Finite Group Databasebeta

← C2×#9414 #200630

Subgroups — C2×#9414 #200630

Order 512.

1516 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2591C211yesmaximal, characteristic
2C2×#2313C211yesmaximal, characteristic, complemented
3C2×#1507C212yesmaximal
4C2×#1463C211yesmaximal, characteristic, complemented
5#9414C218yesmaximal, direct product factor
6C2×#1297C212yesmaximal, complemented
7C22×#121C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9C2×#407C2212yes—
10#2591—22no—
11#2591—22no—
12#2591C414yescomplemented
13#2591C2214yes—
14C2×#400C412yescomplemented
15C2×#394C412yescomplemented
16#2313—24no—
17#2313—22no—
18#2313C2214yescomplemented
19C2×#388—22no—
20C2×#387—24no—
21C2×#386—21no—
22C2×#386—21no—
23C2×#381—21no—
24C2×#380—21no—
25C2×C4×C22⋊C4C2211yescharacteristic
26C2×C4×C22⋊C4C2212yes—
27#1507—24no—
28#1507C2218yes—
29C2×#327—24no—
30#1463—22no—
31#1463C2214yescomplemented
32C2×#324—22no—
33#1297C2218yescomplemented
34C23×D4—21no—
35C23×D4C2×C411yescharacteristic
36C24×C4D411yescharacteristic
37C24×C4D411yescharacteristic
38C24×C4C2311yescharacteristic
39C22×M16—22no—
40C2×#121—21no—
41C2×#121—21no—
42C2×#121—22no—
43C2×#121—22no—
44C2×#121—22no—
45C2×#121—22no—
46C2×#121C2×C412yes—
47C2×#121C2312yes—
48C22×C4⋊C4—22no—
49C22×C4⋊C4—22no—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C412yes—
55C22×C4⋊C4C2×C412yes—
56C22×C4⋊C4D412yes—
57C22×C4⋊C4D412yes—
58C22×C4⋊C4D412yes—
59C22×C4⋊C4C2312yes—
60C22×C22⋊C4—22no—
61C22×C22⋊C4—21no—
62C22×C22⋊C4—22no—
63C22×C22⋊C4—21no—
64C22×C22⋊C4—22no—
65C22×C42—22no—
66C22×C42—21no—
67#407—22no—
68#407—22no—
69#407—22no—
70#407C2314yes—
71C2×C22⋊C8—22no—
72C2×C22⋊C8—22no—
73#400—24no—
74#400C2×C418yescomplemented
75#394—24no—
76#394C2×C418yescomplemented
77#388—28no—
78#388—28no—
79#387—216no—
80#387—216no—
81#386—24no—
82#386—24no—
83#386—24no—
84#386—24no—
85#381—24no—
86#381—24no—
87#380—24no—
88#380—24no—
89C4×C22⋊C4—22no—
90C4×C22⋊C4—22no—
91C4×C22⋊C4—21no—
92C4×C22⋊C4—21no—
93C4×C22⋊C4C2×C412yes—
94C4×C22⋊C4D414yes—
95C4×C22⋊C4C2312yes—
96C4×C22⋊C4C2314yes—
97C2×#95—22no—
98C2×#95—24no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95C2×C412yes—
102C2×#95D414yes—
103#327—216no—
104#324—28no—
105C25—21no—
106C25C2×D411yescharacteristic
107C22×D4—22no—
108C22×D4—22no—
109C22×D4—21no—
110C22×D4—22no—
111C22×D4—22no—
112C22×D4—48no—
113C22×D4—41no—
114C22×D4—41no—
115C22×D4—41no—
116C22×D4—41no—
117C22×D4—82no—
118C22×D4C22×C412yes—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—21no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—24no—
130C23×C4—44no—
131C23×C4—82no—
132C23×C4—82no—
133C23×C4C22⋊C412yes—
134C23×C4C22⋊C412yes—
135C23×C4C22⋊C412yes—
136C23×C4C22⋊C412yes—
137C23×C4C22×C411yescharacteristic
138C23×C4C22×C411yescharacteristic
139C23×C4C2×D412yes—
140C23×C4C2×D412yes—
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D412yes—
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D412yes—
146C23×C4#4112yes—
147C23×C4#4112yes—
148C23×C4C2411yescharacteristic
149C2×M16—24no—
150C2×M16—42no—
151C2×M16—84no—
152C22×C8—42no—
153#121—24no—
154#121—24no—
155#121—24no—
156#121—24no—
157#121—42no—
158#121—42no—
159#121—42no—
160#121—42no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—28no—
177C2×C4⋊C4—84no—
178C2×C4⋊C4C22⋊C414yes—
179C2×C4⋊C4C22⋊C414yes—
180C2×C4⋊C4C22×C412yes—
181C2×C4⋊C4C22×C414yes—
182C2×C4⋊C4C2×D414yes—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—24no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—28no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—28no—
191C2×C22⋊C4—48no—
192C2×C22⋊C4—48no—
193C2×C22⋊C4—44no—
194C2×C22⋊C4—42no—
195C2×C22⋊C4—42no—
196C2×C22⋊C4—84no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—22no—
201C2×C42—82no—
202C2×C42—84no—
203C22⋊C8—24no—
204C22⋊C8—24no—
205C22⋊C8—42no—
206C22⋊C8—42no—
207#95—28no—
208#95—216no—
209#95—28no—
210#95—28no—
211#95—22no—
212#95—24no—
