Finite Group Databasebeta

← #25106583

Subgroups — #25106583

Order 11008.

1142 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583503C211yesmaximal, characteristic
2C2×#14582924C211yesmaximal, characteristic, complemented
3#19137200C211yesmaximal, characteristic, complemented
4#19135552C211yesmaximal, characteristic, complemented
5#19135550C211yesmaximal, characteristic, complemented
6#19135523C211yesmaximal, characteristic, complemented
7#19135030C211yesmaximal, characteristic, complemented
8#19135030C211yesmaximal, characteristic, complemented
9#19135020C211yesmaximal, characteristic, complemented
10#19135020C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#1982C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583503—24no—
19#14583503C418yescomplemented
20C2×#13063317C2211yescharacteristic
21C2×#13063306—21no—
22C2×#13063306—21no—
23C2×#13063297—21no—
24C2×#13063297—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063296C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C2×#13063282C2211yescharacteristic
30#14582924—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×Dic43⋊C8C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38#14582790—21no—
39#14582788—21no—
40#14582783—21no—
41#14582781—21no—
42#14582768C2211yescharacteristic
43#14582764C2211yescharacteristic
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#127×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C4×D43C2311yescharacteristic
67C2×#10621872—22no—
68C2×#10621872—41no—
69C2×#10621872—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C2×C8×D43—22no—
73C2×C8×D43—41no—
74C2×C8×D43—41no—
75#13063317—22no—
76#13063317C2×C414yes—
77#13063306—28no—
78#13063306—28no—
79#13063297—28no—
80#13063297—28no—
81#13063296—22no—
82#13063296—22no—
83#13063296C2×C414yes—
84#13063296C2×C414yes—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43C2×C414yes—
88D4×Dic43C2×C414yes—
89#13063282C2×C414yes—
90#13063282D414yes—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C2×Dic43⋊C4D411yescharacteristic
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C4⋊(C43⋊C8)—22no—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114#13063246—41no—
115#13063246—41no—
116#13063246—41no—
117#13063246—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43—21no—
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#127×C43—22no—
130#127×C43C2×C414yes—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136#102×C43—41no—
137#102×C43—41no—
138#102×C43—41no—
139#102×C43—41no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C23×D43C2×D411yescharacteristic
144C2×D4×C43—24no—
145C2×D4×C43—24no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—81no—
157C2×D4×C43—81no—
158C2×D4×C43—81no—
159C2×D4×C43—81no—
160C2×D4×C43C22×C412yes—
161C2×D4×C43C22×C412yes—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—81no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C2×C22⋊D43—81no—
173C22×Dic43—24no—
174C22×Dic43—24no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—81no—
180C22×Dic43—81no—
181C22×Dic43—81no—
182C22×Dic43—81no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43C22×C412yes—
191C2×C4×D43C2×D412yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C42×C43—81no—
203C42×C43C22×C412yes—
204C42×C43C2×D412yes—
205C22⋊Dic43—24no—
206C22⋊Dic43—24no—
207C22⋊Dic43—24no—
208C22⋊Dic43—24no—
209(C2×D43)⋊C4—81no—
210(C2×D43)⋊C4—81no—
211(C2×D43)⋊C4C22⋊C414yes—
212(C2×D43)⋊C4C22⋊C414yes—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22×C412yes—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—24no—
222Dic43⋊C4—24no—
223Dic43⋊C4—81no—
224Dic43⋊C4—81no—
225Dic43⋊C4C22⋊C414yes—
226Dic43⋊C4C22⋊C414yes—
227C4×Dic43—81no—
228C4×Dic43C22×C412yes—
229C4×Dic43C2×D412yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236#10621872—44no—
237C8×D43—44no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43C2×C22⋊C412yes—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—22no—
264D4×C43—41no—
265D4×C43—41no—
266D4×C43—41no—
267D4×C43—41no—
268D4×C43—84no—
269D4×C43—84no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C22⋊D43—84no—
289C22⋊D43—84no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—84no—
309C2×Dic43—84no—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C2×C22⋊C412yes—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C8×C43—41no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#21897—431nomaximal, Sylow
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—81no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43C22×C22⋊C411yescharacteristic
337C22×C43#53711yescharacteristic
338C22×C43#53711yescharacteristic
339C22×C43#57611yescharacteristic
340C22×C43#57611yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57711yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43#52011yescharacteristic
355C4×C43#52011yescharacteristic
356C4×C43#53511yescharacteristic
357C4×C43#53611yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—22no—
361Dic43—42no—
362Dic43—42no—
363Dic43—81no—
364Dic43—81no—
365C2×#540—431no—
366C2×#424—431no—
367#2314—431no—
368#1989—431no—
369#1989—431no—
370#1982—431no—
371#1982D4311yescharacteristic, complemented
372#1895—431no—
373#1895—431no—
374#1893—431no—
375#1893—431no—
376#1804—431no—
377#1804—431no—
378#1802—431no—
379#1802—431no—
380C2×C43—82no—
381C2×C43—82no—
382C2×C43#231111yescharacteristic
383C2×C43#289711yescharacteristic
384C2×C43#289711yescharacteristic
385C2×C43#325711yescharacteristic
386C2×C43#325711yescharacteristic
387C2×C43#325911yescharacteristic
