Finite Group Databasebeta

← #26422227

Subgroups — #26422227

Order 12032.

3110 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689675C211yesmaximal, characteristic, complemented
2C23×C4×Dic47C211yesmaximal, characteristic
3#20251738C212yesmaximal, complemented
4#20251736C212yesmaximal, complemented
5#20251728C211yesmaximal, characteristic, complemented
6#20251724C212yesmaximal, complemented
7#20251722C211yesmaximal, characteristic, complemented
8#20251694C214yesmaximal, complemented
9#20251675C211yesmaximal, characteristic
10#20251673C212yesmaximal
11C22⋊Q8×Dic47C212yesmaximal, complemented
12#20245920C214yesmaximal, complemented
13#20245916C212yesmaximal, complemented
14#20245867C212yesmaximal, complemented
15#20245790C211yesmaximal, characteristic, complemented
16#20245766C212yesmaximal
17C47×#2848C211yesmaximal, characteristic
18C24×Dic47C2211yescharacteristic
19C24×Dic47C2211yescharacteristic
20#15689675—28no—
21C2×#13094023C2211yescharacteristic, complemented
22C2×#13094022C2211yescharacteristic, complemented
23C2×#13094014C2212yescomplemented
24C2×#13094003C2211yescharacteristic
25C2×#13094003C2212yes—
26C2×#13094001C2212yes—
27C2×#13094001C2214yes—
28C2×Q8×Dic47C2211yescharacteristic, complemented
29C2×#13093989C2211yescharacteristic, complemented
30C2×#13093989C2212yescomplemented
31C2×#13093980C2212yes—
32C2×#13093980C2212yes—
33C22×C4×Dic47—28no—
34C22×C4×Dic47C2212yes—
35C22×C4×Dic47C2211yescharacteristic
36C22×C4×Dic47C2211yescharacteristic
37C22×C4×Dic47C2212yes—
38C22×C4×Dic47C2211yescharacteristic
39C22×C4×Dic47C2212yes—
40C22×C4×Dic47C2212yes—
41C22×C4×Dic47C2211yescharacteristic
42#15689030C2212yescomplemented
43#15689028C2212yescomplemented
44#15689027C2214yescomplemented
45#15689022C2212yescomplemented
46#15689020C2214yescomplemented
47#15689019C2212yescomplemented
48#15689018C2214yescomplemented
49#15689018C2214yescomplemented
50#15689009C2214yescomplemented
51#15689008C2214yescomplemented
52#15689005C2214yescomplemented
53#15689004C2214yescomplemented
54#15688998C2214yes—
55#15688998C2212yes—
56#15688996C2214yes—
57#15688996C2212yes—
58#15688995C2214yes—
59#15688995C2212yes—
60#15688992C2212yescomplemented
61#15688987C2212yescomplemented
62#15688984C2212yes—
63#15688984C2212yes—
64#15688983C2211yescharacteristic
65#15688983C2212yes—
66#15688981C2214yes—
67#15688981C2214yes—
68#15688981C2212yes—
69#15688981C2214yes—
70#15688979C2212yes—
71C4⋊C4×Dic47C2212yescomplemented
72C4⋊C4×Dic47C2214yescomplemented
73#15688974C2212yescomplemented
74#15688974C2214yescomplemented
75C22⋊C4×Dic47C2214yes—
76C22⋊C4×Dic47C2214yes—
77C24×C4×C47C2211yescharacteristic
78C2×C22⋊Q8×C47C2211yescharacteristic
79C2×C22⋊Q8×C47C2212yes—
80C47×#385C2214yes—
81C47×#385C2212yes—
82C47×#380C2211yescharacteristic
83C47×#380C2212yes—
84C47×#379C2212yes—
85C22×Dic94C2312yes—
86C22×Dic94C2311yescharacteristic
87C23×Dic47—24no—
88C23×Dic47—24no—
89C23×Dic47—28no—
90C23×Dic47—24no—
