Finite Group Databasebeta

← #26389203

Subgroups — #26389203

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689711C212yesmaximal, complemented
2#20251740C211yesmaximal, characteristic, complemented
3#20251733C211yesmaximal, characteristic, complemented
4#20251670C212yesmaximal, complemented
5#20249316C212yesmaximal, complemented
6#20249122C212yesmaximal, complemented
7#20248511C214yesmaximal, complemented
8#20248481C214yesmaximal, complemented
9#20247810C212yesmaximal, complemented
10#20247751C212yesmaximal, complemented
11#20246976C212yesmaximal, complemented
12#20246902C212yesmaximal, complemented
13#20246091C212yesmaximal, complemented
14C4×#13093998C212yesmaximal, complemented
15C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16#15689711—216no—
17C2×#13094024C2211yescharacteristic, complemented
18C2×#13094021C2211yescharacteristic, complemented
19C2×#13094017C2214yes—
20C2×#13094010C2214yes—
21C2×#13094006C2214yes—
22C2×#13094003C2212yes—
23C2×#13093998C2212yes—
24C2×#13093998C2212yes—
25C2×#13093998C2212yes—
26C2×#13093998C2212yes—
27C2×#13093998C2212yes—
28C2×#13093997C2214yes—
29C2×#13093993C2214yes—
30C2×C4×D188C2212yescomplemented
31C2×C4×C22⋊D47C2214yes—
32#15689063C2214yescomplemented
33#15689050C2214yescomplemented
34#15689048C2214yes—
35#15689041C2214yescomplemented
36#15689039C2214yes—
37#15689039C2214yes—
38#15689036C2214yescomplemented
39#15689032C2214yes—
40#15689029C2212yescomplemented
41#15689025C2212yescomplemented
42#15689025C2212yescomplemented
43#15689025C2212yescomplemented
44#15689025C2212yescomplemented
45#15689021C2212yescomplemented
46#15689021C2212yescomplemented
47#15689021C2212yescomplemented
48#15689015C2214yescomplemented
49#15689014C2214yescomplemented
50#15689008C2214yescomplemented
51#15689002C2214yes—
52#15689002C2214yes—
53#15689002C2214yes—
54#15689002C2214yes—
55#15689001C2214yescomplemented
56#15688997C2214yescomplemented
57#15688993C2211yescharacteristic, complemented
58#15688993C2211yescharacteristic, complemented
59#15688983C2212yes—
60#15688983C2212yes—
61#15688983C2212yes—
62#15688983C2212yes—
63C4×C4⋊Dic47C2212yescomplemented
64C4×(C2×D47)⋊C4C2214yescomplemented
65C24×C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C42×C47C2211yescharacteristic
69C22×C42×C47C2211yescharacteristic
70C4×C22⋊C4×C47C2212yes—
71C4×C22⋊C4×C47C2212yes—
72C4×C22⋊C4×C47C2212yes—
73C4×C22⋊C4×C47C2212yes—
74C2×#95×C47C2211yescharacteristic
75C2×#95×C47C2211yescharacteristic
76C22×Dic94C2312yes—
77C22×D188C2312yes—
78C22×D188C2312yes—
79C22×D188C2312yes—
80C22×C22⋊D47C2314yes—
81C22×C22⋊D47C2314yes—
82C22×C22⋊D47C2314yes—
83C22×C4×D47C2314yes—
84#13094024—42no—
85#13094021—42no—
86#13094017—216no—
87#13094010—216no—
88#13094006—216no—
89#13094003—28no—
90#13093998—28no—
91#13093998—28no—
92#13093998—28no—
93#13093998—44no—
94#13093998—44no—
95#13093997—216no—
96#13093993—216no—
97C4×D188—44no—
98C4×C22⋊D47—216no—
99C2×C4⋊Dic47C2312yes—
100C2×C4⋊Dic47C2312yes—
101C2×C4⋊Dic47C2312yes—
102C2×C4⋊Dic47C2312yes—
103C2×C4⋊Dic47C2312yes—
104C2×C4⋊Dic47C2312yes—
105C2×C4⋊Dic47C2312yes—
106C2×C4⋊Dic47C2312yes—
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×C22⋊Dic47C2314yes—
110C2×C22⋊Dic47C2314yes—
111C2×C22⋊Dic47C2314yes—
112C2×(C2×D47)⋊C4C2314yes—
113C2×(C2×D47)⋊C4C2314yes—
114C2×(C2×D47)⋊C4C2314yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×C4×Dic47C2314yes—
