Finite Group Databasebeta

← C2×#11550 #480468

Subgroups — C2×#11550 #480468

Order 512.

1088 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic
2C2×#1464C211yesmaximal, characteristic, complemented
3C2×#1458C211yesmaximal, characteristic, complemented
4#11550C218yesmaximal, direct product factor
5C2×#1324C212yesmaximal, complemented
6C2×#1318C212yesmaximal, complemented
7C22×#121C411yescharacteristic
8C22×#117C2211yescharacteristic
9C2×#432—21no—
10C2×#431—21no—
11#2500—22no—
12#2500—22no—
13#2500C414yes—
14#2500C2214yes—
15C2×#394—21no—
16C2×#394—21no—
17C2×#390C411yescharacteristic
18C2×#390C2211yescharacteristic
19C2×#388—21no—
20C2×#388—21no—
21C2×#384C411yescharacteristic
22C2×#382C2211yescharacteristic
23C2×C4×C22⋊C4C411yescharacteristic
24#1464—22no—
25#1464C2214yescomplemented
26#1458—22no—
27#1458C2214yescomplemented
28C2×#324C2212yes—
29C2×#324C2212yes—
30C2×#323—21no—
31C2×#323—21no—
32#1324C2218yescomplemented
33#1318C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4C2×C411yescharacteristic
37C2×#121—22no—
38C2×#121—42no—
39C2×#121—41no—
40C2×#121—41no—
41C2×#121C2×C414yes—
42C2×#117—41no—
43C2×#117—41no—
44C2×#117—42no—
45C2×#117C2×C412yes—
46C2×#117D412yes—
47C2×#117D412yes—
48C2×#117C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2311yescharacteristic
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4—21no—
57C22×C22⋊C4—21no—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—21no—
60C22×C22⋊C4D411yescharacteristic
61C22×C22⋊C4D411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42C2×C411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42D411yescharacteristic
66#432—24no—
67#432—42no—
68#431—24no—
69#431—42no—
70C2×C4⋊C8—41no—
71C2×C4⋊C8—41no—
72C2×C22⋊C8—22no—
73C2×C22⋊C8—22no—
74C2×#97—41no—
75C2×C4×C8—41no—
76#394—24no—
77#394—24no—
78#394—24no—
79#394—24no—
80#390—22no—
81#390—21no—
82#390—21no—
83#390C2×C412yes—
84#390C2×C414yes—
85#390C2312yes—
86#388—24no—
87#388—24no—
88#388—24no—
89#388—24no—
90#384—22no—
91#384C2×C414yes—
92#382—21no—
93#382—21no—
94#382C2×C412yes—
95#382C2312yes—
96C4×C22⋊C4—22no—
97C4×C22⋊C4C2×C414yes—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101#324—22no—
102#324—22no—
103#324C2314yes—
104#324C2314yes—
105#323—24no—
106#323—24no—
107C25—21no—
108C25C22⋊C411yescharacteristic
109C22×D4—24no—
110C22×D4—21no—
111C22×D4—24no—
112C22×D4—41no—
113C22×D4—41no—
114C22×D4—42no—
115C22×D4—42no—
116C22×D4—42no—
117C22×D4—82no—
118C22×D4—82no—
119C22×D4C22×C412yes—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—24no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—42no—
128C23×C4C22⋊C412yes—
129C23×C4C22⋊C411yescharacteristic
130C23×C4C22⋊C411yescharacteristic
131C23×C4C22⋊C411yescharacteristic
132C23×C4C22×C412yes—
133C23×C4C22×C411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C22×C8—42no—
137C22×C8—42no—
138#121—44no—
139#121—44no—
140#121—44no—
141#121—44no—
142#117—42no—
143#117—42no—
144#117—42no—
145#117—42no—
146#117—42no—
147#117—42no—
148#117—42no—
149#117—42no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C4⋊C4C22⋊C412yes—
162C2×C4⋊C4C22×C412yes—
163C2×C4⋊C4C22×C412yes—
164C2×C4⋊C4C22×C411yescharacteristic
165C2×C4⋊C4C2×D411yescharacteristic
166C2×C4⋊C4C2×D411yescharacteristic
167C2×C4⋊C4C2411yescharacteristic
168C2×C22⋊C4—24no—
169C2×C22⋊C4—24no—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—24no—
175C2×C22⋊C4—24no—
176C2×C22⋊C4—41no—
177C2×C22⋊C4—41no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—41no—
180C2×C22⋊C4—44no—
181C2×C22⋊C4—44no—
182C2×C22⋊C4—44no—
183C2×C22⋊C4—42no—
184C2×C22⋊C4—41no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—82no—
187C2×C22⋊C4—82no—
188C2×C22⋊C4C22⋊C412yes—
189C2×C22⋊C4C22⋊C412yes—
190C2×C22⋊C4C2×D412yes—
