Finite Group Databasebeta

← #26123014

Subgroups — #26123014

Order 12032.

1262 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689140C211yesmaximal, characteristic
2C2×#15689132C211yesmaximal, characteristic, complemented
3C2×#15689097C211yesmaximal, characteristic
4#20245974C211yesmaximal, characteristic, complemented
5C2×#15688894C211yesmaximal, characteristic, complemented
6C2×#15688880C211yesmaximal, characteristic, complemented
7C22×#137×C47C211yesmaximal, characteristic
8C22×#10625329C2211yescharacteristic
9C2×#13093983C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689140—22no—
13#15689140—22no—
14C2×#13093951—22no—
15#15689132—22no—
16#15689132—22no—
17C2×#13093948—22no—
18#15689097—22no—
19#15689097—22no—
20C2×#13093939—22no—
21#15689030—22no—
22#15689030—22no—
23#15688986—22no—
24#15688894—22no—
25#15688880—22no—
26C22×#41×C47C2211yescharacteristic
27C23×Q8×C47C2211yescharacteristic
28C2×#137×C47—22no—
29C2×#137×C47—22no—
30C2×#137×C47—22no—
31C2×#137×C47—22no—
32C2×#137×C47—22no—
33C2×#137×C47—22no—
34C22×Q16×C47C412yescomplemented
35C22×SD16×C47C412yescomplemented
36C22×M16×C47C2211yescharacteristic
37C2×#10625329—21no—
38C2×#10625329—21no—
39C2×#10625329—21no—
40C2×#10625329—21no—
41C2×#10625329—21no—
42C2×#10625329D412yes—
43C22×C47⋊C8—21no—
44#13093983—21no—
45#13093983—21no—
46#13093983—21no—
47#13093983—21no—
48#13093983—21no—
49#13093983—21no—
50#13093983—21no—
51#13093983—21no—
52#13093983—21no—
53#13093983—21no—
54#13093983—21no—
55#13093983D412yes—
56C2×C4⋊Dic47—21no—
57C2×C4⋊Dic47—21no—
58C2×C4⋊Dic47—21no—
59C2×C22⋊Dic47—21no—
60C2×C22⋊Dic47—21no—
61C2×C22⋊Dic47D412yes—
62C2×C4×Dic47—21no—
63C2×C4×Dic47—21no—
64C2×C4×Dic47D412yes—
65#13093951—28no—
66#13093948—28no—
67#13093939—28no—
68C47⋊#95—28no—
69C2×#41×C47—21no—
70C2×#41×C47—21no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47—21no—
77C2×#41×C47—21no—
78C2×#41×C47—21no—
79C2×#41×C47D412yes—
80C2×#41×C47D412yes—
81C22×Q8×C47—21no—
82C22×Q8×C47—21no—
83C22×Q8×C47—21no—
84C22×Q8×C47—21no—
85C22×Q8×C47—21no—
86C22×Q8×C47—21no—
87C22×Q8×C47—21no—
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47—21no—
91C22×Q8×C47—21no—
92C22×Q8×C47C2×C412yes—
93C22×Q8×C47C2×C411yescharacteristic
94C22×Q8×C47D412yes—
95C22×Q8×C47D412yes—
96C22×D4×C47—21no—
97C22×D4×C47C2×C411yescharacteristic
98C23×C4×C47—21no—
99C23×C4×C47—21no—
100C23×C4×C47C2311yescharacteristic
101#137×C47—28no—
102#137×C47—28no—
103#137×C47—28no—
104#137×C47—28no—
105C2×Q16×C47—24no—
106C2×Q16×C47—24no—
107C2×Q16×C47—24no—
108C2×SD16×C47—24no—
109C2×SD16×C47—24no—
110C2×SD16×C47—24no—
111C2×M16×C47—21no—
112C2×M16×C47—21no—
113C2×M16×C47—21no—
114C2×M16×C47—21no—
115C2×M16×C47D412yes—
116C2×M16×C47D412yes—
117C22×C8×C47C2×C412yes—
118C24×C47—21no—
119C24×C47C2×D411yescharacteristic
120#41×C47—22no—
121#41×C47—22no—
122#41×C47—22no—
123#41×C47—22no—
124#41×C47—22no—
125#41×C47—22no—
126#41×C47—22no—
127#41×C47—22no—
128#41×C47—41no—
129#41×C47—41no—
130#41×C47—41no—
131#41×C47—41no—
132#41×C47—41no—
133#41×C47—41no—
134#41×C47—41no—
135#41×C47—41no—
136C2×Q8×C47—22no—
137C2×Q8×C47—21no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—22no—
149C2×Q8×C47—22no—
150C2×Q8×C47—22no—
151C2×Q8×C47—22no—
152C2×Q8×C47—22no—
153C2×Q8×C47—22no—
154C2×Q8×C47—22no—
155C2×Q8×C47—22no—
156C2×Q8×C47—41no—
157C2×Q8×C47—41no—
158C2×Q8×C47—41no—
159C2×Q8×C47—41no—
160C2×Q8×C47—41no—
161C2×Q8×C47—41no—
162C2×Q8×C47—41no—
163C2×Q8×C47—41no—
164C2×Q8×C47—41no—
165C2×Q8×C47—41no—
166C2×Q8×C47—41no—
167C2×Q8×C47—41no—
168C2×Q8×C47C22⋊C414yes—