91C23×Dic47Q818yescomplemented
92C23×Dic47C2311yescharacteristic
93C23×Dic47C2312yes—
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2312yes—
96C23×Dic47C2312yes—
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2312yes—
99C23×Dic47C2311yescharacteristic
100#13094023—24no—
101#13094022—24no—
102#13094014—28no—
103#13094003—24no—
104#13094003—28no—
105#13094001—28no—
106#13094001—216no—
107Q8×Dic47—24no—
108#13093989—24no—
109#13093989—28no—
110#13093980—28no—
111#13093980—28no—
112C2×C4⋊Dic47C2312yes—
113C2×C4⋊Dic47C2314yes—
114C2×C4⋊Dic47C2311yescharacteristic
115C2×C4⋊Dic47C2312yes—
116C2×Dic47⋊C4C2314yes—
117C2×Dic47⋊C4C2314yes—
118C2×Dic47⋊C4C2314yes—
119C2×Dic47⋊C4C2314yes—
120C2×Dic47⋊C4C2312yes—
121C2×Dic47⋊C4C2312yes—
122C2×Dic47⋊C4C2312yes—
123C2×Dic47⋊C4C2312yes—
124C2×Dic47⋊C4C2312yes—
125C2×C22⋊Dic47C2314yes—
126C2×C22⋊Dic47C2314yes—
127C2×C22⋊Dic47C2312yes—
128C2×C22⋊Dic47C2312yes—
129C2×C4×Dic47—24no—
130C2×C4×Dic47—24no—
131C2×C4×Dic47—24no—
132C2×C4×Dic47—28no—
133C2×C4×Dic47—28no—
134C2×C4×Dic47—28no—
135C2×C4×Dic47—28no—
136C2×C4×Dic47D418yes—
137C2×C4×Dic47C2314yes—
138C2×C4×Dic47C2312yes—
139C2×C4×Dic47C2312yes—
140C2×C4×Dic47C2312yes—
141C2×C4×Dic47C2312yes—
142C2×C4×Dic47C2312yes—
143C2×C4×Dic47C2312yes—
144C2×C4×Dic47C2312yes—
145C2×C4×Dic47C2312yes—
146C2×C4×Dic47C2311yescharacteristic
147C2×C4×Dic47C2311yescharacteristic
148C2×C4×Dic47C2311yescharacteristic
149C2×C4×Dic47C2311yescharacteristic
150C47⋊#95C2314yes—
151C47⋊#95C2314yes—
152C47⋊#95C2314yes—
153C47⋊#95C2314yes—
154C47⋊#95C2314yes—
155C47⋊#95C2312yes—
156C47⋊#95C2314yes—
157C47⋊#95C2314yes—
158C47⋊#95C2314yes—
159C25×C47C2311yescharacteristic
160C22×Q8×C47C2311yescharacteristic
161C23×C4×C47—24no—
162C23×C4×C47—28no—
163C23×C4×C47C2311yescharacteristic
164C23×C4×C47C2312yes—
165C23×C4×C47C2311yescharacteristic
166C23×C4×C47C2312yes—
167C22⋊Q8×C47—24no—
168C22⋊Q8×C47—28no—
169C2×C4⋊C4×C47C2312yes—
170C2×C4⋊C4×C47C2314yes—
171C2×C4⋊C4×C47C2312yes—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C22⋊C4×C47C2314yes—
174C2×C22⋊C4×C47C2314yes—
175C2×C22⋊C4×C47C2312yes—
176C2×C22⋊C4×C47C2312yes—
177#95×C47C2312yes—
178#95×C47C2314yes—
179C24×C47—22no—
180C24×C47—24no—
181C24×C47—24no—
182C24×C47—22no—
183C24×C47C2×Q814yes—
184C24×C47C2411yescharacteristic
185C24×C47C2412yes—
186C2×Q8×C47—22no—
187C2×Q8×C47—24no—
188C22×C4×C47—232no—
189C22×C4×C47—22no—
190C22×C4×C47—24no—
191C22×C4×C47—24no—
192C22×C4×C47—24no—
193C22×C4×C47—24no—
194C22×C4×C47—24no—
195C22×C4×C47—24no—
196C22×C4×C47—24no—
197C22×C4×C47C2×D414yes—
198C22×C4×C47#4118yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2414yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2411yescharacteristic
203C22×C4×C47C2412yes—
204C22×C4×C47C2411yescharacteristic
205C22×Dic47—232no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—24no—
209C22×Dic47—22no—
210C22×Dic47—232no—
211C22×Dic47—24no—
212C22×Dic47—24no—
213C22×Dic47—24no—
