Finite Group Databasebeta

← C2×#8761 #190202

Subgroups — C2×#8761 #190202

Order 512.

1472 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2349C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#8761C218yesmaximal, direct product factor
5C2×#1294C212yesmaximal, complemented
6C2×#1289C212yesmaximal, complemented
7C22×C4×D4—21no—
8C22×C4×D4C2211yescharacteristic
9C22×#99—21no—
10C22×C22⋊C8C2212yes—
11#2349—22no—
12#2349—22no—
13#2349C414yescomplemented
14#2349C2214yes—
15C2×#389—21no—
16C2×#385—21no—
17C2×#385—21no—
18C2×#382C411yescharacteristic, complemented
19C2×#380C411yescharacteristic, complemented
20C2×#380C2212yes—
21C2×#380C2211yescharacteristic
22C2×C4×C4⋊C4C411yescharacteristic, complemented
23C22×#95C411yescharacteristic, complemented
24C22×#95C2211yescharacteristic
25#1799—22no—
26#1799C2214yes—
27C2×#342—21no—
28#1459—22no—
29#1459C2214yes—
30C2×#324—21no—
31C2×#323—21no—
32#1294C2218yescomplemented
33#1289C2218yescomplemented
34C23×D4D411yescharacteristic
35C24×C4—21no—
36C24×C4—21no—
37C24×C4C2×C411yescharacteristic
38C24×C4C2311yescharacteristic
39C23×C8—22no—
40C2×C4×D4—22no—
41C2×C4×D4—22no—
42C2×C4×D4—22no—
43C2×C4×D4—22no—
44C2×C4×D4—24no—
45C2×C4×D4—24no—
46C2×C4×D4—48no—
47C2×C4×D4C2×C412yes—
48C2×C4×D4D412yes—
49C2×C4×D4D412yes—
50C2×C4×D4C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4D411yescharacteristic
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—22no—
60C22×C22⋊C4D411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42—21no—
63C22×C42C2×C411yescharacteristic
64C2×#99—24no—
65C2×#99—44no—
66C2×C22⋊C8—22no—
67C2×C22⋊C8—22no—
68C2×C22⋊C8—22no—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—22no—
71C2×C22⋊C8C2314yes—
72#389—24no—
73#389—24no—
74#385—24no—
75#385—24no—
76#385—24no—
77#385—24no—
78#382—22no—
79#382C2×C414yescomplemented
80#380—22no—
81#380—21no—
82#380—21no—
83#380—22no—
84#380—22no—
85#380—22no—
86#380C2×C412yes—
87#380C2×C414yescomplemented
88#380C2314yes—
89#380C2312yes—
90C4×C4⋊C4—22no—
91C4×C4⋊C4C2×C414yescomplemented
92C2×#95—22no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—22no—
99C2×#95C2×C412yes—
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103C2×#95C2×C411yescharacteristic
104C2×#95C2×C414yescomplemented
105C2×#95C2312yes—
106#342—24no—
107#324—24no—
108#323—24no—
109C25C22⋊C411yescharacteristic
110C25C2×D411yescharacteristic
111C22×D4—22no—
112C22×D4—22no—
113C22×D4—24no—
114C22×D4C22⋊C412yes—
115C22×D4SD1614yes—
116C22×D4Q1614yes—
117C22×D4C2×D412yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—24no—
128C23×C4—22no—
129C23×C4—44no—
130C23×C4—44no—
131C23×C4—44no—
132C23×C4—44no—
133C23×C4—42no—
134C23×C4—82no—
135C23×C4—82no—
136C23×C4—82no—
137C23×C4—82no—
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22×C412yes—
143C23×C4C22×C411yescharacteristic
144C23×C4C22×C411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C23×C4#4112yes—
149C23×C4#4112yes—
150C23×C4#4112yes—
151C23×C4#4112yes—
152C23×C4C2411yescharacteristic
153C22×C8—24no—
154C22×C8—42no—
155C22×C8—42no—
156C22×C8—84no—
157C4×D4—24no—
158C4×D4—24no—
159C4×D4—24no—
160C4×D4—24no—
161C4×D4—24no—
162C4×D4—24no—
163C4×D4—24no—
164C4×D4—24no—
165C4×D4—416no—
166C4×D4—416no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4—84no—
181C2×C4⋊C4C22⋊C412yes—
182C2×C4⋊C4C2×D412yes—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—24no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4C22⋊C412yes—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C2×D412yes—
199C2×C22⋊C4C2×D412yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—24no—
205C2×C42—44no—
206C2×C42C22⋊C412yes—
207C2×C42C22×C412yes—
208#99—48no—
209C22⋊C8—24no—
210C22⋊C8—24no—
211C22⋊C8—42no—
212C22⋊C8—42no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—22no—
217#95—24no—
218#95—24no—
219#95—21no—
220#95—22no—
221#95—24no—
222#95—42no—
223#95C22×C412yes—
224#95C22×C412yes—
225#95C22×C412yes—
226#95C22×C412yes—
227C24—21no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24#10314yes—
235C24C2×C22⋊C411yescharacteristic
236C24C2×C22⋊C412yes—
237C24C2×C22⋊C411yescharacteristic
238C24#12312yes—
239C24#12312yes—
240C24C2×SD1612yes—
241C24C2×Q1612yes—
242C24AGL(1,ℤ/8)14yes—
243C24C22×D411yescharacteristic
244C2×D4—24no—
245C2×D4—24no—
246C2×D4—24no—
247C2×D4—24no—
248C2×D4—28no—
249C2×D4—28no—
250C2×D4—28no—
251C2×D4—28no—
252C2×D4#10318yes—
