Finite Group Databasebeta

← #26139102

Subgroups — #26139102

Order 12032.

1918 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688997C211yesmaximal, characteristic
2C2×#15688985C211yesmaximal, characteristic
3C2×#15688985C211yesmaximal, characteristic
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
5C2×#95×D47C211yesmaximal, characteristic
6#20241649C211yesmaximal, characteristic, complemented
7#20241649C211yesmaximal, characteristic, complemented
8#20241645C211yesmaximal, characteristic, complemented
9#20241644C211yesmaximal, characteristic, complemented
10#20241623C211yesmaximal, characteristic, complemented
11#20241621C211yesmaximal, characteristic, complemented
12#20241614C211yesmaximal, characteristic, complemented
13(C2×D47)⋊#95C211yesmaximal, characteristic
14(C2×D47)⋊#95C211yesmaximal, characteristic
15C47×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C23×C4×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2211yescharacteristic
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26#15688997—24no—
27#15688985—24no—
28#15688985C418yescomplemented
29C4×(C2×D47)⋊C4—24no—
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C2×C47⋊#95C2211yescharacteristic
39C2×C47⋊#95C2211yescharacteristic
40C2×C47⋊#95C2211yescharacteristic
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2211yescharacteristic
43C2×C47⋊#95C2211yescharacteristic
44C2×C47⋊#95C2211yescharacteristic
45C2×C47⋊#95C2211yescharacteristic
46C2×C47⋊#95C2211yescharacteristic
47C2×C47⋊#95C2211yescharacteristic
48#95×D47—24no—
49C22×C42×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C24×D47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C23×Dic47C2311yescharacteristic
63C23×Dic47C2311yescharacteristic
64C22×C4×D47—22no—
65C22×C4×D47—22no—
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47—22no—
73C22×C4×D47—22no—
74C22×C4×D47—22no—
75C22×C4×D47—22no—
76C22×C4×D47—22no—
77C22×C4×D47—22no—
78C22×C4×D47—22no—
79C22×C4×D47—41no—
80C22×C4×D47—41no—
81C22×C4×D47—41no—
82C22×C4×D47—41no—
83C22×C4×D47C2×C414yes—
84C22×C4×D47D414yes—
85C2×C4⋊Dic47—22no—
86C2×C4⋊Dic47—41no—
87C2×C4⋊Dic47—41no—
88C2×Dic47⋊C4—22no—
89C2×Dic47⋊C4—22no—
90C2×Dic47⋊C4—22no—
91C2×(C2×D47)⋊C4—22no—
92C2×(C2×D47)⋊C4—22no—
93C2×(C2×D47)⋊C4—22no—
94C2×(C2×D47)⋊C4—22no—
95C2×(C2×D47)⋊C4—22no—
96C2×(C2×D47)⋊C4—22no—
97C2×(C2×D47)⋊C4—22no—
98C2×(C2×D47)⋊C4—22no—
99C2×(C2×D47)⋊C4—22no—
100C2×(C2×D47)⋊C4C2×C414yes—
101C2×(C2×D47)⋊C4C2×C414yes—
102C2×(C2×D47)⋊C4D414yes—
103C2×C4×Dic47—22no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47—41no—
106C47⋊#95—22no—
107C47⋊#95—22no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C47⋊#95—22no—
111C47⋊#95—22no—
112C47⋊#95—22no—
113C47⋊#95—22no—
114C47⋊#95—22no—
115C47⋊#95—22no—
116C47⋊#95—22no—
117C47⋊#95—22no—
118C47⋊#95—41no—
119C47⋊#95—41no—
120C47⋊#95—41no—
121C47⋊#95C2×C414yescomplemented
122C47⋊#95C2×C414yescomplemented
123C47⋊#95C2×C414yescomplemented
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126C23×C4×C47C2311yescharacteristic
127C23×C4×C47C2311yescharacteristic