191C2×C22⋊C4C2×D412yes—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—21no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—42no—
202C2×C42C22⋊C412yes—
203C2×C42C22⋊C412yes—
204C2×C42C22×C412yes—
205C2×C42C22×C412yes—
206C2×C42C2×D412yes—
207C2×C42C2×D412yes—
208C4⋊C8—44no—
209C4⋊C8—44no—
210C22⋊C8—24no—
211C22⋊C8—24no—
212C22⋊C8—42no—
213C22⋊C8—42no—
214#97—44no—
215C4×C8—44no—
216#95—24no—
217#95—22no—
218#95—22no—
219#95—22no—
220#95—22no—
221C24—21no—
222C24—21no—
223C24—22no—
224C24—22no—
225C24—22no—
226C24—42no—
227C24—42no—
228C24—42no—
229C24—42no—
230C24—42no—
231C24—42no—
232C24—42no—
233C24—41no—
234C24—41no—
235C24—42no—
236C24C2×C22⋊C411yescharacteristic
237C24C2×C22⋊C412yes—
238C2×D4—24no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—48no—
244C2×D4—42no—
245C2×D4—84no—
246C2×D4—84no—
247C2×D4—84no—
248C2×D4—84no—
249C2×D4—88no—
250C2×D4—88no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—24no—
267C22×C4—24no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—48no—
277C22×C4—44no—
278C22×C4—44no—
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—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4#9912yes—
293C22×C4#9911yescharacteristic
294C22×C4#9911yescharacteristic
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4C2×C22⋊C412yes—
297C22×C4C2×C22⋊C411yescharacteristic
298C22×C4C2×C22⋊C411yescharacteristic
299C22×C4C2×C22⋊C412yes—
300C22×C4C2×C22⋊C412yes—
301C22×C4#13114yes—
302C22×C4C23×C411yescharacteristic
303C22×C4C22×D411yescharacteristic
304C22×C4C22×D411yescharacteristic
305C2×C8—44no—
306C2×C8—44no—
307C2×C8—84no—
308C2×C8—84no—
309C4⋊C4—42no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4—42no—
317C4⋊C4—84no—
318C4⋊C4—84no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—44no—
324C22⋊C4—44no—
325C22⋊C4—44no—
326C22⋊C4—44no—
327C22⋊C4—48no—
328C22⋊C4—44no—
329C22⋊C4—44no—
330C22⋊C4—84no—
331C22⋊C4—84no—
332C42—22no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—24no—
341C42—42no—
342C42—42no—
343C42—42no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—84no—
365C23—84no—
366C23—82no—
367C23—84no—
368C23—84no—
369C23—84no—
370C23—84no—
371C23—82no—
372C23—82no—
373C23—82no—
374C23—82no—
375C23—82no—
376C23#40812yes—
377C23C2×#9911yescharacteristic
378C23C2×#9911yescharacteristic
379C23#41312yes—
380C23C22×C22⋊C411yescharacteristic
381D4—84no—
382D4—84no—
383D4—816no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—42no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—84no—
430C2×C4—82no—
431C2×C4—82no—
432C2×C4#40812yes—
433C2×C4C2×#9912yes—
434C2×C4C2×#9912yes—
435C2×C4C2×#13112yes—
436C8—84no—
437C8—84no—
438C22—24no—
439C22—24no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—82no—
448C22—82no—
449C22—84no—
450C22—82no—
451C22—82no—
452C22—82no—
453C22—82no—
454C22—84no—
455C22—82no—
456C22—82no—
457C22—82no—
458C22—164no—
459C22—164no—
460C22#146812yes—
461C22#146812yes—
462C22#212612yes—
463C22#213412yes—
464C22C2×#40811yescharacteristic
465C22C22×#9911yescharacteristic
466C22C2×#41311yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—22no—
471C4—44no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—42no—
477C4—42no—
478C4—82no—
479C4—82no—
480C2—21no—
481C2—21no—
482C2—22no—
483C2—82no—
484C2—162no—
485C2#1155014yesdirect product factor
486C2C2×#146811yescharacteristic
487C2C2×#212611yescharacteristic
488C2C2×#213411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ 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×#1464C2semidirect
3. C2×#1458C2semidirect
4. #11550C2direct (N × H)
5. C2×#1324C2semidirect
6. C2×#1318C2semidirect
25. #1464C22semidirect
27. #1458C22semidirect
32. #1324C22semidirect
33. #1318C22semidirect
485. C2#11550direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#14642
C2×#14582
#115502
C2×#13242
C2×#13182