Finite Group Databasebeta

← C2×#11526 #480323

Subgroups — C2×#11526 #480323

Order 512.

1306 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#123C211yesmaximal, characteristic
2C2×#1466C211yesmaximal, characteristic
3C2×#1465C211yesmaximal, characteristic
4#11526C218yesmaximal, direct product factor
5C2×#1326C212yesmaximal, complemented
6C2×#1317C212yesmaximal, complemented
7C22×#123C411yescharacteristic
8C22×C4×D4C2211yescharacteristic
9C23×C42C411yescharacteristic
10C2×#432—21no—
11C2×#407—21no—
12C4×#123—22no—
13C4×#123—22no—
14C4×#123C414yes—
15C4×#123C2214yes—
16C2×#388—21no—
17C2×#387—21no—
18C2×#386C411yescharacteristic
19C2×#385C2211yescharacteristic
20C2×#381C2211yescharacteristic
21C2×C4×C4⋊C4—21no—
22C2×C4×C22⋊C4—21no—
23C2×C4×C22⋊C4C411yescharacteristic
24#1466—22no—
25#1466C2214yes—
26#1465—22no—
27#1465C2214yes—
28C2×#324—21no—
29C2×#323—21no—
30C2×#323C2212yes—
31C2×#323C2212yes—
32#1326C2218yescomplemented
33#1317C2218yescomplemented
34C23×D4C2×C411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—41no—
40C2×#123—22no—
41C2×#123—24no—
42C2×#123—24no—
43C2×#123C2×C414yes—
44C2×C4×D4—41no—
45C2×C4×D4—41no—
46C2×C4×D4—42no—
47C2×C4×D4C2×C412yes—
48C2×C4×D4D412yes—
49C2×C4×D4D412yes—
50C2×C4×D4C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4D411yescharacteristic
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4C2×C411yescharacteristic
57C22×C22⋊C4C2×C411yescharacteristic
58C22×C22⋊C4D411yescharacteristic
59C22×C22⋊C4C2311yescharacteristic
60C22×C42—21no—
61C22×C42—22no—
62C22×C42—21no—
63C22×C42—21no—
64C22×C42—42no—
65C22×C42—41no—
66C22×C42—41no—
67C22×C42C2×C414yes—
68C22×C42D411yescharacteristic
69#432—24no—
70#432—42no—
71C2×C4⋊C8—41no—
72#407—24no—
73#407—42no—
74C2×C22⋊C8—22no—
75C2×C22⋊C8—22no—
76C2×C22⋊C8—41no—
77C2×#97—41no—
78#388—24no—
79#388—24no—
80#387—24no—
81#387—24no—
82#386—22no—
83#386C2×C414yes—
84#385—21no—
85#385—21no—
86#385C2×C412yes—
87#385C2312yes—
88#381—21no—
89#381—21no—
90#381C2×C412yes—
91#381C2312yes—
92C4×C4⋊C4—24no—
93C4×C4⋊C4—24no—
94C4×C22⋊C4—24no—
95C4×C22⋊C4—22no—
96C4×C22⋊C4—24no—
97C4×C22⋊C4C2×C414yes—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103#324—24no—
104#323—24no—
105#323—22no—
106#323—22no—
107#323C2314yes—
108#323C2314yes—
109C25C22⋊C411yescharacteristic
110C25C22×C411yescharacteristic
111C22×D4—22no—
112C22×D4—22no—
113C22×D4—41no—
114C22×D4—41no—
115C22×D4—42no—
116C22×D4C22⋊C412yes—
117C22×D4C22×C412yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4—22no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—44no—
132C23×C4—44no—
133C23×C4—44no—
134C23×C4—42no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—41no—
138C23×C4—41no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C412yes—
143C23×C4C22⋊C411yescharacteristic
144C23×C4M1614yescomplemented
145C23×C4C22×C412yes—
146C23×C4C22×C412yes—
147C23×C4C22×C412yes—
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C2×M16—44no—
152C2×M16—84no—
153C22×C8—42no—
154C22×C8—42no—
155#123—216no—
156#123—28no—
157#123—28no—
158C4×D4—42no—
159C4×D4—42no—
160C4×D4—42no—
161C4×D4—42no—
162C4×D4—42no—
163C4×D4—42no—
164C4×D4—42no—
165C4×D4—42no—
166C2×C4⋊C4—28no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4C22⋊C412yes—
174C2×C4⋊C4C2×D412yes—
175C2×C22⋊C4—28no—
176C2×C22⋊C4—24no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—44no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4C22⋊C412yes—
188C2×C22⋊C4M1614yescomplemented
189C2×C22⋊C4C22×C412yes—
190C2×C22⋊C4C22×C412yes—
191C2×C22⋊C4C22×C411yescharacteristic
192C2×C22⋊C4C2×D412yes—
193C2×C22⋊C4C2×D411yescharacteristic
194C2×C22⋊C4C2×D411yescharacteristic
195C2×C22⋊C4C2411yescharacteristic
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—22no—
199C2×C42—24no—
200C2×C42—24no—
201C2×C42—24no—
202C2×C42—44no—
203C2×C42—42no—
204C2×C42—42no—
205C2×C42—44no—
206C2×C42—44no—
207C2×C42—42no—
208C2×C42—41no—
209C2×C42—41no—
210C2×C42—44no—
211C2×C42—44no—
212C2×C42C22⋊C412yes—
213C2×C42C2×D412yes—
214C4⋊C8—44no—
215C22⋊C8—24no—
216C22⋊C8—24no—
217C22⋊C8—42no—
218C22⋊C8—42no—
219C22⋊C8—44no—
