Finite Group Databasebeta

← #26121582

Subgroups — #26121582

Order 12032.

1334 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3#20245767C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5C2×#15688894C211yesmaximal, characteristic, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7C2×C47×#344C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625324—21no—
12C2×M16×D47—22no—
13C2×M16×D47—22no—
14C2×M16×D47—22no—
15C2×M16×D47—22no—
16C2×M16×D47—22no—
17C2×M16×D47C414yescomplemented
18C22×C8×D47—21no—
19C2×#13093983C2211yescharacteristic
20#15689086—21no—
21#15689086—21no—
22#15689086—22no—
23C2×(C2×D47)⋊C8C414yescomplemented
24#15688984C412yes—
25#15688980—22no—
26#15688978C412yes—
27C4×(C2×D47)⋊C4—22no—
28#15688895—22no—
29#15688894—22no—
30#15688893—22no—
31C22×M16×C47C2211yescharacteristic
32C22×M16×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C47×#344—22no—
35C24×D47C2×C411yescharacteristic
36C23×Dic47C2×C411yescharacteristic
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×D47C2×C412yes—
46C22×C4×D47C2×C412yes—
47C22×C4×D47D411yescharacteristic
48C22×C4×D47D411yescharacteristic
49C22×C4×D47D412yes—
50C22×C4×D47D412yes—
51C22×C4×D47Q811yescharacteristic
52C22×C4×D47Q811yescharacteristic
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329C2×C412yes—
63C2×#10625329D412yes—
64C2×#10625329D412yes—
65C2×#10625324—24no—
66C2×#10625324—24no—
67C2×#10625324—24no—
68M16×D47—28no—
69M16×D47—28no—
70M16×D47—28no—
71M16×D47—28no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8C2×C412yes—
74C2×C8×D47—24no—
75C2×C8×D47—24no—
76C2×C8×D47—24no—
77#13093983—21no—
78#13093983—21no—
79#13093983—21no—
80#13093983—21no—
81C2×C4⋊Dic47—21no—
82C2×C22⋊Dic47C2×C412yes—
83C2×(C2×D47)⋊C4—24no—
84C2×C4×Dic47—21no—
85(C2×D47)⋊C8—24no—
86(C2×D47)⋊C8—24no—
87C47⋊#95—24no—
88C23×C4×C47C2311yescharacteristic
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47—21no—
98C2×M16×C47C2×C412yes—
99C2×M16×C47D412yes—
100C2×M16×C47D412yes—
101C22×C8×C47—21no—
102C22×C8×C47C2×C412yes—
103#117×C47—21no—
104#117×C47—21no—
105#117×C47—21no—
106#117×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C22⋊C4×C47C2×C412yes—
109C2×C42×C47—21no—
110C24×C47C22×C411yescharacteristic
111C23×D47—21no—
112C23×D47—21no—
113C23×D47—21no—
114C23×D47—21no—
115C23×D47—44no—
116C23×D47C4212yes—
117C23×D47C22⋊C412yes—
118C23×D47C4⋊C411yescharacteristic
119C23×D47C4⋊C411yescharacteristic
120C22×C4×C47—22no—
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×Q811yescharacteristic
131C22×C4×C47#4111yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47C4212yes—
141C22×Dic47C22⋊C412yes—
142C22×Dic47C4⋊C411yescharacteristic
143C22×Dic47C4⋊C411yescharacteristic
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—21no—
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×C4×D47—21no—
166C2×C4×D47—21no—
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47C22⋊C412yes—
177C2×C4×D47C22⋊C412yes—
