Finite Group Databasebeta

← C2×#11854 #482175

Subgroups — C2×#11854 #482175

Order 512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2583C211yesmaximal, characteristic
2C2×#1821C211yesmaximal, characteristic
3C22×#324C211yesmaximal, characteristic
4#11854C218yesmaximal, direct product factor
5C2×#1354C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C22×C22⋊Q8C411yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407—21no—
10C22×C22⋊C8—21no—
11#2583—22no—
12#2583—22no—
13#2583C414yes—
14#2583C2214yes—
15C2×#398C411yescharacteristic
16C2×#398C2211yescharacteristic
17C2×#395C411yescharacteristic
18C2×#395C2211yescharacteristic
19C2×#389—21no—
20C2×#389—21no—
21C2×#385—21no—
22C2×#385—21no—
23C2×C4×C22⋊C4C411yescharacteristic
24#1821—22no—
25#1821C2214yes—
26C2×#343—21no—
27C2×#343C2212yes—
28C2×#324—22no—
29C2×#324—21no—
30C2×#324C2214yes—
31C2×#324C2212yes—
32#1354C2218yescomplemented
33#1346C2218yescomplemented
34C23×Q8C2×C411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4D411yescharacteristic
38C22×M16—22no—
39C23×C8—41no—
40C2×C22⋊Q8—22no—
41C2×C22⋊Q8—42no—
42C2×C22⋊Q8—41no—
43C2×C22⋊Q8—41no—
44C2×C22⋊Q8C2×C414yes—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—41no—
51C22×C4⋊C4—41no—
52C22×C4⋊C4—42no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C412yes—
55C22×C4⋊C4C2×C411yescharacteristic
56C22×C4⋊C4D412yes—
57C22×C4⋊C4D412yes—
58C22×C4⋊C4D411yescharacteristic
59C22×C4⋊C4D411yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2311yescharacteristic
62C22×C22⋊C4—21no—
63C22×C22⋊C4—21no—
64C22×C42—21no—
65#407—24no—
66#407—42no—
67C2×C22⋊C8—22no—
68C2×C22⋊C8—24no—
69C2×C22⋊C8—42no—
70C2×C22⋊C8—41no—
71C2×C22⋊C8—41no—
72C2×C22⋊C8—41no—
73#398—22no—
74#398—21no—
75#398—21no—
76#398C2×C412yes—
77#398C2×C414yes—
78#398C2312yes—
79#395—22no—
80#395—21no—
81#395—21no—
82#395C2×C412yes—
83#395C2×C414yes—
84#395C2312yes—
85#389—24no—
86#389—24no—
87#389—24no—
88#389—24no—
89#385—24no—
90#385—24no—
91#385—24no—
92#385—24no—
93C4×C22⋊C4—22no—
94C4×C22⋊C4C2×C414yes—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95C2×C411yescharacteristic
100C2×#95C2×C411yescharacteristic
101#343—22no—
102#343—24no—
103#343C2314yes—
104#324—24no—
105#324—22no—
106#324C2314yes—
107C25C22⋊C411yescharacteristic
108C22×Q8—21no—
109C22×Q8—41no—
110C22×Q8—41no—
111C22×Q8—82no—
112C22×Q8C22×C412yes—
113C23×C4—21no—
114C23×C4—21no—
115C23×C4—21no—
116C23×C4—22no—
117C23×C4—21no—
118C23×C4—21no—
119C23×C4—22no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4—24no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—42no—
128C23×C4—82no—
129C23×C4—82no—
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22⋊C412yes—
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C412yes—
135C23×C4C22⋊C412yes—
136C23×C4C22×C411yescharacteristic
137C23×C4C22×C412yes—
138C23×C4C2×D412yes—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D412yes—
142C2×M16—24no—
143C2×M16—42no—
144C2×M16—44no—
145C2×M16—44no—
146C22×C8—44no—
147C22×C8—42no—
148C22×C8—42no—
149C22×C8—84no—
150C22⋊Q8—44no—
151C22⋊Q8—44no—
152C22⋊Q8—44no—
153C22⋊Q8—44no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—24no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—42no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—82no—
185C2×C4⋊C4—82no—
186C2×C4⋊C4C22⋊C412yes—
187C2×C4⋊C4C22⋊C412yes—
188C2×C4⋊C4C22⋊C412yes—
189C2×C4⋊C4C22×C412yes—
190C2×C4⋊C4C22×C412yes—
191C2×C4⋊C4C22×C411yescharacteristic
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D411yescharacteristic
