Finite Group Databasebeta

← #26183667

Subgroups — #26183667

Order 12032.

1762 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic
2C2×#15689087C211yesmaximal, characteristic, complemented
3#20241955C214yesmaximal, complemented
4#20241916C214yesmaximal, complemented
5#20241903C214yesmaximal, complemented
6C47×#2280C211yesmaximal, characteristic, complemented
7C23×D188C411yescharacteristic, complemented
8C23×C22⋊D47—21no—
9C22×#10625329—21no—
10C2×#13093998—21no—
11C2×#13093998—21no—
12C2×#13093998—21no—
13C2×#13093998—21no—
14C2×#13093998—21no—
15C2×#13093998—21no—
16C2×#13093998C412yescomplemented
17C2×#13093998C412yescomplemented
18C2×#13093998C412yescomplemented
19C2×#13093998C2212yes—
20C2×#13093998C2212yes—
21C2×#13093998C2212yes—
22C22×C4⋊Dic47C411yescharacteristic, complemented
23C22×(C2×D47)⋊C4—21no—
24#15689087—21no—
25#15689087—21no—
26#15689087C2212yescomplemented
27#15689087C2212yescomplemented
28C2×C22⋊(C47⋊C8)—21no—
29C2×C22⋊(C47⋊C8)C2212yescomplemented
30#15688856C22116yescomplemented
31C24×C4×C47C2211yescharacteristic
32C2×#117×C47—21no—
33C47×#381C2212yescomplemented
34C47×#380—21no—
35C47×#380C2212yescomplemented
36C47×#379—21no—
37C4×C22⋊C4×C47—21no—
38C4×C22⋊C4×C47C2212yescomplemented
39C24×D47—21no—
40C22×D188—21no—
41C22×D188—21no—
42C22×D188—21no—
43C22×D188—44no—
44C22×D188C2×C412yes—
45C22×D188C2×C412yes—
46C22×D188C2×C412yes—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47—22no—
50C22×C22⋊D47—22no—
51C22×C22⋊D47—22no—
52C22×C22⋊D47—22no—
53C22×C22⋊D47—48no—
54C23×Dic47—21no—
55C2×#10625329—22no—
56C2×#10625329—22no—
57C2×#10625329—44no—
58C22×C47⋊C8—22no—
59#13093998—22no—
60#13093998—22no—
61#13093998—22no—
62#13093998—22no—
63#13093998—22no—
64#13093998—22no—
65#13093998—22no—
66#13093998—22no—
67#13093998—22no—
68#13093998—22no—
69#13093998—22no—
70#13093998—22no—
71#13093998C2×C414yes—
72#13093998C2×C414yes—
73#13093998C2×C414yes—
74#13093998C2314yes—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47C2×C412yes—
79C2×C4⋊Dic47C2×C412yes—
80C2×C4⋊Dic47C2×C412yes—
81C2×(C2×D47)⋊C4—22no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—22no—
85C2×(C2×D47)⋊C4—22no—
86C2×(C2×D47)⋊C4—22no—
87C22⋊(C47⋊C8)—22no—
88C22⋊(C47⋊C8)—22no—
89C22⋊(C47⋊C8)—22no—
90C22⋊(C47⋊C8)C2314yescomplemented
91C25×C47D411yescharacteristic
92C23×C4×C47—44no—
93C23×C4×C47C2×C411yescharacteristic
94C23×C4×C47C2×C411yescharacteristic
95C23×C4×C47C2×C411yescharacteristic
96C23×C4×C47C2×C411yescharacteristic
97C23×C4×C47D411yescharacteristic
98C23×C4×C47D411yescharacteristic
99C23×C4×C47D411yescharacteristic
100C23×C4×C47D411yescharacteristic
101C23×C4×C47D411yescharacteristic
102C23×C4×C47D411yescharacteristic
103C23×C4×C47D411yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107#117×C47—44no—
108C2×C4⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C42×C47—22no—
113#95×C47—22no—
114#95×C47C2314yescomplemented
115C24×C47—24no—
116C24×C47—42no—
117C24×C47—42no—
118C24×C47C22⋊C411yescharacteristic
