Finite Group Databasebeta

← C2×#11829 #481911

Subgroups — C2×#11829 #481911

Order 512.

1118 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×#2398C211yesmaximal, characteristic
2C2×#1801C211yesmaximal, characteristic, complemented
3C2×#1467C211yesmaximal, characteristic, complemented
4#11829C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1345C212yesmaximal
7C22×C4×Q8C2211yescharacteristic
8C22×C4×D4C411yescharacteristic
9C2×#432—21no—
10C2×#423—21no—
11C22×#101—21no—
12#2398—22no—
13#2398—22no—
14#2398C414yes—
15#2398C2214yes—
16C2×#400C411yescharacteristic
17C2×#400C2211yescharacteristic
18C2×#397—21no—
19C2×#394C411yescharacteristic
20C2×#394C2211yescharacteristic
21C2×#393—21no—
22C2×C4×C22⋊C4—21no—
23C2×C4×C22⋊C4—21no—
24C2×#376C411yescharacteristic
25#1801—22no—
26#1801C2214yescomplemented
27C2×#343C2212yes—
28#1467—22no—
29#1467C2214yescomplemented
30C2×#324—21no—
31C2×#324C2212yes—
32#1353C2218yescomplemented
33#1345C2218yes—
34C23×Q8D411yescharacteristic
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C22×M16—22no—
38C2×C4×Q8—41no—
39C2×C4×Q8—41no—
40C2×C4×Q8—42no—
41C2×C4×Q8C2×C412yes—
42C2×C4×Q8D412yes—
43C2×C4×Q8D412yes—
44C2×C4×Q8C2312yes—
45C2×C4×D4—22no—
46C2×C4×D4—42no—
47C2×C4×D4—41no—
48C2×C4×D4—41no—
49C2×C4×D4C2×C414yes—
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4D411yescharacteristic
53C22×C4⋊C4C2311yescharacteristic
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C42—21no—
60C22×C42C2×C411yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63#432—24no—
64#432—42no—
65#423—24no—
66#423—42no—
67C2×C4⋊C8—41no—
68C2×C4⋊C8—41no—
69C2×C4⋊C8—41no—
70C2×#101—24no—
71C2×#101—44no—
72C2×C22⋊C8—22no—
73C2×#97—41no—
74#400—22no—
75#400—21no—
76#400—21no—
77#400C2×C414yes—
78#400C2×C412yes—
79#400C2312yes—
80#397—24no—
81#397—24no—
82#394—22no—
83#394—21no—
84#394—21no—
85#394C2×C414yes—
86#394C2×C412yes—
87#394C2312yes—
88#393—24no—
89#393—24no—
90C4×C22⋊C4—24no—
91C4×C22⋊C4—24no—
92C4×C22⋊C4—24no—
93C4×C22⋊C4—24no—
94#376—22no—
95#376C2×C414yes—
96C2×#95—21no—
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—24no—
106#324—22no—
107#324C2314yes—
108C25—21no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—42no—
114C22×Q8C22⋊C412yes—
115C22×Q8C2×D412yes—
116C22×D4—21no—
117C22×D4—41no—
118C22×D4—41no—
119C22×D4—44no—
120C22×D4C22×C412yes—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—24no—
125C23×C4—44no—
126C23×C4—44no—
127C23×C4—42no—
128C23×C4—41no—
129C23×C4—41no—
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22⋊C411yescharacteristic
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22×C411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C2×M16—24no—
138C2×M16—42no—
139C2×M16—44no—
140C2×M16—44no—
141C22×C8—42no—
142C22×C8—42no—
143C4×Q8—42no—
144C4×Q8—42no—
145C4×Q8—42no—
146C4×Q8—42no—
147C4×Q8—42no—
148C4×Q8—42no—
149C4×Q8—42no—
150C4×Q8—42no—
151C4×D4—44no—
152C4×D4—44no—
153C4×D4—44no—
154C4×D4—44no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4C22⋊C412yes—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C22×C412yes—
167C2×C4⋊C4C22×C412yes—
168C2×C4⋊C4C22×C411yescharacteristic
169C2×C4⋊C4C2×D412yes—
170C2×C4⋊C4C2×D411yescharacteristic
171C2×C4⋊C4C2×D411yescharacteristic
172C2×C4⋊C4C2411yescharacteristic
173C2×C22⋊C4—24no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—24no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—44no—
181C2×C22⋊C4—42no—
182C2×C22⋊C4—42no—
183C2×C22⋊C4—44no—
184C2×C22⋊C4—44no—
185C2×C22⋊C4—42no—
186C2×C22⋊C4—42no—
187C2×C42—22no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—24no—
197C2×C42—44no—
198C2×C42C22⋊C412yes—
199C2×C42C22⋊C412yes—
200C2×C42C22⋊C412yes—
