Finite Group Databasebeta

← #26147523

Subgroups — #26147523

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D47C211yesmaximal, characteristic
2C2×#15689022C211yesmaximal, characteristic, complemented
3C2×#15689021C211yesmaximal, characteristic, complemented
4C2×#15688997C212yesmaximal
5C2×#15688980C211yesmaximal, characteristic
6C2×#15688980C211yesmaximal, characteristic
7#20241623C212yesmaximal, complemented
8#20241622C212yesmaximal, complemented
9#20241617C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal
11C47×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C23×C4×D47C2211yescharacteristic
15C22×C4⋊Dic47C2212yes—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C2×C42×D47—24no—
25C2×C42×D47—24no—
26C2×C42×D47—24no—
27#15689022—24no—
28#15689021—24no—
29#15688997—28no—
30#15688980—24no—
31#15688980C418yescomplemented
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C22×C4⋊C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C2×#95×C47C2212yes—
43C24×D47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C22×C4×D47—22no—
50C22×C4×D47—22no—
51C22×C4×D47—22no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—22no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47—22no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47—22no—
65C22×C4×D47C2×C414yes—
66C22×C4×D47D414yes—
67C22×C4×D47D414yes—
68C22×C4×D47Q814yes—
69C22×C4×D47Q814yes—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47—22no—
72C2×C4⋊Dic47—22no—
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—24no—
76C2×C4⋊Dic47—24no—
77C2×C4⋊Dic47—24no—
78C2×C4⋊Dic47C2×C414yescomplemented
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—24no—
81C2×Dic47⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4C2×C418yes—
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×Dic47D414yes—
97C42×D47—232no—
98C47⋊#95—24no—
99C47⋊#95—24no—
100C47⋊#95—24no—
101C47⋊#95—24no—
102C47⋊#95—24no—
103C47⋊#95C2×C418yescomplemented
104C23×C4×C47C2312yes—
105C23×C4×C47C2312yes—
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C23×C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47—22no—
110C2×C4⋊C4×C47—22no—
111C2×C4⋊C4×C47—22no—
112C2×C4⋊C4×C47—22no—
113C2×C4⋊C4×C47—22no—
114C2×C4⋊C4×C47C2×C414yescomplemented
115C2×C42×C47—22no—
116C2×C42×C47—22no—
117C2×C42×C47D414yes—
118#95×C47—24no—
119#95×C47—24no—
120C24×C47C2411yescharacteristic
121C23×D47—21no—
122C23×D47—21no—
123C23×D47—21no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47—21no—
129C23×D47C22×C412yes—
130C23×D47C2×D412yes—
131C23×D47C2×D412yes—
132C23×D47C2×Q812yes—
133C23×D47C2×Q812yes—
134C23×D47#4112yes—
135C23×D47#4112yes—
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—22no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47C22×C414yes—
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D412yes—
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2×D412yes—
164C22×C4×C47C2×D412yes—
165C22×C4×C47C2×Q812yes—
166C22×C4×C47C2×Q812yes—
167C22×C4×C47#4112yes—
168C22×C4×C47#4112yes—
169C22×C4×C47#4112yes—
170C22×C4×C47#4112yes—
171C22×Dic47—21no—
172C22×Dic47—21no—
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—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47C22×C414yes—
197C22×Dic47C22×C412yes—
