Finite Group Databasebeta

← #26243784

Subgroups — #26243784

Order 12032.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689166C211yesmaximal, characteristic, complemented
2C2×#15689124C211yesmaximal, characteristic, complemented
3C2×#15689124C211yesmaximal, characteristic, complemented
4C2×#15689087C211yesmaximal, characteristic, complemented
5C2×#15688983C211yesmaximal, characteristic, complemented
6#20244588C212yesmaximal, complemented
7#20244581C212yesmaximal, complemented
8#20244574C212yesmaximal, complemented
9#20244567C212yesmaximal, complemented
10#20243109C211yesmaximal, characteristic, complemented
11C2×C47×#525C211yesmaximal, characteristic
12C22×#10625329C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×C4⋊Dic47C2211yescharacteristic
16C22×C22⋊Dic47—21no—
17#15689166—24no—
18C2×#13093957C2212yescomplemented
19C2×#13093955C2212yescomplemented
20#15689124—24no—
21#15689124—24no—
22C2×#13093948C2212yescomplemented
23C2×#13093948C2212yescomplemented
24C2×#13093945C2212yescomplemented
25C2×#13093945C2212yescomplemented
26#15689087—24no—
27C2×C22⋊(C47⋊C8)C2212yes—
28C2×C22⋊(C47⋊C8)C2212yes—
29#15688983—21no—
30#15688983—21no—
31#15688983C2212yes—
32#15688983C2212yes—
33C2×C47⋊#95—21no—
34#15688885C2212yescomplemented
35#15688885C2212yescomplemented
36C22×#41×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C47×#525—24no—
39C47×#525—24no—
40C2×#123×C47—21no—
41C2×C22⋊Q8×C47C2211yescharacteristic
42C2×C22⋊Q8×C47C2211yescharacteristic
43C2×#121×C47C2211yescharacteristic
44C2×#121×C47C2211yescharacteristic
45C2×#120×C47—21no—
46C2×C4×D4×C47—21no—
47C2×C4×D4×C47—21no—
48C2×#117×C47C2211yescharacteristic
49C23×Dic47—21no—
50C23×Dic47—21no—
51C2×#10625329—22no—
52C2×#10625329—22no—
53C2×#10625329—22no—
54C2×#10625329—22no—
55C2×#10625329—22no—
56C2×#10625329D414yescomplemented
57C22×C47⋊C8C2312yes—
58C22×C47⋊C8C2312yes—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47—22no—
63C2×C4⋊Dic47—21no—
64C2×C4⋊Dic47—21no—
65C2×C4⋊Dic47C2312yes—
66C2×C4⋊Dic47C2312yes—
67C2×C22⋊Dic47—22no—
68C2×C22⋊Dic47—22no—
69C2×C22⋊Dic47—44no—
70#13093957—24no—
71#13093955—24no—
72#13093948—24no—
73#13093948—24no—
74#13093945—24no—
75#13093945—24no—
76C22⋊(C47⋊C8)—24no—
77C22⋊(C47⋊C8)—24no—
78C47⋊#95—22no—
79C47⋊#95—22no—
80C25×C47D411yescharacteristic
81C2×#41×C47—22no—
82C2×#41×C47—22no—
83C2×#41×C47—22no—
84C2×#41×C47—22no—
85C2×#41×C47—22no—
86C2×#41×C47D414yes—
87C22×Q8×C47C2311yescharacteristic
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—21no—
91C22×D4×C47C2311yescharacteristic
92C23×C4×C47—21no—
93C23×C4×C47—22no—
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47D411yescharacteristic
100C23×C4×C47D411yescharacteristic
101C23×C4×C47D411yescharacteristic
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105#123×C47—28no—
106C22⋊Q8×C47—22no—
107C22⋊Q8×C47—22no—
108C22⋊Q8×C47—22no—
109C22⋊Q8×C47—22no—
110#121×C47—22no—
111#121×C47—22no—
112#121×C47—22no—
113#121×C47—22no—
114#120×C47—28no—
115C4×D4×C47—28no—
116C4×D4×C47—28no—
117#117×C47—22no—
118#117×C47D414yes—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—21no—
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47—21no—
129C24×C47—22no—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—22no—
133C24×C47—22no—
134C24×C47—21no—
135C24×C47—41no—
136C24×C47—41no—