220#97—44no—
221#95—22no—
222#95—22no—
223#95—24no—
224#95—22no—
225#95—24no—
226#95—22no—
227#95—22no—
228#95—22no—
229C24—21no—
230C24—21no—
231C24—22no—
232C24—22no—
233C24—21no—
234C24—21no—
235C24—22no—
236C24—42no—
237C24—42no—
238C24—42no—
239C24—42no—
240C24C2×C22⋊C411yescharacteristic
241C24C2×C22⋊C412yes—
242C24C2×C22⋊C411yescharacteristic
243C24C2×M1612yes—
244C24C2×M1612yes—
245C24C23×C411yescharacteristic
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—24no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—42no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—44no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—44no—
286C22×C4—48no—
287C22×C4—44no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—44no—
300C22×C4—44no—
301C22×C4—48no—
302C22×C4—44no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—44no—
309C22×C4—44no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—44no—
314C22×C4—44no—
315C22×C4—42no—
316C22×C4—44no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—84no—
323C22×C4—82no—
324C22×C4#9912yes—
325C22×C4#9911yescharacteristic
326C22×C4#9911yescharacteristic
327C22×C4C2×C22⋊C412yes—
328C22×C4C2×C22⋊C412yes—
329C22×C4C2×C22⋊C411yescharacteristic
330C22×C4C2×C22⋊C412yes—
331C22×C4C2×C22⋊C411yescharacteristic
332C22×C4C2×M1614yescomplemented
333C22×C4C22×D411yescharacteristic
334C22×C4C22×D411yescharacteristic
335M16—88no—
336C2×C8—44no—
337C2×C8—44no—
338C2×C8—84no—
339C2×C8—84no—
340C4⋊C4—216no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—44no—
344C4⋊C4—44no—
345C22⋊C4—216no—
346C22⋊C4—22no—
347C22⋊C4—24no—
348C22⋊C4—42no—
349C22⋊C4—41no—
350C22⋊C4—42no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—48no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4C2×M1614yescomplemented
358C42—22no—
359C42—22no—
360C42—22no—
361C42—22no—
362C42—48no—
363C42—48no—
364C42—44no—
365C42—44no—
366C23—22no—
367C23—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—22no—
373C23—22no—
374C23—22no—
375C23—22no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—44no—
384C23—44no—
385C23—42no—
386C23—42no—
387C23—48no—
388C23—42no—
389C23—42no—
390C23—48no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—81no—
398C23—81no—
399C23—84no—
400C23#40712yes—
401C23#40712yes—
402C23C2×#9911yescharacteristic
403C23C2×#9911yescharacteristic
404C23#41312yes—
405C23C22×C22⋊C411yescharacteristic
406C23C22×M1611yescharacteristic
407C23C22×M1611yescharacteristic
408D4—44no—
409D4—44no—
410D4—48no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—48no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—48no—
435C2×C4—48no—
436C2×C4—44no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—44no—
457C2×C4—41no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—84no—
467C2×C4#35214yes—
468C2×C4C2×#9912yes—
469C2×C4C2×#9912yes—
470C8—84no—
471C8—84no—
472C22—24no—
473C22—24no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—41no—
482C22—41no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22—44no—
490C22—44no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—82no—
499C22—84no—
500C22—84no—
501C22#146512yes—
502C22#146512yes—
503C22C2×#35212yes—
504C22#212012yes—
505C22C2×#40711yescharacteristic
506C22C22×#9911yescharacteristic
507C22C2×#41311yescharacteristic
508C4—22no—
509C4—44no—
510C4—41no—
511C4—42no—
512C4—41no—
513C4—41no—
514C4—44no—
515C4—41no—
516C4—42no—
517C4—44no—
518C4—82no—
519C4C2×#35214yes—
520C2—21no—
521C2—21no—
522C2—22no—
523C2—41no—
524C2—41no—
525C2—42no—
526C2—82no—
527C2#1152614yesdirect product factor
528C2C2×#146511yescharacteristic
529C2C22×#35211yescharacteristic
530C2C2×#212011yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ 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
4. #11526C2direct (N × H)
5. C2×#1326C2semidirect
6. C2×#1317C2semidirect
32. #1326C22semidirect
33. #1317C22semidirect
144. C23×C4M16semidirect
188. C2×C22⋊C4M16semidirect
332. C22×C4C2×M16semidirect
357. C22⋊C4C2×M16semidirect
527. C2#11526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1232
C2×#14662
C2×#14652
#115262
C2×#13262
C2×#13172