Finite Group Databasebeta

← C2×#11902 #482109

Subgroups — C2×#11902 #482109

Order 512.

1222 conjugacy classes of subgroups.

The subgroup lattice has 523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2564C211yesmaximal, characteristic
2C2×#1799C211yesmaximal, characteristic
3C2×#1460C211yesmaximal, characteristic
4#11902C218yesmaximal, direct product factor
5C2×#1352C212yesmaximal, complemented
6C2×#1351C212yesmaximal, complemented
7C22×C22⋊Q8C411yescharacteristic, complemented
8C22×C4×D4C2211yescharacteristic
9C2×#431—21no—
10C22×#99—21no—
11#2564—22no—
12#2564—22no—
13#2564C414yescomplemented
14#2564C2214yes—
15C2×#400C411yescharacteristic, complemented
16C2×#399C2211yescharacteristic
17C2×#395C411yescharacteristic, complemented
18C2×#393C2211yescharacteristic
19C2×#387—21no—
20C2×#386—21no—
21C2×#385—21no—
22C2×#380—21no—
23C2×#380—21no—
24C22×#95C411yescharacteristic, complemented
25#1799—22no—
26#1799C2214yes—
27C2×#342C2212yes—
28#1460—22no—
29#1460C2214yes—
30C2×#323—21no—
31C2×#323C2212yes—
32#1352C2218yescomplemented
33#1351C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C23×D4D411yescharacteristic
36C24×C4—21no—
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C2×C22⋊Q8—22no—
40C2×C22⋊Q8—42no—
41C2×C22⋊Q8—41no—
42C2×C22⋊Q8—41no—
43C2×C22⋊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—41no—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—22no—
61C22×C22⋊C4D411yescharacteristic
62C22×C22⋊C4C2311yescharacteristic
63C22×C42D411yescharacteristic
64#431—24no—
65#431—42no—
66C2×C4⋊C8—41no—
67C2×#99—24no—
68C2×#99—44no—
69C2×C22⋊C8—22no—
70C2×C4×C8—41no—
71#400—22no—
72#400C2×C414yescomplemented
73#399—21no—
74#399—21no—
75#399C2×C412yes—
76#399C2312yes—
77#395—22no—
78#395C2×C414yescomplemented
79#393—21no—
80#393—21no—
81#393C2×C412yes—
82#393C2312yes—
83#387—24no—
84#387—24no—
85#386—24no—
86#386—24no—
87#385—24no—
88#385—24no—
89#380—24no—
90#380—24no—
91#380—24no—
92#380—42no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—41no—
100C2×#95C2×C411yescharacteristic
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C414yescomplemented
103#342—22no—
104#342C2314yes—
105#323—24no—
106#323—22no—
107#323C2314yes—
108C25C22⋊C411yescharacteristic
109C25C2×D411yescharacteristic
110C22×Q8—21no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—82no—
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—22no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—24no—
133C23×C4—44no—
134C23×C4—44no—
135C23×C4—42no—
136C23×C4—82no—
137C23×C4—82no—
138C23×C4—82no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C412yes—
142C23×C4C22⋊C412yes—
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22×C411yescharacteristic
145C23×C4C22×C412yes—
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D412yes—
148C22×C8—42no—
149C22⋊Q8—44no—
150C22⋊Q8—44no—
151C22⋊Q8—44no—
152C22⋊Q8—44no—
153C4×D4—42no—
154C4×D4—42no—
155C4×D4—42no—
156C4×D4—42no—
157C4×D4—42no—
158C4×D4—42no—
159C4×D4—42no—
160C4×D4—42no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4—82no—
176C2×C4⋊C4—84no—
177C2×C4⋊C4C22⋊C412yes—
178C2×C4⋊C4C22×C412yes—
179C2×C4⋊C4C22×C412yes—
180C2×C22⋊C4—24no—
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—24no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—41no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—44no—
191C2×C22⋊C4—42no—
192C2×C22⋊C4—42no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—44no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—82no—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22×C411yescharacteristic
199C2×C22⋊C4C2×D411yescharacteristic
200C2×C22⋊C4C2×D412yes—
201C2×C22⋊C4C2×D411yescharacteristic
202C2×C22⋊C4C2411yescharacteristic
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—22no—
206C2×C42C22⋊C412yes—
207C2×C42C2×D412yes—
208C4⋊C8—44no—
209#99—48no—
210C22⋊C8—24no—
211C22⋊C8—42no—
212C4×C8—44no—
213#95—21no—
214#95—21no—
215#95—24no—
216#95—24no—
217#95—22no—
218#95—24no—
219#95—24no—
220#95—22no—
221#95—44no—
222#95C22×C412yes—
223#95C22×C412yes—
224C24—21no—
225C24—21no—
