Finite Group Databasebeta

← C2×#11847 #482171

Subgroups — C2×#11847 #482171

Order 512.

1176 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2598C211yesmaximal, characteristic
2C2×#1822C211yesmaximal, characteristic, complemented
3C2×#1458C211yesmaximal, characteristic, complemented
4#11847C218yesmaximal, direct product factor
5C2×#1353C212yesmaximal, complemented
6C2×#1345C212yesmaximal, complemented
7C22×C4×D4C411yescharacteristic
8C22×#117C2211yescharacteristic
9C2×#431—21no—
10C2×#407—21no—
11#2598—22no—
12#2598—22no—
13#2598C414yes—
14#2598C2214yes—
15C2×#400C2211yescharacteristic
16C2×#399C411yescharacteristic
17C2×#394C2211yescharacteristic
18C2×#392C411yescharacteristic
19C2×#388—21no—
20C2×#386—21no—
21C2×#386—21no—
22C2×#385—21no—
23C2×#383C411yescharacteristic
24#1822—22no—
25#1822C2214yescomplemented
26C2×#343—21no—
27C2×#343C2212yes—
28#1458—22no—
29#1458C2214yescomplemented
30C2×#324C2212yes—
31C2×#323—21no—
32#1353C2218yescomplemented
33#1345C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4—21no—
37C24×C4D411yescharacteristic
38C22×M16—22no—
39C2×C4×D4—22no—
40C2×C4×D4—42no—
41C2×C4×D4—41no—
42C2×C4×D4—41no—
43C2×C4×D4C2×C414yes—
44C2×#117—41no—
45C2×#117—41no—
46C2×#117—42no—
47C2×#117C2×C412yes—
48C2×#117D412yes—
49C2×#117D412yes—
50C2×#117C2312yes—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4D411yescharacteristic
54C22×C4⋊C4C2311yescharacteristic
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4C2×C411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42D411yescharacteristic
64#431—24no—
65#431—42no—
66C2×C4⋊C8—41no—
67#407—24no—
68#407—42no—
69C2×C22⋊C8—22no—
70C2×C22⋊C8—41no—
71C2×C22⋊C8—41no—
72C2×C4×C8—41no—
73#400—21no—
74#400—21no—
75#400C2×C412yes—
76#400C2312yes—
77#399—22no—
78#399C2×C414yes—
79#394—21no—
80#394—21no—
81#394C2×C412yes—
82#394C2312yes—
83#392—22no—
84#392C2×C414yes—
85#388—24no—
86#388—24no—
87#386—24no—
88#386—24no—
89#386—24no—
90#386—24no—
91#385—24no—
92#385—24no—
93#383—22no—
94#383C2×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—22no—
105#324C2314yes—
106#323—24no—
107C25—21no—
108C25C22⋊C411yescharacteristic
109C22×D4—24no—
110C22×D4—21no—
111C22×D4—41no—
112C22×D4—41no—
113C22×D4—44no—
114C22×D4—44no—
115C22×D4—44no—
116C22×D4—82no—
117C22×D4C22×C412yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—22no—
121C23×C4—24no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—24no—
126C23×C4—42no—
127C23×C4—42no—
128C23×C4—42no—
129C23×C4—82no—
130C23×C4—82no—
131C23×C4C22⋊C412yes—
132C23×C4C22⋊C411yescharacteristic
133C23×C4C22⋊C411yescharacteristic
134C23×C4C22⋊C411yescharacteristic
135C23×C4C22×C411yescharacteristic
136C23×C4C2×D412yes—
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C2×M16—24no—
140C2×M16—42no—
141C2×M16—44no—
142C2×M16—44no—
143C22×C8—42no—
144C22×C8—42no—
145C4×D4—44no—
146C4×D4—44no—
147C4×D4—44no—
148C4×D4—44no—
149#117—42no—
150#117—42no—
151#117—42no—
152#117—42no—
153#117—42no—
154#117—42no—
155#117—42no—
156#117—42no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—82no—
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—22no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
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—42no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4—41no—
188C2×C22⋊C4—44no—
189C2×C22⋊C4—82no—
190C2×C22⋊C4—82no—
191C2×C22⋊C4C22⋊C412yes—
192C2×C22⋊C4C22⋊C412yes—
193C2×C22⋊C4C22×C412yes—
194C2×C22⋊C4C2×D412yes—
195C2×C42—22no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—22no—
201C2×C42C22⋊C412yes—
202C2×C42C22⋊C412yes—
203C2×C42C22×C412yes—
204C2×C42C2×D412yes—
205C4⋊C8—44no—
206C22⋊C8—24no—
207C22⋊C8—42no—
208C22⋊C8—44no—
209C22⋊C8—44no—
210C4×C8—44no—
211#95—24no—
