Finite Group Databasebeta

← #25097812

Subgroups — #25097812

Order 11008.

1986 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C22×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
5#19134914C212yesmaximal, complemented
6#19134909C212yesmaximal, complemented
7#19134904C212yesmaximal, complemented
8#19134899C212yesmaximal, complemented
9#19134312C211yesmaximal, characteristic, complemented
10#19134311C211yesmaximal, characteristic, complemented
11C2×C43×#416C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14#14583406—24no—
15#14583406C418yescomplemented
16C2×#13063306—21no—
17C2×#13063301C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×#13063293—21no—
22C2×C4×C22⋊D43—21no—
23C2×C4×C22⋊D43—21no—
24C2×#13063284C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26C2×#13063283C2212yes—
27C2×#13063282—21no—
28C2×#13063281—21no—
29#117×D43—24no—
30#117×D43—24no—
31C2×C4⋊C4×D43C2212yes—
32C2×C22⋊C4×D43—21no—
33C2×C42×D43—21no—
34#14582895—24no—
35C2×#13063249C2212yescomplemented
36C2×#13063246C2212yescomplemented
37C2×(C2×D43)⋊C8—24no—
38C2×(C2×D43)⋊C8C2212yes—
39C2×(C2×D43)⋊C8C2212yes—
40#14582662C2212yescomplemented
41#14582662C2212yescomplemented
42#14582661C2212yescomplemented
43#14582661C2212yescomplemented
44C22×#41×C43C2211yescharacteristic
45C23×C8×C43C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C43×#416—24no—
48C2×#103×C43C2212yescomplemented
49C2×#102×C43C2212yescomplemented
50C24×D43D411yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C23×Dic43D411yescharacteristic
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D414yes—
63C22×C4×D43C2311yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C22×C43⋊C8—22no—
66C22×C43⋊C8—22no—
67C22×C43⋊C8—22no—
68C22×C43⋊C8C2312yes—
69#13063306—28no—
70#13063301—22no—
71#13063301—22no—
72#13063301C2×C414yes—
73#13063301C2×C414yescomplemented
74#13063296—22no—
75#13063296—22no—
76#13063296C2×C414yes—
77#13063296C2×C414yescomplemented
78#13063293—28no—
79C4×C22⋊D43—28no—
80C4×C22⋊D43—28no—
81#13063284—22no—
82#13063284—22no—
83#13063284C2×C414yescomplemented
84#13063284D414yescomplemented
85#13063283—24no—
86#13063283—24no—
87#13063282—28no—
88#13063281—28no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2312yes—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C4⋊C4×D43—24no—
96C4⋊C4×D43—24no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—22no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C22⋊C4×D43—28no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C42×D43—28no—
109#13063249—24no—
110#13063246—24no—
111(C2×D43)⋊C8—24no—
112(C2×D43)⋊C8—24no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—22no—
116C2×#41×C43—22no—
117C2×#41×C43—22no—
118C2×#41×C43C2×C414yescomplemented
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43—21no—
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124C22×C8×C43—22no—
125C22×C8×C43—22no—
126C22×C8×C43—22no—
127C22×C8×C43C2312yes—
128#117×C43—22no—
129#117×C43D414yescomplemented
130C2×C4⋊C4×C43C2312yes—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133#103×C43—24no—
134#102×C43—24no—
135C24×C43—21no—
136C24×C43C2×D411yescharacteristic
137C23×D43—22no—
138C23×D43—22no—
139C23×D43—24no—
140C23×D43—42no—
141C23×D43C22⋊C414yes—
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144#41×C43—28no—
145#41×C43—28no—
146#41×C43—44no—
147#41×C43—44no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43C22×C412yes—
154C2×D4×C43—21no—
155C2×D4×C43—24no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43C22×C412yes—
163C22×C4×C43—24no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—42no—
167C22×C4×C43—42no—
