Finite Group Databasebeta

← #20247394

Subgroups — #20247394

Order 6016.

710 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×#13094006C211yesmaximal, characteristic, complemented
2C2×#13093998C211yesmaximal, characteristic, complemented
3C2×#13093997C211yesmaximal, characteristic, complemented
4C2×C4×D188C211yesmaximal, characteristic, complemented
5#15689055C211yesmaximal, characteristic, complemented
6#15689039C211yesmaximal, characteristic, complemented
7#15689033C211yesmaximal, characteristic, complemented
8#15689032C211yesmaximal, characteristic, complemented
9#15689025C211yesmaximal, characteristic, complemented
10#15689014C211yesmaximal, characteristic, complemented
11#15689014C211yesmaximal, characteristic, complemented
12#15689002C211yesmaximal, characteristic, complemented
13#15689001C211yesmaximal, characteristic, complemented
14#15688997C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×D188C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C22⋊D47C2211yescharacteristic
21C22×C22⋊D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23C22×C4×D47C2211yescharacteristic
24#13094006—24no—
25#13093998—24no—
26#13093997—24no—
27C4×D188—24no—
28C2×C4⋊Dic47C2211yescharacteristic
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31C2×Dic47⋊C4C2211yescharacteristic
32C2×Dic47⋊C4C2211yescharacteristic
33C2×C22⋊Dic47C2211yescharacteristic
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×(C2×D47)⋊C4C2211yescharacteristic
42C2×(C2×D47)⋊C4C2211yescharacteristic
43C2×(C2×D47)⋊C4C2211yescharacteristic
44C47⋊#95C2211yescharacteristic
45C47⋊#95C2211yescharacteristic
46C47⋊#95C2211yescharacteristic
47C47⋊#95C2211yescharacteristic
48C23×C4×C47C2211yescharacteristic
49C2×C22⋊C4×C47C2211yescharacteristic
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C42×C47C2211yescharacteristic
52C2×C42×C47C2211yescharacteristic
53#95×C47C2211yescharacteristic
54#95×C47C2211yescharacteristic
55C24×C47C2311yescharacteristic
56C23×D47C2311yescharacteristic
57C23×D47C2311yescharacteristic
58C23×D47C2311yescharacteristic
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—41no—
62C22×C4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—22no—
69C2×C22⋊D47—22no—
70C2×C22⋊D47—22no—
71C2×C22⋊D47—22no—
72C2×C22⋊D47—22no—
73C2×C22⋊D47—22no—
74C2×C22⋊D47—41no—
75C2×C22⋊D47—41no—
76C2×C22⋊D47—41no—
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C22×Dic47C2311yescharacteristic
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—22no—
85C2×D188—22no—
86C2×D188—22no—
87C2×D188—22no—
88C2×D188—22no—
89C2×D188—41no—
90C2×D188—41no—
91C2×C4×D47—22no—
92C2×C4×D47—22no—
93C2×C4×D47—22no—
94C2×C4×D47—22no—
95C2×C4×D47—41no—
96C2×C4×D47—41no—
97C22⋊C4×C47—22no—
98C22⋊C4×C47D414yescomplemented
99C42×C47—22no—
100C42×C47—41no—
101C22⋊Dic47—22no—
102(C2×D47)⋊C4—22no—
103(C2×D47)⋊C4—22no—
104(C2×D47)⋊C4—22no—
105(C2×D47)⋊C4—22no—
106(C2×D47)⋊C4—22no—
107(C2×D47)⋊C4—22no—
108(C2×D47)⋊C4—41no—
109(C2×D47)⋊C4—41no—
110(C2×D47)⋊C4—41no—
111(C2×D47)⋊C4D414yescomplemented
112C4⋊Dic47—22no—
113C4⋊Dic47—22no—
114C4⋊Dic47—22no—
115Dic47⋊C4—22no—
116Dic47⋊C4—22no—
117C23×C47—21no—
118C23×C47—21no—
119C23×C47—21no—
120C23×C47—21no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47C2×D412yes—
124C23×C47C2411yescharacteristic
125C22×D47—21no—
126C22×D47—21no—
127C22×D47—21no—
128C22×D47—21no—
129C22×D47—21no—
130C22×D47—21no—
131C22×D47—21no—
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×D47C2×D412yes—
145C22×D47#4112yes—
146C2×C4×C47—21no—
147C2×C4×C47—21no—
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—44no—
160C2×C4×C47C2×D412yes—
161C2×C4×C47C2×D412yes—
162C2×C4×C47C2×D412yes—
163C2×C4×C47#4112yes—
164C2×C4×C47#4112yes—
165C22⋊D47—44no—
166C22⋊D47—44no—
167C22⋊D47—44no—
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×Dic47C2×D412yes—
183D188—28no—
184D188—44no—
185D188—44no—
186C4×D47—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×C47C22×D411yescharacteristic
196C22×C47C22×D411yescharacteristic
197C22×C47C2×#4111yescharacteristic
198C22×C47C2×#4111yescharacteristic
199C22×C47C2×#4111yescharacteristic
200C22×C47H(5,𝔽2)11yescharacteristic
201C22×C47H(5,𝔽2)11yescharacteristic
202C2×D47—22no—
203C2×D47—22no—
204C2×D47—22no—
205C2×D47—22no—
206C2×D47—22no—
207C2×D47—22no—
208C2×D47—41no—
209C2×D47—41no—
210C2×D47—41no—
211C2×D47—41no—
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—22no—
227C4×C47—22no—
228C4×C47—41no—
229Dic47—22no—
230Dic47—41no—
