Finite Group Databasebeta

← C2×#11775 #481597

Subgroups — C2×#11775 #481597

Order 512.

1488 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2543C211yesmaximal, characteristic
2C2×C4×#99C211yesmaximal, characteristic, complemented
3C2×#1466C211yesmaximal, characteristic, complemented
4#11775C218yesmaximal, direct product factor
5C2×#1344C212yesmaximal, complemented
6C2×#1343C212yesmaximal, complemented
7C22×#121—21no—
8C22×#121C411yescharacteristic, complemented
9C22×C4×D4C2211yescharacteristic
10C2×#432—21no—
11C22×#99—21no—
12#2543—22no—
13#2543—22no—
14#2543C414yescomplemented
15#2543C2214yes—
16C2×#398C411yescharacteristic, complemented
17C2×#397C2211yescharacteristic
18C2×#394C411yescharacteristic, complemented
19C2×#392C2211yescharacteristic
20C2×#388—21no—
21C2×#386—21no—
22C2×#386—21no—
23C2×C4×C22⋊C4—21no—
24C22×#95C411yescharacteristic, complemented
25C4×#99—22no—
26C4×#99C2214yescomplemented
27C2×#342C2212yes—
28#1466—22no—
29#1466C2214yescomplemented
30C2×#323—21no—
31C2×#323C2212yes—
32#1344C2218yescomplemented
33#1343C2218yescomplemented
34C23×D4—21no—
35C23×D4—21no—
36C23×D4C2×C411yescharacteristic
37C23×D4D411yescharacteristic
38C24×C4—21no—
39C24×C4C2×C411yescharacteristic
40C24×C4D411yescharacteristic
41C2×#121—24no—
42C2×#121—24no—
43C2×#121—22no—
44C2×#121—48no—
45C2×#121—42no—
46C2×#121—41no—
47C2×#121—41no—
48C2×#121C2×C414yescomplemented
49C2×C4×D4—41no—
50C2×C4×D4—41no—
51C2×C4×D4—42no—
52C2×C4×D4C2×C412yes—
53C2×C4×D4D412yes—
54C2×C4×D4D412yes—
55C2×C4×D4C2312yes—
56C22×C4⋊C4—21no—
57C22×C4⋊C4C2×C411yescharacteristic
58C22×C4⋊C4C2×C411yescharacteristic
59C22×C22⋊C4—22no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—21no—
65C22×C22⋊C4D411yescharacteristic
66C22×C22⋊C4C2311yescharacteristic
67C22×C42—41no—
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72C2×#99—28no—
73C2×#99—24no—
74C2×C22⋊C8—22no—
75C2×#97—41no—
76#398—22no—
77#398C2×C414yescomplemented
78#397—21no—
79#397—21no—
80#397C2×C412yes—
81#397C2312yes—
82#394—22no—
83#394C2×C414yescomplemented
84#392—21no—
85#392—21no—
86#392C2×C412yes—
87#392C2312yes—
88#388—24no—
89#388—24no—
90#386—24no—
91#386—24no—
92#386—24no—
93#386—24no—
94C4×C22⋊C4—24no—
95C4×C22⋊C4—42no—
96C2×#95—21no—
97C2×#95—22no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—41no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103C2×#95C2×C414yescomplemented
104#342—22no—
105#342C2314yes—
106#323—24no—
107#323—22no—
108#323C2314yes—
109C25—21no—
110C25C22⋊C411yescharacteristic
111C25C2×D411yescharacteristic
112C22×D4—24no—
113C22×D4—24no—
114C22×D4—24no—
115C22×D4—22no—
116C22×D4—22no—
117C22×D4—21no—
118C22×D4—41no—
119C22×D4—41no—
120C22×D4—41no—
121C22×D4—41no—
122C22×D4—44no—
123C22×D4—42no—
124C22×D4—42no—
125C22×D4—44no—
126C22×D4—44no—
127C22×D4—44no—
128C22×D4—82no—
129C22×D4—82no—
130C22×D4C22⋊C412yes—
131C22×D4C22×C412yes—
132C22×D4C2×D412yes—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—22no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—24no—
143C23×C4—44no—
144C23×C4—42no—
145C23×C4—44no—
146C23×C4—82no—
147C23×C4—82no—
148C23×C4—82no—
149C23×C4C22⋊C411yescharacteristic
150C23×C4C22⋊C411yescharacteristic
151C23×C4C22⋊C412yes—
152C23×C4C22⋊C412yes—
153C23×C4C22⋊C411yescharacteristic
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C412yes—
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D412yes—
158C22×C8—42no—
159#121—44no—
160#121—44no—
161#121—416no—
162#121—416no—
163#121—44no—
164#121—44no—
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—24no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4C22⋊C412yes—
181C2×C4⋊C4C22×C412yes—
182C2×C4⋊C4C22×C412yes—
183C2×C22⋊C4—28no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C22⋊C4—44no—
197C2×C22⋊C4—44no—
198C2×C22⋊C4—42no—
199C2×C22⋊C4—44no—
200C2×C22⋊C4—44no—
201C2×C22⋊C4—42no—
202C2×C22⋊C4—41no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—82no—
205C2×C22⋊C4C22⋊C412yes—
206C2×C22⋊C4C22×C411yescharacteristic
207C2×C22⋊C4C2×D411yescharacteristic
208C2×C22⋊C4C2×D412yes—
209C2×C22⋊C4C2×D411yescharacteristic
210C2×C22⋊C4C2411yescharacteristic
211C2×C42—21no—
212C2×C42—21no—
213C2×C42—22no—
214C2×C42—44no—
215C2×C42—84no—
216C2×C42C22⋊C412yes—
217C2×C42C2×D412yes—
218C4⋊C8—44no—
219#99—216no—
220C22⋊C8—24no—
221C22⋊C8—42no—
222#97—44no—
223#95—21no—
224#95—21no—
225#95—24no—
226#95—24no—
227#95—22no—
228#95—22no—
229#95—44no—
230#95C22×C412yes—
231#95C22×C412yes—
232C24—21no—
233C24—21no—
234C24—21no—
235C24—22no—
236C24—21no—
237C24—22no—
238C24—22no—
239C24—42no—
240C24—42no—
