Finite Group Databasebeta

← #25098299

Subgroups — #25098299

Order 11008.

1986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D43C211yesmaximal, characteristic, complemented
2C2×#14583411C211yesmaximal, characteristic
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582898C211yesmaximal, characteristic, complemented
5C2×#14582756C211yesmaximal, characteristic, complemented
6#19135032C212yesmaximal, complemented
7#19135027C212yesmaximal, complemented
8#19135022C212yesmaximal, complemented
9#19135017C212yesmaximal, complemented
10#19134316C211yesmaximal, characteristic, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15C22×#10621872C2212yes—
16C2×M16×D43—24no—
17C2×M16×D43—24no—
18C2×M16×D43—24no—
19C22×C8×D43C2212yes—
20#14583411—24no—
21#14583411C418yescomplemented
22C2×#13063309—21no—
23C2×#13063305C2211yescharacteristic
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063300C2211yescharacteristic
27C2×#13063295—21no—
28C2×C4×D172—21no—
29C2×C4×D172—21no—
30C22×C4⋊Dic43C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32#14582901—24no—
33#14582898—24no—
34C2×#13063250C2212yescomplemented
35C2×#13063248C2212yescomplemented
36C2×#13063247C2212yescomplemented
37C2×#13063245C2212yescomplemented
38#14582756—21no—
39#14582756—21no—
40#14582756C2212yes—
41#14582756C2212yes—
42C2×C43⋊#95—21no—
43#14582661C2212yescomplemented
44#14582661C2212yescomplemented
45C22×M16×C43C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C22×C4⋊C4×C43C2211yescharacteristic
48C43×#340C2212yescomplemented
49C43×#340C2212yescomplemented
50C24×D43D411yescharacteristic
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898—22no—
55C2×#10621898—22no—
56C2×#10621898C2×C414yes—
57C22×Dic86C2311yescharacteristic
58C22×D172—21no—
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43—21no—
63C23×Dic43D411yescharacteristic
64C22×C4×D43—22no—
65C22×C4×D43—22no—
66C22×C4×D43—22no—
67C22×C4×D43—22no—
68C22×C4×D43—21no—
69C22×C4×D43C2×C414yes—
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D414yes—
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
75C2×#10621877—22no—
76C2×#10621877—22no—
77C2×#10621877D414yescomplemented
78C2×#10621872—24no—
79C2×#10621872—24no—
80C2×#10621872—24no—
81M16×D43—232no—
82C22×C43⋊C8C2312yes—
83C2×C8×D43—24no—
84C2×C8×D43—24no—
85C2×C8×D43—24no—
86#13063309—28no—
87#13063305—22no—
88#13063305—22no—
89#13063305C2×C414yescomplemented
90#13063305C2×C414yescomplemented
91#13063300—22no—
92#13063300—22no—
93#13063300C2×C414yescomplemented
94#13063300C2×C414yescomplemented
95#13063295—28no—
96C4×D172—28no—
97C4×D172—28no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—22no—
101C2×C4⋊Dic43—22no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43C2312yes—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—22no—
109C2×(C2×D43)⋊C4—22no—
110C2×(C2×D43)⋊C4—44no—
111#13063250—24no—
112#13063248—24no—
113#13063247—24no—
114#13063245—24no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C23×C4×C43—21no—
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—22no—
120C2×M16×C43—22no—
121C2×M16×C43D414yescomplemented
122C22×C8×C43C2312yes—
123#117×C43—22no—
124#117×C43C2×C414yes—
125C2×C4⋊C4×C43—22no—
126C2×C4⋊C4×C43—22no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43C2312yes—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133C24×C43C2×D411yescharacteristic
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—21no—
139C23×D43—41no—
140C23×D43—41no—
141C23×D43C22⋊C414yes—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—22no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4112yes—
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—24no—
159C2×C22⋊D43—42no—
160C2×C22⋊D43—42no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—42no—
166C22×Dic43—42no—
167C22×Dic43—42no—
