Finite Group Databasebeta

← #26144591

Subgroups — #26144591

Order 12032.

1266 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689030C211yesmaximal, characteristic
2C2×#15689030C211yesmaximal, characteristic
3C2×#15689008C211yesmaximal, characteristic
4#20241657C211yesmaximal, characteristic
5#20241649C211yesmaximal, characteristic
6#20241648C211yesmaximal, characteristic
7#20241644C211yesmaximal, characteristic
8#20241643C211yesmaximal, characteristic
9#20241622C211yesmaximal, characteristic
10#20241619C211yesmaximal, characteristic
11#20241614C211yesmaximal, characteristic
12#20241614C211yesmaximal, characteristic
13#20241613C211yesmaximal, characteristic
14#20241613C211yesmaximal, characteristic
15C47×#1446C211yesmaximal, characteristic
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689030—24no—
23#15689030C418yescomplemented
24#15689008—24no—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
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
47C23×Q8×C47C2211yescharacteristic
48C2×#95×C47C2211yescharacteristic
49C2×#95×C47C2211yescharacteristic
50C2×#95×C47C2211yescharacteristic
51C2×#95×C47C2211yescharacteristic
52C2×#95×C47C2211yescharacteristic
53C2×#95×C47C2211yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2311yescharacteristic
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C23×Dic47C2311yescharacteristic
61C23×Dic47C2311yescharacteristic
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—22no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—41no—
67C2×C4⋊Dic47C2×C414yes—
68C2×Dic47⋊C4—22no—
69C2×Dic47⋊C4—22no—
70C2×Dic47⋊C4—41no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47—22no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47—41no—
76C2×C4×Dic47—41no—
77C2×C4×Dic47—41no—
78C2×C4×Dic47—41no—
79C2×C4×Dic47C2×C414yes—
80C47⋊#95—22no—
81C47⋊#95—22no—
82C47⋊#95—22no—
83C47⋊#95—22no—
84C47⋊#95—22no—
85C47⋊#95—22no—
86C47⋊#95—22no—
87C47⋊#95—22no—
88C47⋊#95—22no—
89C47⋊#95—41no—
90C47⋊#95—41no—
91C47⋊#95—41no—
92C47⋊#95—41no—
93C47⋊#95—41no—
94C47⋊#95—41no—
95C47⋊#95—41no—
96C47⋊#95—41no—
97C47⋊#95C2×C414yes—
98C47⋊#95C2×C414yes—
99C47⋊#95C2×C414yes—
100C47⋊#95C2×C414yes—
101C47⋊#95D414yes—
102C22×Q8×C47—22no—
103C22×Q8×C47—22no—
104C22×Q8×C47—22no—
105C22×Q8×C47—22no—
106C22×Q8×C47—41no—
107C22×Q8×C47—41no—
108C22×Q8×C47C2×C414yes—
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116#95×C47—22no—
117#95×C47—22no—
118#95×C47—22no—
119#95×C47—22no—
120#95×C47—41no—
121#95×C47—41no—
122C24×C47C2411yescharacteristic
123C2×Q8×C47—28no—
124C2×Q8×C47—28no—
125C2×Q8×C47—44no—
126C2×Q8×C47—44no—
127C2×Q8×C47—44no—
128C2×Q8×C47—44no—
129C2×Q8×C47—44no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
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×C47C22×C412yes—
172C22×C4×C47C22×C412yes—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47#4112yes—
176C22×C4×C47#4112yes—
177C22×C4×C47#4112yes—
178C22×C4×C47#4112yes—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
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×Dic47—21no—
225C22×Dic47—21no—
226C22×Dic47—21no—
227C22×Dic47—21no—
228C22×Dic47C22×C412yes—
229C22×Dic47C22×C412yes—
230C22×Dic47C22×C412yes—
231C22×Dic47C22×C412yes—
232C22×Dic47C2×D412yes—
233C22×Dic47C2×D412yes—
234C22×Dic47#4112yes—
235C4⋊Dic47—28no—