168C22×C4×C43C22×C412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43#4112yes—
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—44no—
179C2×C22⋊D43—44no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43C22⋊C414yes—
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C2×C4×D43—28no—
189C2×C4×D43—28no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—28no—
193C2×C4×D43—28no—
194C2×C4×D43—22no—
195C2×C4×D43—22no—
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—21no—
204C2×C4×D43—28no—
205C2×C4×D43—44no—
206C2×C4×D43—44no—
207C2×C4×D43C22⋊C414yes—
208C2×C4×D43C22⋊C414yes—
209C2×C4×D43C22×C412yes—
210C2×C4×D43C22×C412yes—
211C2×C4×D43C2×D412yes—
212C2×C4×D43C2×D412yes—
213C2×C8×C43—22no—
214C2×C8×C43—22no—
215C2×C8×C43—22no—
216C2×C8×C43—44no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43C2×D414yes—
219C22⋊C4×C43—24no—
220C42×C43—24no—
221C22⋊Dic43—24no—
222C22⋊Dic43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—24no—
225(C2×D43)⋊C4—28no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—24no—
228C4⋊Dic43—22no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C2×D414yes—
234Dic43⋊C4—28no—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237C4×Dic43—28no—
238C4×Dic43—24no—
239C4×Dic43—24no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8—22no—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—44no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43C2×C22⋊C412yes—
252C23×C43#12012yes—
253C23×C43#12312yes—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—22no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—28no—
263C22×D43—28no—
264C22×D43—44no—
265C22×D43—48no—
266C22×D43—48no—
267C22×D43C2×C22⋊C412yes—
268C22×D43C2×C22⋊C412yes—
269C22×D43#13514yes—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43—41no—
273Q8×C43—41no—
274D4×C43—22no—
275D4×C43—22no—
276D4×C43—48no—
277D4×C43—41no—
278D4×C43—41no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—48no—
286C2×C4×C43C2×C22⋊C412yes—
287C2×C4×C43C4×D414yes—
288C2×C4×C43C4×D414yes—
289C2×C4×C43#12012yes—
290C2×C4×C43#12114yes—
291C2×C4×C43#12114yes—
292C2×C4×C43#12312yes—
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C22⋊D43—48no—
300C22⋊D43—48no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—28no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—24no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43C2×C22⋊C412yes—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—28no—
324C4×D43—28no—
325C4×D43—416no—
326C8×C43—42no—
327C43⋊C8—42no—
328#20908—431nomaximal, Sylow
329C22×C43—24no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—24no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—82no—
337C22×C43—82no—
338C22×C43#38614yes—
339C22×C43C22×C22⋊C411yescharacteristic
340C22×C43C2×#12011yescharacteristic
341C22×C43C2×#12311yescharacteristic
342C22×C43C2×#13512yes—
343C22×C43#57512yes—
344C2×D43—24no—
345C2×D43—22no—
346C2×D43—24no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—416no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43#41614yescomplemented
355C4×C43—44no—
356C4×C43—42no—
357C4×C43#38614yes—
358C4×C43C2×C4×D411yescharacteristic
359C4×C43C2×C4×D411yescharacteristic
360C4×C43C2×#12111yescharacteristic
361C4×C43C2×#12111yescharacteristic
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366Dic43—44no—
367C2×#525—431no—
368C22×#117—431no—
369C2×#416—431no—
370C2×#416D4311yescharacteristic, complemented
371C22×C22⋊C8—431no—
372#1875—432no—
373#1874—432no—
374#1873—432no—
375#1872—432no—
376#1735—431no—
377#1735—431no—
378C2×C43—24no—
379C2×C43—82no—
380C2×C43C2×#38611yescharacteristic
381C2×C43C2×#41611yescharacteristic