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24—42no—
233C24—42no—
234C24#10314yes—
235C24C2×C22⋊C411yescharacteristic
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C412yes—
238C24C2×SD1612yes—
239C24C2×Q1612yes—
240C24C22×D411yescharacteristic
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—82no—
244C2×Q8—82no—
245C2×Q8—84no—
246C2×Q8—84no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—44no—
251C2×D4—44no—
252C2×D4—44no—
253C2×D4—44no—
254C2×D4—42no—
255C2×D4#10318yes—
256C2×D4C2×SD1614yes—
257C2×D4C2×Q1614yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
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—42no—
281C22×C4—44no—
282C22×C4—48no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—48no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—82no—
302C22×C4—82no—
303C22×C4—82no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—84no—
307C22×C4—84no—
308C22×C4—84no—
309C22×C4—82no—
310C22×C4—82no—
311C22×C4—816no—
312C22×C4—84no—
313C22×C4—84no—
314C22×C4—84no—
315C22×C4#9911yescharacteristic
316C22×C4#9911yescharacteristic
317C22×C4#9912yes—
318C22×C4#10314yes—
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C411yescharacteristic
323C22×C4C2×C22⋊C412yes—
324C22×C4C23×C411yescharacteristic
325C22×C4C22×D411yescharacteristic
326C2×C8—44no—
327C2×C8—84no—
328C4⋊C4—42no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—44no—
332C4⋊C4—44no—
333C4⋊C4—42no—
334C4⋊C4—44no—
335C4⋊C4—44no—
336C4⋊C4—84no—
337C4⋊C4—88no—
338C22⋊C4—42no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—42no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—44no—
345C22⋊C4—44no—
346C22⋊C4—48no—
347C22⋊C4—44no—
348C22⋊C4—44no—
349C22⋊C4—82no—
350C22⋊C4—82no—
351C22⋊C4—84no—
352C42—22no—
353C42—22no—
354C42—22no—
355C42—22no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—22no—
363C23—24no—
364C23—24no—
365C23—22no—
366C23—21no—
367C23—21no—
368C23—22no—
369C23—22no—
370C23—42no—
371C23—42no—
372C23—48no—
373C23—42no—
374C23—48no—
375C23—42no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—44no—
381C23—44no—
382C23—42no—
383C23—42no—
384C23—42no—
385C23—42no—
386C23—81no—
387C23—81no—
388C23—84no—
389C23C2×#9911yescharacteristic
390C23C2×#9911yescharacteristic
391C23C2×#10312yes—
392C23C2×#10312yes—
393C23C2×#10314yes—
394C23#42112yes—
395C23C22×C22⋊C411yescharacteristic
396C23C22×SD1611yescharacteristic
397C23C22×Q1611yescharacteristic
398Q8—84no—
399Q8—84no—
400D4—48no—
401D4—44no—
402D4—44no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—42no—
420C2×C4—48no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—816no—
449C2×C4—82no—
450C2×C4—84no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—84no—
455C2×C4—84no—
456C2×C4—84no—
457C2×C4—168no—
458C2×C4C2×#9912yes—
459C2×C4C2×#9912yes—
460C2×C4C2×#10314yes—
461C8—84no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—24no—
467C22—24no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—44no—
475C22—42no—
476C22—44no—
477C22—48no—
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#152012yes—
492C22#152012yes—
493C22#212112yes—
494C22#212612yes—
495C22C22×#9911yescharacteristic
496C22C22×#10311yescharacteristic
497C22C2×#42111yescharacteristic
498C4—22no—
499C4—22no—
500C4—24no—
501C4—44no—
502C4—42no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—82no—
508C4—82no—
509C4—82no—
510C4—164no—
511C2—21no—
512C2—21no—
513C2—22no—
514C2—41no—
515C2—44no—
516C2—41no—
517C2—42no—
518C2#1190214yesdirect product factor
519C2C2×#152011yescharacteristic
520C2C2×#212111yescharacteristic
521C2C2×#212611yescharacteristic
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. #11902C2direct (N × H)
5. C2×#1352C2semidirect
6. C2×#1351C2semidirect
7. C22×C22⋊Q8C4semidirect
13. #2564C4semidirect
15. C2×#400C4semidirect
17. C2×#395C4semidirect
24. C22×#95C4semidirect
32. #1352C22semidirect
33. #1351C22semidirect
43. C2×C22⋊Q8C2×C4semidirect
72. #400C2×C4semidirect
78. #395C2×C4semidirect
102. C2×#95C2×C4semidirect
518. C2#11902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25642
C2×#17992
C2×#14602
#119022
C2×#13522
C2×#13512