Finite Group Databasebeta

← C47×#16274 #26055972

Subgroups — C47×#16274 #26055972

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#397C211yesmaximal, characteristic, complemented
2C2×C47×#394C211yesmaximal, characteristic, complemented
3C2×C47×#394C211yesmaximal, characteristic, complemented
4C2×C47×#392C211yesmaximal, characteristic
5C2×C47×#390C211yesmaximal, characteristic, complemented
6C2×C47×#388C211yesmaximal, characteristic, complemented
7C47×#1441C211yesmaximal, characteristic, complemented
8C47×#1439C211yesmaximal, characteristic, complemented
9C47×#1439C211yesmaximal, characteristic, complemented
10C47×#1439C211yesmaximal, characteristic, complemented
11C47×#1439C211yesmaximal, characteristic, complemented
12C47×#1438C211yesmaximal, characteristic, complemented
13C47×#1438C211yesmaximal, characteristic, complemented
14C47×#1438C211yesmaximal, characteristic, complemented
15C47×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C22×C4⋊C4×C47C2211yescharacteristic
23C22×C22⋊C4×C47C2211yescharacteristic
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2211yescharacteristic
28C22×C22⋊C4×C47C2211yescharacteristic
29C22×C22⋊C4×C47C2211yescharacteristic
30C22×C22⋊C4×C47C2211yescharacteristic
31C22×C22⋊C4×C47C2211yescharacteristic
32C22×C22⋊C4×C47C2211yescharacteristic
33C22×C22⋊C4×C47C2211yescharacteristic
34C22×C22⋊C4×C47C2211yescharacteristic
35C22×C22⋊C4×C47C2211yescharacteristic
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C47×#397—24no—
40C47×#394—24no—
41C47×#394—24no—
42C47×#392—24no—
43C47×#390—24no—
44C47×#388—24no—
45C2×#95×C47C2211yescharacteristic
46C2×#95×C47C2211yescharacteristic
47C2×#95×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C2×#95×C47C2211yescharacteristic
57C25×C47C2311yescharacteristic
58C25×C47C2311yescharacteristic
59C25×C47C2311yescharacteristic
60C22×D4×C47—22no—
61C22×D4×C47—22no—
62C22×D4×C47—22no—
63C22×D4×C47—22no—
64C22×D4×C47—22no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—22no—
68C22×D4×C47—22no—
69C22×D4×C47—22no—
70C22×D4×C47—22no—
71C22×D4×C47—41no—
72C22×D4×C47—41no—
73C22×D4×C47—41no—
74C22×D4×C47—41no—
75C22×D4×C47—41no—
76C22×D4×C47—41no—
77C22×D4×C47—41no—
78C22×D4×C47—41no—
79C22×D4×C47—41no—
80C22×D4×C47—41no—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2311yescharacteristic
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47—22no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47—22no—
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—41no—
101C2×C4⋊C4×C47—41no—
102C2×C4⋊C4×C47—41no—
103C2×C4⋊C4×C47—41no—
104C2×C4⋊C4×C47—41no—
105C2×C22⋊C4×C47—22no—
106C2×C22⋊C4×C47—22no—
107C2×C22⋊C4×C47—22no—
