Finite Group Databasebeta

← C2×#10377 #238255

Subgroups — C2×#10377 #238255

Order 512.

1102 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2569C211yesmaximal, characteristic
2C2×#1996C211yesmaximal, characteristic
3C2×#1520C211yesmaximal, characteristic
4C22×#328C211yesmaximal, characteristic
5#10377C218yesmaximal, direct product factor
6C2×#1294C211yesmaximal, characteristic
7C2×#1289C211yesmaximal, characteristic
8C2×#1282C211yesmaximal, characteristic
9C22×C22⋊Q8C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2569—22no—
13#2569—22no—
14#2569—22no—
15#2569C2214yes—
16C2×#400—21no—
17C2×#398—21no—
18C2×#387—21no—
19C2×#387—21no—
20C2×#385—21no—
21C2×#380—21no—
22C2×#380C2211yescharacteristic
23C2×#380C2211yescharacteristic
24C2×C4×C22⋊C4C2211yescharacteristic
25C22×#95C2211yescharacteristic
26#1996—22no—
27#1996C2214yes—
28C2×#342—21no—
29C2×#342—21no—
30#1520—22no—
31#1520C2214yes—
32C2×#328—22no—
33C2×#328—21no—
34C2×#328—21no—
35C2×#328—21no—
36C2×#328—21no—
37C2×#328C2214yes—
38#1294C2214yes—
39#1289C2214yes—
40#1282C2214yes—
41C23×Q8Q811yescharacteristic
42C24×C4—21no—
43C24×C4C2311yescharacteristic
44C23×C8—21no—
45C23×C8—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8—21no—
48C2×C22⋊Q8—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—21no—
51C2×C22⋊Q8—21no—
52C2×C22⋊Q8—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—21no—
55C2×C22⋊Q8—21no—
56C2×C22⋊Q8Q812yes—
57C2×C22⋊Q8C2312yes—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4—21no—
63C22×C4⋊C4—21no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4Q811yescharacteristic
66C22×C22⋊C4—21no—
67C22×C22⋊C4—21no—
68C22×C22⋊C4—21no—
69C22×C22⋊C4D411yescharacteristic
70C22×C22⋊C4D411yescharacteristic
71C22×C42—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8—21no—
74C2×C22⋊C8—21no—
75C2×C22⋊C8—21no—
76C2×C22⋊C8—21no—
77C2×C22⋊C8—21no—
78C2×C22⋊C8—21no—
79C2×C22⋊C8—21no—
80C2×C22⋊C8—21no—
81C2×C22⋊C8—21no—
82C2×C22⋊C8C2312yes—
83C2×C22⋊C8C2312yes—
84#400—24no—
85#400—24no—
86#398—24no—
87#398—24no—
88#387—24no—
89#387—24no—
90#387—24no—
91#387—24no—
92#385—24no—
93#385—24no—
94#380—24no—
95#380—21no—
96#380—21no—
97#380—24no—
98#380—21no—
99#380—21no—
100#380—21no—
101#380D412yes—
102#380C2312yes—
103#380C2312yes—
104C4×C22⋊C4—21no—
105C4×C22⋊C4—21no—
106C4×C22⋊C4D412yes—
107C4×C22⋊C4C2312yes—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95D412yes—
118C2×#95D411yescharacteristic
119C2×#95D411yescharacteristic
120C2×#95D411yescharacteristic
121C2×#95D411yescharacteristic
122C2×#95C2312yes—
123#342—24no—
124#342—24no—
125#328—24no—
126#328—24no—
127#328—24no—
128#328—24no—
129C25C2×D411yescharacteristic
130C22×Q8—21no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—82no—
136C22×Q8C2×Q812yes—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—22no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—44no—
148C23×C4—42no—
149C23×C4—42no—
150C23×C4—41no—
151C23×C4—82no—
152C23×C4—82no—
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4C2×Q811yescharacteristic
159C23×C4C2×Q811yescharacteristic
160C23×C4#4111yescharacteristic
161C23×C4#4111yescharacteristic
162C23×C4#4111yescharacteristic
163C23×C4#4111yescharacteristic
164C23×C4#4111yescharacteristic
165C23×C4#4111yescharacteristic
166C23×C4C2411yescharacteristic
167C22×C8—22no—
168C22×C8—22no—
169C22×C8—41no—
170C22×C8—41no—
171C22×C8—41no—
172C22×C8—41no—
173C22×C8—82no—
174C22×C8—82no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—41no—
184C22⋊Q8—41no—
185C22⋊Q8—41no—
186C22⋊Q8—41no—
187C22⋊Q8—41no—
188C22⋊Q8—41no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—82no—
213C2×C4⋊C4—82no—
214C2×C4⋊C4—82no—
215C2×C4⋊C4—82no—
216C2×C4⋊C4C2×Q812yes—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—41no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4—42no—
234C2×C22⋊C4—42no—
235C2×C22⋊C4—42no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4C2×D412yes—
238C2×C22⋊C4C2×D412yes—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—82no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—41no—
247C22⋊C8—41no—
248C22⋊C8—41no—
249C22⋊C8—41no—
250#95—24no—
251#95—24no—
252#95—24no—
253#95—24no—
254#95—22no—
255#95—21no—
256#95—21no—
257#95—22no—
258#95—21no—
259#95—21no—
260#95—22no—
261#95—22no—
262#95—22no—
263#95—41no—
264#95C2×D412yes—
265#95C2×D412yes—
266#95C2×D412yes—
267#95C2×D412yes—
268C24—42no—
269C24—42no—
270C24#12011yescharacteristic
271C24#12011yescharacteristic
272C24C22⋊Q811yescharacteristic
273C24C22⋊Q811yescharacteristic
274C24#12411yescharacteristic
