Finite Group Databasebeta

← C4×#1472 #181978

Subgroups — C4×#1472 #181978

Order 512.

1548 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Q8C211yesmaximal, characteristic
2C4×#407C211yesmaximal, characteristic
3C2×C4×C22⋊C8C211yesmaximal, characteristic
4C2×#1472C212yesmaximal
5#8154C214yesmaximal, complemented
6C4×#324C214yesmaximal, complemented
7#7915C212yesmaximal
8C22×C22⋊Q8C2211yescharacteristic
9C22×C4×Q8C411yescharacteristic
10C23×C42C2211yescharacteristic
11C2×#407C2212yes—
12C22×C22⋊C8C2212yes—
13C2×C4×M16—21no—
14C22×C4×C8—21no—
15C4×C22⋊Q8—21no—
16C4×C22⋊Q8—21no—
17C4×C22⋊Q8—21no—
18C4×C22⋊Q8—21no—
19C4×C22⋊Q8—21no—
20C4×C22⋊Q8—21no—
21C4×C22⋊Q8—21no—
22C4×C22⋊Q8—21no—
23C2×#391C411yescharacteristic
24C2×#389C411yescharacteristic
25C2×#387C2212yes—
26C2×#385C412yes—
27C2×#380C2211yescharacteristic
28C2×C4×C4⋊C4C411yescharacteristic
29C2×C4×C4⋊C4C2212yes—
30C2×C4×C22⋊C4C412yes—
31#1749—21no—
32#1749C2212yes—
33C4×C22⋊C8—21no—
34C4×C22⋊C8—21no—
35C4×C22⋊C8—21no—
36C4×C22⋊C8C2212yes—
37C4×C22⋊C8C2212yes—
38C4×C22⋊C8C2212yes—
39#1728—21no—
40C2×#336—21no—
41#1472C4116yesdirect product factor
42C2×#324C2218yes—
43#1280C2218yes—
44C23×Q8C2×C411yescharacteristic
45C24×C4C2×C411yescharacteristic
46C24×C4C2×C411yescharacteristic
47C24×C4C2311yescharacteristic
48C22×M16—22no—
49C23×C8—22no—
50C2×C22⋊Q8—21no—
51C2×C22⋊Q8—21no—
52C2×C22⋊Q8—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—24no—
55C2×C22⋊Q8C2×C418yes—
56C2×C4×Q8—21no—
57C2×C4×Q8—21no—
58C2×C4×Q8—21no—
59C2×C4×Q8—21no—
60C2×C4×Q8—44no—
61C22×C4⋊C4C2×C412yes—
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4C2×C411yescharacteristic
64C22×C4⋊C4C2×C412yes—
65C22×C4⋊C4C2×C411yescharacteristic
66C22×C4⋊C4C2312yes—
67C22×C22⋊C4C2×C412yes—
68C22×C22⋊C4C2×C412yes—
69C22×C42—44no—
70C22×C42C2×C412yes—
71C22×C42C2×C411yescharacteristic
72C22×C42C2×C412yes—
73C22×C42C2×C411yescharacteristic
74C22×C42D411yescharacteristic
75C22×C42D411yescharacteristic
76C22×C42D411yescharacteristic
77C22×C42D411yescharacteristic
78C22×C42D411yescharacteristic
79C22×C42D411yescharacteristic
80C22×C42D411yescharacteristic
81C22×C42D411yescharacteristic
82C22×C42C2311yescharacteristic
83C22×C42C2311yescharacteristic
84#407—24no—
85#407C2×C418yes—
86C2×C22⋊C8—22no—
87C2×C22⋊C8—22no—
88C2×C22⋊C8—24no—
89C2×C22⋊C8C2×C418yes—
90C2×C22⋊C8C2314yes—
91C2×C22⋊C8C2314yes—
92C4×M16—44no—
93C2×#97—22no—
94C2×C4×C8—22no—
95C2×C4×C8—22no—
96C2×C4×C8—22no—
97C2×C4×C8—44no—
98#391—21no—
99#391—21no—
100#391—21no—
101#391—21no—
102#389—21no—
103#389—21no—
104#389—21no—
105#389—21no—
106#387—22no—
107#387—22no—
108#387—22no—
109#387—22no—
110#385—22no—
111#385—22no—
112#385—22no—
113#385—22no—
114#380—21no—
115#380—21no—
116#380—21no—
117#380—21no—
118C4×C4⋊C4—21no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4—21no—
122C4×C4⋊C4—22no—
123C4×C4⋊C4—22no—
124C4×C4⋊C4—22no—
125C4×C4⋊C4—22no—
126C4×C22⋊C4—22no—
127C4×C22⋊C4—22no—
128C4×C22⋊C4—22no—
129C4×C22⋊C4—22no—
130C2×#95C2×C412yes—
131C2×#95C2×C412yes—
132C2×#95C2×C412yes—
133C2×#95C2×C412yes—
134C2×#95C2312yes—
135#336—22no—
136#336—22no—
137#336—22no—
138#336—22no—
139#324C2×C4132yescomplemented
140C25C22×C411yescharacteristic
141C22×Q8—21no—
142C22×Q8—21no—
143C22×Q8—22no—
144C22×Q8—42no—
145C22×Q8—42no—
146C22×Q8C4214yes—
147C23×C4—24no—
148C23×C4—24no—
