Finite Group Databasebeta

← C4×#1464 #182000

Subgroups — C4×#1464 #182000

Order 512.

1570 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#117C211yesmaximal, characteristic
2C4×#432C212yesmaximal, complemented
3C2×#1464C212yesmaximal
4#8153C212yesmaximal, complemented
5#8152C212yesmaximal
6C4×#324C212yesmaximal, complemented
7C4×#323C212yesmaximal
8#7910C212yesmaximal, complemented
9C22×#117C411yescharacteristic
10C22×#117C2211yescharacteristic
11C23×C42C411yescharacteristic
12C2×#432C2214yes—
13C4×#117—22no—
14C4×#117—22no—
15C4×#117—22no—
16C4×#117—22no—
17C2×C4×C4⋊C4C411yescharacteristic
18C2×C4×C4⋊C4C411yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C22⋊C4C411yescharacteristic
22C2×C4×C22⋊C4C411yescharacteristic
23C2×C4×C22⋊C4C2211yescharacteristic
24C2×C4×C22⋊C4C2211yescharacteristic
25C2×#376C411yescharacteristic
26C2×#376C2211yescharacteristic
27C2×C43C411yescharacteristic
28C2×C43C2211yescharacteristic
29#1767—22no—
30C4×C4⋊C8—22no—
31#1749C2214yes—
32C4×C22⋊C8C2214yes—
33#1745—22no—
34C4×#97—22no—
35#1464C4116yesdirect product factor
36C2×#324C2214yes—
37C2×#323C2214yes—
38#1280C2214yes—
39#1280C2214yes—
40C24×C4C2×C411yescharacteristic
41C24×C4C2×C411yescharacteristic
42C24×C4C2×C411yescharacteristic
43C2×#117—24no—
44C2×#117—24no—
45C2×#117—22no—
46C2×#117—22no—
47C2×#117—22no—
48C2×#117—22no—
49C2×#117—24no—
50C2×#117C2×C418yes—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4C2×C411yescharacteristic
57C22×C22⋊C4C2×C411yescharacteristic
58C22×C22⋊C4C2311yescharacteristic
59C22×C42—24no—
60C22×C42—21no—
61C22×C42—21no—
62C22×C42—21no—
63C22×C42—21no—
64C22×C42—24no—
65C22×C42C2×C411yescharacteristic
66C22×C42C2×C411yescharacteristic
67C22×C42C2×C411yescharacteristic
68C22×C42C2×C411yescharacteristic
69C22×C42C2×C411yescharacteristic
70C22×C42C2×C411yescharacteristic
71C22×C42C2×C411yescharacteristic
72C22×C42C2×C411yescharacteristic
73C22×C42C2×C411yescharacteristic
74C22×C42C2×C411yescharacteristic
75C22×C42C2×C411yescharacteristic
76C22×C42C2×C411yescharacteristic
77C22×C42C2×C411yescharacteristic
78C22×C42C2311yescharacteristic
79C22×C42C2311yescharacteristic
80C22×C42C2311yescharacteristic
81#432—28no—
82#432C2×C4116yescomplemented
83C2×C4⋊C8—24no—
84C2×C22⋊C8C2318yes—
85C2×#97—24no—
86C2×#97—24no—
87C2×C4×C8—24no—
88C4×C4⋊C4—22no—
89C4×C4⋊C4—22no—
90C4×C4⋊C4—22no—
91C4×C4⋊C4—22no—
92C4×C4⋊C4—22no—
93C4×C4⋊C4—22no—
94C4×C4⋊C4—22no—
95C4×C4⋊C4—22no—
96C4×C22⋊C4—22no—
97C4×C22⋊C4—22no—
98C4×C22⋊C4—22no—
99C4×C22⋊C4—22no—
100C4×C22⋊C4—22no—
101C4×C22⋊C4—22no—
102C4×C22⋊C4—22no—
103C4×C22⋊C4—22no—
104#376—22no—
105#376—22no—
106#376—22no—
107#376—22no—
108C2×#95C2×C411yescharacteristic
109C2×#95C2×C411yescharacteristic
110C2×#95C2×C411yescharacteristic
111C2×#95C2×C411yescharacteristic
112C2×#95C2×C411yescharacteristic
113C2×#95C2×C411yescharacteristic
114C2×#95C2311yescharacteristic
115C2×#95C2311yescharacteristic
116C43—21no—
117C43—21no—
118C43—21no—
119C43—21no—
120C43D412yes—
121C43D412yes—
122C43D412yes—
123C43D412yes—
124#336—24no—
125#336—24no—
