Finite Group Databasebeta

← #370636

Subgroups — #370636

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2569C211yesmaximal, characteristic
2#13908C211yesmaximal, characteristic
3#13802C211yesmaximal, characteristic
4#11353C212yesmaximal
5#11203C212yesmaximal
6#10912C212yesmaximal
7#10854C211yesmaximal, characteristic
8#10854C211yesmaximal, characteristic
9#10854C212yesmaximal
10#10846C211yesmaximal, characteristic
11C4×#342C211yesmaximal, characteristic
12#2569—21no—
13#2569—21no—
14#2569—22no—
15#2569—22no—
16#2569—21no—
17#2569—21no—
18C2×#400C412yescomplemented
19C2×#398C412yescomplemented
20C2×#387C412yescomplemented
21C2×#387C412yescomplemented
22C2×#385C2212yes—
23C2×#380C2211yescharacteristic
24C2×#380C2212yes—
25C2×#380C2211yescharacteristic
26C2×#380C2212yes—
27C2×#380C2211yescharacteristic
28C2×C4×C22⋊C4C2211yescharacteristic
29C2×C4×C22⋊C4C2212yes—
30C2×C4×C22⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32C22×#95C2211yescharacteristic
33C2×#342C2211yescharacteristic
34C2×#342C2212yes—
35C2×#342C2212yes—
36C2×#342C2211yescharacteristic
37C2×#342C2211yescharacteristic
38C2×#342C2211yescharacteristic
39C2×#342C2212yes—
40C2×#342C2212yes—
41C2×#342C2212yes—
42C2×#342C2212yes—
43#1444—21no—
44#1442—21no—
45#1436—22no—
46#1436—22no—
47#1434—21no—
48C22⋊#95C2212yes—
49C22⋊#95C2212yes—
50C4×#95—21no—
51C24×C4C2312yes—
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—21no—
54C22×C4⋊C4—22no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C412yes—
59C22×C4⋊C4C2×C412yes—
60C22×C4⋊C4C2×C412yes—
61C22×C22⋊C4C2312yes—
62C22×C22⋊C4C2311yescharacteristic
63C22×C22⋊C4C2311yescharacteristic
64C22×C22⋊C4C2312yes—
65C22×C22⋊C4C2311yescharacteristic
66C22×C22⋊C4C2312yes—
67C22×C22⋊C4C2311yescharacteristic
68C22×C22⋊C4C2311yescharacteristic
69C22×C22⋊C4C2311yescharacteristic
70C22×C42—21no—
71C22×C42—22no—
72C22×C42—21no—
73C22×C42C2×C412yes—
74#400—22no—
75#400—22no—
76#400—22no—
77#400—22no—
78#398—22no—
79#398—22no—
80#398—22no—
81#398—22no—
82#387—22no—
83#387—22no—
84#387—22no—
85#387—22no—
86#387—22no—
87#387—22no—
88#387—22no—
89#387—22no—
90#385—22no—
91#385—22no—
92#385—22no—
93#385—22no—
94#380—21no—
95#380—21no—
96#380—21no—
97#380—21no—
98#380—22no—
99#380—22no—
100#380—22no—
101#380—22no—
102#380—22no—
103#380—22no—
104#380—22no—
105#380—24no—
106#380—42no—
107#380Q814yes—
108C4×C22⋊C4—21no—
109C4×C22⋊C4—21no—
110C4×C22⋊C4—21no—
111C4×C22⋊C4—21no—
112C4×C22⋊C4—22no—
113C4×C22⋊C4—22no—
114C4×C22⋊C4—22no—
115C4×C22⋊C4—24no—
116C4×C22⋊C4—42no—
117C4×C22⋊C4Q814yes—
118C2×#95—21no—
119C2×#95—21no—
120C2×#95—22no—
121C2×#95—22no—
122C2×#95—22no—
123C2×#95—21no—
124C2×#95—22no—
125C2×#95—21no—
126C2×#95—22no—
127C2×#95—22no—
128C2×#95C2×C412yes—
129C2×#95C2×C412yes—
130C2×#95C2×C412yes—
131C2×#95C2×C412yes—
132C2×#95C2×C412yes—
133C2×#95C2×C411yescharacteristic
134C2×#95C2×C411yescharacteristic
135C2×#95C2×C411yescharacteristic
136C2×#95C2×C411yescharacteristic
137C2×#95C2×C412yes—
138C2×#95D411yescharacteristic
139C2×#95D411yescharacteristic
140C2×#95D412yes—
141C2×#95D412yes—
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144#342—22no—
145#342—24no—
146#342—22no—
147#342—22no—
148#342—22no—
149#342—24no—
150#342—42no—
151#342—42no—
152#342—42no—
153#342—42no—
