Finite Group Databasebeta

← C4×#1890 #354284

Subgroups — C4×#1890 #354284

Order 512.

2358 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#123C211yesmaximal, characteristic
2C4×#518C211yesmaximal, characteristic
3C2×#1890C212yesmaximal
4C2×C4×#99C211yesmaximal, characteristic
5C4×#381C212yesmaximal, complemented
6#10936C212yesmaximal, complemented
7#10918C212yesmaximal, complemented
8#10745C212yesmaximal
9C4×#342C212yesmaximal, complemented
10C22×#123C2211yescharacteristic
11C2×#518C2212yes—
12C22×C4×D4C2211yescharacteristic
13C23×C42C2211yescharacteristic
14C22×#99C2212yes—
15C4×#123—24no—
16C4×#123C418yescomplemented
17C2×#388—21no—
18C2×#387—21no—
19C2×#386C2211yescharacteristic
20C2×#385C2211yescharacteristic
21C2×#381C2211yescharacteristic
22C2×#381C2214yes—
23#2275—24no—
24#2274—21no—
25#2273—21no—
26#2273C2212yes—
27C42×D4—24no—
28C4×#117—21no—
29C2×C4×C4⋊C4—21no—
30C2×C4×C22⋊C4—21no—
31C2×C4×C22⋊C4—21no—
32C2×C4×C22⋊C4C2212yes—
33C2×C4×C22⋊C4C2211yescharacteristic
34C2×C4×C22⋊C4C2212yes—
35#1890C4116yesdirect product factor
36C4×#99—24no—
37C2×#342C2212yes—
38C2×#342C2214yes—
39C2×#342C2214yes—
40#1434—24no—
41C22⋊#95C2214yes—
42C4×#95—24no—
43C23×D4C2311yescharacteristic
44C24×C4D411yescharacteristic
45C24×C4C2311yescharacteristic
46C24×C4C2311yescharacteristic
47C24×C4C2311yescharacteristic
48C2×#123—22no—
49C2×#123—24no—
50C2×#123C2×C418yes—
51C2×#123C2×C414yes—
52#518—24no—
53#518—28no—
54#518C2×C418yes—
55C2×C4×D4—22no—
56C2×C4×D4—22no—
57C2×C4×D4—28no—
58C2×C4×D4—24no—
59C2×C4×D4C2×C414yes—
60C2×C4×D4D414yes—
61C2×#117—22no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4D411yescharacteristic
65C22×C22⋊C4—22no—
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4D411yescharacteristic
69C22×C22⋊C4C2314yes—
70C22×C22⋊C4C2311yescharacteristic
71C22×C22⋊C4C2311yescharacteristic
72C22×C22⋊C4C2314yes—
73C22×C22⋊C4C2311yescharacteristic
74C22×C42—22no—
75C22×C42—22no—
76C22×C42—21no—
77C22×C42—21no—
78C22×C42—22no—
79C22×C42—21no—
80C22×C42—24no—
81C22×C42—22no—
82C22×C42—22no—
83C22×C42C2×C414yescomplemented
84C22×C42D411yescharacteristic
85C22×C42D414yes—
86C2×#99—24no—
87C2×#99—24no—
88C2×#99C2×C418yes—
89#388—28no—
90#387—28no—
91#386—22no—
92#386C2×C414yes—
93#385—22no—
94#385C2×C414yescomplemented
95#381—22no—
96#381—28no—
97#381C2×C4116yescomplemented
98#381C2×C414yescomplemented
99C4×C4⋊C4—22no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—28no—
102C4×C4⋊C4—28no—
103C4×C22⋊C4—22no—
104C4×C22⋊C4—22no—
105C4×C22⋊C4—28no—
106C4×C22⋊C4—28no—
107C4×C22⋊C4—22no—
108C4×C22⋊C4—22no—
109C4×C22⋊C4—22no—
110C4×C22⋊C4—22no—
111C4×C22⋊C4—22no—
112C4×C22⋊C4—22no—
113C4×C22⋊C4—22no—
114C4×C22⋊C4—28no—
115C4×C22⋊C4—24no—
116C4×C22⋊C4—24no—
117C4×C22⋊C4C2×C414yescomplemented
118#376—22no—
119C2×#95—22no—
120C2×#95—28no—
121C2×#95—21no—
122C2×#95—21no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—28no—
127C2×#95—22no—
128C2×#95D414yes—
129C43—22no—
130#342—24no—
131#342—28no—
132#342C2×C4116yescomplemented
133C25C2×D411yescharacteristic
134C25C2411yescharacteristic
135C22×D4—22no—
136C22×D4—22no—
137C22×D4—24no—
138C22×D4C22×C412yes—
139C22×D4C22×C414yes—
140C22×D4C2×D412yes—
141C22×D4#4114yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—22no—
147C23×C4—22no—
148C23×C4—22no—
149C23×C4—24no—
150C23×C4—22no—
151C23×C4—24no—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—22no—
155C23×C4—21no—
156C23×C4—24no—
157C23×C4—21no—
158C23×C4—22no—
159C23×C4—44no—
160C23×C4—44no—
161C23×C4—44no—
162C23×C4C22⋊C414yes—
163C23×C4C22×C414yes—
164C23×C4C22×C412yes—
165C23×C4C22×C412yes—
166C23×C4C22×C412yes—
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D412yes—