198C22×Dic47C2×D412yes—
199C22×Dic47C2×D412yes—
200C22×Dic47C2×D412yes—
201C22×Dic47C2×D412yes—
202C22×Dic47C2×Q812yes—
203C22×Dic47C2×Q812yes—
204C22×Dic47#4112yes—
205C22×Dic47#4112yes—
206C2×C4×D47—28no—
207C2×C4×D47—28no—
208C2×C4×D47—28no—
209C2×C4×D47—28no—
210C2×C4×D47—28no—
211C2×C4×D47—28no—
212C2×C4×D47—28no—
213C2×C4×D47—28no—
214C2×C4×D47—28no—
215C2×C4×D47—28no—
216C2×C4×D47—28no—
217C2×C4×D47—28no—
218C2×C4×D47—28no—
219C2×C4×D47—28no—
220C2×C4×D47—28no—
221C2×C4×D47—28no—
222C2×C4×D47—28no—
223C2×C4×D47—28no—
224C2×C4×D47—28no—
225C2×C4×D47—28no—
226C2×C4×D47C4⋊C4116yescomplemented
227C4⋊C4×C47—28no—
228C4⋊C4×C47—44no—
229C42×C47—28no—
230(C2×D47)⋊C4—216no—
231(C2×D47)⋊C4—48no—
232C4⋊Dic47—28no—
233C4⋊Dic47—44no—
234C4⋊Dic47—48no—
235Dic47⋊C4—48no—
236C4×Dic47—28no—
237C4×Dic47—28no—
238C4×Dic47—28no—
239C23×C47C23×C411yescharacteristic
240C23×C47C22×D411yescharacteristic
241C23×C47C22×D411yescharacteristic
242C23×C47C22×D411yescharacteristic
243C23×C47C22×D411yescharacteristic
244C23×C47C22×Q811yescharacteristic
245C23×C47C22×Q811yescharacteristic
246C23×C47C2×#4111yescharacteristic
247C23×C47C2×#4111yescharacteristic
248C23×C47C2×#4111yescharacteristic
249C23×C47C2×#4111yescharacteristic
250C23×C47C2×#4111yescharacteristic
251C23×C47C2×#4111yescharacteristic
252C23×C47C2×#4111yescharacteristic
253C23×C47C2×#4111yescharacteristic
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—22no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—22no—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47—22no—
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47C2×C4⋊C414yes—
283C22×D47C4×D414yes—
284C22×D47C4×Q814yes—
285C22×D47#12114yes—
286C22×D47C22⋊Q814yes—
287C22×D47#12514yes—
288C22×D47C4⋊Q814yes—
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—22no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47C2×C4⋊C414yes—
316C2×C4×C47C4×D414yes—
317C2×C4×C47C4×D414yes—
318C2×C4×C47#12014yes—
319C2×C4×C47#12114yes—
320C2×C4×C47C22⋊Q814yes—
321C2×C4×C47C22⋊Q814yes—
322C2×C4×C47C22⋊Q814yes—
323C2×C4×C47#12314yes—
324C2×Dic47—22no—
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—24no—
343C2×Dic47—24no—
344C2×Dic47—24no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355C2×Dic47—42no—
356C2×Dic47C2×C4⋊C414yes—
357C2×Dic47#12114yes—
358C2×Dic47C22⋊Q814yes—
359C4×D47—232no—
360C4×D47—232no—
361C4×D47—232no—
362#14697—471nomaximal, Sylow
363C22×C47C22×C4⋊C411yescharacteristic
364C22×C47C2×C4×D411yescharacteristic
365C22×C47C2×C4×D411yescharacteristic
366C22×C47C2×C4×D411yescharacteristic
367C22×C47C2×C4×Q811yescharacteristic
368C22×C47C4×#4111yescharacteristic
369C22×C47C4×#4111yescharacteristic
370C22×C47C2×#12011yescharacteristic
371C22×C47C2×#12111yescharacteristic
372C22×C47C2×#12111yescharacteristic
373C22×C47C2×#12111yescharacteristic
374C22×C47C2×C22⋊Q811yescharacteristic
375C22×C47C2×C22⋊Q811yescharacteristic
376C22×C47C2×C22⋊Q811yescharacteristic
377C22×C47C2×C22⋊Q811yescharacteristic
378C22×C47C2×C22⋊Q811yescharacteristic
379C22×C47C2×#12311yescharacteristic
380C22×C47#52511yescharacteristic
381C22×C47#52511yescharacteristic
382C22×C47#52511yescharacteristic
383C22×C47#52511yescharacteristic
384C22×C47#52511yescharacteristic
