Finite Group Databasebeta

← #20249662

Subgroups — #20249662

Order 6016.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094013C211yesmaximal, characteristic
3C2×#13094009C211yesmaximal, characteristic
4C2×#13094002C211yesmaximal, characteristic, complemented
5#15689058C211yesmaximal, characteristic, complemented
6#15689052C211yesmaximal, characteristic, complemented
7#15689047C211yesmaximal, characteristic, complemented
8#15689041C211yesmaximal, characteristic
9#15689036C211yesmaximal, characteristic, complemented
10#15689018C211yesmaximal, characteristic, complemented
11#15689013C211yesmaximal, characteristic, complemented
12#15689012C211yesmaximal, characteristic, complemented
13#15689005C211yesmaximal, characteristic, complemented
14#15688994C211yesmaximal, characteristic, complemented
15C47×#395C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×C4×D47C2211yescharacteristic
19#13094022—24no—
20#13094013—24no—
21#13094009—24no—
22#13094002—24no—
23C2×Dic47⋊C4C2211yescharacteristic
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×(C2×D47)⋊C4C2211yescharacteristic
31C2×(C2×D47)⋊C4C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×(C2×D47)⋊C4C2211yescharacteristic
40C2×(C2×D47)⋊C4C2211yescharacteristic
41C2×C4×Dic47C2211yescharacteristic
42C2×C4×Dic47C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C4⋊C4×C47C2211yescharacteristic
51C2×C4⋊C4×C47C2211yescharacteristic
52#95×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C23×D47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C2×Q8×C47—22no—
58C2×Q8×C47—22no—
59C2×Q8×C47—41no—
60C22×C4×C47C2311yescharacteristic
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×Dic47C2311yescharacteristic
68C22×Dic47C2311yescharacteristic
69C22×Dic47C2311yescharacteristic
70C22×Dic47C2311yescharacteristic
71C22×Dic47C2311yescharacteristic
72C22×Dic47C2311yescharacteristic
73C2×D188—22no—
74C2×D188—22no—
75C2×D188—41no—
76C2×C4×D47—22no—
77C2×C4×D47—22no—
78C2×C4×D47—41no—
79C2×Dic94—22no—
80C2×Dic94—22no—
81C2×Dic94—41no—
82C4⋊C4×C47—22no—
83C4⋊C4×C47—22no—
84C4⋊C4×C47—41no—
85(C2×D47)⋊C4—22no—
86(C2×D47)⋊C4—22no—
87(C2×D47)⋊C4—22no—
88(C2×D47)⋊C4—22no—
89(C2×D47)⋊C4—22no—
90(C2×D47)⋊C4—22no—
91(C2×D47)⋊C4—22no—
92(C2×D47)⋊C4—22no—
93(C2×D47)⋊C4—22no—
94(C2×D47)⋊C4—41no—
95(C2×D47)⋊C4D414yes—
96Dic47⋊C4—22no—
97Dic47⋊C4—22no—
98Dic47⋊C4—22no—
99Dic47⋊C4—22no—
100Dic47⋊C4—22no—
101Dic47⋊C4—22no—
102Dic47⋊C4D414yes—
103C4×Dic47—22no—
104C4×Dic47—22no—
105C23×C47C2411yescharacteristic
106C22×D47—21no—
107C22×D47—21no—
108C22×D47—21no—
109C22×D47—21no—
110C22×D47—21no—
111C22×D47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—21no—
117C22×D47—21no—
118C22×D47—21no—
119C22×D47C2×D412yes—
120Q8×C47—44no—
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×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—21no—
138C2×C4×C47—21no—
139C2×C4×C47—21no—
140C2×C4×C47C2×D412yes—
141C2×C4×C47C2×D412yes—
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×Dic47C2×D412yes—
157C2×Dic47C2×D412yes—
158C2×Dic47C2×D412yes—
159C2×Dic47#4112yes—
160D188—44no—
161C4×D47—44no—
162Dic94—44no—
163C22×C47C22×D411yescharacteristic
164C22×C47C22×D411yescharacteristic
165C22×C47C2×#4111yescharacteristic
166C22×C47H(5,𝔽2)11yescharacteristic
167C22×C472−1+411yescharacteristic
168C22×C472−1+411yescharacteristic
169C22×C472−1+411yescharacteristic
170C2×D47—22no—
171C2×D47—22no—
172C2×D47—22no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—41no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—41no—
184C4×C47—22no—
185C4×C47—22no—
186C4×C47—41no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47—41no—
190C4×C47—41no—
191Dic47—22no—
192Dic47—22no—
193Dic47—22no—
194Dic47—22no—
195Dic47—41no—
196Dic47—41no—
197#2674—471nomaximal, Sylow
198C2×C47#53611yescharacteristic
199C2×C47#53611yescharacteristic
