Finite Group Databasebeta

← #26123519

Subgroups — #26123519

Order 12032.

1230 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093955C211yesmaximal, characteristic, complemented
2C22×(C2×D47)⋊C8C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×#15688980C211yesmaximal, characteristic
5C2×#15688886C211yesmaximal, characteristic, complemented
6C2×#15688885C211yesmaximal, characteristic, complemented
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×(C2×D47)⋊C4—21no—
13C22×(C2×D47)⋊C4—21no—
14C2×#13093955—22no—
15C2×#13093955—22no—
16C2×#13093955—22no—
17C2×(C2×D47)⋊C8—22no—
18C2×(C2×D47)⋊C8—22no—
19C2×(C2×D47)⋊C8C414yescomplemented
20#15688980—22no—
21#15688980—22no—
22#15688980—22no—
23#15688980—22no—
24C2×C47⋊#95—21no—
25C2×C47⋊#95—21no—
26#15688886—22no—
27#15688885—22no—
28C23×C8×C47C2211yescharacteristic
29C22×C4⋊C4×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C47×#340—22no—
32C24×D47D411yescharacteristic
33C23×Dic47—21no—
34C23×Dic47—21no—
35C23×Dic47D411yescharacteristic
36C22×C4×D47—21no—
37C22×C4×D47—21no—
38C22×C4×D47—21no—
39C22×C4×D47—21no—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—21no—
47C22×C4×D47—21no—
48C22×C4×D47C2×C412yes—
49C22×C4×D47Q812yes—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52C22×C47⋊C8—21no—
53C22×C47⋊C8—21no—
54C22×C47⋊C8C2×C412yes—
55C22×C47⋊C8D412yes—
56C22×C47⋊C8D412yes—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C4⋊Dic47—21no—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47—21no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47D412yes—
68C2×C4⋊Dic47D412yes—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—42no—
72C2×(C2×D47)⋊C4—42no—
73C2×(C2×D47)⋊C4—42no—
74C2×(C2×D47)⋊C4—42no—
75#13093955—28no—
76(C2×D47)⋊C8—28no—
77C47⋊#95—24no—
78C47⋊#95—24no—
79C23×C4×C47—21no—
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47—21no—
88C22×C8×C47C2×C412yes—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—21no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47D412yes—
100C2×C4⋊C4×C47D412yes—
101C24×C47C2×D411yescharacteristic
102C23×D47—21no—
103C23×D47—21no—
104C23×D47—21no—
105C23×D47—21no—
106C23×D47—21no—
107C23×D47—21no—
108C23×D47—21no—
109C23×D47—21no—
110C23×D47—21no—
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—21no—
114C23×D47C4⋊C412yes—
115C23×D47SD1612yes—
116C23×D47SD1612yes—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—41no—
120C22×C4×C47—41no—
121C22×C4×C47—41no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—41no—
127C22×C4×C47—41no—
128C22×C4×C47—41no—
129C22×C4×C47—41no—
130C22×C4×C47—41no—
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×Q811yescharacteristic
139C22×C4×C47#4111yescharacteristic
140C22×C4×C47#4111yescharacteristic
141C22×C4×C47#4111yescharacteristic
142C22×C4×C47#4111yescharacteristic
143C22×C4×C47#4111yescharacteristic
144C22×C4×C47#4111yescharacteristic
145C22×Dic47—21no—
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—41no—
154C22×Dic47—41no—
155C22×Dic47—41no—
156C22×Dic47—41no—
157C22×Dic47—41no—
