Finite Group Databasebeta

← C4×#14583051 #25102179

Subgroups — C4×#14583051 #25102179

Order 11008.

1880 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D43C211yesmaximal, characteristic
2C2×#14583051C211yesmaximal, characteristic
3C2×C4×#10621873C211yesmaximal, characteristic, complemented
4C2×C4×#10621883C211yesmaximal, characteristic, complemented
5C4×#13063305C211yesmaximal, characteristic, complemented
6#19134930C211yesmaximal, characteristic, complemented
7#19134927C211yesmaximal, characteristic, complemented
8#19134901C211yesmaximal, characteristic, complemented
9#19134858C211yesmaximal, characteristic, complemented
10#19134857C211yesmaximal, characteristic, complemented
11#19134789C211yesmaximal, characteristic, complemented
12#19134524C211yesmaximal, characteristic
13C4×#13063245C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C23×C4×D43—21no—
18C22×#10621873C2211yescharacteristic
19C22×#10621883C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic, complemented
22C2×C4×D172C2211yescharacteristic
23C2×D4×Dic43C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×C4×C22⋊D43—21no—
26C2×(C22⋊D43)⋊C4—21no—
27C4×D4×D43—24no—
28C4×D4×D43—24no—
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31C2×C42×D43C2211yescharacteristic
32#14583051C418yesdirect product factor
33C4×#10621873—24no—
34C4×#10621883—24no—
35C2×#13063257C2211yescharacteristic, complemented
36C2×#13063256C2211yescharacteristic, complemented
37C2×#13063250C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×C4×C43⋊C8C2211yescharacteristic, complemented
46#14582804C2211yescharacteristic, complemented
47#14582798C2211yescharacteristic, complemented
48#14582784—21no—
49#14582773—21no—
50#14582756C2211yescharacteristic
51C4×C4⋊Dic43—21no—
52C4×(C2×D43)⋊C4—21no—
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C2×C4×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic, complemented
61C4×C4⋊C4×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×Dic86C2311yescharacteristic
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—22no—
73C2×D4×D43C2×C414yes—
74C23×Dic43—21no—
75C22×C4×D43—28no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C22×C4×D43—21no—
79C22×C4×D43—44no—
80C22×C4×D43—44no—
81C22×C4×D43D411yescharacteristic
82C22×C4×D43D411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621873—22no—
85C2×#10621873—22no—
86C2×#10621873C2×C414yescomplemented
87C2×#10621883—22no—
88C2×#10621883—22no—
89C2×#10621883C2×C414yescomplemented
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063305—22no—
93#13063305C2×C414yescomplemented
94C4×Dic86—22no—
95C4×Dic86—22no—
96C4×D172—22no—
97C4×D172D414yes—
98D4×Dic43—22no—
99D4×Dic43—22no—
100#13063287—22no—
101#13063287—22no—
102C4×C22⋊D43—28no—
103(C22⋊D43)⋊C4—28no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×Dic43⋊C4—21no—
109C2×Dic43⋊C4—21no—
110C4⋊C4×D43—22no—
111C4⋊C4×D43—22no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C22⋊C4×D43—28no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43D411yescharacteristic
120C2×C4×Dic43D411yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122C42×D43—22no—
123C42×D43—22no—
124#13063257—22no—
125#13063256—22no—
126#13063250—22no—
127#13063248—22no—
128#13063247—22no—
129#13063246—22no—
130#13063245—22no—
131#13063245C2×C414yescomplemented
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8C2×C414yescomplemented
134C4×C43⋊C8—22no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C4×D4×C43—22no—
144C4×D4×C43D414yes—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C4⋊C4×C43C2311yescharacteristic
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150C2×C42×C43C2311yescharacteristic
151#102×C43—22no—
152#102×C43C2×C414yescomplemented
153C4×C8×C43—22no—
154#95×C43—21no—
155C24×C43—21no—
156C23×D43—24no—
157C23×D43—24no—
158C23×D43—21no—
159C23×D43—24no—
160C23×D43—42no—
161C23×D43—42no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43C2×D411yescharacteristic
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43C22×C412yes—
169C2×D4×C43C2×D412yes—
170C2×D4×C43#4112yes—
171C22×C4×C43—24no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—24no—
181C2×C22⋊D43—24no—
182C2×C22⋊D43—24no—
183C22×Dic43—24no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192D4×D43—28no—