178C2×C4×D47C22⋊C412yes—
179C2×C4×D47C22⋊C412yes—
180C2×C4×D47C4⋊C412yes—
181C2×C4×D47C4⋊C412yes—
182C2×C4×D47C4⋊C412yes—
183C2×C4×D47C4⋊C412yes—
184M16×C47—22no—
185M16×C47—22no—
186M16×C47—22no—
187M16×C47—41no—
188M16×C47—41no—
189M16×C47—41no—
190M16×C47—41no—
191M16×C47C22⋊C414yescomplemented
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C2×C8×C47—22no—
195C2×C8×C47—22no—
196C2×C8×C47—22no—
197C2×C8×C47—22no—
198C4⋊C4×C47—41no—
199C4⋊C4×C47—41no—
200C22⋊C4×C47—22no—
201C22⋊C4×C47—22no—
202C42×C47—41no—
203C42×C47—41no—
204C22⋊Dic47—22no—
205C22⋊Dic47—22no—
206(C2×D47)⋊C4—48no—
207C4⋊Dic47—41no—
208C4⋊Dic47—41no—
209C4×Dic47—41no—
210C4×Dic47—41no—
211#10625329—22no—
212#10625329—22no—
213#10625329—22no—
214#10625329—41no—
215#10625329—41no—
216#10625329—41no—
217#10625329—41no—
218#10625329C22⋊C414yescomplemented
219C2×C47⋊C8—22no—
220C2×C47⋊C8—22no—
221C2×C47⋊C8—22no—
222C2×C47⋊C8—22no—
223C2×C47⋊C8—22no—
224C2×C47⋊C8—22no—
225#10625324—216no—
226C8×D47—216no—
227C23×C47—42no—
228C23×C47C2×C4211yescharacteristic
229C23×C47C2×C22⋊C411yescharacteristic
230C23×C47C2×C4⋊C411yescharacteristic
231C23×C47C4×D411yescharacteristic
232C23×C47C4×D411yescharacteristic
233C23×C47C4×D411yescharacteristic
234C23×C47C4×D411yescharacteristic
235C22×D47—21no—
236C22×D47—21no—
237C22×D47—24no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47—21no—
241C22×D47—21no—
242C22×D47—22no—
243C22×D47—22no—
244C22×D47—24no—
245C22×D47—24no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47—42no—
249C22×D47—44no—
250C22×D47—44no—
251C22×D47—44no—
252C22×D47—44no—
253C22×D47#9512yes—
254C22×D47#9512yes—
255C2×C4×C47—44no—
256C2×C4×C47—42no—
257C2×C4×C47C2×C22⋊C411yescharacteristic
258C2×C4×C47C2×C22⋊C411yescharacteristic
259C2×C4×C47C2×C22⋊C411yescharacteristic
260C2×C4×C47C2×C22⋊C411yescharacteristic
261C2×C4×C47C2×C4⋊C411yescharacteristic
262C2×C4×C47C2×C4⋊C411yescharacteristic
263C2×C4×C47#11711yescharacteristic
264C2×C4×C47#11711yescharacteristic
265C2×C4×C47C4×D411yescharacteristic
266C2×C4×C47C4×D411yescharacteristic
267C2×C4×C47C4×D411yescharacteristic
268C2×C4×C47C4×D411yescharacteristic
269C2×C4×C47#12011yescharacteristic
270C2×C4×C47#12011yescharacteristic
271C2×C4×C47#12011yescharacteristic
272C2×C4×C47#12011yescharacteristic
273C2×C4×C47#12111yescharacteristic
274C2×C4×C47#12111yescharacteristic
275C2×C4×C47#12111yescharacteristic
276C2×C4×C47#12111yescharacteristic
277C2×C4×C47C22⋊Q811yescharacteristic
278C2×C4×C47C22⋊Q811yescharacteristic
279C2×C4×C47C22⋊Q811yescharacteristic
280C2×C4×C47C22⋊Q811yescharacteristic
281C2×C4×C47#12311yescharacteristic
282C2×C4×C47#12311yescharacteristic
283C2×C4×C47#12311yescharacteristic
284C2×C4×C47#12311yescharacteristic
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—44no—
294C2×Dic47—42no—
295C2×Dic47#9512yes—
296C2×Dic47#9512yes—
297C4×D47—22no—
298C4×D47—22no—
299C4×D47—22no—
300C4×D47—22no—
301C4×D47—22no—
302C4×D47—22no—
303C4×D47—22no—
304C4×D47—22no—
