Finite Group Databasebeta

← #26147576

Subgroups — #26147576

Order 12032.

1630 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689027C211yesmaximal, characteristic
2C2×#15689027C211yesmaximal, characteristic
3C2×#15689027C211yesmaximal, characteristic
4C2×#15689018C211yesmaximal, characteristic
5C2×C42×Dic47C211yesmaximal, characteristic
6#20241623C211yesmaximal, characteristic
7#20241621C211yesmaximal, characteristic
8#20241620C211yesmaximal, characteristic
9Dic47⋊#95C211yesmaximal, characteristic
10Dic47⋊#95C211yesmaximal, characteristic
11#20241613C211yesmaximal, characteristic
12#20241613C211yesmaximal, characteristic
13#20241612C211yesmaximal, characteristic
14#20241612C211yesmaximal, characteristic
15C47×#1436C211yesmaximal, characteristic
16C23×Dic94C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×Dic47⋊C4C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C22×C4×Dic47C2211yescharacteristic
25C22×C4×Dic47C2211yescharacteristic
26C22×C4×Dic47C2211yescharacteristic
27#15689027—24no—
28#15689027—24no—
29#15689027C418yescomplemented
30#15689018—24no—
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
48C42×Dic47—24no—
49C22×C4⋊C4×C47C2211yescharacteristic
50C22×C42×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C2×#95×C47C2211yescharacteristic
55C2×#95×C47C2211yescharacteristic
56C22×Dic94—22no—
57C22×Dic94—22no—
58C22×Dic94—22no—
59C22×Dic94—22no—
60C22×Dic94—22no—
61C22×Dic94—22no—
62C22×Dic94C2×C414yes—
63C23×Dic47C2311yescharacteristic
64C23×Dic47C2311yescharacteristic
65C23×Dic47C2311yescharacteristic
66C23×Dic47C2311yescharacteristic
67C23×Dic47C2311yescharacteristic
68C23×Dic47C2311yescharacteristic
69C23×Dic47C2311yescharacteristic
70C23×Dic47C2311yescharacteristic
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4—22no—
75C2×Dic47⋊C4—22no—
76C2×Dic47⋊C4—22no—
77C2×Dic47⋊C4—22no—
78C2×Dic47⋊C4—22no—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—22no—
81C2×Dic47⋊C4—22no—
82C2×Dic47⋊C4C2×C414yes—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C2×C4×Dic47—22no—
89C2×C4×Dic47—22no—
90C2×C4×Dic47—22no—
91C2×C4×Dic47—22no—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—22no—
94C2×C4×Dic47—22no—
95C2×C4×Dic47—22no—
96C2×C4×Dic47C2×C414yes—
97C2×C4×Dic47D414yes—
98C2×C4×Dic47D414yes—
99C2×C4×Dic47Q814yescomplemented
100C2×C4×Dic47Q814yescomplemented
101C47⋊#95—22no—
102C47⋊#95—22no—
103C47⋊#95—22no—
104C47⋊#95—22no—
105C47⋊#95—22no—
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⋊#95C2×C414yes—
116C47⋊#95C2×C414yes—
117C47⋊#95C2×C414yes—
118C23×C4×C47C2311yescharacteristic
119C23×C4×C47C2311yescharacteristic
120C23×C4×C47C2311yescharacteristic
121C23×C4×C47C2311yescharacteristic
122C23×C4×C47C2311yescharacteristic
123C23×C4×C47C2311yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47—22no—
127C2×C4⋊C4×C47—22no—
128C2×C42×C47—22no—
129C2×C42×C47—22no—
130C2×C42×C47—22no—
131#95×C47—22no—
132#95×C47—22no—
133#95×C47—22no—
134#95×C47—22no—
135#95×C47C2×C414yes—
136C24×C47C2411yescharacteristic
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
