Finite Group Databasebeta

← C4×#14583111 #25102811

Subgroups — C4×#14583111 #25102811

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583111C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic
4C42×D172C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic, complemented
6#19135361C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135219C211yesmaximal, characteristic, complemented
9#19134946C211yesmaximal, characteristic
10#19134932C211yesmaximal, characteristic, complemented
11#19134602C211yesmaximal, characteristic, complemented
12C4×C4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14C4×#13063246C211yesmaximal, characteristic, complemented
15C4×#124×C43C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C42×D43—21no—
22#14583111C418yesdirect product factor
23C4×#10621884—24no—
24C4×#10621882—24no—
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42C4×(C2×D43)⋊C4—21no—
43C4×(C2×D43)⋊C4—21no—
44C4×(C2×D43)⋊C4—21no—
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C2×#124×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C43×#391C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#388—21no—
57C43×#388—21no—
58C43×#382C2211yescharacteristic
59C4×C22⋊C4×C43—21no—
60C4×C22⋊C4×C43—21no—
61C43×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884C2×C414yescomplemented
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882C2×C414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C4×D172—22no—
77C4×D172—22no—
78C4×D172—22no—
79C4×D172—22no—
80C4×D172C2×C414yescomplemented
81C4×D172D414yes—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C42×D43—44no—
92#13063258—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95C4⋊(C43⋊C8)C2×C414yescomplemented
96#13063249—22no—
97#13063249—22no—
98#13063249C2×C414yescomplemented
99#13063246—22no—
100#13063246—22no—
101#13063246C2×C414yescomplemented
102#13063245—22no—
103#13063245—22no—
104C4×C43⋊C8—22no—
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×Q8×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112#124×C43—22no—
113#124×C43C2×C414yescomplemented
114C4×Q8×C43—22no—
115C4×Q8×C43—22no—
116C4×D4×C43—22no—
117C4×D4×C43—22no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43—21no—
127C2×C42×C43D411yescharacteristic
128C2×C42×C43D411yescharacteristic
129C2×C42×C43D411yescharacteristic
130C2×C42×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134#95×C43—21no—
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138C24×C43—21no—
139C23×D43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43C22×C412yes—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C412yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172C22×C412yes—
172C2×D172C2×D412yes—
173C2×D172#4112yes—
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—24no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×C4×D43—42no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—24no—
190C22⋊C4×C43—42no—
191C22⋊C4×C43—42no—
192C22⋊C4×C43—42no—
193C42×C43—22no—
194C42×C43—22no—
195C42×C43—22no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—41no—
199C42×C43—42no—
200C42×C43C22×C412yes—
201C42×C43C2×D412yes—
202C42×C43#4112yes—
203C42×C43#4112yes—
204#10621884—28no—
205#10621882—28no—
206(C2×D43)⋊C4—24no—
207(C2×D43)⋊C4—24no—
208(C2×D43)⋊C4—24no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43C22×C412yes—
213C4⋊Dic43C2×D412yes—
214C4⋊Dic43#4112yes—
215C4×Dic43—42no—
216C4×Dic43—42no—
217C4×Dic43—42no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C22×C412yes—
229C2×C43⋊C8C22×C412yes—
230C23×C43—22no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43C22×D411yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245Q8×C43—22no—
246Q8×C43—22no—
247Q8×C43—41no—
248Q8×C43—41no—
249D4×C43—22no—
250D4×C43—22no—
251D4×C43—41no—
252D4×C43—41no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—22no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—84no—
274C2×C4×C43C4×D412yes—
275C2×C4×C43C4×D412yes—
276C2×C4×C43#12112yes—
277C2×C4×C43#12112yes—
278C2×C4×C43#13512yes—
279C2×C4×C43#13512yes—