126#324C2×C4116yescomplemented
127#323C2×C4116yes—
128C25C22×C411yescharacteristic
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—22no—
134C23×C4—22no—
135C23×C4—22no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—22no—
142C23×C4—22no—
143C23×C4—42no—
144C23×C4—42no—
145C23×C4—42no—
146C23×C4—42no—
147C23×C4C4214yes—
148C23×C4M1614yes—
149C23×C4C22×C411yescharacteristic
150C23×C4C22×C411yescharacteristic
151C23×C4C22×C411yescharacteristic
152C23×C4C22×C411yescharacteristic
153C23×C4C22×C411yescharacteristic
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C22×C411yescharacteristic
157C23×C4C22×C411yescharacteristic
158C23×C4C22×C411yescharacteristic
159C23×C4C22×C411yescharacteristic
160C23×C4C22×C411yescharacteristic
161C23×C4C22×C411yescharacteristic
162C23×C4C2411yescharacteristic
163C22×C8—28no—
164#117—216no—
165#117—216no—
166#117—216no—
167#117—216no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4C4214yes—
178C2×C4⋊C4M1614yes—
179C2×C4⋊C4C22×C414yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4C4214yes—
190C2×C22⋊C4M1614yes—
191C2×C22⋊C4C22×C414yes—
192C2×C42—28no—
193C2×C42—28no—
194C2×C42—28no—
195C2×C42—28no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42—21no—
225C2×C42—21no—
226C2×C42—42no—
227C2×C42—42no—
228C2×C42—42no—
229C2×C42—42no—
230C2×C42—42no—
231C2×C42—42no—
232C2×C42—42no—
233C2×C42—42no—
234C2×C42C4214yes—
235C2×C42C22⋊C412yes—
236C2×C42C22⋊C412yes—
237C2×C42C22⋊C411yescharacteristic
238C2×C42C22⋊C411yescharacteristic
239C2×C42C22⋊C412yes—
240C2×C42C22⋊C411yescharacteristic
241C2×C42C22⋊C411yescharacteristic
242C2×C42C22⋊C412yes—
243C2×C42C22⋊C412yes—
244C2×C42C22⋊C412yes—
245C2×C42M1614yes—
246C2×C42C22×C414yes—
247C2×C42C2×D412yes—
248C2×C42C2×D412yes—
249C2×C42C2×D412yes—
250C2×C42C2×D412yes—
251C2×C42C2×D412yes—
252C2×C42C2×D412yes—
253C2×C42#4114yes—
254C4⋊C8—216no—
255C22⋊C8—28no—
256C22⋊C8C22×C4116yes—
257#97—216no—
258#97—48no—
259C4×C8—48no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95—22no—
267#95—22no—
268C24—21no—
269C24—21no—
270C24—21no—
271C24—21no—
272C24—41no—
273C24—41no—
274C24—41no—
275C24—41no—
276C24C2×C4212yes—
277C24C2×M1612yes—
278C24C2×M1612yes—
279C24C23×C411yescharacteristic
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—28no—
285C22×C4—28no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—28no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—28no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—48no—
331C22×C4—48no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—48no—
337C22×C4—48no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4C2×C4212yes—
355C22×C4C2×C4212yes—
356C22×C4C2×C4212yes—
357C22×C4C2×C4212yes—
358C22×C4C2×C4212yes—
359C22×C4C2×C22⋊C412yes—
360C22×C4C2×C22⋊C412yes—
361C22×C4C2×C22⋊C411yescharacteristic
362C22×C4C2×C22⋊C411yescharacteristic
363C22×C4C2×C22⋊C412yes—
364C22×C4C2×C22⋊C411yescharacteristic
365C22×C4C2×C22⋊C411yescharacteristic
366C22×C4C2×C22⋊C411yescharacteristic
367C22×C4C2×C22⋊C411yescharacteristic
368C22×C4#11712yes—
369C22×C4#11712yes—
370C22×C4C2×M1612yes—