212#95—24no—
213#95—22no—
214#95—22no—
215#95—21no—
216#95—21no—
217#95—22no—
218#95—22no—
219#95C22×C412yes—
220#95C22×C412yes—
221C24—24no—
222C24—22no—
223C24—21no—
224C24—22no—
225C24—21no—
226C24—22no—
227C24—42no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24—42no—
232C24—41no—
233C24—41no—
234C24—42no—
235C24—42no—
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C412yes—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—48no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—48no—
246C2×D4—48no—
247C2×D4—84no—
248C2×D4—816no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
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—24no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—48no—
276C22×C4—48no—
277C22×C4—42no—
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—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—84no—
292C22×C4—84no—
293C22×C4—88no—
294C22×C4—88no—
295C22×C4#9912yes—
296C22×C4#9911yescharacteristic
297C22×C4#9911yescharacteristic
298C22×C4C2×C22⋊C412yes—
299C22×C4C2×C22⋊C411yescharacteristic
300C22×C4C2×C22⋊C411yescharacteristic
301C22×C4C2×C22⋊C411yescharacteristic
302C22×C4C2×C22⋊C412yes—
303C22×C4C2×C22⋊C412yes—
304C22×C4#13514yes—
305C22×C4C23×C411yescharacteristic
306C22×C4C22×D411yescharacteristic
307C22×C4C22×D411yescharacteristic
308M16—44no—
309M16—44no—
310M16—84no—
311C2×C8—44no—
312C2×C8—44no—
313C2×C8—84no—
314C2×C8—84no—
315C4⋊C4—42no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—42no—
322C4⋊C4—42no—
323C4⋊C4—84no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—42no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C22⋊C4—44no—
332C22⋊C4—44no—
333C22⋊C4—44no—
334C22⋊C4—84no—
335C22⋊C4—84no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—22no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—44no—
356C23—48no—
357C23—48no—
358C23—48no—
359C23—42no—
360C23—44no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—81no—
368C23—81no—
369C23—84no—
370C23—82no—
371C23—84no—
372C23—84no—
373C23—82no—
374C23—82no—
375C23—82no—
376C23C2×#9911yescharacteristic
377C23C2×#9911yescharacteristic
378C23#41612yes—
379C23#42112yes—
380C23C22×C22⋊C411yescharacteristic
381D4—44no—
382D4—44no—
383D4—48no—
384D4—816no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—22no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—816no—
430C2×C4—84no—
431C2×C4—82no—
432C2×C4—84no—
433C2×C4—82no—
434C2×C4C2×#9912yes—
435C2×C4C2×#9912yes—
436C2×C4#41612yes—
437C2×C4C2×#13512yes—
438C8—84no—
439C8—84no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—24no—
444C22—21no—
445C22—21no—
446C22—44no—
447C22—44no—
448C22—44no—
449C22—44no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—82no—
454C22—82no—
455C22—82no—
456C22—84no—
457C22—88no—
458C22—84no—
459C22—88no—
460C22—82no—
461C22—82no—
462C22#151612yes—
463C22#151612yes—
464C22#212012yes—
465C22#213412yes—
466C22C22×#9911yescharacteristic
467C22C2×#41611yescharacteristic
468C22C2×#42111yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4—82no—
481C4—82no—
482C2—21no—
483C2—21no—
484C2—22no—
485C2—82no—
486C2—84no—
487C2#1184714yesdirect product factor
488C2C2×#151611yescharacteristic
489C2C2×#212011yescharacteristic
490C2C2×#213411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC2×#392C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#117 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#1822C2semidirect
3. C2×#1458C2semidirect
4. #11847C2direct (N × H)
5. C2×#1353C2semidirect
6. C2×#1345C2semidirect
25. #1822C22semidirect
29. #1458C22semidirect
32. #1353C22semidirect
33. #1345C22semidirect
487. C2#11847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25982
C2×#18222
C2×#14582
#118472
C2×#13532
C2×#13452