Finite Group Databasebeta

← C2×#10296 #234126

Subgroups — C2×#10296 #234126

Order 512.

1374 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic
2C2×#3229C211yesmaximal, characteristic
3C2×#2862C211yesmaximal, characteristic
4C2×#1994C211yesmaximal, characteristic
5C2×#1549C211yesmaximal, characteristic
6C2×#1546C211yesmaximal, characteristic
7#10296C218yesmaximal, direct product factor
8C2×#1276C211yesmaximal, characteristic
9C2×#533C2211yescharacteristic
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4⋊Q8C2211yescharacteristic
12#3230—22no—
13#3230—22no—
14#3230—22no—
15#3230C2214yes—
16#3229—22no—
17#3229—22no—
18#3229—22no—
19#3229C2214yes—
20C2×#500—21no—
21C2×#498—21no—
22C2×#487—21no—
23C2×#487—21no—
24C2×#484—22no—
25C2×#483—22no—
26C2×#477—22no—
27C2×#475—22no—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30C2×#423C2211yescharacteristic
31#2862—22no—
32#2862—22no—
33#2862—22no—
34#2862C2214yes—
35C2×#391—22no—
36C2×#391—22no—
37C2×#382—22no—
38C2×C43C2211yescharacteristic
39#1994—22no—
40#1994C2214yes—
41C2×#339—22no—
42#1549—22no—
43#1549C2214yes—
44#1546—22no—
45#1546C2214yes—
46C2×#332—22no—
47C2×#332—22no—
48#1276C2214yes—
49C23×Q8—21no—
50C23×Q8—21no—
51C22×M16—21no—
52#533—21no—
53#533—21no—
54#533—21no—
55#533—21no—
56#533—21no—
57#533—21no—
58#533D412yes—
59#533C2312yes—
60C2×C4⋊Q8—21no—
61C2×C4⋊Q8—21no—
62C2×C4⋊Q8—21no—
63C2×C4⋊Q8—21no—
64C2×C4⋊Q8—21no—
65C2×C4⋊Q8—21no—
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⋊Q8—21no—
73C2×C4⋊Q8—21no—
74C2×C4⋊Q8—21no—
75C2×C4⋊Q8—21no—
76C2×C4⋊Q8—21no—
77C2×C4⋊Q8—21no—
78C2×C4⋊Q8—21no—
79C2×C4⋊Q8—21no—
80C2×C4⋊Q8D411yescharacteristic
81C2×C4⋊Q8D411yescharacteristic
82C2×C4⋊Q8D412yes—
83C2×C4⋊Q8D412yes—
84C2×C4⋊Q8C2312yes—
85C2×C4⋊Q8C2312yes—
86C2×#125—21no—
87C2×C22⋊Q8—21no—
88C2×C22⋊Q8—21no—
89C2×C4×Q8—21no—
90C2×C4×Q8—21no—
91C2×#117—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4D412yes—
95C22×C4⋊C4D412yes—
96C22×C42—21no—
97C22×C42—21no—
98C22×C42D412yes—
99C22×C42C2311yescharacteristic
100#500—24no—
101#500—24no—
102#498—24no—
103#498—24no—
104#487—24no—
105#487—24no—
106#487—24no—
107#487—24no—
108#484—28no—
109#484—28no—
110#483—28no—
111#483—28no—
112#477—28no—
113#477—28no—
114#475—28no—
115#475—28no—
116#431—21no—
117#431—21no—
118#431—21no—
119#431—21no—
120#431D412yes—
121#431D412yes—
122#431C2312yes—
123#431C2312yes—
124C2×#107—24no—
125C2×#106—24no—
126#423—21no—
127#423—21no—
128#423—21no—
129#423C2312yes—
130C2×C4⋊C8—21no—
131C2×C4⋊C8—21no—
132C2×C4⋊C8D412yes—
133C2×C4⋊C8D412yes—
134C2×#103—24no—
135C2×#103—24no—
136C2×C22⋊C8—21no—
137C2×C22⋊C8—21no—
138C2×C4×C8—21no—
139C2×C4×C8—21no—
140#391—28no—
141#391—28no—
142#391—28no—
143#391—28no—
144#382—28no—
145#382—28no—
146C2×#95—28no—
147C43—21no—
148C43—21no—
149C43D412yes—
150C43C2312yes—
151#339—28no—
152#332—28no—
153#332—28no—
154C22×Q8—22no—
155C22×Q8—22no—
156C22×Q8—22no—
157C22×Q8—22no—
158C22×Q8—21no—
159C22×Q8—21no—
160C22×Q8—48no—
161C22×Q8—41no—
162C22×Q8—41no—
163C22×Q8—41no—
164C22×Q8—41no—
165C22×Q8—41no—
166C22×Q8—41no—
167C22×Q8—41no—
168C22×Q8—41no—
169C22×Q8—44no—
170C22×Q8—44no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C2×M16—22no—