137C24×C47C2×D411yescharacteristic
138C24×C47C2×D411yescharacteristic
139C24×C47C2×D411yescharacteristic
140#41×C47—28no—
141#41×C47—28no—
142#41×C47—44no—
143#41×C47—44no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47C2×D412yes—
150C2×D4×C47—24no—
151C2×D4×C47—24no—
152C2×D4×C47—24no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—21no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—42no—
159C2×D4×C47—42no—
160C2×D4×C47—42no—
161C2×D4×C47—42no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47C2×D412yes—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—24no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—44no—
191C22×C4×C47—44no—
192C22×C4×C47—42no—
193C22×C4×C47—44no—
194C22×C4×C47—42no—
195C22×C4×C47—44no—
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47#4112yes—
203C22×C4×C47#4112yes—
204C22×C4×C47#4112yes—
205C22×C4×C47C2411yescharacteristic
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—42no—
209C22×Dic47—42no—
210C22×Dic47—42no—
211C22×Dic47—42no—
212C22×Dic47—42no—
213C22×Dic47—42no—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47C2×D412yes—
219C4⋊C4×C47C2×D412yes—
220C22⋊C4×C47—24no—
221C22⋊C4×C47—24no—
222C22⋊C4×C47—24no—
223C22⋊C4×C47—24no—
224C22⋊C4×C47—24no—
225C42×C47—24no—
226C22⋊Dic47—44no—
227C22⋊Dic47—44no—
228C4⋊Dic47—22no—
229C4⋊Dic47—22no—
230C4⋊Dic47—22no—
231C4⋊Dic47—22no—
232C4⋊Dic47—42no—
233C4⋊Dic47—42no—
234#10625329—28no—
235#10625329—44no—
236C2×C47⋊C8—22no—
237C2×C47⋊C8—22no—
238C2×C47⋊C8—22no—
239C2×C47⋊C8—22no—
240C2×C47⋊C8—22no—
241C2×C47⋊C8C2×D414yes—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—28no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—22no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47#12012yes—
273C23×C47#12112yes—
274C23×C47#12312yes—
275C23×C47AGL(1,ℤ/8)12yes—
276C23×C47#13712yes—
277C23×C47C22×D411yescharacteristic
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—41no—
281Q8×C47—41no—
282D4×C47—22no—
283D4×C47—22no—
284D4×C47—48no—
285D4×C47—48no—
286D4×C47—48no—
287D4×C47—41no—
288D4×C47—41no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—21no—
292C2×C4×C47—21no—
293C2×C4×C47—22no—
294C2×C4×C47—21no—
295C2×C4×C47—21no—
296C2×C4×C47—21no—
297C2×C4×C47—21no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—44no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—44no—
314C2×C4×C47—44no—
315C2×C4×C47—48no—
316C2×C4×C47#12012yes—
317C2×C4×C47#12114yes—
318C2×C4×C47#12114yes—
319C2×C4×C47#12112yes—
320C2×C4×C47#12314yes—
321C2×C4×C47#12312yes—
322C2×C4×C47#12414yes—
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D411yescharacteristic
326C2×C4×C47C2×#4111yescharacteristic
327C2×C4×C47C2×#4111yescharacteristic
328C2×C4×C47C2×#4111yescharacteristic
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—42no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—84no—
336C2×Dic47—84no—
337C47⋊C8—24no—
338C47⋊C8—42no—
339#23482—471nomaximal, Sylow
340C22×C47—22no—
341C22×C47—22no—
342C22×C47—22no—
343C22×C47—22no—
344C22×C47—22no—
345C22×C47—22no—
346C22×C47—22no—
347C22×C47—22no—
348C22×C47—22no—
349C22×C47—22no—
350C22×C47—22no—
351C22×C47—22no—
352C22×C47—416no—
353C22×C47—41no—
354C22×C47—41no—
355C22×C47—41no—
356C22×C47—41no—
357C22×C47—41no—
358C22×C47—41no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—81no—
