Finite Group Databasebeta

← C2×#11877 #482046

Subgroups — C2×#11877 #482046

Order 512.

1872 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic, complemented
3C2×#1459C211yesmaximal, characteristic, complemented
4#11877C218yesmaximal, direct product factor
5C2×#1343C214yesmaximal, complemented
6C22×#127—21no—
7C22×#127C411yescharacteristic, complemented
8C22×#121—21no—
9C22×#121—21no—
10C22×C4×D4C2211yescharacteristic
11C22×#99—21no—
12C22×C22⋊C8—21no—
13#2541—22no—
14#2541—22no—
15#2541C414yescomplemented
16#2541C2214yes—
17C2×#392C412yescomplemented
18C2×#392C2212yes—
19C2×#390—21no—
20C2×#380—21no—
21C2×C4×C4⋊C4C411yescharacteristic, complemented
22#1799—22no—
23#1799C2214yescomplemented
24C2×#342C2212yes—
25#1459—22no—
26#1459C2214yescomplemented
27C2×#324—21no—
28C2×#323C2212yes—
29#1343C22116yescomplemented
30C23×D4—22no—
31C23×D4—22no—
32C23×D4—21no—
33C23×D4—21no—
34C23×D4C2×C412yes—
35C23×D4D411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4D411yescharacteristic
38C23×C8—41no—
39C2×#127—24no—
40C2×#127—24no—
41C2×#127—22no—
42C2×#127—42no—
43C2×#127—41no—
44C2×#127—41no—
45C2×#127—44no—
46C2×#127—44no—
47C2×#127C2×C414yescomplemented
48C2×#121—24no—
49C2×#121—24no—
50C2×#121—24no—
51C2×#121—24no—
52C2×#121—48no—
53C2×#121—48no—
54C2×C4×D4—41no—
55C2×C4×D4—41no—
56C2×C4×D4—42no—
57C2×C4×D4C2×C412yes—
58C2×C4×D4D412yes—
59C2×C4×D4D412yes—
60C2×C4×D4C2312yes—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—41no—
63C22×C4⋊C4D411yescharacteristic
64C22×C22⋊C4—22no—
65C22×C22⋊C4—22no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4C2×C411yescharacteristic
68C22×C22⋊C4C2311yescharacteristic
69C22×C42—21no—
70C22×C42C2×C411yescharacteristic
71C2×#99—24no—
72C2×#99—44no—
73C2×C22⋊C8—22no—
74C2×C22⋊C8—24no—
75C2×C22⋊C8—42no—
76C2×C22⋊C8—41no—
77#392—24no—
78#392—22no—
79#392—22no—
80#392C2×C414yes—
81#392C2×C418yescomplemented
82#392C2314yes—
83#390—24no—
84#390—24no—
85#380—24no—
86#380—42no—
87C4×C4⋊C4—22no—
88C4×C4⋊C4C2×C414yescomplemented
89C2×#95—41no—
90C2×#95C2×C412yes—
91#342—22no—
92#342C2314yes—
93#324—24no—
94#323—22no—
95#323C2314yes—
96C25—22no—
97C25C22⋊C411yescharacteristic
98C25C2×D411yescharacteristic
99C22×D4—24no—
100C22×D4—28no—
101C22×D4—24no—
102C22×D4—24no—
103C22×D4—24no—
104C22×D4—22no—
105C22×D4—41no—
106C22×D4—41no—
107C22×D4—42no—
108C22×D4—42no—
109C22×D4—42no—
110C22×D4—44no—
111C22×D4—44no—
112C22×D4—48no—
113C22×D4—48no—
114C22×D4—42no—
115C22×D4—42no—
116C22×D4—44no—
117C22×D4—48no—
118C22×D4—44no—
119C22×D4—44no—
120C22×D4—42no—
121C22×D4—41no—
122C22×D4—41no—
123C22×D4—44no—
124C22×D4—84no—
125C22×D4—84no—
126C22×D4—84no—
127C22×D4C22⋊C412yes—
128C22×D4D814yes—
129C22×D4SD1614yes—
130C22×D4C22×C414yes—
131C22×D4C2×D412yes—
132C23×C4—22no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—22no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4—44no—
140C23×C4—44no—
141C23×C4—42no—
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C412yes—
145C23×C4C22⋊C412yes—
146C23×C4C22⋊C411yescharacteristic