193D4×D43—28no—
194D4×D43—28no—
195D4×D43—28no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172—21no—
199C2×D172C22×C412yes—
200C2×D172C2×D412yes—
201C2×D172#4112yes—
202C2×C4×D43—22no—
203C2×C4×D43—22no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—24no—
209C2×C4×D43—24no—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×C4×D43—22no—
213C2×C4×D43—41no—
214C2×C4×D43—42no—
215C2×C4×D43—432no—
216C2×C4×D43—42no—
217C2×C4×D43—42no—
218C2×C4×D43—42no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×C4×D43SD1614yescomplemented
222C2×C4×D43C22×C412yes—
223C2×C4×D43#4112yes—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22×C412yescomplemented
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43C22×C412yescomplemented
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C22×C412yescomplemented
241C4⋊C4×C43C2×D412yes—
242C22⋊C4×C43—24no—
243C42×C43—42no—
244C42×C43C2×D412yes—
245C42×C43C2×D412yes—
246C22⋊Dic43—24no—
247#10621883—28no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—42no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—42no—
257C4⋊Dic43C2×D412yes—
258Dic43⋊C4—24no—
259Dic43⋊C4—42no—
260C4×Dic43—22no—
261C4×Dic43—22no—
262C4×Dic43—21no—
263C4×Dic43—21no—
264C4×Dic43—42no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8C22×C412yescomplemented
271#10621873—28no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—41no—
279C23×C43C22×D411yescharacteristic
280C22×D43—21no—
281C22×D43—21no—
282C22×D43—21no—
283C22×D43—21no—
284C22×D43—216no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—48no—
289C22×D43—48no—
290C22×D43—48no—
291C22×D43—48no—
292C22×D43—48no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—48no—
298C22×D43C4×D412yes—
299C22×D43C2×SD1612yes—
300C22×D43#13512yes—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—22no—
304D4×C43C4×D414yes—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—48no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43#12012yes—
318C2×C4×C43#12012yes—
319C2×C4×C43C2×SD1612yes—
320C2×C4×C43AGL(1,ℤ/8)12yes—
321C2×C4×C43C23×C411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2×#4111yescharacteristic
325C2×C4×C43C2×#4111yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C22⋊D43—216no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—22no—
333C2×Dic43—21no—
334C2×Dic43—22no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—48no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43C4×D412yes—
346C2×Dic43C2×SD1612yes—
347D172—22no—
348D172—22no—
349D172—22no—
350D172C4×D414yes—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—22no—
354C4×D43—22no—
355C4×D43—28no—
356C4×D43—48no—
357C4×D43—44no—
358C4×D43—48no—
359C4×D43—48no—
360Dic86—22no—
361Dic86—22no—
362Dic86—41no—
363Dic86—41no—
364C8×C43—22no—
365C8×C43—41no—
366C43⋊C8—22no—
367C43⋊C8—41no—
368C4×#450—431nomaximal, Sylow
369C22×C43—24no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43C2×C4×D411yescharacteristic
377C22×C43C2×#12011yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43C22×SD1611yescharacteristic
380C22×C43C2×#13511yescharacteristic
381C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
382C22×C43#57511yescharacteristic
383C2×D43—22no—
384C2×D43—22no—
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—24no—
390C2×D43—432no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—42no—
397C2×D43C4×SD1614yescomplemented
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43—81no—
402C4×C43#45014yescomplemented
403C4×C43C2×C4×D411yescharacteristic
404C4×C43C2×C4×D411yescharacteristic
405C4×C43#52511yescharacteristic
406C4×C43#52511yescharacteristic
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—41no—
411Dic43—42no—
412Dic43—81no—
413C22×C4×D4—431no—
414C2×#450—431no—
415C2×C4×SD16—431no—
416C2×C4×SD16—431no—
417C4×C22⋊Q8—431no—
418#1877—431no—
419#1877—431no—
420#1872—431no—
421#1864—431no—
422#1864—431no—
423#1853—431no—
424#1786—431no—
425C4×#102—431no—
426C4×#102D4311yescharacteristic, complemented
427C4×C22⋊C8—431no—
428C2×C43—44no—
429C2×C43C4×#12011yescharacteristic
430C2×C43C2×C4×SD1611yescharacteristic
431C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
432C2×C43C2×#45011yescharacteristic
433C2×C43#300211yescharacteristic