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×C47C22×C412yes—
176C22×C4×C47C22×C412yes—
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2×D412yes—
179C22×C4×C47C2×D412yes—
180C22×C4×C47C2×Q812yes—
181C22×C4×C47C2×Q812yes—
182C22×C4×C47#4112yes—
183C22×C4×C47#4112yes—
184C22×C4×C47#4112yes—
185C22×C4×C47#4112yes—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
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×Dic47C22×C412yes—
225C22×Dic47C22×C412yes—
226C22×Dic47C22×C412yes—
227C22×Dic47C22×C412yes—
228C22×Dic47C2×D412yes—
229C22×Dic47C2×D412yes—
230C22×Dic47C2×D412yes—
231C22×Dic47C2×D412yes—
232C22×Dic47C2×Q812yes—
233C22×Dic47C2×Q812yes—
234C22×Dic47C2×Q812yes—
235C22×Dic47C2×Q812yes—
236C22×Dic47#4112yes—
237C22×Dic47#4112yes—
238C22×Dic47#4112yes—
239C22×Dic47#4112yes—
240C22×Dic47#4112yes—
241C22×Dic47#4112yes—
242C2×Dic94—28no—
243C2×Dic94—28no—
244C2×Dic94—28no—
245C2×Dic94—44no—
246C2×Dic94—44no—
247C2×Dic94—44no—
248C2×Dic94—44no—
249C4⋊C4×C47—44no—
250C42×C47—28no—
251Dic47⋊C4—28no—
252Dic47⋊C4—44no—
253Dic47⋊C4—44no—
254Dic47⋊C4—44no—
255C4×Dic47—28no—
256C4×Dic47—28no—
257C4×Dic47—28no—
258C4×Dic47—28no—
259C4×Dic47—28no—
260C4×Dic47—28no—
261C23×C47C23×C411yescharacteristic
262C23×C47C22×D411yescharacteristic
263C23×C47C22×D411yescharacteristic
264C23×C47C22×Q811yescharacteristic
265C23×C47C22×Q811yescharacteristic
266C23×C47C2×#4111yescharacteristic
267C23×C47C2×#4111yescharacteristic
268C23×C47C2×#4111yescharacteristic
269C23×C47C2×#4111yescharacteristic
270C23×C47C2×#4111yescharacteristic
271C23×C47C2×#4111yescharacteristic
272C23×C47C2×#4111yescharacteristic
273C23×C47C2×#4111yescharacteristic
274C23×C47C2×#4111yescharacteristic
275C23×C47C2×#4111yescharacteristic
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47C4×Q814yes—
323C2×C4×C47C22⋊Q814yes—
324C2×C4×C47#12414yes—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—41no—
350C2×Dic47—41no—
351C2×Dic47—41no—
352C2×Dic47—41no—
353C2×Dic47—41no—
354C2×Dic47—41no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—41no—
359C2×Dic47—41no—
360C2×Dic47—41no—
361C2×Dic47—41no—
362C2×Dic47—41no—
363C2×Dic47—41no—
364C2×Dic47—41no—
365C2×Dic47—41no—
366C2×Dic47—41no—
367C2×Dic47—41no—
368C2×Dic47—41no—
369C2×Dic47—41no—
370C2×Dic47—41no—
371C2×Dic47#11714yes—
372C2×Dic47C4×D414yes—
373C2×Dic47C4×D414yes—
374C2×Dic47C4×Q814yes—
375C2×Dic47#12114yes—
376C2×Dic47C22⋊Q814yes—
377C2×Dic47#12314yes—
378C2×Dic47#12414yes—
379C2×Dic47#12614yes—
380C2×Dic47C4⋊Q814yes—
381Dic94—416no—
382#14703—471nomaximal, Sylow
383C22×C47C2×#11711yescharacteristic
384C22×C47C2×C4×D411yescharacteristic
385C22×C47C2×C4×D411yescharacteristic
386C22×C47C2×C4×Q811yescharacteristic
387C22×C47C2×C4×Q811yescharacteristic
388C22×C47C4×#4111yescharacteristic
389C22×C47C4×#4111yescharacteristic
390C22×C47C2×#12111yescharacteristic
391C22×C47C2×C22⋊Q811yescharacteristic
392C22×C47C2×C22⋊Q811yescharacteristic
393C22×C47C2×#12311yescharacteristic
394C22×C47#52511yescharacteristic
395C22×C47#52511yescharacteristic
396C22×C47C2×#12411yescharacteristic
397C22×C47C2×#12411yescharacteristic