119C24×C47C22⋊C411yescharacteristic
120C24×C47C22⋊C411yescharacteristic
121C24×C47C22⋊C411yescharacteristic
122C24×C47C2×D411yescharacteristic
123C24×C47C2×D411yescharacteristic
124C24×C47C2×D411yescharacteristic
125C23×D47—22no—
126C23×D47—22no—
127C23×D47—22no—
128C23×D47—44no—
129C23×D47—44no—
130C23×D47—44no—
131C22×C4×C47—24no—
132C22×C4×C47—24no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—42no—
138C22×C4×C47—42no—
139C22×C4×C47—42no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—42no—
146C22×C4×C47C22⋊C411yescharacteristic
147C22×C4×C47C22⋊C411yescharacteristic
148C22×C4×C47C22⋊C411yescharacteristic
149C22×C4×C47C22⋊C411yescharacteristic
150C22×C4×C47C22⋊C411yescharacteristic
151C22×C4×C47C22⋊C411yescharacteristic
152C22×C4×C47C22⋊C411yescharacteristic
153C22×C4×C47C22⋊C411yescharacteristic
154C22×C4×C47C22⋊C411yescharacteristic
155C22×C4×C47C22⋊C411yescharacteristic
156C22×C4×C47C22⋊C411yescharacteristic
157C22×C4×C47C22⋊C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C22×C411yescharacteristic
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D411yescharacteristic
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47C2×D411yescharacteristic
170C22×C4×C47C2×D411yescharacteristic
171C22×C4×C47C2×D411yescharacteristic
172C22×C4×C47C2×D411yescharacteristic
173C22×C4×C47C2411yescharacteristic
174C2×C22⋊D47—24no—
175C2×C22⋊D47—24no—
176C2×C22⋊D47—24no—
177C2×C22⋊D47—24no—
178C2×C22⋊D47—48no—
179C2×C22⋊D47—48no—
180C2×C22⋊D47—48no—
181C2×C22⋊D47—48no—
182C2×C22⋊D47—48no—
183C2×C22⋊D47—48no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—44no—
188C2×D188—22no—
189C2×D188—22no—
190C2×D188—22no—
191C2×D188—44no—
192C2×D188—44no—
193C2×D188—44no—
194C2×D188—44no—
195C2×D188—44no—
196C2×D188—44no—
197C2×D188C22×C414yes—
198C4⋊C4×C47—44no—
199C22⋊C4×C47—44no—
200C22⋊C4×C47—44no—
201C22⋊C4×C47—44no—
202C42×C47—44no—
203(C2×D47)⋊C4—24no—
204(C2×D47)⋊C4—24no—
205(C2×D47)⋊C4—24no—
206(C2×D47)⋊C4—24no—
207C4⋊Dic47—22no—
208C4⋊Dic47—22no—
209C4⋊Dic47—22no—
210C4⋊Dic47C22×C414yes—
211#10625329—44no—
212#10625329—44no—
213C2×C47⋊C8—24no—
214C2×C47⋊C8—44no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—22no—
221C23×C47—22no—
222C23×C47—22no—
223C23×C47—22no—
224C23×C47—22no—
225C23×C47—22no—
226C23×C47—22no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47—41no—
230C23×C47—41no—
231C23×C47—41no—
232C23×C47—41no—
233C23×C47—41no—
234C23×C47—41no—
235C23×C47—416no—
236C23×C47C2×C22⋊C411yescharacteristic
237C23×C47C2×C22⋊C411yescharacteristic
238C23×C47C2×C22⋊C411yescharacteristic
239C23×C47C2×C22⋊C411yescharacteristic
240C23×C47C2×C22⋊C411yescharacteristic
241C23×C47C2×C22⋊C411yescharacteristic
242C23×C47AGL(1,ℤ/8)14yes—
243C23×C47C22×D411yescharacteristic
244C22×D47—24no—
245C22×D47—44no—
246C22×D47—44no—
247C22×D47—44no—
248C22×D47—44no—
249C22×D47—44no—
250C22×D47—44no—
251C22×D47—44no—
252C22×D47—44no—
253C22×D47—44no—
254C22×D47—816no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—44no—
