Finite Group Databasebeta

← C2×#11735 #481530

Subgroups — C2×#11735 #481530

Order 512.

1178 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2395C211yesmaximal, characteristic
2C2×C4×#100C211yesmaximal, characteristic
3C2×#1459C211yesmaximal, characteristic
4#11735C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1346C212yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C22×#117C411yescharacteristic
9C22×#100—21no—
10C22×C22⋊C8—21no—
11C2×C4×M16—21no—
12#2395—22no—
13#2395—22no—
14#2395C414yes—
15#2395C2214yes—
16C2×#400C2211yescharacteristic
17C2×#399C411yescharacteristic
18C2×#398C2211yescharacteristic
19C2×#397—21no—
20C2×#397C411yescharacteristic
21C2×#394—21no—
22C2×C4×C4⋊C4—21no—
23C2×C4×C22⋊C4—21no—
24C2×C4×C22⋊C4C411yescharacteristic
25C4×#100—22no—
26C4×#100C2214yes—
27C2×#343C2212yes—
28#1459—22no—
29#1459C2214yes—
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1346C2218yescomplemented
34C23×D4D411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C24×C4D411yescharacteristic
37C22×M16—22no—
38C23×C8—41no—
39C2×C4×D4—41no—
40C2×C4×D4—42no—
41C2×C4×D4—41no—
42C2×C4×D4C2×C412yes—
43C2×C4×D4D412yes—
44C2×C4×D4D412yes—
45C2×C4×D4C2312yes—
46C2×#117—22no—
47C2×#117—41no—
48C2×#117—42no—
49C2×#117—41no—
50C2×#117C2×C414yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4C2×C411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42—21no—
63C22×C42—21no—
64C22×C42D411yescharacteristic
65C2×#100—28no—
66C2×#100—24no—
67C2×C22⋊C8—22no—
68C2×C22⋊C8—24no—
69C2×C22⋊C8—42no—
70C2×C22⋊C8—41no—
71C4×M16—24no—
72C4×M16—42no—
73C2×#97—41no—
74C2×C4×C8—41no—
75#400—21no—
76#400—21no—
77#400C2×C412yes—
78#400C2312yes—
79#399—22no—
80#399C2×C414yes—
81#398—21no—
82#398—21no—
83#398C2×C412yes—
84#398C2312yes—
85#397—24no—
86#397—22no—
87#397—24no—
88#397C2×C414yes—
89#394—24no—
90#394—24no—
91C4×C4⋊C4—24no—
92C4×C4⋊C4—24no—
93C4×C22⋊C4—22no—
94C4×C22⋊C4—24no—
95C4×C22⋊C4—24no—
96C4×C22⋊C4C2×C414yes—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95C2×C411yescharacteristic
102C2×#95C2×C411yescharacteristic
103#343—22no—
104#343C2314yes—
105#324—22no—
106#324C2314yes—
107#323—24no—
108C25C22⋊C411yescharacteristic
109C25C22⋊C411yescharacteristic
110C22×D4—24no—
111C22×D4—24no—
112C22×D4—41no—
113C22×D4—41no—
114C22×D4C22⋊C412yes—
115C22×D4C2×D412yes—
116C23×C4—21no—
117C23×C4—22no—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—44no—
127C23×C4—44no—
128C23×C4C22⋊C411yescharacteristic
129C23×C4C22⋊C412yes—
130C23×C4C22⋊C412yes—
131C23×C4C22⋊C411yescharacteristic
132C23×C4C22×C411yescharacteristic
133C23×C4C22×C412yes—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D412yes—
137C2×M16—28no—
138C2×M16—24no—
139C2×M16—42no—
140C2×M16—44no—
141C22×C8—42no—
142C22×C8—42no—
143C22×C8—44no—
144C22×C8—84no—
145C4×D4—42no—
146C4×D4—42no—
147C4×D4—42no—
148C4×D4—42no—
149C4×D4—42no—
150C4×D4—42no—
151C4×D4—42no—
152C4×D4—42no—
153#117—44no—
154#117—44no—
155#117—44no—
156#117—44no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4C22×C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C411yescharacteristic
173C2×C4⋊C4C2×D411yescharacteristic
174C2×C4⋊C4C2×D411yescharacteristic
175C2×C4⋊C4C2411yescharacteristic
176C2×C22⋊C4—24no—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—24no—
179C2×C22⋊C4—24no—
180C2×C22⋊C4—41no—
181C2×C22⋊C4—41no—
182C2×C22⋊C4—41no—
183C2×C22⋊C4—41no—
184C2×C22⋊C4—44no—
185C2×C22⋊C4—44no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4C22⋊C412yes—
190C2×C22⋊C4C22⋊C412yes—
191C2×C22⋊C4C22×C412yes—
192C2×C22⋊C4C2×D412yes—
193C2×C42—21no—
194C2×C42—22no—
195C2×C42—21no—
196C2×C42—24no—
197C2×C42—24no—
198C2×C42—44no—
199C2×C42—41no—
200C2×C42—42no—
201C2×C42—41no—