168C22×Dic43C22⋊C414yes—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171#10621898—28no—
172#10621898—28no—
173#10621898—44no—
174#10621898—44no—
175C2×D172—21no—
176C2×D172—24no—
177C2×D172—24no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—42no—
183C2×D172—42no—
184C2×D172—42no—
185C2×D172—42no—
186C2×D172C22×C412yes—
187C2×C4×D43—28no—
188C2×C4×D43—28no—
189C2×C4×D43—28no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—22no—
193C2×C4×D43—22no—
194C2×C4×D43—28no—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—21no—
203C2×C4×D43—24no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43C22⋊C414yes—
207C2×C4×D43C22⋊C414yes—
208C2×C4×D43C22×C412yes—
209C2×C4×D43C22×C412yes—
210C2×C4×D43C2×D412yes—
211C2×C4×D43C2×D412yes—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C2×Dic86C22×C412yes—
218M16×C43—28no—
219C2×C8×C43—22no—
220C2×C8×C43—22no—
221C2×C8×C43C2×D414yes—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—22no—
226C4⋊C4×C43—42no—
227C4⋊C4×C43C22×C412yes—
228C4⋊C4×C43C22×C412yes—
229C22⋊C4×C43—24no—
230C42×C43—24no—
231(C2×D43)⋊C4—24no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—44no—
236(C2×D43)⋊C4—44no—
237C4⋊Dic43—24no—
238C4⋊Dic43—24no—
239C4⋊Dic43—22no—
240C4⋊Dic43—22no—
241C4⋊Dic43—42no—
242#10621877—28no—
243C2×C43⋊C8—22no—
244C2×C43⋊C8—22no—
245C2×C43⋊C8C2×D414yes—
246#10621872—216no—
247C8×D43—216no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43C2×C22⋊C412yes—
253C23×C43#12112yes—
254C23×C43#12112yes—
255C23×C43C22×D411yescharacteristic
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—28no—
267C22×D43—28no—
268C22×D43—22no—
269C22×D43—44no—
270C22×D43—44no—
271C22×D43—44no—
272C22×D43—44no—
273C22×D43—44no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279C22×D43—41no—
280C22×D43C2×C22⋊C412yes—
281C22×D43C2×C22⋊C412yes—
282C22×D43AGL(1,ℤ/8)12yes—
283C22×D43#13712yes—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—84no—
294C2×C4×C43C2×C22⋊C412yes—
295C2×C4×C43C4×D414yes—
296C2×C4×C43C4×D414yes—
297C2×C4×C43#12014yes—
298C2×C4×C43#12112yes—
299C2×C4×C43#12112yes—
300C2×C4×C43#12314yes—
301C2×C4×C43C23×C411yescharacteristic
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C22⋊D43—48no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—28no—
313C2×Dic43—22no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—84no—
320C2×Dic43C2×C22⋊C412yes—
321C2×Dic43C2×C22⋊C412yes—
322D172—22no—
323D172—22no—
324D172—48no—
325D172—48no—
326D172—41no—
327D172—41no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—22no—
336C4×D43—28no—
337C4×D43—28no—
338C4×D43—48no—
339Dic86—22no—
340Dic86—22no—
341Dic86—41no—
342Dic86—41no—
343C8×C43—24no—
344C43⋊C8—24no—
345#20971—431nomaximal, Sylow
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43#38614yes—
353C22×C43C22×C22⋊C411yescharacteristic
354C22×C43C2×#12111yescharacteristic
355C22×C43C2×#12111yescharacteristic
356C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C43C2×#13711yescharacteristic
358C22×C43#57511yescharacteristic
359C22×C43#57511yescharacteristic
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—416no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—81no—
381C2×D43#41714yescomplemented
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—82no—
385C4×C43#38614yes—
386C4×C43C2×C4×D411yescharacteristic
387C4×C43C2×C4×D411yescharacteristic
388C4×C43C2×#12011yescharacteristic
389C4×C43C2×#12311yescharacteristic
390Dic43—22no—
391Dic43—22no—
392Dic43—42no—
393Dic43—82no—
394C23×M16—431no—
395C2×#525—431no—
396C2×#417—431no—
397C2×#417—431no—
398C2×#380—431no—
399#1895—432no—
400#1894—432no—
401#1893—432no—
402#1892—432no—
403#1736—431no—
404#1736D4311yescharacteristic, complemented
405C2×C43—24no—
406C2×C43C2×#38611yescharacteristic
407C2×C43C2×#41711yescharacteristic
408C2×C43#289611yescharacteristic
409C2×C43#305511yescharacteristic