178C2×M16—41no—
179C2×M16—44no—
180C22×C8—22no—
181C22×C8—22no—
182C22×C8—41no—
183C4⋊Q8—22no—
184C4⋊Q8—22no—
185C4⋊Q8—22no—
186C4⋊Q8—22no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—22no—
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—22no—
198C4⋊Q8—22no—
199C4⋊Q8—22no—
200C4⋊Q8—22no—
201C4⋊Q8—22no—
202C4⋊Q8—22no—
203C4⋊Q8—22no—
204C4⋊Q8—22no—
205C4⋊Q8—41no—
206C4⋊Q8—41no—
207C4⋊Q8—41no—
208C4⋊Q8—41no—
209C4⋊Q8—41no—
210C4⋊Q8—41no—
211C4⋊Q8—41no—
212C4⋊Q8—41no—
213C4⋊Q8—41no—
214C4⋊Q8—41no—
215C4⋊Q8—41no—
216C4⋊Q8—41no—
217C4⋊Q8—41no—
218C4⋊Q8—41no—
219C4⋊Q8—41no—
220C4⋊Q8—41no—
221C4⋊Q8C2×D412yes—
222C4⋊Q8C2×D412yes—
223#125—22no—
224#125—22no—
225#125—41no—
226#125—41no—
227C22⋊Q8—22no—
228C22⋊Q8—22no—
229C22⋊Q8—22no—
230C22⋊Q8—22no—
231C22⋊Q8—41no—
232C22⋊Q8—41no—
233C22⋊Q8—41no—
234C22⋊Q8—41no—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—41no—
240C4×Q8—41no—
241C4×Q8—41no—
242C4×Q8—41no—
243#117—22no—
244#117—22no—
245#117—41no—
246#117—41no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
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⋊C4—41no—
272C2×C4⋊C4—41no—
273C2×C4⋊C4—41no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4C2×D414yes—
276C2×C4⋊C4C2×D414yes—
277C2×C22⋊C4—41no—
278C2×C42—28no—
279C2×C42—22no—
280C2×C42—22no—
281C2×C42—24no—
282C2×C42—24no—
283C2×C42—22no—
284C2×C42—22no—
285C2×C42—22no—
286C2×C42—44no—
287C2×C42—41no—
288C2×C42C2×D414yes—
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42C2×D411yescharacteristic
292C2×C42C2×D411yescharacteristic
293C2×C42C2×D411yescharacteristic
294C2×C42C2×D411yescharacteristic
295C2×C42C2×D411yescharacteristic
296C2×C42C2×D411yescharacteristic
297C2×C42C2×D411yescharacteristic
298C2×C42#4111yescharacteristic
299C2×C42#4111yescharacteristic
300C2×C42C2411yescharacteristic
301#107—216no—
302#106—216no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—41no—
308C4⋊C8—41no—
309C4⋊C8C2×D414yes—
310C4⋊C8C2×D414yes—
311#103—216no—
312#103—216no—
313C22⋊C8—22no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317C4×C8—22no—
318C4×C8—22no—
319C4×C8—22no—
320C4×C8—22no—
321#95—232no—
322C24#12011yescharacteristic
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8—48no—
326C2×Q8—48no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—44no—
332C2×Q8—44no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—42no—
338C2×Q8—42no—
339C2×Q8—48no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—84no—
343C2×Q8—84no—
344C2×Q8—84no—
345C2×Q8—84no—
346C2×Q8—84no—
347C2×Q8—84no—
348C2×Q8—82no—
349C2×Q8—82no—
350C2×Q8—82no—
351C2×Q8—82no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—28no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—24no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—48no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—48no—
368C22×C4#12011yescharacteristic
369C22×C4#12011yescharacteristic
370C22×C4#12011yescharacteristic
371C22×C4#12011yescharacteristic
372C22×C4#12011yescharacteristic
373C22×C4#12011yescharacteristic
374C22×C4#12011yescharacteristic
375C22×C4#12111yescharacteristic
376C22×C4#12111yescharacteristic
377C22×C4#12111yescharacteristic
378C22×C4#12111yescharacteristic
