Finite Group Databasebeta

← #26139083

Subgroups — #26139083

Order 12032.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic, complemented
3C2×#15689025C211yesmaximal, characteristic, complemented
4C2×#15688999C212yesmaximal, complemented
5C2×#15688983C211yesmaximal, characteristic, complemented
6#20241636C212yesmaximal, complemented
7#20241627C212yesmaximal, complemented
8#20241618C211yesmaximal, characteristic, complemented
9#20241618C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C22⋊D47C2212yes—
14C23×C4×D47C2212yes—
15C2×#13093998—24no—
16C2×#13093998—24no—
17C2×#13093998C418yescomplemented
18C2×C4×D188—24no—
19C2×C4×D188—24no—
20C2×C4×D188—24no—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×C22⋊Dic47C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×(C2×D47)⋊C4C2212yes—
28C22×(C2×D47)⋊C4C2212yes—
29#15689025—24no—
30#15688999—28no—
31#15688983—24no—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C24×C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C22×C42×C47C2211yescharacteristic
42C4×C22⋊C4×C47—24no—
43C2×#95×C47C2211yescharacteristic
44C2×#95×C47C2211yescharacteristic
45C24×D47C2312yes—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188—22no—
49C22×D188—22no—
50C22×D188C2×C414yes—
51C22×D188D414yes—
52C22×D188D414yes—
53C22×C22⋊D47—24no—
54C22×C22⋊D47—24no—
55C22×C22⋊D47—24no—
56C22×C22⋊D47—24no—
57C22×C22⋊D47—42no—
58C22×C22⋊D47—42no—
59C22×C22⋊D47C2×C418yescomplemented
60C23×Dic47C2312yes—
61C23×Dic47C2312yes—
62C23×Dic47C2312yes—
63C22×C4×D47—24no—
64C22×C4×D47—24no—
65C22×C4×D47—24no—
66C22×C4×D47—24no—
67C22×C4×D47—24no—
68C22×C4×D47—42no—
69C22×C4×D47—42no—
70#13093998—232no—
71C4×D188—232no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—22no—
76C2×C4⋊Dic47—22no—
77C2×C4⋊Dic47—22no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47C2×C414yescomplemented
80C2×C4⋊Dic47D414yescomplemented
81C2×C22⋊Dic47—24no—
82C2×C22⋊Dic47—24no—
83C2×C22⋊Dic47—42no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—24no—
90C2×(C2×D47)⋊C4—24no—
91C2×(C2×D47)⋊C4—24no—
92C2×(C2×D47)⋊C4—24no—
93C2×(C2×D47)⋊C4—42no—
94C2×(C2×D47)⋊C4—42no—
95C2×(C2×D47)⋊C4C2×C418yescomplemented
96C47⋊#95—24no—
97C47⋊#95—24no—
98C47⋊#95—24no—
99C47⋊#95—42no—
100C47⋊#95—42no—
101C25×C47C2311yescharacteristic
102C23×C4×C47—22no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—22no—
106C23×C4×C47—22no—
107C23×C4×C47—22no—
108C23×C4×C47C2×C414yescomplemented
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
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×C47D414yescomplemented
121C2×C42×C47—22no—
122C2×C42×C47—22no—
123C2×C42×C47—22no—
124C2×C42×C47—22no—
125C2×C42×C47—22no—
126C2×C42×C47D414yescomplemented
127#95×C47—22no—
128#95×C47—22no—
129C24×C47—21no—
130C24×C47—21no—
131C24×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47—21no—
136C24×C47—21no—
137C24×C47—21no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47—21no—
141C24×C47C22×C412yes—
142C24×C47C2×D412yes—
143C24×C47#4112yes—
144C24×C47C2411yescharacteristic