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—22no—
114C2×C22⋊C4×C47—22no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47—22no—
120C2×C22⋊C4×C47—22no—
121C2×C22⋊C4×C47—22no—
122C2×C22⋊C4×C47—22no—
123C2×C22⋊C4×C47—22no—
124C2×C22⋊C4×C47—22no—
125C2×C22⋊C4×C47—22no—
126C2×C22⋊C4×C47—41no—
127C2×C22⋊C4×C47—41no—
128C2×C22⋊C4×C47—41no—
129C2×C22⋊C4×C47—41no—
130C2×C22⋊C4×C47—41no—
131C2×C22⋊C4×C47—41no—
132C2×C22⋊C4×C47—41no—
133C2×C22⋊C4×C47—41no—
134C2×C22⋊C4×C47—41no—
135C2×C22⋊C4×C47—41no—
136C2×C22⋊C4×C47—41no—
137C2×C22⋊C4×C47—41no—
138C2×C22⋊C4×C47—41no—
139C2×C22⋊C4×C47—41no—
140C2×C22⋊C4×C47—41no—
141C2×C22⋊C4×C47—41no—
142C2×C22⋊C4×C47—41no—
143C2×C22⋊C4×C47—41no—
144C2×C22⋊C4×C47—41no—
145C2×C22⋊C4×C47—41no—
146C2×C22⋊C4×C47—41no—
147C2×C22⋊C4×C47—41no—
148C2×C22⋊C4×C47D414yes—
149C2×C22⋊C4×C47D414yescomplemented
150C2×C42×C47—22no—
151C2×C42×C47—22no—
152C2×C42×C47—41no—
153#95×C47—22no—
154#95×C47—22no—
155#95×C47—22no—
156#95×C47—22no—
157#95×C47—22no—
158#95×C47—22no—
159#95×C47—22no—
160#95×C47—41no—
161#95×C47—41no—
162#95×C47—41no—
163#95×C47—41no—
164#95×C47D414yescomplemented
165C24×C47—21no—
166C24×C47—21no—
167C24×C47—21no—
168C24×C47—21no—
169C24×C47—21no—
170C24×C47—21no—
171C24×C47—21no—
172C24×C47—21no—
173C24×C47—21no—
174C24×C47—21no—
175C24×C47—21no—
176C24×C47—21no—
177C24×C47—21no—
178C24×C47—21no—
179C24×C47—21no—
180C24×C47—21no—
181C24×C47—21no—
182C24×C47—21no—
183C24×C47—21no—
184C24×C47—21no—
185C24×C47—21no—
186C24×C47—21no—
187C24×C47—21no—
188C24×C47—21no—
189C24×C47—21no—
190C24×C47—21no—
191C24×C47—21no—
192C24×C47—21no—
193C24×C47—21no—
194C24×C47—21no—
195C24×C47—21no—
196C24×C47—21no—
197C24×C47—21no—
198C24×C47—21no—
199C24×C47—21no—
200C24×C47—21no—
201C24×C47—21no—
202C24×C47—21no—
203C24×C47—21no—
204C24×C47—21no—
205C24×C47—21no—
206C24×C47—21no—
207C24×C47C2×D412yes—
208C24×C47C2×D412yes—
209C24×C47#4112yes—
210C24×C47C2411yescharacteristic
211C2×D4×C47—28no—
212C2×D4×C47—44no—
213C2×D4×C47—44no—
214C2×D4×C47—44no—
215C2×D4×C47—44no—
216C2×D4×C47—44no—
217C2×D4×C47—44no—
218C2×D4×C47—44no—
219C2×D4×C47—44no—
220C2×D4×C47—44no—
221C2×D4×C47—44no—
222C2×D4×C47—44no—
223C2×D4×C47—44no—
224C2×D4×C47—44no—
225C2×D4×C47—44no—
226C2×D4×C47—44no—
227C2×D4×C47—44no—
228C2×D4×C47—44no—
229C2×D4×C47—44no—
230C2×D4×C47—44no—
231C2×D4×C47—44no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—21no—
240C22×C4×C47—21no—
241C22×C4×C47—21no—
242C22×C4×C47—21no—
243C22×C4×C47—21no—
244C22×C4×C47—21no—
245C22×C4×C47—21no—
246C22×C4×C47—21no—
247C22×C4×C47—21no—
248C22×C4×C47—21no—
249C22×C4×C47—21no—
250C22×C4×C47—21no—
251C22×C4×C47—21no—