149C23×C4—24no—
150C23×C4—42no—
151C23×C4—42no—
152C23×C4—42no—
153C23×C4—42no—
154C23×C4—42no—
155C23×C4C22⋊C411yescharacteristic
156C23×C4C22⋊C411yescharacteristic
157C23×C4C22⋊C411yescharacteristic
158C23×C4C22⋊C411yescharacteristic
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C411yescharacteristic
161C23×C4C22⋊C411yescharacteristic
162C23×C4C22⋊C411yescharacteristic
163C23×C4C22×C412yes—
164C23×C4C22×C411yescharacteristic
165C23×C4C22×C411yescharacteristic
166C23×C4C22×C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C22×C412yes—
169C23×C4C22×C412yes—
170C23×C4C22×C412yes—
171C23×C4C22×C414yes—
172C23×C4C22×C411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4#4114yes—
178C23×C4C2411yescharacteristic
179C2×M16—28no—
180C2×M16—44no—
181C2×M16—44no—
182C22×C8—28no—
183C22×C8—24no—
184C22×C8—24no—
185C22×C8—44no—
186C22×C8—44no—
187C22⋊Q8—28no—
188C22⋊Q8—28no—
189C22⋊Q8—28no—
190C22⋊Q8—28no—
191C4×Q8—44no—
192C4×Q8—44no—
193C4×Q8—44no—
194C4×Q8—44no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—28no—
210C2×C4⋊C4—42no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—44no—
213C2×C4⋊C4C4214yes—
214C2×C4⋊C4C22×C418yes—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—22no—
217C2×C22⋊C4—24no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—44no—
221C2×C22⋊C4C4218yes—
222C2×C42—24no—
223C2×C42—24no—
224C2×C42—24no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—28no—
230C2×C42—42no—
231C2×C42—42no—
232C2×C42—42no—
233C2×C42—42no—
234C2×C42—42no—
235C2×C42—42no—
236C2×C42—42no—
237C2×C42—42no—
238C2×C42—42no—
239C2×C42—44no—
240C2×C42C22⋊C411yescharacteristic
241C2×C42C22⋊C411yescharacteristic
242C2×C42C22⋊C411yescharacteristic
243C2×C42C22⋊C411yescharacteristic
244C2×C42C22⋊C411yescharacteristic
245C2×C42C22⋊C411yescharacteristic
246C2×C42C22⋊C411yescharacteristic
247C2×C42C22⋊C411yescharacteristic
248C2×C42C2×D411yescharacteristic
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42C2×D411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C22⋊C8—28no—
257C22⋊C8—28no—
258C22⋊C8—24no—
259C22⋊C8—24no—
260C22⋊C8C22×C418yes—
261C22⋊C8C22×C418yes—
262#97—44no—
263C4×C8—44no—
264C4×C8—44no—
265C4×C8—44no—
266#95—22no—
267#95—22no—
268#95—22no—
269#95—22no—
270#95—22no—
271#95—22no—
272#95—22no—
273#95—22no—
274#95—22no—
275#95—22no—
276C24—22no—
277C24—22no—
278C24—22no—
279C24—22no—
280C24—41no—
281C24—41no—
282C24C2×C4212yes—
283C24C2×C22⋊C411yescharacteristic
284C24C2×C22⋊C411yescharacteristic
285C24#11712yes—
286C24C23×C411yescharacteristic
287C2×Q8—24no—
288C2×Q8—24no—
289C2×Q8—48no—
290C2×Q8—42no—
291C2×Q8—42no—
292C2×Q8—48no—
293C2×Q8—42no—
294C2×Q8—42no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—48no—
335C22×C4—48no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
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—416no—
353C22×C4—416no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4#10114yes—
361C22×C4C2×C4214yes—
362C22×C4C2×C4212yes—
363C22×C4C2×C4214yes—
364C22×C4C2×C22⋊C411yescharacteristic
365C22×C4C2×C22⋊C411yescharacteristic
366C22×C4C2×C22⋊C411yescharacteristic
367C22×C4C2×C22⋊C411yescharacteristic
368C22×C4C2×C22⋊C411yescharacteristic
369C22×C4C2×C22⋊C411yescharacteristic
370C22×C4C2×C22⋊C411yescharacteristic
371C22×C4C2×C22⋊C411yescharacteristic
372C22×C4C2×C22⋊C411yescharacteristic