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47—22no—
150C23×D47—22no—
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47C22×C414yes—
158C23×D47C2×D414yes—
159C23×D47C2×D414yes—
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—28no—
189C22×C4×C47—28no—
190C22×C4×C47—28no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47—44no—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C22×C412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47C2×D412yes—
205C22×C4×C47#4112yes—
206C22×C4×C47#4112yes—
207C22×C4×C47#4112yes—
208C22×C4×C47#4112yes—
209C2×C22⋊D47—216no—
210C2×C22⋊D47—216no—
211C2×C22⋊D47—48no—
212C2×C22⋊D47—48no—
213C2×C22⋊D47—48no—
214C2×C22⋊D47—48no—
215C2×C22⋊D47—48no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47C22×C414yes—
236C22×Dic47C2×D414yes—
237C2×D188—28no—
238C2×D188—28no—
239C2×D188—28no—
240C2×D188—28no—
241C2×D188—28no—
242C2×D188—28no—
243C2×D188C22⋊C4116yescomplemented
244C2×C4×D47—216no—
245C2×C4×D47—48no—
246C2×C4×D47—48no—
247C2×C4×D47—48no—
248C2×C4×D47—48no—
249C2×C4×D47—48no—
250C2×C4×D47—48no—
251C22⋊C4×C47—28no—
252C22⋊C4×C47—28no—
253C42×C47—28no—
254C42×C47—44no—
255C22⋊Dic47—48no—
256(C2×D47)⋊C4—216no—
257(C2×D47)⋊C4—216no—
258(C2×D47)⋊C4—48no—
259(C2×D47)⋊C4—48no—
260C4⋊Dic47—28no—
261C4⋊Dic47—28no—
262C4⋊Dic47—44no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—22no—
277C23×C47—22no—
278C23×C47—22no—
279C23×C47—22no—
280C23×C47—22no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47—41no—
293C23×C47—41no—
294C23×C47—41no—
295C23×C47—41no—
296C23×C47—41no—
297C23×C47C4×D414yescomplemented
298C23×C47C23×C411yescharacteristic
299C23×C47C22×D411yescharacteristic
300C23×C47C22×D411yescharacteristic
301C23×C47C22×D411yescharacteristic
302C23×C47C22×D411yescharacteristic
303C23×C47C22×D411yescharacteristic
304C23×C47C2×#4111yescharacteristic
305C23×C47C2×#4111yescharacteristic
306C23×C47C2×#4111yescharacteristic
307C23×C47C2×#4111yescharacteristic
308C23×C47C2×#4111yescharacteristic
309C23×C47H(5,𝔽2)11yescharacteristic
310C23×C47H(5,𝔽2)11yescharacteristic
311C23×C47H(5,𝔽2)11yescharacteristic
312C23×C472−1+411yescharacteristic
313C22×D47—24no—
314C22×D47—24no—
315C22×D47—24no—
316C22×D47—24no—
317C22×D47—24no—
318C22×D47—24no—
319C22×D47—24no—
320C22×D47—24no—
321C22×D47—24no—
322C22×D47—24no—
323C22×D47—24no—
324C22×D47—24no—
325C22×D47—24no—
326C22×D47—24no—
327C22×D47—24no—
328C22×D47—24no—
329C22×D47—24no—
330C22×D47—24no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—42no—
340C22×D47—42no—
341C22×D47—42no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—42no—
345C22×D47—42no—
346C22×D47—42no—
347C22×D47C2×C22⋊C418yes—
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—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
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—41no—
382C2×C4×C47—416no—
383C2×C4×C47C2×C22⋊C414yes—
384C2×C4×C47C4×D414yes—
385C2×C4×C47C4×D414yes—
386C2×C4×C47#12014yes—
387C2×C4×C47#12114yes—
388C2×C4×C47#12114yes—
389C2×C4×C47#12114yescomplemented
390C2×C4×C47#12314yes—
391C22⋊D47—432no—
