Finite Group Databasebeta

← #20248461

Subgroups — #20248461

Order 6016.

696 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094011C211yesmaximal, characteristic, complemented
2C2×#13094010C211yesmaximal, characteristic, complemented
3C2×#13093996C211yesmaximal, characteristic, complemented
4#15689043C211yesmaximal, characteristic, complemented
5#15689037C211yesmaximal, characteristic, complemented
6#15689031C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689023C211yesmaximal, characteristic, complemented
9#15689013C211yesmaximal, characteristic, complemented
10#15689011C211yesmaximal, characteristic, complemented
11#15689003C211yesmaximal, characteristic, complemented
12#15689002C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
15C2×#121×C47C211yesmaximal, characteristic, complemented
16C22×Dic94C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C23×Dic47C2211yescharacteristic
21#13094011—24no—
22#13094010—24no—
23#13093996—24no—
24C2×Dic47⋊C4C2211yescharacteristic
25C2×Dic47⋊C4C2211yescharacteristic
26C2×C22⋊Dic47C2211yescharacteristic
27C2×C22⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47C2211yescharacteristic
29C2×C22⋊Dic47C2211yescharacteristic
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×C22⋊Dic47C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×C4×Dic47C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C22×D4×C47C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50C23×C4×C47C2211yescharacteristic
51#121×C47—24no—
52C2×C4⋊C4×C47C2211yescharacteristic
53C2×C22⋊C4×C47C2211yescharacteristic
54C2×C22⋊C4×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C24×C47C2311yescharacteristic
57C24×C47C2311yescharacteristic
58C23×D47C2311yescharacteristic
59C2×D4×C47—22no—
60C2×D4×C47—22no—
61C2×D4×C47—22no—
62C2×D4×C47—22no—
63C2×D4×C47—22no—
64C2×D4×C47—22no—
65C2×D4×C47—41no—
66C2×D4×C47—41no—
67C2×D4×C47—41no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—41no—
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47—22no—
78C2×C22⋊D47—22no—
79C2×C22⋊D47—22no—
80C2×C22⋊D47—41no—
81C2×C22⋊D47—41no—
82C2×C22⋊D47—41no—
83C2×C22⋊D47—41no—
84C22×Dic47—22no—
85C22×Dic47—22no—
86C22×Dic47—41no—
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C22×Dic47C2311yescharacteristic
92C22×Dic47C2311yescharacteristic
93C22×Dic47C2311yescharacteristic
94C2×Dic94—22no—
95C2×Dic94—22no—
96C2×Dic94—41no—
97C4⋊C4×C47—22no—
98C22⋊C4×C47—22no—
99C22⋊C4×C47D414yescomplemented
100C22⋊Dic47—22no—
101C22⋊Dic47—22no—
102C22⋊Dic47—22no—
103C22⋊Dic47—22no—
104C22⋊Dic47—22no—
105C22⋊Dic47—22no—
106C22⋊Dic47—22no—
107C22⋊Dic47D414yescomplemented
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112Dic47⋊C4—22no—
113Dic47⋊C4—41no—
114C4×Dic47—22no—
115C4×Dic47—22no—
116C4×Dic47—41no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47—21no—
129C23×C47—21no—
130C23×C47—21no—
131C23×C47—21no—
132C23×C47—21no—
133C23×C47—21no—
134C23×C47—21no—
135C23×C47—21no—
136C23×C47C2×D412yes—
137C23×C47C2×D412yes—
138C23×C47C2411yescharacteristic
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47—21no—
146D4×C47—44no—
147D4×C47—44no—
148D4×C47—44no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—44no—
159C2×C4×C47C2×D412yes—
160C2×C4×C47C2×D412yes—
161C2×C4×C47#4112yes—
162C22⋊D47—44no—
163C22⋊D47—44no—
164C22⋊D47—44no—
165C2×Dic47—21no—
166C2×Dic47—21no—
167C2×Dic47—21no—
168C2×Dic47—21no—
169C2×Dic47—21no—
170C2×Dic47—21no—
171C2×Dic47—21no—
172C2×Dic47—21no—
173C2×Dic47—21no—
174C2×Dic47—21no—
175C2×Dic47—21no—
176C2×Dic47—21no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—44no—
183C2×Dic47C2×D412yes—
184C2×Dic47C2×D412yes—
185C2×Dic47#4112yes—
186C2×Dic47#4112yes—
187Dic94—44no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—22no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—41no—
195C22×C47—41no—
196C22×C47—41no—
197C22×C47—41no—
198C22×C47—41no—
199C22×C47—41no—
200C22×C47—41no—
201C22×C47—41no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47C22×D411yescharacteristic
210C22×C47C22×D411yescharacteristic
211C22×C47C2×#4111yescharacteristic
212C22×C47C2×#4111yescharacteristic
213C22×C47C2×#4111yescharacteristic
214C22×C47H(5,𝔽2)11yescharacteristic
215C22×C47H(5,𝔽2)11yescharacteristic
216C2×D47—41no—
217C2×D47—41no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—41no—
223C4×C47—22no—
224C4×C47—22no—
225C4×C47—22no—
226C4×C47—41no—
227Dic47—22no—
228Dic47—22no—
229Dic47—22no—
230Dic47—22no—
231Dic47—41no—
232Dic47—41no—
233Dic47—41no—
234#2555—471nomaximal, Sylow
235C2×C47—42no—
236C2×C47—42no—
237C2×C47—81no—
