—472no—
364C2×C4—472no—
365C2×C4—472no—
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—941no—
375C2×C4—941no—
376C2×C4—941no—
377C2×C4—941no—
378C2×C4—941no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—1884no—
385C2×C4D4×D4712yes—
386C2×C4#1062535212yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—1881no—
402C22—1881no—
403C22—1881no—
404C22—1881no—
405C22—1881no—
406C22—1881no—
407C22—1881no—
408C22C2×D4×D4711yescharacteristic
409C22#41×D4711yescharacteristic
410C22C2×#1062535211yescharacteristic
411C22C2×#1062535211yescharacteristic
412C22C2×#1062535011yescharacteristic
413C22#1309406911yescharacteristic
414C22#1309407011yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—942no—
421C4—942no—
422C4—942no—
423C4—1881no—
424C4—1881no—
425C4—1881no—
426C4—1881no—
427C2—42no—
428C2—42no—
429C2—3761no—
430C2#1568962911yescharacteristic
431C2#1568965311yescharacteristic
432C2#1568972611yescharacteristic
433C2#1568976911yescharacteristic
434C2#1568979111yescharacteristic
435C2#1568979611yescharacteristic
436C2#1568979911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#386C2
hypercenter#386D47
hypocenterC47#2471
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13094008C2semidirect
2. C2×#13093983C2semidirect
3. #15689059C2semidirect
4. #15689050C2semidirect
5. #15689046C2semidirect
7. #15689023C2semidirect
8. #15689023C2semidirect
9. #15689012C2semidirect
10. #15689010C2semidirect
11. #15689008C2semidirect
12. #15689003C2semidirect
13. #15689002C2semidirect
14. C22⋊C4×Dic47C2semidirect
15. C47×#386C2semidirect
98. C4⋊Dic47D4semidirect
232. #386D47semidirect
234. C47#2471semidirect