169C2×Q8×C47C22⋊C412yes—
170C2×D4×C47—22no—
171C2×D4×C47—22no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—41no—
178C2×D4×C47—41no—
179C2×D4×C47—41no—
180C2×D4×C47—41no—
181C2×D4×C47C22⋊C412yes—
182C22×C4×C47—21no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—41no—
189C22×C4×C47—41no—
190C22×C4×C47—41no—
191C22×C4×C47—41no—
192C22×C4×C47—41no—
193C22×C4×C47—41no—
194C22×C4×C47—41no—
195C22×C4×C47—41no—
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47#4111yescharacteristic
207C22×C4×C47#4111yescharacteristic
208C22×C4×C47#4111yescharacteristic
209C22×C4×C47#4111yescharacteristic
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—41no—
213Q16×C47—216no—
214SD16×C47—216no—
215M16×C47—22no—
216M16×C47—22no—
217M16×C47—22no—
218M16×C47—22no—
219C2×C8×C47—22no—
220C2×C8×C47—22no—
221C2×C8×C47C22⋊C414yes—
222C22⋊Dic47—22no—
223C22⋊Dic47—22no—
224C22⋊Dic47—22no—
225C22⋊Dic47—41no—
226C22⋊Dic47—41no—
227C22⋊Dic47—41no—
228C4⋊Dic47—22no—
229C4⋊Dic47—41no—
230C4⋊Dic47—41no—
231C4⋊Dic47—41no—
232C4⋊Dic47—41no—
233C4⋊Dic47—41no—
234C4×Dic47—22no—
235C4×Dic47—22no—
236C4×Dic47—22no—
237C4×Dic47—41no—
238C4×Dic47—41no—
239C4×Dic47—41no—
240#10625329—22no—
241#10625329—22no—
242#10625329—41no—
243#10625329—41no—
244C2×C47⋊C8—22no—
245C2×C47⋊C8—41no—
246C2×C47⋊C8—41no—
247C23×C47—22no—
248C23×C47—42no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—82no—
252C23×C47C4×D411yescharacteristic
253C23×C47#12011yescharacteristic
254C23×C47#12011yescharacteristic
255C23×C47#12111yescharacteristic
256C23×C47#12111yescharacteristic
257C23×C47#12111yescharacteristic
258C23×C47#12711yescharacteristic
259Q8×C47—24no—
260Q8×C47—22no—
261Q8×C47—24no—
262Q8×C47—22no—
263Q8×C47—42no—
264Q8×C47—41no—
265Q8×C47—42no—
266Q8×C47—41no—
267Q8×C47—42no—
268Q8×C47—42no—
269Q8×C47—42no—
270Q8×C47—42no—
271D4×C47—22no—
272D4×C47—22no—
273D4×C47—42no—
274D4×C47—42no—
275D4×C47—42no—
276D4×C47—42no—
277D4×C47—41no—
278D4×C47—41no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—41no—
282C2×C4×C47—42no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47C2×C22⋊C411yescharacteristic
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47#12011yescharacteristic
300C2×C4×C47#12011yescharacteristic
301C2×C4×C47#12011yescharacteristic
302C2×C4×C47#12011yescharacteristic
303C2×C4×C47#12011yescharacteristic
304C2×C4×C47#12011yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12111yescharacteristic
309C2×C4×C47#12111yescharacteristic
310C2×C4×C47#12111yescharacteristic
311C2×C4×C47#12111yescharacteristic
312C2×C4×C47#12111yescharacteristic
313C2×C4×C47#12111yescharacteristic
314C2×C4×C47#12311yescharacteristic
315C2×C4×C47#12311yescharacteristic
316C2×C4×C47#12311yescharacteristic
317C2×C4×C47#12311yescharacteristic
318C2×C4×C47#12411yescharacteristic
319C2×C4×C47#12411yescharacteristic
320C2×C4×C47#12711yescharacteristic
321C2×Dic47—44no—
322C2×Dic47—44no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—82no—
327C8×C47—24no—
328C47⋊C8—42no—
329#11013—471nomaximal, Sylow
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—42no—
338C22×C47—82no—
339C22×C47—82no—
340C22×C47—82no—
341C22×C47#38611yescharacteristic
342C22×C47#38611yescharacteristic
343C22×C47#39011yescharacteristic
344C22×C47#39211yescharacteristic
345C22×C47#39211yescharacteristic
346C22×C47#39211yescharacteristic
347C22×C47#39411yescharacteristic
348C4×C47—42no—
349C4×C47—44no—
350C4×C47#37911yescharacteristic
351C4×C47#38611yescharacteristic
352C4×C47#38611yescharacteristic
353C4×C47#39011yescharacteristic
354C4×C47#39211yescharacteristic