398C22×C47C2×#12611yescharacteristic
399C22×C47#52911yescharacteristic
400C22×C47#52911yescharacteristic
401C22×C47#52911yescharacteristic
402C22×C47#52911yescharacteristic
403C22×C47#52911yescharacteristic
404C22×C47#52911yescharacteristic
405C22×C47#52911yescharacteristic
406C22×C47#52911yescharacteristic
407C22×C47C2×C4⋊Q811yescharacteristic
408C22×C47#53211yescharacteristic
409C22×C47#53211yescharacteristic
410C22×C47#53311yescharacteristic
411C22×C47#53311yescharacteristic
412C22×C47#53311yescharacteristic
413C22×C47#53311yescharacteristic
414C22×C47#53311yescharacteristic
415C22×C47#53311yescharacteristic
416C22×C47#53311yescharacteristic
417C22×C47#53311yescharacteristic
418C4×C47—24no—
419C4×C47—24no—
420C4×C47—24no—
421C4×C47—42no—
422C4×C47—42no—
423C4×C47—81no—
424C4×C47—81no—
425Dic47—24no—
426Dic47—24no—
427Dic47—24no—
428Dic47—42no—
429Dic47—42no—
430Dic47—81no—
431Dic47—81no—
432Dic47#38818yes—
433C2×#391—471no—
434C2×#391—471no—
435C2×#391—471no—
436C2×#389—471no—
437C2×C43—471no—
438#1436—471no—
439#1436—471no—
440#1436—471no—
441#1436D4711yescharacteristic
442C4⋊#95—471no—
443C4⋊#95—471no—
444#1434—471no—
445#1434—471no—
446#1434—471no—
447#1434—471no—
448C2×C47C2×#38811yescharacteristic
449C2×C47#229511yescharacteristic
450C2×C47#229511yescharacteristic
451C2×C47C4×C22⋊Q811yescharacteristic
452C2×C47C4×C22⋊Q811yescharacteristic
453C2×C47C4×#12411yescharacteristic
454C2×C47C4×C4⋊Q811yescharacteristic
455C2×C47#285011yescharacteristic
456C2×C47#285511yescharacteristic
457C2×C47#285511yescharacteristic
458C2×C47#285711yescharacteristic
459C2×C47#286111yescharacteristic
460C2×C47#286211yescharacteristic
461C2×C47#286311yescharacteristic
462C2×C47#286311yescharacteristic
463C23×Q8—471no—
464C22×C4⋊C4—471no—
465C22×C4⋊C4—471no—
466C22×C4⋊C4—471no—
467C22×C4⋊C4—471no—
468C22×C4⋊C4C2×D4711yescharacteristic
469C22×C42—471no—
470C22×C42—471no—
471C22×C42—471no—
472C22×C42—471no—
473C22×C42—471no—
474C22×C42—471no—
475C22×C42C2×D4711yescharacteristic
476#391—478no—
477#391—944no—
478#391—944no—
479#389—944no—
480C2×#95—471no—
481C2×#95—471no—
482C2×#95—471no—
483C2×#95—471no—
484C2×#95—471no—
485C2×#95—471no—
486C2×#95—471no—
487C2×#95—471no—
488C2×#95—471no—
489C2×#95—471no—
490C2×#95—471no—
491C2×#95—471no—
492C2×#95—471no—
493C2×#95—471no—
494C2×#95—471no—
495C2×#95—471no—
496C2×#95—471no—
497C2×#95C2×D4711yescharacteristic
498C2×#95C2×D4711yescharacteristic
499C2×#95C2×D4711yescharacteristic
500C2×#95C2×D4711yescharacteristic
501C2×#95C2×D4711yescharacteristic
502C43—944no—
503C47#1470311yescharacteristic, complemented, Sylow
504C22×Q8—474no—
505C22×Q8—942no—
506C22×Q8—942no—
507C22×Q8—942no—
508C22×Q8—942no—
509C22×Q8—942no—
510C22×Q8—942no—
511C23×C4—471no—
512C23×C4—471no—
513C23×C4—471no—
514C23×C4—471no—
515C23×C4—471no—
516C23×C4—471no—
517C23×C4—471no—
518C23×C4—471no—
519C23×C4C22×D4711yescharacteristic
520C23×C4C22×D4711yescharacteristic
521C23×C4C22×D4711yescharacteristic
522C23×C4C22×D4711yescharacteristic
523C23×C4C22×D4711yescharacteristic
524C23×C4C22×D4711yescharacteristic