158C22×Dic47—41no—
159C22×Dic47—41no—
160C22×Dic47—41no—
161C22×Dic47—41no—
162C22×Dic47—41no—
163C22×Dic47—41no—
164C22×Dic47—41no—
165C22×Dic47C4⋊C412yes—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—22no—
174C2×C4×D47—22no—
175C2×C4×D47—22no—
176C2×C4×D47—22no—
177C2×C4×D47—22no—
178C2×C4×D47—41no—
179C2×C4×D47—41no—
180C2×C4×D47—41no—
181C2×C4×D47—41no—
182C2×C4×D47—41no—
183C2×C4×D47—41no—
184C2×C4×D47—41no—
185C2×C4×D47—41no—
186C2×C4×D47—41no—
187C2×C4×D47—41no—
188C2×C4×D47—41no—
189C2×C4×D47—41no—
190C2×C4×D47—41no—
191C2×C4×D47—41no—
192C2×C4×D47—41no—
193C2×C4×D47—41no—
194C2×C8×C47—22no—
195C2×C8×C47—22no—
196C2×C8×C47—22no—
197C2×C8×C47—41no—
198C2×C8×C47—41no—
199C2×C8×C47—41no—
200C2×C8×C47—41no—
201C4⋊C4×C47—22no—
202C4⋊C4×C47—22no—
203C4⋊C4×C47—22no—
204C4⋊C4×C47—22no—
205C4⋊C4×C47—41no—
206C4⋊C4×C47—41no—
207C4⋊C4×C47—41no—
208C4⋊C4×C47—41no—
209(C2×D47)⋊C4—48no—
210(C2×D47)⋊C4—48no—
211C4⋊Dic47—22no—
212C4⋊Dic47—22no—
213C4⋊Dic47—22no—
214C4⋊Dic47—22no—
215C4⋊Dic47—41no—
216C4⋊Dic47—41no—
217C4⋊Dic47—41no—
218C4⋊Dic47—41no—
219C2×C47⋊C8—22no—
220C2×C47⋊C8—22no—
221C2×C47⋊C8—22no—
222C2×C47⋊C8—22no—
223C2×C47⋊C8—22no—
224C2×C47⋊C8—22no—
225C2×C47⋊C8C22⋊C414yescomplemented
226C23×C47C2×C4⋊C411yescharacteristic
227C23×C47#12011yescharacteristic
228C23×C47#12011yescharacteristic
229C23×C47#12111yescharacteristic
230C23×C47#12111yescharacteristic
231C23×C47#12311yescharacteristic
232C23×C47#12311yescharacteristic
233C23×C47C2×SD1611yescharacteristic
234C23×C47C2×SD1611yescharacteristic
235C23×C47#13511yescharacteristic
236C23×C47#13511yescharacteristic
237C23×C47AGL(1,ℤ/8)11yescharacteristic
238C23×C47AGL(1,ℤ/8)11yescharacteristic
239C23×C47#13711yescharacteristic
240C23×C47#13711yescharacteristic
241C22×D47—22no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—22no—
245C22×D47—22no—
246C22×D47—22no—
247C22×D47—22no—
248C22×D47—22no—
249C22×D47—22no—
250C22×D47—22no—
251C22×D47—22no—
252C22×D47—22no—
253C22×D47—22no—
254C22×D47—22no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—41no—
260C22×D47—41no—
261C22×D47—41no—
262C22×D47—41no—
263C22×D47—41no—
264C22×D47—41no—
265C22×D47—41no—
266C22×D47—41no—
267C22×D47—41no—
268C22×D47—41no—
269C22×D47—41no—
270C22×D47—41no—
271C22×D47—41no—
272C22×D47—41no—
273C22×D47—41no—
274C22×D47—41no—
275C22×D47#10614yescomplemented
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—42no—
282C2×C4×C47—81no—
283C2×C4×C47—81no—
284C2×C4×C47—81no—
285C2×C4×C47—81no—
286C2×C4×C47—81no—
287C2×C4×C47—81no—
288C2×C4×C47—81no—
289C2×C4×C47—81no—
290C2×C4×C47C2×C22⋊C411yescharacteristic
291C2×C4×C47#11711yescharacteristic
292C2×C4×C47C4×D411yescharacteristic
293C2×C4×C47C4×D411yescharacteristic
294C2×C4×C47C4×D411yescharacteristic
295C2×C4×C47C4×D411yescharacteristic
296C2×C4×C47#12011yescharacteristic
297C2×C4×C47#12111yescharacteristic
298C2×C4×C47#12111yescharacteristic
299C2×C4×C47#12111yescharacteristic
300C2×C4×C47#12111yescharacteristic
301C2×C4×C47#12111yescharacteristic
302C2×C4×C47#12111yescharacteristic