231Dic47—41no—
232Dic47—41no—
233Dic47—41no—
234#2464—471nomaximal, Sylow
235C2×C47—42no—
236C2×C47#52511yescharacteristic
237C2×C47#53211yescharacteristic
238C2×C47#54011yescharacteristic
239C2×C47D4211yescharacteristic
240C2×C47#54611yescharacteristic
241C2×C47#54611yescharacteristic
242C2×C47#55311yescharacteristic
243D47—42no—
244D47—42no—
245D47—81no—
246C2×#123—471no—
247C2×#121—471no—
248C2×#121—471no—
249C2×C4×D4—471no—
250#398—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—
259#385—471no—
260C4×C22⋊C4D4711yescharacteristic, complemented
261C47#246411yescharacteristic, complemented, Sylow
262C22×D4—471no—
263C22×D4—471no—
264C22×D4—471no—
265C22×D4—471no—
266C22×D4—471no—
267C22×D4—471no—
268C23×C4—471no—
269C23×C4—471no—
270C23×C4C2×D4711yescharacteristic
271#123—944no—
272#121—944no—
273#121—944no—
274C4×D4—944no—
275C2×C4⋊C4—471no—
276C2×C4⋊C4—471no—
277C2×C4⋊C4—471no—
278C2×C4⋊C4—471no—
279C2×C4⋊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⋊C4—471no—
291C2×C22⋊C4C2×D4711yescharacteristic
292C2×C22⋊C4C2×D4711yescharacteristic
293C2×C42C2×D4711yescharacteristic
294C2×C42C2×D4711yescharacteristic
295#95—471no—
296#95—471no—
297#95—471no—
298#95—471no—
299#95C2×D4711yescharacteristic
300#95C2×D4711yescharacteristic
301C24—471no—
302C24—471no—
303C24—471no—
304C24C22×D4711yescharacteristic
305C2×D4—942no—
306C2×D4—942no—
307C2×D4—942no—
308C2×D4—942no—
309C2×D4—942no—
310C2×D4—942no—
311C2×D4—942no—
312C2×D4—942no—
313C2×D4—942no—
314C2×D4—942no—
315C2×D4—942no—
316C2×D4—942no—
317C2×D4—942no—
318C2×D4—1881no—
319C2×D4—1881no—
320C2×D4—1881no—
321C2×D4—1881no—
322C2×D4—1881no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—41no—
326C22×C4—471no—
327C22×C4—471no—
328C22×C4—471no—
329C22×C4—471no—
330C22×C4—471no—
331C22×C4—942no—
332C22×C4—942no—
333C22×C4—942no—
334C22×C4—942no—
335C22×C4—1881no—
336C22×C4—1881no—
337C22×C4C22×D4711yescharacteristic
338C22×C4C22×D4711yescharacteristic
339C22×C4C22×D4711yescharacteristic
340C22×C4C22×D4711yescharacteristic
341C22×C4C22×D4711yescharacteristic
342C22×C4C22×D4711yescharacteristic
343C4⋊C4—942no—
344C4⋊C4—942no—
345C4⋊C4—942no—
346C4⋊C4—942no—
347C4⋊C4—942no—
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—1881no—
358C22⋊C4—1881no—
359C22⋊C4—1881no—
360C22⋊C4D18814yescomplemented
361C42—22no—
362C42—41no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—472no—
370C23—472no—
371C23—941no—
372C23—941no—
373C23—941no—
374C23—941no—
375C23—941no—
376C23—941no—
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×D18812yes—
391C23C23×D4711yescharacteristic
392D4—948no—
393D4—1884no—
394D4—1884no—
395D4—1884no—
396D4—1884no—
397D4—1884no—
398C2×C4—21no—
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—44no—
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—1884no—
428C2×C4—1884no—
429C2×C4C2×D18812yes—
430C2×C4C2×D18812yes—
431C2×C4#1062535012yes—
432C2×C4#1062535012yes—
433C2×C4D4×D4712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—942no—
442C22—942no—
443C22—942no—
444C22—942no—
445C22—942no—
446C22—942no—
447C22—1881no—
448C22—1881no—
449C22—1881no—
450C22—1881no—
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×D18811yescharacteristic
464C22#41×D4711yescharacteristic
465C22C2×#1062535011yescharacteristic
466C22C2×#1062535011yescharacteristic
467C22#1309406911yescharacteristic
468C22#1309407011yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—41no—
475C4—942no—
476C4—1881no—
477C4—1881no—
478C4—1881no—
479C4—1881no—
480C2—42no—
481C2—3761no—
482C2—1882no—
483C2—1882no—
484C2#1568963211yescharacteristic
485C2#1568967311yescharacteristic
486C2#1568972411yescharacteristic
487C2D4×D18811yescharacteristic
488C2#1568976311yescharacteristic
489C2#1568976811yescharacteristic
490C2#1568981711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC4×C22⋊C4×C47C2
hypercenterC4×C22⋊C4D47
hypocenterC47#2464
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13094006C2semidirect
2. C2×#13093998C2semidirect
3. C2×#13093997C2semidirect
4. C2×C4×D188C2semidirect
5. #15689055C2semidirect
6. #15689039C2semidirect
7. #15689033C2semidirect
8. #15689032C2semidirect
9. #15689025C2semidirect
10. #15689014C2semidirect
11. #15689014C2semidirect
12. #15689002C2semidirect
13. #15689001C2semidirect
14. #15688997C2semidirect
15. C4×C22⋊C4×C47C2semidirect
98. C22⋊C4×C47D4semidirect
111. (C2×D47)⋊C4D4semidirect
260. C4×C22⋊C4D47semidirect
261. C47#2464semidirect
360. C22⋊C4D188semidirect