Finite Group Databasebeta

← C2×#19139523 #25266627

Subgroups — C2×#19139523 #25266627

Order 11008.

5726 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063309C211yesmaximal, characteristic, complemented
2C22×#13063306C211yesmaximal, characteristic, complemented
3C22×#13063297C211yesmaximal, characteristic, complemented
4C22×#13063294C211yesmaximal, characteristic, complemented
5C23×C22⋊Dic43C211yesmaximal, characteristic, complemented
6#19139523C2116yesmaximal, direct product factor
7C2×#14582835C212yesmaximal, complemented
8C2×#14582807C212yesmaximal, complemented
9C2×#14582802C212yesmaximal, complemented
10C2×#14582799C212yesmaximal, complemented
11C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C22×#120×C43C211yesmaximal, characteristic, complemented
13C23×C22⋊D43C2211yescharacteristic
14C23×C22⋊D43C2212yes—
15C23×C22⋊D43C2211yescharacteristic, complemented
16C24×Dic43C2211yescharacteristic
17C24×Dic43C2211yescharacteristic
18C2×#13063309—28no—
19C2×#13063309C2218yescomplemented
20C2×#13063306—28no—
21C2×#13063306C2218yescomplemented
22C2×#13063297—28no—
23C2×#13063297C2218yescomplemented
24C2×#13063294—28no—
25C2×#13063294C2218yescomplemented
26C22×C4⋊Dic43C2212yescomplemented
27C22×Dic43⋊C4C2212yescomplemented
28C22×Dic43⋊C4C2211yescharacteristic, complemented
29C22×C22⋊Dic43—28no—
30C22×C22⋊Dic43C2212yes—
31C22×C22⋊Dic43C2212yes—
32C22×C22⋊Dic43C2212yes—
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2218yescomplemented
35C22×C22⋊Dic43C2211yescharacteristic, complemented
36C22×C22⋊Dic43C2212yescomplemented
37C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
38C22×(C2×D43)⋊C4C2212yescomplemented
39C22×C4×Dic43C2212yescomplemented
40#14582835C22116yescomplemented
41#14582807C22116yescomplemented
42#14582802C22116yescomplemented
43#14582799C22116yescomplemented
44C22⋊C4×Dic43C2218yescomplemented
45C2×C43⋊#95C2212yescomplemented
46C26×C43C2211yescharacteristic
47C23×D4×C43C2211yescharacteristic
48C23×D4×C43C2212yes—
49C2×#120×C43—28no—
50C2×#120×C43C2218yescomplemented
51C22×C22⋊C4×C43C2212yes—
52C22×C22⋊C4×C43C2211yescharacteristic
53C24×D43C2311yescharacteristic
54C22×C22⋊D43—24no—
55C22×C22⋊D43—24no—
56C22×C22⋊D43—24no—
57C22×C22⋊D43—28no—
58C22×C22⋊D43—28no—
59C22×C22⋊D43—24no—
60C22×C22⋊D43—44no—
61C22×C22⋊D43—44no—
62C22×C22⋊D43C2314yes—
63C22×C22⋊D43C2318yes—
64C22×C22⋊D43C2314yescomplemented
65C23×Dic43—24no—
66C23×Dic43—24no—
67C23×Dic43—24no—
68C23×Dic43—44no—
69C23×Dic43D418yescomplemented
70C23×Dic43C2312yes—
71C23×Dic43C2311yescharacteristic
72C23×Dic43C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2312yes—
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2314yes—
77#13063309—232no—
78#13063306—232no—
79#13063297—232no—
80#13063294—232no—
81C2×C4⋊Dic43—28no—
82C2×C4⋊Dic43C2318yescomplemented
83C2×Dic43⋊C4—24no—
84C2×Dic43⋊C4—28no—
85C2×Dic43⋊C4C2318yescomplemented
86C2×Dic43⋊C4C2314yescomplemented