252C22×C4×C47—21no—
253C22×C4×C47—21no—
254C22×C4×C47—21no—
255C22×C4×C47—21no—
256C22×C4×C47—21no—
257C22×C4×C47—21no—
258C22×C4×C47—21no—
259C22×C4×C47—21no—
260C22×C4×C47—21no—
261C22×C4×C47—21no—
262C22×C4×C47—21no—
263C22×C4×C47—21no—
264C22×C4×C47—21no—
265C22×C4×C47—21no—
266C22×C4×C47—21no—
267C22×C4×C47—21no—
268C22×C4×C47—21no—
269C22×C4×C47—21no—
270C22×C4×C47—21no—
271C22×C4×C47—21no—
272C22×C4×C47—21no—
273C22×C4×C47—21no—
274C22×C4×C47—21no—
275C22×C4×C47—21no—
276C22×C4×C47—21no—
277C22×C4×C47—21no—
278C22×C4×C47—21no—
279C22×C4×C47—21no—
280C22×C4×C47—21no—
281C22×C4×C47—21no—
282C22×C4×C47—21no—
283C22×C4×C47—21no—
284C22×C4×C47—21no—
285C22×C4×C47—21no—
286C22×C4×C47—21no—
287C22×C4×C47—21no—
288C22×C4×C47—21no—
289C22×C4×C47—21no—
290C22×C4×C47—21no—
291C22×C4×C47—21no—
292C22×C4×C47—21no—
293C22×C4×C47—21no—
294C22×C4×C47—21no—
295C22×C4×C47—21no—
296C22×C4×C47—21no—
297C22×C4×C47—21no—
298C22×C4×C47—21no—
299C22×C4×C47—21no—
300C22×C4×C47—21no—
301C22×C4×C47—21no—
302C22×C4×C47—21no—
303C22×C4×C47—21no—
304C22×C4×C47—21no—
305C22×C4×C47—21no—
306C22×C4×C47C2×D412yes—
307C22×C4×C47C2×D412yes—
308C22×C4×C47C2×D412yes—
309C22×C4×C47C2×D412yes—
310C22×C4×C47C2×D412yes—
311C22×C4×C47C2×D412yes—
312C22×C4×C47C2×D412yes—
313C22×C4×C47#4112yes—
314C22×C4×C47#4112yes—
315C22×C4×C47#4112yes—
316C4⋊C4×C47—44no—
317C4⋊C4×C47—44no—
318C4⋊C4×C47—44no—
319C4⋊C4×C47—44no—
320C22⋊C4×C47—28no—
321C22⋊C4×C47—44no—
322C22⋊C4×C47—44no—
323C22⋊C4×C47—44no—
324C22⋊C4×C47—44no—
325C22⋊C4×C47—44no—
326C22⋊C4×C47—44no—
327C22⋊C4×C47—44no—
328C22⋊C4×C47—44no—
329C22⋊C4×C47—44no—
330C22⋊C4×C47—44no—
331C22⋊C4×C47—44no—
332C22⋊C4×C47—44no—
333C22⋊C4×C47—44no—
334C22⋊C4×C47—44no—
335C42×C47—44no—
336C23×C47—22no—
337C23×C47—22no—
338C23×C47—22no—
339C23×C47—22no—
340C23×C47—22no—
341C23×C47—22no—
342C23×C47—22no—
343C23×C47—22no—
344C23×C47—22no—
345C23×C47—22no—
346C23×C47—22no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—41no—
358C23×C47—41no—
359C23×C47—41no—
360C23×C47—41no—
361C23×C47—41no—
362C23×C47—41no—
363C23×C47—41no—
364C23×C47—41no—
365C23×C47—41no—
366C23×C47—41no—
367C23×C47—41no—
368C23×C47—41no—
369C23×C47—41no—
370C23×C47—41no—
371C23×C47—41no—
372C23×C47—41no—
373C23×C47—41no—
374C23×C47—41no—
375C23×C47—41no—
376C23×C47—41no—
377C23×C47—41no—
378C23×C47—41no—
379C23×C47—41no—
380C23×C47—41no—
381C23×C47—41no—
382C23×C47—41no—
383C23×C47—41no—
384C23×C47—41no—
385C23×C47—41no—
386C23×C47—41no—
387C23×C47—41no—
388C23×C47—41no—
389C23×C47—41no—
390C23×C47—41no—
391C23×C47—41no—
392C23×C47—41no—
393C23×C47—41no—
394C23×C47—41no—
395C23×C47—41no—
396C23×C47—41no—
397C23×C47—41no—
398C23×C47—41no—