214C22×Dic47—24no—
215C22×Dic47—24no—
216C22×Dic47—24no—
217C22×Dic47—24no—
218C22×Dic47—24no—
219C22×Dic47—24no—
220C22×Dic47—24no—
221C22×Dic47C2×D414yes—
222C22×Dic47C2×D414yes—
223C22×Dic47C2×Q814yes—
224C22×Dic47C2×Q818yes—
225C22×Dic47C2×Q818yes—
226C22×Dic47C2×Q814yes—
227C22×Dic47#4118yes—
228C22×Dic47#4114yes—
229C22×Dic47C2414yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2411yescharacteristic
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C22×Dic47C2411yescharacteristic
236C22×Dic47C2411yescharacteristic
237C22×Dic47C2411yescharacteristic
238C2×Dic94—22no—
239C2×Dic94—24no—
240C2×Dic94—24no—
241C2×Dic94—28no—
242C4⋊C4×C47—24no—
243C4⋊C4×C47—22no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—28no—
246C22⋊C4×C47—24no—
247C22⋊C4×C47—28no—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—28no—
250C22⋊Dic47—24no—
251C22⋊Dic47—24no—
252C22⋊Dic47—28no—
253C22⋊Dic47—28no—
254C4⋊Dic47—22no—
255C4⋊Dic47—24no—
256C4⋊Dic47—24no—
257C4⋊Dic47—28no—
258Dic47⋊C4—24no—
259Dic47⋊C4—28no—
260Dic47⋊C4—24no—
261Dic47⋊C4—24no—
262Dic47⋊C4—24no—
263Dic47⋊C4—24no—
264Dic47⋊C4—28no—
265Dic47⋊C4—28no—
266Dic47⋊C4—28no—
267C4×Dic47—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47—24no—
273C4×Dic47—24no—
274C4×Dic47—24no—
275C4×Dic47—28no—
276C4×Dic47C2×D414yes—
277C4×Dic47C2×D414yes—
278C4×Dic47C2×D414yes—
279C4×Dic47C2×D414yes—
280C23×C47—28no—
281C23×C47—28no—
282C23×C47—216no—
283C23×C47—28no—
284C23×C47—216no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47C22×D412yes—
292C23×C47C22×Q812yes—
293C23×C47C22×Q814yes—
294C23×C47C2×#4112yes—
295C23×C47C2×#4114yes—
296C23×C47C2×#4114yes—
297C23×C47C2511yescharacteristic
298Q8×C47—44no—
299C2×C4×C47—216no—
300C2×C4×C47—28no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—28no—
305C2×C4×C47—216no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47C22×D412yes—
314C2×C4×C47C22×D412yes—
315C2×C4×C47C2×#4114yes—
316C2×C4×C47C2×#4114yes—
317C2×Dic47—216no—
318C2×Dic47—28no—
319C2×Dic47—28no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—216no—
326C2×Dic47—216no—
327C2×Dic47—28no—
328C2×Dic47—216no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—24no—
332C2×Dic47—24no—
333C2×Dic47—24no—
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47C22⋊Q8116yescomplemented
337C2×Dic47C22×D412yes—
338C2×Dic47C22×D412yes—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×Q814yes—
342C2×Dic47C22×Q812yes—
343C2×Dic47C22×Q812yes—
344C2×Dic47C2×#4114yes—
345C2×Dic47C2×#4112yes—
346C2×Dic47C2×#4112yes—
347C2×Dic47C2×#4114yes—
348Dic94—44no—
349Dic94—48no—
350#36625—471nomaximal, Sylow
351C22×C47—232no—
352C22×C47—24no—
353C22×C47—22no—
354C22×C47—24no—
355C22×C47—22no—
356C22×C47—24no—
357C22×C47—24no—
358C22×C47—24no—
359C22×C47—24no—
360C22×C47—24no—
361C22×C47—24no—
362C22×C47C2×C22⋊Q814yes—
363C22×C47#53318yescomplemented
364C22×C47C23×D411yescharacteristic
365C22×C47C23×Q811yescharacteristic
