Finite Group Databasebeta

← #25106579

Subgroups — #25106579

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×#14583502C211yesmaximal, characteristic
2C2×#14582925C211yesmaximal, characteristic, complemented
3#19137202C211yesmaximal, characteristic, complemented
4#19135551C211yesmaximal, characteristic, complemented
5#19135549C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135520C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic, complemented
9#19135031C211yesmaximal, characteristic, complemented
10#19135023C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134603C211yesmaximal, characteristic, complemented
13#19134594C211yesmaximal, characteristic, complemented
14#19134593C211yesmaximal, characteristic, complemented
15C43×#1893C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17#14583502—24no—
18#14583502C418yescomplemented
19C2×#13063321C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063309—21no—
22C2×#13063307—21no—
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063296—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#14582925—24no—
30C2×Dic43⋊C8C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×Dic43⋊C8C2211yescharacteristic
33C2×Dic43⋊C8C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40#14582793—21no—
41#14582787—21no—
42#14582784—21no—
43#14582782—21no—
44#14582768C2211yescharacteristic
45#14582764C2211yescharacteristic
46#14582759C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C23×C8×C43C2211yescharacteristic
56C2×#121×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621877—22no—
69C2×#10621877—41no—
70C2×#10621877—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063321—22no—
74#13063321C2×C414yes—
75#13063316—22no—
76#13063316C2×C414yes—
77#13063309—28no—
78#13063307—28no—
79#13063299—22no—
80#13063299C2×C414yes—
81#13063297—28no—
82#13063296—28no—
83D4×Dic43—22no—
84D4×Dic43C2×C414yes—
85#13063287—22no—
86#13063287C2×C414yes—
87#13063284C2×C414yes—
88#13063284D414yes—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43D411yescharacteristic
91C2×C4⋊Dic43D411yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×C22⋊Dic43D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43C2311yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108Dic43⋊C8—22no—
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111Dic43⋊C8—22no—
112#13063247—41no—
113#13063247—41no—
114#13063246—41no—
115#13063246—41no—
116#13063245—41no—
117#13063245—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43—22no—
127C22×C8×C43—41no—
128C22×C8×C43—41no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#121×C43—22no—
132#121×C43C2×C414yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138#102×C43—41no—
139#102×C43—41no—
140#95×C43—21no—
141C24×C43—21no—
142C24×C43C2×D411yescharacteristic
143C23×D43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—24no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—81no—
151C2×D4×C43—81no—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C22×C412yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—24no—
166C2×C22⋊D43—24no—
167C2×C22⋊D43—81no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C2×C22⋊D43—81no—
171C2×C22⋊D43—81no—
172C2×C22⋊D43—81no—
173C22×Dic43—24no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—81no—
178C22×Dic43—81no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172C22×C412yes—
189C2×C4×D43—24no—
190C2×C4×D43—81no—
191C2×C4×D43—81no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—44no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43C22×C412yes—
205C22⋊C4×C43—24no—
206C22⋊C4×C43—81no—
207C22⋊Dic43—24no—
208C22⋊Dic43—81no—
209C22⋊Dic43C22⋊C414yes—
210C22⋊Dic43C22⋊C414yes—
211(C2×D43)⋊C4—24no—
212(C2×D43)⋊C4—24no—
213C4⋊Dic43—21no—
214C4⋊Dic43—24no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43C22⋊C414yes—
220C4⋊Dic43C22⋊C414yes—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—24no—
223Dic43⋊C4—81no—
224Dic43⋊C4—81no—
225C4×Dic43—81no—
226C4×Dic43—81no—
227C4×Dic43C22×C412yes—
228C4×Dic43C22×C412yes—
229C4×Dic43C2×D412yes—
230C4×Dic43C2×D412yes—
231#10621877—44no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C2×C22⋊C412yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—84no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
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×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C22⋊D43—84no—
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—21no—
297C2×Dic43—21no—
298C2×Dic43—22no—
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—84no—
308C2×Dic43C2×C22⋊C412yes—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312D172—22no—
313D172—22no—
314D172—41no—
315D172—41no—
316C4×D43—84no—
317C8×C43—41no—
318C8×C43—41no—
319C43⋊C8—41no—
320C43⋊C8—41no—
321#21897—431nomaximal, Sylow
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
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—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C2×D43—81no—
350C4×C43—22no—
351C4×C43—42no—
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—22no—
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#1982—431no—
372#1895—431no—
373#1895—431no—
374#1893—431no—
375#1893D4311yescharacteristic, complemented
376#1804—431no—
377#1804—431no—
