Finite Group Databasebeta

← #26152978

Subgroups — #26152978

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689045C212yesmaximal, complemented
2C2×#15689025C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15689024C211yesmaximal, characteristic
5C2×#15689022C211yesmaximal, characteristic, complemented
6C2×#15689019C211yesmaximal, characteristic, complemented
7#20241634C212yesmaximal, complemented
8#20241632C212yesmaximal, complemented
9#20241630C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C47×#389C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C22×C4⋊Dic47C2212yes—
14C22×C4⋊Dic47C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2212yes—
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×(C2×D47)⋊C4C2212yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689045—28no—
25#15689025—24no—
26#15689024—24no—
27#15689024—24no—
28#15689022—24no—
29#15689019—24no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C22×C4⋊C4×C47C2212yes—
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C47×#389—24no—
41C2×#95×C47C2212yes—
42C24×D47C2312yes—
43C22×D188—22no—
44C22×D188—22no—
45C22×D188—22no—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188—22no—
49C22×D188Q814yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—24no—
58C2×C4⋊Dic47—24no—
59C2×C4⋊Dic47—42no—
60C2×C4⋊Dic47D414yes—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—42no—
64C2×(C2×D47)⋊C4—24no—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—24no—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—24no—
75C2×(C2×D47)⋊C4—24no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4—42no—
79C2×(C2×D47)⋊C4—42no—
80C2×(C2×D47)⋊C4—42no—
81C2×(C2×D47)⋊C4—42no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C47⋊#95—24no—
89C47⋊#95—22no—
90C47⋊#95—24no—
91C47⋊#95—22no—
92C47⋊#95—22no—
93C47⋊#95D414yescomplemented
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2312yes—
96C23×C4×C47C2312yes—
97C23×C4×C47C2311yescharacteristic
98C23×C4×C47C2311yescharacteristic
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—22no—
103C2×C4⋊C4×C47—24no—
104C2×C4⋊C4×C47—24no—
105C2×C4⋊C4×C47—42no—
106C2×C4⋊C4×C47D414yes—
107C2×C4⋊C4×C47D414yes—
108C2×C42×C47—22no—
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111#95×C47—24no—
112C24×C47C2411yescharacteristic
113C23×D47—22no—
114C23×D47—22no—
115C23×D47—22no—
116C23×D47—22no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47—22no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—22no—
123C23×D47—22no—
124C23×D47—22no—
125C23×D47—22no—
126C23×D47—22no—
127C23×D47C2×Q814yes—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—21no—
152C22×C4×C47C2×D414yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D414yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×Q812yes—
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
161C22×C4×C47#4112yes—
162C22×C4×C47#4112yes—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—22no—
182C22×Dic47—22no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47C2×D414yes—
194C22×Dic47C2×D412yes—
195C22×Dic47C2×D412yes—
196C22×Dic47#4112yes—
197C22×Dic47#4112yes—
198C2×D188—28no—
199C2×D188—28no—
200C2×D188—28no—
201C2×D188—44no—
202C2×D188—44no—
203C2×D188—44no—
204C2×D188—44no—
205C4⋊C4×C47—28no—
206C4⋊C4×C47—28no—
207C4⋊C4×C47—48no—
208C42×C47—44no—
209(C2×D47)⋊C4—48no—
210(C2×D47)⋊C4—48no—
211(C2×D47)⋊C4—48no—
212(C2×D47)⋊C4—48no—
213(C2×D47)⋊C4—48no—
214(C2×D47)⋊C4—48no—
215C4⋊Dic47—28no—
216C4⋊Dic47—48no—
217Dic47⋊C4—48no—
218C4×Dic47—44no—
219C4×Dic47—44no—
220C23×C47C22×D411yescharacteristic
221C23×C47C22×D411yescharacteristic
222C23×C47C22×D411yescharacteristic
223C23×C47C22×D411yescharacteristic
224C23×C47C22×Q811yescharacteristic
225C23×C47C2×#4111yescharacteristic
226C23×C47C2×#4111yescharacteristic
227C23×C47C2×#4111yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C23×C47C2×#4111yescharacteristic
230C23×C47C2×#4111yescharacteristic
231C23×C47H(5,𝔽2)11yescharacteristic
