Finite Group Databasebeta

← C2×#11906 #482122

Subgroups — C2×#11906 #482122

Order 512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 503 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2564C211yesmaximal, characteristic
2C2×#1800C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11906C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1353C212yesmaximal, complemented
7C22×C22⋊Q8C411yescharacteristic
8C22×C4×D4C2211yescharacteristic
9C2×#423—21no—
10C22×#100—21no—
11C22×C22⋊C8—21no—
12#2564—22no—
13#2564—22no—
14#2564C414yes—
15#2564C2214yes—
16C2×#400C2211yescharacteristic
17C2×#399C411yescharacteristic
18C2×#395C2211yescharacteristic
19C2×#393C411yescharacteristic
20C2×#387—21no—
21C2×#386—21no—
22C2×#385—21no—
23C2×#380—21no—
24C22×#95C411yescharacteristic
25#1800—22no—
26#1800C2214yes—
27C2×#343C2212yes—
28#1459—22no—
29#1459C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1354C2218yescomplemented
33#1353C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C23×D4D411yescharacteristic
36C24×C4—21no—
37C24×C4C2×C411yescharacteristic
38C24×C4D411yescharacteristic
39C22×M16—22no—
40C23×C8—41no—
41C2×C22⋊Q8—22no—
42C2×C22⋊Q8—42no—
43C2×C22⋊Q8—41no—
44C2×C22⋊Q8—41no—
45C2×C22⋊Q8C2×C414yes—
46C2×C4×D4—41no—
47C2×C4×D4—41no—
48C2×C4×D4—42no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4D412yes—
51C2×C4×D4D412yes—
52C2×C4×D4C2312yes—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2×C411yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4—21no—
61C22×C22⋊C4C2×C411yescharacteristic
62C22×C22⋊C4D411yescharacteristic
63C22×C42D411yescharacteristic
64#423—24no—
65#423—42no—
66C2×C4⋊C8—41no—
67C2×C4⋊C8—41no—
68C2×#100—24no—
69C2×#100—44no—
70C2×C22⋊C8—22no—
71C2×C22⋊C8—24no—
72C2×C22⋊C8—42no—
73C2×C22⋊C8—41no—
74#400—21no—
75#400—21no—
76#400C2×C412yes—
77#400C2312yes—
78#399—22no—
79#399C2×C414yes—
80#395—21no—
81#395—21no—
82#395C2×C412yes—
83#395C2312yes—
84#393—22no—
85#393C2×C414yes—
86#387—24no—
87#387—24no—
88#386—24no—
89#386—24no—
90#385—24no—
91#385—24no—
92#380—24no—
93#380—24no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95C2×C414yes—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—22no—
106#324C2314yes—
107#323—24no—
108C25C22⋊C411yescharacteristic
109C25C22⋊C411yescharacteristic
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—82no—
136C23×C4—82no—
137C23×C4—82no—
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C412yes—
140C23×C4C22⋊C412yes—
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22×C411yescharacteristic
143C23×C4C22×C412yes—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D412yes—
147C2×M16—24no—
148C2×M16—42no—
149C2×M16—44no—
150C2×M16—44no—
151C22×C8—42no—
152C22×C8—44no—
153C22×C8—42no—
154C22×C8—84no—
155C22⋊Q8—44no—
156C22⋊Q8—44no—
157C22⋊Q8—44no—
158C22⋊Q8—44no—
159C4×D4—42no—
160C4×D4—42no—
161C4×D4—42no—
162C4×D4—42no—
163C4×D4—42no—
164C4×D4—42no—
165C4×D4—42no—
166C4×D4—42no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—44no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—82no—
181C2×C4⋊C4C22×C412yes—
182C2×C4⋊C4C22×C411yescharacteristic
183C2×C4⋊C4C2×D411yescharacteristic
184C2×C4⋊C4C2×D411yescharacteristic
185C2×C4⋊C4C2411yescharacteristic
186C2×C22⋊C4—24no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—24no—
189C2×C22⋊C4—41no—
190C2×C22⋊C4—41no—
191C2×C22⋊C4—41no—
192C2×C22⋊C4—41no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—42no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—82no—
197C2×C22⋊C4C22⋊C412yes—
198C2×C22⋊C4C22⋊C412yes—
199C2×C22⋊C4C22×C412yes—
200C2×C22⋊C4C2×D412yes—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—22no—
204C2×C42C22⋊C412yes—
205C2×C42C2×D412yes—
206C4⋊C8—44no—
207C4⋊C8—44no—
208#100—48no—
209C22⋊C8—24no—
210C22⋊C8—42no—
211C22⋊C8—44no—
212#95—24no—
213#95—21no—