373C22×C4C2×C22⋊C411yescharacteristic
374C22×C4#11712yes—
375C22×C4C4×D414yes—
376C22×C4C4×D414yes—
377C22×C4C4×D414yes—
378C22×C4C4×D414yes—
379C22×C4#13114yes—
380C22×C4#13114yes—
381C22×C4C23×C412yes—
382C22×C4C22×D411yescharacteristic
383C22×C4C22×D411yescharacteristic
384C22×C4C2×#4112yes—
385M16—416no—
386C2×C8—28no—
387C2×C8—28no—
388C2×C8—44no—
389C2×C8—44no—
390C2×C8—44no—
391C2×C8—416no—
392C2×C8—44no—
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—44no—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—44no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C22⋊C4—28no—
406C22⋊C4—28no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C42—22no—
410C42—22no—
411C42—22no—
412C42—22no—
413C42—22no—
414C42—22no—
415C42—22no—
416C42—22no—
417C42—22no—
418C42—41no—
419C42—41no—
420C42—41no—
421C42—41no—
422C42—41no—
423C42—41no—
424C42—44no—
425C42—44no—
426C42—44no—
427C42—44no—
428C42#9914yes—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—24no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—24no—
445C23—24no—
446C23—24no—
447C23—42no—
448C23—42no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23C4×C22⋊C412yes—
454C23C4×C22⋊C412yes—
455C23C2×#10112yes—
456C23#41312yes—
457C23C22×C4211yescharacteristic
458C23C22×C22⋊C411yescharacteristic
459C23C2×#11711yescharacteristic
460C23C2×#13112yes—
461C23C2×#13112yes—
462Q8—48no—
463Q8—48no—
464C2×C4—28no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—28no—
482C2×C4—28no—
483C2×C4—28no—
484C2×C4—28no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—28no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—84no—
523C2×C4—84no—
524C2×C4C4×C22⋊C412yes—
525C2×C4C4×C22⋊C412yes—
526C2×C4#40812yes—
527C2×C4#40812yes—
528C2×C4#40812yes—
529C2×C4#40812yes—
530C2×C4C2×#9912yes—
531C2×C4C2×#9912yes—
532C2×C4C2×#9912yes—
533C2×C4#41012yes—
534C2×C4C2×#10112yes—
535C2×C4C2×#10112yes—
536C2×C4C2×C4×D412yes—
537C2×C4C2×C4×D412yes—
538C8—48no—
539C8—48no—
540C22—22no—
541C22—21no—
542C22—21no—
543C22—22no—
544C22—21no—
545C22—21no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—48no—
558C22—48no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C4×#10114yes—
564C22C2×C4×C22⋊C411yescharacteristic
565C22C4×#13112yes—
566C22C2×#40811yescharacteristic
567C22C2×#40811yescharacteristic
568C22C22×#9911yescharacteristic
569C22C2×#41011yescharacteristic
570C22C22×#10111yescharacteristic
571C22C2×#41311yescharacteristic
572C22#292212yes—
573C4—22no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—22no—
581C4—44no—
582C4—44no—
583C4—41no—
584C4—41no—
585C4—82no—
586C4—82no—
587C4#147214yesdirect product factor
588C4C4×#9914yes—
589C2—22no—
590C2—22no—
591C2—24no—
592C2—42no—
593C2C2×#147211yescharacteristic
594C2#1738011yescharacteristic
595C2#1738111yescharacteristic
596C2#1738511yescharacteristic
597C2C4×#40811yescharacteristic
598C2C2×C4×#9911yescharacteristic
599C2C2×C4×#10111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊C4
commutatorC23C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC25C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #8154C2semidirect
6. C4×#324C2semidirect
41. #1472C4direct (N × H)
139. #324C2×C4semidirect
587. C4#1472direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Q82
C4×#4072
C2×C4×C22⋊C82
C2×#14722
#81542
C4×#3242
#79152