525C23×C4C22×D4711yescharacteristic
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—942no—
531C2×C4⋊C4—942no—
532C2×C4⋊C4—942no—
533C2×C4⋊C4—942no—
534C2×C4⋊C4—942no—
535C2×C4⋊C4—942no—
536C2×C4⋊C4—942no—
537C2×C4⋊C4—942no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—474no—
545C2×C42—474no—
546C2×C42—474no—
547C2×C42—474no—
548C2×C42—474no—
549C2×C42—942no—
550C2×C42—942no—
551C2×C42—942no—
552C2×C42—942no—
553C2×C42—942no—
554C2×C42—942no—
555C2×C42—942no—
556C2×C42—942no—
557C2×C42—942no—
558C2×C42—942no—
559C2×C42—942no—
560C2×C42—942no—
561C2×C42—942no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—942no—
570#95—942no—
571#95—942no—
572#95—942no—
573#95—942no—
574#95—942no—
575#95—942no—
576#95—942no—
577#95—942no—
578#95—942no—
579#95—942no—
580#95—942no—
581#95—942no—
582#95—942no—
583#95C4×D4714yes—
584C24C23×D4711yescharacteristic
585C2×Q8—948no—
586C2×Q8—948no—
587C2×Q8—948no—
588C2×Q8—1884no—
589C2×Q8—1884no—
590C2×Q8—1884no—
591C2×Q8—1884no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—472no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—472no—
635C22×C4—472no—
636C22×C4—472no—
637C22×C4—472no—
638C22×C4—472no—
639C22×C4—472no—
640C22×C4—472no—
641C22×C4—472no—
642C22×C4—472no—
643C22×C4—472no—
644C22×C4—472no—
645C22×C4—472no—
646C22×C4—472no—
647C22×C4—472no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—941no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—941no—
656C22×C4—941no—
657C22×C4—941no—
658C22×C4—941no—
659C22×C4—941no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—941no—
667C22×C4—941no—
668C22×C4—941no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—941no—
674C22×C4—941no—
675C22×C4—941no—
676C22×C4—941no—
677C22×C4—941no—
678C22×C4—941no—
679C22×C4—941no—
680C22×C4—941no—
681C22×C4—941no—
682C22×C4—941no—
683C22×C4—941no—
684C22×C4—941no—
685C22×C4—941no—
686C22×C4C2×C4×D4712yes—
687C22×C4C2×C4×D4712yes—
688C22×C4C2×C4×D4712yes—
689C22×C4#1062535012yes—
690C22×C4#1062535012yes—
691C22×C4D4×D4712yes—
692C22×C4D4×D4712yes—
693C22×C4#1062535212yes—
694C22×C4#1062535212yes—
695C22×C4Q8×D4712yes—
696C22×C4Q8×D4712yes—
697C4⋊C4—44no—
698C4⋊C4—948no—
699C4⋊C4—1884no—
700C4⋊C4—1884no—
701C4⋊C4—1884no—
702C42—28no—
703C42—948no—
704C42—948no—
705C42—948no—
706C42—948no—
707C42—948no—
708C42—948no—
709C23C22×C4×D4711yescharacteristic
710C23C2×D4×D4711yescharacteristic
711C23C2×D4×D4711yescharacteristic
712C23C2×Q8×D4711yescharacteristic
713C23C2×Q8×D4711yescharacteristic
714C23#41×D4711yescharacteristic
715C23#41×D4711yescharacteristic
716C23#41×D4711yescharacteristic
717C23#41×D4711yescharacteristic
718C23#41×D4711yescharacteristic
719C23#41×D4711yescharacteristic
720C23C2×#1062535211yescharacteristic
721C23C2×#1062535211yescharacteristic
722C23C2×#1062535011yescharacteristic
723C23C2×#1062535011yescharacteristic
724Q8—18816no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—474no—
772C2×C4—474no—
773C2×C4—474no—
774C2×C4—474no—
775C2×C4—474no—
776C2×C4—474no—
777C2×C4—474no—
778C2×C4—474no—
779C2×C4—474no—
780C2×C4—474no—
781C2×C4—942no—
782C2×C4—942no—