121C47⋊#95C2314yes—
122C47⋊#95C2314yes—
123C47⋊#95C2314yes—
124C47⋊#95C2314yes—
125C47⋊#95C2314yes—
126C47⋊#95C2314yes—
127C25×C47C2311yescharacteristic
128C23×C4×C47—24no—
129C23×C4×C47—42no—
130C23×C4×C47—42no—
131C23×C4×C47C2312yes—
132C23×C4×C47C2311yescharacteristic
133C23×C4×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2312yes—
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—24no—
140C2×C22⋊C4×C47D418yescomplemented
141C2×C22⋊C4×C47C2312yes—
142C2×C22⋊C4×C47C2312yes—
143C2×C22⋊C4×C47C2312yes—
144C2×C22⋊C4×C47C2312yes—
145C2×C42×C47—42no—
146C2×C42×C47—42no—
147C2×C42×C47C2312yes—
148C2×C42×C47C2311yescharacteristic
149C2×C42×C47C2311yescharacteristic
150C2×C42×C47C2312yes—
151C2×C42×C47C2311yescharacteristic
152C2×C42×C47C2311yescharacteristic
153#95×C47C2312yes—
154#95×C47C2312yes—
155#95×C47C2312yes—
156#95×C47C2312yes—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47—41no—
160C24×C47—41no—
161C24×C47—41no—
162C24×C47—41no—
163C24×C47C2×D414yes—
164C24×C47C2412yes—
165C24×C47C2411yescharacteristic
166C23×D47C2414yes—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—24no—
172C22×C4×C47—24no—
173C22×C4×C47—24no—
174C22×C4×C47—24no—
175C22×C4×C47—41no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—41no—
182C22×C4×C47—41no—
183C22×C4×C47—41no—
184C22×C4×C47—41no—
185C22×C4×C47—41no—
186C22×C4×C47—41no—
187C22×C4×C47—416no—
188C22×C4×C47C2×D414yes—
189C22×C4×C47C2×D414yes—
190C22×C4×C47#4114yes—
191C22×C4×C47#4114yes—
192C22×C4×C47C2412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×C4×C47C2411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—28no—
202C2×C22⋊D47—28no—
203C2×C22⋊D47—28no—
204C2×C22⋊D47—28no—
205C2×C22⋊D47—28no—
206C2×C22⋊D47—44no—
207C2×C22⋊D47—44no—
208C2×C22⋊D47—44no—
209C2×C22⋊D47—44no—
210C22×Dic47C2414yes—
211C22×Dic47C2414yes—
212C22×Dic47C2414yes—
213C2×D188—24no—
214C2×D188—24no—
215C2×D188—24no—
216C2×D188—24no—
217C2×D188—24no—
218C2×D188—42no—
219C2×D188—42no—
220C2×D188—42no—
221C2×D188—42no—
222C2×C4×D47—28no—
223C2×C4×D47—44no—
224C2×C4×D47—44no—
225C2×Dic94—24no—
226C2×Dic94—42no—
227C2×Dic94—42no—
228C22⋊C4×C47—24no—
229C22⋊C4×C47—24no—
230C22⋊C4×C47C2×D418yes—
231C22⋊C4×C47C2×D418yes—
232C42×C47—24no—
233C42×C47—22no—
234C42×C47—22no—
235C42×C47—41no—
236C42×C47—41no—
237C42×C47—42no—
238C22⋊Dic47—28no—
239C22⋊Dic47—28no—
240C22⋊Dic47—28no—
241(C2×D47)⋊C4—28no—
242(C2×D47)⋊C4—28no—
243(C2×D47)⋊C4—28no—
244(C2×D47)⋊C4—28no—
245(C2×D47)⋊C4—44no—
246(C2×D47)⋊C4—44no—
247(C2×D47)⋊C4—44no—
248(C2×D47)⋊C4—44no—
249C4⋊Dic47—24no—
250C4⋊Dic47—24no—
251C4⋊Dic47—24no—
252C4⋊Dic47—24no—
253C4⋊Dic47—24no—
254C4⋊Dic47—24no—
255C4⋊Dic47—42no—
256C4⋊Dic47—42no—
257Dic47⋊C4—28no—
258Dic47⋊C4—28no—
259C4×Dic47—28no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—28no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—44no—
272C23×C47—44no—
273C23×C47—44no—
274C23×C47—44no—
275C23×C47—44no—
276C23×C47—44no—
277C23×C47C22×D414yes—
278C23×C47C22×D412yes—
279C23×C47C2×#4112yes—
280C23×C47C2×#4112yes—
281C23×C47C2511yescharacteristic
282C22×D47—24no—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—24no—
286C22×D47—24no—
287C22×D47—24no—
288C22×D47—24no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—22no—
292C2×C4×C47—21no—