305C4×D47—22no—
306C4×D47—22no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—22no—
311C4×D47—22no—
312C4×D47—22no—
313C8×C47—24no—
314C8×C47—42no—
315C47⋊C8—24no—
316C47⋊C8—42no—
317#10737—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47C2×#9511yescharacteristic
326C22×C47C4×C22⋊C411yescharacteristic
327C22×C47C4×C22⋊C411yescharacteristic
328C22×C47#38511yescharacteristic
329C22×C47#38511yescharacteristic
330C22×C47#38611yescharacteristic
331C22×C47#38611yescharacteristic
332C2×D47—24no—
333C2×D47—24no—
334C2×D47—22no—
335C2×D47—22no—
336C2×D47—22no—
337C2×D47—22no—
338C2×D47—22no—
339C2×D47—44no—
340C2×D47—44no—
341C2×D47—44no—
342C2×D47—44no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47#34414yescomplemented
346C4×C47—82no—
347C4×C47#37911yescharacteristic
348C4×C47#38011yescharacteristic
349C4×C47#38011yescharacteristic
350C4×C47#38111yescharacteristic
351C4×C47#38511yescharacteristic
352C4×C47#38511yescharacteristic
353C4×C47#38611yescharacteristic
354C4×C47#38611yescharacteristic
355Dic47—22no—
356Dic47—22no—
357Dic47—82no—
358C23×M16—471no—
359C2×#407—471no—
360#2280—471no—
361C2×#344—471no—
362C2×#344—471no—
363C2×#344—471no—
364C2×#344D4711yescharacteristic, complemented
365C2×C47—21no—
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—21no—
369C2×C47—21no—
370C2×C47—21no—
371C2×C47C22⋊#9511yescharacteristic
372C2×C47C2×#34412yes—
373D47—24no—
374D47—42no—
375C24×C4—471no—
376C22×M16—471no—
377C22×M16—471no—
378C22×M16—474no—
379C22×M16—941no—
380C22×M16—942no—
381C22×M16—942no—
382C22×M16—942no—
383C22×M16—942no—
384C22×M16—942no—
385C22×M16C2×D4711yescharacteristic
386C22×M16C2×D4711yescharacteristic
387C23×C8—941no—
388C2×#117—471no—
389C2×#117C2×D4711yescharacteristic
390#407—941no—
391#407—941no—
392#407—942no—
393C2×C22⋊C8—474no—
394#381—472no—
395#380—942no—
396#379—472no—
397C4×C22⋊C4—942no—
398#344—22no—
399#344—942no—
400#344—942no—
401#344—942no—
402C47#1073711yescharacteristic, complemented, Sylow
403C25—471no—
404C23×C4—471no—
405C23×C4—472no—
406C23×C4—472no—
407C23×C4—471no—
408C23×C4—472no—
409C23×C4—471no—
410C23×C4—472no—
411C23×C4—471no—
412C23×C4—471no—
413C23×C4—941no—
414C23×C4—941no—
415C23×C4—941no—
416C23×C4—941no—
417C23×C4—941no—
418C23×C4—941no—
419C23×C4—941no—
420C23×C4—941no—
421C23×C4C22×D4711yescharacteristic
422C2×M16—21no—
423C2×M16—21no—
424C2×M16—21no—
425C2×M16—21no—
426C2×M16—21no—
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—472no—
432C2×M16—472no—
433C2×M16—472no—
434C2×M16—944no—
435C2×M16—944no—
436C2×M16—944no—
437C2×M16—948no—
438C2×M16—948no—
439C2×M16—948no—
440C2×M16—941no—
441C2×M16—941no—
442C2×M16—941no—
443C2×M16—948no—
444C2×M16—941no—
445C2×M16—941no—
446C2×M16—941no—
447C2×M16—941no—
448C2×M16—941no—
449C2×M16—941no—
450C2×M16C4×D4712yes—
451C2×M16D18812yes—
452C2×M16C22⋊D4712yes—
453C22×C8—21no—
454C22×C8—472no—
455C22×C8—944no—
456C22×C8—944no—
457C22×C8—944no—
458C22×C8—941no—
