Finite Group Databasebeta

← C2×#9377 #200239

Subgroups — C2×#9377 #200239

Order 512.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3239C211yesmaximal, characteristic
2C2×#2992C211yesmaximal, characteristic
3C2×#1981C211yesmaximal, characteristic, complemented
4C2×#1556C211yesmaximal, characteristic, complemented
5C2×#1509C211yesmaximal, characteristic
6#9377C218yesmaximal, direct product factor
7C2×#1290C211yesmaximal, characteristic, complemented
8C2×#1285C211yesmaximal, characteristic, complemented
9C22×C4⋊Q8C2211yescharacteristic
10C2×#529C2211yescharacteristic
11#3239—22no—
12#3239—22no—
13#3239C414yescomplemented
14#3239C2214yes—
15C2×#501C412yescomplemented
16C2×#489C412yescomplemented
17C2×#484—21no—
18C2×#481—21no—
19C2×#475—21no—
20C2×#474—21no—
21#2992—22no—
22#2992—22no—
23#2992—22no—
24#2992C2214yes—
25C2×#446—21no—
26C2×#435—21no—
27C2×#435—21no—
28C2×C8×D4—21no—
29C2×#433—21no—
30C2×#432C2211yescharacteristic
31C2×#432C2211yescharacteristic
32C2×#432C2211yescharacteristic
33C2×#424—21no—
34C22×C4⋊C8C2211yescharacteristic
35C22×#103—21no—
36C22×#103—21no—
37C2×C4×C4⋊C4C2211yescharacteristic
38#1981—22no—
39#1981C2214yescomplemented
40#1556—22no—
41#1556C2214yescomplemented
42C2×#332—21no—
43C2×#332—21no—
44#1509—22no—
45#1509C2214yes—
46C2×#328—21no—
47C2×#327—21no—
48#1290C2214yescomplemented
49#1285C2214yescomplemented
50C23×Q8—21no—
51C22×M16—21no—
52C23×C8—21no—
53C23×C8D411yescharacteristic
54C23×C8D411yescharacteristic
55C2×C4⋊Q8—21no—
56C2×C4⋊Q8—21no—
57C2×C4⋊Q8—21no—
58C2×C4⋊Q8—21no—
59C2×C4⋊Q8—21no—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8—21no—
62C2×C4⋊Q8—21no—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8C2×C412yes—
65C2×C4⋊Q8C2×C412yes—
66C2×C4⋊Q8C2312yes—
67#529—21no—
68#529—21no—
69#529—21no—
70#529—21no—
71#529C2×C412yes—
72#529D412yes—
73#529D412yes—
74#529C2312yes—
75C2×#126—21no—
76C2×#125C2×C411yescharacteristic
77C2×#124C2×C411yescharacteristic
78C2×#123—21no—
79C2×C22⋊Q8D411yescharacteristic
80C2×#121D411yescharacteristic
81C2×C4×Q8D411yescharacteristic
82C2×C4×D4—21no—
83C2×C4×D4D411yescharacteristic
84C2×#117—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C42—21no—
89C22×C42C2311yescharacteristic
90#501—24no—
91#501C2×C418yescomplemented
92#489—24no—
93#489C2×C418yescomplemented
94#484—24no—
95#484—24no—
96#481—24no—
97#481—24no—
98#475—24no—
99#475—24no—
100#474—24no—
101#474—24no—
102#446—24no—
103#446—24no—
104#435—24no—
105#435—24no—
106#435—24no—
107#435—24no—
108C8×D4—24no—
109C8×D4—24no—
110#433—24no—
111#433—24no—
112#432—21no—
113#432—21no—
114#432—21no—
115#432—21no—
116#432—21no—
117#432—21no—
118#432—21no—
119#432C2×C412yes—
120#432D412yes—
121#432C2312yes—
122#432C2312yes—
123#432C2312yes—
124C2×#107—22no—
125C2×#106—22no—
126#424—24no—
127#424—24no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8—21no—
136C2×C4⋊C8D412yes—
137C2×C4⋊C8D411yescharacteristic
138C2×C4⋊C8D411yescharacteristic
139C2×C4⋊C8C2312yes—
140C2×#103—22no—
141C2×#103—24no—
142C2×#103—24no—
143C2×#103—44no—
144C2×#103—44no—
145C2×#102—22no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×#97—21no—
152C2×#97—21no—
153C2×#97—21no—
154C2×#97C2×C412yes—
155C2×C4×C8—21no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4—21no—
158C4×C4⋊C4—21no—
159C4×C4⋊C4C2312yes—
160C2×#95—21no—
161#332—24no—
162#332—24no—
163#328—24no—
164#327—24no—
165C22×Q8—22no—
166C22×Q8—22no—
167C22×Q8—22no—
168C22×Q8—42no—
169C22×Q8—42no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—41no—
173C22×Q8—41no—
174C22×Q8—41no—