253C2×D4C2×SD1614yes—
254C2×D4C2×Q1614yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—42no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—48no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—48no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—44no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—44no—
294C22×C4—44no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4—82no—
301C22×C4—82no—
302C22×C4—81no—
303C22×C4—82no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—84no—
308C22×C4—82no—
309C22×C4—82no—
310C22×C4—816no—
311C22×C4—816no—
312C22×C4—84no—
313C22×C4—84no—
314C22×C4—84no—
315C22×C4#10314yes—
316C22×C4C2×C22⋊C412yes—
317C22×C4C2×C22⋊C412yes—
318C22×C4C2×C22⋊C412yes—
319C22×C4C2×C22⋊C411yescharacteristic
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4#11711yescharacteristic
322C22×C4#11711yescharacteristic
323C22×C4#11711yescharacteristic
324C22×C4#11711yescharacteristic
325C22×C4#11712yes—
326C22×C4#11712yes—
327C22×C4#12312yes—
328C22×C4#12312yes—
329C22×C4#12312yes—
330C22×C4#12312yes—
331C22×C4#12312yes—
332C22×C4#12312yes—
333C22×C4C23×C411yescharacteristic
334C22×C4C22×D411yescharacteristic
335C22×C4C2×#4112yes—
336C22×C4C2×#4112yes—
337C2×C8—44no—
338C2×C8—84no—
339C2×C8—84no—
340C2×C8—84no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—48no—
344C4⋊C4—48no—
345C4⋊C4—82no—
346C4⋊C4—82no—
347C4⋊C4—84no—
348C4⋊C4—84no—
349C4⋊C4—84no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—48no—
355C22⋊C4—44no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—44no—
359C22⋊C4—84no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C42—48no—
365C23—22no—
366C23—24no—
367C23—22no—
368C23—24no—
369C23—24no—
370C23—24no—
371C23—22no—
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—42no—
378C23—48no—
379C23—42no—
380C23—44no—
381C23—44no—
382C23—42no—
383C23—42no—
384C23—48no—
385C23—48no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23#38112yes—
391C23#38111yescharacteristic
392C23#38111yescharacteristic
393C23C2×#10312yes—
394C23C2×#10314yes—
395C23C2×#10312yes—
396C23#41812yes—
397C23#41812yes—
398C23#48114yes—
399C23#48114yes—
400C23#48414yes—
401C23#48414yes—
402C23C22×C22⋊C411yescharacteristic
403C23C2×#12312yes—
404C23C22×SD1611yescharacteristic
405C23C22×Q1611yescharacteristic
406C23C2×AGL(1,ℤ/8)12yes—
407D4—28no—
408D4—28no—
409D4—216no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—48no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—88no—
458C2×C4—88no—
459C2×C4—816no—
460C2×C4—84no—
461C2×C4—84no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—168no—
467C2×C4#38111yescharacteristic
468C2×C4#38111yescharacteristic
469C2×C4#38112yes—
470C2×C4C2×#10314yes—
471C2×C4C2×#11711yescharacteristic
472C2×C4C2×#11711yescharacteristic
473C2×C4C2×#12312yes—
474C8—84no—
475C22—24no—
476C22—28no—
477C22—24no—
478C22—28no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—22no—
483C22—21no—
484C22—21no—
485C22—22no—
486C22—22no—
487C22—24no—
488C22—42no—
489C22—42no—
490C22—41no—
491C22—41no—
492C22—42no—
493C22—44no—
494C22—44no—
495C22—44no—
496C22—44no—
497C22—48no—
498C22—48no—
499C22—42no—
500C22—42no—
501C22#182412yes—
502C22#182414yes—
503C22#182412yes—
504C22#182712yes—
505C22#182812yes—
506C22C2×#38111yescharacteristic
507C22C22×#10311yescharacteristic
508C22C2×#41811yescharacteristic
509C22C2×#48112yes—
510C22C2×#48412yes—
511C4—24no—
512C4—22no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—22no—
518C4—44no—
519C4—42no—
520C4—42no—
521C4—82no—
522C4—82no—
523C4—82no—
524C4—164no—
525C2—21no—
526C2—22no—
527C2—22no—
528C2—21no—
529C2—22no—
530C2—24no—
531C2—44no—
532C2#876114yesdirect product factor
533C2C2×#182411yescharacteristic
534C2C2×#182711yescharacteristic
535C2C2×#182811yescharacteristic
subgroupG/H
center, socleC23#381
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
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
4. #8761C2direct (N × H)
5. C2×#1294C2semidirect
6. C2×#1289C2semidirect
13. #2349C4semidirect
18. C2×#382C4semidirect
19. C2×#380C4semidirect
22. C2×C4×C4⋊C4C4semidirect
23. C22×#95C4semidirect
32. #1294C22semidirect
33. #1289C22semidirect
79. #382C2×C4semidirect
87. #380C2×C4semidirect
91. C4×C4⋊C4C2×C4semidirect
104. C2×#95C2×C4semidirect
532. C2#8761direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23492
C2×#17992
C2×#14592
#87612
C2×#12942
C2×#12892