Finite Group Databasebeta

← C2×#9246 #198183

Subgroups — C2×#9246 #198183

Order 512.

1084 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#479C211yesmaximal, characteristic
2C2×#2984C211yesmaximal, characteristic
3C2×#1528C211yesmaximal, characteristic
4C2×#1491C211yesmaximal, characteristic
5C2×#1470C211yesmaximal, characteristic
6#9246C218yesmaximal, direct product factor
7C2×#1290C211yesmaximal, characteristic
8C2×#1283C211yesmaximal, characteristic
9C22×#125C2211yescharacteristic
10C22×C4×Q8C2211yescharacteristic
11C2×#479—21no—
12C2×#479—21no—
13C2×#479—22no—
14C2×#479—21no—
15C2×#479—21no—
16C2×#479—22no—
17C2×#479C414yes—
18C2×#479C2214yes—
19#2984—22no—
20#2984—22no—
21#2984—22no—
22#2984C2214yes—
23C2×#446—22no—
24C2×#446—21no—
25C2×C8×Q8—21no—
26C2×#432—21no—
27C2×#432C2211yescharacteristic
28C2×#432C2211yescharacteristic
29C2×#431—21no—
30C2×#431C2211yescharacteristic
31C22×#107C411yescharacteristic
32C22×#106C411yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C411yescharacteristic
35C22×#103C411yescharacteristic
36C2×C4×M16C2211yescharacteristic
37#1528—22no—
38#1528C2214yes—
39C2×#330—22no—
40#1491—22no—
41#1491C2214yes—
42C2×Q8⋊C8—21no—
43C2×Q8⋊C8—21no—
44#1470—22no—
45#1470C2214yes—
46C2×#324—21no—
47C2×#324—21no—
48#1290C2214yes—
49#1283C2214yes—
50C23×Q8C2×C411yescharacteristic
51C22×M16—21no—
52C23×C8C2×C411yescharacteristic
53C23×C8C2×C411yescharacteristic
54C2×#125—21no—
55C2×#125—21no—
56C2×#125—21no—
57C2×#125—21no—
58C2×#125—21no—
59C2×#125—21no—
60C2×#125—21no—
61C2×#125—21no—
62C2×#125—21no—
63C2×#125—21no—
64C2×#125C2×C412yes—
65C2×#125C2312yes—
66C2×C4×Q8—21no—
67C2×C4×Q8—21no—
68C2×C4×Q8—21no—
69C2×C4×Q8—21no—
70C2×C4×Q8—21no—
71C2×C4×Q8—21no—
72C2×C4×Q8C2×C412yes—
73C2×C4×Q8D411yescharacteristic
74C2×C4×Q8D411yescharacteristic
75C2×C4×Q8D412yes—
76C2×C4×Q8D411yescharacteristic
77C2×C4×Q8D411yescharacteristic
78C2×C4×Q8D412yes—
79C2×C4×Q8C2312yes—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4C2×C411yescharacteristic
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C411yescharacteristic
86C22×C42—21no—
87C22×C42C2311yescharacteristic
88#479—24no—
89#479—24no—
90#479—24no—
91#479—24no—
92#479—24no—
93#479—24no—
94#479—24no—
95#479—24no—
96#446—28no—
97#446—24no—
98#446—24no—
99#446—28no—
100C8×Q8—24no—
101C8×Q8—24no—
102#432—24no—
103#432—21no—
104#432—21no—
105#432—24no—
106#432—21no—
107#432—21no—
108#432—21no—
109#432D412yes—
110#432C2312yes—
111#432C2312yes—
112#431—24no—
113#431—21no—
114#431—21no—
115#431—24no—
116#431D412yes—
117#431C2312yes—
118C2×#107—22no—
119C2×#107—21no—
120C2×#107—21no—
121C2×#107C2×C414yes—
122C2×#106—22no—
123C2×#106—21no—
124C2×#106—21no—
125C2×#106C2×C414yes—
126C2×C4⋊C8—22no—
127C2×C4⋊C8—22no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—21no—
134C2×C4⋊C8—21no—
135C2×C4⋊C8C2×C412yes—
136C2×C4⋊C8C2312yes—
137C2×#103—21no—
138C2×#103—22no—
139C2×#103—21no—
140C2×#103—21no—
141C2×#103—22no—
142C2×#103—21no—
143C2×#103C2×C414yes—
144C2×#103C2×C414yes—
145C2×C22⋊C8—21no—
146C2×C22⋊C8—21no—
147C2×C22⋊C8D411yescharacteristic
148C2×C22⋊C8D411yescharacteristic
149C4×M16—21no—
150C4×M16—21no—
151C4×M16—21no—
152C4×M16C2312yes—
153C2×#97—22no—
154C2×#97—21no—
155C2×#97—21no—
156C2×#97D412yes—
157C2×C4×C8—22no—
158C2×C4×C8—21no—