128C23×C4×C47C2311yescharacteristic
129C23×C4×C47C2311yescharacteristic
130C23×C4×C47C2311yescharacteristic
131C2×C42×C47—22no—
132C2×C42×C47—22no—
133C2×C42×C47—41no—
134#95×C47—22no—
135#95×C47—22no—
136#95×C47—22no—
137#95×C47—22no—
138#95×C47—41no—
139#95×C47C2×C414yescomplemented
140C24×C47C2411yescharacteristic
141C23×D47—21no—
142C23×D47—21no—
143C23×D47—21no—
144C23×D47—21no—
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47C22×C412yes—
150C23×D47C2×D412yes—
151C23×D47C2×D412yes—
152C23×D47#4112yes—
153C23×D47#4112yes—
154C23×D47#4112yes—
155C23×D47#4112yes—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47C22×C412yes—
198C22×C4×C47C22×C412yes—
199C22×C4×C47C22×C412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47#4112yes—
203C22×C4×C47#4112yes—
204C22×C4×C47#4112yes—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—21no—
217C22×Dic47—21no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221C22×Dic47—21no—
222C22×Dic47—21no—
223C22×Dic47—21no—
224C22×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47—21no—
229C22×Dic47—21no—
230C22×Dic47—21no—
231C22×Dic47—21no—
232C22×Dic47—21no—
233C22×Dic47—21no—
234C22×Dic47—21no—
235C22×Dic47—21no—
236C22×Dic47—21no—
237C22×Dic47—21no—
238C22×Dic47—21no—
239C22×Dic47—21no—
240C22×Dic47—21no—
241C22×Dic47—21no—
242C22×Dic47—21no—
243C22×Dic47—21no—
244C22×Dic47—21no—
245C22×Dic47—21no—
246C22×Dic47—21no—
247C22×Dic47—21no—
248C22×Dic47C22×C412yes—
249C22×Dic47C22×C412yes—
250C22×Dic47C22×C412yes—
251C22×Dic47C2×D412yes—
252C22×Dic47C2×D412yes—
253C22×Dic47#4112yes—
254C2×C4×D47—28no—
255C2×C4×D47—28no—
256C2×C4×D47—28no—
257C2×C4×D47—28no—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—44no—
261C2×C4×D47—44no—
262C2×C4×D47—44no—
263C2×C4×D47—44no—
264C2×C4×D47—44no—
265C2×C4×D47—44no—
266C2×C4×D47—44no—
267C2×C4×D47—44no—
268C2×C4×D47—44no—
269C2×C4×D47—44no—
270C2×C4×D47—44no—
271C2×C4×D47—44no—
272C2×C4×D47—44no—
273C2×C4×D47—44no—
274C2×C4×D47—44no—
275C42×C47—44no—
276(C2×D47)⋊C4—28no—
277(C2×D47)⋊C4—28no—
278(C2×D47)⋊C4—28no—
279(C2×D47)⋊C4—44no—
280C4⋊Dic47—44no—
281Dic47⋊C4—44no—
282C4×Dic47—44no—
283C23×C47C23×C411yescharacteristic
284C23×C47C22×D411yescharacteristic
285C23×C47C22×D411yescharacteristic
286C23×C47C2×#4111yescharacteristic
287C23×C47C2×#4111yescharacteristic
288C23×C47C2×#4111yescharacteristic
289C23×C47C2×#4111yescharacteristic
290C23×C47C2×#4111yescharacteristic
291C23×C47C2×#4111yescharacteristic
292C23×C47C2×#4111yescharacteristic
293C23×C47C2×#4111yescharacteristic
294C23×C47H(5,𝔽2)11yescharacteristic
295C23×C47H(5,𝔽2)11yescharacteristic
296C23×C472−1+411yescharacteristic
297C23×C472−1+411yescharacteristic
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—22no—
321C22×D47—22no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47#11714yes—
327C22×D47C4×D414yes—
328C22×D47C4×D414yes—
329C22×D47#12114yes—
330C22×D47#12314yes—
331C22×D47#12414yes—
332C22×D47#12614yes—
333C2×C4×C47—22no—
334C2×C4×C47—22no—
335C2×C4×C47—22no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—41no—