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D418yes—
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D412yes—
175C23×C4C2×D412yes—
176C23×C4#4114yes—
177#123—28no—
178#123—216no—
179#123C42116yescomplemented
180C4×D4—232no—
181C4×D4—28no—
182C4×D4—28no—
183C4×D4—232no—
184C4×D4—28no—
185C4×D4—28no—
186#117—28no—
187#117—28no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—28no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4C22⋊C414yes—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—28no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—28no—
200C2×C22⋊C4—28no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—24no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—24no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—24no—
216C2×C22⋊C4—24no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—24no—
219C2×C22⋊C4—44no—
220C2×C22⋊C4C22⋊C414yes—
221C2×C22⋊C4C22×C418yes—
222C2×C22⋊C4C22×C412yes—
223C2×C22⋊C4C22×C412yes—
224C2×C22⋊C4C22×C418yes—
225C2×C22⋊C4C22×C414yes—
226C2×C22⋊C4C22×C412yes—
227C2×C22⋊C4C2×D412yes—
228C2×C22⋊C4#4118yes—
229C2×C42—24no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42—24no—
234C2×C42—24no—
235C2×C42—24no—
236C2×C42—28no—
237C2×C42—28no—
238C2×C42—24no—
239C2×C42—24no—
240C2×C42—24no—
241C2×C42—24no—
242C2×C42—44no—
243C2×C42—41no—
244C2×C42—42no—
245C2×C42—41no—
246C2×C42—44no—
247C2×C42—44no—
248C2×C42—42no—
249C2×C42—42no—
250C2×C42—48no—
251C2×C42—48no—
252C2×C42—44no—
253C2×C42—84no—
254C2×C42C22⋊C414yes—
255#99—216no—
256#95—24no—
257#95—24no—
258#95—24no—
259#95—24no—
260#95—24no—
261#95—24no—
262#95—24no—
263#95—232no—
264#95—24no—
265#95—24no—
266#95—416no—
267#95—44no—
268C24—21no—
269C24—21no—
270C24—22no—
271C24—42no—
272C24—42no—
273C24—42no—
274C24—42no—
275C24C2×C22⋊C412yes—
276C24C4×D414yes—
277C24C23×C411yescharacteristic
278C24C23×C412yes—
279C24C22×D411yescharacteristic
280C24C22×D412yes—
281C24C22×D411yescharacteristic
282C24C2×#4112yes—
283C24C2×#4112yes—
284C24C2×#4114yes—
285C2×D4—24no—
286C2×D4—28no—
287C2×D4—24no—
288C2×D4—28no—
289C2×D4—24no—
290C2×D4—28no—
291C2×D4—28no—
292C2×D4—24no—
293C2×D4C2×C4214yes—
294C2×D4#11714yes—
295C2×D4C4×D418yes—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—28no—
300C22×C4—24no—
301C22×C4—28no—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—28no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—28no—
315C22×C4—21no—
316C22×C4—28no—
317C22×C4—21no—
318C22×C4—216no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—28no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—28no—
326C22×C4—44no—
327C22×C4—44no—
328C22×C4—44no—
329C22×C4—48no—
330C22×C4—42no—
331C22×C4—44no—
332C22×C4—44no—
333C22×C4—48no—
334C22×C4—48no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—44no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—44no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—42no—
349C22×C4—44no—
350C22×C4—48no—
351C22×C4—48no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—48no—
355C22×C4—42no—
356C22×C4—48no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—42no—
360C22×C4—44no—
361C22×C4—84no—
362C22×C4—82no—
363C22×C4—84no—
364C22×C4—84no—
365C22×C4C2×C4214yescomplemented
366C22×C4C2×C22⋊C412yes—
367C22×C4C2×C22⋊C412yes—
368C22×C4C2×C22⋊C412yes—
369C22×C4C2×C22⋊C412yes—
370C22×C4C2×C22⋊C412yes—
371C22×C4C4×D414yes—
372C22×C4C4×D414yes—
373C22×C4C4×D4116yes—
374C22×C4C4×D414yes—
375C22×C4#12011yescharacteristic
376C22×C4#12012yes—
377C22×C4#12011yescharacteristic
378C22×C4#12114yes—
379C22×C4#12114yes—
380C22×C4#12312yes—
381C22×C4#12312yes—
382C4⋊C4—216no—
383C4⋊C4—216no—
384C4⋊C4—28no—
385C4⋊C4—48no—
386C22⋊C4—216no—
