Finite Group Databasebeta

← D43×#1826 #25096421

Subgroups — D43×#1826 #25096421

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2#407×D43C211yesmaximal, characteristic
3C4×C22⋊C4×D43C211yesmaximal, characteristic
4#19134695C211yesmaximal, characteristic, complemented
5#19134694C211yesmaximal, characteristic, complemented
6#19134693C214yesmaximal, complemented
7#19134692C211yesmaximal, characteristic, complemented
8#339×D43C214yesmaximal, complemented
9C43×#1826C211yesmaximal, characteristic, complemented
10C23×C4×D43C2211yescharacteristic
11C2×M16×D43C2212yes—
12C2×#13063284C2211yescharacteristic
13C2×#13063283C411yescharacteristic, complemented
14C2×#13063283C411yescharacteristic, complemented
15C2×#13063282—21no—
16C2×#13063281—21no—
17#117×D43—21no—
18#117×D43—21no—
19#117×D43—21no—
20#117×D43—21no—
21#117×D43C412yescomplemented
22#117×D43C412yescomplemented
23#117×D43C2212yes—
24#117×D43C2212yes—
25C2×C4⋊C4×D43C411yescharacteristic, complemented
26C2×C4⋊C4×D43C411yescharacteristic, complemented
27C2×C22⋊C4×D43—21no—
28C2×C22⋊C4×D43—21no—
29C2×C42×D43—21no—
30C2×C42×D43C2212yes—
31#14582863C2211yescharacteristic
32#14582862C2212yes—
33#14582861—21no—
34#14582861—21no—
35C22⋊C8×D43—21no—
36C22⋊C8×D43—21no—
37C22⋊C4×Dic43—21no—
38C4×(C2×D43)⋊C4C2212yes—
39C4×C22⋊Dic43C2211yescharacteristic
40#14582746—21no—
41#95×D43—21no—
42#14582660C2214yescomplemented
43#14582659C2214yescomplemented
44#14582658C2214yescomplemented
45C2×#117×C43C2211yescharacteristic
46C43×#407C2211yescharacteristic
47C4×C22⋊C4×C43C2211yescharacteristic
48C43×#339C2214yescomplemented
49C24×D43D411yescharacteristic
50C23×Dic43D411yescharacteristic
51C22×C4×D43—28no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—22no—
55C22×C4×D43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C411yescharacteristic
59C22×C4×D43D411yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43C2311yescharacteristic
66C22×C4×D43C2311yescharacteristic
67C2×#10621877C2312yes—
68C2×#10621872—22no—
69M16×D43—28no—
70C2×C8×D43—22no—
71#13063284—21no—
72#13063284—21no—
73#13063284C2×C412yescomplemented
74#13063284C2312yes—
75#13063283—21no—
76#13063283—21no—
77#13063283—21no—
78#13063283—21no—
79#13063283C2×C412yes—
80#13063283C2×C412yes—
81#13063283C2×C412yescomplemented
82#13063283C2×C412yescomplemented
83#13063282—22no—
84#13063282—22no—
85#13063282—22no—
86#13063282—22no—
87#13063281—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43C2×C411yescharacteristic, complemented
92C2×C4⋊Dic43C2×C411yescharacteristic, complemented
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43—21no—
99C4⋊C4×D43C2×C412yes—
100C4⋊C4×D43C2×C412yes—
101C4⋊C4×D43C2×C412yescomplemented
102C4⋊C4×D43C2×C412yescomplemented
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—22no—
108C22⋊C4×D43—28no—
109C22⋊C4×D43—22no—
110C22⋊C4×D43—22no—
111C22⋊C4×D43—22no—
112C22⋊C4×D43—22no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116C2×C4×Dic43—22no—
117C2×C4×Dic43C2312yes—
118C42×D43—22no—
119C42×D43—22no—
120C42×D43—22no—
121C42×D43—22no—
122C42×D43—28no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127C43⋊#95—21no—
128C43⋊#95—22no—
129C23×C4×C43C2311yescharacteristic
130C2×M16×C43C2312yes—
131#117×C43—21no—
132#117×C43—21no—
133#117×C43C2×C412yescomplemented
134#117×C43C2312yes—
135C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
136C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43C2312yes—
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143#95×C43—21no—
144C24×C43C2×D411yescharacteristic
145C23×D43—24no—
146C23×D43—24no—
147C23×D43—42no—
148C23×D43C22⋊C411yescharacteristic
149C23×D43C22⋊C411yescharacteristic
150C23×D43C22⋊C411yescharacteristic
151C23×D43C22⋊C411yescharacteristic