410C2×C43#305511yescharacteristic
411C2×C43#305611yescharacteristic
412C2×C43#305611yescharacteristic
413D43—24no—
414D43—42no—
415D43—82no—
416C22×#41—431no—
417C24×C4—431no—
418C22×M16—431no—
419C22×M16—432no—
420C22×M16—864no—
421C22×M16—864no—
422C22×M16—864no—
423C22×M16C2×D4311yescharacteristic
424C23×C8—432no—
425#525—438no—
426#525—864no—
427C2×#123—861no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8—431no—
430C2×#121—431no—
431C2×#121—431no—
432C2×#120—861no—
433C2×C4×D4—861no—
434C2×C4×D4—861no—
435C2×#117C2×D4311yescharacteristic
436C22×C4⋊C4—431no—
437C22×C4⋊C4C2×D4311yescharacteristic
438C22×C22⋊C4—861no—
439#417—864no—
440#417—864no—
441C2×#103—432no—
442C2×#103—432no—
443C2×#102—432no—
444C2×#102—432no—
445#380—432no—
446#380—432no—
447#380—861no—
448#380—861no—
449C2×#95—861no—
450#340—432no—
451#340—432no—
452#340C2×D4312yescomplemented
453#340C2×D4312yescomplemented
454C43#2097111yescharacteristic, complemented, Sylow
455C25—431no—
456C2×#41—434no—
457C2×#41—862no—
458C2×#41—862no—
459C2×#41—862no—
460C2×#41—862no—
461C2×#41—862no—
462C22×Q8—431no—
463C22×D4—431no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4—861no—
467C23×C4—21no—
468C23×C4—431no—
469C23×C4—434no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—434no—
473C23×C4—431no—
474C23×C4—431no—
475C23×C4—862no—
476C23×C4—862no—
477C23×C4—862no—
478C23×C4—862no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C2×M16—22no—
483C2×M16—22no—
484C2×M16—434no—
485C2×M16—864no—
486C2×M16—864no—
487C2×M16—8632no—
488C2×M16—862no—
489C2×M16—862no—
490C2×M16—864no—
491C2×M16D17214yescomplemented
492C22×C8—432no—
493C22×C8—864no—
494C22×C8—864no—
495C22×C8—864no—
496C22×C8C22×D4312yes—
497#123—868no—
498C22⋊Q8—434no—
499C22⋊Q8—434no—
500C22⋊Q8—862no—
501C22⋊Q8—862no—
502#121—434no—
503#121—434no—
504#121—862no—
505#121—862no—
506#120—868no—
507C4×D4—868no—
508C4×D4—868no—
509#117—22no—
510#117C4×D4314yes—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—432no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4—861no—
520C2×C4⋊C4C22×D4312yes—
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4311yescharacteristic
523C2×C22⋊C4—21no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—1724no—
531C2×C42—21no—
532#103—864no—
533#103—864no—
534#102—864no—
535#102—864no—
536#95—862no—
537#95—862no—
538C24—431no—
539C24—431no—
540C24—434no—
541C24—862no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—861no—
546C24—1721no—
547C24—1721no—
548C24D4×D4311yescharacteristic
549#41—868no—
550#41—868no—
551#41—1724no—
552#41—1724no—
553C2×Q8—432no—
554C2×Q8—861no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×D4—432no—
560C2×D4—864no—
561C2×D4—864no—
562C2×D4—864no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—1722no—
569C2×D4—1722no—
570C2×D4—1722no—
571C2×D4—1722no—
572C2×D4—1722no—
573C2×D4—1722no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—434no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—434no—
584C22×C4—434no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—432no—
588C22×C4—432no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—868no—
592C22×C4—868no—
593C22×C4—868no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—868no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—864no—
609C22×C4—862no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4—1722no—
614C22×C4—1722no—
615C22×C4C2×C4×D4312yes—
616C22×C4C2×D17212yes—
617C22×C4#1062189812yes—
618C22×C4D4×D4311yescharacteristic
619C22×C4D4×D4312yes—
620C22×C4D4×D4312yes—
621C22×C4#1062190212yes—
622C22×C4C23×D4311yescharacteristic
623M16—28no—
624M16—8616no—
625M16—868no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—434no—
629C2×C8—8616no—
630C2×C8—862no—
631C2×C8—862no—
632C2×C8C2×D17214yes—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—42no—
638C4⋊C4—864no—