236C4⋊Dic47—44no—
237Dic47⋊C4—44no—
238C4×Dic47—44no—
239C4×Dic47—44no—
240C4×Dic47—44no—
241C23×C47C23×C411yescharacteristic
242C23×C47C22×D411yescharacteristic
243C23×C47C2×#4111yescharacteristic
244C23×C47C2×#4111yescharacteristic
245C23×C47C2×#4111yescharacteristic
246C23×C47C2×#4111yescharacteristic
247C23×C47C2×#4111yescharacteristic
248C23×C47H(5,𝔽2)11yescharacteristic
249C23×C47H(5,𝔽2)11yescharacteristic
250C23×C47H(5,𝔽2)11yescharacteristic
251C23×C472−1+411yescharacteristic
252C23×C472−1+411yescharacteristic
253C23×C472−1+411yescharacteristic
254C23×C472−1+411yescharacteristic
255C23×C472−1+411yescharacteristic
256Q8×C47—416no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47#11714yes—
305C2×C4×C47C4×D414yes—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341C2×Dic47—41no—
342C2×Dic47—41no—
343C2×Dic47—41no—
344C2×Dic47—41no—
345C2×Dic47—41no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348C2×Dic47—41no—
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—
362#14432—471nomaximal, Sylow
363C22×C47C2×#11711yescharacteristic
364C22×C47C2×C4×D411yescharacteristic
365C22×C47C4×#4111yescharacteristic
366C22×C47#51811yescharacteristic
367C22×C47#51911yescharacteristic
368C22×C47#51911yescharacteristic
369C22×C47#52011yescharacteristic
370C22×C47#53611yescharacteristic
371C22×C47#53611yescharacteristic
372C22×C47#53911yescharacteristic
373C22×C47#53911yescharacteristic
374C22×C47#54111yescharacteristic
375C22×C47#54111yescharacteristic
376C22×C47#54111yescharacteristic
377C22×C47#54111yescharacteristic
378C22×C47#54211yescharacteristic
379C22×C47#54211yescharacteristic
380C22×C47#54211yescharacteristic
381C22×C47#54211yescharacteristic
382C22×C47#54611yescharacteristic
383C22×C47#54611yescharacteristic
384C22×C47#54611yescharacteristic
385C22×C47#54811yescharacteristic
386C22×C47#55111yescharacteristic
387C22×C47#55111yescharacteristic
388C22×C47#55211yescharacteristic
389C22×C47#55211yescharacteristic
390C22×C47#55611yescharacteristic
391C22×C47#55611yescharacteristic
392C22×C47#55611yescharacteristic
393C22×C47#55911yescharacteristic
394C22×C47#56211yescharacteristic
395C22×C47#56211yescharacteristic
396C22×C47#56311yescharacteristic
397C22×C47#56311yescharacteristic
398C4×C47—24no—
399C4×C47—24no—
400C4×C47—42no—
401C4×C47—42no—
402C4×C47—81no—
403C4×C47—81no—
404C4×C47—81no—
405Dic47—42no—
406Dic47—42no—
407Dic47—42no—
408Dic47—42no—
409Dic47—42no—
410Dic47—42no—
411Dic47—42no—
412Dic47—81no—
413C2×#391—471no—
414C2×#391—471no—
415C2×#387—471no—
416#1446D4711yescharacteristic
417#1445—471no—
418#1443—471no—
419#1443—471no—
420#1442—471no—
421#1442—471no—
422#1436—471no—
423#1436—471no—
424#1434—471no—
425#1434—471no—
426#1434—471no—
427#1434—471no—
428C2×C47#232011yescharacteristic
429C2×C47#232711yescharacteristic
430C2×C47#233211yescharacteristic
431C2×C47#234211yescharacteristic
432C2×C47#235611yescharacteristic
433C2×C47#236711yescharacteristic
434C2×C47#237811yescharacteristic
435C2×C47#268711yescharacteristic
436C2×C47#269011yescharacteristic
437C2×C47#270011yescharacteristic
438C2×C47#271611yescharacteristic
439C2×C47#275411yescharacteristic
440C2×C47#275811yescharacteristic
441C2×C47#278911yescharacteristic
442C2×C47#279811yescharacteristic
443C23×Q8C2×D4711yescharacteristic