459C22×C8C4×D4712yes—
460#117—21no—
461#117—21no—
462#117—21no—
463#117—21no—
464#117—941no—
465#117—941no—
466#117—941no—
467#117—941no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—941no—
470C2×C22⋊C4—472no—
471C2×C22⋊C4—944no—
472C2×C22⋊C4C4×D4712yes—
473C2×C42—21no—
474C2×C42—941no—
475C22⋊C8—944no—
476C22⋊C8—944no—
477#95—944no—
478C24—471no—
479C24—472no—
480C24—472no—
481C24—471no—
482C24—941no—
483C24—941no—
484C24—941no—
485C24—941no—
486C24—1884no—
487C24C2×C4×D4711yescharacteristic
488C22×C4—22no—
489C22×C4—472no—
490C22×C4—472no—
491C22×C4—471no—
492C22×C4—471no—
493C22×C4—472no—
494C22×C4—472no—
495C22×C4—472no—
496C22×C4—472no—
497C22×C4—472no—
498C22×C4—472no—
499C22×C4—472no—
500C22×C4—472no—
501C22×C4—941no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—941no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—941no—
514C22×C4—941no—
515C22×C4—942no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—941no—
529C22×C4—941no—
530C22×C4—941no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—942no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4C2×C4×D4711yescharacteristic
539C22×C4C2×C4×D4711yescharacteristic
540C22×C4C2×D18811yescharacteristic
541C22×C4#1062535011yescharacteristic
542C22×C4#1062535011yescharacteristic
543C22×C4D4×D4711yescharacteristic
544C22×C4D4×D4711yescharacteristic
545C22×C4D4×D4711yescharacteristic
546C22×C4D4×D4711yescharacteristic
547C22×C4D4×D4711yescharacteristic
548C22×C4#1062535211yescharacteristic
549C22×C4Q8×D4711yescharacteristic
550C22×C4#1062535411yescharacteristic
551C22×C4C2×C22⋊D4711yescharacteristic
552M16—22no—
553M16—22no—
554M16—22no—
555M16—41no—
556M16—41no—
557M16—41no—
558M16—41no—
559M16—474no—
560M16—9416no—
561M16—942no—
562M16—942no—
563M16—942no—
564M16—1881no—
565M16—1881no—
566M16—1881no—
567M16—1881no—
568M16(C2×D47)⋊C414yescomplemented
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—9416no—
576C2×C8—942no—
577C2×C8—942no—
578C2×C8—942no—
579C2×C8—942no—
580C2×C8—942no—
581C2×C8—942no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—1881no—
585C4⋊C4—1881no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—942no—
589C22⋊C4—942no—
590C22⋊C4—1888no—
591C42—41no—
592C42—41no—
593C42—1881no—
594C42—1881no—
595C23—42no—
596C23—472no—
597C23—472no—
598C23—944no—
599C23—944no—
600C23—944no—
601C23—941no—
602C23—941no—
603C23—942no—
604C23—942no—
605C23—941no—
606C23—941no—
607C23—942no—
608C23—942no—
609C23—1882no—
610C23—1882no—
611C23—1882no—
612C23—1884no—
613C23—1884no—
614C23—1884no—
615C23—1884no—
616C23C42×D4711yescharacteristic
617C23C22⋊C4×D4711yescharacteristic
618C23C4⋊C4×D4711yescharacteristic
619C23(C22⋊D47)⋊C411yescharacteristic
620C23C4×C22⋊D4711yescharacteristic
621C23#1309398611yescharacteristic
622C23C4×D18811yescharacteristic
623C2×C4—44no—
624C2×C4—42no—
625C2×C4—472no—
626C2×C4—472no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—941no—
630C2×C4—941no—
631C2×C4—941no—