355C2×C4×C47—41no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—41no—
359C2×C4×C47—41no—
360C2×C4×C47—41no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47#12314yes—
382C2×Dic47—22no—
383C2×Dic47—22no—
384C2×Dic47—22no—
385C2×Dic47—22no—
386C2×Dic47—22no—
387C2×Dic47—22no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—41no—
401C2×Dic47—41no—
402C2×Dic47—41no—
403C2×Dic47—41no—
404C2×Dic47—41no—
405C2×Dic47—41no—
406C2×Dic47—41no—
407C2×Dic47—41no—
408C2×Dic47—41no—
409C2×Dic47—41no—
410C2×Dic47—41no—
411C2×Dic47—41no—
412C2×Dic47—41no—
413C2×Dic47—41no—
414C2×Dic47—41no—
415C2×Dic47—41no—
416C2×Dic47—41no—
417C2×Dic47—41no—
418C2×Dic47—41no—
419C2×Dic47—41no—
420C2×Dic47—41no—
421C2×Dic47—41no—
422C2×Dic47—41no—
423C2×Dic47—41no—
424C2×Dic47—41no—
425C2×Dic47—41no—
426C2×Dic47—41no—
427C2×Dic47—41no—
428C2×Dic47—41no—
429C2×Dic47—41no—
430C2×Dic47—41no—
431C4×D47—416no—
432C4×D47—416no—
433C4×D47—416no—
434#13972—471nomaximal, Sylow
435C22×C47C2×#11711yescharacteristic
436C22×C47C2×C4×D411yescharacteristic
437C22×C47C2×C4×D411yescharacteristic
438C22×C47C4×#4111yescharacteristic
439C22×C47C4×#4111yescharacteristic
440C22×C47#52011yescharacteristic
441C22×C47#52011yescharacteristic
442C22×C47C2×#12111yescharacteristic
443C22×C47C2×#12311yescharacteristic
444C22×C47C2×#12311yescharacteristic
445C22×C47#52511yescharacteristic
446C22×C47C2×#12411yescharacteristic
447C22×C47C2×#12611yescharacteristic
448C22×C47#52911yescharacteristic
449C22×C47#52911yescharacteristic
450C22×C47#53411yescharacteristic
451C22×C47#53611yescharacteristic
452C22×C47#53911yescharacteristic
453C22×C47#53911yescharacteristic
454C22×C47#54611yescharacteristic
455C22×C47#54611yescharacteristic
456C22×C47#54711yescharacteristic
457C22×C47#54711yescharacteristic
458C22×C47#55111yescharacteristic
459C22×C47#55111yescharacteristic
460C22×C47#55111yescharacteristic
461C22×C47#55111yescharacteristic
462C22×C47#55111yescharacteristic
463C22×C47#55111yescharacteristic
464C22×C47#55211yescharacteristic
465C22×C47#55211yescharacteristic
466C22×C47#55211yescharacteristic
467C22×C47#55211yescharacteristic
468C22×C47#55211yescharacteristic
469C22×C47#55211yescharacteristic
470C2×D47—24no—
471C2×D47—24no—
472C2×D47—24no—
473C2×D47—24no—
474C2×D47—24no—
475C2×D47—24no—
476C2×D47—24no—
477C2×D47—24no—
478C2×D47—24no—
479C2×D47—24no—
480C2×D47—24no—
481C2×D47—24no—
482C2×D47—24no—
483C2×D47—24no—
484C2×D47#38818yes—
485C4×C47—24no—
486C4×C47—42no—
487C4×C47—42no—
488C4×C47—42no—
489C4×C47—42no—
490C4×C47—42no—
491C4×C47—81no—
492Dic47—42no—
493Dic47—42no—
494Dic47—42no—
495Dic47—42no—
496Dic47—42no—
497Dic47—42no—
498Dic47—81no—
499C2×#385—471no—
500C2×#381—471no—
501C2×#381—471no—
502C2×C4×C22⋊C4—471no—
503C22×#95—471no—
504#1443—471no—
505#1443—471no—
506#1442—471no—
507#1442—471no—
508#1436—471no—
509#1436—471no—
510#1434—471no—
511#1434D4711yescharacteristic, complemented
512C22⋊#95—471no—
513C22⋊#95—471no—
514C2×C47C2×#38811yescharacteristic
515C2×C47C4×#12311yescharacteristic
516C2×C47#232211yescharacteristic