355C4×C47#39411yescharacteristic
356C4×C47#39411yescharacteristic
357C4×C47#39411yescharacteristic
358Dic47—82no—
359Dic47—82no—
360Dic47—82no—
361C22×#137D4711yescharacteristic
362C2×#421—471no—
363C2×#419—471no—
364C2×#410—471no—
365#2310—471no—
366C2×#344—471no—
367C2×H(3,ℤ/4)—471no—
368C2×C47—21no—
369C2×C47—21no—
370C2×C47—21no—
371C2×C47—21no—
372C2×C47—21no—
373C2×C47—21no—
374C2×C47—82no—
375C2×C47#143811yescharacteristic
376C2×C47#190512yes—
377C22×#41C2×D4711yescharacteristic
378C23×Q8C2×D4711yescharacteristic
379C2×#137—22no—
380C2×#137—22no—
381C2×#137—22no—
382C2×#137—22no—
383C2×#137—22no—
384C2×#137—22no—
385C22×Q16Dic4712yescomplemented
386C22×SD16Dic4712yescomplemented
387C22×M16—471no—
388C22×M16C2×D4711yescharacteristic
389C2×#117—471no—
390C2×#117—471no—
391C2×#117—471no—
392#421—942no—
393#421—942no—
394C2×#104—942no—
395#419—942no—
396#419—942no—
397C2×#103—942no—
398#410—942no—
399#410—942no—
400C2×#99—942no—
401#391—942no—
402#391—942no—
403#381—942no—
404#344—942no—
405H(3,ℤ/4)—942no—
406C47#1101311yescharacteristic, complemented, Sylow
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41C22⋊D4712yes—
418C2×#41C22⋊D4712yes—
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8C2×Dic4712yes—
431C22×Q8C2×Dic4711yescharacteristic
432C22×Q8C22⋊D4712yes—
433C22×Q8C22⋊D4712yes—
434C22×D4—21no—
435C22×D4C2×Dic4711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C22×D4711yescharacteristic
439#137—28no—
440#137—28no—
441#137—28no—
442#137—28no—
443C2×Q16—24no—
444C2×Q16—24no—
445C2×Q16—24no—
446C2×SD16—24no—
447C2×SD16—24no—
448C2×SD16—24no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16—472no—
454C2×M16—941no—
455C2×M16—941no—
456C2×M16—941no—
457C2×M16—941no—
458C2×M16—941no—
459C2×M16C22⋊D4712yes—
460C2×M16C22⋊D4712yes—
461C22×C8—941no—
462C22×C8C2×Dic4712yes—
463#117—472no—
464#117—941no—
465#117—941no—
466#117—941no—
467#117—941no—
468#117—941no—
469#117—941no—
470#117—941no—
471#117—941no—
472#117—941no—
473#117—941no—
474#117—941no—
475C2×C4⋊C4—941no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—941no—
478C2×C22⋊C4—472no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4—941no—
481C2×C42—472no—
482C2×C42—941no—
483C2×C42—941no—
484#104—948no—
485#103—948no—
486#99—948no—
487#95—948no—
488C24—21no—
489C24D4×D4711yescharacteristic
490#41—22no—
491#41—22no—
492#41—22no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—41no—
499#41—41no—
500#41—41no—
501#41—41no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506C2×Q8—22no—
507C2×Q8—21no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—41no—
527C2×Q8—41no—
528C2×Q8—41no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8C22⋊Dic4714yes—
539C2×Q8C22⋊Dic4712yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—41no—
551C2×D4C22⋊Dic4712yes—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—1881no—
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4D4×D4711yescharacteristic
572C22×C4#1062535211yescharacteristic
573C22×C4#1062535211yescharacteristic
574C22×C4#1062535211yescharacteristic
575C22×C4#1062535211yescharacteristic
576C22×C4C22×Dic4711yescharacteristic
577C22×C4C2×C22⋊D4711yescharacteristic
578C22×C4C2×C22⋊D4711yescharacteristic
579C22×C4C2×C22⋊D4711yescharacteristic
580C22×C4C2×C22⋊D4711yescharacteristic
581C22×C4C2×C22⋊D4711yescharacteristic
582C22×C4C2×C22⋊D4711yescharacteristic
583Q16—216no—
584SD16—216no—
585M16—22no—
586M16—22no—
587M16—22no—
588M16—22no—
589M16—942no—
590M16—942no—
591M16—1881no—
592M16—1881no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—942no—
