Finite Group Databasebeta

← C2×#11880 #482054

Subgroups — C2×#11880 #482054

Order 512.

2506 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic, complemented
3C2×#1459C211yesmaximal, characteristic, complemented
4#11880C218yesmaximal, direct product factor
5C2×#1345C214yesmaximal, complemented
6C24×D4C411yescharacteristic
7C22×#121—21no—
8C22×#120—21no—
9C22×C4×D4C2211yescharacteristic
10C2×#423—21no—
11C22×#100—21no—
12C22×C22⋊C8—21no—
13#2408—22no—
14#2408—22no—
15#2408C414yes—
16#2408C2214yes—
17C2×#394C2212yes—
18C2×#392C412yes—
19C2×#390—21no—
20C2×#380C411yescharacteristic
21C2×#379—21no—
22#1800—22no—
23#1800C2214yescomplemented
24C2×#343C2212yescomplemented
25#1459—22no—
26#1459C2214yescomplemented
27C2×#324C2212yescomplemented
28C2×#323—21no—
29#1345C22116yescomplemented
30C26—21no—
31C23×D4—22no—
32C23×D4—22no—
33C23×D4—21no—
34C23×D4—42no—
35C23×D4—41no—
36C23×D4—41no—
37C23×D4—48no—
38C23×D4C2×C412yes—
39C23×D4C2×C414yes—
40C23×D4D411yescharacteristic
41C24×C4C2×C411yescharacteristic
42C24×C4D411yescharacteristic
43C22×M16—22no—
44C23×C8—41no—
45C2×#121—24no—
46C2×#121—24no—
47C2×#121—48no—
48C2×#120—24no—
49C2×#120—24no—
50C2×#120—44no—
51C2×#120—44no—
52C2×C4×D4—41no—
53C2×C4×D4—41no—
54C2×C4×D4—42no—
55C2×C4×D4C2×C412yes—
56C2×C4×D4D412yes—
57C2×C4×D4D412yes—
58C2×C4×D4C2312yes—
59C22×C4⋊C4—21no—
60C22×C4⋊C4C2311yescharacteristic
61C22×C22⋊C4—21no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—22no—
64C22×C22⋊C4—22no—
65C22×C22⋊C4C2×C411yescharacteristic
66C22×C22⋊C4D411yescharacteristic
67C22×C42D411yescharacteristic
68#423—24no—
69#423—42no—
70C2×C4⋊C8—41no—
71C2×C4⋊C8—41no—
72C2×#100—24no—
73C2×#100—44no—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—24no—
76C2×C22⋊C8—42no—
77C2×C22⋊C8—41no—
78#394—22no—
79#394—22no—
80#394C2×C414yes—
81#394C2314yes—
82#392—24no—
83#392C2×C418yes—
84#390—24no—
85#390—24no—
86#380—22no—
87#380C2×C414yes—
88#379—24no—
89#379—24no—
90C2×#95C2×C412yes—
91#343—22no—
92#343C2314yescomplemented
93#324—22no—
94#324C2314yescomplemented
95#323—24no—
96C25—22no—
97C25—24no—
98C25—42no—
99C25—42no—
100C25—48no—
101C25—44no—
102C25—44no—
103C25—84no—
104C25C22⋊C411yescharacteristic
105C25C22⋊C411yescharacteristic
106C22×D4—28no—
107C22×D4—28no—
108C22×D4—24no—
109C22×D4—22no—
110C22×D4—41no—
111C22×D4—41no—
112C22×D4—42no—
113C22×D4—42no—
114C22×D4—42no—
115C22×D4—44no—
116C22×D4—44no—
117C22×D4—44no—
118C22×D4—44no—
119C22×D4—44no—
120C22×D4—416no—
121C22×D4—416no—
122C22×D4—416no—
123C22×D4—432no—
124C22×D4—48no—
125C22×D4—48no—
126C22×D4—48no—
127C22×D4—48no—
128C22×D4—48no—
129C22×D4—42no—
130C22×D4—41no—
131C22×D4—41no—
132C22×D4—84no—
133C22×D4C22⋊C412yes—
134C22×D4D814yes—
135C22×D4SD1614yes—
136C22×D4C22×C414yes—
137C22×D4C2×D412yes—
138C23×C4—21no—
139C23×C4—22no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—44no—
146C23×C4—44no—
147C23×C4C22⋊C411yescharacteristic
148C23×C4C22⋊C412yes—
149C23×C4C22⋊C412yes—
150C23×C4C22⋊C411yescharacteristic