366C22×C47C22×#4111yescharacteristic
367C22×C47C22×#4112yes—
368C22×C47C22×#4112yes—
369C4×C47—22no—
370C4×C47—24no—
371C4×C47—42no—
372C4×C47—42no—
373C4×C47—44no—
374C4×C47#52514yes—
375Dic47—24no—
376Dic47—22no—
377Dic47—24no—
378Dic47—42no—
379Dic47—42no—
380Dic47—44no—
381Dic47C2×C22⋊Q814yes—
382Dic47C2×C22⋊Q814yes—
383Dic47#52514yes—
384C2×#533—471no—
385C23×C42—471no—
386#2857—472no—
387#2857—472no—
388#2855—472no—
389#2855—471no—
390#2855—471no—
391#2851—474no—
392#2848—472no—
393#2848—471no—
394#2848D4711yescharacteristic
395C4×C22⋊Q8—474no—
396C4×C22⋊Q8—472no—
397C4×C22⋊Q8—472no—
398#2296—472no—
399#2285—471no—
400#2280—472no—
401C2×C47—24no—
402C2×C47—28no—
403C2×C47C22×C22⋊Q811yescharacteristic
404C2×C47C2×#52511yescharacteristic
405C2×C47C2×#52511yescharacteristic
406C2×C47C2×#53312yes—
407C2×C47#344412yes—
408C24×C4—471no—
409C24×C4—471no—
410C24×C4C2×D4711yescharacteristic
411#533—948no—
412C2×C4⋊Q8—471no—
413C2×C4⋊Q8—471no—
414C2×#125—472no—
415C2×C22⋊Q8—471no—
416C2×C22⋊Q8—472no—
417C2×C22⋊Q8—472no—
418C2×C22⋊Q8—474no—
419C2×C22⋊Q8C2×D4711yescharacteristic
420C2×C22⋊Q8C2×D4712yes—
421C2×C4×Q8—471no—
422C2×C4×Q8—471no—
423C2×C4×Q8—472no—
424C2×#117—472no—
425C2×#117—472no—
426C22×C42—471no—
427C22×C42—472no—
428C22×C42—471no—
429C22×C42—471no—
430C22×C42—472no—
431C22×C42—471no—
432C22×C42—472no—
433C22×C42—472no—
434C22×C42—948no—
435#391—472no—
436#391—472no—
437#391—474no—
438#389—474no—
439#389—474no—
440#389—472no—
441#389—472no—
442#389—474no—
443#387—474no—
444#387—474no—
445#387—474no—
446#387—474no—
447#385—474no—
448#385—472no—
449#385—474no—
450#385—474no—
451#385—472no—
452#385—472no—
453#385C2×D4714yes—
454#385C2×D4712yes—
455#384—472no—
456#382—472no—
457#381—472no—
458#381—472no—
459#380—471no—
460#380—472no—
461#380—472no—
462#380—474no—
463#380—474no—
464#380—474no—
465#380C2×D4711yescharacteristic
466#380C2×D4712yes—
467#379—472no—
468#379C2×D4712yes—
469C4×C4⋊C4—472no—
470C4×C4⋊C4—474no—
471C4×C4⋊C4—472no—
472C4×C4⋊C4—474no—
473C4×C22⋊C4—474no—
474C4×C22⋊C4—474no—
475C47#3662511yescharacteristic, complemented, Sylow
476C25C22×D4711yescharacteristic
477C22×Q8—472no—
478C22×Q8—471no—
479C22×Q8C22×D4711yescharacteristic
480C23×C4—24no—
481C23×C4—28no—
482C23×C4—471no—
483C23×C4—478no—
484C23×C4—471no—
485C23×C4—472no—
486C23×C4—472no—
487C23×C4—472no—
488C23×C4—471no—
489C23×C4—472no—
490C23×C4—471no—
491C23×C4—944no—
492C23×C4—948no—
493C23×C4—944no—
494C23×C4—944no—
495C23×C4C22×D4711yescharacteristic
496C23×C4C22×D4712yes—
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4712yes—
499C4⋊Q8—944no—
500C4⋊Q8—944no—
501#125—948no—
502C22⋊Q8—24no—
503C22⋊Q8—28no—
504C22⋊Q8—948no—
505C22⋊Q8—9416no—
506C22⋊Q8—944no—
507C22⋊Q8—948no—
508C4×Q8—948no—
509C4×Q8—944no—
510C4×Q8—944no—
511#117—948no—
512#117—948no—
513C2×C4⋊C4—472no—
514C2×C4⋊C4—472no—
515C2×C4⋊C4—474no—
516C2×C4⋊C4—472no—
517C2×C4⋊C4—472no—
518C2×C4⋊C4—472no—