87C2×C22⋊Dic43—28no—
88C2×C22⋊Dic43—28no—
89C2×C22⋊Dic43—28no—
90C2×C22⋊Dic43—24no—
91C2×C22⋊Dic43—28no—
92C2×C22⋊Dic43—232no—
93C2×C22⋊Dic43D418yescomplemented
94C2×C22⋊Dic43C2318yes—
95C2×C22⋊Dic43C2318yes—
96C2×C22⋊Dic43C2318yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yescomplemented
99C2×C22⋊Dic43C2318yescomplemented
100C2×(C2×D43)⋊C4—28no—
101C2×(C2×D43)⋊C4—24no—
102C2×(C2×D43)⋊C4C2314yescomplemented
103C2×(C2×D43)⋊C4C2318yescomplemented
104C2×C4×Dic43—44no—
105C2×C4×Dic43C2318yescomplemented
106C43⋊#95C2318yescomplemented
107C25×C43—24no—
108C25×C43—28no—
109C25×C43—24no—
110C25×C43—24no—
111C25×C43—44no—
112C25×C43C2311yescharacteristic
113C25×C43C2312yes—
114C25×C43C2314yes—
115C25×C43C2311yescharacteristic
116C22×D4×C43—24no—
117C22×D4×C43—24no—
118C22×D4×C43—24no—
119C22×D4×C43—28no—
120C22×D4×C43—28no—
121C22×D4×C43—44no—
122C22×D4×C43C2314yes—
123C22×D4×C43C2318yes—
124C23×C4×C43C2311yescharacteristic
125C23×C4×C43C2312yes—
126#120×C43—232no—
127C2×C22⋊C4×C43—28no—
128C2×C22⋊C4×C43D418yescomplemented
129C2×C22⋊C4×C43C2318yes—
130C2×C22⋊C4×C43C2314yes—
131C24×C43—24no—
132C24×C43—24no—
133C24×C43—232no—
134C24×C43—24no—
135C24×C43—28no—
136C24×C43—24no—
137C24×C43—24no—
138C24×C43—216no—
139C24×C43—24no—
140C24×C43—24no—
141C24×C43—24no—
142C24×C43—28no—
143C24×C43—22no—
144C24×C43—22no—
145C24×C43—22no—
146C24×C43—28no—
147C24×C43—24no—
148C24×C43—24no—
149C24×C43—48no—
150C24×C43—432no—
151C24×C43—432no—
152C24×C43—416no—
153C24×C43—416no—
154C24×C43C2×D414yes—
155C24×C43C2×D414yes—
156C24×C43C2×D414yes—
157C24×C43#4118yes—
158C24×C43C2412yes—
159C24×C43C2414yes—
160C24×C43C2412yes—
161C24×C43C2411yescharacteristic
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—24no—
166C23×D43—24no—
167C23×D43C2412yes—
168C2×D4×C43—216no—
169C2×D4×C43—28no—
170C2×D4×C43—28no—
171C2×D4×C43—28no—
172C2×D4×C43—216no—
173C2×D4×C43—48no—
174C2×D4×C43—432no—
175C2×D4×C43—416no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—24no—
180C22×C4×C43—24no—
181C22×C4×C43C2×D418yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2414yes—
184C2×C22⋊D43—216no—
185C2×C22⋊D43—28no—
186C2×C22⋊D43—28no—
187C2×C22⋊D43—28no—
188C2×C22⋊D43—28no—
189C2×C22⋊D43—216no—
190C2×C22⋊D43—48no—
191C2×C22⋊D43—48no—
192C2×C22⋊D43—432no—
193C2×C22⋊D43—416no—
194C2×C22⋊D43—416no—
195C22×Dic43—24no—
196C22×Dic43—28no—
197C22×Dic43—24no—
198C22×Dic43—22no—
199C22×Dic43—24no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—28no—
203C22×Dic43—28no—
204C22×Dic43—24no—
205C22×Dic43—24no—
206C22×Dic43—24no—
207C22×Dic43—24no—
208C22×Dic43—416no—
209C22×Dic43—48no—
210C22×Dic43—416no—
211C22×Dic43C2×D414yes—
212C22×Dic43C2×D418yes—
213C22×Dic43C2×D414yes—
214C22×Dic43C2×D4116yescomplemented
215C22×Dic43C2414yes—
216C22×Dic43C2412yes—
217C22×Dic43C2412yes—
218C22×Dic43C2414yes—
219C22×Dic43C2412yes—
220C22⋊C4×C43—216no—
221C22⋊C4×C43C2×D4116yescomplemented
222C22⋊Dic43—216no—