152C23×D43C2×D411yescharacteristic
153C23×D43C2×D411yescharacteristic
154C22×C4×C43—24no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—22no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C22×Dic43—24no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—22no—
168C22×Dic43C22⋊C411yescharacteristic
169C22×Dic43C22⋊C411yescharacteristic
170C22×Dic43C22⋊C411yescharacteristic
171C22×Dic43C22⋊C411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—24no—
177C2×C4×D43—24no—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—24no—
183C2×C4×D43—24no—
184C2×C4×D43—28no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—24no—
190C2×C4×D43—44no—
191C2×C4×D43—44no—
192C2×C4×D43—44no—
193C2×C4×D43—44no—
194C2×C4×D43C22⋊C411yescharacteristic
195C2×C4×D43C22⋊C411yescharacteristic
196C2×C4×D43C22⋊C411yescharacteristic
197C2×C4×D43C22⋊C411yescharacteristic
198C2×C4×D43C22⋊C411yescharacteristic
199C2×C4×D43C22⋊C411yescharacteristic
200C2×C4×D43C22⋊C411yescharacteristic
201C2×C4×D43C22⋊C411yescharacteristic
202C2×C4×D43C22×C411yescharacteristic
203C2×C4×D43C22×C411yescharacteristic
204C2×C4×D43C22×C411yescharacteristic
205C2×C4×D43C22×C411yescharacteristic
206C2×C4×D43C2×D411yescharacteristic
207C2×C4×D43C2×D411yescharacteristic
208C2×C4×D43C2×D411yescharacteristic
209C2×C4×D43C2×D411yescharacteristic
210C2×C4×D43#4118yes—
211M16×C43—24no—
212C2×C8×C43—22no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43C22×C412yes—
216C4⋊C4×C43C22×C412yes—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C42×C43—22no—
221C42×C43—22no—
222C42×C43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226(C2×D43)⋊C4—28no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C22×C412yes—
234C4⋊Dic43C22×C412yes—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—22no—
244C4×Dic43—22no—
245C4×Dic43—24no—
246C4×Dic43—44no—
247#10621877—24no—
248C2×C43⋊C8—22no—
249#10621872—44no—
250C8×D43—44no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—41no—
254C23×C43C2×C22⋊C411yescharacteristic
255C23×C43C2×C22⋊C411yescharacteristic
256C23×C43C22×D411yescharacteristic
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—22no—
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—416no—
274C22×D43#10414yes—
275C22×D43C2×C22⋊C411yescharacteristic
276C22×D43C2×C22⋊C411yescharacteristic
277C22×D43C2×C22⋊C411yescharacteristic
278C22×D43C2×C22⋊C411yescharacteristic
279C22×D43#12314yes—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43C2×C22⋊C411yescharacteristic
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4114yes—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—24no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43C2×C22⋊C411yescharacteristic
310C2×Dic43C2×C22⋊C411yescharacteristic
311C2×Dic43C2×C22⋊C411yescharacteristic
312C2×Dic43C2×C22⋊C411yescharacteristic
313C2×Dic43#12314yes—
314C4×D43—22no—
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—22no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—416no—
327C4×D43—44no—
328C4×D43—44no—
329C4×D43—44no—
330C4×D43—44no—
331C4×D43#11714yes—
332C4×D43#11714yes—
333C4×D43#12314yes—
334C4×D43#12314yes—
335C8×C43—42no—
336C43⋊C8—42no—
337C2×#1826—431nomaximal, Sylow
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—44no—
346C22×C43C2×#10412yes—
347C22×C43C22×C22⋊C411yescharacteristic
348C22×C43C2×#12312yes—
349C2×D43—21no—
350C2×D43—21no—
351C2×D43—21no—
352C2×D43—21no—
353C2×D43—28no—
354C2×D43—28no—
355C2×D43—21no—
356C2×D43—21no—
357C2×D43—21no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43—44no—
361C2×D43—44no—
362C2×D43#38112yes—
363C2×D43#38112yes—
364C2×D43C2×#10412yes—
365C2×D43C2×#10412yes—
366C2×D43#42112yes—
367C4×C43—21no—
368C4×C43—21no—