385C22×C47#52511yescharacteristic
386C22×C47C2×#12511yescharacteristic
387C22×C47#52911yescharacteristic
388C22×C47#52911yescharacteristic
389C22×C47#52911yescharacteristic
390C22×C47#52911yescharacteristic
391C22×C47C2×C4⋊Q811yescharacteristic
392C22×C47#53211yescharacteristic
393C22×C47#53211yescharacteristic
394C22×C47#53311yescharacteristic
395C22×C47#53311yescharacteristic
396C22×C47#53311yescharacteristic
397C22×C47#53311yescharacteristic
398C2×D47—24no—
399C2×D47—24no—
400C2×D47—24no—
401C2×D47—24no—
402C2×D47—24no—
403C2×D47—24no—
404C2×D47—24no—
405C2×D47—24no—
406C2×D47—24no—
407C2×D47—24no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47#38918yescomplemented
413C4×C47—24no—
414C4×C47—24no—
415C4×C47—44no—
416C4×C47—82no—
417C4×C47#38518yescomplemented
418Dic47—24no—
419Dic47—24no—
420Dic47—24no—
421Dic47—44no—
422Dic47—82no—
423C23×C42—471no—
424C2×#389—471no—
425C2×#389—471no—
426C2×#385—472no—
427C2×#380—471no—
428C2×#380—471no—
429#1436—472no—
430#1436—472no—
431C4⋊#95—471no—
432C4⋊#95D4711yescharacteristic, complemented
433C22⋊#95—472no—
434C2×C47C2×#38511yescharacteristic
435C2×C47C2×#38911yescharacteristic
436C2×C47#229611yescharacteristic
437C2×C47C4×#12111yescharacteristic
438C2×C47C4×#12111yescharacteristic
439C2×C47C4×C22⋊Q811yescharacteristic
440C2×C47C4×C22⋊Q811yescharacteristic
441C2×C47#284711yescharacteristic
442C2×C47#284811yescharacteristic
443C2×C47#285111yescharacteristic
444C2×C47#285111yescharacteristic
445C2×C47#285411yescharacteristic
446C2×C47#285511yescharacteristic
447C2×C47#285711yescharacteristic
448C2×C47#285711yescharacteristic
449D47—28no—
450C24×C4—471no—
451C24×C4—471no—
452C24×C4—471no—
453C22×C4⋊C4—471no—
454C22×C4⋊C4—472no—
455C22×C4⋊C4—472no—
456C22×C4⋊C4—471no—
457C22×C4⋊C4C2×D4711yescharacteristic
458C22×C4⋊C4C2×D4711yescharacteristic
459C22×C22⋊C4—472no—
460C22×C22⋊C4—472no—
461C22×C42—471no—
462C22×C42—471no—
463C22×C42—471no—
464C22×C42—944no—
465C22×C42—944no—
466C22×C42—944no—
467C22×C42C2×D4711yescharacteristic
468#389—944no—
469#389—944no—
470#385—948no—
471#380—478no—
472#380—944no—
473C2×#95—472no—
474C2×#95—472no—
475C2×#95—472no—
476C2×#95—472no—
477C2×#95—472no—
478C2×#95—472no—
479C2×#95C2×D4712yes—
480C2×#95C2×D4712yes—
481C47#1469711yescharacteristic, complemented, Sylow
482C25—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—474no—
487C23×C4—474no—
488C23×C4—474no—
489C23×C4—472no—
490C23×C4—474no—
491C23×C4—474no—
492C23×C4—472no—
493C23×C4—942no—
494C23×C4—942no—
495C23×C4—942no—
496C23×C4—942no—
497C23×C4—942no—
498C23×C4—942no—
499C23×C4—942no—
500C23×C4—942no—
501C23×C4—942no—
502C23×C4—942no—
503C23×C4—942no—
504C23×C4—942no—
505C23×C4—942no—
506C23×C4—942no—
507C23×C4—942no—
508C23×C4—942no—
509C23×C4C22×D4712yes—
510C23×C4C22×D4712yes—
511C23×C4C22×D4711yescharacteristic
512C23×C4C22×D4711yescharacteristic
513C23×C4C22×D4711yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—474no—
520C2×C4⋊C4—942no—
521C2×C4⋊C4—942no—
522C2×C4⋊C4—944no—
523C2×C4⋊C4—944no—
524C2×C4⋊C4—944no—
525C2×C4⋊C4—944no—
526C2×C4⋊C4—942no—
527C2×C4⋊C4—944no—
528C2×C4⋊C4—942no—
529C2×C4⋊C4—942no—
530C2×C4⋊C4—944no—
531C2×C4⋊C4C4×D4714yescomplemented
532C2×C22⋊C4—478no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—944no—