223C22⋊Dic43—216no—
224C22⋊Dic43—216no—
225C22⋊Dic43—28no—
226C22⋊Dic43—216no—
227C22⋊Dic43C2×D4116yescomplemented
228(C2×D43)⋊C4—216no—
229(C2×D43)⋊C4—28no—
230C4⋊Dic43—216no—
231Dic43⋊C4—28no—
232Dic43⋊C4—216no—
233C4×Dic43—48no—
234C23×C43—28no—
235C23×C43—28no—
236C23×C43—216no—
237C23×C43—216no—
238C23×C43—24no—
239C23×C43—24no—
240C23×C43—232no—
241C23×C43—216no—
242C23×C43—216no—
243C23×C43—216no—
244C23×C43—24no—
245C23×C43—24no—
246C23×C43—24no—
247C23×C43—24no—
248C23×C43—24no—
249C23×C43—24no—
250C23×C43—22no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—24no—
254C23×C43—24no—
255C23×C43—432no—
256C23×C43—432no—
257C23×C43—416no—
258C23×C43—4128no—
259C23×C43—416no—
260C23×C43—48no—
261C23×C43—48no—
262C23×C43—48no—
263C23×C43—48no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—48no—
268C23×C43—48no—
269C23×C43#127116yes—
270C23×C43C22×D414yes—
271C23×C43C22×D414yes—
272C23×C43C22×D412yes—
273C23×C43C22×D412yes—
274C23×C43C22×D414yes—
275C23×C43C22×D412yes—
276C23×C43C2×#4118yes—
277C23×C43C2×#4114yes—
278C23×C43H(5,𝔽2)14yes—
279C23×C43C2511yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—24no—
284C22×D43—24no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—48no—
289C22×D43—48no—
290D4×C43—432no—
291D4×C43—416no—
292C2×C4×C43—216no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—44no—
299C2×C4×C43C22×D418yes—
300C22⋊D43—432no—
301C22⋊D43—416no—
302C22⋊D43—416no—
303C2×Dic43—28no—
304C2×Dic43—28no—
305C2×Dic43—216no—
306C2×Dic43—24no—
307C2×Dic43—24no—
308C2×Dic43—24no—
309C2×Dic43—24no—
310C2×Dic43—24no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—24no—
314C2×Dic43—24no—
315C2×Dic43—22no—
316C2×Dic43—416no—
317C2×Dic43—416no—
318C2×Dic43—48no—
319C2×Dic43—44no—
320C2×Dic43C22×D418yes—
321C2×Dic43C22×D414yes—
322C2×Dic43C22×D414yes—
323C2×#2539—431nomaximal, Sylow
324C22×C43—24no—
325C22×C43—24no—
326C22×C43—28no—
327C22×C43—28no—
328C22×C43—232no—
329C22×C43—28no—
330C22×C43—28no—
331C22×C43—28no—
332C22×C43—464no—
333C22×C43—44no—
334C22×C43—44no—
335C22×C43—44no—
336C22×C43—44no—
337C22×C43—432no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—44no—
342C22×C43—44no—
343C22×C43—88no—
344C22×C43#52514yes—
345C22×C43C2×#12718yes—
346C22×C43C2×#12714yes—
347C22×C43#53414yes—
348C22×C43#54618yes—
349C22×C43#54618yes—
350C22×C43C23×D411yescharacteristic
351C22×C43C23×D411yescharacteristic
352C22×C43C23×D411yescharacteristic
353C22×C43C22×#4112yes—
354C22×C43C2×H(5,𝔽2)12yes—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—44no—
359C2×D43—44no—
360C2×D43—88no—
361C4×C43—28no—
362C4×C43—42no—
363Dic43—24no—
364Dic43—24no—
365Dic43—28no—
366Dic43—44no—
367Dic43—42no—
368C22×#123—431no—
369C22×#123—431no—
370C22×#121—431no—
371C22×#120—431no—
372C22×#120D4311yescharacteristic, complemented
373C23×C22⋊C4—431no—
374#2539—4316no—
375C2×#399—432no—
376C2×#392—432no—
377C2×#390—432no—
378C2×#390—432no—