151C23×C4C22×C411yescharacteristic
152C23×C4C22×C412yes—
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D412yes—
156C2×M16—24no—
157C2×M16—42no—
158C2×M16—44no—
159C2×M16—44no—
160C22×C8—42no—
161C22×C8—44no—
162C22×C8—42no—
163C22×C8—84no—
164#121—416no—
165#121—416no—
166#120—416no—
167#120—48no—
168#120—48no—
169C4×D4—42no—
170C4×D4—42no—
171C4×D4—42no—
172C4×D4—42no—
173C4×D4—42no—
174C4×D4—42no—
175C4×D4—42no—
176C4×D4—42no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4C22×C411yescharacteristic
182C2×C4⋊C4C2×D411yescharacteristic
183C2×C4⋊C4C2×D411yescharacteristic
184C2×C4⋊C4C2411yescharacteristic
185C2×C22⋊C4—24no—
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—24no—
190C2×C22⋊C4—28no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—41no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—48no—
196C2×C22⋊C4—44no—
197C2×C22⋊C4—44no—
198C2×C22⋊C4—44no—
199C2×C22⋊C4—84no—
200C2×C22⋊C4C22⋊C412yes—
201C2×C22⋊C4C22⋊C412yes—
202C2×C22⋊C4C22×C412yes—
203C2×C22⋊C4C2×D412yes—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42C22⋊C412yes—
208C2×C42C2×D412yes—
209C4⋊C8—44no—
210C4⋊C8—44no—
211#100—48no—
212C22⋊C8—24no—
213C22⋊C8—42no—
214C22⋊C8—44no—
215#95—22no—
216#95C22×C414yes—
217C24—21no—
218C24—21no—
219C24—21no—
220C24—22no—
221C24—21no—
222C24—22no—
223C24—28no—
224C24—24no—
225C24—42no—
226C24—42no—
227C24—42no—
228C24—42no—
229C24—44no—
230C24—44no—
231C24—48no—
232C24—416no—
233C24—44no—
234C24—48no—
235C24—416no—
236C24—416no—
237C24—42no—
238C24—42no—
239C24—44no—
240C24—44no—
241C24—48no—
242C24—88no—
243C24—88no—
244C24—88no—
245C24—832no—
246C24—832no—
247C24—88no—
248C24—88no—
249C24#10214yes—
250C24#10214yes—
251C24C2×C22⋊C411yescharacteristic
252C24C2×C22⋊C412yes—
253C24C2×C22⋊C412yes—
254C2×D4—216no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—44no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—48no—
265C2×D4—48no—
266C2×D4—416no—
267C2×D4—44no—
268C2×D4—48no—
269C2×D4—48no—
270C2×D4—432no—
271C2×D4—432no—
272C2×D4—416no—
273C2×D4—48no—
274C2×D4—432no—
275C2×D4—416no—
276C2×D4—48no—
277C2×D4—416no—
278C2×D4—416no—
279C2×D4—416no—
280C2×D4—48no—
281C2×D4—44no—
282C2×D4—44no—
283C2×D4—88no—
284C2×D4—832no—
285C2×D4#10218yes—
286C2×D4C2×D814yes—
287C2×D4C2×SD1614yes—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—24no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—44no—
308C22×C4—48no—
309C22×C4—44no—
310C22×C4—44no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—44no—
319C22×C4—44no—
320C22×C4—44no—
321C22×C4—84no—
322C22×C4—82no—
323C22×C4#9912yes—
324C22×C4#9911yescharacteristic
325C22×C4#9911yescharacteristic
326C22×C4C2×C22⋊C412yes—
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4C2×C22⋊C411yescharacteristic
329C22×C4C2×C22⋊C412yes—
330C22×C4C2×C22⋊C411yescharacteristic
331C22×C4C2×D812yes—
332C22×C4C2×SD1612yes—
333C22×C4C23×C411yescharacteristic
334C22×C4C22×D411yescharacteristic
335C22×C4C22×D411yescharacteristic