596C2×C8—1881no—
597C2×C8—1881no—
598C2×C8C22⋊Dic4714yes—
599C4⋊C4—942no—
600C4⋊C4—1881no—
601C4⋊C4—1881no—
602C4⋊C4—1881no—
603C4⋊C4—1881no—
604C4⋊C4—1881no—
605C22⋊C4—942no—
606C22⋊C4—942no—
607C22⋊C4—942no—
608C22⋊C4—1881no—
609C22⋊C4—1881no—
610C22⋊C4—1881no—
611C42—942no—
612C42—942no—
613C42—942no—
614C42—1881no—
615C42—1881no—
616C42—1881no—
617C23—22no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23—82no—
622C23D4×Dic4711yescharacteristic
623C23#1309399211yescharacteristic
624C23#1309399211yescharacteristic
625C23#1309399511yescharacteristic
626C23#1309399611yescharacteristic
627C23#1309399611yescharacteristic
628C23#1309402011yescharacteristic
629Q8—24no—
630Q8—22no—
631Q8—24no—
632Q8—22no—
633Q8—42no—
634Q8—41no—
635Q8—42no—
636Q8—41no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641D4—22no—
642D4—22no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—41no—
648D4—41no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—3762no—
664C2×C4—1884no—
665C2×C4—1884no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4C2×C22⋊Dic4711yescharacteristic
670C2×C4C2×C22⋊Dic4711yescharacteristic
671C2×C4C2×C22⋊Dic4711yescharacteristic
672C2×C4D4×Dic4711yescharacteristic
673C2×C4D4×Dic4711yescharacteristic
674C2×C4D4×Dic4711yescharacteristic
675C2×C4#1309399211yescharacteristic
676C2×C4#1309399211yescharacteristic
677C2×C4#1309399311yescharacteristic
678C2×C4#1309399311yescharacteristic
679C2×C4#1309399311yescharacteristic
680C2×C4#1309399311yescharacteristic
681C2×C4#1309399511yescharacteristic
682C2×C4#1309399511yescharacteristic
683C2×C4#1309399511yescharacteristic
684C2×C4#1309399611yescharacteristic
685C2×C4#1309399611yescharacteristic
686C2×C4#1309399611yescharacteristic
687C2×C4#1309399611yescharacteristic
688C2×C4#1309399611yescharacteristic
689C2×C4#1309399611yescharacteristic
690C2×C4#1309400511yescharacteristic
691C2×C4#1309400511yescharacteristic
692C2×C4#1309400511yescharacteristic
693C2×C4#1309400511yescharacteristic
694C2×C4#1309401111yescharacteristic
695C2×C4#1309401111yescharacteristic
696C2×C4#1309402011yescharacteristic
697C8—24no—
698C8—1882no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22#1568900311yescharacteristic
711C22#1568900311yescharacteristic
712C22#1568902611yescharacteristic
713C22#1568903111yescharacteristic
714C22#1568903111yescharacteristic
715C22#1568903111yescharacteristic
716C22#1568903711yescharacteristic
717C4—42no—
718C4—44no—
719C4—3762no—
720C4—3762no—
721C4—3762no—
722C4#1568897911yescharacteristic
723C4#1568900311yescharacteristic
724C4#1568900311yescharacteristic
725C4#1568902611yescharacteristic
726C4#1568903111yescharacteristic
727C4#1568903711yescharacteristic
728C4#1568903711yescharacteristic
729C4#1568903711yescharacteristic
730C2—21no—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—82no—
737C2#2024162911yescharacteristic
738C2#2024388412yes—
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC22×#137×C47C2
socleC22×C47#386
prime radicalC22×#41×C47C22
cosocleC23×C4×C47C23
hypercenterC22×#137D47
hypocenterC47#11013
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C2×#15689132C2semidirect
4. #20245974C2semidirect
5. C2×#15688894C2semidirect
6. C2×#15688880C2semidirect
34. C22×Q16×C47C4semidirect
35. C22×SD16×C47C4semidirect
385. C22×Q16Dic47semidirect
386. C22×SD16Dic47semidirect
406. C47#11013semidirect

Maximal subgroups

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

subgroupindex
C2×#156891402
C2×#156891322
C2×#156890972
#202459742
C2×#156888942
C2×#156888802
C22×#137×C472
#1101347