Finite Group Databasebeta

← C2×#9248 #198258

Subgroups — C2×#9248 #198258

Order 512.

1278 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#462C211yesmaximal, characteristic
2C2×Q8×M16C211yesmaximal, characteristic
3C2×#1997C211yesmaximal, characteristic
4C2×#1548C211yesmaximal, characteristic
5C2×#1487C211yesmaximal, characteristic
6#9248C218yesmaximal, direct product factor
7C2×#1292C211yesmaximal, characteristic
8C2×#1283C211yesmaximal, characteristic
9C23×Q16C412yes—
10C22×C4⋊Q8C2211yescharacteristic
11C22×C4×Q8C2211yescharacteristic
12C2×#462—21no—
13C2×#462—21no—
14C2×#462—22no—
15C2×#462—21no—
16C2×#462—21no—
17C2×#462—22no—
18C2×#462C414yes—
19C2×#462C2214yes—
20Q8×M16—22no—
21Q8×M16—22no—
22Q8×M16—22no—
23Q8×M16C2214yes—
24C2×#446—22no—
25C2×#446—21no—
26C2×C8×Q8—21no—
27C2×#431C2211yescharacteristic
28C2×#423—21no—
29C2×#423C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×#103C412yes—
33C2×C4×M16—21no—
34C2×C4×M16C2211yescharacteristic
35#1997—22no—
36#1997C2214yes—
37C2×#343—21no—
38C2×#343—21no—
39#1548—22no—
40#1548C2214yes—
41C2×#333—22no—
42#1487—22no—
43#1487C2214yes—
44C2×Q8⋊C8—21no—
45C2×Q8⋊C8—21no—
46#1292C2214yes—
47#1283C2214yes—
48C23×Q8C2×C411yescharacteristic
49C23×Q8C2×C412yes—
50C22×Q16—22no—
51C22×Q16—24no—
52C22×Q16—22no—
53C22×Q16—48no—
54C22×Q16C2×C418yes—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16D411yescharacteristic
58C22×M16D411yescharacteristic
59C23×C8C2×C412yes—
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⋊Q8C2×C412yes—
71C2×C4⋊Q8C2312yes—
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×Q8C2×C412yes—
79C2×C4×Q8D411yescharacteristic
80C2×C4×Q8D411yescharacteristic
81C2×C4×Q8D412yes—
82C2×C4×Q8D411yescharacteristic
83C2×C4×Q8D411yescharacteristic
84C2×C4×Q8D412yes—
85C2×C4×Q8C2312yes—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4C2×C411yescharacteristic
90C22×C42—21no—
91C22×C42C2311yescharacteristic
92#462—24no—
93#462—24no—
94#462—24no—
95#462—24no—
96#462—24no—
97#462—24no—
98#462—24no—
99#462—24no—
100#446—28no—
101#446—24no—
102#446—24no—
103#446—28no—
104C8×Q8—24no—
105C8×Q8—24no—
106#431—21no—
107#431—21no—
108#431—21no—
109#431C2312yes—
110#423—24no—
111#423—24no—
112#423—21no—
113#423—21no—
114#423—21no—
115#423—21no—
116#423—21no—
117#423D412yes—
118#423C2312yes—
119#423C2312yes—
120C2×C4⋊C8—22no—
121C2×C4⋊C8—22no—
122C2×C4⋊C8—21no—
123C2×C4⋊C8—21no—
124C2×C4⋊C8—21no—
125C2×C4⋊C8—21no—
126C2×C4⋊C8—21no—
127C2×C4⋊C8—21no—
128C2×C4⋊C8—21no—
129C2×C4⋊C8—21no—
130C2×C4⋊C8C2×C412yes—
131C2×C4⋊C8D412yes—
132C2×C4⋊C8C2312yes—
133C2×#103—22no—
134C2×#103—22no—
135C2×#103—24no—
136C2×#103C2×C418yes—
137C2×C22⋊C8—21no—
138C4×M16—24no—
139C4×M16—24no—
140C4×M16—21no—
141C4×M16—21no—
142C4×M16D412yes—
143C4×M16C2312yes—
144C2×#97—22no—
145C2×#97—21no—
146C2×C4×C8—22no—
147C2×C4×C8—21no—
148C2×C4×C8—21no—
149#343—24no—
150#343—24no—
151#333—28no—
152Q8⋊C8—24no—
153Q8⋊C8—24no—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8—21no—
157C22×Q8—22no—
158C22×Q8—24no—
159C22×Q8—22no—
160C22×Q8—22no—
161C22×Q8—22no—
162C22×Q8—22no—
163C22×Q8—42no—
164C22×Q8—44no—
165C22×Q8—44no—
166C22×Q8C22⋊C411yescharacteristic
167C22×Q8C22⋊C412yes—
168C22×Q8C22⋊C411yescharacteristic
169C22×Q8C22×C412yes—
170C22×Q8C22×C414yes—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4C22×C411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4#4111yescharacteristic
177C2×Q16—28no—
178C2×Q16—28no—
179C2×Q16—416no—
180C2×Q16—48no—
181C2×Q16—48no—
182C2×Q16—416no—
183C2×M16—21no—
184C2×M16—22no—