280C2×C4×C43AGL(1,ℤ/8)12yes—
281C2×C4×C43C23×C411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296D172—22no—
297D172—22no—
298D172—22no—
299D172C4×D414yes—
300C4×D43—48no—
301C4×D43—48no—
302C4×D43—48no—
303C43⋊C8—22no—
304C43⋊C8—22no—
305C43⋊C8—41no—
306C43⋊C8—41no—
307C4×#463—431nomaximal, Sylow
308C22×C43—42no—
309C22×C43—42no—
310C22×C43—42no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43C2×C4×D411yescharacteristic
316C22×C43C2×#12111yescharacteristic
317C22×C43#52511yescharacteristic
318C22×C43C2×#13511yescharacteristic
319C22×C43C2×#13511yescharacteristic
320C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C43#57511yescharacteristic
322C2×D43—24no—
323C2×D43—42no—
324C2×D43—42no—
325C2×D43—42no—
326C2×D43—42no—
327C2×D43—42no—
328C2×D43—42no—
329C4×C43—22no—
330C4×C43—22no—
331C4×C43—22no—
332C4×C43—22no—
333C4×C43—41no—
334C4×C43—42no—
335C4×C43—81no—
336C4×C43—81no—
337C4×C43#46314yescomplemented
338C4×C43C2×C4×D411yescharacteristic
339C4×C43C4×#4111yescharacteristic
340C4×C43#52911yescharacteristic
341C4×C43#53211yescharacteristic
342Dic43—42no—
343Dic43—42no—
344Dic43—42no—
345C2×#463—431no—
346C2×C4×SD16—431no—
347C2×C4×D8—431no—
348C4×#124D4311yescharacteristic, complemented
349C42×D4—431no—
350#1983—431no—
351#1949—431no—
352#1928—431no—
353#1926—431no—
354#1879—431no—
355#1877—431no—
356#1804—431no—
357C4×C4⋊C8—431no—
358C4×#103—431no—
359C4×#102—431no—
360C2×C43—82no—
361C2×C43C4×#12111yescharacteristic
362C2×C43C4×#13511yescharacteristic
363C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
364C2×C43C2×#46311yescharacteristic
365C2×C43#303511yescharacteristic
366C2×C43#310211yescharacteristic
367C2×C43#310511yescharacteristic
368D43—44no—
369C22×SD16—431no—
370C22×D8—431no—
371C2×#124C2×D4311yescharacteristic
372C2×C4×Q8C2×D4311yescharacteristic
373C2×C4×D4—431no—
374C2×C4×D4—431no—
375C2×C4×D4—431no—
376C2×C4×D4C2×D4311yescharacteristic
377C22×C42—861no—
378#463—438no—
379C4×SD16—864no—
380C4×D8—864no—
381C2×#107—431no—
382C2×#106—431no—
383C2×C4⋊C8—431no—
384C2×C4⋊C8—431no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×#102—431no—
389C2×#102—431no—
390C2×#102—431no—
391C2×#102—431no—
392C2×#102—431no—
393C2×C4×C8—431no—
394C2×C4×C8—431no—
395#391C2×D4311yescharacteristic
396#390C2×D4311yescharacteristic
397#388—21no—
398#388—21no—
399#382C2×D4311yescharacteristic
400C4×C4⋊C4—431no—
401C4×C4⋊C4—431no—
402C4×C4⋊C4—431no—
403C4×C22⋊C4—21no—
404C4×C22⋊C4—21no—
405C4×C22⋊C4—861no—
406C4×C22⋊C4—861no—
407C4×C22⋊C4—861no—
408C43C2×D4311yescharacteristic
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#336—431no—
414#336—431no—
415C43C4×#46311yescharacteristic, complemented, Sylow
416C22×Q8C22×D4311yescharacteristic
417C22×D4—431no—
418C22×D4C22×D4311yescharacteristic
419C23×C4—21no—
420C23×C4—861no—
421C23×C4—861no—
422C23×C4—861no—
423C2×SD16—434no—
424C2×SD16—862no—
425C2×SD16—862no—
426C2×D8—434no—
427C2×D8—862no—
428C2×D8—862no—
429C22×C8—431no—
430C22×C8—431no—
431C22×C8—431no—
432C22×C8—431no—
433#124—22no—
434#124C4×D4314yescomplemented
435C4×Q8—22no—
436C4×Q8—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—434no—
440C4×D4—434no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—862no—
444C4×D4—862no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4C22×D4311yescharacteristic
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—21no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—1724no—
464C2×C42C22⋊D4311yescharacteristic
465C2×C42C22⋊D4311yescharacteristic
466C2×C42C22⋊D4311yescharacteristic
467C2×C42C22⋊D4311yescharacteristic
468C2×C42C22×D4311yescharacteristic
469C2×C42C22×D4311yescharacteristic
470C2×C42C22×D4311yescharacteristic
471#107—862no—
472#106—862no—
473C4⋊C8—434no—
474C4⋊C8—862no—
475#103—434no—
476#103—862no—
477#103—862no—
478#102—434no—
479#102—862no—
480#102—862no—
481#102—862no—
482#102—862no—
483C4×C8—862no—
484C4×C8—862no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—861no—
490#95—861no—
491#95—861no—
492C24—21no—