379C2×C4×C22⋊C4—431no—
380C2×C43—28no—
381C2×C43—48no—
382C2×C43—82no—
383C2×C43#253918yescomplemented
384C2×C43C2×#52511yescharacteristic
385C2×C43C22×#12711yescharacteristic
386C2×C43C2×#53411yescharacteristic
387C2×C43C2×#54612yes—
388C2×C43C2×#54612yes—
389D43—82no—
390C26C2×D4311yescharacteristic
391C23×D4—431no—
392C23×D4—432no—
393C23×D4—431no—
394C23×D4C2×D4311yescharacteristic
395C23×D4C2×D4312yes—
396C24×C4—431no—
397C24×C4—431no—
398C2×#123—438no—
399C2×#123—438no—
400C2×#123—868no—
401C2×#123—868no—
402C2×#121—438no—
403C2×#121—868no—
404C2×#120—28no—
405C2×#120—438no—
406C2×#120—868no—
407C2×#120C2×D4318yescomplemented
408C22×C4⋊C4—431no—
409C22×C4⋊C4—432no—
410C22×C4⋊C4—432no—
411C22×C22⋊C4—431no—
412C22×C22⋊C4—432no—
413C22×C22⋊C4—432no—
414C22×C22⋊C4—432no—
415C22×C22⋊C4—432no—
416C22×C22⋊C4—438no—
417C22×C22⋊C4—431no—
418C22×C22⋊C4—432no—
419C22×C22⋊C4—431no—
420C22×C22⋊C4—868no—
421C22×C22⋊C4C2×D4312yes—
422C22×C22⋊C4C2×D4311yescharacteristic
423C22×C42—432no—
424#399—4316no—
425#392—4316no—
426#390—4316no—
427#390—4316no—
428C4×C22⋊C4—438no—
429C2×#95—432no—
430C43C2×#253911yescharacteristic, complemented, Sylow
431C25—24no—
432C25—28no—
433C25—24no—
434C25—24no—
435C25—44no—
436C25—431no—
437C25C22×D4311yescharacteristic
438C25C22×D4312yes—
439C25C22×D4314yes—
440C25C22×D4311yescharacteristic
441C22×D4—24no—
442C22×D4—24no—
443C22×D4—28no—
444C22×D4—24no—
445C22×D4—28no—
446C22×D4—44no—
447C22×D4—434no—
448C22×D4—438no—
449C22×D4—434no—
450C22×D4—868no—
451C22×D4—864no—
452C22×D4—864no—
453C22×D4—864no—
454C22×D4—868no—
455C22×D4—864no—
456C22×D4—1724no—
457C22×D4—1724no—
458C22×D4C22×D4314yes—
459C22×D4C22×D4318yes—
460C23×C4—431no—
461C23×C4—432no—
462C23×C4—431no—
463C23×C4—438no—
464C23×C4—434no—
465C23×C4—434no—
466C23×C4—432no—
467C23×C4—431no—
468C23×C4—864no—
469C23×C4—864no—
470C23×C4—864no—
471C23×C4—1724no—
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4312yes—
474#123—8632no—
475#123—8632no—
476#121—8632no—
477#120—232no—
478#120—8632no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—438no—
481C2×C4⋊C4—438no—
482C2×C4⋊C4—864no—
483C2×C4⋊C4—868no—
484C2×C4⋊C4—868no—
485C2×C22⋊C4—28no—
486C2×C22⋊C4—438no—
487C2×C22⋊C4—434no—
488C2×C22⋊C4—438no—
489C2×C22⋊C4—438no—
490C2×C22⋊C4—438no—
491C2×C22⋊C4—434no—
492C2×C22⋊C4—438no—
493C2×C22⋊C4—434no—
494C2×C22⋊C4—438no—
495C2×C22⋊C4—864no—
496C2×C22⋊C4—868no—
497C2×C22⋊C4—868no—
498C2×C22⋊C4—8632no—
499C2×C22⋊C4—868no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4—868no—
502C2×C22⋊C4—868no—
503C2×C22⋊C4C22⋊D4318yescomplemented
504C2×C22⋊C4C22×D4318yes—
505C2×C22⋊C4C22×D4314yes—
506C2×C42—438no—
507C2×C42—1724no—
508#95—438no—
509C24—24no—
510C24—24no—
511C24—232no—
512C24—28no—
513C24—24no—
514C24—24no—
515C24—24no—
516C24—216no—
517C24—24no—
518C24—24no—
519C24—24no—
520C24—22no—
521C24—22no—
522C24—28no—
523C24—28no—
524C24—22no—
525C24—24no—
526C24—24no—
527C24—48no—