175C22×Q8C22⋊C411yescharacteristic
176C22×D4—21no—
177C22×D4C22⋊C411yescharacteristic
178C23×C4—21no—
179C23×C4—41no—
180C23×C4—41no—
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4#4111yescharacteristic
184C2×M16—24no—
185C2×M16—82no—
186C22×C8—22no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—24no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—42no—
195C22×C8—42no—
196C22×C8—41no—
197C22×C8—82no—
198C22×C8C2×D412yes—
199C22×C8C2×D412yes—
200C4⋊Q8—22no—
201C4⋊Q8—22no—
202C4⋊Q8—22no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—22no—
206C4⋊Q8—22no—
207C4⋊Q8—22no—
208C4⋊Q8—22no—
209C4⋊Q8—41no—
210C4⋊Q8—41no—
211C4⋊Q8—41no—
212C4⋊Q8—41no—
213C4⋊Q8—41no—
214C4⋊Q8—41no—
215C4⋊Q8C22×C414yes—
216#126—22no—
217#126—22no—
218#126—22no—
219#126—22no—
220#125—21no—
221#125—21no—
222#125C22⋊C412yes—
223#125C22×C412yes—
224#124—21no—
225#124—21no—
226#124C22⋊C412yes—
227#124C22×C412yes—
228#123—22no—
229#123—22no—
230#123—22no—
231#123—22no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8C22⋊C412yes—
235C22⋊Q8C2×D412yes—
236#121—21no—
237#121—21no—
238#121C22⋊C412yes—
239#121C2×D412yes—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8C22⋊C412yes—
243C4×Q8C2×D412yes—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4—22no—
247C4×D4—22no—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4C22⋊C412yes—
251C4×D4C2×D412yes—
252#117—22no—
253#117—22no—
254#117—22no—
255#117—22no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4C22⋊C411yescharacteristic
277C2×C4⋊C4C22⋊C411yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C42—21no—
284C2×C42—22no—
285C2×C42—41no—
286C2×C42—82no—
287C2×C42C22×C411yescharacteristic
288C2×C42C22×C411yescharacteristic
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42C2×D411yescharacteristic
292C2×C42C2×D411yescharacteristic
293C2×C42C2×D411yescharacteristic
294C2×C42C2×D411yescharacteristic
295C2×C42#4111yescharacteristic
296C2×C42#4111yescharacteristic
297C2×C42#4111yescharacteristic
298C2×C42C2411yescharacteristic
299#107—28no—
300#106—28no—
301C4⋊C8—24no—
302C4⋊C8—24no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C4⋊C8—22no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—22no—
309C4⋊C8—22no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312C4⋊C8—41no—
313C4⋊C8C2×D412yes—
314C4⋊C8C2×D412yes—
315#103—28no—
316#103—48no—
317#103—48no—
318#102—28no—
319C22⋊C8—24no—
320C22⋊C8—24no—
321C22⋊C8—22no—
322C22⋊C8—22no—
323C22⋊C8—22no—
324C22⋊C8—22no—
325C22⋊C8—22no—
326C22⋊C8—41no—
327#97—24no—
328#97—22no—
329#97—22no—
330#97—22no—
331#97—22no—
332#97—41no—
333#97C22×C414yes—
334C4×C8—24no—
335#95—22no—
336#95—41no—
337C24—21no—
338C24#12111yescharacteristic
339C2×Q8—21no—
340C2×Q8—24no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—44no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—82no—
354C2×Q8—82no—
355C2×Q8—82no—
356C2×Q8—82no—
357C2×Q8—82no—
358C2×Q8—82no—
359C2×Q8C2×C22⋊C412yes—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4C2×C22⋊C412yes—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—82no—
385C22×C4—82no—
386C22×C4—82no—
387C22×C4—82no—
388C22×C4C2×C22⋊C411yescharacteristic
389C22×C4C2×C22⋊C411yescharacteristic
390C22×C4C4×D411yescharacteristic
391C22×C4C4×D411yescharacteristic
392C22×C4C4×D411yescharacteristic
393C22×C4C4×D411yescharacteristic
394C22×C4#12011yescharacteristic
395C22×C4#12011yescharacteristic
396C22×C4#12111yescharacteristic
397C22×C4#12111yescharacteristic
398C22×C4#12111yescharacteristic
399C22×C4#12111yescharacteristic
400C22×C4#12111yescharacteristic
