Finite Group Databasebeta

← C2×#9384 #200389

Subgroups — C2×#9384 #200389

Order 512.

1814 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2972C211yesmaximal, characteristic, complemented
2C2×#2543C211yesmaximal, characteristic
3C2×#1799C211yesmaximal, characteristic, complemented
4C2×#1519C212yesmaximal, complemented
5#9384C218yesmaximal, direct product factor
6C2×#1294C212yesmaximal, complemented
7C22×#121—21no—
8C22×#121C2211yescharacteristic
9C22×C4×D4C2211yescharacteristic
10#2972—24no—
11#2972—22no—
12#2972C2214yescomplemented
13C2×C8×D4—24no—
14C2×#431—21no—
15C22×#99—21no—
16C22×C22⋊C8—21no—
17C22×C22⋊C8C2212yes—
18#2543—22no—
19#2543—22no—
20#2543C414yescomplemented
21#2543C2214yes—
22C2×#398C411yescharacteristic, complemented
23C2×#397C411yescharacteristic, complemented
24C2×#394C411yescharacteristic, complemented
25C2×#392C411yescharacteristic, complemented
26C2×#388—21no—
27C2×#386—21no—
28C2×#386—21no—
29C2×#380C2212yes—
30C22×#95C2211yescharacteristic
31#1799—22no—
32#1799C2214yescomplemented
33C2×#342—21no—
34#1519—24no—
35#1519C2218yescomplemented
36C2×#327—24no—
37#1294C2218yescomplemented
38C23×D4—21no—
39C23×D4—21no—
40C23×D4C2×C411yescharacteristic
41C23×D4D411yescharacteristic
42C24×C4—21no—
43C24×C4D411yescharacteristic
44C24×C4C2311yescharacteristic
45C23×C8—22no—
46C23×C8—22no—
47C2×#121—24no—
48C2×#121—24no—
49C2×#121—21no—
50C2×#121—21no—
51C2×#121—22no—
52C2×#121—22no—
53C2×#121—22no—
54C2×#121—22no—
55C2×#121—44no—
56C2×#121—44no—
57C2×#121C2×C412yes—
58C2×#121C2312yes—
59C2×C4×D4—22no—
60C2×C4×D4—22no—
61C2×C4×D4—22no—
62C2×C4×D4—22no—
63C2×C4×D4C2×C412yes—
64C2×C4×D4D412yes—
65C2×C4×D4D412yes—
66C2×C4×D4C2312yes—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4C2×C411yescharacteristic
70C22×C4⋊C4C2×C411yescharacteristic
71C22×C22⋊C4—21no—
72C22×C22⋊C4—21no—
73C22×C22⋊C4—21no—
74C22×C22⋊C4—21no—
75C22×C22⋊C4—21no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4C2×C411yescharacteristic
78C22×C22⋊C4D411yescharacteristic
79C22×C42D411yescharacteristic
80C8×D4—216no—
81C8×D4—216no—
82#431—24no—
83#431—24no—
84C2×C4⋊C8—22no—
85C2×#99—24no—
86C2×#99—44no—
87C2×C22⋊C8—22no—
88C2×C22⋊C8—24no—
89C2×C22⋊C8—22no—
90C2×C22⋊C8—24no—
91C2×C22⋊C8—22no—
92C2×C22⋊C8—22no—
93C2×C22⋊C8D414yescomplemented
94C2×C22⋊C8D414yescomplemented
95C2×C22⋊C8C2314yes—
96C2×C4×C8—22no—
97#398—22no—
98#398C2×C414yescomplemented
99#397—22no—
100#397C2×C414yescomplemented
101#394—22no—
102#394C2×C414yescomplemented
103#392—22no—
104#392C2×C414yescomplemented
105#388—24no—
106#388—24no—
107#386—24no—
108#386—24no—
109#386—24no—
110#386—24no—
111#380—22no—
112#380—22no—
113#380—22no—
114#380C2314yes—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—22no—
121C2×#95C2×C411yescharacteristic
122C2×#95C2×C411yescharacteristic
123C2×#95C2×C412yes—
124C2×#95C2312yes—
125#342—24no—
126#327—216no—
127C25—21no—
128C25C22⋊C411yescharacteristic
129C25C2×D411yescharacteristic
130C22×D4—22no—
131C22×D4—22no—
132C22×D4—24no—
133C22×D4—22no—
134C22×D4—22no—
135C22×D4—24no—
136C22×D4—21no—
137C22×D4—22no—
138C22×D4—22no—
139C22×D4—44no—
140C22×D4—44no—
141C22×D4—42no—
142C22×D4—42no—
143C22×D4—42no—
144C22×D4—42no—
145C22×D4—44no—
146C22×D4—82no—
147C22×D4—82no—
148C22×D4C22⋊C412yes—
149C22×D4D814yes—
150C22×D4SD1614yes—
151C22×D4C22×C412yes—
152C22×D4C2×D412yes—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—44no—
163C23×C4—42no—
164C23×C4—42no—
165C23×C4—42no—
166C23×C4—82no—
167C23×C4—82no—
168C23×C4—82no—
169C23×C4C22⋊C411yescharacteristic
170C23×C4C22⋊C411yescharacteristic
171C23×C4C22⋊C411yescharacteristic
172C23×C4C22⋊C412yes—
173C23×C4C22×C411yescharacteristic
