Finite Group Databasebeta

← C2×#9474 #201378

Subgroups — C2×#9474 #201378

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2973C211yesmaximal, characteristic
2C2×#2486C211yesmaximal, characteristic
3C2×#1823C212yesmaximal, complemented
4C2×#1799C211yesmaximal, characteristic
5#9474C218yesmaximal, direct product factor
6C2×#1289C212yesmaximal, complemented
7C22×#123—21no—
8C22×C4×D4C2211yescharacteristic
9C23×C4⋊C4C2211yescharacteristic
10#2973—24no—
11#2973—22no—
12#2973C2214yes—
13C2×#435—24no—
14C2×#432—21no—
15C22×#99—21no—
16C2×#407—21no—
17C22×C22⋊C8C2212yes—
18#2486—22no—
19#2486—22no—
20#2486C414yescomplemented
21#2486C2214yes—
22C2×#398C412yescomplemented
23C2×#397C412yescomplemented
24C2×#389—21no—
25C2×#381—21no—
26C2×#380—21no—
27C2×#380C2212yes—
28C2×#380C2211yescharacteristic
29#1823—24no—
30#1823C2218yescomplemented
31#1799—22no—
32#1799C2214yes—
33C2×#342—21no—
34C2×#340—24no—
35#1289C2218yescomplemented
36C23×D4D411yescharacteristic
37C24×C4—21no—
38C24×C4D411yescharacteristic
39C24×C4C2311yescharacteristic
40C22×M16—22no—
41C23×C8D414yes—
42C2×#123—24no—
43C2×#123—24no—
44C2×#123—48no—
45C2×C4×D4—22no—
46C2×C4×D4—22no—
47C2×C4×D4—22no—
48C2×C4×D4—22no—
49C2×C4×D4C2×C412yes—
50C2×C4×D4D412yes—
51C2×C4×D4D412yes—
52C2×C4×D4C2312yes—
53C22×C4⋊C4—22no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—22no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4C2×C412yes—
64C22×C4⋊C4C2×C412yes—
65C22×C4⋊C4C2×C411yescharacteristic
66C22×C4⋊C4C2312yes—
67C22×C22⋊C4—22no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4—22no—
70C22×C22⋊C4C2×C411yescharacteristic
71C22×C22⋊C4D411yescharacteristic
72C22×C42D411yescharacteristic
73#435—216no—
74#435—216no—
75#432—24no—
76#432—24no—
77C2×C4⋊C8—22no—
78C2×#99—24no—
79C2×#99—44no—
80#407—24no—
81#407—24no—
82C2×C22⋊C8—22no—
83C2×C22⋊C8—22no—
84C2×C22⋊C8—22no—
85C2×C22⋊C8—22no—
86C2×C22⋊C8—22no—
87C2×C22⋊C8D414yes—
88C2×C22⋊C8C2314yes—
89C2×#97—22no—
90#398—24no—
91#398C2×C418yescomplemented
92#397—24no—
93#397C2×C418yescomplemented
94#389—24no—
95#389—24no—
96#381—24no—
97#381—24no—
98#380—24no—
99#380—21no—
100#380—21no—
101#380—24no—
102#380—22no—
103#380—22no—
104#380—22no—
105#380C2×C412yes—
106#380C2314yes—
107#380C2312yes—
108C2×#95—22no—
109C2×#95—22no—
110C2×#95—22no—
111C2×#95C2×C412yes—
112#342—24no—
113#340—216no—
114C25C22⋊C411yescharacteristic
115C25C2×D411yescharacteristic
116C22×D4—22no—
117C22×D4—22no—
118C22×D4—24no—
119C22×D4—22no—
120C22×D4—22no—
121C22×D4C22⋊C412yes—
122C22×D4C2×D412yes—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—22no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—44no—
132C23×C4—44no—
133C23×C4—42no—
134C23×C4—42no—
135C23×C4—44no—
136C23×C4—42no—
137C23×C4—42no—
138C23×C4—42no—
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22⋊C411yescharacteristic
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C412yes—
143C23×C4C22×C411yescharacteristic