382C2×C43#289611yescharacteristic
383C2×C43#300212yes—
384C2×C43#309112yes—
385D43—24no—
386D43—42no—
387C22×#41C2×D4311yescharacteristic
388C24×C4—431no—
389C23×C8—431no—
390C23×C8C2×D4311yescharacteristic
391#525—438no—
392#525—864no—
393C2×#123—861no—
394C2×C22⋊Q8—431no—
395C2×C22⋊Q8—431no—
396C2×#121—431no—
397C2×#121—431no—
398C2×#120—861no—
399C2×C4×D4—861no—
400C2×C4×D4—861no—
401C2×#117—431no—
402C2×#117—431no—
403C2×#117—432no—
404C2×#117—861no—
405C2×#117—861no—
406C2×#117—864no—
407C2×#117—864no—
408C2×#117C2×D4311yescharacteristic
409C22×C4⋊C4—432no—
410C22×C22⋊C4—861no—
411C22×C42—861no—
412#416—24no—
413#416—864no—
414C2×#103—432no—
415C2×#103C2×D4312yescomplemented
416C2×#102—432no—
417C2×#102C2×D4312yescomplemented
418C2×C22⋊C8—432no—
419C2×C22⋊C8—432no—
420C2×C22⋊C8—864no—
421#340—432no—
422#340—432no—
423#340—432no—
424#340—432no—
425C43#2090811yescharacteristic, complemented, Sylow
426C25—431no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41—22no—
431C2×#41—22no—
432C2×#41C4×D4314yescomplemented
433C22×Q8C22×D4311yescharacteristic
434C22×D4—21no—
435C22×D4—861no—
436C22×D4—861no—
437C22×D4C22×D4311yescharacteristic
438C23×C4—21no—
439C23×C4—431no—
440C23×C4—434no—
441C23×C4—434no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—862no—
447C23×C4—862no—
448C23×C4—862no—
449C23×C4—862no—
450C23×C4—862no—
451C23×C4C22×D4311yescharacteristic
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8—432no—
456C22×C8—862no—
457C22×C8—862no—
458C22×C8—862no—
459C22×C8C22×D4312yes—
460#123—868no—
461C22⋊Q8—434no—
462C22⋊Q8—434no—
463C22⋊Q8—862no—
464C22⋊Q8—862no—
465#121—434no—
466#121—434no—
467#121—862no—
468#121—862no—
469#120—868no—
470C4×D4—868no—
471C4×D4—868no—
472#117—22no—
473#117—434no—
474#117—434no—
475#117—868no—
476#117—868no—
477#117—864no—
478#117—862no—
479#117—862no—
480#117—864no—
481#117C22⋊D4314yescomplemented
482C2×C4⋊C4—432no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—864no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—864no—
490C2×C4⋊C4C22×D4312yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—868no—
493C2×C22⋊C4—862no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C42—21no—
501C2×C42—868no—
502C2×C42—862no—
503C2×C42—861no—
504C2×C42—861no—
505#103—24no—
506#103—864no—
507#102—24no—
508#102—864no—
509C22⋊C8—864no—
510C22⋊C8—864no—
511C24—21no—
512C24—431no—
513C24—431no—
514C24—434no—
515C24—864no—
516C24—862no—
517C24—862no—
518C24—1722no—
519C24D4×D4311yescharacteristic
520#41—28no—
521#41—28no—
522#41—44no—
523#41—44no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8C2×C4×D4312yes—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—864no—
539C2×D4—864no—
540C2×D4—1724no—
541C2×D4—1724no—
542C2×D4C2×C4×D4312yes—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—434no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—434no—
552C22×C4—434no—
553C22×C4—432no—
554C22×C4—432no—
555C22×C4—432no—
556C22×C4—432no—
557C22×C4—868no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—868no—
561C22×C4—868no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—868no—
565C22×C4—868no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—862no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—1724no—
580C22×C4—1724no—
581C22×C4C2×C4×D4312yes—
582C22×C4#1062189812yes—
583C22×C4D4×D4312yes—
584C22×C4D4×D4312yes—
585C22×C4D4×D4311yescharacteristic
586C22×C4#1062190012yes—
587C22×C4C2×C22⋊D4312yes—
588C22×C4C23×D4311yescharacteristic
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—44no—
593C2×C8—862no—
594C2×C8—862no—
595C2×C8—862no—
596C2×C8—1724no—
597C4⋊C4—22no—
598C4⋊C4—432no—
599C4⋊C4—432no—