434C2×C43#310111yescharacteristic
435C2×C43#310511yescharacteristic
436D43—24no—
437D43—44no—
438C23×D4—431no—
439C24×C4—861no—
440C22×SD16—431no—
441C22×SD16—431no—
442C2×C22⋊Q8—431no—
443C2×C4×Q8—431no—
444C2×C4×D4—431no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×C4×D4—861no—
449C2×C4×D4—864no—
450C2×C4×D4—864no—
451C2×C4×D4C2×D4311yescharacteristic
452C22×C4⋊C4—431no—
453C22×C22⋊C4—861no—
454C22×C42—431no—
455#450—438no—
456C4×SD16—864no—
457C4×SD16—864no—
458C2×#106—431no—
459C2×#106—431no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102C2×D4311yescharacteristic
467C2×#102C2×D4311yescharacteristic
468C2×C22⋊C8—431no—
469C2×C22⋊C8—431no—
470C2×C4×C8—431no—
471C2×C4×C8C2×D4311yescharacteristic, complemented
472#391—431no—
473#389—431no—
474#387—861no—
475#385—861no—
476#380—431no—
477C4×C4⋊C4—861no—
478C4×C4⋊C4C2×D4311yescharacteristic, complemented
479C4×C22⋊C4—861no—
480#340—431no—
481#340—431no—
482#340C2×D4311yescharacteristic, complemented
483#340C2×D4311yescharacteristic, complemented
484#336—431no—
485#336—431no—
486C43C4×#45011yescharacteristic, complemented, Sylow
487C25—861no—
488C22×Q8—431no—
489C22×D4—434no—
490C22×D4—431no—
491C22×D4—862no—
492C22×D4—861no—
493C22×D4—862no—
494C22×D4—862no—
495C22×D4—862no—
496C22×D4—862no—
497C22×D4C22×D4311yescharacteristic
498C23×C4—21no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—861no—
503C23×C4—861no—
504C23×C4—868no—
505C23×C4—861no—
506C23×C4—861no—
507C23×C4—1724no—
508C23×C4—1724no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—862no—
512C2×SD16—862no—
513C2×SD16—862no—
514C2×SD16—862no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8C22×D4311yescharacteristic
518C22×C8C22×D4311yescharacteristic
519C22⋊Q8—434no—
520C22⋊Q8—862no—
521C4×Q8—862no—
522C4×Q8—862no—
523C4×D4—22no—
524C4×D4—434no—
525C4×D4—868no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—868no—
529C4×D4—862no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4D17214yes—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—862no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—862no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—868no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C42—21no—
552C2×C42—431no—
553C2×C42—431no—
554C2×C42—431no—
555C2×C42—862no—
556C2×C42—862no—
557C2×C42—861no—
558C2×C42C22×D4311yescharacteristic
559#106—862no—
560#106—862no—
561#103—862no—
562#103—862no—
563#102—22no—
564#102—434no—
565#102—862no—
566#102—862no—
567#102—862no—
568#102C4×D4314yescomplemented
569C22⋊C8—434no—
570C22⋊C8—862no—
571C4×C8—22no—
572C4×C8—862no—
573#95—21no—
574#95—861no—
575#95—861no—
576#95—861no—
577#95—861no—
578C24—21no—
579C24—431no—
580C24—864no—
581C24—864no—
582C24—864no—
583C24—861no—
584C24—1722no—
585C24—1722no—
586C24—1722no—
587C24—1722no—
588C2×Q8—432no—
589C2×Q8—861no—
590C2×Q8—861no—
591C2×Q8—861no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—432no—
598C2×D4—432no—
599C2×D4—432no—
600C2×D4—864no—
601C2×D4—868no—
602C2×D4—868no—
603C2×D4—868no—
604C2×D4—864no—
605C2×D4—864no—
606C2×D4—868no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4C2×C4×D4312yes—
611C2×D4C2×D17212yes—
612C2×D4#1062189812yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—434no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—431no—
625C22×C4—862no—
626C22×C4—864no—
627C22×C4—864no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—862no—
638C22×C4—864no—
639C22×C4—861no—
640C22×C4—1721no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—17232no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4C23×D4311yescharacteristic
653SD16—868no—
654SD16—868no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—432no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8C2×C4×D4312yescomplemented
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—432no—
672C4⋊C4—864no—
673C4⋊C4—864no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—861no—
677C4⋊C4—1722no—
678C4⋊C4—1722no—
679C4⋊C4C2×C4×D4312yescomplemented
680C4⋊C4C2×D17212yes—
681C22⋊C4—24no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C22⋊C4—864no—
686C22⋊C4—1722no—
687C42—42no—
688C42—862no—
689C42—862no—
690C42—861no—
691C42—861no—
692C42—1722no—
693C42C2×D17212yes—