232C23×C47H(5,𝔽2)11yescharacteristic
233C23×C47H(5,𝔽2)11yescharacteristic
234C23×C472−1+411yescharacteristic
235C22×D47—24no—
236C22×D47—24no—
237C22×D47—24no—
238C22×D47—24no—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47—24no—
242C22×D47—42no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—42no—
250C22×D47—42no—
251C22×D47—42no—
252C22×D47—42no—
253C22×D47—42no—
254C22×D47—42no—
255C22×D47—42no—
256C22×D47—42no—
257C22×D47—42no—
258C22×D47—42no—
259C22×D47—42no—
260C22×D47—42no—
261C22×D47—42no—
262C22×D47—42no—
263C22×D47—42no—
264C22×D47—42no—
265C22×D47—42no—
266C22×D47—42no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C2×C4×C47—24no—
271C2×C4×C47—24no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—24no—
275C2×C4×C47—22no—
276C2×C4×C47—24no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—24no—
280C2×C4×C47—24no—
281C2×C4×C47—22no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—41no—
288C2×C4×C47—42no—
289C2×C4×C47—41no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—42no—
296C2×C4×C47—41no—
297C2×C4×C47—42no—
298C2×C4×C47#12114yes—
299C2×C4×C47#12114yes—
300C2×C4×C47#12114yes—
301C2×C4×C47C22⋊Q814yes—
302C2×C4×C47C22⋊Q814yes—
303C2×C4×C47C22⋊Q814yes—
304C2×C4×C47#12614yes—
305C2×Dic47—24no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—24no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—24no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—42no—
325C2×Dic47—41no—
326C2×Dic47—42no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—41no—
330C2×Dic47—42no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—41no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—42no—
339C2×Dic47—41no—
340D188—416no—
341#15141—471nomaximal, Sylow
342C22×C47C2×#12111yescharacteristic
343C22×C47C2×#12111yescharacteristic
344C22×C47C2×#12111yescharacteristic
345C22×C47C2×C22⋊Q811yescharacteristic
346C22×C47C2×C22⋊Q811yescharacteristic
347C22×C47C2×C22⋊Q811yescharacteristic
348C22×C47C2×#12611yescharacteristic
349C22×C47#52911yescharacteristic
350C22×C47#52911yescharacteristic
351C22×C47#52911yescharacteristic
352C22×C47#53211yescharacteristic
353C22×C47#53211yescharacteristic
354C22×C47#53211yescharacteristic
355C22×C47#54011yescharacteristic
356C22×C47#54011yescharacteristic
357C22×C47#54011yescharacteristic
358C22×C47#54211yescharacteristic
359C22×C47#54211yescharacteristic
360C22×C47#54211yescharacteristic
361C22×C47D4211yescharacteristic
362C22×C47D4211yescharacteristic
363C22×C47D4211yescharacteristic
364C22×C47#54611yescharacteristic
365C22×C47#54611yescharacteristic
366C22×C47#54611yescharacteristic
367C22×C47#54811yescharacteristic
368C22×C47#54811yescharacteristic
369C22×C47#54811yescharacteristic
370C22×C47D4×Q811yescharacteristic
371C22×C47#55011yescharacteristic
372C22×C47#55011yescharacteristic
373C22×C47#55011yescharacteristic
374C22×C47#55411yescharacteristic
375C22×C47#55411yescharacteristic
376C22×C47#55411yescharacteristic
377C2×D47—44no—
378C2×D47—44no—
379C2×D47—44no—
380C2×D47—44no—
381C2×D47—44no—
382C2×D47—44no—
383C2×D47—44no—
384C2×D47—82no—
385C2×D47—82no—
386C2×D47—82no—
387C2×D47—82no—
388C2×D47—82no—
389C2×D47—82no—
390C2×D47—82no—
391C2×D47—82no—
392C4×C47—42no—
393C4×C47—44no—
394C4×C47—44no—
395C4×C47—42no—
396C4×C47#39618yescomplemented
397Dic47—42no—
398Dic47—42no—
399Dic47—42no—
400Dic47—44no—
401Dic47—42no—
402C2×#396—472no—
403C2×#390—471no—
404C2×#390—471no—
405C2×#390—471no—
406C2×#389—471no—
407C2×#389—471no—
408C2×#389D4711yescharacteristic, complemented
409#1439—472no—
410#1439—472no—
411#1439—472no—
412C4×#95—471no—
413C2×C47C2×#39611yescharacteristic
414C2×C47#242611yescharacteristic
415C2×C47#242611yescharacteristic
416C2×C47#242611yescharacteristic
417C2×C47#242811yescharacteristic
418C2×C47#242811yescharacteristic
419C2×C47#242811yescharacteristic
420C2×C47#245211yescharacteristic
421C2×C47#245211yescharacteristic
422C2×C47#245211yescharacteristic
423C2×C47#245411yescharacteristic