528C24—432no—
529C24—432no—
530C24—416no—
531C24—416no—
532C24—432no—
533C24—862no—
534C24—862no—
535C24—862no—
536C24—864no—
537C24—864no—
538C24D4×D4314yes—
539C24D4×D4314yes—
540C24#1062190018yes—
541C24C2×C22⋊D4314yes—
542C24C23×D4312yes—
543C24C23×D4314yes—
544C24C23×D4312yes—
545C24C23×D4311yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—216no—
550C2×D4—216no—
551C2×D4—48no—
552C2×D4—432no—
553C2×D4—416no—
554C2×D4—8616no—
555C2×D4—868no—
556C2×D4—868no—
557C2×D4—868no—
558C2×D4—868no—
559C2×D4—8616no—
560C2×D4—1728no—
561C2×D4—1728no—
562C2×D4—17232no—
563C2×D4—17216no—
564C2×D4—17216no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—438no—
571C22×C4—434no—
572C22×C4—434no—
573C22×C4—432no—
574C22×C4—434no—
575C22×C4—432no—
576C22×C4—4316no—
577C22×C4—434no—
578C22×C4—432no—
579C22×C4—864no—
580C22×C4—864no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—868no—
584C22×C4—864no—
585C22×C4—862no—
586C22×C4—864no—
587C22×C4—862no—
588C22×C4—868no—
589C22×C4—864no—
590C22×C4—862no—
591C22×C4—868no—
592C22×C4—17216no—
593C22×C4—1728no—
594C22×C4—17216no—
595C22×C4C2×C22⋊D4318yes—
596C22×C4C23×D4312yes—
597C22×C4C23×D4314yes—
598C4⋊C4—868no—
599C4⋊C4—8616no—
600C4⋊C4—8616no—
601C22⋊C4—216no—
602C22⋊C4—4316no—
603C22⋊C4—868no—
604C22⋊C4—8616no—
605C22⋊C4—8616no—
606C22⋊C4—8616no—
607C22⋊C4—868no—
608C22⋊C4—8616no—
609C22⋊C4—8616no—
610C22⋊C4C2×C22⋊D43116yescomplemented
611C42—1728no—
612C23—28no—
613C23—28no—
614C23—24no—
615C23—24no—
616C23—216no—
617C23—216no—
618C23—232no—
619C23—216no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—216no—
627C23—216no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—432no—
634C23—432no—
635C23—416no—
636C23—4128no—
637C23—416no—
638C23—48no—
639C23—48no—
640C23—48no—
641C23—48no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—48no—
646C23—48no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—864no—
651C23—864no—
652C23—1724no—
653C23—1724no—
654C23—1724no—
655C23—1728no—
656C23—1728no—
657C23#13063321116yes—
658C23C2×D4×D4314yes—
659C23C2×D4×D4314yes—
660C23C2×D4×D4312yes—
661C23C2×D4×D4312yes—
662C23C22×C22⋊D4314yes—
663C23C22×C22⋊D4312yes—
664C23C2×#1062190018yes—
665C23C2×#1062190014yes—
666C23#1306337014yes—
667C23C24×D4311yescharacteristic
668D4—432no—
669D4—416no—
670D4—17232no—
671D4—17216no—
672D4—17216no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—216no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—44no—
680C2×C4—438no—
681C2×C4—434no—
682C2×C4—434no—
683C2×C4—868no—
684C2×C4—868no—
685C2×C4—864no—
686C2×C4—864no—
687C2×C4—864no—
688C2×C4—864no—
689C2×C4—8616no—
690C2×C4—864no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—864no—
695C2×C4—862no—
696C2×C4—17216no—
697C2×C4—17216no—
698C2×C4—1728no—
699C2×C4—1724no—
700C2×C4C22×C22⋊D4318yes—
701C22—28no—
702C22—28no—
703C22—24no—
704C22—24no—
705C22—232no—
706C22—28no—
707C22—28no—
708C22—28no—
709C22—464no—