365C22×C47—81no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47#39414yes—
369C22×C47C2×#12011yescharacteristic
370C22×C47C2×#12111yescharacteristic
371C22×C47C2×#12311yescharacteristic
372C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C47C2×#13711yescharacteristic
374C22×C47#57511yescharacteristic
375C22×C47#57511yescharacteristic
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—42no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47#39414yes—
382C4×C47C2×#12111yescharacteristic
383C4×C47C2×#12111yescharacteristic
384C4×C47C2×#12311yescharacteristic
385C4×C47C2×#12411yescharacteristic
386Dic47—82no—
387Dic47—82no—
388C2×#525D4711yescharacteristic
389C2×#428—471no—
390C2×#417—471no—
391C2×#417—471no—
392C2×#407—471no—
393C2×#380—471no—
394#2036—472no—
395#2035—472no—
396#2034—472no—
397#2033—472no—
398#1736—471no—
399C2×C47—24no—
400C2×C47—42no—
401C2×C47—42no—
402C2×C47—82no—
403C2×C47C2×#39411yescharacteristic
404C2×C47#300611yescharacteristic
405C2×C47#300711yescharacteristic
406C2×C47#305511yescharacteristic
407C2×C47#305611yescharacteristic
408C2×C47#309211yescharacteristic
409C2×C47#309311yescharacteristic
410C22×#41C2×D4711yescharacteristic
411C24×C4C2×D4711yescharacteristic
412C22×M16—471no—
413C22×M16—471no—
414#525—24no—
415#525—24no—
416C2×#123—21no—
417C2×C22⋊Q8C2×D4711yescharacteristic
418C2×C22⋊Q8C2×D4711yescharacteristic
419C2×#121C2×D4711yescharacteristic
420C2×#121C2×D4711yescharacteristic
421C2×#120—21no—
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×#117C2×D4711yescharacteristic
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C22⋊C4—941no—
428#428—944no—
429C2×#107—472no—
430C2×#106—472no—
431#417—944no—
432#417—944no—
433C2×#103—472no—
434C2×#103—472no—
435C2×#102—472no—
436C2×#102—472no—
437#407—944no—
438C2×C22⋊C8—472no—
439C2×C22⋊C8—472no—
440#380—472no—
441#380—472no—
442#380—941no—
443#380—941no—
444C2×#95—941no—
445#340—472no—
446#340—472no—
447C47#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D4711yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D4714yes—
455C22×Q8C22×D4711yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C22×D4711yescharacteristic
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4C22⋊D4711yescharacteristic
470C23×C4C22⋊D4711yescharacteristic
471C23×C4C22⋊D4711yescharacteristic
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4711yescharacteristic
475C2×M16—474no—
476C2×M16—942no—
477C2×M16—942no—
478C2×M16—942no—
479C2×M16—942no—
480C2×M16—942no—
481C22×C8—472no—
482C22×C8—472no—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117C22⋊D4714yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—472no—
500C2×C4⋊C4—472no—
501C2×C4⋊C4—942no—
502C2×C4⋊C4—942no—
503C2×C4⋊C4—942no—
504C2×C4⋊C4—942no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—942no—
516C2×C22⋊C4—1884no—
517C2×C42—21no—
518#107—944no—
519#106—944no—
520#103—944no—
521#103—944no—
522#102—944no—
523#102—944no—
524C22⋊C8—944no—
525C22⋊C8—944no—
526#95—942no—
527#95—942no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×C22⋊D4711yescharacteristic
537C24C2×C22⋊D4711yescharacteristic
538C24C2×C22⋊D4711yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D4712yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×C22⋊D4712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—942no—
596C22×C4—942no—