174C23×C4C22×C411yescharacteristic
175C23×C4C2×D412yes—
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D412yes—
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D412yes—
181C23×C4#4112yes—
182C23×C4#4112yes—
183C23×C4C2411yescharacteristic
184C22×C8—24no—
185C22×C8—28no—
186C22×C8—24no—
187C22×C8—24no—
188C22×C8—84no—
189C22×C8—84no—
190#121—24no—
191#121—24no—
192#121—24no—
193#121—24no—
194#121—416no—
195#121—48no—
196#121—48no—
197#121—42no—
198#121—42no—
199#121—42no—
200#121—42no—
201C4×D4—24no—
202C4×D4—24no—
203C4×D4—24no—
204C4×D4—24no—
205C4×D4—24no—
206C4×D4—24no—
207C4×D4—24no—
208C4×D4—24no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—44no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—84no—
219C2×C4⋊C4C22⋊C412yes—
220C2×C4⋊C4C22×C412yes—
221C2×C4⋊C4C22×C412yes—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—24no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—24no—
232C2×C22⋊C4—24no—
233C2×C22⋊C4—44no—
234C2×C22⋊C4—44no—
235C2×C22⋊C4—44no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4—41no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—44no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—42no—
243C2×C22⋊C4—82no—
244C2×C22⋊C4C22⋊C412yes—
245C2×C22⋊C4C22⋊C412yes—
246C2×C22⋊C4C22×C412yes—
247C2×C22⋊C4C2×D412yes—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C22⋊C412yes—
253C2×C42C2×D412yes—
254C4⋊C8—28no—
255#99—48no—
256C22⋊C8—28no—
257C22⋊C8—24no—
258C22⋊C8—24no—
259C22⋊C8—24no—
260C22⋊C8C2×D418yescomplemented
261C4×C8—28no—
262#95—22no—
263#95—21no—
264#95—21no—
265#95—24no—
266#95—24no—
267#95—22no—
268#95—24no—
269#95—42no—
270#95C22×C412yes—
271#95C22×C412yes—
272C24—21no—
273C24—21no—
274C24—22no—
275C24—22no—
276C24—42no—
277C24—42no—
278C24—42no—
279C24—42no—
280C24—42no—
281C24—42no—
282C24—42no—
283C24—42no—
284C24—41no—
285C24—41no—
286C24—42no—
287C24—42no—
288C24#10214yes—
289C24C2×C22⋊C411yescharacteristic
290C24C2×C22⋊C412yes—
291C24C2×C22⋊C411yescharacteristic
292C24#12112yes—
293C24#12112yes—
294C24C2×D812yes—
295C24C2×SD1612yes—
296C24#13514yes—
297C24C22×D411yescharacteristic
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—24no—
301C2×D4—24no—
302C2×D4—28no—
303C2×D4—28no—
304C2×D4—28no—
305C2×D4—28no—
306C2×D4—24no—
307C2×D4—48no—
308C2×D4—44no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—44no—
312C2×D4—44no—
313C2×D4—48no—
314C2×D4—44no—
315C2×D4—44no—
316C2×D4—42no—
317C2×D4—84no—
318C2×D4—82no—
319C2×D4—84no—
320C2×D4—816no—
321C2×D4—84no—
322C2×D4—82no—
323C2×D4—84no—
324C2×D4—84no—
325C2×D4—84no—
326C2×D4—84no—
327C2×D4#10218yes—
328C2×D4C2×D814yes—
329C2×D4C2×SD1614yes—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—44no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—44no—
365C22×C4—42no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—82no—
371C22×C4—81no—
372C22×C4—82no—
373C22×C4—81no—
374C22×C4—82no—
375C22×C4—82no—
376C22×C4—82no—
377C22×C4—82no—
378C22×C4—82no—
379C22×C4—82no—
380C22×C4—88no—
381C22×C4—88no—
382C22×C4—84no—
383C22×C4—84no—
384C22×C4—84no—
385C22×C4#10214yes—
386C22×C4C2×C22⋊C412yes—
387C22×C4C2×C22⋊C412yes—
388C22×C4C2×C22⋊C412yes—
389C22×C4C2×C22⋊C411yescharacteristic
390C22×C4C2×C22⋊C411yescharacteristic
391C22×C4C4×D412yes—
392C22×C4C4×D412yes—
393C22×C4C4×D412yes—
394C22×C4C4×D412yes—
395C22×C4#12011yescharacteristic
396C22×C4#12011yescharacteristic
397C22×C4#12012yes—
398C22×C4#12112yes—
399C22×C4#12112yes—
400C22×C4#12311yescharacteristic
401C22×C4#12311yescharacteristic
402C22×C4#12312yes—
403C22×C4C23×C411yescharacteristic
404C22×C4C22×D412yes—
405C22×C4C22×D411yescharacteristic
406C22×C4C2×#4112yes—