399C23×C47—41no—
400C23×C47—41no—
401C23×C47—41no—
402C23×C47—41no—
403C23×C47—41no—
404C23×C47—41no—
405C23×C47—41no—
406C23×C47—41no—
407C23×C47—41no—
408C23×C47—41no—
409C23×C47—41no—
410C23×C47—41no—
411C23×C47—41no—
412C23×C47—41no—
413C23×C47—41no—
414C23×C47—41no—
415C23×C47—41no—
416C23×C47—41no—
417C23×C47—41no—
418C23×C47—41no—
419C23×C47—41no—
420C23×C47—41no—
421C23×C47—41no—
422C23×C47—41no—
423C23×C47—41no—
424C23×C47—41no—
425C23×C47—41no—
426C23×C47—41no—
427C23×C47—41no—
428C23×C47—41no—
429C23×C47—41no—
430C23×C47—41no—
431C23×C47—41no—
432C23×C47—41no—
433C23×C47—41no—
434C23×C47—41no—
435C23×C47—41no—
436C23×C47—41no—
437C23×C47—41no—
438C23×C47—41no—
439C23×C47—41no—
440C23×C47—41no—
441C23×C47C22×D411yescharacteristic
442C23×C47C22×D411yescharacteristic
443C23×C47C22×D411yescharacteristic
444C23×C47C2×#4111yescharacteristic
445C23×C47C2×#4111yescharacteristic
446C23×C47C2×#4111yescharacteristic
447C23×C47C2×#4111yescharacteristic
448C23×C47H(5,𝔽2)11yescharacteristic
449C23×C47H(5,𝔽2)11yescharacteristic
450C23×C47H(5,𝔽2)11yescharacteristic
451C23×C47H(5,𝔽2)11yescharacteristic
452C23×C47H(5,𝔽2)11yescharacteristic
453C23×C47H(5,𝔽2)11yescharacteristic
454C23×C47H(5,𝔽2)11yescharacteristic
455C23×C472−1+411yescharacteristic
456D4×C47—416no—
457D4×C47—416no—
458D4×C47—416no—
459C2×C4×C47—22no—
460C2×C4×C47—22no—
461C2×C4×C47—22no—
462C2×C4×C47—22no—
463C2×C4×C47—22no—
464C2×C4×C47—22no—
465C2×C4×C47—22no—
466C2×C4×C47—22no—
467C2×C4×C47—22no—
468C2×C4×C47—22no—
469C2×C4×C47—22no—
470C2×C4×C47—22no—
471C2×C4×C47—22no—
472C2×C4×C47—22no—
473C2×C4×C47—22no—
474C2×C4×C47—22no—
475C2×C4×C47—22no—
476C2×C4×C47—22no—
477C2×C4×C47—22no—
478C2×C4×C47—22no—
479C2×C4×C47—22no—
480C2×C4×C47—22no—
481C2×C4×C47—22no—
482C2×C4×C47—22no—
483C2×C4×C47—22no—
484C2×C4×C47—22no—
485C2×C4×C47—22no—
486C2×C4×C47—41no—
487C2×C4×C47—41no—
488C2×C4×C47—41no—
489C2×C4×C47—41no—
490C2×C4×C47—41no—
491C2×C4×C47—41no—
492C2×C4×C47—41no—
493C2×C4×C47—41no—
494C2×C4×C47—41no—
495C2×C4×C47—41no—
496C2×C4×C47—41no—
497C2×C4×C47—41no—
498C2×C4×C47—41no—
499C2×C4×C47—41no—
500C2×C4×C47—41no—
501C2×C4×C47—41no—
502C2×C4×C47—41no—
503C2×C4×C47—41no—
504C2×C4×C47—41no—
505C2×C4×C47—41no—
506C2×C4×C47—41no—
507C2×C4×C47—41no—
508C2×C4×C47—41no—
509C2×C4×C47—41no—
510C2×C4×C47—41no—
511C2×C4×C47—41no—
512C2×C4×C47—41no—
513C2×C4×C47—41no—
514C2×C4×C47—41no—
515C2×C4×C47—41no—
516C2×C4×C47—41no—
517C2×C4×C47—41no—
518C2×C4×C47—41no—
519C2×C4×C47—41no—
520C2×C4×C47—41no—
521C2×C4×C47—41no—
522C2×C4×C47—41no—
523C2×C4×C47—41no—
524C2×C4×C47—41no—
525C2×C4×C47—41no—
526C2×C4×C47—41no—
527C2×C4×C47—41no—
528C2×C4×C47—41no—