632C2×C4—941no—
633C2×C4—942no—
634C2×C4—942no—
635C2×C4—942no—
636C2×C4—942no—
637C2×C4—942no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—942no—
643C2×C4—942no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—1884no—
652C2×C4—1882no—
653C2×C4C22⋊C4×D4711yescharacteristic
654C2×C4C22⋊C4×D4711yescharacteristic
655C2×C4C22⋊C4×D4711yescharacteristic
656C2×C4C2×(C2×D47)⋊C411yescharacteristic
657C2×C4C4⋊C4×D4711yescharacteristic
658C2×C4C4⋊C4×D4711yescharacteristic
659C2×C4#1309398111yescharacteristic
660C2×C4#1309398211yescharacteristic
661C2×C4(C22⋊D47)⋊C411yescharacteristic
662C2×C4C4×C22⋊D4711yescharacteristic
663C2×C4#1309398611yescharacteristic
664C2×C4C4×D18811yescharacteristic
665C2×C4#1309399211yescharacteristic
666C2×C4#1309399211yescharacteristic
667C2×C4#1309399411yescharacteristic
668C2×C4#1309399411yescharacteristic
669C2×C4#1309399511yescharacteristic
670C2×C4#1309399711yescharacteristic
671C2×C4#1309399711yescharacteristic
672C2×C4#1309399911yescharacteristic
673C2×C4#1309400011yescharacteristic
674C2×C4#1309400211yescharacteristic
675C2×C4#1309400211yescharacteristic
676C2×C4#1309400411yescharacteristic
677C2×C4#1309400611yescharacteristic
678C2×C4#1309400611yescharacteristic
679C2×C4#1309400911yescharacteristic
680C2×C4#1309400911yescharacteristic
681C8—24no—
682C8—42no—
683C8—944no—
684C8—1882no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—474no—
693C22—944no—
694C22—944no—
695C22—942no—
696C22—942no—
697C22—942no—
698C22—942no—
699C22—942no—
700C22—1884no—
701C22—1884no—
702C22—1884no—
703C22—1884no—
704C22—1882no—
705C22—1882no—
706C22#95×D4711yescharacteristic
707C22#1568897011yescharacteristic
708C22C4×(C2×D47)⋊C411yescharacteristic
709C22#1568899411yescharacteristic
710C22#1568899711yescharacteristic
711C22#1568899911yescharacteristic
712C22#1568900111yescharacteristic
713C4—82no—
714C4—942no—
715C4—942no—
716C4—3762no—
717C4#1568897811yescharacteristic
718C4#1568898011yescharacteristic
719C4#1568898211yescharacteristic
720C4#1568898511yescharacteristic
721C4#1568899411yescharacteristic
722C4#1568899711yescharacteristic
723C4#1568899911yescharacteristic
724C4#1568900111yescharacteristic
725C2—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—944no—
732C2—1882no—
733C2(C2×D47)⋊#9511yescharacteristic
734C2#344×D4712yes—
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#344C2
socleC22×C47C2×#95
prime radicalC24×D47C2×C4
cosocleC23×C4×C47C23
hypercenterC2×#344D47
hypocenterC47#10737
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. C2×#15688894C2semidirect
6. C2×#15688893C2semidirect
7. C2×C47×#344C2semidirect
17. C2×M16×D47C4semidirect
23. C2×(C2×D47)⋊C8C4semidirect
191. M16×C47C22⋊C4semidirect
218. #10625329C22⋊C4semidirect
345. C2×D47#344semidirect
364. C2×#344D47semidirect
402. C47#10737semidirect
568. M16(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156890862
#202457672
C2×#156888952
C2×#156888942
C2×#156888932
C2×C47×#3442
#1073747