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—471no—
447C22×C42—471no—
448C22×C42—471no—
449C22×C42—471no—
450#391—478no—
451#391—944no—
452#387—944no—
453C2×#95—471no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—471no—
457C2×#95—471no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95—471no—
463C2×#95—471no—
464C2×#95—471no—
465C2×#95—471no—
466C2×#95—471no—
467C2×#95—471no—
468C2×#95—471no—
469C2×#95—471no—
470C2×#95—471no—
471C2×#95—471no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95C2×D4711yescharacteristic
476C2×#95C2×D4711yescharacteristic
477C2×#95C2×D4711yescharacteristic
478C2×#95C2×D4711yescharacteristic
479C2×#95C2×D4711yescharacteristic
480C2×#95C2×D4711yescharacteristic
481C47#1443211yescharacteristic, complemented, Sylow
482C22×Q8—22no—
483C22×Q8—22no—
484C22×Q8—22no—
485C22×Q8—22no—
486C22×Q8—41no—
487C22×Q8—41no—
488C22×Q8C4×D4714yes—
489C23×C4—471no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C23×C4C22×D4711yescharacteristic
500C23×C4C22×D4711yescharacteristic
501C23×C4C22×D4711yescharacteristic
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C2×C4⋊C4—474no—
505C2×C4⋊C4—942no—
506C2×C4⋊C4—942no—
507C2×C4⋊C4—942no—
508C2×C4⋊C4—942no—
509C2×C4⋊C4—942no—
510C2×C4⋊C4—942no—
511C2×C4⋊C4—1881no—
512C2×C4⋊C4—1881no—
513C2×C42—474no—
514C2×C42—942no—
515C2×C42—942no—
516C2×C42—942no—
517C2×C42—942no—
518C2×C42—1881no—
519C2×C42—1881no—
520C2×C42—1881no—
521C2×C42—1881no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—41no—
527#95—41no—
528#95—474no—
529#95—474no—
530#95—474no—
531#95—474no—
532#95—474no—
533#95—942no—
534#95—942no—
535#95—942no—
536#95—942no—
537#95—942no—
538#95—942no—
539#95—942no—
540#95—942no—
541#95—942no—
542#95—1881no—
543#95—1881no—
544#95—1881no—
545#95—1881no—
546#95—1881no—
547#95—1881no—
548#95—1881no—
549#95—1881no—
550C24C23×D4711yescharacteristic
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—472no—
604C22×C4—472no—
605C22×C4—472no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—941no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—941no—
618C22×C4—941no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—941no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—941no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—941no—
635C22×C4—941no—
636C22×C4—941no—
637C22×C4—941no—
638C22×C4—941no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—941no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—941no—
646C22×C4—941no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—941no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4C2×C4×D4712yes—
656C22×C4C2×C4×D4712yes—
657C22×C4C2×C4×D4712yes—
658C22×C4D4×D4712yes—
659C22×C4#1062535212yes—
660C22×C4#1062535212yes—
661C22×C4#1062535212yes—
662C22×C4#1062535412yes—
663C4⋊C4—948no—
664C4⋊C4—1884no—
665C4⋊C4—1884no—
666C42—1884no—
667C42—1884no—
668C42—1884no—
669C23C22×C4×D4711yescharacteristic
670C23C2×D4×D4711yescharacteristic
671C23#41×D4711yescharacteristic
672C23C2×#1062535211yescharacteristic
673C23C2×#1062535211yescharacteristic
674C23C2×#1062535211yescharacteristic
675C23C2×#1062535411yescharacteristic
676C23#1309406911yescharacteristic
677C23#1309406911yescharacteristic
678C23#1309407011yescharacteristic
679C23#1309407111yescharacteristic
680C23#1309407111yescharacteristic