388C2×C43#326011yescharacteristic
389D43—42no—
390C22×M16—431no—
391C23×C8—431no—
392#540—438no—
393#540—864no—
394C2×#127C2×D4311yescharacteristic
395C2×#125—431no—
396C2×#123—861no—
397C2×#123—861no—
398C2×#121—431no—
399C2×#121—431no—
400C2×#121—861no—
401C2×#121—861no—
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×#117—431no—
405#424—864no—
406C2×C4⋊C8—431no—
407C2×C4⋊C8—431no—
408C2×C4⋊C8—431no—
409C2×C4⋊C8C2×D4311yescharacteristic
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102C2×D4311yescharacteristic
415C2×#102C2×D4311yescharacteristic
416C2×#102C2×D4311yescharacteristic
417C2×#102C2×D4311yescharacteristic
418#388—861no—
419#388—861no—
420#387—861no—
421#387—861no—
422#384—431no—
423#382—431no—
424#380—431no—
425#380—431no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4C2×D4311yescharacteristic
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436C43#2189711yescharacteristic, complemented, Sylow
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—861no—
440C22×D4—861no—
441C22×D4C22×D4311yescharacteristic
442C22×D4C22×D4311yescharacteristic
443C23×C4—431no—
444C23×C4—861no—
445C23×C4—861no—
446C2×M16—862no—
447C2×M16—1721no—
448C2×M16—1721no—
449C22×C8—431no—
450C22×C8—431no—
451C22×C8—862no—
452C22×C8—1721no—
453C22×C8—1721no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#127—22no—
457#127C4×D4314yes—
458#125—434no—
459#125—862no—
460#123—868no—
461#123—868no—
462#121—434no—
463#121—434no—
464#121—868no—
465#121—868no—
466#121—862no—
467#121—862no—
468C4×D4—434no—
469C4×D4—434no—
470C4×D4—862no—
471C4×D4—862no—
472#117—434no—
473#117—434no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—431no—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C42—21no—
495C2×C42—431no—
496C2×C42—861no—
497C2×C42C22×D4311yescharacteristic
498C4⋊C8—22no—
499C4⋊C8—862no—
500C4⋊C8—862no—
501C4⋊C8—862no—
502#102—41no—
503#102—41no—
504#102—41no—
505#102—41no—
506#102—1721no—
507#102—1721no—
508#102—1721no—
509#102—1721no—
510#95—21no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—21no—
518C24—431no—
519C2×D4—24no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—864no—
536C2×D4—864no—
537C2×D4—3441no—
538C2×D4—3441no—
539C2×D4—3441no—
540C2×D4—3441no—
541C2×D4C2×C4×D4312yes—
542C2×D4C2×C4×D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—864no—
551C22×C4—864no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—3441no—
561C22×C4—3441no—
562C22×C4—3441no—
563C22×C4—3441no—
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4311yescharacteristic
566C22×C4C23×D4311yescharacteristic
567M16—1724no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—1724no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—434no—
586C4⋊C4—434no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—864no—
590C4⋊C4—864no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—3441no—
598C4⋊C4—3441no—
599C22⋊C4—434no—
600C22⋊C4—434no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C42—81no—
608C42—432no—
609C42—432no—
610C42—3441no—
611C42C2×C4×D4312yes—
612C42D4×D4312yes—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—432no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23C2×D4×D4311yescharacteristic
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—84no—
644D4—84no—
645D4—3444no—
646D4—3444no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—3444no—
673C2×C4—3444no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4C22⋊C4×D4312yes—
685C2×C4C22⋊C4×D4312yes—
686C2×C4C22×C4×D4311yescharacteristic
687C2×C4C2×D4×D4311yescharacteristic
688C2×C4#1306337011yescharacteristic
689C2×C4#1306337011yescharacteristic
690C2×C4#1306337211yescharacteristic
691C2×C4#1306337211yescharacteristic
692C8—41no—
693C8—41no—
694C8—1721no—
695C8—1721no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—1721no—
714C22—1721no—
715C22—1721no—
716C22—1721no—
717C22C2×C22⋊C4×D4311yescharacteristic
718C22#1458347811yescharacteristic
719C22#1458347811yescharacteristic
720C22#1458370011yescharacteristic
721C22#1458370311yescharacteristic
722C22#1458370511yescharacteristic
723C22#1458370911yescharacteristic
724C4—22no—
725C4—22no—
726C4—81no—
727C4—81no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—3441no—
732C4—3441no—
733C4—1722no—
734C4—1722no—
735C4#1458337811yescharacteristic
736C4#1458337811yescharacteristic
737C4#1458346211yescharacteristic
738C4#1458346911yescharacteristic
739C2—82no—
740C2—82no—
741C2—1722no—
742C2#1913718511yescharacteristic
743C2#1914311611yescharacteristic
744C2#1914312011yescharacteristic
745C2#1914600211yescharacteristic
746C2#1914600411yescharacteristic
747C2#1914603211yescharacteristic
748C2#1914603911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1982C2
socleC23×C43C22×D4
prime radicalC2×#14583503C2
cosocleC22×C4×C43C24
hypercenter#1982D43
hypocenterC43#21897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#14582924C2semidirect
3. #19137200C2semidirect
4. #19135552C2semidirect
5. #19135550C2semidirect
6. #19135523C2semidirect
7. #19135030C2semidirect
8. #19135030C2semidirect
9. #19135020C2semidirect
10. #19135020C2semidirect
11. #19134603C2semidirect
12. #19134603C2semidirect
13. #19134593C2semidirect
14. #19134593C2semidirect
15. C43×#1982C2semidirect
19. #14583503C4semidirect
371. #1982D43semidirect
436. C43#21897semidirect

Maximal subgroups

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

subgroupindex
C2×#145835032
C2×#145829242
#191372002
#191355522
#191355502
#191355232
#191350302
#191350202
#191346032
#191345932
C43×#19822
#2189743