147C23×C4C22×C411yescharacteristic
148C23×C4C2×D412yes—
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C22×C8—42no—
152C22×C8—44no—
153C22×C8—84no—
154#127—44no—
155#127—44no—
156#127—44no—
157#127—44no—
158#127—416no—
159#127—48no—
160#127—48no—
161#121—416no—
162#121—416no—
163#121—416no—
164#121—416no—
165C4×D4—42no—
166C4×D4—42no—
167C4×D4—42no—
168C4×D4—42no—
169C4×D4—42no—
170C4×D4—42no—
171C4×D4—42no—
172C4×D4—42no—
173C2×C4⋊C4—28no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—44no—
178C2×C4⋊C4—84no—
179C2×C4⋊C4C22⋊C412yes—
180C2×C4⋊C4C2×D412yes—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—28no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—48no—
190C2×C22⋊C4—48no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—42no—
194C2×C22⋊C4C22⋊C412yes—
195C2×C22⋊C4C22×C412yes—
196C2×C22⋊C4C22×C411yescharacteristic
197C2×C22⋊C4C2×D411yescharacteristic
198C2×C22⋊C4C2×D411yescharacteristic
199C2×C22⋊C4C2411yescharacteristic
200C2×C42—22no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—24no—
204C2×C42—44no—
205C2×C42C22⋊C412yes—
206C2×C42C22×C412yes—
207#99—48no—
208C22⋊C8—24no—
209C22⋊C8—42no—
210C22⋊C8—44no—
211#95—22no—
212#95—44no—
213#95C22×C414yes—
214C24—21no—
215C24—21no—
216C24—21no—
217C24—21no—
218C24—22no—
219C24—22no—
220C24—24no—
221C24—42no—
222C24—42no—
223C24—42no—
224C24—42no—
225C24—44no—
226C24—44no—
227C24—44no—
228C24—44no—
229C24—42no—
230C24—42no—
231C24—44no—
232C24—44no—
233C24#10214yes—
234C24C2×C22⋊C411yescharacteristic
235C24C2×C22⋊C412yes—
236C24C2×C22⋊C411yescharacteristic
237C24C2×D812yes—
238C24C2×SD1612yes—
239C24C22×D411yescharacteristic
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—42no—
248C2×D4—44no—
249C2×D4—48no—
250C2×D4—48no—
251C2×D4—48no—
252C2×D4—416no—
253C2×D4—48no—
254C2×D4—48no—
255C2×D4—44no—
256C2×D4—48no—
257C2×D4—44no—
258C2×D4—44no—
259C2×D4—48no—
260C2×D4—416no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—48no—
264C2×D4—84no—
265C2×D4—88no—
266C2×D4—88no—
267C2×D4—88no—
268C2×D4—84no—
269C2×D4—88no—
270C2×D4—84no—
271C2×D4—84no—
272C2×D4—832no—
273C2×D4—816no—
274C2×D4—816no—
275C2×D4—88no—
276C2×D4—88no—
277C2×D4—84no—
278C2×D4—84no—
279C2×D4#10218yes—
280C2×D4C2×D814yes—
281C2×D4C2×SD1614yes—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—28no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—44no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—44no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—84no—
315C22×C4—84no—
316C22×C4—82no—
317C22×C4—82no—
318C22×C4—84no—
319C22×C4—84no—
320C22×C4—84no—
321C22×C4#9912yes—
322C22×C4#9911yescharacteristic
323C22×C4#9911yescharacteristic
324C22×C4#10214yes—
325C22×C4C2×C22⋊C412yes—
326C22×C4C2×C22⋊C412yes—
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4C2×C22⋊C412yes—
329C22×C4C2×C22⋊C411yescharacteristic
330C22×C4C23×C411yescharacteristic
331C22×C4C22×D411yescharacteristic
332C2×C8—44no—
333C2×C8—84no—
334C2×C8—88no—
335C4⋊C4—216no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—88no—