517C2×C47#234311yescharacteristic
518C2×C47#234311yescharacteristic
519C2×C47#235911yescharacteristic
520C2×C47#235911yescharacteristic
521C2×C47#241211yescharacteristic
522C2×C47#241311yescharacteristic
523C2×C47#241911yescharacteristic
524C2×C47#241911yescharacteristic
525C2×C47#249311yescharacteristic
526C2×C47#249311yescharacteristic
527C2×C47#250311yescharacteristic
528C2×C47#256111yescharacteristic
529D47—28no—
530C24×C4—471no—
531C24×C4—471no—
532C24×C4—471no—
533C22×C4⋊C4—471no—
534C22×C4⋊C4—471no—
535C22×C22⋊C4—471no—
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C42—471no—
540C22×C42C2×D4711yescharacteristic
541#385—944no—
542#381—478no—
543#381—944no—
544C4×C22⋊C4—944no—
545C2×#95—471no—
546C2×#95—471no—
547C2×#95—471no—
548C2×#95—471no—
549C2×#95—471no—
550C2×#95—471no—
551C2×#95—471no—
552C2×#95—471no—
553C2×#95—471no—
554C2×#95—471no—
555C2×#95—471no—
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95—471no—
561C2×#95—471no—
562C2×#95—471no—
563C2×#95—944no—
564C2×#95C2×D4711yescharacteristic
565C2×#95C2×D4711yescharacteristic
566C2×#95C2×D4711yescharacteristic
567C2×#95C2×D4711yescharacteristic
568C2×#95C2×D4711yescharacteristic
569C2×#95C2×D4711yescharacteristic
570C47#1397211yescharacteristic, complemented, Sylow
571C25—471no—
572C23×C4—471no—
573C23×C4—471no—
574C23×C4—471no—
575C23×C4—471no—
576C23×C4—471no—
577C23×C4—471no—
578C23×C4—474no—
579C23×C4—474no—
580C23×C4—471no—
581C23×C4—942no—
582C23×C4—942no—
583C23×C4—942no—
584C23×C4—942no—
585C23×C4—942no—
586C23×C4—942no—
587C23×C4—942no—
588C23×C4—942no—
589C23×C4—942no—
590C23×C4—942no—
591C23×C4—942no—
592C23×C4—942no—
593C23×C4—942no—
594C23×C4—942no—
595C23×C4—942no—
596C23×C4—1881no—
597C23×C4—1881no—
598C23×C4—1881no—
599C23×C4—1881no—
600C23×C4C22×D4711yescharacteristic
601C23×C4C22×D4711yescharacteristic
602C23×C4C22×D4711yescharacteristic
603C23×C4C22×D4711yescharacteristic
604C23×C4C22×D4711yescharacteristic
605C23×C4C22×D4711yescharacteristic
606C23×C4C22×D4711yescharacteristic
607C2×C4⋊C4—942no—
608C2×C4⋊C4—942no—
609C2×C4⋊C4—942no—
610C2×C4⋊C4—942no—
611C2×C4⋊C4—1881no—
612C2×C4⋊C4—1881no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—474no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—942no—
617C2×C22⋊C4—942no—
618C2×C22⋊C4—942no—
619C2×C22⋊C4—942no—
620C2×C22⋊C4—942no—
621C2×C22⋊C4—942no—
622C2×C22⋊C4—942no—
623C2×C22⋊C4—942no—
624C2×C22⋊C4—942no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—942no—
629C2×C42—942no—
630C2×C42—1881no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—41no—
636#95—474no—
637#95—474no—
638#95—474no—
639#95—942no—
640#95—942no—
641#95—942no—
642#95—942no—
643#95—942no—
644#95—942no—
645#95—942no—
646#95—942no—
647#95—942no—
648#95—942no—
649#95—942no—
650#95—942no—
651#95—1881no—
652#95—1881no—
653#95—1881no—
654#95C4×D4714yescomplemented
655C24—472no—
656C24—472no—
657C24—472no—
658C24—472no—
659C24—472no—
660C24—472no—
661C24—472no—
662C24—941no—
663C24—941no—
664C24—941no—
665C24—941no—
666C24—941no—
667C24—941no—
668C24—941no—