681C23#1309407211yescharacteristic
682C23#1309407211yescharacteristic
683C23#1309407211yescharacteristic
684Q8—416no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—942no—
741C2×C4—942no—
742C2×C4—942no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—942no—
746C2×C4—942no—
747C2×C4—942no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4—1881no—
757C2×C4—1881no—
758C2×C4—1881no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4—1881no—
764C2×C4—1881no—
765C2×C4—1881no—
766C2×C4—1881no—
767C2×C4—1881no—
768C2×C4—1881no—
769C2×C4—1881no—
770C2×C4—1881no—
771C2×C4—1881no—
772C2×C4—1881no—
773C2×C4—1881no—
774C2×C4—1881no—
775C2×C4—1881no—
776C2×C4—1881no—
777C2×C4—1881no—
778C2×C4—1881no—
779C2×C4—1881no—
780C2×C4—1881no—
781C2×C4—1881no—
782C2×C4—1881no—
783C2×C4—1881no—
784C2×C4—1881no—
785C2×C4—1881no—
786C2×C4—1881no—
787C2×C4—1881no—
788C2×C4#1309398014yes—
789C2×C4(C22⋊D47)⋊C414yes—
790C22C2×#1309398011yescharacteristic
791C22C2×(C22⋊D47)⋊C411yescharacteristic
792C22C4×#1062535411yescharacteristic
793C22#1568959611yescharacteristic
794C22#1568959911yescharacteristic
795C22#1568959911yescharacteristic
796C22#1568960511yescharacteristic
797C22#1568969311yescharacteristic
798C22#1568969811yescharacteristic
799C22#1568971911yescharacteristic
800C22#1568972211yescharacteristic
801C22#1568973311yescharacteristic
802C22#1568973311yescharacteristic
803C22#1568973311yescharacteristic
804C22#1568973411yescharacteristic
805C22#1568973711yescharacteristic
806C22#1568974211yescharacteristic
807C22#1568974611yescharacteristic
808C22#1568974711yescharacteristic
809C22#1568976011yescharacteristic
810C22#1568976011yescharacteristic
811C22#1568976411yescharacteristic
812C22#1568978311yescharacteristic
813C22#1568980411yescharacteristic
814C22#1568980411yescharacteristic
815C22#1568980711yescharacteristic
816C22#1568981511yescharacteristic
817C22#1568984211yescharacteristic
818C22#1568984711yescharacteristic
819C22#1568984711yescharacteristic
820C22#1568985511yescharacteristic
821C22#1568986711yescharacteristic
822C22#1568986911yescharacteristic
823C22#1568987211yescharacteristic
824C22#1568987411yescharacteristic
825C4—24no—
826C4—24no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4—3761no—
833C4—1882no—
834C4—1882no—
835C4—1882no—
836C4—1882no—
837C4—1882no—
838C4—1882no—
839C4—1882no—
840C2#2024603311yescharacteristic
841C2#2024610611yescharacteristic
842C2#2024614311yescharacteristic
843C2#2024623911yescharacteristic
844C2#2024635211yescharacteristic
845C2#2024646411yescharacteristic
846C2#2024654911yescharacteristic
847C2#2024980811yescharacteristic
848C2#2024985311yescharacteristic
849C2#2024998511yescharacteristic
850C2#2025020711yescharacteristic
851C2#2025068211yescharacteristic
852C2#2025074211yescharacteristic
853C2#2025115011yescharacteristic
854C2#2025126211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×#1446C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1446D47
hypocenterC47#14432
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
23. #15689030C4semidirect
481. C47#14432semidirect

Maximal subgroups

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

subgroupindex
C2×#156890302
C2×#156890082
#202416572
#202416492
#202416482
#202416442
#202416432
#202416222
#202416192
#202416142
#202416132
C47×#14462
#1443247