378#1802—431no—
379#1802—431no—
380C2×C43—42no—
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—82no—
390C22×M16—431no—
391C23×C8C2×D4311yescharacteristic
392#540—438no—
393#540—864no—
394C2×#127—431no—
395C2×#125—431no—
396C2×#123—861no—
397C2×#123—861no—
398C2×#121—431no—
399C2×#121—861no—
400C2×#121—861no—
401C2×#121C2×D4311yescharacteristic
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⋊C8—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
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#380C2×D4311yescharacteristic
426C4×C4⋊C4—431no—
427C4×C4⋊C4—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340—431no—
434#340C2×D4311yescharacteristic
435#340C2×D4311yescharacteristic
436C43#2189711yescharacteristic, complemented, Sylow
437C22×D4—21no—
438C22×D4—431no—
439C22×D4—861no—
440C22×D4—861no—
441C22×D4—861no—
442C22×D4C22×D4311yescharacteristic
443C23×C4—861no—
444C23×C4—861no—
445C23×C4C22×D4311yescharacteristic
446C2×M16—862no—
447C2×M16—1721no—
448C2×M16—1721no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8—41no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#127—434no—
457#127—862no—
458#125—434no—
459#125—862no—
460#123—868no—
461#123—868no—
462#121—22no—
463#121—434no—
464#121—868no—
465#121—868no—
466#121—862no—
467#121C4×D4314yes—
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—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4C22×D4311yescharacteristic
484C2×C4⋊C4C22×D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C42—431no—
495C2×C42—431no—
496C2×C42—861no—
497C2×C42—861no—
498C4⋊C8—862no—
499C4⋊C8—862no—
500C4⋊C8—862no—
501C4⋊C8—862no—
502#102—41no—
503#102—41no—
504#102—1721no—
505#102—1721no—
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—861no—
518C24D4×D4311yescharacteristic
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—432no—
528C2×D4—864no—
529C2×D4—864no—
530C2×D4—864no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—3441no—
537C2×D4—3441no—
538C2×D4—3441no—
539C2×D4—3441no—
540C2×D4—3441no—
541C2×D4—3441no—
542C2×D4C2×C4×D4312yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—431no—
551C22×C4—431no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—864no—
555C22×C4—864no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—3441no—
560C22×C4—3441no—
561C22×C4—3441no—
562C22×C4—3441no—
563C22×C4C2×C4×D4312yes—
564C22×C4D4×D4311yescharacteristic
565C22×C4D4×D4312yes—
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—44no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—434no—
587C4⋊C4—434no—
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—3441no—
597C4⋊C4—3441no—
598C4⋊C4C2×C4×D4312yes—
599C22⋊C4—24no—
600C22⋊C4—81no—
601C22⋊C4—434no—
602C22⋊C4—434no—
603C22⋊C4—864no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—3441no—
607C42—432no—
608C42—432no—
609C42—432no—
610C42—432no—
611C42—3441no—
612C42—3441no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—862no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23C22⋊C4×D4312yes—
634C23C2×D4×D4311yescharacteristic
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—84no—
640D4—862no—
641D4—862no—
642D4—3444no—
643D4—3444no—
644D4—3444no—
645D4—1721no—
646D4—1721no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—432no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—862no—
675C2×C4—3444no—
676C2×C4—3444no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
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—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—3441no—
711C22—3441no—
712C22—3441no—
713C22—3441no—
714C22—1722no—
715C22—1722no—
716C22—1722no—
717C22C2×C22⋊C4×D4311yescharacteristic
718C22#1458347611yescharacteristic
719C22#1458347611yescharacteristic
720C22#1458370011yescharacteristic
721C22#1458370111yescharacteristic
722C22#1458370511yescharacteristic
723C22#1458370611yescharacteristic
724C4—22no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4—862no—
729C4—862no—
730C4—862no—
731C4—862no—
732C4—3441no—
733C4—3441no—
734C4—1722no—
735C4#1458337811yescharacteristic
736C4#1458337811yescharacteristic
737C4#1458346411yescharacteristic
738C4#1458347111yescharacteristic
739C2—42no—
740C2—82no—
741C2—3442no—
742C2#1913718211yescharacteristic
743C2#1914311611yescharacteristic
744C2#1914311711yescharacteristic
745C2#1914599911yescharacteristic
746C2#1914600911yescharacteristic
747C2#1914602911yescharacteristic
748C2#1914603511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583502C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#21897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#14582925C2semidirect
3. #19137202C2semidirect
4. #19135551C2semidirect
5. #19135549C2semidirect
6. #19135520C2semidirect
7. #19135520C2semidirect
8. #19135034C2semidirect
9. #19135031C2semidirect
10. #19135023C2semidirect
11. #19134604C2semidirect
12. #19134603C2semidirect
13. #19134594C2semidirect
14. #19134593C2semidirect
15. C43×#1893C2semidirect
18. #14583502C4semidirect
375. #1893D43semidirect
436. C43#21897semidirect

Maximal subgroups

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

subgroupindex
C2×#145835022
C2×#145829252
#191372022
#191355512
#191355492
#191355202
#191350342
#191350312
#191350232
#191346042
#191346032
#191345942
#191345932
C43×#18932
#2189743