283C2×C4×C47—44no—
284C2×C4×C47—44no—
285C2×C4×C47#9914yes—
286C2×C4×C47C2×C22⋊C411yescharacteristic
287C2×C4×C47C2×C22⋊C411yescharacteristic
288C2×C4×C47C2×C22⋊C411yescharacteristic
289C2×C4×C47C2×C22⋊C411yescharacteristic
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47C2×C22⋊C411yescharacteristic
292C2×C4×C47C23×C411yescharacteristic
293C2×C4×C47C22×D411yescharacteristic
294C22⋊D47—48no—
295C22⋊D47—48no—
296C22⋊D47—48no—
297C22⋊D47—48no—
298C2×Dic47—24no—
299C2×Dic47—44no—
300C2×Dic47—44no—
301C2×Dic47—44no—
302D188—44no—
303D188—44no—
304D188—44no—
305D188—44no—
306C47⋊C8—44no—
307#17577—471nomaximal, Sylow
308C22×C47—28no—
309C22×C47—21no—
310C22×C47—21no—
311C22×C47—21no—
312C22×C47—21no—
313C22×C47—21no—
314C22×C47—21no—
315C22×C47—21no—
316C22×C47—21no—
317C22×C47—21no—
318C22×C47—21no—
319C22×C47—21no—
320C22×C47—21no—
321C22×C47—21no—
322C22×C47—21no—
323C22×C47—21no—
324C22×C47—21no—
325C22×C47—44no—
326C22×C47—44no—
327C22×C47—44no—
328C22×C47—44no—
329C22×C47—44no—
330C22×C47—44no—
331C22×C47C2×#9912yes—
332C22×C47#41812yes—
333C22×C47#41812yes—
334C22×C47#42112yes—
335C22×C47C22×C22⋊C411yescharacteristic
336C22×C47C2×AGL(1,ℤ/8)12yes—
337C2×D47—44no—
338C2×D47—44no—
339C2×D47—44no—
340C2×D47—88no—
341C2×D47—88no—
342C2×D47—88no—
343C4×C47—21no—
344C4×C47—21no—
345C4×C47—21no—
346C4×C47—21no—
347C4×C47—21no—
348C4×C47—21no—
349C4×C47—84no—
350C4×C47C2×#9912yes—
351C4×C47C2×#9912yes—
352Dic47—44no—
353C22×#121—471no—
354C2×#407—471no—
355#2280D4711yescharacteristic, complemented
356#1519—474no—
357#1510—474no—
358#1507—474no—
359C2×C47—22no—
360C2×C47—22no—
361C2×C47—22no—
362C2×C47—22no—
363C2×C47—22no—
364C2×C47—41no—
365C2×C47—41no—
366C2×C47C22×#9911yescharacteristic
367C2×C47C2×#41811yescharacteristic
368C2×C47C2×#42111yescharacteristic
369D47—84no—
370C23×D4—471no—
371C23×D4—941no—
372C24×C4C2×D4711yescharacteristic
373C22×M16—941no—
374C2×#121—472no—
375C2×#121—472no—
376C2×#121—472no—
377C2×#121—472no—
378C2×#121—472no—
379C2×#121—472no—
380C2×#121—941no—
381C2×#121—941no—
382C2×#121—941no—
383C2×#121—941no—
384C2×#121—941no—
385C2×#121—941no—
386C2×#117—21no—
387C22×C4⋊C4—471no—
388C22×C22⋊C4—941no—
389#407—472no—
390#407—472no—
391#407—941no—
392#407—941no—
393C2×C22⋊C8—472no—
394C2×C22⋊C8—941no—
395#381C2×D4712yescomplemented
396#380—21no—
397#380C2×D4712yescomplemented
398#379—21no—
399C4×C22⋊C4—21no—
400C4×C22⋊C4C2×D4712yescomplemented
401#327—4716no—
402C47#1757711yescharacteristic, complemented, Sylow
403C25—941no—
404C25C22⋊D4711yescharacteristic
405C22×D4—472no—
406C22×D4—472no—
407C22×D4—472no—
408C22×D4—942no—
409C22×D4—942no—
410C22×D4—942no—
411C22×D4—942no—
412C22×D4—942no—
413C22×D4—942no—
414C22×D4—941no—
415C22×D4—941no—
416C22×D4—941no—
417C22×D4—1884no—
418C22×D4—1888no—
419C23×C4—44no—
420C23×C4—941no—
421C23×C4C4×D4711yescharacteristic
422C23×C4C4×D4711yescharacteristic
423C23×C4C4×D4711yescharacteristic
424C23×C4C4×D4711yescharacteristic
425C23×C4D18811yescharacteristic