213#95C22×C414yes—
214#95C2×D418yes—
215C24—24no—
216C24—24no—
217C24—22no—
218C24—42no—
219C24—44no—
220C24—44no—
221C24—41no—
222C24—41no—
223C24—44no—
224C24C2×C22⋊C411yescharacteristic
225C24C2×C22⋊C411yescharacteristic
226C24#12011yescharacteristic
227C24#12011yescharacteristic
228C24#12311yescharacteristic
229C24#12311yescharacteristic
230C24C22×D411yescharacteristic
231C2×D4—24no—
232C2×D4—48no—
233C2×D4—48no—
234C2×D4—42no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—84no—
240C2×D4—82no—
241C2×D4—84no—
242C2×D4—82no—
243C2×D4—84no—
244C2×D4—84no—
245C2×D4—84no—
246C2×D4—84no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—42no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4—44no—
274C22×C4—44no—
275C22×C4—44no—
276C22×C4—44no—
277C22×C4—48no—
278C22×C4—44no—
279C22×C4—48no—
280C22×C4—44no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—44no—
284C22×C4—48no—
285C22×C4—81no—
286C22×C4—81no—
287C22×C4—82no—
288C22×C4—81no—
289C22×C4—82no—
290C22×C4—81no—
291C22×C4—82no—
292C22×C4—82no—
293C22×C4—82no—
294C22×C4—82no—
295C22×C4—82no—
296C22×C4C2×C22⋊C414yes—
297C22×C4C2×C22⋊C414yes—
298C22×C4C2×C22⋊C411yescharacteristic
299C22×C4C2×C22⋊C411yescharacteristic
300C22×C4C4×D412yes—
301C22×C4C4×D412yes—
302C22×C4C4×D412yes—
303C22×C4C4×D412yes—
304C22×C4#12012yes—
305C22×C4#12112yes—
306C22×C4#12112yes—
307C22×C4#12112yes—
308C22×C4#12112yes—
309C22×C4#12312yes—
310C22×C4C23×C411yescharacteristic
311C22×C4C22×D412yes—
312C22×C4C22×D411yescharacteristic
313C22×C4C2×#4112yes—
314M16—84no—
315M16—84no—
316C2×C8—44no—
317C2×C8—84no—
318C4⋊C4—28no—
319C4⋊C4—28no—
320C4⋊C4—28no—
321C4⋊C4—28no—
322C4⋊C4—24no—
323C4⋊C4—42no—
324C4⋊C4—88no—
325C22⋊C4—416no—
326C22⋊C4—48no—
327C22⋊C4—44no—
328C22⋊C4—48no—
329C22⋊C4—44no—
330C22⋊C4—44no—
331C22⋊C4—44no—
332C22⋊C4—88no—
333C42—82no—
334C42—84no—
335C42—82no—
336C42—84no—
337C23—22no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—416no—
357C23—44no—
358C23—44no—
359C23—44no—
360C23—42no—
361C23—82no—
362C23—82no—
363C23—816no—
364C23—82no—
365C23—82no—
366C23—82no—
367C23—82no—
368C23#38611yescharacteristic
369C23#38611yescharacteristic
370C23#38611yescharacteristic
371C23#38611yescharacteristic
372C23#42114yes—
373C23#45414yes—
374C23C22×C22⋊C411yescharacteristic
375C23C2×#12011yescharacteristic
376C23C2×#12311yescharacteristic
377D4—84no—
378D4—84no—
379D4—84no—
380D4—84no—
381D4—84no—
382D4—84no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—48no—
415C2×C4—44no—
416C2×C4—48no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—816no—
425C2×C4—88no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4#38612yes—
429C2×C4#38612yes—
430C2×C4C2×C4×D412yes—
431C2×C4C2×#12112yes—
432C8—84no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—28no—
438C22—28no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—44no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—44no—
454C22—88no—
455C22—82no—
456C22—82no—
457C22—82no—
458C22—164no—
459C22—164no—
460C22#188812yes—
461C22#188812yes—
462C22#189712yes—
463C22#189712yes—
464C22#191312yes—
465C22C2×#38611yescharacteristic
466C22C2×#42112yes—
467C22C2×#45412yes—
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—44no—
473C4—44no—
474C4—88no—
475C4—84no—
476C4—82no—
477C2—22no—
478C2—22no—
479C2—22no—
480C2—22no—
481C2—41no—
482C2—41no—
483C2—162no—
484C2#941414yesdirect product factor
485C2C2×#188811yescharacteristic
486C2C2×#189711yescharacteristic
487C2C2×#191311yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2313C2semidirect
4. C2×#1463C2semidirect
5. #9414C2direct (N × H)
6. C2×#1297C2semidirect
12. #2591C4semidirect
14. C2×#400C4semidirect
15. C2×#394C4semidirect
18. #2313C22semidirect
31. #1463C22semidirect
33. #1297C22semidirect
74. #400C2×C4semidirect
76. #394C2×C4semidirect
484. C2#9414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25912
C2×#23132
C2×#15072
C2×#14632
#94142
C2×#12972