293C2×C4×C47—21no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—22no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—28no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—48no—
312C2×C4×C47—44no—
313C2×C4×C47—44no—
314C2×C4×C47—48no—
315C2×C4×C47C22×D414yes—
316C2×C4×C47C22×D412yes—
317C2×C4×C47C22×D412yes—
318C2×C4×C47C2×#4112yes—
319C2×C4×C47C2×#4112yes—
320C2×C4×C47C2×#4112yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47H(5,𝔽2)12yes—
323C2×C4×C47H(5,𝔽2)12yes—
324C22⋊D47—416no—
325C22⋊D47—88no—
326C22⋊D47—88no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—24no—
330C2×Dic47—24no—
331C2×Dic47—24no—
332C2×Dic47—24no—
333C2×Dic47—24no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336D188—48no—
337D188—84no—
338D188—84no—
339C4×D47—88no—
340Dic94—84no—
341#35005—471nomaximal, Sylow
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—24no—
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—416no—
352C22×C47—42no—
353C22×C47—42no—
354C22×C47—42no—
355C22×C47—42no—
356C22×C47#53214yes—
357C22×C47C23×D411yescharacteristic
358C22×C47C22×#4111yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C2×H(5,𝔽2)11yescharacteristic
361C22×C47C2×H(5,𝔽2)11yescharacteristic
362C22×C47#58511yescharacteristic
363C22×C47#58511yescharacteristic
364C2×D47—44no—
365C2×D47—44no—
366C2×D47—44no—
367C2×D47—44no—
368C2×D47—44no—
369C2×D47—44no—
370C2×D47—44no—
371C4×C47—22no—
372C4×C47—22no—
373C4×C47—24no—
374C4×C47—22no—
375C4×C47—22no—
376C4×C47—22no—
377C4×C47—42no—
378C4×C47—42no—
379C4×C47#53814yescomplemented
380Dic47—44no—
381Dic47—44no—
382Dic47—44no—
383C2×#538—472no—
384#2857—471no—
385#2856—471no—
386#2847—472no—
387#2639—472no—
388#2617—472no—
389#2559—474no—
390#2557—474no—
391#2496—472no—
392#2491—472no—
393#2428—472no—
394#2422—472no—
395#2325—472no—
396C4×#121—472no—
397C2×C4×C22⋊C4D4711yescharacteristic, complemented
398C2×C47—24no—
399C2×C47—44no—
400C2×C47C2×#53211yescharacteristic
401C2×C47C2×#53811yescharacteristic
402C2×C47#345511yescharacteristic
403C2×C47#349611yescharacteristic
404C2×C47#349611yescharacteristic
405C2×C47#350511yescharacteristic
406C2×C47#350611yescharacteristic
407D47—84no—
408C24×C4C2×D4711yescharacteristic
409#538—9416no—
410C2×C4⋊Q8—471no—
411C2×#127—471no—
412C2×#126—474no—
413C2×#124—474no—
414C2×#123—474no—
415C2×C22⋊Q8—472no—
416C2×#121—472no—
417C2×#121—472no—
418C2×#121—472no—
419C2×#121—472no—
420C2×#121—472no—
421C2×#121—474no—
422C2×#120—474no—
423C2×C4×D4—474no—
424C2×C4×D4—472no—
425C22×C22⋊C4C2×D4711yescharacteristic
426C22×C22⋊C4C2×D4711yescharacteristic
427C22×C42C2×D4711yescharacteristic
428C22×C42C2×D4711yescharacteristic
429#400—474no—
430#397—474no—
431#397—474no—
432#394—474no—
433#394—474no—
434#394—474no—
435#393—474no—
436#392—474no—
437#391—472no—
438#390—472no—
439#390—472no—
440#390—472no—
441#390—472no—
442#389—472no—
443#389—472no—
444#389—472no—
445#388—474no—
446#388—474no—
447#387—474no—
448#386—474no—
449#386—474no—
450#386—474no—
451#386—474no—
452#386—474no—
453#385—474no—
454#384—471no—
455#384—471no—
456#380—472no—
457#380—472no—
458#380—472no—
459#380—472no—
460C4×C4⋊C4—472no—
461C4×C22⋊C4—474no—
462C4×C22⋊C4C2×D4712yes—
463C4×C22⋊C4C2×D4712yes—
464C4×C22⋊C4C2×D4712yes—
465C4×C22⋊C4C2×D4712yes—
466C2×#95C2×D4711yescharacteristic
467C2×#95C2×D4711yescharacteristic
468C47#3500511yescharacteristic, complemented, Sylow