694C42D4×D4312yes—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—432no—
703C23—432no—
704C23—432no—
705C23—8616no—
706C23—861no—
707C23—861no—
708C23—861no—
709C23—861no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—1728no—
714C23—1728no—
715C23—1728no—
716C23—1728no—
717C23—1728no—
718C23—1728no—
719C23—1721no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23C2×D4×D4311yescharacteristic
724Q8—862no—
725Q8—862no—
726Q8—1721no—
727Q8—1721no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—434no—
732D4—8616no—
733D4—862no—
734D4—862no—
735D4—862no—
736D4C4×D17214yes—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—48no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—861no—
752C2×C4—861no—
753C2×C4—861no—
754C2×C4—861no—
755C2×C4—868no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—861no—
762C2×C4—862no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—1724no—
766C2×C4—1728no—
767C2×C4—1728no—
768C2×C4—1728no—
769C2×C4—1721no—
770C2×C4—1721no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1728no—
777C2×C4#1306329512yes—
778C2×C4#1306329512yes—
779C2×C4SD16×D4312yes—
780C2×C4#1306334912yes—
781C2×C4C22×C4×D4311yescharacteristic
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4C22×D17211yescharacteristic
784C2×C4#41×D4311yescharacteristic
785C2×C4#41×D4311yescharacteristic
786C2×C4C2×#1062189811yescharacteristic
787C8—22no—
788C8—41no—
789C8—862no—
790C8—1721no—
791C22—24no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—434no—
799C22—862no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—862no—
805C22—864no—
806C22—17232no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1722no—
813C22C4×D4×D4311yescharacteristic
814C22C2×#1306329511yescharacteristic
815C22#1458340811yescharacteristic
816C22C2×SD16×D4311yescharacteristic
817C22#135×D4311yescharacteristic
818C22C2×#1306334911yescharacteristic
819C22#1458369611yescharacteristic
820C4—22no—
821C4—42no—
822C4—42no—
823C4—81no—
824C4—862no—
825C4—862no—
826C4—3441no—
827C4—1722no—
828C4—1722no—
829C4—1721no—
830C4#1458305114yesdirect product factor
831C4C4×D4×D4311yescharacteristic
832C4C2×C4×D17211yescharacteristic
833C4#1458340811yescharacteristic
834C4#1458341111yescharacteristic
835C2—44no—
836C2—864no—
837C2—1724no—
838C2C4×#1306329511yescharacteristic
839C2C4×SD16×D4311yescharacteristic
840C2C4×#1306334911yescharacteristic
841C2C2×#1458305111yescharacteristic
842C2#1914381511yescharacteristic
843C2#1914460111yescharacteristic
844C2#1914464011yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43C4×#450
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621873C2semidirect
4. C2×C4×#10621883C2semidirect
5. C4×#13063305C2semidirect
6. #19134930C2semidirect
7. #19134927C2semidirect
8. #19134901C2semidirect
9. #19134858C2semidirect
10. #19134857C2semidirect
11. #19134789C2semidirect
13. C4×#13063245C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C4×#102×C43C2semidirect
21. C2×C4×Dic86C22semidirect
32. #14583051C4direct (N × H)
35. C2×#13063257C22semidirect
36. C2×#13063256C22semidirect
37. C2×#13063250C22semidirect
38. C2×#13063248C22semidirect
45. C2×C4×C43⋊C8C22semidirect
46. #14582804C22semidirect
47. #14582798C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
60. C2×C4×C8×C43C22semidirect
61. C4×C4⋊C4×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
86. C2×#10621873C2×C4semidirect
89. C2×#10621883C2×C4semidirect
93. #13063305C2×C4semidirect
131. #13063245C2×C4semidirect
133. (C2×D43)⋊C8C2×C4semidirect
152. #102×C43C2×C4semidirect
221. C2×C4×D43SD16semidirect
229. C2×Dic86C22×C4semidirect
235. C2×C8×C43C22×C4semidirect
240. C4⋊C4×C43C22×C4semidirect
270. C2×C43⋊C8C22×C4semidirect
397. C2×D43C4×SD16semidirect
402. C4×C43#450semidirect
426. C4×#102D43semidirect
471. C2×C4×C8C2×D43semidirect
478. C4×C4⋊C4C2×D43semidirect
482. #340C2×D43semidirect
483. #340C2×D43semidirect
486. C43C4×#450semidirect
568. #102C4×D43semidirect
666. C2×C8C2×C4×D43semidirect
679. C4⋊C4C2×C4×D43semidirect
830. C4#14583051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D432
C2×#145830512
C2×C4×#106218732
C2×C4×#106218832
C4×#130633052
#191349302
#191349272
#191349012
#191348582
#191348572
#191347892
#191345242
C4×#130632452
C4×(C2×D43)⋊C82
C4×#102×C432
C4×#45043