426C23×C4D18811yescharacteristic
427C23×C4D18811yescharacteristic
428C23×C4D18811yescharacteristic
429C23×C4C22⋊D4711yescharacteristic
430C23×C4C22⋊D4711yescharacteristic
431C23×C4C22⋊D4711yescharacteristic
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4711yescharacteristic
434C23×C4C22×D4711yescharacteristic
435C2×M16—942no—
436C2×M16—942no—
437C2×M16—1884no—
438C22×C8—942no—
439#121—474no—
440#121—474no—
441#121—474no—
442#121—474no—
443#121—942no—
444#121—942no—
445#121—942no—
446#121—942no—
447#121—942no—
448#121—942no—
449#121—942no—
450#121—942no—
451#121—942no—
452#121—942no—
453#121—942no—
454#121—942no—
455#117—44no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—472no—
458C2×C4⋊C4—472no—
459C2×C4⋊C4—472no—
460C2×C4⋊C4—941no—
461C2×C4⋊C4—941no—
462C2×C4⋊C4—941no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—942no—
467C2×C22⋊C4—942no—
468C2×C22⋊C4—942no—
469C2×C22⋊C4—942no—
470C2×C22⋊C4—942no—
471C2×C22⋊C4—942no—
472C2×C42—22no—
473C22⋊C8—474no—
474C22⋊C8—942no—
475C22⋊C8—942no—
476C22⋊C8—942no—
477#95—22no—
478#95C22×D4714yescomplemented
479C24—24no—
480C24—42no—
481C24—42no—
482C24—942no—
483C24—942no—
484C24—942no—
485C24—1884no—
486C24—1884no—
487C24—1884no—
488C24(C2×D47)⋊C411yescharacteristic
489C24(C2×D47)⋊C411yescharacteristic
490C24(C2×D47)⋊C411yescharacteristic
491C24(C2×D47)⋊C411yescharacteristic
492C24C2×C22⋊D4711yescharacteristic
493C24C2×C22⋊D4711yescharacteristic
494C24C2×C22⋊D4711yescharacteristic
495C2×D4—474no—
496C2×D4—944no—
497C2×D4—944no—
498C2×D4—944no—
499C2×D4—944no—
500C2×D4—942no—
501C2×D4—942no—
502C2×D4—942no—
503C2×D4—1884no—
504C2×D4—1884no—
505C2×D4—1884no—
506C2×D4—1884no—
507C2×D4—1884no—
508C2×D4—1888no—
509C2×D4—1888no—
510C2×D4—1888no—
511C2×D4—1888no—
512C2×D4—1888no—
513C2×D4—1888no—
514C2×D4—1884no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—942no—
531C22×C4—942no—
532C22×C4—942no—
533C22×C4—1884no—
534C22×C4(C2×D47)⋊C411yescharacteristic
535C22×C4(C2×D47)⋊C411yescharacteristic
536C22×C4(C2×D47)⋊C411yescharacteristic
537C22×C4(C2×D47)⋊C411yescharacteristic
538C22×C4(C2×D47)⋊C411yescharacteristic
539C22×C4(C2×D47)⋊C411yescharacteristic
540C22×C4(C2×D47)⋊C411yescharacteristic
541C22×C4(C2×D47)⋊C411yescharacteristic
542C22×C4(C2×D47)⋊C411yescharacteristic
543C22×C4(C2×D47)⋊C411yescharacteristic
544C22×C4(C2×D47)⋊C411yescharacteristic
545C22×C4(C2×D47)⋊C411yescharacteristic
546C22×C4C2×C4×D4711yescharacteristic
547C22×C4C2×C4×D4711yescharacteristic
548C22×C4C2×C4×D4711yescharacteristic
549C22×C4C2×C4×D4711yescharacteristic
550C22×C4C2×C4×D4711yescharacteristic
551C22×C4C2×C4×D4711yescharacteristic
552C22×C4C2×D18811yescharacteristic
553C22×C4C2×D18811yescharacteristic
554C22×C4C2×D18811yescharacteristic
555C22×C4C2×D18811yescharacteristic
556C22×C4C2×D18811yescharacteristic
557C22×C4C2×D18811yescharacteristic
558C22×C4C2×C22⋊D4711yescharacteristic
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C23×D4711yescharacteristic
562M16—1884no—
563M16—1884no—