201C2×C42C22×C412yes—
202C2×C42C2×D412yes—
203C2×C42C2×D412yes—
204C4⋊C8—44no—
205C4⋊C8—44no—
206C4⋊C8—44no—
207#101—48no—
208C22⋊C8—24no—
209C22⋊C8—42no—
210#97—44no—
211#95—24no—
212#95—24no—
213#95—22no—
214#95—22no—
215#95—24no—
216#95—21no—
217#95—21no—
218#95—22no—
219#95—22no—
220#95C22×C412yes—
221#95C22×C412yes—
222C24—24no—
223C24—22no—
224C24—42no—
225C24—42no—
226C24—42no—
227C24—41no—
228C24—41no—
229C24—42no—
230C24—42no—
231C24C2×C22⋊C411yescharacteristic
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—24no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—44no—
240C2×Q8—44no—
241C2×Q8—44no—
242C2×Q8—44no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—44no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—48no—
272C22×C4—48no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—84no—
289C22×C4—88no—
290C22×C4—84no—
291C22×C4#9912yes—
292C22×C4#9911yescharacteristic
293C22×C4#9911yescharacteristic
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C412yes—
296C22×C4C2×C22⋊C412yes—
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C2×C22⋊C411yescharacteristic
299C22×C4C2×C22⋊C411yescharacteristic
300C22×C4C2×C22⋊C412yes—
301C22×C4AGL(1,ℤ/8)12yes—
302C22×C4#13712yes—
303C22×C4C23×C411yescharacteristic
304C22×C4C22×D411yescharacteristic
305C22×C4C22×D411yescharacteristic
306M16—44no—
307M16—44no—
308M16—84no—
309C2×C8—44no—
310C2×C8—44no—
311C2×C8—84no—
312C2×C8—84no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C22⋊C4—48no—
324C22⋊C4—48no—
325C22⋊C4—48no—
326C22⋊C4—44no—
327C22⋊C4—44no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—44no—
331C42—22no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—48no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—44no—
351C23—48no—
352C23—48no—
353C23—42no—
354C23—44no—
355C23—42no—
356C23—42no—
357C23—82no—
358C23—84no—
359C23—84no—
360C23—82no—
361C23—82no—
362C23—82no—
363C23C2×#9911yescharacteristic
364C23C2×#9911yescharacteristic
365C23#41712yes—
366C23#42112yes—
367C23C22×C22⋊C411yescharacteristic
368Q8—44no—
369Q8—44no—
370Q8—48no—
371D4—44no—
372D4—44no—
373D4—48no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
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—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—88no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—84no—
422C2×C4—84no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—88no—
426C2×C4#35514yes—
427C2×C4C2×#9912yes—
428C2×C4C2×#9912yes—
429C2×C4#41712yes—
430C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
431C2×C4C2×#13711yescharacteristic
432C8—84no—
433C8—84no—
434C22—24no—
435C22—24no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—44no—
441C22—44no—
442C22—44no—
443C22—82no—
444C22—82no—
445C22—88no—
446C22—88no—
447C22—82no—
448C22—82no—
449C22#151312yes—
450C22#151312yes—
451C22#212012yes—
452C22C2×#35512yes—
453C22C22×#9911yescharacteristic
454C22C2×#41711yescharacteristic
455C22C2×#42111yescharacteristic
456C4—22no—
457C4—21no—
458C4—21no—
459C4—22no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—42no—
465C4—42no—
466C4—42no—
467C4—82no—
468C4—82no—
469C4—82no—
470C4C2×#35514yes—
471C2—21no—
472C2—21no—
473C2—22no—
474C2—84no—
475C2#1182914yesdirect product factor
476C2C2×#151311yescharacteristic
477C2C2×#212011yescharacteristic
478C2C22×#35511yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1801C2semidirect
3. C2×#1467C2semidirect
4. #11829C2direct (N × H)
5. C2×#1353C2semidirect
26. #1801C22semidirect
29. #1467C22semidirect
32. #1353C22semidirect
475. C2#11829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#23982
C2×#18012
C2×#14672
#118292
C2×#13532
C2×#13452