392C2×Dic47—24no—
393C2×Dic47—24no—
394C2×Dic47—24no—
395C2×Dic47—24no—
396C2×Dic47—24no—
397C2×Dic47—24no—
398C2×Dic47—42no—
399C2×Dic47—42no—
400C2×Dic47—42no—
401C2×Dic47—42no—
402C2×Dic47—42no—
403C2×Dic47—42no—
404C2×Dic47—42no—
405C2×Dic47—42no—
406C2×Dic47—42no—
407C2×Dic47—42no—
408C2×Dic47—42no—
409C2×Dic47—42no—
410C2×Dic47—42no—
411C2×Dic47—42no—
412C2×Dic47—42no—
413D188—232no—
414C4×D47—432no—
415#13970—471nomaximal, Sylow
416C22×C47—24no—
417C22×C47—24no—
418C22×C47—24no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—42no—
431C22×C47C22×C22⋊C411yescharacteristic
432C22×C47C2×C4×D411yescharacteristic
433C22×C47C2×C4×D411yescharacteristic
434C22×C47C2×C4×D411yescharacteristic
435C22×C47C4×#4111yescharacteristic
436C22×C47#51811yescharacteristic
437C22×C47#52011yescharacteristic
438C22×C47C2×#12011yescharacteristic
439C22×C47C2×#12111yescharacteristic
440C22×C47C2×#12111yescharacteristic
441C22×C47C2×#12111yescharacteristic
442C22×C47C2×#12311yescharacteristic
443C22×C47#52511yescharacteristic
444C22×C47#52911yescharacteristic
445C22×C47#53211yescharacteristic
446C22×C47#53511yescharacteristic
447C22×C47#53711yescharacteristic
448C22×C47#54011yescharacteristic
449C22×C47#54211yescharacteristic
450C22×C47D4211yescharacteristic
451C22×C47D4211yescharacteristic
452C22×C47D4211yescharacteristic
453C22×C47#54611yescharacteristic
454C22×C47#54611yescharacteristic
455C22×C47#54611yescharacteristic
456C22×C47#54611yescharacteristic
457C22×C47#54611yescharacteristic
458C22×C47#54711yescharacteristic
459C22×C47#54711yescharacteristic
460C22×C47#54711yescharacteristic
461C22×C47#54811yescharacteristic
462C22×C47#55011yescharacteristic
463C22×C47#55311yescharacteristic
464C22×C47#55311yescharacteristic
465C22×C47#55511yescharacteristic
466C2×D47—28no—
467C2×D47—28no—
468C2×D47—28no—
469C2×D47—44no—
470C2×D47—44no—
471C2×D47—44no—
472C2×D47—44no—
473C2×D47—44no—
474C2×D47—44no—
475C2×D47—44no—
476C2×D47—44no—
477C2×D47—44no—
478C2×D47—44no—
479C2×D47—44no—
480C2×D47—44no—
481C4×C47—24no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47#38618yescomplemented
487Dic47—44no—
488Dic47—44no—
489Dic47—82no—
490C22×#121—471no—
491C22×C4×D4—471no—
492C2×#390—471no—
493C2×#386—472no—
494C2×#380—471no—
495C2×C4×C22⋊C4D4711yescharacteristic, complemented
496#1440—472no—
497#1438—472no—
498C4⋊#95—471no—
499C4⋊#95—471no—
500C22⋊#95—472no—
501C2×C47—44no—
502C2×C47C2×#38611yescharacteristic
503C2×C47C4×#12111yescharacteristic
504C2×C47#232411yescharacteristic
505C2×C47D4×C22⋊C411yescharacteristic
506C2×C47#233911yescharacteristic
507C2×C47#236111yescharacteristic
508C2×C47#236311yescharacteristic
509C2×C47#240711yescharacteristic
510C2×C47#240811yescharacteristic
511C2×C47#242011yescharacteristic
512C2×C47#242211yescharacteristic
513C2×C47#242711yescharacteristic
514C2×C47#242811yescharacteristic
515C2×C47#253511yescharacteristic
516C2×C47#253711yescharacteristic
517D47—48no—
518C23×D4—472no—
519C23×D4—471no—
520C24×C4—472no—
521C24×C4C2×D4711yescharacteristic
522C2×#121—478no—