401C22×C4#12311yescharacteristic
402C22×C4#12311yescharacteristic
403C22×C4C22×D411yescharacteristic
404C22×C4C22×D411yescharacteristic
405C22×C4C2×#4111yescharacteristic
406M16—84no—
407C2×C8—24no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—44no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—42no—
416C2×C8—42no—
417C2×C8—42no—
418C2×C8—42no—
419C2×C8—42no—
420C2×C8—81no—
421C2×C8—81no—
422C2×C8—84no—
423C2×C8—82no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—44no—
438C4⋊C4—42no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—42no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4C2×C22⋊C412yes—
446C4⋊C4C2×C22⋊C412yes—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C42—22no—
458C42—22no—
459C42—82no—
460C42—82no—
461C42C2×C22⋊C411yescharacteristic
462C42C2×C22⋊C411yescharacteristic
463C42C4×D411yescharacteristic
464C42C4×D411yescharacteristic
465C42C4×D411yescharacteristic
466C42C4×D411yescharacteristic
467C42#12011yescharacteristic
468C42#12011yescharacteristic
469C42#12111yescharacteristic
470C42#12111yescharacteristic
471C42#12311yescharacteristic
472C42#12311yescharacteristic
473C42C23×C411yescharacteristic
474C42C22×D411yescharacteristic
475C42C22×D411yescharacteristic
476C42C2×#4111yescharacteristic
477C23—22no—
478C23—22no—
479C23—22no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23#38611yescharacteristic
484C23#38611yescharacteristic
485C23#47112yes—
486C23#47312yes—
487C23C2×#12111yescharacteristic
488Q8—42no—
489Q8—44no—
490Q8—44no—
491Q8—81no—
492Q8—84no—
493Q8—84no—
494Q8—82no—
495Q8—82no—
496D4—42no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—81no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—82no—
534C2×C4—88no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4—82no—
540C2×C4#38611yescharacteristic
541C2×C4#38611yescharacteristic
542C2×C4#38611yescharacteristic
543C2×C4#38611yescharacteristic
544C2×C4#38611yescharacteristic
545C2×C4#38611yescharacteristic
546C2×C4#45312yes—
547C2×C4#45412yes—
548C2×C4C22×C22⋊C411yescharacteristic
549C2×C4C2×C4×D411yescharacteristic
550C2×C4C2×C4×D411yescharacteristic
551C2×C4C2×#12011yescharacteristic
552C2×C4C2×#12111yescharacteristic
553C2×C4C2×#12311yescharacteristic
554C8—44no—
555C8—42no—
556C8—42no—
557C8—42no—
558C8—42no—
559C8—82no—
560C22—21no—
561C22—21no—
562C22—24no—
563C22—24no—
564C22—21no—
565C22—21no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—84no—
570C22#188312yes—
571C22#190812yes—
572C22#190812yes—
573C22#190912yes—
574C22C2×#38611yescharacteristic
575C22C2×#47111yescharacteristic
576C22C2×#47311yescharacteristic
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—84no—
591C4—84no—
592C4#188312yes—
593C4C2×#45311yescharacteristic
594C4C2×#45411yescharacteristic
595C2—21no—
596C2—22no—
597C2—21no—
598C2—82no—
599C2#937714yesdirect product factor
600C2C2×#188311yescharacteristic
601C2C2×#190811yescharacteristic
602C2C2×#190911yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC42C23×C4
Frattini, cosocleC2×C42C24
prime radicalC2×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#1981C2semidirect
4. C2×#1556C2semidirect
6. #9377C2direct (N × H)
7. C2×#1290C2semidirect
8. C2×#1285C2semidirect
13. #3239C4semidirect
15. C2×#501C4semidirect
16. C2×#489C4semidirect
39. #1981C22semidirect
41. #1556C22semidirect
48. #1290C22semidirect
49. #1285C22semidirect
91. #501C2×C4semidirect
93. #489C2×C4semidirect
599. C2#9377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32392
C2×#29922
C2×#19812
C2×#15562
C2×#15092
#93772
C2×#12902
C2×#12852