536C2×C22⋊C4—944no—
537C2×C22⋊C4—944no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—474no—
541C2×C42—9432no—
542C2×C42—942no—
543C2×C42—942no—
544C2×C42—942no—
545C2×C42—942no—
546C2×C42—942no—
547C2×C42—942no—
548C2×C42—942no—
549C2×C42—942no—
550C2×C42D18814yes—
551#95—24no—
552#95—24no—
553#95—478no—
554#95—944no—
555#95—944no—
556#95—944no—
557#95—944no—
558#95—944no—
559C24—472no—
560C24—472no—
561C24—472no—
562C24—472no—
563C24—472no—
564C24—472no—
565C24—472no—
566C24—941no—
567C24—941no—
568C24—941no—
569C24—941no—
570C24—941no—
571C24—941no—
572C24—941no—
573C24—941no—
574C24C23×D4711yescharacteristic
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—472no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—472no—
604C22×C4—472no—
605C22×C4—4716no—
606C22×C4—474no—
607C22×C4—948no—
608C22×C4—948no—
609C22×C4—948no—
610C22×C4—948no—
611C22×C4—948no—
612C22×C4—948no—
613C22×C4—948no—
614C22×C4—948no—
615C22×C4—948no—
616C22×C4—948no—
617C22×C4—948no—
618C22×C4—948no—
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—948no—
632C22×C4—948no—
633C22×C4—948no—
634C22×C4—948no—
635C22×C4—948no—
636C22×C4—948no—
637C22×C4—948no—
638C22×C4—948no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—942no—
647C22×C4—942no—
648C22×C4—942no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4C2×C4×D4714yes—
653C22×C4C2×C4×D4712yes—
654C22×C4C2×D18812yes—
655C22×C4C2×D18812yes—
656C22×C4C2×D18812yes—
657C22×C4#1062535012yes—
658C22×C4D4×D4712yes—
659C22×C4D4×D4712yes—
660C22×C4D4×D4712yes—
661C22×C4#1062535212yes—
662C22×C4#1062535212yes—
663C22×C4Q8×D4712yes—
664C22×C4Q8×D4712yes—
665C22×C4#1062535412yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—948no—
669C4⋊C4—1888no—
670C4⋊C4—1884no—
671C4⋊C4—1888no—
672C22⋊C4—9416no—
673C22⋊C4—1888no—
674C42—28no—
675C42—948no—
676C42—948no—
677C42—948no—
678C23—474no—
679C23—474no—
680C23—474no—
681C23—474no—
682C23—474no—
683C23—474no—
684C23—474no—
685C23—942no—
686C23—942no—
687C23—942no—
688C23—942no—
689C23—942no—
690C23—942no—
691C23—942no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23—942no—
709C23—942no—
710C23—942no—
711C23—942no—
712C23—942no—
713C23C22×C4×D4711yescharacteristic
714C23C2×D4×D4711yescharacteristic
715C23C2×D4×D4711yescharacteristic
716C23C2×D4×D4711yescharacteristic
717C23C22×D18811yescharacteristic
718C23C2×Q8×D4711yescharacteristic
719C23C2×Q8×D4711yescharacteristic
720C23#41×D4711yescharacteristic
721C23#41×D4711yescharacteristic
722C23#41×D4711yescharacteristic
723C23#41×D4711yescharacteristic
724C23C2×#1062535211yescharacteristic
725C23C2×#1062535211yescharacteristic
726C23C2×#1062535011yescharacteristic
727C23C2×#1062535411yescharacteristic
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—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—474no—
755C2×C4—474no—
756C2×C4—474no—
757C2×C4—9432no—
758C2×C4—9432no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—942no—
769C2×C4—942no—
770C2×C4—942no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—942no—
775C2×C4—942no—
776C2×C4—942no—
777C2×C4—9432no—
778C2×C4—944no—
779C2×C4—944no—
780C2×C4—944no—
781C2×C4—1882no—
782C2×C4—1882no—
783C2×C4—1882no—
784C2×C4—1882no—
785C2×C4—1882no—
786C2×C4—1882no—
787C2×C4—1882no—