529C2×C4×C47—41no—
530C2×C4×C47—41no—
531C2×C4×C47—41no—
532C2×C4×C47—41no—
533C2×C4×C47—41no—
534C2×C4×C47—41no—
535C2×C4×C47—41no—
536C2×C4×C47—41no—
537C2×C4×C47—41no—
538C2×C4×C47—41no—
539C2×C4×C47—41no—
540C2×C4×C47—41no—
541C2×C4×C47—41no—
542C2×C4×C47#12314yes—
543#16274C4711yesmaximal, characteristic, direct product factor, Sylow
544C22×C47—42no—
545C22×C47—42no—
546C22×C47—42no—
547C22×C47—42no—
548C22×C47—42no—
549C22×C47—42no—
550C22×C47—42no—
551C22×C47—42no—
552C22×C47—42no—
553C22×C47—42no—
554C22×C47—42no—
555C22×C47—42no—
556C22×C47—42no—
557C22×C47—42no—
558C22×C47—42no—
559C22×C47—42no—
560C22×C47—42no—
561C22×C47—42no—
562C22×C47—42no—
563C22×C47—42no—
564C22×C47—42no—
565C22×C47—81no—
566C22×C47—81no—
567C22×C47—81no—
568C22×C47—81no—
569C22×C47—81no—
570C22×C47—81no—
571C22×C47—81no—
572C22×C47—81no—
573C22×C47—81no—
574C22×C47—81no—
575C22×C47—81no—
576C22×C47—81no—
577C22×C47—81no—
578C22×C47—81no—
579C22×C47—81no—
580C22×C47—81no—
581C22×C47—81no—
582C22×C47—81no—
583C22×C47—81no—
584C22×C47—81no—
585C22×C47—81no—
586C22×C47—81no—
587C22×C47—81no—
588C22×C47—81no—
589C22×C47C2×#12311yescharacteristic
590C22×C47#52511yescharacteristic
591C22×C47#53211yescharacteristic
592C22×C47#53411yescharacteristic
593C22×C47#53511yescharacteristic
594C22×C47#53511yescharacteristic
595C22×C47#53711yescharacteristic
596C22×C47#53711yescharacteristic
597C22×C47#53711yescharacteristic
598C22×C47#53811yescharacteristic
599C22×C47#53811yescharacteristic
600C22×C47#53811yescharacteristic
601C22×C47#53911yescharacteristic
602C22×C47#54011yescharacteristic
603C22×C47#54011yescharacteristic
604C22×C47#54011yescharacteristic
605C22×C47#54211yescharacteristic
606C22×C47#54211yescharacteristic
607C22×C47#54211yescharacteristic
608C22×C47D4211yescharacteristic
609C22×C47D4211yescharacteristic
610C22×C47D4211yescharacteristic
611C22×C47#54611yescharacteristic
612C22×C47#54611yescharacteristic
613C22×C47#54611yescharacteristic
614C22×C47#54611yescharacteristic
615C22×C47#54611yescharacteristic
616C22×C47#55011yescharacteristic
617C22×C47#55111yescharacteristic
618C22×C47#55311yescharacteristic
619C22×C47#55911yescharacteristic
620C22×C47#56011yescharacteristic
621C22×C47#56011yescharacteristic
622C22×C47#56011yescharacteristic
623C22×C47H(3,𝔽4)11yescharacteristic
624C4×C47—24no—
625C4×C47—42no—
626C4×C47—42no—
627C4×C47—42no—
628C4×C47—42no—
629C4×C47—42no—
630C4×C47—42no—
631C4×C47—42no—
632C4×C47—81no—
633C4×C47—81no—
634C4×C47—81no—
635C4×C47—81no—
636C2×#397C2×C4711yescharacteristic, complemented
637C2×#394C2×C4711yescharacteristic, complemented
638C2×#394C2×C4711yescharacteristic, complemented