303C2×C4×C47C22⋊Q811yescharacteristic
304C2×C4×C47C22⋊Q811yescharacteristic
305C2×C4×C47C22⋊Q811yescharacteristic
306C2×C4×C47C22⋊Q811yescharacteristic
307C2×C4×C47C22⋊Q811yescharacteristic
308C2×C4×C47C22⋊Q811yescharacteristic
309C2×C4×C47#12311yescharacteristic
310C2×C4×C47#12311yescharacteristic
311C2×C4×C47#12311yescharacteristic
312C2×C4×C47#12411yescharacteristic
313C2×C4×C47#12411yescharacteristic
314C2×C4×C47#12411yescharacteristic
315C2×C4×C47#12611yescharacteristic
316C2×C4×C47#12611yescharacteristic
317C2×C4×C47#12711yescharacteristic
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C2×Dic47—42no—
326C2×Dic47—42no—
327C2×Dic47—42no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—81no—
332C2×Dic47—81no—
333C2×Dic47—81no—
334C2×Dic47—81no—
335C2×Dic47—81no—
336C2×Dic47—81no—
337C2×Dic47—81no—
338C2×Dic47—81no—
339C4×D47—42no—
340C4×D47—42no—
341C4×D47—42no—
342C4×D47—42no—
343C4×D47—42no—
344C4×D47—42no—
345C4×D47—42no—
346C4×D47—42no—
347C8×C47—42no—
348C47⋊C8—24no—
349#11095—471nomaximal, Sylow
350C22×C47#38011yescharacteristic
351C22×C47#38511yescharacteristic
352C22×C47#38511yescharacteristic
353C22×C47#39211yescharacteristic
354C22×C47#39411yescharacteristic
355C22×C47#39411yescharacteristic
356C22×C47#39711yescharacteristic
357C22×C47C2×#10611yescharacteristic
358C22×C47#42711yescharacteristic
359C22×C47#42811yescharacteristic
360C22×C47#42811yescharacteristic
361C22×C47#44811yescharacteristic
362C22×C47#44811yescharacteristic
363C22×C47#44911yescharacteristic
364C22×C47#44911yescharacteristic
365C22×C47#45011yescharacteristic
366C22×C47#45011yescharacteristic
367C22×C47#45211yescharacteristic
368C22×C47#45211yescharacteristic
369C22×C47#46511yescharacteristic
370C22×C47#46511yescharacteristic
371C22×C47#46511yescharacteristic
372C22×C47#46511yescharacteristic
373C22×C47#46811yescharacteristic
374C22×C47#46811yescharacteristic
375C22×C47#46911yescharacteristic
376C22×C47#47011yescharacteristic
377C22×C47#48111yescharacteristic
378C22×C47#48111yescharacteristic
379C22×C47#48211yescharacteristic
380C22×C47#48211yescharacteristic
381C22×C47#48311yescharacteristic
382C22×C47#48311yescharacteristic
383C22×C47#48511yescharacteristic
384C22×C47#48511yescharacteristic
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—42no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—42no—
395C2×D47—42no—
396C2×D47—42no—
397C2×D47—42no—
398C2×D47—42no—
399C2×D47—42no—
400C4×C47—82no—
401C4×C47—82no—
402C4×C47#38611yescharacteristic
403C4×C47#38811yescharacteristic
404C4×C47#38811yescharacteristic
405C4×C47#39011yescharacteristic
406C4×C47#39311yescharacteristic
407C4×C47#39611yescharacteristic
408C4×C47#39611yescharacteristic
409C4×C47#39911yescharacteristic
410Dic47—42no—
411Dic47—82no—
412Dic47—82no—
413C22×#106—471no—
414C22×C22⋊C8—471no—
415C2×#380—471no—
416C2×#380—471no—
417C2×#340—471no—
418C2×#340—471no—
419C2×#340D4711yescharacteristic, complemented
420C2×C47#143911yescharacteristic
421C2×C47#180711yescharacteristic
422C2×C47#180911yescharacteristic
