Finite Group Databasebeta

← #25119005

Subgroups — #25119005

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583092C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3#19137657C211yesmaximal, characteristic, complemented
4#19137500C211yesmaximal, characteristic, complemented
5#19135417C211yesmaximal, characteristic, complemented
6#19135364C211yesmaximal, characteristic, complemented
7#19135292C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134853C211yesmaximal, characteristic, complemented
12#19134842C211yesmaximal, characteristic, complemented
13#19134471C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C2×C43×#442C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×D4×Dic43C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22#14583092C418yescomplemented
23#14582979—24no—
24C2×#13063258C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582799—21no—
37#14582797C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582778—21no—
40#14582775—21no—
41#14582772—21no—
42#14582771—21no—
43#14582764C2211yescharacteristic
44#14582757—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4C2211yescharacteristic
47C2×C43⋊#95—21no—
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4×D4×C43C2211yescharacteristic
57C43×#442—24no—
58C2×#106×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#97×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C23×Dic43—21no—
67C22×C4×D43—21no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063321—22no—
74#13063321C2×C414yescomplemented
75D4×Dic43—22no—
76D4×Dic43—22no—
77D4×Dic43—41no—
78D4×Dic43C2×C414yescomplemented
79#13063287—22no—
80#13063287—41no—
81C4×C22⋊D43—44no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4D411yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063258—22no—
100Dic43⋊C8C2×C414yescomplemented
101#13063247—22no—
102#13063247C2×C414yescomplemented
103#13063246—22no—
104#13063246—41no—
105#13063246C2×C414yescomplemented
106#13063245—41no—
107#13063235—22no—
108C8×Dic43—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95D411yescharacteristic
115C43⋊#95D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C23×C4×C43—21no—
120C2×D8×C43—22no—
121C2×D8×C43—22no—
122C2×D8×C43C2×C414yescomplemented
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C4×D4×C43—41no—
128C4×D4×C43—41no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#106×C43—22no—
135#102×C43—22no—
136#102×C43D414yescomplemented
137#97×C43—22no—
138C24×C43—21no—
139C24×C43—21no—
140C23×D43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C2×D4×C43C22×C412yes—
151C2×D4×C43C2×D412yes—
152C2×D4×C43#4112yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—81no—
160C22×C4×C43—81no—
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2411yescharacteristic
164C2×C22⋊D43—24no—
165C2×C22⋊D43—24no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—81no—
169C2×C22⋊D43—81no—
170C22×Dic43—24no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—81no—
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—42no—
190C2×C4×D43—42no—
191C2×C4×D43—81no—
192D8×C43—28no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43C22×C412yes—
198C2×C8×C43C2×D412yes—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C2×D412yes—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C42×C43—21no—
206C42×C43—21no—
207C22⋊Dic43—24no—
208C22⋊Dic43—42no—
209C22⋊Dic43—42no—
210C22⋊Dic43—81no—
211#10621882—28no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—81no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22×C412yes—
221Dic43⋊C4—22no—
222Dic43⋊C4—41no—
223Dic43⋊C4—81no—
224Dic43⋊C4—81no—
225C4×Dic43—21no—
226C4×Dic43—21no—
227C4×Dic43—42no—
228C4×Dic43C22×C412yes—
229C4×Dic43#4112yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8C22×C412yes—
236C23×C43—22no—
237C23×C43—22no—
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×C43C22×D411yescharacteristic
251C22×D43—22no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258D4×C43—22no—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—22no—
263D4×C43—41no—
264D4×C43—41no—