154C25C2411yescharacteristic
155C23×C4—21no—
156C23×C4—22no—
157C23×C4—22no—
158C23×C4—22no—
159C23×C4—22no—
160C23×C4—21no—
161C23×C4—22no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—22no—
165C23×C4—44no—
166C23×C4—82no—
167C23×C4—82no—
168C23×C4C22×C412yes—
169C23×C4C22×C412yes—
170C23×C4C22×C412yes—
171C23×C4C22×C412yes—
172C23×C4C22×C412yes—
173C23×C4C22×C412yes—
174C23×C4C22×C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C2×D412yes—
177C23×C4C2×D412yes—
178C23×C4C2×D412yes—
179C23×C4C2×D412yes—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×Q812yes—
185C23×C4C2×Q812yes—
186C23×C4#4112yes—
187C23×C4#4112yes—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—44no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—82no—
205C2×C4⋊C4—82no—
206C2×C4⋊C4—82no—
207C2×C4⋊C4—82no—
208C2×C4⋊C4—82no—
209C2×C4⋊C4—82no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—22no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4C2×Q812yes—
258C2×C22⋊C4C2×Q814yes—
259C2×C22⋊C4C2×Q812yes—
260C2×C22⋊C4#4112yes—
261C2×C22⋊C4#4112yes—
262C2×C22⋊C4#4112yes—
263C2×C22⋊C4#4112yes—
264C2×C42—22no—
265C2×C42—22no—
266C2×C42—24no—
267C2×C42—44no—
268C2×C42—44no—
269C2×C42—42no—
270C2×C42—82no—
271C2×C42—82no—
272C2×C42—82no—
273C2×C42—82no—
274#95—22no—
275#95—22no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—22no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—24no—
289#95—24no—
290#95—44no—
291#95—44no—
292#95—44no—
293#95—44no—
294#95—42no—
295#95—42no—
296#95—82no—
297#95—82no—
298#95C22⋊C412yes—
299#95C22⋊C412yes—
300#95C22⋊C412yes—
301#95C22⋊C412yes—
302#95C22⋊C411yescharacteristic
303#95C22⋊C412yes—
304#95C22⋊C411yescharacteristic
305#95C22⋊C411yescharacteristic
306#95C22⋊C411yescharacteristic
307#95C22⋊C412yes—
308C24—42no—
309C24—42no—
310C24C23×C411yescharacteristic
311C24C22×D411yescharacteristic
312C24C22×D411yescharacteristic
313C24C22×Q811yescharacteristic
314C24C22×Q811yescharacteristic
315C24C2×#4111yescharacteristic
316C24C2×#4111yescharacteristic
317C24C2×#4111yescharacteristic
318C24C2×#4111yescharacteristic
319C24C2×#4111yescharacteristic
320C24C2×#4111yescharacteristic
321C24H(5,𝔽2)11yescharacteristic
322C24H(5,𝔽2)11yescharacteristic
323C242−1+411yescharacteristic
324C242−1+411yescharacteristic
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—42no—
393C22×C4—41no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4—82no—
413C22×C4—84no—
414C22×C4—84no—
415C22×C4—84no—
416C22×C4—84no—
417C22×C4C2×C22⋊C412yes—
418C22×C4C2×C22⋊C412yes—
419C22×C4C2×C22⋊C412yes—
420C22×C4C2×C22⋊C411yescharacteristic
421C22×C4C2×C22⋊C411yescharacteristic
422C22×C4C2×C22⋊C411yescharacteristic
423C22×C4C2×C22⋊C411yescharacteristic
424C22×C4C2×C22⋊C412yes—
425C22×C4C4×Q812yes—
426C22×C4C4×Q812yes—
427C22×C4C4×Q812yes—
428C22×C4C4×Q812yes—
429C22×C4C22⋊Q812yes—
430C22×C4C22⋊Q812yes—
431C22×C4C22⋊Q812yes—
432C22×C4C22⋊Q812yes—
433C22×C4#12412yes—
434C22×C4#12412yes—
435C22×C4C4⋊Q812yes—
436C22×C4C4⋊Q812yes—
437C4⋊C4—44no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—82no—
442C4⋊C4—82no—
443C4⋊C4—82no—
444C4⋊C4—82no—
445C4⋊C4—82no—
446C4⋊C4—82no—
447C4⋊C4—84no—
448C4⋊C4—88no—
449C4⋊C4—84no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C22⋊C4—42no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—41no—