423C2×C47#185311yescharacteristic
424C2×C47#185311yescharacteristic
425C2×C47#185411yescharacteristic
426C2×C47#185411yescharacteristic
427C2×C47#200011yescharacteristic
428C2×C47#200011yescharacteristic
429C2×C47#203411yescharacteristic
430C2×C47#203411yescharacteristic
431C2×C47#203511yescharacteristic
432C2×C47#203511yescharacteristic
433C2×C47#207711yescharacteristic
434C2×C47#207711yescharacteristic
435D47—44no—
436C24×C4—471no—
437C23×C8—471no—
438C23×C8C2×D4711yescharacteristic
439C22×C4⋊C4—471no—
440C22×C4⋊C4—471no—
441C22×C4⋊C4C2×D4711yescharacteristic
442C22×C4⋊C4C2×D4711yescharacteristic
443C22×C22⋊C4—941no—
444C22×C22⋊C4—941no—
445C2×#106—942no—
446C2×#106—942no—
447C2×#106—942no—
448C2×C22⋊C8—474no—
449C2×C22⋊C8—942no—
450C2×C22⋊C8—942no—
451#380—942no—
452#380—942no—
453#380—942no—
454#380—942no—
455C2×#95—941no—
456C2×#95—941no—
457#340—22no—
458#340—942no—
459#340—942no—
460C47#1109511yescharacteristic, complemented, Sylow
461C25—471no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—471no—
465C23×C4—472no—
466C23×C4—472no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4—941no—
470C23×C4—941no—
471C23×C4—941no—
472C23×C4—941no—
473C23×C4—941no—
474C23×C4—941no—
475C23×C4—941no—
476C23×C4—941no—
477C23×C4—941no—
478C23×C4—941no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—21no—
487C22×C8—21no—
488C22×C8—472no—
489C22×C8—472no—
490C22×C8—472no—
491C22×C8—941no—
492C22×C8—941no—
493C22×C8—941no—
494C22×C8—941no—
495C22×C8C4×D4712yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—472no—
507C2×C4⋊C4—472no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C4⋊C4—941no—
516C2×C4⋊C4—941no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4D18812yes—
519C2×C4⋊C4C22⋊D4712yes—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—1882no—
523C2×C22⋊C4—1882no—
524C2×C22⋊C4—1882no—
525C2×C22⋊C4—1882no—
526#106—948no—
527C22⋊C8—948no—
528#95—944no—
529#95—944no—
530C24—472no—
531C24—472no—
532C24—472no—
533C24—941no—
534C24—941no—
535C24—941no—
536C24—941no—
537C24—941no—
538C24—941no—
539C24—941no—
540C24—941no—
541C24—941no—
542C24—941no—
543C24—941no—
544C24—941no—
545C24D4×D4711yescharacteristic
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—472no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—942no—
574C22×C4—942no—
575C22×C4—942no—
576C22×C4—942no—
577C22×C4—942no—
578C22×C4—942no—
579C22×C4—942no—
580C22×C4—942no—
581C22×C4—1881no—
582C22×C4—1881no—
583C22×C4—1881no—
584C22×C4—1881no—
585C22×C4—1881no—
586C22×C4—1881no—
587C22×C4—1881no—
588C22×C4—1881no—
589C22×C4—1881no—
590C22×C4—1881no—
591C22×C4—1881no—
592C22×C4—1881no—
593C22×C4—1881no—
594C22×C4—1881no—
595C22×C4—1881no—
596C22×C4—1881no—
597C22×C4—1881no—
598C22×C4—1881no—
599C22×C4—1881no—
600C22×C4—1881no—
601C22×C4—1881no—
602C22×C4—1881no—
603C22×C4—1881no—
604C22×C4—1881no—
605C22×C4—1881no—
606C22×C4—1881no—
607C22×C4—1881no—
608C22×C4—1881no—
609C22×C4C2×C4×D4711yescharacteristic
610C22×C4C2×D18811yescharacteristic
611C22×C4#1062535011yescharacteristic
612C22×C4#1062535011yescharacteristic