185C2×M16—22no—
186C2×M16—21no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—42no—
192C2×M16—42no—
193C2×M16—41no—
194C2×M16—42no—
195C2×M16—42no—
196C2×M16Q1614yescomplemented
197C2×M16C2×D412yes—
198C2×M16C2×D412yes—
199C22×C8—21no—
200C22×C8—22no—
201C22×C8—22no—
202C22×C8—22no—
203C22×C8—21no—
204C22×C8—44no—
205C22×C8—41no—
206C22×C8—41no—
207C22×C8C22×C414yes—
208C4⋊Q8—22no—
209C4⋊Q8—22no—
210C4⋊Q8—22no—
211C4⋊Q8—22no—
212C4⋊Q8—22no—
213C4⋊Q8—22no—
214C4⋊Q8—22no—
215C4⋊Q8—22no—
216C4⋊Q8—41no—
217C4⋊Q8—41no—
218C4⋊Q8—41no—
219C4⋊Q8—41no—
220C4⋊Q8—41no—
221C4⋊Q8—41no—
222C4⋊Q8—41no—
223C4⋊Q8—41no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—21no—
227C4×Q8—22no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—22no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—22no—
235C4×Q8—21no—
236C4×Q8—21no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×Q8C22⋊C412yes—
241C4×Q8C22⋊C412yes—
242C4×Q8C22⋊C412yes—
243C4×Q8C22⋊C412yes—
244C4×Q8C2×D412yes—
245C4×Q8C2×D412yes—
246C4×Q8C2×D412yes—
247C4×Q8C2×D412yes—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
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⋊C411yescharacteristic
272C2×C4⋊C4C22⋊C411yescharacteristic
273C2×C4⋊C4C22⋊C412yes—
274C2×C4⋊C4C22×C412yes—
275C2×C42—22no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42—22no—
279C2×C42—21no—
280C2×C42—22no—
281C2×C42—21no—
282C2×C42—22no—
283C2×C42C22×C411yescharacteristic
284C2×C42C2×D411yescharacteristic
285C2×C42C2×D411yescharacteristic
286C2×C42C2×D411yescharacteristic
287C2×C42C2×D411yescharacteristic
288C2×C42C2×D411yescharacteristic
289C2×C42C2×D411yescharacteristic
290C2×C42C2×D411yescharacteristic
291C2×C42#4111yescharacteristic
292C2×C42#4111yescharacteristic
293C2×C42#4111yescharacteristic
294C2×C42C2411yescharacteristic
295C4⋊C8—28no—
296C4⋊C8—28no—
297C4⋊C8—22no—
298C4⋊C8—22no—
299C4⋊C8—22no—
300C4⋊C8—22no—
301C4⋊C8—22no—
302C4⋊C8—22no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—41no—
308C4⋊C8—41no—
309C4⋊C8—41no—
310C4⋊C8C2×D414yes—
311#103—28no—
312#103—28no—
313C22⋊C8—22no—
314C22⋊C8—41no—
315#97—28no—
316#97—22no—
317#97—22no—
318C4×C8—28no—
319C4×C8—22no—
320C4×C8—22no—
321C4×C8—22no—
322C4×C8—41no—
323C24C4×D411yescharacteristic
324C2×Q8—22no—
325C2×Q8—21no—
326C2×Q8—22no—
327C2×Q8—21no—
328C2×Q8—22no—
329C2×Q8—24no—
330C2×Q8—24no—
331C2×Q8—24no—
332C2×Q8—24no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—44no—
336C2×Q8—42no—
337C2×Q8—42no—
338C2×Q8—44no—
339C2×Q8—44no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—44no—
343C2×Q8—44no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—84no—
349C2×Q8—84no—
350C2×Q8—84no—
351C2×Q8#10014yes—
352C2×Q8C2×C22⋊C412yes—
353C2×Q8C2×C22⋊C412yes—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—42no—
366C22×C4—44no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—82no—
370C22×C4—84no—
371C22×C4C2×C22⋊C411yescharacteristic
372C22×C4C2×C22⋊C411yescharacteristic
373C22×C4C4×D411yescharacteristic
374C22×C4C4×D411yescharacteristic
375C22×C4C4×D411yescharacteristic
376C22×C4C4×D411yescharacteristic
377C22×C4C4×D411yescharacteristic
378C22×C4#12011yescharacteristic
379C22×C4#12011yescharacteristic
380C22×C4#12111yescharacteristic
381C22×C4#12111yescharacteristic
382C22×C4#12111yescharacteristic
383C22×C4#12111yescharacteristic
384C22×C4#12311yescharacteristic
385C22×C4#12311yescharacteristic
386C22×C4C2×Q1612yes—
387C22×C4#13512yes—
388C22×C4#13712yes—
389C22×C4#13712yes—
390C22×C4C23×C411yescharacteristic
391C22×C4C22×D411yescharacteristic