387C22⋊C4—22no—
388C22⋊C4—28no—
389C22⋊C4—24no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—28no—
394C22⋊C4—28no—
395C22⋊C4—216no—
396C22⋊C4—28no—
397C22⋊C4—28no—
398C22⋊C4—24no—
399C22⋊C4—28no—
400C22⋊C4—48no—
401C22⋊C4—44no—
402C22⋊C4—42no—
403C22⋊C4—44no—
404C22⋊C4C2×C4214yescomplemented
405C42—216no—
406C42—24no—
407C42—24no—
408C42—48no—
409C42—44no—
410C42—48no—
411C42—44no—
412C42—48no—
413C42—84no—
414C42—88no—
415C42—84no—
416C42—84no—
417C23—24no—
418C23—22no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—24no—
423C23—22no—
424C23—24no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—48no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—48no—
437C23—42no—
438C23—42no—
439C23—81no—
440C23—81no—
441C23—84no—
442C23C4×C22⋊C414yes—
443C23C22×C4211yescharacteristic
444C23C22×C22⋊C411yescharacteristic
445C23C2×#11711yescharacteristic
446C23C2×C4×D412yes—
447C23C2×C4×D412yes—
448C23C2×C4×D414yes—
449C23C2×C4×D412yes—
450C23C4×#4112yes—
451C23C4×#4114yes—
452C23C2×#12011yescharacteristic
453C23C2×#12112yes—
454C23C2×#12311yescharacteristic
455C23#52514yes—
456C23#52512yes—
457C23#52914yes—
458C23#53212yes—
459D4—28no—
460D4—28no—
461D4—216no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—24no—
471C2×C4—28no—
472C2×C4—24no—
473C2×C4—28no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—28no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—216no—
480C2×C4—42no—
481C2×C4—44no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—48no—
487C2×C4—42no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—48no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—48no—
502C2×C4—44no—
503C2×C4—48no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—416no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—416no—
510C2×C4—42no—
511C2×C4—48no—
512C2×C4—84no—
513C2×C4—81no—
514C2×C4—88no—
515C2×C4—81no—
516C2×C4—816no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4—88no—
520C2×C4—84no—
521C2×C4C4×C22⋊C414yes—
522C2×C4#38612yes—
523C2×C4#38614yes—
524C2×C4#38612yes—
525C2×C4#45814yes—
526C22—21no—
527C22—22no—
528C22—21no—
529C22—22no—
530C22—21no—
531C22—22no—
532C22—22no—
533C22—21no—
534C22—28no—
535C22—24no—
536C22—28no—
537C22—24no—
538C22—24no—
539C22—41no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—44no—
544C22—42no—
545C22—41no—
546C22—44no—
547C22—42no—
548C22—42no—
549C22—48no—
550C22—82no—
551C22—84no—
552C22C2×C4×C22⋊C411yescharacteristic
553C22C42×D412yes—
554C22C2×#38611yescharacteristic
555C22#229012yes—
556C22#229711yescharacteristic
557C22C4×#12012yes—
558C22C4×#12114yes—
559C22C4×#12312yes—
560C22C2×#45812yes—
561C22#302512yes—
562C4—24no—
563C4—22no—
564C4—24no—
565C4—44no—
566C4—44no—
567C4—42no—
568C4—44no—
569C4—42no—
570C4—416no—
571C4—82no—
572C4—88no—
573C4#189014yesdirect product factor
574C2—21no—
575C2—21no—
576C2—24no—
577C2—22no—
578C2—22no—
579C2—22no—
580C2—44no—
581C2C4×#38611yescharacteristic
582C2C2×#189011yescharacteristic
583C2#2095911yescharacteristic
584C2C4×#45814yes—
subgroupG/H
centerC22×C4#120
commutatorC23C22×C42
Frattini, cosocleC25C24
socleC23C2×#120
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
5. C4×#381C2semidirect
6. #10936C2semidirect
7. #10918C2semidirect
9. C4×#342C2semidirect
16. C4×#123C4semidirect
35. #1890C4direct (N × H)
83. C22×C42C2×C4semidirect
94. #385C2×C4semidirect
97. #381C2×C4semidirect
98. #381C2×C4semidirect
117. C4×C22⋊C4C2×C4semidirect
132. #342C2×C4semidirect
179. #123C42semidirect
365. C22×C4C2×C42semidirect
404. C22⋊C4C2×C42semidirect
573. C4#1890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1232
C4×#5182
C2×#18902
C2×C4×#992
C4×#3812
#109362
#109182
#107452
C4×#3422