379C22×C4#12111yescharacteristic
380C22×C4#12111yescharacteristic
381C22×C4#12711yescharacteristic
382C22×C4#12711yescharacteristic
383C22×C4#13514yes—
384C22×C4#13714yes—
385C22×C4C22×D411yescharacteristic
386C22×C4C22×D411yescharacteristic
387C22×C4C22×D411yescharacteristic
388M16—44no—
389M16—82no—
390C2×C8—24no—
391C2×C8—24no—
392C2×C8—44no—
393C2×C8—44no—
394C2×C8—42no—
395C2×C8—82no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C42—28no—
427C42—28no—
428C42—24no—
429C42—24no—
430C42—44no—
431C42—44no—
432C42—42no—
433C42—42no—
434C42—44no—
435C42#12011yescharacteristic
436C42#12011yescharacteristic
437C42#12011yescharacteristic
438C42#12011yescharacteristic
439C42#12111yescharacteristic
440C42#12111yescharacteristic
441C42#12111yescharacteristic
442C42#12111yescharacteristic
443C42#12111yescharacteristic
444C42#12111yescharacteristic
445C42#12711yescharacteristic
446C42#12711yescharacteristic
447C42C22×D411yescharacteristic
448C42C22×D411yescharacteristic
449C42C22×D411yescharacteristic
450C42C2×#4111yescharacteristic
451C23—22no—
452C23—22no—
453C23#39211yescharacteristic
454C23#39211yescharacteristic
455C23#45214yes—
456C23C2×#12011yescharacteristic
457Q8—44no—
458Q8—44no—
459Q8—84no—
460Q8—84no—
461Q8—82no—
462Q8—82no—
463Q8—84no—
464Q8—82no—
465Q8—84no—
466Q8—82no—
467Q8—84no—
468Q8—84no—
469Q8—84no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—28no—
481C2×C4—44no—
482C2×C4—416no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—84no—
491C2×C4—84no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—84no—
495C2×C4—84no—
496C2×C4#39211yescharacteristic
497C2×C4#39211yescharacteristic
498C2×C4#39211yescharacteristic
499C2×C4#39211yescharacteristic
500C2×C4#39211yescharacteristic
501C2×C4#39211yescharacteristic
502C2×C4#45214yes—
503C2×C4#45414yes—
504C2×C4#45614yes—
505C2×C4#46414yes—
506C2×C4#46414yes—
507C2×C4#49512yes—
508C2×C4#49512yes—
509C2×C4#49712yes—
510C2×C4#49712yes—
511C2×C4C2×#12011yescharacteristic
512C2×C4C2×#12011yescharacteristic
513C2×C4C2×#12111yescharacteristic
514C2×C4C2×#12111yescharacteristic
515C2×C4C2×#12111yescharacteristic
516C2×C4C2×#12711yescharacteristic
517C2×C4C2×#13512yes—
518C2×C4C2×#13712yes—
519C8—44no—
520C8—44no—
521C8—82no—
522C22—28no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22#200312yes—
528C22#200512yes—
529C22#201512yes—
530C22#201512yes—
531C22C2×#39211yescharacteristic
532C22C2×#45212yes—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—48no—
538C4—84no—
539C4—82no—
540C4—82no—
541C4—84no—
542C4#200312yes—
543C4#200512yes—
544C4#201512yes—
545C4#201512yes—
546C4C2×#45412yes—
547C4C2×#45612yes—
548C4C2×#46412yes—
549C4C2×#49511yescharacteristic
550C4C2×#49711yescharacteristic
551C2—22no—
552C2—22no—
553C2#1029614yesdirect product factor
554C2C2×#200311yescharacteristic
555C2C2×#200511yescharacteristic
556C2C2×#201511yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC2×C42C24
prime radicalC24#120
LCSG ▷ C2×C42 ▷ 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
7. #10296C2direct (N × H)
553. C2#10296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#32292
C2×#28622
C2×#19942
C2×#15492
C2×#15462
#102962
C2×#12762