519C2×C4⋊C4—472no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—474no—
522C2×C4⋊C4—474no—
523C2×C4⋊C4—474no—
524C2×C4⋊C4—472no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4C22×D4712yes—
527C2×C4⋊C4C22×D4711yescharacteristic
528C2×C4⋊C4C22×D4712yes—
529C2×C4⋊C4C22×D4714yes—
530C2×C22⋊C4—472no—
531C2×C22⋊C4—472no—
532C2×C22⋊C4—474no—
533C2×C22⋊C4—474no—
534C2×C22⋊C4C22×D4712yes—
535C2×C22⋊C4C22×D4712yes—
536C2×C22⋊C4C22×D4714yes—
537C2×C22⋊C4C22×D4714yes—
538C2×C42—478no—
539C2×C42—471no—
540C2×C42—471no—
541C2×C42—471no—
542C2×C42—471no—
543C2×C42—472no—
544C2×C42—472no—
545C2×C42—474no—
546C2×C42—472no—
547C2×C42—472no—
548C2×C42—472no—
549C2×C42—472no—
550C2×C42—472no—
551C2×C42—472no—
552C2×C42—948no—
553C2×C42—948no—
554C2×C42—948no—
555C2×C42—948no—
556C2×C42—944no—
557C2×C42—944no—
558C2×C42—944no—
559#95—474no—
560#95—474no—
561#95—474no—
562#95—474no—
563#95—474no—
564#95—472no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95C22×D4712yes—
569#95C22×D4714yes—
570C24—22no—
571C24—24no—
572C24—22no—
573C24—24no—
574C24Q8×D4714yes—
575C24C23×D4711yescharacteristic
576C24C23×D4712yes—
577C2×Q8—22no—
578C2×Q8—24no—
579C2×Q8—944no—
580C2×Q8—948no—
581C2×Q8—942no—
582C2×Q8—944no—
583C22×C4—232no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—474no—
593C22×C4—474no—
594C22×C4—474no—
595C22×C4—471no—
596C22×C4—471no—
597C22×C4—471no—
598C22×C4—474no—
599C22×C4—478no—
600C22×C4—478no—
601C22×C4—474no—
602C22×C4—478no—
603C22×C4—472no—
604C22×C4—471no—
605C22×C4—472no—
606C22×C4—474no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—944no—
610C22×C4—944no—
611C22×C4—944no—
612C22×C4—944no—
613C22×C4—9432no—
614C22×C4—944no—
615C22×C4—944no—
616C22×C4—944no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4—944no—
620C22×C4—9432no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—944no—
624C22×C4—942no—
625C22×C4D4×D4714yes—
626C22×C4#1062535218yes—
627C22×C4C23×D4714yes—
628C22×C4C23×D4712yes—
629C22×C4C23×D4712yes—
630C22×C4C23×D4711yescharacteristic
631C22×C4C23×D4712yes—
632C22×C4C23×D4711yescharacteristic
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—28no—
637C4⋊C4—948no—
638C4⋊C4—944no—
639C4⋊C4—944no—
640C4⋊C4—944no—
641C4⋊C4—944no—
642C4⋊C4—948no—
643C4⋊C4—948no—
644C4⋊C4—944no—
645C4⋊C4—948no—
646C4⋊C4—944no—
647C4⋊C4—942no—
648C4⋊C4—948no—
649C4⋊C4—944no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—944no—
655C22⋊C4—944no—
656C22⋊C4—948no—
657C22⋊C4—948no—
658C42—474no—
659C42—474no—
660C42—474no—
661C42—474no—
662C42—944no—
663C42—944no—
664C42—944no—
665C42—944no—
666C42—948no—
667C42—944no—
668C42—944no—
669C42—944no—
670C42—944no—
671C23—28no—
672C23—28no—
673C23—216no—
674C23—28no—
675C23—216no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23C2×D4×D4712yes—
683C23C2×Q8×D4712yes—
684C23C2×Q8×D4714yes—
685C23#41×D4712yes—
686C23#41×D4714yes—
687C23C2×#1062535214yes—
688C23C24×D4711yescharacteristic
689Q8—44no—
690Q8—1888no—
691Q8—1884no—