469C25C22×D4711yescharacteristic
470C22×Q8—472no—
471C22×D4—474no—
472C22×D4—474no—
473C22×D4—474no—
474C22×D4—472no—
475C22×D4—472no—
476C22×D4—472no—
477C23×C4—24no—
478C23×C4—42no—
479C23×C4—42no—
480C23×C4—474no—
481C23×C4C22×D4712yes—
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4712yes—
486C23×C4C22×D4711yescharacteristic
487C23×C4C22×D4711yescharacteristic
488C23×C4C22×D4711yescharacteristic
489C4⋊Q8—1882no—
490#127—1882no—
491#126—9416no—
492#124—9416no—
493#123—9416no—
494C22⋊Q8—948no—
495#121—948no—
496#121—948no—
497#121—948no—
498#121—9416no—
499#121—1884no—
500#121—1884no—
501#120—9416no—
502C4×D4—9416no—
503C4×D4—1884no—
504C2×C4⋊C4—472no—
505C2×C4⋊C4—474no—
506C2×C4⋊C4—474no—
507C2×C4⋊C4—472no—
508C2×C4⋊C4—472no—
509C2×C4⋊C4—472no—
510C2×C4⋊C4—472no—
511C2×C4⋊C4—472no—
512C2×C4⋊C4—472no—
513C2×C4⋊C4—472no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—474no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—474no—
523C2×C22⋊C4—474no—
524C2×C22⋊C4—474no—
525C2×C22⋊C4—474no—
526C2×C22⋊C4D18818yescomplemented
527C2×C22⋊C4C22×D4712yes—
528C2×C22⋊C4C22×D4712yes—
529C2×C22⋊C4C22×D4712yes—
530C2×C22⋊C4C22×D4712yes—
531C2×C42—42no—
532C2×C42—42no—
533C2×C42—474no—
534C2×C42C22×D4712yes—
535C2×C42C22×D4711yescharacteristic
536C2×C42C22×D4711yescharacteristic
537C2×C42C22×D4712yes—
538C2×C42C22×D4711yescharacteristic
539C2×C42C22×D4711yescharacteristic
540#95—474no—
541#95—474no—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95C22×D4712yes—
547#95C22×D4712yes—
548#95C22×D4712yes—
549#95C22×D4712yes—
550C24—22no—
551C24—22no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—41no—
556C24—474no—
557C24C2×D18814yes—
558C24C23×D4712yes—
559C24C23×D4711yescharacteristic
560C2×Q8—944no—
561C2×Q8—1882no—
562C2×Q8—1882no—
563C2×D4—948no—
564C2×D4—948no—
565C2×D4—948no—
566C2×D4—948no—
567C2×D4—948no—
568C2×D4—944no—
569C2×D4—944no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—944no—
573C2×D4—1882no—
574C2×D4—1882no—
575C2×D4—1882no—
576C2×D4—1882no—
577C2×D4—1884no—
578C2×D4—1884no—
579C2×D4—1884no—
580C2×D4—1884no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—416no—
602C22×C4—474no—
603C22×C4—474no—
604C22×C4—474no—
605C22×C4—948no—
606C22×C4—1884no—
607C22×C4—1884no—
608C22×C4C2×D18814yes—
609C22×C4C2×D18814yes—
610C22×C4#1062535014yes—
611C22×C4#1062535014yes—
612C22×C4C23×D4712yes—
613C22×C4C23×D4712yes—
614C22×C4C23×D4712yes—
615C22×C4C23×D4711yescharacteristic
616C22×C4C23×D4711yescharacteristic
617C22×C4C23×D4711yescharacteristic
618C22×C4C23×D4711yescharacteristic
619C22×C4C23×D4711yescharacteristic
620C22×C4C23×D4711yescharacteristic
621C4⋊C4—948no—
622C4⋊C4—948no—
623C4⋊C4—944no—
624C4⋊C4—944no—
625C4⋊C4—944no—
626C4⋊C4—944no—
627C4⋊C4—944no—
628C4⋊C4—944no—
629C4⋊C4—1882no—
630C4⋊C4—1882no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—948no—
634C22⋊C4—948no—
635C22⋊C4—948no—
636C22⋊C4—948no—
637C22⋊C4—948no—
638C22⋊C4—948no—
639C22⋊C4—948no—
640C22⋊C4—1884no—
641C22⋊C4—1884no—
642C22⋊C4—1884no—
643C22⋊C4—1884no—
644C22⋊C4C2×D18818yes—
645C22⋊C4C2×D18818yes—
646C42—24no—
647C42—22no—
648C42—22no—
649C42—41no—
650C42—42no—
651C42—41no—
652C42—948no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—28no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23—944no—
674C23—944no—
675C23—944no—