202C2×C42C22⋊C412yes—
203C2×C42C2×D412yes—
204#100—216no—
205C22⋊C8—24no—
206C22⋊C8—42no—
207C22⋊C8—44no—
208#97—44no—
209C4×C8—44no—
210#95—22no—
211#95—22no—
212#95—22no—
213#95—24no—
214#95—21no—
215#95—21no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95C22×C412yes—
220#95C22×C412yes—
221C24—21no—
222C24—21no—
223C24—22no—
224C24—21no—
225C24—21no—
226C24—22no—
227C24—22no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24—42no—
232C24#10414yes—
233C24C2×C22⋊C411yescharacteristic
234C24C2×C22⋊C412yes—
235C24C2×C22⋊C412yes—
236C2×D4—24no—
237C2×D4—24no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—48no—
243C2×D4—48no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—24no—
248C22×C4—24no—
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—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—44no—
268C22×C4—48no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—84no—
292C22×C4—82no—
293C22×C4#9911yescharacteristic
294C22×C4#9912yes—
295C22×C4#9911yescharacteristic
296C22×C4C2×C22⋊C412yes—
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C2×C22⋊C411yescharacteristic
299C22×C4C2×C22⋊C412yes—
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4#13514yes—
302C22×C4C23×C411yescharacteristic
303C22×C4C22×D411yescharacteristic
304C22×C4C22×D411yescharacteristic
305M16—28no—
306M16—48no—
307M16—44no—
308C2×C8—44no—
309C2×C8—48no—
310C2×C8—44no—
311C2×C8—84no—
312C2×C8—88no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4—48no—
320C4⋊C4—42no—
321C4⋊C4—42no—
322C4⋊C4—44no—
323C4⋊C4—44no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—48no—
329C22⋊C4—48no—
330C22⋊C4—48no—
331C22⋊C4—48no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—48no—
337C42—44no—
338C42—44no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—24no—
343C23—22no—
344C23—24no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—48no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—81no—
362C23—81no—
363C23—84no—
364C23—84no—
365C23—84no—
366C23C2×#9911yescharacteristic
367C23C2×#9911yescharacteristic
368C23#41612yes—
369C23C2×#10412yes—
370C23C2×#10414yes—
371C23C22×C22⋊C411yescharacteristic
372D4—48no—
373D4—48no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—48no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—84no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#35214yes—
426C2×C4C2×#9912yes—
427C2×C4C2×#9912yes—
428C2×C4#41612yes—
429C2×C4C2×#13512yes—
430C8—48no—
431C8—84no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—24no—
437C22—24no—
438C22—24no—
439C22—44no—
440C22—42no—
441C22—42no—
442C22—48no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—84no—
448C22—82no—
449C22—82no—
450C22—84no—
451C22—84no—
452C22#150112yes—
453C22#150112yes—
454C22C2×#35212yes—
455C22#213212yes—
456C22C22×#9911yescharacteristic
457C22C2×#41611yescharacteristic
458C22C22×#10411yescharacteristic
459C4—22no—
460C4—22no—
461C4—22no—
462C4—44no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—42no—
468C4—82no—
469C4—82no—
470C4—82no—
471C4C2×#35214yes—
472C2—21no—
473C2—21no—
474C2—22no—
475C2—44no—
476C2—82no—
477C2#1173514yesdirect product factor
478C2C2×#150111yescharacteristic
479C2C22×#35211yescharacteristic
480C2C2×#213211yescharacteristic
subgroupG/H
centerC22×C4#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
socleC23C2×#99
prime radicalC23×D4D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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. #11735C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1346C2semidirect
32. #1353C22semidirect
33. #1346C22semidirect
477. C2#11735direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23952
C2×C4×#1002
C2×#14592
#117352
C2×#13532
C2×#13462