613C22×C4#1062535011yescharacteristic
614C22×C4#1062535011yescharacteristic
615C22×C4D4×D4711yescharacteristic
616C22×C4D4×D4711yescharacteristic
617C22×C4D4×D4711yescharacteristic
618C22×C4D4×D4711yescharacteristic
619C22×C4#1062535211yescharacteristic
620C22×C4Q8×D4711yescharacteristic
621C22×C4#1062535411yescharacteristic
622C22×C4C2×C22⋊D4711yescharacteristic
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—474no—
631C2×C8—942no—
632C2×C8—942no—
633C2×C8—942no—
634C2×C8—942no—
635C2×C8—942no—
636C2×C8—942no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C4⋊C4—942no—
646C4⋊C4—942no—
647C4⋊C4—942no—
648C4⋊C4—942no—
649C4⋊C4—1881no—
650C4⋊C4—1881no—
651C4⋊C4—1881no—
652C4⋊C4—1881no—
653C22⋊C4—1888no—
654C22⋊C4—1888no—
655C23—474no—
656C23—942no—
657C23—942no—
658C23—942no—
659C23—942no—
660C23—942no—
661C23—942no—
662C23—942no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—1881no—
675C23—1881no—
676C23—1881no—
677C23—1881no—
678C23—1881no—
679C23—1881no—
680C23—1881no—
681C23—1881no—
682C23—1881no—
683C23—1881no—
684C23—1881no—
685C23—1881no—
686C23—1881no—
687C23—1881no—
688C23—1881no—
689C23—1881no—
690C23C4⋊C4×D4711yescharacteristic
691C23#1309399211yescharacteristic
692C23#1309399411yescharacteristic
693C23#1309399711yescharacteristic
694C23#1309399711yescharacteristic
695C23#1309400611yescharacteristic
696C23#1309400911yescharacteristic
697C23SD16×D4711yescharacteristic
698C23SD16×D4711yescharacteristic
699C23#1309404311yescharacteristic
700C23#1309404711yescharacteristic
701C23#1309404811yescharacteristic
702C23#1309405111yescharacteristic
703C23#1309405311yescharacteristic
704C23#1309405611yescharacteristic
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—3761no—
723C2×C4—3761no—
724C2×C4—3761no—
725C2×C4—3761no—
726C2×C4—3761no—
727C2×C4—3761no—
728C2×C4—3761no—
729C2×C4—3761no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1881no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1881no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4—1882no—
745C2×C4—1882no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4C22⋊C4×D4711yescharacteristic
749C2×C4#1309398111yescharacteristic
750C2×C4(C22⋊D47)⋊C411yescharacteristic
751C2×C4C4×C22⋊D4711yescharacteristic
752C2×C4#1309398611yescharacteristic
753C2×C4C4×D18811yescharacteristic
754C2×C4#1309399411yescharacteristic
755C2×C4#1309399611yescharacteristic
756C2×C4#1309399711yescharacteristic
757C2×C4#1309399711yescharacteristic
758C2×C4#1309399711yescharacteristic
759C2×C4#1309399811yescharacteristic
760C2×C4#1309399911yescharacteristic
761C2×C4#1309400011yescharacteristic
762C2×C4#1309400211yescharacteristic
763C2×C4#1309400211yescharacteristic
764C2×C4#1309400211yescharacteristic
765C2×C4#1309400211yescharacteristic
766C2×C4#1309400411yescharacteristic
767C2×C4#1309400711yescharacteristic
768C2×C4#1309400911yescharacteristic
769C2×C4#1309400911yescharacteristic
770C2×C4#1309401011yescharacteristic
771C2×C4#1309401011yescharacteristic
772C2×C4#1309401211yescharacteristic