523C2×#121—944no—
524C2×#121—944no—
525C2×C4×D4—944no—
526C2×C4×D4—944no—
527C2×C4×D4—944no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C22⋊C4—472no—
532C22×C22⋊C4—472no—
533C22×C22⋊C4—472no—
534C22×C22⋊C4—472no—
535C22×C22⋊C4—472no—
536C22×C22⋊C4C2×D4711yescharacteristic
537C22×C22⋊C4C2×D4711yescharacteristic
538C22×C42C2×D4711yescharacteristic
539C22×C42C2×D4711yescharacteristic
540#390—944no—
541#386—948no—
542#380—944no—
543C4×C22⋊C4—24no—
544C2×#95—472no—
545C2×#95—472no—
546C2×#95—472no—
547C2×#95—472no—
548C2×#95—472no—
549C2×#95C2×D4711yescharacteristic
550C2×#95C2×D4711yescharacteristic
551C47#1397011yescharacteristic, complemented, Sylow
552C25—472no—
553C25C22×D4711yescharacteristic
554C22×D4—478no—
555C22×D4—474no—
556C22×D4—474no—
557C22×D4—474no—
558C22×D4—944no—
559C22×D4—944no—
560C22×D4—944no—
561C22×D4—944no—
562C22×D4—942no—
563C22×D4—942no—
564C22×D4—942no—
565C22×D4—942no—
566C22×D4—1882no—
567C22×D4—1882no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—472no—
575C23×C4—472no—
576C23×C4—472no—
577C23×C4—944no—
578C23×C4—944no—
579C23×C4—944no—
580C23×C4—944no—
581C23×C4—944no—
582C23×C4—1882no—
583C23×C4—1882no—
584C23×C4C4×D4714yescomplemented
585C23×C4C22×D4711yescharacteristic
586C23×C4C22×D4711yescharacteristic
587C23×C4C22×D4711yescharacteristic
588C23×C4C22×D4711yescharacteristic
589C23×C4C22×D4711yescharacteristic
590C23×C4C22×D4711yescharacteristic
591#121—9432no—
592C4×D4—9432no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—474no—
595C2×C4⋊C4—942no—
596C2×C4⋊C4—942no—
597C2×C4⋊C4—942no—
598C2×C4⋊C4—942no—
599C2×C4⋊C4—942no—
600C2×C4⋊C4—942no—
601C2×C4⋊C4—942no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—478no—
608C2×C22⋊C4—944no—
609C2×C22⋊C4—944no—
610C2×C22⋊C4—944no—
611C2×C22⋊C4—944no—
612C2×C22⋊C4—944no—
613C2×C22⋊C4—944no—
614C2×C22⋊C4—944no—
615C2×C22⋊C4—944no—
616C2×C22⋊C4—944no—
617C2×C22⋊C4—944no—
618C2×C22⋊C4—944no—
619C2×C22⋊C4—1882no—
620C2×C22⋊C4—1882no—
621C2×C22⋊C4—1882no—
622C2×C22⋊C4D18814yescomplemented
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—22no—
628C2×C42C22⋊D4714yescomplemented
629#95—22no—
630#95—22no—
631#95—944no—
632#95—944no—
633#95—944no—
634#95—1882no—
635#95—1882no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—474no—
649C24—474no—
650C24—474no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—942no—
656C24—942no—
657C24—942no—
658C24—942no—
659C24—942no—
660C24—942no—
661C24—942no—
662C24—942no—
663C24C2×C4×D4712yes—
664C24C2×D18812yes—
665C24#1062535012yes—
666C24C23×D4711yescharacteristic
667C2×D4—4716no—
668C2×D4—9416no—
669C2×D4—9416no—
670C2×D4—948no—
671C2×D4—948no—
672C2×D4—948no—
673C2×D4—948no—
674C2×D4—948no—
675C2×D4—948no—
676C2×D4—1888no—
677C2×D4—1888no—
678C2×D4—1888no—
679C2×D4—1888no—
680C2×D4—1888no—
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—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—474no—
717C22×C4—474no—
718C22×C4—9416no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4—942no—
731C22×C4—942no—
732C22×C4—942no—
733C22×C4—942no—