214#95—21no—
215#95—22no—
216#95—24no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221#95—22no—
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—
235C24#10314yes—
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C412yes—
238C24C2×C22⋊C412yes—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—82no—
242C2×Q8—82no—
243C2×Q8—84no—
244C2×Q8—84no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—44no—
249C2×D4—44no—
250C2×D4—44no—
251C2×D4—44no—
252C2×D4—42no—
253C2×D4#10318yes—
254C2×D4C2×SD1614yes—
255C2×D4C2×Q1614yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
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—42no—
279C22×C4—44no—
280C22×C4—48no—
281C22×C4—42no—
282C22×C4—42no—
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—48no—
292C22×C4—42no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—42no—
298C22×C4—82no—
299C22×C4—82no—
300C22×C4—82no—
301C22×C4—82no—
302C22×C4—82no—
303C22×C4—84no—
304C22×C4—84no—
305C22×C4—84no—
306C22×C4—82no—
307C22×C4—82no—
308C22×C4—816no—
309C22×C4#9911yescharacteristic
310C22×C4#9911yescharacteristic
311C22×C4#9912yes—
312C22×C4C2×C22⋊C411yescharacteristic
313C22×C4C2×C22⋊C412yes—
314C22×C4C2×C22⋊C411yescharacteristic
315C22×C4C2×C22⋊C411yescharacteristic
316C22×C4C2×C22⋊C412yes—
317C22×C4C2×SD1612yes—
318C22×C4C2×Q1612yes—
319C22×C4C23×C411yescharacteristic
320C22×C4C22×D411yescharacteristic
321C22×C4C22×D411yescharacteristic
322M16—44no—
323M16—44no—
324M16—84no—
325C2×C8—44no—
326C2×C8—44no—
327C2×C8—84no—
328C2×C8—88no—
329C2×C8—84no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—42no—
335C4⋊C4—48no—
336C4⋊C4—42no—
337C4⋊C4—44no—
338C4⋊C4—44no—
339C4⋊C4—82no—
340C4⋊C4—82no—
341C22⋊C4—42no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—48no—
346C22⋊C4—48no—
347C22⋊C4—84no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—24no—
358C23—24no—
359C23—24no—
360C23—22no—
361C23—24no—
362C23—42no—
363C23—42no—
364C23—48no—
365C23—42no—
366C23—48no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—48no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—84no—
378C23C2×#9911yescharacteristic
379C23C2×#9911yescharacteristic
380C23C2×#10312yes—
381C23C2×#10314yes—
382C23C2×#10314yes—
383C23#42112yes—
384C23C22×C22⋊C411yescharacteristic
385Q8—84no—
386Q8—84no—
387D4—48no—
388D4—44no—
389D4—44no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—48no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—816no—
440C2×C4—82no—
441C2×C4—84no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4C2×#9912yes—
446C2×C4C2×#9912yes—
447C2×C4C2×#10312yes—
448C2×C4C22×SD1611yescharacteristic
449C2×C4C22×Q1611yescharacteristic
450C8—84no—
451C8—84no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—24no—
457C22—24no—
458C22—24no—
459C22—24no—
460C22—44no—
461C22—44no—
462C22—44no—
463C22—48no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—48no—
469C22—48no—
470C22—82no—
471C22—84no—
472C22#152012yes—
473C22#152012yes—
474C22#212112yes—
475C22#213212yes—
476C22C22×#9911yescharacteristic
477C22C22×#10311yescharacteristic
478C22C2×#42111yescharacteristic
479C4—22no—
480C4—22no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—44no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—42no—
490C4—82no—
491C4—82no—
492C4—82no—
493C2—21no—
494C2—21no—
495C2—22no—
496C2—44no—
497C2—44no—
498C2#1190614yesdirect product factor
499C2C2×#152011yescharacteristic
500C2C2×#212111yescharacteristic
501C2C2×#213211yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4D4
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
4. #11906C2direct (N × H)
5. C2×#1354C2semidirect
6. C2×#1353C2semidirect
32. #1354C22semidirect
33. #1353C22semidirect
498. C2#11906direct (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×#18002
C2×#14592
#119062
C2×#13542
C2×#13532