639C2×#392C2×C4711yescharacteristic
640C2×#390C2×C4711yescharacteristic, complemented
641C2×#388C2×C4711yescharacteristic, complemented
642#1441C2×C4711yescharacteristic, complemented
643#1439C2×C4711yescharacteristic, complemented
644#1439C2×C4711yescharacteristic, complemented
645#1439C2×C4711yescharacteristic, complemented
646#1439C2×C4711yescharacteristic, complemented
647#1438C2×C4711yescharacteristic, complemented
648#1438C2×C4711yescharacteristic, complemented
649#1438C2×C4711yescharacteristic, complemented
650#1436C2×C4711yescharacteristic, complemented
651C2×C47—82no—
652C2×C47—82no—
653C2×C47—82no—
654C2×C47#241811yescharacteristic
655C2×C47#244511yescharacteristic
656C2×C47#246411yescharacteristic
657C2×C47#262411yescharacteristic
658C2×C47#263011yescharacteristic
659C2×C47#266211yescharacteristic
660C2×C47#267011yescharacteristic
661C2×C47#267311yescharacteristic
662C2×C47#267511yescharacteristic
663C2×C47#267811yescharacteristic
664C2×C47#269111yescharacteristic
665C2×C47#270511yescharacteristic
666C2×C47#271211yescharacteristic
667C2×C47#279711yescharacteristic
668C2×C47#282811yescharacteristic
669C23×D4C22×C4711yescharacteristic
670C23×D4C22×C4711yescharacteristic
671C23×D4C22×C4711yescharacteristic
672C22×C4⋊C4C22×C4711yescharacteristic
673C22×C4⋊C4C22×C4711yescharacteristic
674C22×C4⋊C4C22×C4711yescharacteristic
675C22×C4⋊C4C22×C4711yescharacteristic
676C22×C22⋊C4C22×C4711yescharacteristic
677C22×C22⋊C4C22×C4711yescharacteristic
678C22×C22⋊C4C22×C4711yescharacteristic
679C22×C22⋊C4C22×C4711yescharacteristic
680C22×C22⋊C4C22×C4711yescharacteristic
681C22×C22⋊C4C22×C4711yescharacteristic
682C22×C22⋊C4C22×C4711yescharacteristic
683C22×C22⋊C4C22×C4711yescharacteristic
684C22×C22⋊C4C22×C4711yescharacteristic
685C22×C22⋊C4C22×C4711yescharacteristic
686C22×C22⋊C4C22×C4711yescharacteristic
687C22×C22⋊C4C22×C4711yescharacteristic
688C22×C22⋊C4C22×C4711yescharacteristic
689C22×C22⋊C4C22×C4711yescharacteristic
690C22×C22⋊C4C22×C4711yescharacteristic
691C22×C42C22×C4711yescharacteristic
692#397—24no—
693#394—24no—
694#394—24no—
695#392—24no—
696#390—24no—
697#388—24no—
698C2×#95C22×C4711yescharacteristic
699C2×#95C22×C4711yescharacteristic
700C2×#95C22×C4711yescharacteristic
701C2×#95C22×C4711yescharacteristic
702C2×#95C22×C4711yescharacteristic
703C2×#95C22×C4711yescharacteristic
704C2×#95C22×C4711yescharacteristic
705C2×#95C22×C4711yescharacteristic
706C2×#95C22×C4711yescharacteristic
707C2×#95C22×C4711yescharacteristic
708C2×#95C22×C4711yescharacteristic
709C2×#95C22×C4711yescharacteristic
710C47#1627411yescharacteristic, direct product factor, Sylow
711C25C23×C4711yescharacteristic
712C25C23×C4711yescharacteristic