265D4×C43C4×D414yescomplemented
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—84no—
279C2×C4×C43—84no—
280C2×C4×C43C23×C411yescharacteristic
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C432−1+411yescharacteristic
286C22⋊D43—48no—
287C22⋊D43—84no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
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—84no—
307C2×Dic43—84no—
308C2×Dic43C4×D412yes—
309C2×Dic43C4×D412yes—
310C2×Dic43AGL(1,ℤ/8)12yes—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—22no—
318C43⋊C8—22no—
319C43⋊C8—41no—
320#23008—431nomaximal, Sylow
321C22×C43—24no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—42no—
325C22×C43—42no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43C2×C4×D411yescharacteristic
336C22×C43D4211yescharacteristic
337C22×C43#54811yescharacteristic
338C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C43#57511yescharacteristic
340C22×C43#57611yescharacteristic
341C22×C43#57611yescharacteristic
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—42no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—81no—
353C4×C43C2×C4×D411yescharacteristic
354C4×C43#52011yescharacteristic
355C4×C43#54711yescharacteristic
356C4×C43#55311yescharacteristic
357Dic43—22no—
358Dic43—22no—
359Dic43—22no—
360Dic43—42no—
361Dic43—41no—
362Dic43—81no—
363Dic43—81no—
364C2×#459—431no—
365C2×#442D4311yescharacteristic, complemented
366C2×C4×D8—431no—
367#2366—431no—
368#2349—431no—
369#1961—431no—
370#1949—431no—
371#1936—431no—
372#1934—431no—
373#1879—431no—
374#1879—431no—
375#1864—431no—
376#1862—431no—
377#1771—431no—
378#1762—431no—
379C2×C43—44no—
380C2×C43—82no—
381C2×C43#236111yescharacteristic
382C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C43#294811yescharacteristic
384C2×C43#326411yescharacteristic
385C2×C43#326811yescharacteristic
386C2×C43#336611yescharacteristic
387C2×C43#337011yescharacteristic
388D43—82no—
389C22×D8—431no—
390C22×D8C2×D4311yescharacteristic
391C2×#127—431no—
392C2×C4×D4—431no—
393C2×C4×D4—431no—
394C2×C4×D4—431no—
395C2×C4×D4—861no—
396C2×C4×D4C2×D4311yescharacteristic
397C2×C4×D4C2×D4311yescharacteristic
398#459—438no—
399#442—24no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106C2×D4311yescharacteristic
403C2×C4⋊C8—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102C2×D4311yescharacteristic
411C2×#102C2×D4311yescharacteristic
412C2×#97—431no—
413C2×#97C2×D4311yescharacteristic
414C2×C4×C8—431no—
415#390—431no—
416#390—431no—
417#390—861no—
418#389—431no—
419#389—431no—
420#386—861no—
421#386—861no—
422#385—861no—
423#385—861no—
424#382—431no—
425#380—861no—
426C4×C4⋊C4—431no—
427C4×C4⋊C4—431no—
428C2×#95—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#336—431no—
434#336—431no—
435C43#2300811yescharacteristic, complemented, Sylow
436C22×D4—431no—
437C22×D4—861no—
438C22×D4—861no—
439C22×D4C22×D4311yescharacteristic
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—434no—
449C2×D8—862no—
450C2×D8—862no—
451C2×D8C4×D4314yescomplemented
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456#127—434no—
457#127—862no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—41no—
461C4×D4—41no—
462C4×D4—434no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—1721no—
467C4×D4—1721no—
468C4×D4—1724no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—861no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4C22×D4311yescharacteristic
477C2×C4⋊C4C22×D4311yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—861no—
490C2×C42C22×D4311yescharacteristic
491#107—862no—
492#106—22no—
493C4⋊C8—434no—
494#102—22no—
495#102—434no—
496#102—434no—
497#102—862no—
498#102—862no—
499#102—1721no—
500#102—1721no—
501#102C22⋊D4314yescomplemented
502#97—22no—
503#97—862no—
504C4×C8—862no—
505#95—431no—
506#95—431no—
507#95—861no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512C24—21no—
513C24—21no—
514C24—861no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—432no—
524C2×D4—864no—
525C2×D4—864no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—861no—
531C2×D4—3441no—
532C2×D4—3441no—