692C2×C4—216no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—216no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—4716no—
707C2×C4—472no—
708C2×C4—472no—
709C2×C4—472no—
710C2×C4—472no—
711C2×C4—472no—
712C2×C4—472no—
713C2×C4—472no—
714C2×C4—474no—
715C2×C4—472no—
716C2×C4—474no—
717C2×C4—474no—
718C2×C4—9416no—
719C2×C4—9416no—
720C2×C4—948no—
721C2×C4—9416no—
722C2×C4—948no—
723C2×C4—9416no—
724C2×C4—948no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—944no—
733C2×C4—944no—
734C2×C4—944no—
735C2×C4—944no—
736C2×C4—944no—
737C2×C4C2×D4×D4712yes—
738C2×C4C2×D4×D4712yes—
739C2×C4C2×#1062535214yes—
740C2×C4C2×#1062535214yes—
741C22—232no—
742C22—24no—
743C22—22no—
744C22—24no—
745C22—22no—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22C22⋊Q8×D4714yes—
753C22#1568967518yescomplemented
754C22C22×D4×D4711yescharacteristic
755C22C22×Q8×D4711yescharacteristic
756C22C2×#41×D4711yescharacteristic
757C22C2×#41×D4712yes—
758C22C22×#1062535212yes—
759C4—22no—
760C4—24no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4—474no—
765C4—474no—
766C4—474no—
767C4—944no—
768C4—942no—
769C4—944no—
770C4—1882no—
771C4—1882no—
772C4—1884no—
773C4#1568962914yes—
774C2—24no—
775C2—28no—
776C2C2×C22⋊Q8×D4711yescharacteristic
777C2#525×D4711yescharacteristic
778C2C2×#1568962911yescharacteristic
779C2C2×#1568967512yes—
780C2#2025668012yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2848C2
prime radicalC25×C47C23
hypercenter#2848D47
hypocenterC47#36625
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#15689675C2semidirect
3. #20251738C2semidirect
4. #20251736C2semidirect
5. #20251728C2semidirect
6. #20251724C2semidirect
7. #20251722C2semidirect
8. #20251694C2semidirect
11. C22⋊Q8×Dic47C2semidirect
12. #20245920C2semidirect
13. #20245916C2semidirect
14. #20245867C2semidirect
15. #20245790C2semidirect
21. C2×#13094023C22semidirect
22. C2×#13094022C22semidirect
23. C2×#13094014C22semidirect
28. C2×Q8×Dic47C22semidirect
29. C2×#13093989C22semidirect
30. C2×#13093989C22semidirect
42. #15689030C22semidirect
43. #15689028C22semidirect
44. #15689027C22semidirect
45. #15689022C22semidirect
46. #15689020C22semidirect
47. #15689019C22semidirect
48. #15689018C22semidirect
49. #15689018C22semidirect
50. #15689009C22semidirect
51. #15689008C22semidirect
52. #15689005C22semidirect
53. #15689004C22semidirect
60. #15688992C22semidirect
61. #15688987C22semidirect
71. C4⋊C4×Dic47C22semidirect
72. C4⋊C4×Dic47C22semidirect
73. #15688974C22semidirect
74. #15688974C22semidirect
91. C23×Dic47Q8semidirect
336. C2×Dic47C22⋊Q8semidirect
363. C22×C47#533semidirect
475. C47#36625semidirect
753. C22#15689675semidirect

Maximal subgroups

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

subgroupindex
C2×#156896752
C23×C4×Dic472
#202517382
#202517362
#202517282
#202517242
#202517222
#202516942
#202516752
#202516732
C22⋊Q8×Dic472
#202459202
#202459162
#202458672
#202457902
#202457662
C47×#28482
#3662547