710C22—44no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—432no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—88no—
721C22—3448no—
722C22—1724no—
723C22—1724no—
724C22—1722no—
725C22—1722no—
726C22—1722no—
727C22#1458340514yes—
728C22C2×#1306332118yes—
729C22C2×#1306332114yes—
730C22#1458345914yes—
731C22#1458353618yes—
732C22#1458354318yes—
733C22C22×D4×D4311yescharacteristic
734C22C22×D4×D4311yescharacteristic
735C22C23×C22⋊D4311yescharacteristic
736C22C22×#1062190012yes—
737C22C2×#1306337012yes—
738C4—28no—
739C4—42no—
740C4—868no—
741C4—864no—
742C4—864no—
743C4—1724no—
744C4—1722no—
745C2—28no—
746C2—48no—
747C2—82no—
748C2—3442no—
749C2#1913952318yesdirect product factor
750C2C2×#1458340511yescharacteristic
751C2C22×#1306332111yescharacteristic
752C2C2×#1458345911yescharacteristic
753C2C2×#1458353612yes—
754C2C2×#1458354312yes—
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#120×C43C2
socleC24×C43C24
hypercenterC22×#120D43
hypocenterC43C2×#2539
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C22×#13063309C2semidirect
2. C22×#13063306C2semidirect
3. C22×#13063297C2semidirect
4. C22×#13063294C2semidirect
5. C23×C22⋊Dic43C2semidirect
6. #19139523C2direct (N × H)
7. C2×#14582835C2semidirect
8. C2×#14582807C2semidirect
9. C2×#14582802C2semidirect
10. C2×#14582799C2semidirect
11. C2×C22⋊C4×Dic43C2semidirect
12. C22×#120×C43C2semidirect
15. C23×C22⋊D43C22semidirect
19. C2×#13063309C22semidirect
21. C2×#13063306C22semidirect
23. C2×#13063297C22semidirect
25. C2×#13063294C22semidirect
26. C22×C4⋊Dic43C22semidirect
27. C22×Dic43⋊C4C22semidirect
28. C22×Dic43⋊C4C22semidirect
34. C22×C22⋊Dic43C22semidirect
35. C22×C22⋊Dic43C22semidirect
36. C22×C22⋊Dic43C22semidirect
37. C22×(C2×D43)⋊C4C22semidirect
38. C22×(C2×D43)⋊C4C22semidirect
39. C22×C4×Dic43C22semidirect
40. #14582835C22semidirect
41. #14582807C22semidirect
42. #14582802C22semidirect
43. #14582799C22semidirect
44. C22⋊C4×Dic43C22semidirect
45. C2×C43⋊#95C22semidirect
50. C2×#120×C43C22semidirect
64. C22×C22⋊D43C23semidirect
69. C23×Dic43D4semidirect
82. C2×C4⋊Dic43C23semidirect
85. C2×Dic43⋊C4C23semidirect
86. C2×Dic43⋊C4C23semidirect
93. C2×C22⋊Dic43D4semidirect
98. C2×C22⋊Dic43C23semidirect
99. C2×C22⋊Dic43C23semidirect
102. C2×(C2×D43)⋊C4C23semidirect
103. C2×(C2×D43)⋊C4C23semidirect
105. C2×C4×Dic43C23semidirect
106. C43⋊#95C23semidirect
128. C2×C22⋊C4×C43D4semidirect
214. C22×Dic43C2×D4semidirect
221. C22⋊C4×C43C2×D4semidirect
227. C22⋊Dic43C2×D4semidirect
372. C22×#120D43semidirect
383. C2×C43#2539semidirect
407. C2×#120C2×D43semidirect
430. C43C2×#2539semidirect
503. C2×C22⋊C4C22⋊D43semidirect
610. C22⋊C4C2×C22⋊D43semidirect
749. C2#19139523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633092
C22×#130633062
C22×#130632972
C22×#130632942
C23×C22⋊Dic432
#191395232
C2×#145828352
C2×#145828072
C2×#145828022
C2×#145827992
C2×C22⋊C4×Dic432
C22×#120×C432
C2×#253943