Finite Group Databasebeta

← C2×#11897 #482115

Subgroups — C2×#11897 #482115

Order 512.

1212 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2580C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11897C218yesmaximal, direct product factor
5C2×#1352C212yesmaximal, complemented
6C2×#1351C212yesmaximal, complemented
7C22×C4×Q8C411yescharacteristic, complemented
8C22×C4×D4C2211yescharacteristic
9C22×#99—21no—
10C22×C22⋊C8—21no—
11#2580—22no—
12#2580—22no—
13#2580C414yescomplemented
14#2580C2214yes—
15C2×#399C411yescharacteristic, complemented
16C2×#399C2211yescharacteristic
17C2×#393C411yescharacteristic, complemented
18C2×#393C2211yescharacteristic
19C2×#390—21no—
20C2×#389—21no—
21C2×#385—21no—
22C2×#385—21no—
23C2×#382C411yescharacteristic, complemented
24C2×#380—21no—
25#1799—22no—
26#1799C2214yes—
27C2×#342C2212yes—
28#1459—22no—
29#1459C2214yes—
30C2×#324—21no—
31C2×#323C2212yes—
32#1352C2218yescomplemented
33#1351C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C23×D4D411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4D411yescharacteristic
38C23×C8—41no—
39C2×C4×Q8—22no—
40C2×C4×Q8—42no—
41C2×C4×Q8—41no—
42C2×C4×Q8—41no—
43C2×C4×Q8C2×C414yescomplemented
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⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—41no—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4D411yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4C2×C411yescharacteristic
64C22×C22⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42C2×C411yescharacteristic
67C2×#99—24no—
68C2×#99—44no—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—24no—
71C2×C22⋊C8—42no—
72C2×C22⋊C8—41no—
73#399—22no—
74#399—21no—
75#399—21no—
76#399C2×C412yes—
77#399C2×C414yescomplemented
78#399C2312yes—
79#393—22no—
80#393—21no—
81#393—21no—
82#393C2×C412yes—
83#393C2×C414yescomplemented
84#393C2312yes—
85#390—24no—
86#390—24no—
87#389—24no—
88#389—24no—
89#385—24no—
90#385—24no—
91#385—24no—
92#385—24no—
93#382—22no—
94#382C2×C414yescomplemented
95#380—24no—
96#380—42no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—41no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#342—22no—
104#342C2314yes—
105#324—24no—
106#323—22no—
107#323C2314yes—
108C25C22⋊C411yescharacteristic
109C25C2×D411yescharacteristic
110C22×Q8—21no—
111C22×Q8—44no—
112C22×Q8—41no—
113C22×Q8—41no—
114C22×Q8C22×C412yes—
115C22×D4—41no—
116C22×D4—41no—
117C22×D4—42no—
118C22×D4C22⋊C412yes—
119C22×D4SD1614yes—
120C22×D4Q1614yes—
121C22×D4C2×D412yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—42no—
133C23×C4—82no—
134C23×C4—82no—
135C23×C4C22⋊C411yescharacteristic
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C412yes—
138C23×C4C22⋊C412yes—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22×C411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D412yes—
143C23×C4C2×D412yes—
144C22×C8—42no—
145C22×C8—44no—
146C22×C8—84no—
147C4×Q8—44no—
148C4×Q8—44no—
149C4×Q8—44no—
150C4×Q8—44no—
151C4×D4—42no—
152C4×D4—42no—
153C4×D4—42no—
154C4×D4—42no—
155C4×D4—42no—
156C4×D4—42no—
157C4×D4—42no—
158C4×D4—42no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—82no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—84no—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C22×C412yes—
179C2×C4⋊C4C2×D412yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—44no—
192C2×C22⋊C4—44no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—82no—
197C2×C22⋊C4—82no—
198C2×C22⋊C4C22⋊C412yes—
199C2×C22⋊C4C22×C412yes—
200C2×C22⋊C4C22×C411yescharacteristic
201C2×C22⋊C4C2×D411yescharacteristic
202C2×C22⋊C4C2×D411yescharacteristic
203C2×C22⋊C4C2411yescharacteristic
204C2×C42—22no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—24no—
208C2×C42—42no—
209C2×C42—42no—
210C2×C42C22⋊C412yes—
211C2×C42C22×C412yes—
212#99—48no—
213C22⋊C8—24no—
214C22⋊C8—42no—
215C22⋊C8—44no—
216#95—24no—
217#95—22no—
218#95—24no—
219#95—21no—
220#95—21no—
221#95—22no—
222#95—44no—
223#95C22×C412yes—
224#95C22×C412yes—
225C24—21no—
226C24—21no—
227C24—21no—
228C24—21no—
229C24—22no—