392C22×C4C2×#4111yescharacteristic
393Q16—416no—
394Q16—416no—
395M16—22no—
396M16—24no—
397M16—22no—
398M16—22no—
399M16—42no—
400M16—42no—
401M16—42no—
402M16—44no—
403M16—42no—
404M16—42no—
405M16—82no—
406M16C2×Q1614yescomplemented
407C2×C8—22no—
408C2×C8—24no—
409C2×C8—24no—
410C2×C8—22no—
411C2×C8—24no—
412C2×C8—44no—
413C2×C8—44no—
414C2×C8—42no—
415C2×C8—44no—
416C2×C8—44no—
417C2×C8—42no—
418C2×C8—42no—
419C2×C8—82no—
420C2×C8—82no—
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—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—42no—
439C4⋊C4—42no—
440C4⋊C4—42no—
441C4⋊C4C2×C22⋊C412yes—
442C4⋊C4C2×C22⋊C412yes—
443C42—22no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—22no—
450C42—22no—
451C42C2×C22⋊C411yescharacteristic
452C42C2×C22⋊C411yescharacteristic
453C42C4×D411yescharacteristic
454C42C4×D411yescharacteristic
455C42#12011yescharacteristic
456C42#12011yescharacteristic
457C42#12111yescharacteristic
458C42#12111yescharacteristic
459C42#12111yescharacteristic
460C42#12111yescharacteristic
461C42#12311yescharacteristic
462C42#12311yescharacteristic
463C42C22×D411yescharacteristic
464C42C22×D411yescharacteristic
465C42C22×D411yescharacteristic
466C42C2×#4111yescharacteristic
467C23—22no—
468C23—22no—
469C23#38611yescharacteristic
470C23#38611yescharacteristic
471C23C4×Q1612yes—
472C23#44112yes—
473C23C2×C4×D411yescharacteristic
474Q8—22no—
475Q8—24no—
476Q8—22no—
477Q8—22no—
478Q8—44no—
479Q8—44no—
480Q8—42no—
481Q8—44no—
482Q8—44no—
483Q8—84no—
484Q8—84no—
485Q8—84no—
486Q8C2×#10014yes—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—84no—
514C2×C4—84no—
515C2×C4—84no—
516C2×C4#38611yescharacteristic
517C2×C4#38611yescharacteristic
518C2×C4#38611yescharacteristic
519C2×C4#38611yescharacteristic
520C2×C4#38611yescharacteristic
521C2×C4#38611yescharacteristic
522C2×C4C2×#10012yes—
523C2×C4#41312yes—
524C2×C4C4×Q1612yes—
525C2×C4#44112yes—
526C2×C4#45112yes—
527C2×C4#45112yes—
528C2×C4#45212yes—
529C2×C4#45212yes—
530C2×C4#46212yes—
531C2×C4#46212yes—
532C2×C4#46412yes—
533C2×C4#46412yes—
534C2×C4C22×C22⋊C411yescharacteristic
535C2×C4C2×C4×D411yescharacteristic
536C2×C4C2×#12011yescharacteristic
537C2×C4C2×#12111yescharacteristic
538C2×C4C2×#12111yescharacteristic
539C2×C4C2×#12311yescharacteristic
540C2×C4C22×Q1611yescharacteristic
541C2×C4C2×#13511yescharacteristic
542C2×C4C2×#13711yescharacteristic
543C2×C4C2×#13711yescharacteristic
544C8—24no—
545C8—44no—
546C8—42no—
547C8—44no—
548C8—82no—
549C8—82no—
550C22—21no—
551C22—21no—
552C22—24no—
553C22—24no—
554C22—21no—
555C22—21no—
556C22#187812yes—
557C22#187812yes—
558C22#190012yes—
559C22#190212yes—
560C22C2×#38611yescharacteristic
561C22C2×C4×Q1611yescharacteristic
562C22C2×#44111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—24no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—84no—
574C4#187812yes—
575C4#187812yes—
576C4#190012yes—
577C4C22×#10011yescharacteristic
578C4C2×#41311yescharacteristic
579C4C2×#45111yescharacteristic
580C4C2×#45211yescharacteristic
581C4C2×#46211yescharacteristic
582C4C2×#46411yescharacteristic
583C2—22no—
584C2—21no—
585C2—21no—
586C2#924814yesdirect product factor
587C2C2×#187811yescharacteristic
588C2C2×#190011yescharacteristic
589C2C2×#190211yescharacteristic
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. #9248C2direct (N × H)
196. C2×M16Q16semidirect
406. M16C2×Q16semidirect
586. C2#9248direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4622
C2×Q8×M162
C2×#19972
C2×#15482
C2×#14872
#92482
C2×#12922
C2×#12832