144C23×C4C22×C411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D412yes—
147C23×C4C2×D412yes—
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D411yescharacteristic
150C23×C4C2×D412yes—
151C23×C4#4112yes—
152C23×C4#4112yes—
153C23×C4C2411yescharacteristic
154C2×M16—28no—
155C2×M16—84no—
156C22×C8—24no—
157C22×C8—24no—
158C22×C8—48no—
159C22×C8C2×D418yes—
160#123—416no—
161#123—416no—
162C4×D4—24no—
163C4×D4—24no—
164C4×D4—24no—
165C4×D4—24no—
166C4×D4—24no—
167C4×D4—24no—
168C4×D4—24no—
169C4×D4—24no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—48no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—41no—
195C2×C4⋊C4—48no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4C22⋊C412yes—
198C2×C4⋊C4C22×C414yes—
199C2×C4⋊C4C22×C412yes—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—28no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—48no—
209C2×C22⋊C4—44no—
210C2×C22⋊C4—44no—
211C2×C22⋊C4—44no—
212C2×C22⋊C4—42no—
213C2×C22⋊C4C22⋊C412yes—
214C2×C22⋊C4C22⋊C412yes—
215C2×C22⋊C4C22×C412yes—
216C2×C22⋊C4C2×D412yes—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42C22⋊C412yes—
222C2×C42C2×D412yes—
223C4⋊C8—28no—
224#99—48no—
225C22⋊C8—28no—
226C22⋊C8—24no—
227C22⋊C8—24no—
228C22⋊C8—24no—
229C22⋊C8—24no—
230#97—28no—
231#95—28no—
232#95—28no—
233#95—22no—
234#95—24no—
235#95—42no—
236#95C22×C414yes—
237C24—21no—
238C24—22no—
239C24—21no—
240C24—22no—
241C24—42no—
242C24—42no—
243C24—42no—
244C24—42no—
245C24C2×C22⋊C411yescharacteristic
246C24C2×C22⋊C412yes—
247C24C2×C22⋊C411yescharacteristic
248C24#12112yes—
249C24#12112yes—
250C24AGL(1,ℤ/8)12yes—
251C24AGL(1,ℤ/8)14yes—
252C24#13712yes—
253C24C22×D411yescharacteristic
254C2×D4—24no—
255C2×D4—22no—
256C2×D4—24no—
257C2×D4—22no—
258C2×D4—24no—
259C2×D4—24no—
260C2×D4—24no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—44no—
265C22×C4—28no—
266C22×C4—24no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—42no—
285C22×C4—44no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—44no—
289C22×C4—44no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—44no—
297C22×C4—44no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—44no—
304C22×C4—44no—
305C22×C4—44no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4—82no—
310C22×C4—82no—
311C22×C4—82no—
312C22×C4—84no—
313C22×C4—84no—
314C22×C4—84no—
315C22×C4—84no—
316C22×C4—84no—
317C22×C4—84no—
318C22×C4—84no—
319C22×C4C2×C22⋊C412yes—
320C22×C4C2×C22⋊C411yescharacteristic
321C22×C4C2×C22⋊C412yes—
322C22×C4C2×C22⋊C412yes—
323C22×C4C2×C22⋊C411yescharacteristic
324C22×C4C4×D412yes—
325C22×C4C4×D412yes—
326C22×C4C4×D412yes—
327C22×C4C4×D412yes—
328C22×C4#12011yescharacteristic
329C22×C4#12012yes—
330C22×C4#12011yescharacteristic
331C22×C4#12112yes—
332C22×C4#12112yes—
333C22×C4#12311yescharacteristic
334C22×C4#12311yescharacteristic
335C22×C4#12312yes—
336C22×C4C23×C411yescharacteristic
337C22×C4C22×D412yes—
338C22×C4C22×D411yescharacteristic
339C22×C4C2×#4112yes—
340M16—88no—
