Finite Group Databasebeta

← #20248459

Subgroups — #20248459

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×#13094013C211yesmaximal, characteristic, complemented
2C2×#13093997C211yesmaximal, characteristic, complemented
3C2×#13093996C211yesmaximal, characteristic, complemented
4#15689042C211yesmaximal, characteristic, complemented
5#15689038C211yesmaximal, characteristic, complemented
6#15689032C211yesmaximal, characteristic, complemented
7#15689031C211yesmaximal, characteristic, complemented
8#15689023C211yesmaximal, characteristic, complemented
9#15689017C211yesmaximal, characteristic, complemented
10#15689014C211yesmaximal, characteristic, complemented
11#15689000C211yesmaximal, characteristic, complemented
12#15688999C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#124×C47C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×C22⋊D47C2211yescharacteristic
18C22×C22⋊D47C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C23×Dic47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23#13094013—24no—
24#13093997—24no—
25#13093996—24no—
26C2×Dic47⋊C4C2211yescharacteristic
27C2×Dic47⋊C4C2211yescharacteristic
28C2×Dic47⋊C4C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic
39C2×C4×Dic47C2211yescharacteristic
40C2×C4×Dic47C2211yescharacteristic
41C47⋊#95C2211yescharacteristic
42C47⋊#95C2211yescharacteristic
43C47⋊#95C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C22×Q8×C47C2211yescharacteristic
48C22×D4×C47C2211yescharacteristic
49#124×C47—24no—
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
58C23×D47C2311yescharacteristic
59C2×Q8×C47—22no—
60C2×Q8×C47—22no—
61C2×Q8×C47—41no—
62C2×D4×C47—22no—
63C2×D4×C47—22no—
64C2×D4×C47—41no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—22no—
76C2×C22⋊D47—22no—
77C2×C22⋊D47—41no—
78C2×C22⋊D47—41no—
79C2×C22⋊D47—41no—
80C2×C22⋊D47—41no—
81C2×C22⋊D47—41no—
82C22×Dic47—22no—
83C22×Dic47—22no—
84C22×Dic47—41no—
85C22×Dic47C2311yescharacteristic
86C22×Dic47C2311yescharacteristic
87C22×Dic47C2311yescharacteristic
88C22×Dic47C2311yescharacteristic
89C22×Dic47C2311yescharacteristic
90C22×Dic47C2311yescharacteristic
91C2×D188—22no—
92C2×D188—22no—
93C2×D188—41no—
94C2×C4×D47—22no—
95C2×C4×D47—22no—
96C2×C4×D47—41no—
97C22⋊C4×C47—22no—
98C22⋊C4×C47—22no—
99C22⋊C4×C47—22no—
100C22⋊C4×C47D414yescomplemented
101C42×C47—22no—
102C22⋊Dic47—22no—
103C22⋊Dic47—22no—
104C22⋊Dic47—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4D414yescomplemented
112Dic47⋊C4—22no—
113Dic47⋊C4—22no—
114Dic47⋊C4—41no—
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×C47C2×D412yes—
131C23×C47C2411yescharacteristic
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—21no—
145C22×D47C2×D412yes—
146Q8×C47—44no—
147D4×C47—44no—
148C2×C4×C47—21no—
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—21no—
159C2×C4×C47—21no—
160C2×C4×C47C2×D412yes—
161C2×C4×C47C2×D412yes—
162C2×C4×C47C2×D412yes—
163C22⋊D47—44no—
164C22⋊D47—44no—
165C22⋊D47—44no—
166C22⋊D47—44no—
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—44no—
182C2×Dic47C2×D412yes—
183C2×Dic47#4112yes—
184C2×Dic47#4112yes—
185C2×Dic47#4112yes—
186D188—44no—
187C4×D47—44no—
188C22×C47—22no—
189C22×C47—22no—
190C22×C47—22no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
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×C47C22×D411yescharacteristic
203C22×C47C22×D411yescharacteristic
204C22×C47C2×#4111yescharacteristic
205C22×C47C2×#4111yescharacteristic
206C22×C47C2×#4111yescharacteristic
207C22×C47H(5,𝔽2)11yescharacteristic
208C22×C47H(5,𝔽2)11yescharacteristic
209C2×D47—22no—
210C2×D47—22no—
211C2×D47—22no—
212C2×D47—41no—
213C2×D47—41no—
214C2×D47—41no—
215C2×D47—41no—
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—
227C4×C47—41no—
228Dic47—22no—
229Dic47—22no—
230Dic47—22no—
231Dic47—22no—
232Dic47—41no—
233Dic47—41no—
234#2555—471nomaximal, Sylow
235C2×C47—42no—
236C2×C47—81no—
237C2×C47#53211yescharacteristic
238C2×C47#53211yescharacteristic