474C22⋊C4—42no—
475C22⋊C4—41no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4#12514yes—
486C42—82no—
487C42—82no—
488C42—84no—
489C42—88no—
490C42—84no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23C22×C22⋊C411yescharacteristic
514C23C2×C4×Q811yescharacteristic
515C23C2×C4×Q811yescharacteristic
516C23C4×#4111yescharacteristic
517C23C4×#4111yescharacteristic
518C23#52011yescharacteristic
519C23#52011yescharacteristic
520C23C2×C22⋊Q811yescharacteristic
521C23C2×C22⋊Q811yescharacteristic
522C23C2×#12411yescharacteristic
523C23C2×#12511yescharacteristic
524C23#52911yescharacteristic
525C23#52911yescharacteristic
526C23C2×C4⋊Q811yescharacteristic
527C23#53311yescharacteristic
528C23#54011yescharacteristic
529C23#54111yescharacteristic
530C23#54411yescharacteristic
531C23#54411yescharacteristic
532C23#54611yescharacteristic
533C23#54611yescharacteristic
534C23#54711yescharacteristic
535C23#54711yescharacteristic
536C23#54811yescharacteristic
537C23#54811yescharacteristic
538C23#55011yescharacteristic
539C23#55011yescharacteristic
540C23#55211yescharacteristic
541C23#55211yescharacteristic
542C23#55311yescharacteristic
543C23#55311yescharacteristic
544C23#55411yescharacteristic
545C23#55411yescharacteristic
546C23#55711yescharacteristic
547C23#55711yescharacteristic
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—42no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—82no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—82no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4—82no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—82no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4—82no—
628C2×C4—82no—
629C2×C4—82no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4—82no—
633C2×C4—82no—
634C2×C4—82no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4#39112yes—
642C2×C4#39112yes—
643C2×C4#39112yes—
644C2×C4#39112yes—
645C2×C4#41014yes—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22C2×#39111yescharacteristic
687C22C4×#12511yescharacteristic
688C22#233011yescharacteristic
689C22#233911yescharacteristic
690C22#234111yescharacteristic
691C22#237011yescharacteristic
692C22#237011yescharacteristic
693C22#244111yescharacteristic
694C22#244211yescharacteristic
695C22#245311yescharacteristic
696C22#245411yescharacteristic
697C22#248911yescharacteristic
698C22#249011yescharacteristic
699C22#255011yescharacteristic
700C22#255211yescharacteristic
701C22C2×#41012yes—
702C22#288312yes—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—24no—
708C4—44no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—84no—
713C4—82no—
714C4—82no—
715C4—82no—
716C4—82no—
717C4—82no—
718C4—82no—
719C4—82no—
720C4—162no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—21no—
733C2#1405411yescharacteristic
734C2#2133211yescharacteristic
735C2#2133311yescharacteristic
736C2#2247712yes—
737C2#2253512yes—
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#95 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
18. C2×#400C4semidirect
19. C2×#398C4semidirect
20. C2×#387C4semidirect
21. C2×#387C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25692
#139082
#138022
#113532
#112032
#109122
#108542
#108462
C4×#3422