230C24—22no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24—42no—
235C24#10314yes—
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C412yes—
238C24C2×C22⋊C411yescharacteristic
239C24C2×SD1612yes—
240C24C2×Q1612yes—
241C24C22×D411yescharacteristic
242C2×Q8—44no—
243C2×Q8—42no—
244C2×Q8—44no—
245C2×Q8—42no—
246C2×Q8—48no—
247C2×Q8—44no—
248C2×Q8—44no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—42no—
257C2×D4#10318yes—
258C2×D4C2×SD1614yes—
259C2×D4C2×Q1614yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—44no—
302C22×C4—82no—
303C22×C4—82no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4—82no—
308C22×C4—84no—
309C22×C4—84no—
310C22×C4—84no—
311C22×C4—84no—
312C22×C4—84no—
313C22×C4#9911yescharacteristic
314C22×C4#9911yescharacteristic
315C22×C4#9912yes—
316C22×C4#10314yes—
317C22×C4C2×C22⋊C412yes—
318C22×C4C2×C22⋊C411yescharacteristic
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C412yes—
322C22×C4C23×C411yescharacteristic
323C22×C4C22×D411yescharacteristic
324C2×C8—44no—
325C2×C8—88no—
326C2×C8—84no—
327C4⋊C4—42no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—48no—
331C4⋊C4—42no—
332C4⋊C4—44no—
333C4⋊C4—44no—
334C4⋊C4—82no—
335C4⋊C4—84no—
336C4⋊C4—82no—
337C4⋊C4—88no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—48no—
346C22⋊C4—44no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—82no—
350C22⋊C4—84no—
351C22⋊C4—82no—
352C22⋊C4—84no—
353C42—22no—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—48no—
358C23—22no—
359C23—22no—
360C23—21no—
361C23—22no—
362C23—21no—
363C23—22no—
364C23—24no—
365C23—22no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—22no—
370C23—24no—
371C23—22no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—42no—
377C23—41no—
378C23—48no—
379C23—44no—
380C23—44no—
381C23—42no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23—84no—
390C23—84no—
391C23C2×#9911yescharacteristic
392C23C2×#9911yescharacteristic
393C23C2×#10312yes—
394C23C2×#10312yes—
395C23C2×#10314yes—
396C23#42112yes—
397C23C22×C22⋊C411yescharacteristic
398C23C22×SD1611yescharacteristic
399C23C22×Q1611yescharacteristic
400Q8—44no—
401Q8—44no—
402Q8—48no—
403D4—48no—
404D4—44no—
405D4—44no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
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—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—84no—
453C2×C4—84no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—84no—
457C2×C4—84no—
458C2×C4—84no—
459C2×C4—168no—
460C2×C4C2×#9912yes—
461C2×C4C2×#9912yes—
462C2×C4C2×#10314yes—
463C8—84no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—24no—
469C22—24no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—24no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—42no—
478C22—41no—
479C22—41no—
480C22—42no—
481C22—41no—
482C22—42no—
483C22—41no—
484C22—44no—
485C22—48no—
486C22—44no—
487C22—81no—
488C22—81no—
489C22—82no—
490C22—82no—
491C22—84no—
492C22—82no—
493C22#152012yes—
494C22#152012yes—
495C22#212012yes—
496C22#212712yes—
497C22C22×#9911yescharacteristic
498C22C22×#10311yescharacteristic
499C22C2×#42111yescharacteristic
500C4—22no—
501C4—22no—
502C4—24no—
503C4—44no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—42no—
508C4—41no—
509C4—82no—
510C4—82no—
511C4—82no—
512C4—164no—
513C2—21no—
514C2—21no—
515C2—22no—
516C2—41no—
517C2—41no—
518C2—42no—
519C2—44no—
520C2#1189714yesdirect product factor
521C2C2×#152011yescharacteristic
522C2C2×#212011yescharacteristic
523C2C2×#212711yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C22⋊C4C24
prime radicalC23×D4D4
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
4. #11897C2direct (N × H)
5. C2×#1352C2semidirect
6. C2×#1351C2semidirect
7. C22×C4×Q8C4semidirect
13. #2580C4semidirect
15. C2×#399C4semidirect
17. C2×#393C4semidirect
23. C2×#382C4semidirect
32. #1352C22semidirect
33. #1351C22semidirect
43. C2×C4×Q8C2×C4semidirect
77. #399C2×C4semidirect
83. #393C2×C4semidirect
94. #382C2×C4semidirect
520. C2#11897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25802
C2×#17992
C2×#14592
#118972
C2×#13522
C2×#13512