Finite Group Databasebeta

← #20246951

Subgroups — #20246951

Order 6016.

632 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094010C211yesmaximal, characteristic, complemented
2C2×#13094001C211yesmaximal, characteristic, complemented
3C2×#13093996C211yesmaximal, characteristic
4C2×C4×Dic94C211yesmaximal, characteristic, complemented
5#15689046C211yesmaximal, characteristic, complemented
6#15689045C211yesmaximal, characteristic, complemented
7#15689039C211yesmaximal, characteristic, complemented
8#15689037C211yesmaximal, characteristic, complemented
9#15689023C211yesmaximal, characteristic, complemented
10#15689023C211yesmaximal, characteristic, complemented
11#15689018C211yesmaximal, characteristic, complemented
12#15689016C211yesmaximal, characteristic, complemented
13#15689014C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
15C47×#390C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C23×Dic47C2211yescharacteristic
20#13094010—24no—
21#13094001—24no—
22#13093996—24no—
23C4×Dic94—24no—
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
29C2×Dic47⋊C4C2211yescharacteristic
30C2×Dic47⋊C4C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×C22⋊Dic47C2211yescharacteristic
35C2×C22⋊Dic47C2211yescharacteristic
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
43C2×C4×Dic47C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49C2×C4⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C42×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C24×C47C2311yescharacteristic
57C23×D47C2311yescharacteristic
58C2×D4×C47—22no—
59C2×D4×C47—22no—
60C2×D4×C47—41no—
61C22×C4×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C2×C22⋊D47—22no—
67C2×C22⋊D47—22no—
68C2×C22⋊D47—22no—
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—41no—
72C22×Dic47—22no—
73C22×Dic47—22no—
74C22×Dic47—22no—
75C22×Dic47C2311yescharacteristic
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C2×Dic94—22no—
83C2×Dic94—22no—
84C2×Dic94D414yescomplemented
85C4⋊C4×C47—41no—
86C22⋊C4×C47—22no—
87C22⋊C4×C47—22no—
88C22⋊C4×C47—22no—
89C22⋊C4×C47—22no—
90C42×C47—22no—
91C22⋊Dic47—22no—
92C22⋊Dic47—22no—
93C22⋊Dic47—22no—
94C22⋊Dic47—22no—
95C22⋊Dic47—41no—
96(C2×D47)⋊C4—22no—
97(C2×D47)⋊C4—22no—
98(C2×D47)⋊C4—22no—
99(C2×D47)⋊C4—22no—
100(C2×D47)⋊C4—41no—
101C4⋊Dic47—22no—
102C4⋊Dic47—22no—
103Dic47⋊C4—22no—
104Dic47⋊C4—22no—
105Dic47⋊C4—22no—
106Dic47⋊C4—41no—
107Dic47⋊C4D414yes—
108C4×Dic47—22no—
109C4×Dic47—22no—
110C4×Dic47—22no—
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—21no—
116C23×C47—21no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47#4112yes—
125C23×C47C2411yescharacteristic
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133D4×C47—44no—
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×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—21no—
146C2×C4×C47C2×D412yes—
147C2×C4×C47C2×D412yes—
148C2×C4×C47#4112yes—
149C22⋊D47—44no—
150C22⋊D47—44no—
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—21no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—44no—
168C2×Dic47C2×D412yes—
169C2×Dic47C2×D412yes—
170C2×Dic47C2×D412yes—
171C2×Dic47C2×D412yes—
172C2×Dic47#4112yes—
173Dic94—28no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—41no—
184C22×C47—41no—
185C22×C47—41no—
186C22×C47—41no—
187C22×C47—41no—
188C22×C47C22×D411yescharacteristic
189C22×C47C22×D411yescharacteristic
190C22×C47C2×#4111yescharacteristic
191C22×C47C2×#4111yescharacteristic
192C22×C47C2×#4111yescharacteristic
193C22×C47H(5,𝔽2)11yescharacteristic
194C22×C472−1+411yescharacteristic
195C2×D47—41no—
196C2×D47—41no—
197C2×D47—41no—
198C2×D47—41no—
199C2×D47—41no—
200C2×D47—41no—
201C2×D47—41no—
202C4×C47—22no—
203C4×C47—22no—
204C4×C47—22no—
205C4×C47—41no—
206C4×C47—41no—
207Dic47—22no—
208Dic47—22no—
209Dic47—41no—
210Dic47—41no—
211Dic47—41no—
212Dic47—41no—
213Dic47#12114yes—
214#2426—471nomaximal, Sylow
215C2×C47—42no—
216C2×C47—81no—
217C2×C47C2×#12111yescharacteristic
218C2×C47#52911yescharacteristic
219C2×C47#54211yescharacteristic
220C2×C47#54611yescharacteristic
221C2×C47#54811yescharacteristic
222C2×C47#54811yescharacteristic
223C2×C47#55011yescharacteristic
224D47—81no—
225C2×#124—471no—
226C2×C22⋊Q8—471no—