734C22×C4—942no—
735C22×C4—942no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4—1888no—
739C22×C4—1888no—
740C22×C4—1888no—
741C22×C4—1888no—
742C22×C4—1888no—
743C22×C4—1888no—
744C22×C4C2×C4×D4712yes—
745C22×C4C2×C4×D4712yes—
746C22×C4C2×D18812yes—
747C22×C4C2×D18812yes—
748C22×C4#1062535012yes—
749C22×C4#1062535012yes—
750C22×C4#1062535012yes—
751C22×C4D4×D4712yes—
752C22×C4D4×D4712yes—
753C22×C4D4×D4712yes—
754C22×C4#1062535212yes—
755C22×C4C2×C22⋊D4712yes—
756C22×C4C2×C22⋊D4712yes—
757C22×C4C2×C22⋊D4712yes—
758C4⋊C4—948no—
759C4⋊C4—948no—
760C4⋊C4—1884no—
761C22⋊C4—28no—
762C22⋊C4—28no—
763C22⋊C4—9416no—
764C22⋊C4—9416no—
765C22⋊C4—1888no—
766C22⋊C4—1888no—
767C22⋊C4—1888no—
768C42—28no—
769C42—44no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—478no—
805C23—944no—
806C23—944no—
807C23—944no—
808C23—944no—
809C23—944no—
810C23—944no—
811C23—944no—
812C23—944no—
813C23—944no—
814C23—944no—
815C23—944no—
816C23—944no—
817C23—944no—
818C23—944no—
819C23—944no—
820C23—944no—
821C23—944no—
822C23—944no—
823C23—1882no—
824C23—1882no—
825C23—1882no—
826C23—1882no—
827C23—1882no—
828C23—1882no—
829C23—1882no—
830C23—1882no—
831C23—1882no—
832C23—1882no—
833C23—1882no—
834C23—1882no—
835C23—1882no—
836C23—1882no—
837C23—1882no—
838C23—1882no—
839C23C4×D18814yescomplemented
840C23C22×C4×D4711yescharacteristic
841C23C2×D4×D4711yescharacteristic
842C23C2×D4×D4711yescharacteristic
843C23C2×D4×D4711yescharacteristic
844C23C22×C22⋊D4711yescharacteristic
845C23C22×D18811yescharacteristic
846C23C2×#1062535211yescharacteristic
847C23C2×#1062535011yescharacteristic
848C23C2×#1062535011yescharacteristic
849C23C2×#1062535011yescharacteristic
850C23C2×#1062535011yescharacteristic
851C23#1309407011yescharacteristic
852C23#1309407011yescharacteristic
853C23#1309407011yescharacteristic
854C23#1309407111yescharacteristic
855D4—9432no—
856D4—18832no—
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—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
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—416no—
892C2×C4—944no—
893C2×C4—944no—
894C2×C4—944no—
895C2×C4—944no—
896C2×C4—944no—
897C2×C4—944no—
898C2×C4—18832no—
899C2×C4—1882no—
900C2×C4—1882no—
901C2×C4—1882no—
902C2×C4—1882no—
903C2×C4—1882no—
904C2×C4—1882no—
905C2×C4—1882no—
906C2×C4—1882no—
907C2×C4—1882no—
908C2×C4—1882no—
909C2×C4—1882no—
910C2×C4—1882no—
911C2×C4—1882no—
912C2×C4—1882no—
913C2×C4—1882no—
914C2×C4C22⋊C4×D4714yes—
915C2×C4(C22⋊D47)⋊C414yes—
916C2×C4C4×C22⋊D4714yes—
917C2×C4#1309399214yes—
918C2×C4#1309399514yes—
919C2×C4#1309399714yes—
920C2×C4#1309399814yescomplemented
921C2×C4#1309400614yes—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—948no—
938C22—948no—
939C22—948no—
940C22—1884no—
941C22—1884no—
942C22—1884no—
943C22—1884no—
944C22—1884no—
945C22—1884no—
946C22—1884no—
947C22—1884no—
948C22—1884no—
949C22—1884no—
950C22—1884no—
951C22—1884no—
952C22C2×C22⋊C4×D4711yescharacteristic
953C22C2×(C22⋊D47)⋊C411yescharacteristic
954C22C2×C4×C22⋊D4711yescharacteristic
955C22C2×C4×D18811yescharacteristic