600C4⋊C4—434no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—868no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—862no—
607C4⋊C4C2×C22⋊D4314yes—
608C22⋊C4—24no—
609C22⋊C4—864no—
610C22⋊C4—864no—
611C22⋊C4—868no—
612C22⋊C4—864no—
613C22⋊C4—864no—
614C22⋊C4—864no—
615C22⋊C4—864no—
616C42—24no—
617C42—868no—
618C42—864no—
619C42—864no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—432no—
628C23—434no—
629C23—432no—
630C23—868no—
631C23—861no—
632C23—861no—
633C23—862no—
634C23—861no—
635C23—861no—
636C23—862no—
637C23—862no—
638C23—868no—
639C23—1724no—
640C23—1728no—
641C23—1728no—
642C23C22⋊C4×D4312yes—
643C23#1306329312yes—
644C23#1306330712yes—
645C23C2×D4×D4311yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—41no—
649Q8—41no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—41no—
654D4—41no—
655D4—1728no—
656D4—1728no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—48no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—868no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—868no—
680C2×C4—868no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—864no—
684C2×C4—17216no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4C22⋊C4×D4312yes—
690C2×C4(C22⋊D43)⋊C414yes—
691C2×C4C4×C22⋊D4314yes—
692C2×C4#1306329312yes—
693C2×C4#1306329614yes—
694C2×C4#1306329814yes—
695C2×C4#1306330712yes—
696C2×C4C22×C4×D4311yescharacteristic
697C2×C4C2×D4×D4311yescharacteristic
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C22×C22⋊D4311yescharacteristic
700C2×C4C2×#1062190011yescharacteristic
701C2×C4C2×#1062189811yescharacteristic
702C8—42no—
703C8—1722no—
704C22—24no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—82no—
712C22—82no—
713C22—434no—
714C22—864no—
715C22—864no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—17216no—
722C22—1722no—
723C22—1722no—
724C22#1458277514yes—
725C22C2×C22⋊C4×D4311yescharacteristic
726C22C2×#1306329311yescharacteristic
727C22C2×#1306330711yescharacteristic
728C22#135×D4312yes—
729C22#1458369612yes—
730C4—44no—
731C4—42no—
732C4—862no—
733C4—862no—
734C4—1724no—
735C4—1722no—
736C4—1722no—
737C4#1458277514yes—
738C4C2×(C22⋊D43)⋊C411yescharacteristic
739C4C2×C4×C22⋊D4311yescharacteristic
740C4C2×#1306329611yescharacteristic
741C4C2×#1306329811yescharacteristic
742C2—24no—
743C2—82no—
744C2—864no—
745C2—1722no—
746C2C2×#1458277511yescharacteristic
747C2#416×D4311yescharacteristic
748C2#1914311011yescharacteristic
749C2#1914380912yes—
750C2#1914450612yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
cosocleC22×C4×C43C24
hypercenterC2×#416D43
hypocenterC43#20908
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. C2×#14582895C2semidirect
4. C22×(C2×D43)⋊C8C2semidirect
5. #19134914C2semidirect
6. #19134909C2semidirect
7. #19134904C2semidirect
8. #19134899C2semidirect
9. #19134312C2semidirect
10. #19134311C2semidirect
11. C2×C43×#416C2semidirect
15. #14583406C4semidirect
35. C2×#13063249C22semidirect
36. C2×#13063246C22semidirect
40. #14582662C22semidirect
41. #14582662C22semidirect
42. #14582661C22semidirect
43. #14582661C22semidirect
48. C2×#103×C43C22semidirect
49. C2×#102×C43C22semidirect
73. #13063301C2×C4semidirect
77. #13063296C2×C4semidirect
83. #13063284C2×C4semidirect
84. #13063284D4semidirect
118. C2×#41×C43C2×C4semidirect
129. #117×C43D4semidirect
354. C2×D43#416semidirect
370. C2×#416D43semidirect
415. C2×#103C2×D43semidirect
417. C2×#102C2×D43semidirect
425. C43#20908semidirect
432. C2×#41C4×D43semidirect
481. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#117×D432
C2×#145828952
C22×(C2×D43)⋊C82
#191349142
#191349092
#191349042
#191348992
#191343122
#191343112
C2×C43×#4162
#2090843