424C2×C47#245411yescharacteristic
425C2×C47#245411yescharacteristic
426C2×C47#264411yescharacteristic
427C2×C47#286011yescharacteristic
428D47—84no—
429C23×D4—471no—
430C22×C4⋊C4—471no—
431C22×C4⋊C4—472no—
432C22×C4⋊C4—472no—
433C22×C4⋊C4C2×D4712yes—
434C22×C4⋊C4C2×D4711yescharacteristic
435C22×C4⋊C4C2×D4711yescharacteristic
436C22×C22⋊C4—472no—
437C22×C22⋊C4—472no—
438C22×C22⋊C4—472no—
439C22×C22⋊C4—472no—
440C22×C22⋊C4—472no—
441C22×C22⋊C4—472no—
442C22×C42—471no—
443C22×C42—471no—
444C22×C42C2×D4711yescharacteristic
445#396—948no—
446#390—944no—
447#390—944no—
448#390—944no—
449#389—24no—
450#389—944no—
451#389—944no—
452C2×#95—471no—
453C2×#95—471no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—472no—
457C2×#95—472no—
458C2×#95C2×D4712yes—
459C47#1514111yescharacteristic, complemented, Sylow
460C25—472no—
461C22×D4—474no—
462C22×D4—942no—
463C22×D4—942no—
464C22×D4—942no—
465C22×D4—942no—
466C22×D4—942no—
467C22×D4—942no—
468C23×C4—472no—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4C22×D4712yes—
474C23×C4C22×D4711yescharacteristic
475C23×C4C22×D4711yescharacteristic
476C23×C4C22×D4712yes—
477C23×C4C22×D4711yescharacteristic
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—942no—
487C2×C4⋊C4—942no—
488C2×C4⋊C4—944no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4—944no—
491C2×C4⋊C4—944no—
492C2×C4⋊C4—1882no—
493C2×C4⋊C4—1882no—
494C2×C4⋊C4D18814yes—
495C2×C4⋊C4C22⋊D4714yes—
496C2×C22⋊C4—944no—
497C2×C22⋊C4—944no—
498C2×C22⋊C4—944no—
499C2×C22⋊C4—944no—
500C2×C22⋊C4—944no—
501C2×C22⋊C4—944no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C22⋊C4—1882no—
509C2×C22⋊C4—1882no—
510C2×C22⋊C4—1882no—
511C2×C22⋊C4—1882no—
512C2×C22⋊C4—1882no—
513C2×C22⋊C4—1882no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—942no—
518C2×C42—942no—
519C2×C42—942no—
520C2×C42—942no—
521C2×C42—942no—
522C2×C42—942no—
523#95—24no—
524#95—474no—
525#95—942no—
526#95—942no—
527#95—944no—
528#95—944no—
529#95—942no—
530C24—474no—
531C24—942no—
532C24—942no—
533C24—942no—
534C24—942no—
535C24—942no—
536C24—942no—
537C24—942no—
538C24—942no—
539C24—942no—
540C24—942no—
541C24—942no—
542C24—942no—
543C24—942no—
544C24—942no—
545C24C23×D4711yescharacteristic
546C2×D4—948no—
547C2×D4—948no—
548C2×D4—948no—
549C2×D4—1884no—
550C2×D4—1884no—
551C2×D4—1884no—
552C2×D4—1884no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—474no—
580C22×C4—472no—
581C22×C4—472no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—942no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—941no—
588C22×C4—942no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—941no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—941no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4C2×D18814yes—
613C22×C4C2×D18812yes—
614C22×C4#1062535012yes—
615C22×C4D4×D4712yes—
616C22×C4D4×D4712yes—
617C22×C4#1062535212yes—
618C22×C4Q8×D4712yes—
619C22×C4#1062535412yes—
620C22×C4#1062535412yes—
621C22×C4C2×C22⋊D4714yes—
622C22×C4C2×C22⋊D4712yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—48no—
626C4⋊C4—948no—
627C4⋊C4—1888no—
628C4⋊C4—1888no—
629C22⋊C4—1888no—
630C22⋊C4—1888no—
631C22⋊C4—1888no—
632C22⋊C4—1888no—
633C22⋊C4—1888no—
634C22⋊C4—1888no—
635C42—44no—
636C42—1884no—
637C42—1884no—
638C23—944no—
639C23—944no—
640C23—944no—
641C23—944no—
642C23—944no—
643C23—944no—
644C23—944no—
645C23—1882no—
646C23—1882no—
647C23—1882no—
648C23—1882no—
649C23—1882no—
650C23—1882no—
651C23—1882no—
652C23—1882no—
653C23—1882no—
654C23—1882no—
655C23—1882no—
656C23—1882no—
657C23—1882no—
658C23—1882no—
659C23—1882no—
660C23—1882no—
661C23—1882no—
662C23—1882no—
663C23—1882no—
664C23—1882no—
665C23—1882no—
666C23—1882no—
667C23—1882no—
668C23—1882no—
669C23—1882no—
670C23—1882no—
671C23—1882no—
672C23—1882no—
673C23C2×D4×D4711yescharacteristic
674C23C2×D4×D4711yescharacteristic
675C23C22×C22⋊D4711yescharacteristic
676C23C22×D18811yescharacteristic
677C23C2×Q8×D4711yescharacteristic
678C23#41×D4711yescharacteristic