200C2×C47#54211yescharacteristic
201C2×C47D4211yescharacteristic
202C2×C47#54711yescharacteristic
203C2×C47#54811yescharacteristic
204C2×C47#56311yescharacteristic
205D47—42no—
206D47—81no—
207C2×C4⋊Q8—471no—
208C2×#124—471no—
209C2×#123—471no—
210C2×C22⋊Q8—471no—
211#399—471no—
212#397—471no—
213#396—471no—
214#395D4711yescharacteristic, complemented
215#394—471no—
216#393—471no—
217#389—471no—
218#388—471no—
219#388—471no—
220#387—471no—
221#385—471no—
222C47#267411yescharacteristic, complemented, Sylow
223C22×Q8—471no—
224C22×Q8C2×D4711yescharacteristic
225C22×D4—471no—
226C23×C4—471no—
227C4⋊Q8—944no—
228#124—944no—
229#123—944no—
230C22⋊Q8—944no—
231C2×C4⋊C4—471no—
232C2×C4⋊C4—471no—
233C2×C4⋊C4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C4⋊C4—471no—
237C2×C4⋊C4—471no—
238C2×C4⋊C4C2×D4711yescharacteristic
239C2×C4⋊C4C2×D4711yescharacteristic
240C2×C4⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
249C2×C22⋊C4—471no—
250C2×C22⋊C4—471no—
251C2×C22⋊C4—471no—
252C2×C42—471no—
253C2×C42—471no—
254#95—471no—
255#95—471no—
256#95—471no—
257#95—471no—
258#95—471no—
259#95C2×D4711yescharacteristic
260#95C2×D4711yescharacteristic
261#95C2×D4711yescharacteristic
262C24—471no—
263C24—471no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×Q8—942no—
268C2×Q8—942no—
269C2×Q8—1881no—
270C2×D4—942no—
271C2×D4—942no—
272C2×D4—1881no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—471no—
277C22×C4—471no—
278C22×C4—471no—
279C22×C4—942no—
280C22×C4—942no—
281C22×C4—1881no—
282C22×C4C22×D4711yescharacteristic
283C22×C4C22×D4711yescharacteristic
284C22×C4C22×D4711yescharacteristic
285C22×C4C22×D4711yescharacteristic
286C22×C4C22×D4711yescharacteristic
287C22×C4C22×D4711yescharacteristic
288C22×C4C22×D4711yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—41no—
292C4⋊C4—474no—
293C4⋊C4—942no—
294C4⋊C4—942no—
295C4⋊C4—942no—
296C4⋊C4—942no—
297C4⋊C4—942no—
298C4⋊C4—942no—
299C22⋊C4—474no—
300C22⋊C4—942no—
301C22⋊C4—942no—
302C22⋊C4—942no—
303C22⋊C4—942no—
304C22⋊C4—942no—
305C22⋊C4—942no—
306C22⋊C4—942no—
307C22⋊C4—942no—
308C22⋊C4—942no—
309C22⋊C4—1881no—
310C42—942no—
311C42—942no—
312C23—472no—
313C23—941no—
314C23—941no—
315C23—941no—
316C23—941no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23—941no—
321C23—941no—
322C23—941no—
323C23—941no—
324C23—941no—
325C23—941no—
326C23C23×D4711yescharacteristic
327Q8—44no—
328Q8—1884no—
329D4—1884no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
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—472no—
350C2×C4—472no—
351C2×C4—472no—
352C2×C4—472no—
353C2×C4—941no—
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—1884no—
368C2×C4D4×D4712yes—
369C2×C4D4×D4712yes—
370C22—942no—
371C22—942no—
372C22—942no—
373C22—1881no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22—1881no—
384C22C2×D4×D4711yescharacteristic
385C22C2×D4×D4711yescharacteristic
386C22#41×D4711yescharacteristic
387C22#1309406911yescharacteristic
388C22#1309407211yescharacteristic
389C22#1309407211yescharacteristic
390C22#1309407211yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—942no—
399C4—942no—
400C4—942no—
401C4—942no—
402C4—1881no—
403C4—1881no—
404C2—3761no—
405C2—1882no—
406C2#1568969811yescharacteristic
407C2#1568969811yescharacteristic
408C2#1568974311yescharacteristic
409C2#1568975511yescharacteristic
410C2#1568977511yescharacteristic
411C2#1568978311yescharacteristic
412C2#1568987211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2674
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
4. C2×#13094002C2semidirect
5. #15689058C2semidirect
6. #15689052C2semidirect
7. #15689047C2semidirect
9. #15689036C2semidirect
10. #15689018C2semidirect
11. #15689013C2semidirect
12. #15689012C2semidirect
13. #15689005C2semidirect
14. #15688994C2semidirect
15. C47×#395C2semidirect
214. #395D47semidirect
222. C47#2674semidirect