Finite Group Databasebeta

← C2×#9469 #201367

Subgroups — C2×#9469 #201367

Order 512.

1592 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2972C211yesmaximal, characteristic
2C2×#2487C211yesmaximal, characteristic
3C2×#1824C212yesmaximal, complemented
4C2×#1799C211yesmaximal, characteristic
5#9469C218yesmaximal, direct product factor
6C2×#1289C212yesmaximal, complemented
7C22×C4×D4C2211yescharacteristic
8C23×C4⋊C4C2211yescharacteristic
9#2972—24no—
10#2972—22no—
11#2972C2214yes—
12C2×C8×D4—24no—
13C2×#431—21no—
14C22×#99—21no—
15C22×C22⋊C8—21no—
16C22×C22⋊C8C2212yes—
17#2487—22no—
18#2487—22no—
19#2487C414yescomplemented
20#2487C2214yes—
21C2×#400C412yescomplemented
22C2×#399C412yescomplemented
23C2×#389—21no—
24C2×#386—21no—
25C2×#385—21no—
26C2×#380—21no—
27C2×#380C2212yes—
28C2×#380C2211yescharacteristic
29#1824—24no—
30#1824C2218yescomplemented
31#1799—22no—
32#1799C2214yes—
33C2×#342—21no—
34C2×#340—24no—
35#1289C2218yescomplemented
36C23×D4D411yescharacteristic
37C24×C4—21no—
38C24×C4D411yescharacteristic
39C24×C4C2311yescharacteristic
40C23×C8—22no—
41C23×C8D414yes—
42C2×C4×D4—22no—
43C2×C4×D4—22no—
44C2×C4×D4—22no—
45C2×C4×D4—22no—
46C2×C4×D4C2×C412yes—
47C2×C4×D4D412yes—
48C2×C4×D4D412yes—
49C2×C4×D4C2312yes—
50C22×C4⋊C4—22no—
51C22×C4⋊C4—22no—
52C22×C4⋊C4—22no—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4C2×C412yes—
61C22×C4⋊C4C2×C412yes—
62C22×C4⋊C4C2×C411yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C22⋊C4—21no—
65C22×C22⋊C4—22no—
66C22×C22⋊C4—22no—
67C22×C22⋊C4C2×C411yescharacteristic
68C22×C22⋊C4D411yescharacteristic
69C22×C42D411yescharacteristic
70C8×D4—216no—
71C8×D4—216no—
72#431—24no—
73#431—24no—
74C2×C4⋊C8—22no—
75C2×#99—24no—
76C2×#99—44no—
77C2×C22⋊C8—22no—
78C2×C22⋊C8—24no—
79C2×C22⋊C8—22no—
80C2×C22⋊C8—24no—
81C2×C22⋊C8—22no—
82C2×C22⋊C8—22no—
83C2×C22⋊C8—22no—
84C2×C22⋊C8D414yes—
85C2×C22⋊C8C2314yes—
86C2×C4×C8—22no—
87#400—24no—
88#400C2×C418yescomplemented
89#399—24no—
90#399C2×C418yescomplemented
91#389—24no—
92#389—24no—
93#386—24no—
94#386—24no—
95#385—24no—
96#385—24no—
97#380—24no—
98#380—21no—
99#380—21no—
100#380—24no—
101#380—22no—
102#380—22no—
103#380—22no—
104#380C2×C412yes—
105#380C2314yes—
106#380C2312yes—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95C2×C412yes—
111#342—24no—
112#340—216no—
113C25C22⋊C411yescharacteristic
114C25C2×D411yescharacteristic
115C22×D4—22no—
116C22×D4—22no—
117C22×D4—24no—
118C22×D4C22⋊C412yes—
119C22×D4SD1614yes—
120C22×D4Q1614yes—
121C22×D4C2×D412yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—44no—
131C23×C4—44no—
132C23×C4—42no—
133C23×C4—42no—
134C23×C4—42no—
135C23×C4—84no—
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C412yes—
140C23×C4C22×C411yescharacteristic
141C23×C4C22×C411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D412yes—
144C23×C4C2×D412yes—
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D412yes—
148C23×C4#4112yes—
149C23×C4#4112yes—
150C23×C4C2411yescharacteristic