564C2×C8—944no—
565C2×C8—1884no—
566C4⋊C4—44no—
567C4⋊C4—474no—
568C4⋊C4—942no—
569C4⋊C4—942no—
570C4⋊C4—942no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—44no—
574C22⋊C4—944no—
575C22⋊C4—944no—
576C22⋊C4—944no—
577C22⋊C4—944no—
578C42—44no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—416no—
600C23—944no—
601C23—37616no—
602C23—1884no—
603C23—1884no—
604C23—1884no—
605C23—1884no—
606C23—1884no—
607C23—1884no—
608C23—1884no—
609C23—1884no—
610C23—1884no—
611C23C2×(C2×D47)⋊C411yescharacteristic
612C23C2×(C2×D47)⋊C411yescharacteristic
613C23C2×(C2×D47)⋊C411yescharacteristic
614C23C2×(C2×D47)⋊C411yescharacteristic
615C23C2×(C2×D47)⋊C411yescharacteristic
616C23C2×(C2×D47)⋊C411yescharacteristic
617C23#1309404914yes—
618C23C22×C22⋊D4711yescharacteristic
619D4—1884no—
620D4—1884no—
621D4—1888no—
622D4—1888no—
623D4—1888no—
624D4—1888no—
625D4—1884no—
626D4—1884no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—44no—
657C2×C4—944no—
658C2×C4—1884no—
659C2×C4—1884no—
660C2×C4—1884no—
661C2×C4#1309393814yes—
662C2×C4C2×(C2×D47)⋊C411yescharacteristic
663C2×C4C2×(C2×D47)⋊C411yescharacteristic
664C2×C4C2×(C2×D47)⋊C411yescharacteristic
665C2×C4C2×(C2×D47)⋊C411yescharacteristic
666C2×C4C2×(C2×D47)⋊C411yescharacteristic
667C2×C4C2×(C2×D47)⋊C411yescharacteristic
668C2×C4C22×C4×D4711yescharacteristic
669C2×C4C22×D18811yescharacteristic
670C8—1884no—
671C22—28no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—3768no—
695C22—3768no—
696C22—3768no—
697C22—1884no—
698C22—1884no—
699C22—1884no—
700C22C2×#1309393812yes—
701C22#1568912712yes—
702C22#1568912712yes—
703C22#1568914112yes—
704C22C22×(C2×D47)⋊C411yescharacteristic
705C22C2×#1309404912yes—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—21no—
712C4—84no—
713C4—1884no—
714C4C2×#1309393812yes—
715C4C2×#1309393812yes—
716C2—22no—
717C2—22no—
718C2—22no—
719C2—22no—
720C2—22no—
721C2—41no—
722C2—41no—
723C2—3764no—
724C2C22×#1309393811yescharacteristic
725C2C2×#1568912711yescharacteristic
726C2C2×#1568914111yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#13093998C2
cosocleC22×C4×C47C24
hypercenter#2280D47
hypocenterC47#17577
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#15689087C2semidirect
3. #20241955C2semidirect
4. #20241916C2semidirect
5. #20241903C2semidirect
6. C47×#2280C2semidirect
7. C23×D188C4semidirect
16. C2×#13093998C4semidirect
17. C2×#13093998C4semidirect
18. C2×#13093998C4semidirect
22. C22×C4⋊Dic47C4semidirect
26. #15689087C22semidirect
27. #15689087C22semidirect
29. C2×C22⋊(C47⋊C8)C22semidirect
30. #15688856C22semidirect
33. C47×#381C22semidirect
35. C47×#380C22semidirect
38. C4×C22⋊C4×C47C22semidirect
90. C22⋊(C47⋊C8)C23semidirect
114. #95×C47C23semidirect
355. #2280D47semidirect
395. #381C2×D47semidirect
397. #380C2×D47semidirect
400. C4×C22⋊C4C2×D47semidirect
402. C47#17577semidirect
478. #95C22×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#130939982
C2×#156890872
#202419552
#202419162
#202419032
C47×#22802
#1757747