639C4⋊C4—864no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—1722no—
643C4⋊C4C2×C4×D4312yes—
644C4⋊C4C2×C4×D4312yes—
645C22⋊C4—24no—
646C22⋊C4—864no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—1724no—
651C22⋊C4—1724no—
652C42—24no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—432no—
658C23—432no—
659C23—432no—
660C23—432no—
661C23—868no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—868no—
673C23—862no—
674C23—1724no—
675C23—1724no—
676C23—1724no—
677C23—1724no—
678C23—1724no—
679C23—1721no—
680C23—1721no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23C22⋊C4×D4312yes—
686C23#1306329812yes—
687C23#1306330012yes—
688C23C2×D4×D4311yescharacteristic
689Q8—862no—
690Q8—862no—
691Q8—1721no—
692Q8—1721no—
693D4—862no—
694D4—862no—
695D4—1728no—
696D4—1728no—
697D4—1728no—
698D4—1721no—
699D4—1721no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—84no—
710C2×C4—432no—
711C2×C4—432no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—868no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—868no—
726C2×C4—868no—
727C2×C4—862no—
728C2×C4—3444no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1728no—
735C2×C4C22⋊C4×D4312yes—
736C2×C4#1306328714yes—
737C2×C4C4×D17214yes—
738C2×C4#1306329514yes—
739C2×C4#1306329812yes—
740C2×C4#1306330012yes—
741C2×C4#1306331014yes—
742C2×C4C22×C4×D4311yescharacteristic
743C2×C4C2×D4×D4311yescharacteristic
744C2×C4C2×D4×D4311yescharacteristic
745C2×C4C22×D17211yescharacteristic
746C2×C4C2×#1062189811yescharacteristic
747C2×C4C2×#1062190211yescharacteristic
748C8—24no—
749C8—864no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—434no—
757C22—862no—
758C22—862no—
759C22—862no—
760C22—862no—
761C22—862no—
762C22—862no—
763C22—862no—
764C22—862no—
765C22—862no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22—3441no—
770C22—17216no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22#1458277714yes—
779C22C2×C22⋊C4×D4311yescharacteristic
780C22C2×#1306329811yescharacteristic
781C22C2×#1306330011yescharacteristic
782C22AGL(1,ℤ/8)×D4311yescharacteristic
783C22#137×D4311yescharacteristic
784C22#1458369511yescharacteristic
785C22#1458369811yescharacteristic
786C4—42no—
787C4—42no—
788C4—82no—
789C4—862no—
790C4—862no—
791C4—3442no—
792C4—1722no—
793C4#1458277714yes—
794C4C2×#1306328711yescharacteristic
795C4C2×C4×D17211yescharacteristic
796C4C2×#1306329511yescharacteristic
797C4C2×#1306331011yescharacteristic
798C2—24no—
799C2—864no—
800C2—3442no—
801C2—1722no—
802C2C2×#1458277711yescharacteristic
803C2#417×D4311yescharacteristic
804C2#1914311111yescharacteristic
805C2#1914421211yescharacteristic
806C2#1914421511yescharacteristic
807C2#1914422311yescharacteristic
808C2#1914422611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20971
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
1. C22×M16×D43C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582898C2semidirect
5. C2×#14582756C2semidirect
6. #19135032C2semidirect
7. #19135027C2semidirect
8. #19135022C2semidirect
9. #19135017C2semidirect
10. #19134316C2semidirect
11. C43×#1736C2semidirect
21. #14583411C4semidirect
34. C2×#13063250C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063247C22semidirect
37. C2×#13063245C22semidirect
43. #14582661C22semidirect
44. #14582661C22semidirect
48. C43×#340C22semidirect
49. C43×#340C22semidirect
77. C2×#10621877D4semidirect
89. #13063305C2×C4semidirect
90. #13063305C2×C4semidirect
93. #13063300C2×C4semidirect
94. #13063300C2×C4semidirect
121. C2×M16×C43D4semidirect
381. C2×D43#417semidirect
404. #1736D43semidirect
452. #340C2×D43semidirect
453. #340C2×D43semidirect
454. C43#20971semidirect
491. C2×M16D172semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D432
C2×#145834112
C2×#145829012
C2×#145828982
C2×#145827562
#191350322
#191350272
#191350222
#191350172
#191343162
C43×#17362
#2097143