341C2×C8—28no—
342C2×C8—48no—
343C2×C8—48no—
344C2×C8—84no—
345C4⋊C4—24no—
346C4⋊C4—24no—
347C4⋊C4—28no—
348C4⋊C4—44no—
349C4⋊C4—44no—
350C4⋊C4—416no—
351C4⋊C4—48no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—44no—
356C4⋊C4—42no—
357C4⋊C4—84no—
358C22⋊C4—24no—
359C22⋊C4—24no—
360C22⋊C4—24no—
361C22⋊C4—24no—
362C22⋊C4—416no—
363C22⋊C4—44no—
364C22⋊C4—44no—
365C22⋊C4—44no—
366C22⋊C4—44no—
367C22⋊C4—84no—
368C42—22no—
369C42—22no—
370C42—22no—
371C42—22no—
372C23—22no—
373C23—24no—
374C23—22no—
375C23—24no—
376C23—22no—
377C23—22no—
378C23—22no—
379C23—41no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—42no—
384C23—48no—
385C23—44no—
386C23—44no—
387C23—41no—
388C23—42no—
389C23—42no—
390C23—48no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—81no—
396C23—81no—
397C23—84no—
398C23#38612yes—
399C23#38611yescharacteristic
400C23#38611yescharacteristic
401C23#41712yes—
402C23#41712yes—
403C23#41812yes—
404C23#41812yes—
405C23#46814yes—
406C23#46814yes—
407C23#46914yes—
408C23#46914yes—
409C23C22×C22⋊C411yescharacteristic
410C23C2×#12112yes—
411C23C2×AGL(1,ℤ/8)12yes—
412C23C2×AGL(1,ℤ/8)11yescharacteristic
413C23C2×#13711yescharacteristic
414D4—48no—
415D4—44no—
416D4—44no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—88no—
458C2×C4—84no—
459C2×C4—88no—
460C2×C4—84no—
461C2×C4—84no—
462C2×C4—84no—
463C2×C4—84no—
464C2×C4—84no—
465C2×C4—84no—
466C2×C4—168no—
467C2×C4#38611yescharacteristic
468C2×C4#38612yes—
469C2×C4#38611yescharacteristic
470C2×C4#45814yes—
471C2×C4C2×C4×D412yes—
472C2×C4C2×#12011yescharacteristic
473C2×C4C2×#12311yescharacteristic
474C8—48no—
475C22—24no—
476C22—28no—
477C22—24no—
478C22—28no—
479C22—21no—
480C22—22no—
481C22—21no—
482C22—22no—
483C22—21no—
484C22—22no—
485C22—21no—
486C22—22no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—42no—
491C22—42no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—82no—
499C22—84no—
500C22—84no—
501C22#189012yes—
502C22#189512yes—
503C22#189514yes—
504C22#189512yes—
505C22#190912yes—
506C22C2×#38611yescharacteristic
507C22C2×#41811yescharacteristic
508C22C2×#41711yescharacteristic
509C22C2×#46812yes—
510C22C2×#46912yes—
511C4—21no—
512C4—21no—
513C4—22no—
514C4—22no—
515C4—42no—
516C4—42no—
517C4—42no—
518C4—84no—
519C4—84no—
520C4—164no—
521C4#189012yes—
522C4C2×#45812yes—
523C2—21no—
524C2—22no—
525C2—21no—
526C2—22no—
527C2—24no—
528C2—22no—
529C2—82no—
530C2#947414yesdirect product factor
531C2C2×#189011yescharacteristic
532C2C2×#189511yescharacteristic
533C2C2×#190911yescharacteristic
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×#1823C2semidirect
5. #9474C2direct (N × H)
6. C2×#1289C2semidirect
20. #2486C4semidirect
22. C2×#398C4semidirect
23. C2×#397C4semidirect
30. #1823C22semidirect
35. #1289C22semidirect
91. #398C2×C4semidirect
93. #397C2×C4semidirect
530. C2#9474direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#29732
C2×#24862
C2×#18232
C2×#17992
#94742
C2×#12892