713C25C23×C4711yescharacteristic
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C23×C4C23×C4711yescharacteristic
736C23×C4C23×C4711yescharacteristic
737C23×C4C23×C4711yescharacteristic
738C23×C4C23×C4711yescharacteristic
739C23×C4C23×C4711yescharacteristic
740C23×C4C23×C4711yescharacteristic
741C23×C4C23×C4711yescharacteristic
742C23×C4C23×C4711yescharacteristic
743C23×C4C23×C4711yescharacteristic
744C23×C4C23×C4711yescharacteristic
745C23×C4C23×C4711yescharacteristic
746C23×C4C23×C4711yescharacteristic
747C2×C4⋊C4—22no—
748C2×C4⋊C4—22no—
749C2×C4⋊C4—22no—
750C2×C4⋊C4—22no—
751C2×C4⋊C4—22no—
752C2×C4⋊C4—22no—
753C2×C4⋊C4—22no—
754C2×C4⋊C4—41no—
755C2×C4⋊C4—41no—
756C2×C4⋊C4—41no—
757C2×C4⋊C4—41no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4D4×C4714yes—
803C2×C22⋊C4D4×C4714yescomplemented
804C2×C42—22no—
805C2×C42—22no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95D4×C4714yescomplemented
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24C2×D4×C4712yes—
862C24C2×D4×C4712yes—
863C24#41×C4712yes—
864C24C24×C4711yescharacteristic
865C2×D4—28no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4C2×D4×C4712yes—
961C22×C4C2×D4×C4712yes—
962C22×C4C2×D4×C4712yes—
963C22×C4C2×D4×C4712yes—
964C22×C4C2×D4×C4712yes—
965C22×C4C2×D4×C4712yes—
966C22×C4C2×D4×C4712yes—
967C22×C4#41×C4712yes—
968C22×C4#41×C4712yes—
969C22×C4#41×C4712yes—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C22⋊C4—28no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C42—44no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23C22×D4×C4711yescharacteristic
1096C23C22×D4×C4711yescharacteristic
1097C23C22×D4×C4711yescharacteristic
1098C23C2×#41×C4711yescharacteristic
1099C23C2×#41×C4711yescharacteristic
1100C23C2×#41×C4711yescharacteristic
1101C23C2×#41×C4711yescharacteristic
1102C23H(5,𝔽2)×C4711yescharacteristic
1103C23H(5,𝔽2)×C4711yescharacteristic
1104C23H(5,𝔽2)×C4711yescharacteristic
1105C23H(5,𝔽2)×C4711yescharacteristic
1106C23H(5,𝔽2)×C4711yescharacteristic
1107C23H(5,𝔽2)×C4711yescharacteristic
1108C23H(5,𝔽2)×C4711yescharacteristic
1109C232−1+4×C4711yescharacteristic
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4#123×C4714yes—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22C2×#123×C4711yescharacteristic
1243C22C47×#52511yescharacteristic
1244C22C47×#53211yescharacteristic
1245C22C47×#53411yescharacteristic
1246C22C47×#53511yescharacteristic
1247C22C47×#53511yescharacteristic
1248C22C47×#53711yescharacteristic
1249C22C47×#53711yescharacteristic
1250C22C47×#53711yescharacteristic
1251C22C47×#53811yescharacteristic
1252C22C47×#53811yescharacteristic
1253C22C47×#53811yescharacteristic