159C2×C4×C8—21no—
160#330—28no—
161Q8⋊C8—24no—
162Q8⋊C8—24no—
163#324—24no—
164#324—24no—
165C22×Q8—21no—
166C22×Q8—21no—
167C22×Q8—21no—
168C22×Q8—24no—
169C22×Q8—42no—
170C22×Q8C22⋊C411yescharacteristic
171C22×Q8C22⋊C412yes—
172C22×Q8C22⋊C411yescharacteristic
173C22×Q8C22×C412yes—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4C22×C411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4#4111yescharacteristic
181C2×M16—24no—
182C2×M16—22no—
183C2×M16—42no—
184C2×M16—41no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—22no—
192C22×C8—41no—
193C22×C8—42no—
194C22×C8—42no—
195C22×C8—41no—
196C22×C8C22×C412yes—
197C22×C8C22×C412yes—
198#125—22no—
199#125—22no—
200#125—22no—
201#125—22no—
202#125—22no—
203#125—22no—
204#125—22no—
205#125—22no—
206#125—41no—
207#125—41no—
208#125—41no—
209#125—41no—
210#125—41no—
211#125—41no—
212#125—41no—
213#125—41no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×Q8—21no—
217C4×Q8—22no—
218C4×Q8—21no—
219C4×Q8—22no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—22no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—22no—
228C4×Q8—22no—
229C4×Q8—22no—
230C4×Q8C22⋊C412yes—
231C4×Q8C22⋊C412yes—
232C4×Q8C22⋊C412yes—
233C4×Q8C22⋊C412yes—
234C4×Q8C2×D412yes—
235C4×Q8C2×D412yes—
236C4×Q8C2×D412yes—
237C4×Q8C2×D412yes—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—41no—
266C2×C4⋊C4—41no—
267C2×C4⋊C4—41no—
268C2×C4⋊C4—41no—
269C2×C4⋊C4—41no—
270C2×C4⋊C4—41no—
271C2×C4⋊C4C22⋊C412yes—
272C2×C4⋊C4C22⋊C411yescharacteristic
273C2×C4⋊C4C22⋊C411yescharacteristic
274C2×C4⋊C4C22×C412yes—
275C2×C4⋊C4C22×C412yes—
276C2×C4⋊C4C22×C412yes—
277C2×C42—22no—
278C2×C42—21no—
279C2×C42—21no—
280C2×C42—22no—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42—21no—
284C2×C42—22no—
285C2×C42C22×C411yescharacteristic
286C2×C42C2×D411yescharacteristic
287C2×C42C2×D411yescharacteristic
288C2×C42C2×D411yescharacteristic
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42C2×D411yescharacteristic
292C2×C42C2×D411yescharacteristic
293C2×C42#4111yescharacteristic
294C2×C42#4111yescharacteristic
295C2×C42#4111yescharacteristic
296C2×C42C2411yescharacteristic
297#107—24no—
298#107—24no—
299#106—24no—
300#106—24no—
301C4⋊C8—28no—
302C4⋊C8—28no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308C4⋊C8—22no—
309C4⋊C8—22no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312C4⋊C8—41no—
313#103—24no—
314#103—24no—
315#103—24no—
316#103—24no—
317C22⋊C8—22no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—22no—
321C22⋊C8—22no—
322C22⋊C8—41no—
323C22⋊C8C2×D412yes—
324C22⋊C8C2×D412yes—
325#97—28no—
326#97—22no—
327#97—22no—
328#97—22no—
329#97—41no—
330#97—41no—
331#97C2×D414yes—
332C4×C8—28no—
333C4×C8—22no—
334C4×C8—22no—
335C4×C8—22no—
336C4×C8—41no—
337C24C4×D411yescharacteristic
338C2×Q8—22no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—24no—
344C2×Q8—24no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—44no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8—44no—
351C2×Q8—44no—
352C2×Q8#10114yes—
353C2×Q8C2×C22⋊C412yes—
354C2×Q8C2×C22⋊C412yes—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—44no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—82no—
380C22×C4C2×C22⋊C411yescharacteristic
381C22×C4C2×C22⋊C411yescharacteristic
382C22×C4C4×D411yescharacteristic