339C22⋊C4—42no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—48no—
346C22⋊C4—416no—
347C22⋊C4—48no—
348C22⋊C4—44no—
349C22⋊C4—44no—
350C22⋊C4—84no—
351C42—22no—
352C42—22no—
353C42—22no—
354C42—22no—
355C42—48no—
356C23—22no—
357C23—22no—
358C23—21no—
359C23—22no—
360C23—21no—
361C23—22no—
362C23—24no—
363C23—22no—
364C23—21no—
365C23—21no—
366C23—22no—
367C23—22no—
368C23—24no—
369C23—22no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—48no—
374C23—42no—
375C23—41no—
376C23—44no—
377C23—44no—
378C23—41no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—44no—
388C23—44no—
389C23—44no—
390C23—81no—
391C23—81no—
392C23—81no—
393C23—81no—
394C23—84no—
395C23—84no—
396C23—84no—
397C23—84no—
398C23—88no—
399C23—88no—
400C23—88no—
401C23—88no—
402C23—84no—
403C23—84no—
404C23—84no—
405C23—84no—
406C23C2×#9911yescharacteristic
407C23C2×#9911yescharacteristic
408C23C2×#10212yes—
409C23C2×#10212yes—
410C23C2×#10214yes—
411C23#42112yes—
412C23C22×C22⋊C411yescharacteristic
413C23C22×D811yescharacteristic
414C23C22×SD1611yescharacteristic
415D4—48no—
416D4—44no—
417D4—44no—
418D4—88no—
419D4—816no—
420D4—88no—
421D4—88no—
422D4—832no—
423D4—816no—
424D4—88no—
425D4—88no—
426D4—88no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—44no—
441C2×C4—416no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—168no—
466C2×C4#35314yes—
467C2×C4C2×#9912yes—
468C2×C4C2×#9912yes—
469C2×C4C2×#10214yes—
470C8—84no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—24no—
476C22—24no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—24no—
481C22—41no—
482C22—41no—
483C22—44no—
484C22—42no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—42no—
490C22—41no—
491C22—44no—
492C22—48no—
493C22—44no—
494C22—81no—
495C22—81no—
496C22—82no—
497C22—82no—
498C22—84no—
499C22—82no—
500C22—84no—
501C22—84no—
502C22—84no—
503C22—84no—
504C22—84no—
505C22—84no—
506C22—84no—
507C22—168no—
508C22—168no—
509C22#151912yes—
510C22#151912yes—
511C22#212212yes—
512C22C2×#35312yes—
513C22C22×#9911yescharacteristic
514C22C22×#10211yescharacteristic
515C22C2×#42111yescharacteristic
516C4—22no—
517C4—24no—
518C4—48no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—42no—
524C4—164no—
525C4C2×#35314yes—
526C2—21no—
527C2—21no—
528C2—22no—
529C2—41no—
530C2—41no—
531C2—42no—
532C2—44no—
533C2—164no—
534C2#1187714yesdirect product factor
535C2C2×#151911yescharacteristic
536C2C2×#212211yescharacteristic
537C2C22×#35311yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#2541C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1799C2semidirect
3. C2×#1459C2semidirect
4. #11877C2direct (N × H)
5. C2×#1343C2semidirect
7. C22×#127C4semidirect
15. #2541C4semidirect
17. C2×#392C4semidirect
21. C2×C4×C4⋊C4C4semidirect
23. #1799C22semidirect
26. #1459C22semidirect
29. #1343C22semidirect
47. C2×#127C2×C4semidirect
81. #392C2×C4semidirect
88. C4×C4⋊C4C2×C4semidirect
534. C2#11877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#17992
C2×#14592
#118772
C2×#13432