275C24#12411yescharacteristic
276C24#13512yes—
277C24#13512yes—
278C24#13712yes—
279C24#13712yes—
280C24C22×D411yescharacteristic
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—82no—
286C2×Q8—82no—
287C2×Q8—82no—
288C2×Q8—82no—
289C2×Q8—82no—
290C2×Q8—82no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—44no—
307C22×C4—44no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—44no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—81no—
334C22×C4—81no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4—81no—
341C22×C4—82no—
342C22×C4—82no—
343C22×C4—88no—
344C22×C4—88no—
345C22×C4—82no—
346C22×C4—82no—
347C22×C4—82no—
348C22×C4—82no—
349C22×C4—82no—
350C22×C4#12011yescharacteristic
351C22×C4#12011yescharacteristic
352C22×C4C22⋊Q811yescharacteristic
353C22×C4C22⋊Q811yescharacteristic
354C22×C4C22⋊Q811yescharacteristic
355C22×C4C22⋊Q811yescharacteristic
356C22×C4C22⋊Q811yescharacteristic
357C22×C4C22⋊Q811yescharacteristic
358C22×C4C22⋊Q811yescharacteristic
359C22×C4C22⋊Q811yescharacteristic
360C22×C4C22⋊Q811yescharacteristic
361C22×C4C22⋊Q811yescharacteristic
362C22×C4#12411yescharacteristic
363C22×C4#12411yescharacteristic
364C22×C4#12411yescharacteristic
365C22×C4#12411yescharacteristic
366C22×C4#12411yescharacteristic
367C22×C4#12411yescharacteristic
368C22×C4#12411yescharacteristic
369C22×C4#12411yescharacteristic
370C22×C4#12411yescharacteristic
371C22×C4#12411yescharacteristic
372C22×C4C22×D411yescharacteristic
373C22×C4C22×D411yescharacteristic
374C22×C4C22×Q811yescharacteristic
375C22×C4C2×#4111yescharacteristic
376C22×C4C2×#4111yescharacteristic
377C22×C4C2×#4111yescharacteristic
378C2×C8—42no—
379C2×C8—42no—
380C2×C8—82no—
381C2×C8—82no—
382C2×C8—82no—
383C2×C8—82no—
384C2×C8—82no—
385C2×C8—82no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—48no—
389C4⋊C4—48no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—82no—
397C4⋊C4—82no—
398C4⋊C4—84no—
399C4⋊C4—84no—
400C4⋊C4—82no—
401C4⋊C4—82no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—42no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C22⋊C4—44no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—82no—
418C42—82no—
419C42—82no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—44no—
433C23—44no—
434C23—41no—
435C23—41no—
436C23—44no—
437C23—44no—
438C23#39311yescharacteristic
439C23#39311yescharacteristic
440C23#39311yescharacteristic
441C23#39311yescharacteristic
442C23#45212yes—
443C23#45212yes—
444C23#45212yes—
445C23#45212yes—
446C23#47912yes—
447C23#47912yes—
448C23#47912yes—
449C23#47912yes—
450C23#48812yes—
451C23#48812yes—
452C23#49112yes—
453C23#49112yes—
454C23C2×#12011yescharacteristic
455C23C2×C22⋊Q811yescharacteristic
456C23C2×#12411yescharacteristic
457C23C2×#13511yescharacteristic
458C23C2×#13511yescharacteristic
459C23C2×#13711yescharacteristic
460C23C2×#13711yescharacteristic
461Q8—82no—
462Q8—82no—
463Q8—82no—
464Q8—82no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—84no—
515C2×C4—84no—
516C2×C4—88no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4—84no—
521C2×C4—84no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—164no—
532C2×C4#39311yescharacteristic
533C2×C4#39311yescharacteristic
534C2×C4#39311yescharacteristic
535C2×C4#39311yescharacteristic
536C2×C4C2×C22⋊Q811yescharacteristic
537C2×C4C2×C22⋊Q811yescharacteristic
538C2×C4C2×#12411yescharacteristic
539C2×C4C2×#12411yescharacteristic
540C8—82no—
541C8—82no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—24no—
547C22—24no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22#202612yes—
571C22#202612yes—
572C22#202612yes—
573C22#202612yes—
574C22#203112yes—
575C22#203212yes—
576C22C2×#39311yescharacteristic
577C22C2×#45211yescharacteristic
578C22C2×#45211yescharacteristic
579C22C2×#47911yescharacteristic
580C22C2×#47911yescharacteristic
581C22C2×#48811yescharacteristic
582C22C2×#49111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—44no—
592C4—82no—
593C4—82no—
594C4—82no—
595C4—82no—
596C4—82no—
597C4—82no—
598C4—82no—
599C4—162no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—22no—
607C2—22no—
608C2—22no—
609C2#1037714yesdirect product factor
610C2C2×#202611yescharacteristic
611C2C2×#203111yescharacteristic
612C2C2×#203211yescharacteristic
subgroupG/H
center, socleC23#393
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×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
5. #10377C2direct (N × H)
609. C2#10377direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#25692
C2×#19962
C2×#15202
C22×#3282
#103772
C2×#12942
C2×#12892
C2×#12822