369C4×C43—44no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43C2×#11712yes—
373C4×C43C2×#12312yes—
374Dic43—21no—
375Dic43—21no—
376Dic43—44no—
377Dic43—42no—
378Dic43—42no—
379Dic43#38112yes—
380Dic43#38112yes—
381C22×#117—431no—
382C2×#407—431no—
383C2×C4×C22⋊C4—431no—
384#1826—431no—
385#1826—431no—
386#1826—434no—
387#1826—431no—
388#1826D4311yescharacteristic, direct product factor
389C2×#339—434no—
390C2×C43—22no—
391C2×C43—22no—
392C2×C43—41no—
393C2×C43C2×#38111yescharacteristic
394C2×C43C22×#10411yescharacteristic
395C2×C43C2×#42111yescharacteristic
396D43—22no—
397D43—22no—
398D43—41no—
399D43#182614yesdirect product factor
400C24×C4—431no—
401C22×M16—432no—
402C2×#117—431no—
403C2×#117—432no—
404C2×#117—432no—
405C2×#117—432no—
406C2×#117—432no—
407C2×#117—431no—
408C2×#117—431no—
409C2×#117—861no—
410C2×#117—861no—
411C2×#117—861no—
412C2×#117—861no—
413C2×#117—861no—
414C2×#117—861no—
415C2×#117C2×D4311yescharacteristic
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418C22×C22⋊C4—861no—
419C22×C22⋊C4—861no—
420C22×C42—432no—
421C22×C42—861no—
422#407—431no—
423#407—432no—
424#407—861no—
425#407—861no—
426#407C2×D4311yescharacteristic
427C2×C22⋊C8—861no—
428C2×C22⋊C8—861no—
429C4×C22⋊C4—431no—
430C4×C22⋊C4—432no—
431C4×C22⋊C4—861no—
432C4×C22⋊C4—861no—
433C4×C22⋊C4C2×D4311yescharacteristic
434C2×#95—861no—
435#339—434no—
436#339—434no—
437#339—434no—
438#339C2×D4314yescomplemented
439C43C2×#182611yescharacteristic, complemented, Sylow
440C25—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—431no—
445C23×C4—431no—
446C23×C4—431no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—431no—
454C23×C4—868no—
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—862no—
458C23×C4C22×D4311yescharacteristic
459C2×M16—432no—
460C2×M16—862no—
461C2×M16—868no—
462C2×M16C22×D4312yes—
463C22×C8—862no—
464#117—21no—
465#117—21no—
466#117—432no—
467#117—432no—
468#117—432no—
469#117—432no—
470#117—432no—
471#117—432no—
472#117—862no—
473#117—862no—
474#117—862no—
475#117—862no—
476#117—862no—
477#117—862no—
478#117—862no—
479#117—862no—
480#117—861no—
481#117—861no—
482#117—861no—
483#117—861no—
484#117—861no—
485#117—861no—
486#117C4×D4312yescomplemented
487#117C22×D4312yes—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—432no—
491C2×C4⋊C4—432no—
492C2×C4⋊C4—432no—
493C2×C4⋊C4—432no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C4×D4311yescharacteristic, complemented
501C2×C4⋊C4C4×D4311yescharacteristic, complemented
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—862no—
505C2×C22⋊C4—862no—
506C2×C22⋊C4—862no—
507C2×C22⋊C4—862no—
508C2×C22⋊C4—868no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—21no—
515C2×C42—432no—
516C2×C42—862no—
517C2×C42—862no—
518C2×C42—862no—
519C2×C42—862no—
520C2×C42—868no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42—861no—
524C2×C42—862no—
525C2×C42C22×D4312yes—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—862no—
529C22⋊C8—862no—
530C22⋊C8—861no—
531C22⋊C8—861no—
532#95—21no—
533#95—862no—
534#95—861no—
535C24—431no—
536C24—431no—
537C24—431no—
538C24—431no—
539C24—431no—
540C24—431no—
541C24—864no—
542C24—864no—
543C24—1722no—
544C24D4×D4311yescharacteristic
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—438no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—864no—
573C22×C4—864no—
574C22×C4—864no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—862no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—868no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—862no—
592C22×C4—1724no—
593C22×C4—1724no—
594C22×C4—1724no—
595C22×C4—1724no—
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4D4×D4311yescharacteristic
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602M16—24no—