533C2×D4—1722no—
534C2×D4—1722no—
535C2×D4C2×C4×D4312yes—
536C2×D4C2×C4×D4312yes—
537C2×D4#1062189812yes—
538C2×D4C2×C22⋊D4312yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—431no—
548C22×C4—431no—
549C22×C4—431no—
550C22×C4—431no—
551C22×C4—864no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—3441no—
556C22×C4—3441no—
557C22×C4—3441no—
558C22×C4—3441no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4—1722no—
562C22×C4—1722no—
563C22×C4D4×D4311yescharacteristic
564C22×C4D4×D4311yescharacteristic
565C22×C4C23×D4311yescharacteristic
566D8—28no—
567D8—868no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—432no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8C2×C4×D4312yes—
579C2×C8C2×C22⋊D4312yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—432no—
584C4⋊C4—862no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—3441no—
591C4⋊C4—3441no—
592C4⋊C4—1721no—
593C4⋊C4C2×C22⋊D4312yes—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—864no—
597C22⋊C4—3441no—
598C22⋊C4—3441no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—21no—
604C42—21no—
605C42—432no—
606C42—432no—
607C42—861no—
608C42—861no—
609C42—1722no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—862no—
625C23—1721no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23C2×D4×D4311yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—41no—
638D4—41no—
639D4—862no—
640D4—862no—
641D4—3444no—
642D4—1728no—
643D4—1721no—
644D4—1721no—
645D4C4×C22⋊D4314yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—84no—
659C2×C4—84no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—3444no—
674C2×C4—3444no—
675C2×C4—3444no—
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×D4311yescharacteristic
685C2×C4C22×C22⋊D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4C2×#1062189811yescharacteristic
688C2×C4#1306337011yescharacteristic
689C2×C4#1306337211yescharacteristic
690C8—22no—
691C8—22no—
692C8—862no—
693C8—1721no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—3441no—
709C22—3441no—
710C22—3441no—
711C22—3441no—
712C22—1722no—
713C22—1722no—
714C22—1722no—
715C22C4×D4×D4311yescharacteristic
716C22D4×C22⋊D4311yescharacteristic
717C22#1458355811yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22#1458369511yescharacteristic
720C22#1458370311yescharacteristic
721C22#1458370311yescharacteristic
722C4—41no—
723C4—42no—
724C4—41no—
725C4—81no—
726C4—862no—
727C4—862no—
728C4—862no—
729C4—3441no—
730C4—3441no—
731C4—1722no—
732C4—1721no—
733C4C2×C4×C22⋊D4311yescharacteristic
734C4#1458337811yescharacteristic
735C4#1458354811yescharacteristic
736C4#1458359811yescharacteristic
737C2—44no—
738C2—82no—
739C2—3442no—
740C2#1913761211yescharacteristic
741C2#1914340611yescharacteristic
742C2#1914344411yescharacteristic
743C2#1914606911yescharacteristic
744C2#1914612911yescharacteristic
745C2#1914730311yescharacteristic
746C2#1914735311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC2×#14583092C2
cosocleC22×C4×C43C24
hypercenterC2×#442D43
hypocenterC43#23008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#14582979C2semidirect
3. #19137657C2semidirect
4. #19137500C2semidirect
5. #19135417C2semidirect
6. #19135364C2semidirect
7. #19135292C2semidirect
8. #19135275C2semidirect
9. #19134945C2semidirect
10. #19134943C2semidirect
11. #19134853C2semidirect
12. #19134842C2semidirect
13. #19134471C2semidirect
14. #19134422C2semidirect
15. C2×C43×#442C2semidirect
22. #14583092C4semidirect
70. C2×#10621882C2×C4semidirect
74. #13063321C2×C4semidirect
78. D4×Dic43C2×C4semidirect
100. Dic43⋊C8C2×C4semidirect
102. #13063247C2×C4semidirect
105. #13063246C2×C4semidirect
122. C2×D8×C43C2×C4semidirect
136. #102×C43D4semidirect
265. D4×C43C4×D4semidirect
365. C2×#442D43semidirect
435. C43#23008semidirect
451. C2×D8C4×D43semidirect
501. #102C22⋊D43semidirect
645. D4C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830922
C2×#145829792
#191376572
#191375002
#191354172
#191353642
#191352922
#191352752
#191349452
#191349432
#191348532
#191348422
#191344712
#191344222
C2×C43×#4422
#2300843