1254C22C47×#53911yescharacteristic
1255C22C47×#54011yescharacteristic
1256C22C47×#54011yescharacteristic
1257C22C47×#54011yescharacteristic
1258C22C47×#54211yescharacteristic
1259C22C47×#54211yescharacteristic
1260C22C47×#54211yescharacteristic
1261C22D42×C4711yescharacteristic
1262C22D42×C4711yescharacteristic
1263C22D42×C4711yescharacteristic
1264C22C47×#54611yescharacteristic
1265C22C47×#54611yescharacteristic
1266C22C47×#54611yescharacteristic
1267C22C47×#54611yescharacteristic
1268C22C47×#54611yescharacteristic
1269C22C47×#55011yescharacteristic
1270C22C47×#55111yescharacteristic
1271C22C47×#55311yescharacteristic
1272C22C47×#55911yescharacteristic
1273C22C47×#56011yescharacteristic
1274C22C47×#56011yescharacteristic
1275C22C47×#56011yescharacteristic
1276C22C47×H(3,𝔽4)11yescharacteristic
1277C4—24no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C2—82no—
1290C2—82no—
1291C2—82no—
1292C2C47×#241811yescharacteristic
1293C2C47×#244511yescharacteristic
1294C2C47×#246411yescharacteristic
1295C2C47×#262411yescharacteristic
1296C2C47×#263011yescharacteristic
1297C2C47×#266211yescharacteristic
1298C2C47×#267011yescharacteristic
1299C2C47×#267311yescharacteristic
1300C2C47×#267511yescharacteristic
1301C2C47×#267811yescharacteristic
1302C2C47×#269111yescharacteristic
1303C2C47×#270511yescharacteristic
1304C2C47×#271211yescharacteristic
1305C2C47×#279711yescharacteristic
1306C2C47×#282811yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutator, Frattini, cosocleC24C24×C47
prime radicalC2×C47×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#397C2semidirect
2. C2×C47×#394C2semidirect
3. C2×C47×#394C2semidirect
5. C2×C47×#390C2semidirect
6. C2×C47×#388C2semidirect
7. C47×#1441C2semidirect
8. C47×#1439C2semidirect
9. C47×#1439C2semidirect
10. C47×#1439C2semidirect
11. C47×#1439C2semidirect
12. C47×#1438C2semidirect
13. C47×#1438C2semidirect
14. C47×#1438C2semidirect
15. C47×#1436C2semidirect
149. C2×C22⋊C4×C47D4semidirect
164. #95×C47D4semidirect
543. #16274C47direct (N × H)
636. C2×#397C2×C47semidirect
637. C2×#394C2×C47semidirect
638. C2×#394C2×C47semidirect
640. C2×#390C2×C47semidirect
641. C2×#388C2×C47semidirect
642. #1441C2×C47semidirect
643. #1439C2×C47semidirect
644. #1439C2×C47semidirect
645. #1439C2×C47semidirect
646. #1439C2×C47semidirect
647. #1438C2×C47semidirect
648. #1438C2×C47semidirect
649. #1438C2×C47semidirect
650. #1436C2×C47semidirect
710. C47#16274direct (N × H)
803. C2×C22⋊C4D4×C47semidirect
818. #95D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3972
C2×C47×#3942
C2×C47×#3922
C2×C47×#3902
C2×C47×#3882
C47×#14412
C47×#14392
C47×#14382
C47×#14362
#1627447