383C22×C4C4×D411yescharacteristic
384C22×C4C4×D411yescharacteristic
385C22×C4C4×D411yescharacteristic
386C22×C4C4×D411yescharacteristic
387C22×C4#12011yescharacteristic
388C22×C4#12011yescharacteristic
389C22×C4#12111yescharacteristic
390C22×C4#12111yescharacteristic
391C22×C4#12111yescharacteristic
392C22×C4#12111yescharacteristic
393C22×C4#12311yescharacteristic
394C22×C4#12311yescharacteristic
395C22×C4C23×C411yescharacteristic
396C22×C4C22×D411yescharacteristic
397C22×C4C2×#4111yescharacteristic
398M16—24no—
399M16—44no—
400M16—42no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—24no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—44no—
409C2×C8—42no—
410C2×C8—42no—
411C2×C8—44no—
412C2×C8—42no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—42no—
416C2×C8—42no—
417C2×C8—42no—
418C2×C8—82no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—42no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4—42no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4C2×C22⋊C412yes—
448C4⋊C4C2×C22⋊C412yes—
449C42—22no—
450C42—22no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42C2×C22⋊C411yescharacteristic
458C42C2×C22⋊C411yescharacteristic
459C42C4×D411yescharacteristic
460C42C4×D411yescharacteristic
461C42#12011yescharacteristic
462C42#12011yescharacteristic
463C42#12111yescharacteristic
464C42#12111yescharacteristic
465C42#12111yescharacteristic
466C42#12111yescharacteristic
467C42#12311yescharacteristic
468C42#12311yescharacteristic
469C42C22×D411yescharacteristic
470C42C22×D411yescharacteristic
471C42C22×D411yescharacteristic
472C42C2×#4111yescharacteristic
473C23—22no—
474C23—22no—
475C23#38611yescharacteristic
476C23#38611yescharacteristic
477C23#44312yes—
478C23#44412yes—
479C23C2×C4×D411yescharacteristic
480Q8—22no—
481Q8—24no—
482Q8—22no—
483Q8—22no—
484Q8—44no—
485Q8—44no—
486Q8—42no—
487Q8C2×#10114yes—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4#38611yescharacteristic
532C2×C4#38611yescharacteristic
533C2×C4#38611yescharacteristic
534C2×C4#38611yescharacteristic
535C2×C4#38611yescharacteristic
536C2×C4#38611yescharacteristic
537C2×C4C2×#10112yes—
538C2×C4#41312yes—
539C2×C4C22×C22⋊C411yescharacteristic
540C2×C4C2×C4×D411yescharacteristic
541C2×C4C2×#12011yescharacteristic
542C2×C4C2×#12111yescharacteristic
543C2×C4C2×#12111yescharacteristic
544C2×C4C2×#12311yescharacteristic
545C8—42no—
546C8—42no—
547C8—44no—
548C8—44no—
549C8—42no—
550C8—42no—
551C8—82no—
552C22—21no—
553C22—21no—
554C22—24no—
555C22—24no—
556C22—21no—
557C22—21no—
558C22#187612yes—
559C22#187612yes—
560C22#190112yes—
561C22#190512yes—
562C22C2×#38611yescharacteristic
563C22C2×#44311yescharacteristic
564C22C2×#44411yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—24no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—82no—
580C4—82no—
581C4#190112yes—
582C4C22×#10111yescharacteristic
583C4C2×#41311yescharacteristic
584C2—22no—
585C2—21no—
586C2—21no—
587C2#924614yesdirect product factor
588C2C2×#187611yescharacteristic
589C2C2×#190111yescharacteristic
590C2C2×#190511yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
6. #9246C2direct (N × H)
587. C2#9246direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4792
C2×#29842
C2×#15282
C2×#14912
C2×#14702
#92462
C2×#12902
C2×#12832