238C2×C47#53211yescharacteristic
239C2×C47#53211yescharacteristic
240C2×C47#53811yescharacteristic
241C2×C47D4211yescharacteristic
242C2×C47#54611yescharacteristic
243C2×C47#54611yescharacteristic
244C2×C47#55511yescharacteristic
245D47—81no—
246C2×#124—471no—
247C2×#124—471no—
248C2×#121—471no—
249C2×#121D4711yescharacteristic, complemented
250#395—471no—
251#394—471no—
252#392—471no—
253#392—471no—
254#390—471no—
255#388—471no—
256#388—471no—
257#386—471no—
258#386—471no—
259C4×C22⋊C4—471no—
260C4×C22⋊C4—471no—
261C47#255511yescharacteristic, complemented, Sylow
262C22×Q8—471no—
263C22×D4—471no—
264C22×D4—471no—
265C22×D4—471no—
266C22×D4C2×D4711yescharacteristic
267C22×D4C2×D4711yescharacteristic
268C22×D4C2×D4711yescharacteristic
269C23×C4—471no—
270C23×C4C2×D4711yescharacteristic
271#124—944no—
272#124—944no—
273#121—24no—
274#121—944no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4C2×D4711yescharacteristic
278C2×C22⋊C4—471no—
279C2×C22⋊C4—471no—
280C2×C22⋊C4—471no—
281C2×C22⋊C4—471no—
282C2×C22⋊C4—471no—
283C2×C22⋊C4—471no—
284C2×C22⋊C4—471no—
285C2×C22⋊C4—471no—
286C2×C22⋊C4—471no—
287C2×C22⋊C4—471no—
288C2×C22⋊C4—471no—
289C2×C22⋊C4—471no—
290C2×C22⋊C4C2×D4711yescharacteristic
291C2×C22⋊C4C2×D4711yescharacteristic
292C2×C42—471no—
293C2×C42—471no—
294C2×C42—471no—
295#95—471no—
296#95—471no—
297#95—471no—
298#95—471no—
299#95—471no—
300#95—471no—
301C24—471no—
302C24C22×D4711yescharacteristic
303C24C22×D4711yescharacteristic
304C24C22×D4711yescharacteristic
305C2×Q8—942no—
306C2×Q8—942no—
307C2×Q8—1881no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—942no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—942no—
321C2×D4—942no—
322C2×D4—1881no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1881no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—471no—
332C22×C4—471no—
333C22×C4—471no—
334C22×C4—471no—
335C22×C4—471no—
336C22×C4—942no—
337C22×C4—942no—
338C22×C4—1881no—
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C22×C4C22×D4711yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—942no—
345C4⋊C4—1881no—
346C22⋊C4—22no—
347C22⋊C4—474no—
348C22⋊C4—942no—
349C22⋊C4—942no—
350C22⋊C4—942no—
351C22⋊C4—942no—
352C22⋊C4—942no—
353C22⋊C4—942no—
354C22⋊C4—942no—
355C22⋊C4—942no—
356C22⋊C4—942no—
357C22⋊C4—942no—
358C22⋊C4—942no—
359C22⋊C4C22⋊D4714yescomplemented
360C42—942no—
361C42—942no—
362C42—1881no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23—941no—
386C23—941no—
387C23—941no—
388C23—941no—
389C23D4×D4712yes—
390C23C2×C22⋊D4712yes—
391C23C23×D4711yescharacteristic
392Q8—1884no—
393D4—44no—
394D4—44no—
395D4—44no—
396D4—1884no—
397D4—1884no—
398D4—1884no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—44no—
409C2×C4—472no—
410C2×C4—472no—
411C2×C4—472no—
412C2×C4—472no—
413C2×C4—941no—
414C2×C4—941no—
415C2×C4—941no—
416C2×C4—941no—
417C2×C4—941no—
418C2×C4—941no—
419C2×C4—941no—
420C2×C4—941no—
421C2×C4—941no—
422C2×C4—941no—
423C2×C4—941no—
424C2×C4—941no—
425C2×C4—941no—
426C2×C4—941no—
427C2×C4—941no—
428C2×C4—941no—
429C2×C4—941no—
430C2×C4—1884no—
431C2×C4#1062535212yes—
432C2×C4C2×C22⋊D4712yes—
433C2×C4C2×C22⋊D4712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—1881no—
456C22—1881no—
457C22—1881no—
458C22—1881no—
459C22—1881no—
460C22—1881no—
461C22—1881no—
462C22C2×D4×D4711yescharacteristic
463C22C22×C22⋊D4711yescharacteristic
464C22#41×D4711yescharacteristic
465C22#41×D4711yescharacteristic
466C22C2×#1062535211yescharacteristic
467C22#1309406911yescharacteristic
468C22#1309406911yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—942no—
474C4—942no—
475C4—942no—
476C4—942no—
477C4—1881no—
478C4—1881no—
479C4—1881no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—3761no—
484C2#1568966811yescharacteristic
485C2#1568966911yescharacteristic
486C2#1568970511yescharacteristic
487C2D4×C22⋊D4711yescharacteristic
488C2#1568976211yescharacteristic
489C2#1568976711yescharacteristic
490C2#1568983711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2555
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13094011C2semidirect
2. C2×#13094010C2semidirect
3. C2×#13093996C2semidirect
4. #15689043C2semidirect
5. #15689037C2semidirect
6. #15689031C2semidirect
7. #15689031C2semidirect
8. #15689023C2semidirect
9. #15689013C2semidirect
10. #15689011C2semidirect
11. #15689003C2semidirect
12. #15689002C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×C22⋊Dic47C2semidirect
15. C2×#121×C47C2semidirect
99. C22⋊C4×C47D4semidirect
107. C22⋊Dic47D4semidirect
249. C2×#121D47semidirect
261. C47#2555semidirect
359. C22⋊C4C22⋊D47semidirect