603M16—864no—
604M16—1724no—
605C2×C8—22no—
606C2×C8—862no—
607C2×C8—1724no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—862no—
613C4⋊C4—862no—
614C4⋊C4—862no—
615C4⋊C4—862no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4C2×C4×D4312yes—
619C4⋊C4C2×C4×D4312yes—
620C22⋊C4—24no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—862no—
624C22⋊C4—862no—
625C22⋊C4—862no—
626C22⋊C4—862no—
627C22⋊C4—868no—
628C22⋊C4—864no—
629C22⋊C4—862no—
630C22⋊C4—862no—
631C42—22no—
632C42—22no—
633C42—24no—
634C42—862no—
635C42—862no—
636C42—862no—
637C42—862no—
638C42—862no—
639C42—862no—
640C42—864no—
641C42—1724no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—431no—
646C23—431no—
647C23—431no—
648C23—434no—
649C23—434no—
650C23—431no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—862no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—862no—
662C23—862no—
663C23—862no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—17216no—
668C23C22⋊C4×D4311yescharacteristic
669C23C22⋊C4×D4311yescharacteristic
670C23C2×D4×D4311yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—431no—
684C2×C4—431no—
685C2×C4—434no—
686C2×C4—434no—
687C2×C4—434no—
688C2×C4—434no—
689C2×C4—434no—
690C2×C4—431no—
691C2×C4—431no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—864no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—1724no—
713C2×C4—1724no—
714C2×C4—1724no—
715C2×C4—17216no—
716C2×C4—1724no—
717C2×C4—1722no—
718C2×C4—1722no—
719C2×C4—1722no—
720C2×C4—1722no—
721C2×C4C22⋊C4×D4311yescharacteristic
722C2×C4C22⋊C4×D4311yescharacteristic
723C2×C4C22×C4×D4311yescharacteristic
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4#41×D4314yes—
726C8—42no—
727C8—1722no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—44no—
736C22—432no—
737C22—432no—
738C22—432no—
739C22—432no—
740C22—432no—
741C22—868no—
742C22—868no—
743C22—861no—
744C22—861no—
745C22—861no—
746C22—861no—
747C22—861no—
748C22—861no—
749C22—861no—
750C22—1724no—
751C22—1724no—
752C22—1724no—
753C22—1724no—
754C22#104×D4312yes—
755C22C2×C22⋊C4×D4311yescharacteristic
756C22#123×D4312yes—
757C4—21no—
758C4—21no—
759C4—44no—
760C4—42no—
761C4—42no—
762C4—432no—
763C4—432no—
764C4—861no—
765C4—861no—
766C4—1724no—
767C4—1722no—
768C4—1722no—
769C4#117×D4312yes—
770C4#123×D4312yes—
771C2—22no—
772C2—22no—
773C2—41no—
774C2—434no—
775C2—862no—
776C2—862no—
777C2—1721no—
778C2#381×D4311yescharacteristic
779C2C2×#104×D4311yescharacteristic
780C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1826C2
socleC22×C43C22×C22⋊C4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1826D43
hypocenterC43C2×#1826
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #19134695C2semidirect
5. #19134694C2semidirect
6. #19134693C2semidirect
7. #19134692C2semidirect
8. #339×D43C2semidirect
9. C43×#1826C2semidirect
13. C2×#13063283C4semidirect
14. C2×#13063283C4semidirect
21. #117×D43C4semidirect
22. #117×D43C4semidirect
25. C2×C4⋊C4×D43C4semidirect
26. C2×C4⋊C4×D43C4semidirect
42. #14582660C22semidirect
43. #14582659C22semidirect
44. #14582658C22semidirect
48. C43×#339C22semidirect
73. #13063284C2×C4semidirect
81. #13063283C2×C4semidirect
82. #13063283C2×C4semidirect
91. C2×C4⋊Dic43C2×C4semidirect
92. C2×C4⋊Dic43C2×C4semidirect
101. C4⋊C4×D43C2×C4semidirect
102. C4⋊C4×D43C2×C4semidirect
133. #117×C43C2×C4semidirect
135. C2×C4⋊C4×C43C2×C4semidirect
136. C2×C4⋊C4×C43C2×C4semidirect
388. #1826D43direct (N × H)
399. D43#1826direct (N × H)
438. #339C2×D43semidirect
439. C43C2×#1826semidirect
486. #117C4×D43semidirect
500. C2×C4⋊C4C4×D43semidirect
501. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
#407×D432
C4×C22⋊C4×D432
#191346952
#191346942
#191346932
#191346922
#339×D432
C43×#18262
C2×#182643