371C22×C4C2×M1612yes—
372C22×C4C2×M1612yes—
373C22×C4C2×M1612yes—
374C22×C4C2×M1612yes—
375C22×C4C2×M1612yes—
376C22×C4C2×M1612yes—
377C22×C4C2×M1612yes—
378C22×C4C2×M1612yes—
379C22×C4C2×M1612yes—
380C22×C4C23×C412yes—
381C22×C4C22×D412yes—
382C22×C4C2×#4112yes—
383C2×C8—216no—
384C2×C8—48no—
385C2×C8—48no—
386C4⋊C4—28no—
387C4⋊C4—28no—
388C4⋊C4—28no—
389C4⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C42—24no—
395C42—24no—
396C42—24no—
397C42—24no—
398C42—24no—
399C42—24no—
400C42—24no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42—24no—
407C42—24no—
408C42—24no—
409C42—24no—
410C42—24no—
411C42—24no—
412C42—24no—
413C42—24no—
414C42—42no—
415C42—42no—
416C42—42no—
417C42—42no—
418C42—42no—
419C42—42no—
420C42—42no—
421C42—42no—
422C42—42no—
423C42—42no—
424C42—42no—
425C42—42no—
426C42C4×D418yes—
427C42C4×D418yes—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23C4×M1614yes—
455C23C22×C4211yescharacteristic
456C23C22×C22⋊C411yescharacteristic
457C23C2×#11711yescharacteristic
458C23C22×M1611yescharacteristic
459C23C22×M1611yescharacteristic
460C23C22×M1611yescharacteristic
461C23C22×M1611yescharacteristic
462C2×C4—216no—
463C2×C4—216no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—48no—
510C2×C4—48no—
511C2×C4—48no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—48no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4C4×C22⋊C412yes—
540C2×C4C4×C22⋊C412yes—
541C2×C4C4×C22⋊C414yes—
542C2×C4C4×M1614yes—
543C2×C4#40712yes—
544C2×C4#40714yes—
545C2×C4#40712yes—
546C2×C4#41012yes—
547C2×C4#41012yes—
548C2×C4#41312yes—
549C2×C4#41312yes—
550C2×C4C2×C4×D414yes—
551C8—416no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—24no—
565C22—44no—
566C22—44no—
567C22—44no—
568C22—44no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22C2×C4×C22⋊C411yescharacteristic
576C22C2×C4×M1611yescharacteristic
577C22C2×C4×M1611yescharacteristic
578C22C2×#40711yescharacteristic
579C22C2×#40711yescharacteristic
580C22C2×#41011yescharacteristic
581C22C2×#41011yescharacteristic
582C22C2×#41311yescharacteristic
583C22C2×#41311yescharacteristic
584C22#292011yescharacteristic
585C22#292011yescharacteristic
586C4—22no—
587C4—22no—
588C4—24no—
589C4—24no—
590C4—24no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—24no—
595C4—42no—
596C4—42no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4#146414yesdirect product factor
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—44no—
608C2C2×#146411yescharacteristic
609C2#1735711yescharacteristic
610C2#1736311yescharacteristic
611C2#1736611yescharacteristic
612C2C4×#40711yescharacteristic
613C2C4×#41011yescharacteristic
614C2C4×#41311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC23C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#432C2semidirect
4. #8153C2semidirect
6. C4×#324C2semidirect
8. #7910C2semidirect
35. #1464C4direct (N × H)
82. #432C2×C4semidirect
126. #324C2×C4semidirect
602. C4#1464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1172
C4×#4322
C2×#14642
#81532
#81522
C4×#3242
C4×#3232
#79102