227C2×#121—471no—
228C2×C4×Q8—471no—
229#396—471no—
230#396—471no—
231#394—471no—
232#394—471no—
233#390—471no—
234#390—471no—
235#390D4711yescharacteristic, complemented
236#389—471no—
237#388—471no—
238#388—471no—
239C4×C22⋊C4—471no—
240C47#242611yescharacteristic, complemented, Sylow
241C22×Q8—471no—
242C22×D4—471no—
243C22×D4—471no—
244C22×D4C2×D4711yescharacteristic
245C23×C4—471no—
246#124—944no—
247C22⋊Q8—944no—
248#121—944no—
249C4×Q8—944no—
250C2×C4⋊C4—471no—
251C2×C4⋊C4—471no—
252C2×C4⋊C4—471no—
253C2×C4⋊C4—471no—
254C2×C4⋊C4—471no—
255C2×C4⋊C4—471no—
256C2×C4⋊C4—471no—
257C2×C4⋊C4C2×D4711yescharacteristic
258C2×C22⋊C4—471no—
259C2×C22⋊C4—471no—
260C2×C22⋊C4—471no—
261C2×C22⋊C4—471no—
262C2×C22⋊C4—471no—
263C2×C22⋊C4—471no—
264C2×C22⋊C4—471no—
265C2×C22⋊C4—471no—
266C2×C22⋊C4—471no—
267C2×C22⋊C4—471no—
268C2×C22⋊C4C2×D4711yescharacteristic
269C2×C22⋊C4C2×D4711yescharacteristic
270C2×C22⋊C4C2×D4711yescharacteristic
271C2×C22⋊C4C2×D4711yescharacteristic
272C2×C42—471no—
273C2×C42—471no—
274C2×C42—471no—
275C2×C42C2×D4711yescharacteristic
276#95—471no—
277#95—471no—
278#95—471no—
279#95—471no—
280C24—471no—
281C24C22×D4711yescharacteristic
282C24C22×D4711yescharacteristic
283C2×Q8—474no—
284C2×Q8—942no—
285C2×Q8—942no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—41no—
289C2×D4—942no—
290C2×D4—942no—
291C2×D4—942no—
292C2×D4—942no—
293C2×D4—942no—
294C2×D4—1881no—
295C22×C4—471no—
296C22×C4—471no—
297C22×C4—471no—
298C22×C4—471no—
299C22×C4—471no—
300C22×C4—471no—
301C22×C4—471no—
302C22×C4—942no—
303C22×C4—942no—
304C22×C4—942no—
305C22×C4C22×D4711yescharacteristic
306C22×C4C22×D4711yescharacteristic
307C22×C4C22×D4711yescharacteristic
308C22×C4C22×D4711yescharacteristic
309C22×C4C22×D4711yescharacteristic
310C4⋊C4—41no—
311C4⋊C4—474no—
312C4⋊C4—942no—
313C4⋊C4—942no—
314C4⋊C4—942no—
315C4⋊C4—942no—
316C4⋊C4—942no—
317C4⋊C4—1881no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—942no—
323C22⋊C4—942no—
324C22⋊C4—942no—
325C22⋊C4—942no—
326C22⋊C4—942no—
327C22⋊C4—942no—
328C22⋊C4—942no—
329C22⋊C4—942no—
330C22⋊C4—1881no—
331C22⋊C4—1881no—
332C42—22no—
333C42—942no—
334C42—942no—
335C42—942no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—941no—
350C23—941no—
351C23—941no—
352C23—941no—
353C23—941no—
354C23—941no—
355C23—941no—
356C23#1062535012yes—
357C23C23×D4711yescharacteristic
358Q8—948no—
359D4—44no—
360D4—1884no—
361D4—1884no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—472no—
375C2×C4—472no—
376C2×C4—472no—
377C2×C4—472no—
378C2×C4—472no—
379C2×C4—941no—
380C2×C4—941no—
381C2×C4—941no—
382C2×C4—941no—
383C2×C4—941no—
384C2×C4—941no—
385C2×C4—941no—
386C2×C4—941no—
387C2×C4—941no—
388C2×C4—941no—
389C2×C4—941no—
390C2×C4—941no—
391C2×C4—941no—
392C2×C4—941no—
393C2×C4—941no—
394C2×C4—941no—
395C2×C4—1884no—
396C2×C4D4×D4712yes—
397C2×C4D4×D4712yes—
398C2×C4#1062535212yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—1881no—
414C22—1881no—
415C22—1881no—
416C22—1881no—
417C22—1881no—
418C22—1881no—
419C22—1881no—
420C22C2×D4×D4711yescharacteristic
421C22C2×D4×D4711yescharacteristic
422C22#41×D4711yescharacteristic
423C22C2×#1062535211yescharacteristic
424C22C2×#1062535011yescharacteristic
425C22#1309406911yescharacteristic
426C22#1309407111yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—474no—
433C4—942no—
434C4—942no—
435C4—1881no—
436C4—1881no—
437C4—1881no—
438C4—1881no—
439C2—42no—
440C2—81no—
441C2—3761no—
442C2#121×D4711yescharacteristic
443C2#1568965311yescharacteristic
444C2#1568973711yescharacteristic
445C2#1568976311yescharacteristic
446C2#1568977911yescharacteristic
447C2#1568978211yescharacteristic
448C2#1568979311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#390C2
hypercenter#390D47
hypocenterC47#2426
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. C2×#13094001C2semidirect
4. C2×C4×Dic94C2semidirect
5. #15689046C2semidirect
6. #15689045C2semidirect
7. #15689039C2semidirect
8. #15689037C2semidirect
9. #15689023C2semidirect
10. #15689023C2semidirect
11. #15689018C2semidirect
12. #15689016C2semidirect
13. #15689014C2semidirect
14. C22⋊C4×Dic47C2semidirect
15. C47×#390C2semidirect
84. C2×Dic94D4semidirect
235. #390D47semidirect
240. C47#2426semidirect