773C2×C4#1309401811yescharacteristic
774C2×C4#1309401911yescharacteristic
775C2×C4#1309402011yescharacteristic
776C8—42no—
777C8—944no—
778C22—944no—
779C22—944no—
780C22—944no—
781C22—1882no—
782C22—1882no—
783C22—1882no—
784C22—1882no—
785C22—1882no—
786C22—1882no—
787C22—1882no—
788C22—1882no—
789C22—1882no—
790C22—1882no—
791C22—1882no—
792C22—1882no—
793C22#1568898211yescharacteristic
794C22#1568899411yescharacteristic
795C22#1568899711yescharacteristic
796C22#1568903211yescharacteristic
797C22#1568903811yescharacteristic
798C22#1568904111yescharacteristic
799C22#1568905211yescharacteristic
800C22#106×D4711yescharacteristic
801C22#1568916011yescharacteristic
802C22#1568916211yescharacteristic
803C22#1568916411yescharacteristic
804C22#1568926011yescharacteristic
805C22#1568926311yescharacteristic
806C22#1568926511yescharacteristic
807C22#1568927111yescharacteristic
808C22#1568927211yescharacteristic
809C22#1568927511yescharacteristic
810C22#1568928411yescharacteristic
811C22#1568928611yescharacteristic
812C22#1568935111yescharacteristic
813C22#1568935111yescharacteristic
814C22#1568935511yescharacteristic
815C22#1568935511yescharacteristic
816C22#1568936811yescharacteristic
817C22#1568937211yescharacteristic
818C22#1568937511yescharacteristic
819C22#1568938011yescharacteristic
820C22#1568944011yescharacteristic
821C22#1568944311yescharacteristic
822C22#1568944511yescharacteristic
823C22#1568945011yescharacteristic
824C22#1568945211yescharacteristic
825C22#1568945511yescharacteristic
826C22#1568946311yescharacteristic
827C22#1568946611yescharacteristic
828C4—82no—
829C4—82no—
830C4—3762no—
831C4—3762no—
832C4—1882no—
833C4#1568900111yescharacteristic
834C4#1568901211yescharacteristic
835C4#1568901411yescharacteristic
836C4#1568902311yescharacteristic
837C4#1568903611yescharacteristic
838C4#1568904511yescharacteristic
839C4#1568904711yescharacteristic
840C4#1568905811yescharacteristic
841C2—1884no—
842C2#2024163211yescharacteristic
843C2#2024341211yescharacteristic
844C2#2024342011yescharacteristic
845C2#2024357911yescharacteristic
846C2#2024358211yescharacteristic
847C2#2024358411yescharacteristic
848C2#2024359011yescharacteristic
849C2#2024439011yescharacteristic
850C2#2024439211yescharacteristic
851C2#2024457511yescharacteristic
852C2#2024458011yescharacteristic
853C2#2024458211yescharacteristic
854C2#2024458711yescharacteristic
855C2#2024482611yescharacteristic
856C2#2024482711yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socleC24×C47C2×D4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#11095
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C22×#13093955C2semidirect
5. C2×#15688886C2semidirect
6. C2×#15688885C2semidirect
7. C2×C47×#340C2semidirect
19. C2×(C2×D47)⋊C8C4semidirect
225. C2×C47⋊C8C22⋊C4semidirect
275. C22×D47#106semidirect
419. C2×#340D47semidirect
460. C47#11095semidirect

Maximal subgroups

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

subgroupindex
C22×#130939552
C22×(C2×D47)⋊C82
C2×#156889802
C2×#156888862
C2×#156888852
C2×C47×#3402
#1109547