241C24—42no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24—42no—
246C24—42no—
247C24—41no—
248C24—41no—
249C24—42no—
250C24—42no—
251C24#10414yes—
252C24C2×C22⋊C411yescharacteristic
253C24C2×C22⋊C411yescharacteristic
254C24C2×C22⋊C412yes—
255C24AGL(1,ℤ/8)14yes—
256C24C22×D411yescharacteristic
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—24no—
260C2×D4—24no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—48no—
268C2×D4—48no—
269C2×D4—48no—
270C2×D4—48no—
271C2×D4—44no—
272C2×D4—44no—
273C2×D4—48no—
274C2×D4—82no—
275C2×D4—82no—
276C2×D4—82no—
277C2×D4—816no—
278C2×D4—84no—
279C2×D4—84no—
280C2×D4—82no—
281C2×D4—88no—
282C2×D4—88no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
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—42no—
306C22×C4—44no—
307C22×C4—48no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—48no—
315C22×C4—42no—
316C22×C4—48no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—82no—
324C22×C4—82no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4—82no—
328C22×C4—84no—
329C22×C4—84no—
330C22×C4—84no—
331C22×C4—82no—
332C22×C4—82no—
333C22×C4—816no—
334C22×C4—84no—
335C22×C4—84no—
336C22×C4#9911yescharacteristic
337C22×C4#9911yescharacteristic
338C22×C4#9912yes—
339C22×C4C2×C22⋊C412yes—
340C22×C4C2×C22⋊C411yescharacteristic
341C22×C4C2×C22⋊C412yes—
342C22×C4C2×C22⋊C411yescharacteristic
343C22×C4C2×C22⋊C412yes—
344C22×C4C23×C411yescharacteristic
345C22×C4C22×D411yescharacteristic
346C2×C8—44no—
347C2×C8—84no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—48no—
353C22⋊C4—28no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—42no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—44no—
361C22⋊C4—44no—
362C22⋊C4—48no—
363C22⋊C4—48no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—44no—
367C22⋊C4—44no—
368C22⋊C4—44no—
369C22⋊C4—84no—
370C42—22no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42—88no—
375C23—22no—
376C23—22no—
377C23—21no—
378C23—22no—
379C23—21no—
380C23—22no—
381C23—24no—
382C23—24no—
383C23—24no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—48no—
390C23—42no—
391C23—48no—
392C23—42no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—48no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23—81no—
410C23—81no—
411C23—84no—
412C23—82no—
413C23—84no—
414C23—82no—
415C23—84no—
416C23—84no—
417C23—84no—
418C23—82no—
419C23—82no—
420C23—82no—
421C23—82no—
422C23C2×#9911yescharacteristic
423C23C2×#9911yescharacteristic
424C23#41812yes—
425C23#41812yes—
426C23C2×#10412yes—
427C23C2×#10414yes—
428C23C22×C22⋊C411yescharacteristic
429C23C2×AGL(1,ℤ/8)12yes—
430D4—48no—
431D4—48no—
432D4—88no—
433D4—88no—
434D4—84no—
435D4—84no—
436D4—816no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—48no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—48no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—816no—
482C2×C4—84no—
483C2×C4—84no—
484C2×C4—84no—
485C2×C4—816no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4C2×#9912yes—
489C2×C4C2×#9912yes—
490C8—84no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—24no—
496C22—24no—
497C22—22no—
498C22—24no—
499C22—22no—
500C22—42no—
501C22—42no—
502C22—44no—
503C22—44no—
504C22—48no—
505C22—41no—
506C22—41no—
507C22—42no—
508C22—41no—
509C22—42no—
510C22—41no—
511C22—48no—
512C22—48no—
513C22—81no—
514C22—81no—
515C22—84no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—164no—
524C22—164no—
525C22#150712yes—
526C22#150712yes—
527C22#212112yes—
528C22#212612yes—
529C22C22×#9911yescharacteristic
530C22C2×#41811yescharacteristic
531C22C22×#10411yescharacteristic
532C4—22no—
533C4—22no—
534C4—44no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—42no—
541C4—82no—
542C4—88no—
543C4—82no—
544C2—21no—
545C2—21no—
546C2—22no—
547C2—42no—
548C2—44no—
549C2—42no—
550C2—162no—
551C2#1177514yesdirect product factor
552C2C2×#150711yescharacteristic
553C2C2×#212111yescharacteristic
554C2C2×#212611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC2×#2543C2
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×C4×#99C2semidirect
3. C2×#1466C2semidirect
4. #11775C2direct (N × H)
5. C2×#1344C2semidirect
6. C2×#1343C2semidirect
8. C22×#121C4semidirect
14. #2543C4semidirect
16. C2×#398C4semidirect
18. C2×#394C4semidirect
24. C22×#95C4semidirect
26. C4×#99C22semidirect
29. #1466C22semidirect
32. #1344C22semidirect
33. #1343C22semidirect
48. C2×#121C2×C4semidirect
77. #398C2×C4semidirect
83. #394C2×C4semidirect
103. C2×#95C2×C4semidirect
551. C2#11775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25432
C2×C4×#992
C2×#14662
#117752
C2×#13442
C2×#13432