783C2×C4—942no—
784C2×C4—942no—
785C2×C4—942no—
786C2×C4—942no—
787C2×C4—942no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—942no—
801C2×C4—942no—
802C2×C4—942no—
803C2×C4—942no—
804C2×C4—942no—
805C2×C4—1881no—
806C2×C4—1881no—
807C2×C4—1881no—
808C2×C4—1881no—
809C2×C4—1881no—
810C2×C4—1881no—
811C2×C4—1881no—
812C2×C4—1881no—
813C2×C4—1881no—
814C2×C4—1881no—
815C2×C4—1881no—
816C2×C4—1881no—
817C2×C4—1881no—
818C2×C4—1881no—
819C2×C4—1881no—
820C2×C4—1881no—
821C2×C4—1881no—
822C2×C4—1881no—
823C2×C4—1881no—
824C2×C4—1881no—
825C2×C4—1881no—
826C2×C4—1881no—
827C2×C4#1309398914yes—
828C2×C4#1309400214yes—
829C2×C4#1309401014yes—
830C22#117×D4711yescharacteristic
831C22C4×D4×D4711yescharacteristic
832C22C4×D4×D4711yescharacteristic
833C22C4×Q8×D4711yescharacteristic
834C22C2×#1309398911yescharacteristic
835C22C4×#1062535211yescharacteristic
836C22C4×#1062535011yescharacteristic
837C22#121×D4711yescharacteristic
838C22C22⋊Q8×D4711yescharacteristic
839C22C2×#1309400211yescharacteristic
840C22#123×D4711yescharacteristic
841C22#1568962911yescharacteristic
842C22#1568963211yescharacteristic
843C22#124×D4711yescharacteristic
844C22C2×#1309401011yescharacteristic
845C22#126×D4711yescharacteristic
846C22#1568965011yescharacteristic
847C22#1568965011yescharacteristic
848C22#1568965111yescharacteristic
849C22#1568965111yescharacteristic
850C22#1568965311yescharacteristic
851C22#1568965311yescharacteristic
852C22#1568965311yescharacteristic
853C22#1568965611yescharacteristic
854C22C4⋊Q8×D4711yescharacteristic
855C22#1568966811yescharacteristic
856C22#1568967011yescharacteristic
857C22#1568967511yescharacteristic
858C22#1568967511yescharacteristic
859C22#1568967511yescharacteristic
860C22#1568967711yescharacteristic
861C22#1568967711yescharacteristic
862C22#1568967711yescharacteristic
863C22#1568967911yescharacteristic
864C22#1568967911yescharacteristic
865C4—24no—
866C4—24no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—478no—
873C4—944no—
874C4—944no—
875C4—944no—
876C4—3761no—
877C4—3761no—
878C4—1882no—
879C4—1882no—
880C2#388×D4711yescharacteristic
881C2#2024586111yescharacteristic
882C2#2024586411yescharacteristic
883C2#2024592011yescharacteristic
884C2C4×#1309400211yescharacteristic
885C2C4×#1309401011yescharacteristic
886C2#2024595911yescharacteristic
887C2#2025168511yescharacteristic
888C2#2025172311yescharacteristic
889C2#2025172411yescharacteristic
890C2#2025173911yescharacteristic
891C2#2025175711yescharacteristic
892C2#2025176311yescharacteristic
893C2#2025176911yescharacteristic
894C2#2025176911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1436C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1436D47
hypocenterC47#14703
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
29. #15689027C4semidirect
99. C2×C4×Dic47Q8semidirect
100. C2×C4×Dic47Q8semidirect
503. C47#14703semidirect

Maximal subgroups

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

subgroupindex
C2×#156890272
C2×#156890182
C2×C42×Dic472
#202416232
#202416212
#202416202
Dic47⋊#952
#202416132
#202416122
C47×#14362
#1470347