151C22×C8—24no—
152C22×C8—28no—
153C22×C8—24no—
154C22×C8—48no—
155C22×C8—84no—
156C22×C8C2×D418yes—
157C4×D4—24no—
158C4×D4—24no—
159C4×D4—24no—
160C4×D4—24no—
161C4×D4—24no—
162C4×D4—24no—
163C4×D4—24no—
164C4×D4—24no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
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—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—48no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—84no—
192C2×C4⋊C4C22⋊C412yes—
193C2×C4⋊C4C22×C414yes—
194C2×C4⋊C4C22×C412yes—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—24no—
202C2×C22⋊C4—28no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4—44no—
205C2×C22⋊C4—44no—
206C2×C22⋊C4—42no—
207C2×C22⋊C4—84no—
208C2×C22⋊C4C22⋊C412yes—
209C2×C22⋊C4C22⋊C412yes—
210C2×C22⋊C4C22×C412yes—
211C2×C22⋊C4C2×D412yes—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—21no—
215C2×C42—21no—
216C2×C42C22⋊C412yes—
217C2×C42C2×D412yes—
218C4⋊C8—28no—
219#99—48no—
220C22⋊C8—28no—
221C22⋊C8—24no—
222C22⋊C8—24no—
223C22⋊C8—24no—
224C22⋊C8—24no—
225C4×C8—28no—
226#95—28no—
227#95—28no—
228#95—22no—
229#95—24no—
230#95—42no—
231#95C22×C414yes—
232C24—21no—
233C24—21no—
234C24—22no—
235C24—42no—
236C24—42no—
237C24—42no—
238C24—42no—
239C24#10314yes—
240C24C2×C22⋊C411yescharacteristic
241C24C2×C22⋊C412yes—
242C24C2×C22⋊C411yescharacteristic
243C24#12112yes—
244C24#12112yes—
245C24C2×SD1612yes—
246C24C2×Q1612yes—
247C24#13514yes—
248C24C22×D411yescharacteristic
249C2×D4—24no—
250C2×D4—24no—
251C2×D4—24no—
252C2×D4—24no—
253C2×D4—28no—
254C2×D4—28no—
255C2×D4—28no—
256C2×D4—28no—
257C2×D4#10318yes—
258C2×D4C2×SD1614yes—
259C2×D4C2×Q1614yes—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—22no—
263C22×C4—28no—
264C22×C4—24no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—44no—
278C22×C4—42no—
279C22×C4—44no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—44no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—44no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—44no—
293C22×C4—42no—
294C22×C4—44no—
295C22×C4—42no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—82no—
299C22×C4—82no—
300C22×C4—82no—
301C22×C4—84no—
302C22×C4—84no—
303C22×C4—88no—
304C22×C4—88no—
305C22×C4—84no—
306C22×C4—84no—
307C22×C4—84no—
308C22×C4#10314yes—
309C22×C4C2×C22⋊C411yescharacteristic
310C22×C4C2×C22⋊C412yes—
311C22×C4C2×C22⋊C412yes—
312C22×C4C2×C22⋊C412yes—
313C22×C4C2×C22⋊C411yescharacteristic
314C22×C4C4×D412yes—
315C22×C4C4×D412yes—
316C22×C4C4×D412yes—
317C22×C4C4×D412yes—
318C22×C4#12011yescharacteristic
319C22×C4#12012yes—
320C22×C4#12011yescharacteristic
321C22×C4#12112yes—
322C22×C4#12112yes—
323C22×C4#12311yescharacteristic
324C22×C4#12311yescharacteristic
325C22×C4#12312yes—
326C22×C4C23×C411yescharacteristic
327C22×C4C22×D412yes—
328C22×C4C22×D411yescharacteristic
329C22×C4C2×#4112yes—
330C2×C8—28no—
331C2×C8—48no—
332C2×C8—48no—
333C2×C8—84no—
334C2×C8—88no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—28no—