676C23—944no—
677C23C22×D18814yes—
678C23C22×D18812yes—
679C23C2×#1062535012yes—
680C23C2×#1062535012yes—
681C23C24×D4711yescharacteristic
682Q8—3764no—
683D4—3764no—
684D4—3764no—
685D4—3768no—
686D4—3768no—
687D4—18816no—
688D4—1888no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—48no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—944no—
716C2×C4—944no—
717C2×C4—944no—
718C2×C4—944no—
719C2×C4—944no—
720C2×C4—944no—
721C2×C4—944no—
722C2×C4—944no—
723C2×C4—944no—
724C2×C4—3768no—
725C2×C4C22×D18814yes—
726C2×C4C22×D18812yes—
727C2×C4C22×D18812yes—
728C2×C4C2×#1062535012yes—
729C2×C4C2×#1062535012yes—
730C2×C4C2×#1062535012yes—
731C2×C4C2×#1062535012yes—
732C2×C4#1309406912yes—
733C2×C4#1309406912yes—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—24no—
741C22—24no—
742C22—24no—
743C22—416no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—1884no—
749C22—1884no—
750C22—1884no—
751C22—1884no—
752C22—1884no—
753C22—1884no—
754C22—1884no—
755C22#1568967314yes—
756C22C23×D18811yescharacteristic
757C22C22×#1062535011yescharacteristic
758C22C22×#1062535011yescharacteristic
759C22C2×#1309406911yescharacteristic
760C22C2×#1309406911yescharacteristic
761C22#1568995911yescharacteristic
762C22#1568995911yescharacteristic
763C4—24no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—1884no—
772C4—1884no—
773C4—1884no—
774C4#1568971114yescomplemented
775C2—24no—
776C2—44no—
777C2—3764no—
778C2C2×#1568967311yescharacteristic
779C2C2×#1568971111yescharacteristic
780C2#2025677811yescharacteristic
781C2#2025715211yescharacteristic
782C2#2025715211yescharacteristic
783C2#2025722711yescharacteristic
784C2#2025724011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC2×C4×C22⋊C4×C47C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#35005
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#15689711C2semidirect
2. #20251740C2semidirect
3. #20251733C2semidirect
4. #20251670C2semidirect
5. #20249316C2semidirect
6. #20249122C2semidirect
7. #20248511C2semidirect
8. #20248481C2semidirect
9. #20247810C2semidirect
10. #20247751C2semidirect
11. #20246976C2semidirect
12. #20246902C2semidirect
13. #20246091C2semidirect
14. C4×#13093998C2semidirect
15. C2×C4×C22⋊C4×C47C2semidirect
17. C2×#13094024C22semidirect
18. C2×#13094021C22semidirect
30. C2×C4×D188C22semidirect
32. #15689063C22semidirect
33. #15689050C22semidirect
35. #15689041C22semidirect
38. #15689036C22semidirect
40. #15689029C22semidirect
41. #15689025C22semidirect
42. #15689025C22semidirect
43. #15689025C22semidirect
44. #15689025C22semidirect
45. #15689021C22semidirect
46. #15689021C22semidirect
47. #15689021C22semidirect
48. #15689015C22semidirect
49. #15689014C22semidirect
50. #15689008C22semidirect
55. #15689001C22semidirect
56. #15688997C22semidirect
57. #15688993C22semidirect
58. #15688993C22semidirect
63. C4×C4⋊Dic47C22semidirect
64. C4×(C2×D47)⋊C4C22semidirect
140. C2×C22⋊C4×C47D4semidirect
379. C4×C47#538semidirect
397. C2×C4×C22⋊C4D47semidirect
468. C47#35005semidirect
526. C2×C22⋊C4D188semidirect
774. C4#15689711semidirect

Maximal subgroups

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

subgroupindex
C2×#156897112
#202517402
#202517332
#202516702
#202493162
#202491222
#202485112
#202484812
#202478102
#202477512
#202469762
#202469022
#202460912
C4×#130939982
C2×C4×C22⋊C4×C472
#3500547