336M16—44no—
337M16—44no—
338M16—84no—
339C2×C8—44no—
340C2×C8—44no—
341C2×C8—84no—
342C2×C8—84no—
343C2×C8—88no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—48no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—48no—
354C22⋊C4—48no—
355C22⋊C4—48no—
356C22⋊C4—44no—
357C22⋊C4—44no—
358C22⋊C4—48no—
359C22⋊C4—88no—
360C42—22no—
361C42—22no—
362C42—22no—
363C42—22no—
364C23—22no—
365C23—22no—
366C23—22no—
367C23—22no—
368C23—22no—
369C23—24no—
370C23—24no—
371C23—24no—
372C23—22no—
373C23—24no—
374C23—28no—
375C23—42no—
376C23—48no—
377C23—42no—
378C23—42no—
379C23—42no—
380C23—48no—
381C23—42no—
382C23—48no—
383C23—42no—
384C23—44no—
385C23—44no—
386C23—48no—
387C23—44no—
388C23—416no—
389C23—416no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—432no—
395C23—44no—
396C23—48no—
397C23—44no—
398C23—44no—
399C23—81no—
400C23—81no—
401C23—84no—
402C23—84no—
403C23—88no—
404C23—88no—
405C23—816no—
406C23—832no—
407C23—832no—
408C23—864no—
409C23—816no—
410C23—864no—
411C23—84no—
412C23—84no—
413C23—84no—
414C23C2×#9911yescharacteristic
415C23C2×#9911yescharacteristic
416C23C2×#10212yes—
417C23C2×#10214yes—
418C23C2×#10214yes—
419C23#42112yes—
420C23C22×C22⋊C411yescharacteristic
421D4—48no—
422D4—44no—
423D4—44no—
424D4—416no—
425D4—48no—
426D4—48no—
427D4—416no—
428D4—416no—
429D4—832no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—88no—
469C2×C4AΣL(1,𝔽16)14yes—
470C2×C4C2×#9912yes—
471C2×C4C2×#9912yes—
472C2×C4C2×#10212yes—
473C2×C4C22×D811yescharacteristic
474C2×C4C22×SD1611yescharacteristic
475C8—84no—
476C8—84no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—24no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22—48no—
489C22—48no—
490C22—48no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—48no—
496C22—48no—
497C22—48no—
498C22—82no—
499C22—84no—
500C22—84no—
501C22—84no—
502C22—816no—
503C22—864no—
504C22—84no—
505C22—816no—
506C22—84no—
507C22#151912yes—
508C22#151912yes—
509C22C2×AΣL(1,𝔽16)12yes—
510C22#213412yes—
511C22C22×#9911yescharacteristic
512C22C22×#10211yescharacteristic
513C22C2×#42111yescharacteristic
514C4—22no—
515C4—21no—
516C4—21no—
517C4—22no—
518C4—41no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—42no—
523C4—84no—
524C4C2×AΣL(1,𝔽16)14yes—
525C2—21no—
526C2—21no—
527C2—22no—
528C2—44no—
529C2—44no—
530C2—88no—
531C2#1188014yesdirect product factor
532C2C2×#151911yescharacteristic
533C2C22×AΣL(1,𝔽16)11yescharacteristic
534C2C2×#213411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#2408C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×D4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1800C2semidirect
3. C2×#1459C2semidirect
4. #11880C2direct (N × H)
5. C2×#1345C2semidirect
23. #1800C22semidirect
24. C2×#343C22semidirect
26. #1459C22semidirect
27. C2×#324C22semidirect
29. #1345C22semidirect
92. #343C23semidirect
94. #324C23semidirect
531. C2#11880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#18002
C2×#14592
#118802
C2×#13452