669C24—941no—
670C24C23×D4711yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—472no—
713C22×C4—472no—
714C22×C4—472no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—472no—
718C22×C4—948no—
719C22×C4—948no—
720C22×C4—948no—
721C22×C4—948no—
722C22×C4—948no—
723C22×C4—941no—
724C22×C4—941no—
725C22×C4—941no—
726C22×C4—941no—
727C22×C4—941no—
728C22×C4—941no—
729C22×C4—941no—
730C22×C4—941no—
731C22×C4—941no—
732C22×C4—941no—
733C22×C4—941no—
734C22×C4—941no—
735C22×C4—941no—
736C22×C4—941no—
737C22×C4—941no—
738C22×C4—941no—
739C22×C4—941no—
740C22×C4—941no—
741C22×C4—941no—
742C22×C4—941no—
743C22×C4—941no—
744C22×C4—941no—
745C22×C4—941no—
746C22×C4—941no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4—941no—
751C22×C4—941no—
752C22×C4—941no—
753C22×C4—941no—
754C22×C4—941no—
755C22×C4—941no—
756C22×C4—941no—
757C22×C4—941no—
758C22×C4—941no—
759C22×C4—948no—
760C22×C4—941no—
761C22×C4—941no—
762C22×C4—941no—
763C22×C4—941no—
764C22×C4—941no—
765C22×C4—941no—
766C22×C4—941no—
767C22×C4—1884no—
768C22×C4—1884no—
769C22×C4—1884no—
770C22×C4—1884no—
771C22×C4—1884no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—1884no—
775C22×C4—1884no—
776C22×C4—1884no—
777C22×C4—1884no—
778C22×C4—1884no—
779C22×C4—1884no—
780C22×C4—1884no—
781C22×C4—1884no—
782C22×C4C2×C4×D4712yes—
783C22×C4C2×C4×D4712yes—
784C22×C4C2×C4×D4712yes—
785C22×C4#1062535012yes—
786C22×C4#1062535012yes—
787C22×C4D4×D4712yes—
788C22×C4D4×D4712yes—
789C22×C4#1062535412yes—
790C4⋊C4—1884no—
791C4⋊C4—1884no—
792C22⋊C4—948no—
793C22⋊C4—948no—
794C22⋊C4—948no—
795C22⋊C4—1884no—
796C42—44no—
797C42—1884no—
798C23—474no—
799C23—474no—
800C23—474no—
801C23—474no—
802C23—474no—
803C23—474no—
804C23—474no—
805C23—942no—
806C23—942no—
807C23—942no—
808C23—942no—
809C23—942no—
810C23—942no—
811C23—942no—
812C23—942no—
813C23—942no—
814C23—942no—
815C23—942no—
816C23—942no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—942no—
822C23—942no—
823C23—942no—
824C23—942no—
825C23—942no—
826C23—942no—
827C23—942no—
828C23—942no—
829C23—942no—
830C23—942no—
831C23—942no—
832C23—942no—
833C23C22×C4×D4711yescharacteristic
834C23C2×D4×D4711yescharacteristic
835C23C2×D4×D4711yescharacteristic
836C23#41×D4711yescharacteristic
837C23#41×D4711yescharacteristic
838C23#41×D4711yescharacteristic
839C23#41×D4711yescharacteristic
840C23#41×D4711yescharacteristic
841C23C2×#1062535011yescharacteristic
842C23C2×#1062535011yescharacteristic
843C23C2×#1062535411yescharacteristic
844C23#1309406911yescharacteristic
845C23#1309407011yescharacteristic
846C23#1309407111yescharacteristic
847C23#1309407111yescharacteristic
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—942no—
904C2×C4—942no—
905C2×C4—942no—
906C2×C4—942no—
907C2×C4—942no—
908C2×C4—942no—
909C2×C4—942no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—18816no—
915C2×C4—18816no—
916C2×C4—18816no—
917C2×C4—1881no—
918C2×C4—1881no—
919C2×C4—1881no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4—1881no—
938C2×C4—1881no—
939C2×C4—1881no—
940C2×C4—1881no—
941C2×C4—1881no—