493C24—861no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D4312yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—432no—
506C2×D4—432no—
507C2×D4—432no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—861no—
511C2×D4C2×C4×D4312yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—864no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—864no—
523C22×C4—864no—
524C22×C4—1722no—
525C22×C4—1722no—
526C22×C4—1722no—
527C22×C4—1722no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4C2×C22⋊D4311yescharacteristic
531C22×C4C2×C22⋊D4311yescharacteristic
532C22×C4C2×C22⋊D4311yescharacteristic
533C22×C4C2×C22⋊D4311yescharacteristic
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C23×D4311yescharacteristic
537SD16—868no—
538D8—868no—
539C2×C8—432no—
540C2×C8—432no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—432no—
557C4⋊C4—432no—
558C4⋊C4—432no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—864no—
568C22⋊C4—864no—
569C22⋊C4—864no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—21no—
574C42—21no—
575C42—41no—
576C42—42no—
577C42—1722no—
578C42—1722no—
579C42—1722no—
580C42C2×C4×D4312yes—
581C42#1062189812yes—
582C42D4×D4312yes—
583C42#1062190012yes—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—862no—
592C23—862no—
593C23—862no—
594C23—1721no—
595C23—1721no—
596C23—1721no—
597C23—1721no—
598C23C22×C22⋊D4311yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—434no—
608D4—862no—
609D4—862no—
610D4—862no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—1728no—
636C2×C4—1728no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1728no—
644C2×C4C4×C22⋊D4312yes—
645C2×C4C4×C22⋊D4312yes—
646C2×C4#1306329612yes—
647C2×C4#1306329612yes—
648C2×C4#1306334512yes—
649C2×C4#1306334512yes—
650C2×C4#1306335012yes—
651C2×C4C22×C4×D4311yescharacteristic
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4#41×D4311yescharacteristic
654C2×C4#41×D4311yescharacteristic
655C2×C4C2×#1062190011yescharacteristic
656C2×C4C2×#1062189811yescharacteristic
657C8—862no—
658C8—862no—
659C8—1721no—
660C8—1721no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—864no—
669C22—1722no—
670C22—1722no—
671C22—1722no—
672C22—1722no—
673C22—1722no—
674C22—1722no—
675C22C2×C4×C22⋊D4311yescharacteristic
676C22C2×#1306329611yescharacteristic
677C22#1458340611yescharacteristic
678C22C2×#1306334511yescharacteristic
679C22C2×#1306334511yescharacteristic
680C22C2×#1306335011yescharacteristic
681C22#1458369711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—1722no—
691C4—1722no—
692C4—1722no—
693C4#1458311114yesdirect product factor
694C4C4×D4×D4311yescharacteristic
695C4C4×#1062190011yescharacteristic
696C4#1458343111yescharacteristic
697C4#1458344611yescharacteristic
698C2—82no—
699C2—1724no—
700C2C4×#1306329611yescharacteristic
701C2C4×#1306334511yescharacteristic
702C2C4×#1306335011yescharacteristic
703C2C2×#1458311111yescharacteristic
704C2#1914404411yescharacteristic
705C2#1914460711yescharacteristic
706C2#1914463811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#124×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenterC4×#124D43
hypocenterC43C4×#463
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621884C2semidirect
4. C42×D172C2semidirect
5. #19135528C2semidirect
6. #19135361C2semidirect
7. #19135233C2semidirect
8. #19135219C2semidirect
10. #19134932C2semidirect
11. #19134602C2semidirect
12. C4×C4⋊(C43⋊C8)C2semidirect
13. C4×#13063249C2semidirect
14. C4×#13063246C2semidirect
15. C4×#124×C43C2semidirect
22. #14583111C4direct (N × H)
68. C2×#10621884C2×C4semidirect
80. C4×D172C2×C4semidirect
95. C4⋊(C43⋊C8)C2×C4semidirect
98. #13063249C2×C4semidirect
101. #13063246C2×C4semidirect
113. #124×C43C2×C4semidirect
337. C4×C43#463semidirect
348. C4×#124D43semidirect
415. C43C4×#463semidirect
434. #124C4×D43semidirect
693. C4#14583111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831112
C2×C4×#106218842
C2×C4×#106218822
C42×D1722
#191355282
#191353612
#191352332
#191352192
#191349462
#191349322
#191346022
C4×C4⋊(C43⋊C8)2
C4×#130632492
C4×#130632462
C4×#124×C432
C4×#46343