788C2×C4—1882no—
789C2×C4—1882no—
790C2×C4—1882no—
791C2×C4—1882no—
792C2×C4C4⋊C4×D4714yes—
793C2×C4(C22⋊D47)⋊C414yes—
794C2×C4C4×D18814yes—
795C2×C4#1309399414yes—
796C2×C4#1309399914yes—
797C2×C4#1309400214yes—
798C2×C4#1309400414yes—
799C2×C4#1309400414yes—
800C2×C4#1309400614yes—
801C22—478no—
802C22—944no—
803C22—944no—
804C22—944no—
805C22—944no—
806C22—944no—
807C22—944no—
808C22—944no—
809C22—944no—
810C22—944no—
811C22—944no—
812C22—944no—
813C22—944no—
814C22—944no—
815C22—944no—
816C22C2×C4⋊C4×D4711yescharacteristic
817C22C4×D4×D4711yescharacteristic
818C22C2×(C22⋊D47)⋊C411yescharacteristic
819C22C2×C4×D18811yescharacteristic
820C22C4×Q8×D4711yescharacteristic
821C22C4×#1062535211yescharacteristic
822C22C4×#1062535411yescharacteristic
823C22C2×#1309399411yescharacteristic
824C22#121×D4711yescharacteristic
825C22#121×D4711yescharacteristic
826C22C2×#1309399911yescharacteristic
827C22C22⋊Q8×D4711yescharacteristic
828C22C22⋊Q8×D4711yescharacteristic
829C22C2×#1309400211yescharacteristic
830C22C2×#1309400411yescharacteristic
831C22C2×#1309400411yescharacteristic
832C22C2×#1309400611yescharacteristic
833C22#1568963311yescharacteristic
834C22#1568963311yescharacteristic
835C22#1568963511yescharacteristic
836C22#1568963511yescharacteristic
837C22#1568963611yescharacteristic
838C22#1568963611yescharacteristic
839C22#125×D4711yescharacteristic
840C22#1568965211yescharacteristic
841C22#1568965211yescharacteristic
842C22#1568965511yescharacteristic
843C22#1568966011yescharacteristic
844C22C4⋊Q8×D4711yescharacteristic
845C22#1568967011yescharacteristic
846C22#1568967111yescharacteristic
847C22#1568967711yescharacteristic
848C22#1568967811yescharacteristic
849C22#1568967811yescharacteristic
850C22#1568967911yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—944no—
856C4—944no—
857C4—944no—
858C4—3762no—
859C4—1884no—
860C4#1568899718yescomplemented
861C2—948no—
862C2C2×#1568899711yescharacteristic
863C2#389×D4711yescharacteristic
864C2#2024586911yescharacteristic
865C2C4×#1309399911yescharacteristic
866C2#2024590411yescharacteristic
867C2C4×#1309400411yescharacteristic
868C2#2024592611yescharacteristic
869C2#2025167111yescharacteristic
870C2#2025167611yescharacteristic
871C2#2025169711yescharacteristic
872C2#2025169911yescharacteristic
873C2#2025171811yescharacteristic
874C2#2025172911yescharacteristic
875C2#2025173911yescharacteristic
876C2#2025174111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C4⋊#95C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4⋊#95D47
hypocenterC47#14697
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#15689022C2semidirect
3. C2×#15689021C2semidirect
7. #20241623C2semidirect
8. #20241622C2semidirect
9. #20241617C2semidirect
11. C47×C4⋊#95C2semidirect
31. #15688980C4semidirect
78. C2×C4⋊Dic47C2×C4semidirect
103. C47⋊#95C2×C4semidirect
114. C2×C4⋊C4×C47C2×C4semidirect
226. C2×C4×D47C4⋊C4semidirect
412. C2×D47#389semidirect
417. C4×C47#385semidirect
432. C4⋊#95D47semidirect
481. C47#14697semidirect
531. C2×C4⋊C4C4×D47semidirect
860. C4#15688997semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D472
C2×#156890222
C2×#156890212
C2×#156889972
C2×#156889802
#202416232
#202416222
#202416172
(C2×D47)⋊#952
C47×C4⋊#952
#1469747