956C22C4×#1062535011yescharacteristic
957C22#1568959711yescharacteristic
958C22#1568960311yescharacteristic
959C22C2×#1309399211yescharacteristic
960C22C2×#1309399511yescharacteristic
961C22C2×#1309399711yescharacteristic
962C22C2×#1309399811yescharacteristic
963C22C2×#1309400611yescharacteristic
964C22#1568963411yescharacteristic
965C22#1568965711yescharacteristic
966C22#1568967311yescharacteristic
967C22#1568968711yescharacteristic
968C22#1568970111yescharacteristic
969C22#1568972811yescharacteristic
970C22#1568974411yescharacteristic
971C22D4×D18811yescharacteristic
972C22D4×D18811yescharacteristic
973C22D4×D18811yescharacteristic
974C22#1568976911yescharacteristic
975C22#1568976911yescharacteristic
976C22#1568976911yescharacteristic
977C22#1568976911yescharacteristic
978C22#1568976911yescharacteristic
979C22#1568977711yescharacteristic
980C22#1568977811yescharacteristic
981C22#1568977811yescharacteristic
982C22#1568978211yescharacteristic
983C22#1568979411yescharacteristic
984C22#1568981911yescharacteristic
985C22#1568981911yescharacteristic
986C22#1568983811yescharacteristic
987C4—24no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—3762no—
993C4—1884no—
994C4—1884no—
995C4#1568899918yescomplemented
996C2—44no—
997C2—1888no—
998C2C2×#1568899911yescharacteristic
999C2C4×#1309399811yescharacteristic
1000C2#2024608111yescharacteristic
1001C2C22⋊C4×D18811yescharacteristic
1002C2#2024621911yescharacteristic
1003C2#2024640211yescharacteristic
1004C2#2024642411yescharacteristic
1005C2#2024673311yescharacteristic
1006C2#2024674411yescharacteristic
1007C2#2024688011yescharacteristic
1008C2#2024690211yescharacteristic
1009C2#2024696511yescharacteristic
1010C2#2024697611yescharacteristic
1011C2#2024828911yescharacteristic
1012C2#2024830111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC22×#13093998C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13970
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D188C2semidirect
3. C2×#15689025C2semidirect
4. C2×#15688999C2semidirect
5. C2×#15688983C2semidirect
6. #20241636C2semidirect
7. #20241627C2semidirect
8. #20241618C2semidirect
9. #20241618C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C2×C4×C22⋊C4×C47C2semidirect
17. C2×#13093998C4semidirect
59. C22×C22⋊D47C2×C4semidirect
79. C2×C4⋊Dic47C2×C4semidirect
80. C2×C4⋊Dic47D4semidirect
95. C2×(C2×D47)⋊C4C2×C4semidirect
108. C23×C4×C47C2×C4semidirect
120. C2×C22⋊C4×C47D4semidirect
126. C2×C42×C47D4semidirect
243. C2×D188C22⋊C4semidirect
297. C23×C47C4×D4semidirect
389. C2×C4×C47#121semidirect
486. C4×C47#386semidirect
495. C2×C4×C22⋊C4D47semidirect
551. C47#13970semidirect
584. C23×C4C4×D47semidirect
622. C2×C22⋊C4D188semidirect
628. C2×C42C22⋊D47semidirect
839. C23C4×D188semidirect
920. C2×C4#13093998semidirect
995. C4#15688999semidirect

Maximal subgroups

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

subgroupindex
C22×#130939982
C22×C4×D1882
C2×#156890252
C2×#156889992
C2×#156889832
#202416362
#202416272
#202416182
(C2×D47)⋊#952
C2×C4×C22⋊C4×C472
#1397047