407C2×C8—28no—
408C2×C8—48no—
409C2×C8—84no—
410C2×C8—84no—
411C2×C8—88no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—24no—
415C4⋊C4—42no—
416C4⋊C4—48no—
417C4⋊C4—84no—
418C4⋊C4—84no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—48no—
424C22⋊C4—48no—
425C22⋊C4—42no—
426C22⋊C4—42no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—48no—
430C22⋊C4—44no—
431C22⋊C4—44no—
432C22⋊C4—84no—
433C22⋊C4—84no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—22no—
438C23—22no—
439C23—24no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—24no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—44no—
452C23—44no—
453C23—42no—
454C23—48no—
455C23—42no—
456C23—42no—
457C23—48no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—81no—
468C23—84no—
469C23—81no—
470C23—82no—
471C23—84no—
472C23—84no—
473C23—84no—
474C23—84no—
475C23—82no—
476C23—82no—
477C23—82no—
478C23—82no—
479C23—82no—
480C23#38612yes—
481C23#38611yescharacteristic
482C23#38611yescharacteristic
483C23C2×#10212yes—
484C23C2×#10214yes—
485C23C2×#10212yes—
486C23#41612yes—
487C23#41612yes—
488C23#46514yes—
489C23#46514yes—
490C23#46614yes—
491C23#46614yes—
492C23C22×C22⋊C411yescharacteristic
493C23C2×#12112yes—
494C23C22×D811yescharacteristic
495C23C22×SD1611yescharacteristic
496C23C2×#13512yes—
497D4—216no—
498D4—28no—
499D4—28no—
500D4—84no—
501D4—84no—
502D4—816no—
503D4—88no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
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—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—48no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—84no—
551C2×C4—84no—
552C2×C4—88no—
553C2×C4—84no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4—168no—
560C2×C4#38611yescharacteristic
561C2×C4#38611yescharacteristic
562C2×C4#38612yes—
563C2×C4C2×#10214yes—
564C2×C4C2×C4×D412yes—
565C2×C4C2×#12011yescharacteristic
566C2×C4C2×#12311yescharacteristic
567C8—48no—
568C22—21no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—24no—
573C22—28no—
574C22—24no—
575C22—28no—
576C22—21no—
577C22—22no—
578C22—21no—
579C22—22no—
580C22—24no—
581C22—41no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—42no—
590C22—48no—
591C22—42no—
592C22—82no—
593C22—84no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22—164no—
602C22—164no—
603C22#188412yes—
604C22#189312yes—
605C22#189314yes—
606C22#189312yes—
607C22#191312yes—
608C22C2×#38611yescharacteristic
609C22C22×#10211yescharacteristic
610C22C2×#41611yescharacteristic
611C22C2×#46512yes—
612C22C2×#46612yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—22no—
618C4—22no—
619C4—24no—
620C4—44no—
621C4—42no—
622C4—42no—
623C4—82no—
624C4—82no—
625C4—164no—
626C2—21no—
627C2—22no—
628C2—21no—
629C2—22no—
630C2—24no—
631C2—22no—
632C2—44no—
633C2—162no—
634C2#938414yesdirect product factor
635C2C2×#188411yescharacteristic
636C2C2×#189311yescharacteristic
637C2C2×#191311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC2×#2543C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2972C2semidirect
3. C2×#1799C2semidirect
4. C2×#1519C2semidirect
5. #9384C2direct (N × H)
6. C2×#1294C2semidirect
12. #2972C22semidirect
20. #2543C4semidirect
22. C2×#398C4semidirect
23. C2×#397C4semidirect
24. C2×#394C4semidirect
25. C2×#392C4semidirect
32. #1799C22semidirect
35. #1519C22semidirect
37. #1294C22semidirect
93. C2×C22⋊C8D4semidirect
94. C2×C22⋊C8D4semidirect
98. #398C2×C4semidirect
100. #397C2×C4semidirect
102. #394C2×C4semidirect
104. #392C2×C4semidirect
260. C22⋊C8C2×D4semidirect
634. C2#9384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29722
C2×#25432
C2×#17992
C2×#15192
#93842
C2×#12942