338C4⋊C4—44no—
339C4⋊C4—44no—
340C4⋊C4—48no—
341C4⋊C4—42no—
342C4⋊C4—42no—
343C4⋊C4—42no—
344C4⋊C4—44no—
345C4⋊C4—42no—
346C4⋊C4—84no—
347C4⋊C4—88no—
348C22⋊C4—24no—
349C22⋊C4—24no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—44no—
353C22⋊C4—44no—
354C22⋊C4—44no—
355C22⋊C4—44no—
356C22⋊C4—88no—
357C22⋊C4—84no—
358C42—22no—
359C42—22no—
360C42—22no—
361C42—22no—
362C23—22no—
363C23—24no—
364C23—22no—
365C23—24no—
366C23—24no—
367C23—22no—
368C23—22no—
369C23—24no—
370C23—41no—
371C23—42no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—41no—
376C23—44no—
377C23—44no—
378C23—48no—
379C23—42no—
380C23—42no—
381C23—48no—
382C23—42no—
383C23—42no—
384C23—81no—
385C23—81no—
386C23—84no—
387C23#38612yes—
388C23#38611yescharacteristic
389C23#38611yescharacteristic
390C23C2×#10312yes—
391C23C2×#10314yes—
392C23C2×#10312yes—
393C23#41612yes—
394C23#41612yes—
395C23#46514yes—
396C23#46514yes—
397C23#46714yes—
398C23#46714yes—
399C23C22×C22⋊C411yescharacteristic
400C23C2×#12112yes—
401C23C22×SD1611yescharacteristic
402C23C22×Q1611yescharacteristic
403C23C2×#13512yes—
404D4—216no—
405D4—28no—
406D4—28no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—88no—
447C2×C4—84no—
448C2×C4—88no—
449C2×C4—88no—
450C2×C4—84no—
451C2×C4—84no—
452C2×C4—84no—
453C2×C4—84no—
454C2×C4—168no—
455C2×C4#38611yescharacteristic
456C2×C4#38612yes—
457C2×C4#38611yescharacteristic
458C2×C4C2×#10314yes—
459C2×C4#45814yes—
460C2×C4C2×C4×D412yes—
461C2×C4C2×#12011yescharacteristic
462C2×C4C2×#12311yescharacteristic
463C8—48no—
464C22—21no—
465C22—22no—
466C22—21no—
467C22—22no—
468C22—21no—
469C22—22no—
470C22—21no—
471C22—22no—
472C22—24no—
473C22—28no—
474C22—24no—
475C22—28no—
476C22—24no—
477C22—41no—
478C22—41no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—44no—
483C22—44no—
484C22—44no—
485C22—42no—
486C22—42no—
487C22—48no—
488C22—82no—
489C22—84no—
490C22#189012yes—
491C22#189212yes—
492C22#189214yes—
493C22#189212yes—
494C22#191012yes—
495C22C2×#38611yescharacteristic
496C22C22×#10311yescharacteristic
497C22C2×#41611yescharacteristic
498C22C2×#46512yes—
499C22C2×#46712yes—
500C4—21no—
501C4—21no—
502C4—22no—
503C4—22no—
504C4—24no—
505C4—42no—
506C4—42no—
507C4—84no—
508C4—84no—
509C4—164no—
510C4#189012yes—
511C4C2×#45812yes—
512C2—21no—
513C2—22no—
514C2—21no—
515C2—22no—
516C2—24no—
517C2—22no—
518C2—44no—
519C2#946914yesdirect product factor
520C2C2×#189011yescharacteristic
521C2C2×#189211yescharacteristic
522C2C2×#191011yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC23×D4D4
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
3. C2×#1824C2semidirect
5. #9469C2direct (N × H)
6. C2×#1289C2semidirect
19. #2487C4semidirect
21. C2×#400C4semidirect
22. C2×#399C4semidirect
30. #1824C22semidirect
35. #1289C22semidirect
88. #400C2×C4semidirect
90. #399C2×C4semidirect
519. C2#9469direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29722
C2×#24872
C2×#18242
C2×#17992
#94692
C2×#12892