239C2×C47#53811yescharacteristic
240C2×C47D4211yescharacteristic
241C2×C47#54611yescharacteristic
242C2×C47#54611yescharacteristic
243C2×C47#55511yescharacteristic
244D47—42no—
245D47—81no—
246C2×#124—471no—
247C2×#124D4711yescharacteristic, complemented
248C2×#121—471no—
249C2×#121—471no—
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×Q8C2×D4711yescharacteristic
263C22×D4—471no—
264C22×D4—471no—
265C22×D4—471no—
266C22×D4—471no—
267C22×D4—471no—
268C22×D4C2×D4711yescharacteristic
269C23×C4—471no—
270C23×C4—471no—
271#124—24no—
272#124—944no—
273#121—944no—
274#121—944no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4—471no—
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⋊C4C2×D4711yescharacteristic
289C2×C22⋊C4C2×D4711yescharacteristic
290C2×C22⋊C4C2×D4711yescharacteristic
291C2×C22⋊C4C2×D4711yescharacteristic
292C2×C42—471no—
293C2×C42—471no—
294C2×C42C2×D4711yescharacteristic
295#95—471no—
296#95—471no—
297#95—471no—
298#95—471no—
299#95—471no—
300#95—471no—
301C24—471no—
302C24—471no—
303C24C22×D4711yescharacteristic
304C24C22×D4711yescharacteristic
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
311C2×D4—942no—
312C2×D4—942no—
313C2×D4—942no—
314C2×D4—942no—
315C2×D4—942no—
316C2×D4—942no—
317C2×D4—942no—
318C2×D4—942no—
319C2×D4—942no—
320C2×D4—1881no—
321C2×D4—1881no—
322C2×D4—1881no—
323C2×D4—1881no—
324C2×D4—1881no—
325C2×D4—1881no—
326C22×C4—471no—
327C22×C4—471no—
328C22×C4—471no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—471no—
332C22×C4—942no—
333C22×C4—942no—
334C22×C4—942no—
335C22×C4—942no—
336C22×C4—1881no—
337C22×C4—1881no—
338C22×C4C22×D4711yescharacteristic
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C22×C4C22×D4711yescharacteristic
343C4⋊C4—942no—
344C4⋊C4—942no—
345C4⋊C4—1881no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—474no—
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—22no—
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—472no—
377C23—941no—
378C23—941no—
379C23—941no—
380C23—941no—
381C23—941no—
382C23—941no—
383C23—941no—
384C23—941no—
385C23—941no—
386C23—941no—
387C23—941no—
388C23—941no—
389C23—941no—
390C23C2×C22⋊D4712yes—
391C23C23×D4711yescharacteristic
392Q8—44no—
393D4—44no—
394D4—1884no—
395D4—1884no—
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—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—472no—
412C2×C4—472no—
413C2×C4—472no—
414C2×C4—472no—
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—1884no—
430C2×C4—1884no—
431C2×C4D4×D4712yes—
432C2×C4C2×C22⋊D4712yes—
433C2×C4C2×C22⋊D4712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—942no—
449C22—942no—
450C22—942no—
451C22—1881no—
452C22—1881no—
453C22—1881no—
454C22—1881no—
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
466C22#41×D4711yescharacteristic
467C22#1309406911yescharacteristic
468C22#1309407011yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—942no—
475C4—942no—
476C4—942no—
477C4—942no—
478C4—1881no—
479C4—1881no—
480C2—42no—
481C2—81no—
482C2—3761no—
483C2—1882no—
484C2#1568966911yescharacteristic
485C2#1568967211yescharacteristic
486C2#1568970711yescharacteristic
487C2D4×C22⋊D4711yescharacteristic
488C2#1568976111yescharacteristic
489C2#1568976611yescharacteristic
490C2#1568983511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#124×C47C2
hypercenterC2×#124D47
hypocenterC47#2555
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13094013C2semidirect
2. C2×#13093997C2semidirect
3. C2×#13093996C2semidirect
4. #15689042C2semidirect
5. #15689038C2semidirect
6. #15689032C2semidirect
7. #15689031C2semidirect
8. #15689023C2semidirect
9. #15689017C2semidirect
10. #15689014C2semidirect
11. #15689000C2semidirect
12. #15688999C2semidirect
13. C22⋊C4×Dic47C2semidirect
14. C4×(C2×D47)⋊C4C2semidirect
15. C2×#124×C47C2semidirect
100. C22⋊C4×C47D4semidirect
111. (C2×D47)⋊C4D4semidirect
247. C2×#124D47semidirect
261. C47#2555semidirect
359. C22⋊C4C22⋊D47semidirect