597C22×C4—1882no—
598C22×C4—1882no—
599C22×C4—1882no—
600C22×C4—1882no—
601C22×C4—1882no—
602C22×C4—1882no—
603C22×C4D4×D4712yes—
604C22×C4#1062535212yes—
605C22×C4#1062535212yes—
606C22×C4#1062535212yes—
607C22×C4C2×C22⋊D4711yescharacteristic
608C22×C4C2×C22⋊D4711yescharacteristic
609C22×C4C2×C22⋊D4711yescharacteristic
610C22×C4C2×C22⋊D4712yes—
611C22×C4C2×C22⋊D4712yes—
612C22×C4C23×D4711yescharacteristic
613M16—948no—
614M16—1884no—
615C2×C8—474no—
616C2×C8—942no—
617C2×C8—942no—
618C2×C8—942no—
619C2×C8—942no—
620C2×C8—942no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—942no—
626C4⋊C4—942no—
627C4⋊C4—942no—
628C4⋊C4—942no—
629C4⋊C4—1882no—
630C4⋊C4—1882no—
631C4⋊C4C2×C22⋊D4712yes—
632C4⋊C4C2×C22⋊D4712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1884no—
639C22⋊C4—1884no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#1309399312yes—
672C23#1309399612yes—
673C23#1309400512yes—
674C23#1309404912yes—
675C23#1309405412yes—
676C23C22×C22⋊D4711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—3764no—
716C2×C4—3764no—
717C2×C4—1882no—
718C2×C4—1882no—
719C2×C4—1882no—
720C2×C4—1882no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4#1309399312yes—
724C2×C4#1309399514yes—
725C2×C4#1309399612yes—
726C2×C4#1309399614yes—
727C2×C4#1309400512yes—
728C2×C4#1309400514yes—
729C2×C4#1309401114yes—
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4C22×C22⋊D4711yescharacteristic
732C2×C4C22×C22⋊D4711yescharacteristic
733C2×C4C2×#1062535211yescharacteristic
734C2×C4C2×#1062535211yescharacteristic
735C2×C4C2×#1062535211yescharacteristic
736C8—944no—
737C8—1882no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1568903714yes—
767C22C2×#1309399311yescharacteristic
768C22C2×#1309399611yescharacteristic
769C22C2×#1309400511yescharacteristic
770C22C2×#1309404911yescharacteristic
771C22C2×#1309405411yescharacteristic
772C22#1568992111yescharacteristic
773C22#1568992111yescharacteristic
774C4—41no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—3762no—
780C4—3762no—
781C4#1568903714yes—
782C4C2×#1309399511yescharacteristic
783C4C2×#1309399611yescharacteristic
784C4C2×#1309400511yescharacteristic
785C4C2×#1309401111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1568903711yescharacteristic
791C2#2025264011yescharacteristic
792C2#2025264811yescharacteristic
793C2#2025300911yescharacteristic
794C2#2025302011yescharacteristic
795C2#2025330811yescharacteristic
796C2#2025331711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#525C2
socleC23×C47C22×D4
hypercenterC2×#525D47
hypocenterC47#23482
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689166C2semidirect
2. C2×#15689124C2semidirect
3. C2×#15689124C2semidirect
4. C2×#15689087C2semidirect
5. C2×#15688983C2semidirect
6. #20244588C2semidirect
7. #20244581C2semidirect
8. #20244574C2semidirect
9. #20244567C2semidirect
10. #20243109C2semidirect
18. C2×#13093957C22semidirect
19. C2×#13093955C22semidirect
22. C2×#13093948C22semidirect
23. C2×#13093948C22semidirect
24. C2×#13093945C22semidirect
25. C2×#13093945C22semidirect
34. #15688885C22semidirect
35. #15688885C22semidirect
56. C2×#10625329D4semidirect
447. C47#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#156891662
C2×#156891242
C2×#156890872
C2×#156889832
#202445882
#202445812
#202445742
#202445672
#202431092
C2×C47×#5252
#2348247