194C2×C4⋊C4C2×D412yes—
195C2×C4⋊C4C2×D411yescharacteristic
196C2×C4⋊C4C2411yescharacteristic
197C2×C22⋊C4—28no—
198C2×C22⋊C4—24no—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—42no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—41no—
203C2×C42—24no—
204C2×C42—82no—
205C22⋊C8—24no—
206C22⋊C8—42no—
207C22⋊C8—44no—
208C22⋊C8—44no—
209C22⋊C8—44no—
210#95—24no—
211#95—22no—
212#95—24no—
213#95—22no—
214#95—21no—
215#95—21no—
216#95—22no—
217#95—22no—
218#95C22×C412yes—
219#95C22×C412yes—
220C24—24no—
221C24—22no—
222C24—22no—
223C24—42no—
224C24#9911yescharacteristic
225C24#9912yes—
226C24#9911yescharacteristic
227C24C2×C22⋊C412yes—
228C24C2×C22⋊C411yescharacteristic
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—82no—
232C2×Q8—82no—
233C2×Q8—84no—
234C2×Q8—84no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—48no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—82no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4—82no—
297C22×C4—84no—
298C22×C4—84no—
299C22×C4—82no—
300C22×C4—82no—
301C22×C4C2×C22⋊C412yes—
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C412yes—
305C22×C4C2×C22⋊C411yescharacteristic
306C22×C4C2×C22⋊C412yes—
307C22×C4#13514yes—
308C22×C4C23×C411yescharacteristic
309C22×C4C22×D411yescharacteristic
310C22×C4C22×D411yescharacteristic
311M16—44no—
312M16—44no—
313M16—84no—
314C2×C8—44no—
315C2×C8—44no—
316C2×C8—84no—
317C2×C8—88no—
318C2×C8—84no—
319C4⋊C4—42no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—41no—
323C4⋊C4—42no—
324C4⋊C4—42no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—42no—
330C4⋊C4—48no—
331C4⋊C4—48no—
332C4⋊C4—42no—
333C4⋊C4—44no—
334C4⋊C4—44no—
335C4⋊C4—84no—
336C4⋊C4—82no—
337C4⋊C4—82no—
338C22⋊C4—216no—
339C22⋊C4—44no—
340C22⋊C4—44no—
341C42—84no—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—24no—
349C23—24no—
350C23—22no—
351C23—22no—
352C23—24no—
353C23—22no—
354C23—42no—
355C23—42no—
356C23—48no—
357C23—48no—
358C23#35614yes—
359C23C2×#9912yes—
360C23C2×#9912yes—
361C23C2×#9911yescharacteristic
362C23C2×#9911yescharacteristic
363C23#41612yes—
364C23#42112yes—
365C23C22×C22⋊C411yescharacteristic
366Q8—84no—
367Q8—84no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—48no—
393C2×C4—48no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4#41612yes—
430C2×C4C2×#13512yes—
431C8—84no—
432C8—84no—
433C22—21no—
434C22—21no—
435C22—22no—
436C22—24no—
437C22—24no—
438C22—28no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—44no—
446C22—44no—
447C22—48no—
448C22—44no—
449C22#151612yes—
450C22#151612yes—
451C22#212112yes—
452C22C2×#35614yes—
453C22C2×#35612yes—
454C22C22×#9911yescharacteristic
455C22C2×#41611yescharacteristic
456C22C2×#42111yescharacteristic
457C4—22no—
458C4—22no—
459C4—44no—
460C4—44no—
461C4—41no—
462C4—42no—
463C4—41no—
464C4—42no—
465C4—41no—
466C4—41no—
467C4—42no—
468C4—82no—
469C4—82no—
470C2—21no—
471C2—21no—
472C2—24no—
473C2—22no—
474C2—42no—
475C2#1185414yesdirect product factor
476C2C2×#151611yescharacteristic
477C2C2×#212111yescharacteristic
478C2C22×#35611yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC25C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25 ◁ C23×C4⋊C4 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11854C2direct (N × H)
5. C2×#1354C2semidirect
6. C2×#1346C2semidirect
32. #1354C22semidirect
33. #1346C22semidirect
475. C2#11854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25832
C2×#18212
C22×#3242
#118542
C2×#13542
C2×#13462