679C23#41×D4711yescharacteristic
680C23C2×#1062535211yescharacteristic
681C23C2×#1062535011yescharacteristic
682C23C2×#1062535411yescharacteristic
683C23C2×#1062535411yescharacteristic
684C23#1309406911yescharacteristic
685C23#1309407011yescharacteristic
686C23#1309407011yescharacteristic
687C23#1309407211yescharacteristic
688D4—18816no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—942no—
718C2×C4—944no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—944no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—944no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—1881no—
733C2×C4—1882no—
734C2×C4—1881no—
735C2×C4—1881no—
736C2×C4—1882no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4—1881no—
744C2×C4—1882no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1881no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1882no—
751C2×C4—1881no—
752C2×C4#1309399614yes—
753C2×C4#1309399814yes—
754C2×C4#1309399914yes—
755C2×C4#1309400014yes—
756C2×C4#1309400214yes—
757C2×C4#1309400414yes—
758C2×C4#1309401914yes—
759C22—3762no—
760C22—3762no—
761C22—3762no—
762C22—3762no—
763C22—3762no—
764C22—3762no—
765C22—3762no—
766C22—3762no—
767C22—1884no—
768C22—1884no—
769C22—1884no—
770C22—1884no—
771C22—1884no—
772C22—1884no—
773C22—1884no—
774C22C2×#1309399611yescharacteristic
775C22C2×#1309399811yescharacteristic
776C22C2×#1309399911yescharacteristic
777C22C2×#1309400011yescharacteristic
778C22C2×#1309400211yescharacteristic
779C22C2×#1309400411yescharacteristic
780C22C2×#1309401911yescharacteristic
781C22#1568965811yescharacteristic
782C22#1568965911yescharacteristic
783C22#1568966011yescharacteristic
784C22#1568966811yescharacteristic
785C22#1568967011yescharacteristic
786C22#1568967411yescharacteristic
787C22#1568972411yescharacteristic
788C22#1568972611yescharacteristic
789C22#1568972911yescharacteristic
790C22#1568974511yescharacteristic
791C22#1568974611yescharacteristic
792C22#1568974711yescharacteristic
793C22D4×C22⋊D4711yescharacteristic
794C22#1568975711yescharacteristic
795C22D4×D18811yescharacteristic
796C22#1568976111yescharacteristic
797C22#1568976411yescharacteristic
798C22#1568976811yescharacteristic
799C22#1568978311yescharacteristic
800C22#1568978411yescharacteristic
801C22#1568978511yescharacteristic
802C22#1568978811yescharacteristic
803C22#1568979111yescharacteristic
804C22#1568979211yescharacteristic
805C22#1568979511yescharacteristic
806C22#1568982911yescharacteristic
807C22#1568982911yescharacteristic
808C22#1568983411yescharacteristic
809C4—42no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—1882no—
814C4—1882no—
815C4—1882no—
816C4—1884no—
817C4—1882no—
818C4#1568904518yescomplemented
819C2—3764no—
820C2C2×#1568904511yescharacteristic
821C2#2024694811yescharacteristic
822C2#2024695211yescharacteristic
823C2#2024695611yescharacteristic
824C2#2024697011yescharacteristic
825C2#2024697411yescharacteristic
826C2#2024697811yescharacteristic
827C2#2024723411yescharacteristic
828C2#2024723611yescharacteristic
829C2#2024723911yescharacteristic
830C2#2024725611yescharacteristic
831C2#2024725811yescharacteristic
832C2#2024726111yescharacteristic
833C2#2024935111yescharacteristic
834C2#2025175611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, cosocleC24×C47C24
FittingC2×C47×#389C2
prime radicalC23×D188C22
hypercenterC2×#389D47
hypocenterC47#15141
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#15689045C2semidirect
5. C2×#15689022C2semidirect
6. C2×#15689019C2semidirect
7. #20241634C2semidirect
8. #20241632C2semidirect
9. #20241630C2semidirect
10. C4×C47⋊#95C2semidirect
11. C2×C47×#389C2semidirect
93. C47⋊#95D4semidirect
396. C4×C47#396semidirect
408. C2×#389D47semidirect
459. C47#15141semidirect
818. C4#15689045semidirect

Maximal subgroups

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

subgroupindex
C2×#156890452
C2×#156890252
C2×#156890242
C2×#156890222
C2×#156890192
#202416342
#202416322
#202416302
C4×C47⋊#952
C2×C47×#3892
#1514147