942C2×C4—1881no—
943C2×C4—1881no—
944C2×C4—1881no—
945C2×C4—1881no—
946C2×C4—1881no—
947C2×C4—1881no—
948C2×C4#1309400914yes—
949C22—478no—
950C22—944no—
951C22—944no—
952C22—944no—
953C22—944no—
954C22—944no—
955C22—944no—
956C22—944no—
957C22—944no—
958C22—944no—
959C22—944no—
960C22—944no—
961C22—944no—
962C22—944no—
963C22—944no—
964C22#117×D4711yescharacteristic
965C22C4×D4×D4711yescharacteristic
966C22C4×D4×D4711yescharacteristic
967C22C4×#1062535011yescharacteristic
968C22C4×#1062535411yescharacteristic
969C22#1568960211yescharacteristic
970C22#1568960311yescharacteristic
971C22#121×D4711yescharacteristic
972C22#123×D4711yescharacteristic
973C22C2×#1309400911yescharacteristic
974C22#1568963211yescharacteristic
975C22#124×D4711yescharacteristic
976C22#126×D4711yescharacteristic
977C22#1568965111yescharacteristic
978C22#1568966011yescharacteristic
979C22#1568968111yescharacteristic
980C22#1568969311yescharacteristic
981C22#1568971411yescharacteristic
982C22#1568971611yescharacteristic
983C22#1568976311yescharacteristic
984C22#1568976411yescharacteristic
985C22#1568977111yescharacteristic
986C22#1568977811yescharacteristic
987C22#1568979711yescharacteristic
988C22#1568979711yescharacteristic
989C22#1568979811yescharacteristic
990C22#1568980011yescharacteristic
991C22#1568980111yescharacteristic
992C22#1568980211yescharacteristic
993C22#1568980911yescharacteristic
994C22#1568981111yescharacteristic
995C22#1568981111yescharacteristic
996C22#1568981211yescharacteristic
997C22#1568981211yescharacteristic
998C22#1568981211yescharacteristic
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—3761no—
1007C4—1882no—
1008C4—1882no—
1009C4—1882no—
1010C4—1882no—
1011C4—1882no—
1012C4—1882no—
1013C2—948no—
1014C2#388×D4711yescharacteristic
1015C2C4×#1309400911yescharacteristic
1016C2#2024605811yescharacteristic
1017C2#2024624711yescharacteristic
1018C2#2024624911yescharacteristic
1019C2#2024638111yescharacteristic
1020C2#2024638711yescharacteristic
1021C2#2024678111yescharacteristic
1022C2#2024679411yescharacteristic
1023C2#2024686211yescharacteristic
1024C2#2024687211yescharacteristic
1025C2#2024777011yescharacteristic
1026C2#2024778011yescharacteristic
1027C2#2024787011yescharacteristic
1028C2#2024854411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1434C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenter#1434D47
hypocenterC47#13972
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
6. #20241649C2semidirect
7. #20241649C2semidirect
8. #20241645C2semidirect
9. #20241644C2semidirect
10. #20241623C2semidirect
11. #20241621C2semidirect
12. #20241614C2semidirect
15. C47×#1434C2semidirect
28. #15688985C4semidirect
121. C47⋊#95C2×C4semidirect
122. C47⋊#95C2×C4semidirect
123. C47⋊#95C2×C4semidirect
139. #95×C47C2×C4semidirect
511. #1434D47semidirect
570. C47#13972semidirect
654. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156889972
C2×#156889852
C2×C4×(C2×D47)⋊C42
C2×#95×D472
#202416492
#202416452
#202416442
#202416232
#202416212
#202416142
(C2×D47)⋊#952
C47×#14342
#1397247