Finite Group Databasebeta

← #380507

Subgroups — #380507

Order 512.

892 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1921C211yesmaximal, characteristic
2#14266C211yesmaximal, characteristic
3#13783C211yesmaximal, characteristic
4#11328C211yesmaximal, characteristic
5#11316C211yesmaximal, characteristic
6#11315C211yesmaximal, characteristic
7#11293C211yesmaximal, characteristic
8#11292C211yesmaximal, characteristic
9#11256C211yesmaximal, characteristic
10#11219C211yesmaximal, characteristic
11#11219C211yesmaximal, characteristic
12#10907C211yesmaximal, characteristic
13#10884C211yesmaximal, characteristic
14#10806C211yesmaximal, characteristic
15#10796C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C2×#389C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×C4×C4⋊C4C2211yescharacteristic
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×#376C2211yescharacteristic
25#1921C418yescomplemented
26C2×#340C2211yescharacteristic
27C2×#340C2211yescharacteristic
28C2×#340C2211yescharacteristic
29C2×#340C2211yescharacteristic
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46#1445—21no—
47#1443—21no—
48#1442—21no—
49#1441—21no—
50#1436—21no—
51#1436—21no—
52C4⋊#95—21no—
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59#1434—21no—
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C42—21no—
77C22×C42—21no—
78C22×C42C2311yescharacteristic
79C22×C42C2311yescharacteristic
80C22×C42C2311yescharacteristic
81C2×#107—22no—
82C2×#107—22no—
83C2×#107—22no—
84C2×#107—41no—
85C2×#107—41no—
86C2×#107C2×C414yes—
87#389—22no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389—22no—
92#389—41no—
93#389—41no—
94#389C2×C414yes—
95C4×C4⋊C4—22no—
96C4×C4⋊C4—41no—
97C4×C4⋊C4—41no—
98C4×C4⋊C4C2×C414yes—
99#376—41no—
100#376—41no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—21no—
107C2×#95—21no—
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×#95—21no—
118C2×#95—21no—
119C2×#95D411yescharacteristic
120C2×#95D411yescharacteristic
121C2×#95D411yescharacteristic
122C2×#95D411yescharacteristic
123#340—22no—
124#340—22no—
125#340—22no—
126#340—22no—
127#340—22no—
128#340—41no—
129#340—41no—
130#340—41no—
131#340—41no—
132#340—41no—
133#340—41no—
134#340C2×C414yes—
135#340C2×C414yes—
136#340C2×C414yes—
137#336—22no—
138#336—41no—
139#336—41no—
140#336—41no—
141#336—41no—
142#336C2×C414yes—
143C23×C4—21no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4—21no—
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2411yescharacteristic
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—21no—
161C22×C8—21no—
162C22×C8—21no—
163C22×C8—21no—
164C22×C8—21no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—21no—
184C22×C8C22×C412yes—
185C22×C8C22×C412yes—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—24no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—81no—
231C2×C4⋊C4—81no—
232C2×C4⋊C4—81no—
233C2×C4⋊C4—81no—
234C2×C4⋊C4—81no—
235C2×C4⋊C4—81no—
236C2×C4⋊C4—81no—
237C2×C4⋊C4—81no—
238C2×C4⋊C4C22×C412yes—
239C2×C4⋊C4C22×C412yes—
240C2×C4⋊C4C22×C412yes—
241C2×C4⋊C4C22×C412yes—
242C2×C4⋊C4#4112yes—
243C2×C4⋊C4#4112yes—
244C2×C4⋊C4#4112yes—
245C2×C4⋊C4#4112yes—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—24no—
263C2×C42—42no—
264C2×C42—81no—
265C2×C42—81no—
266C2×C42—81no—
267C2×C42—81no—
268C2×C42C22×C412yes—
269C2×C42#4112yes—
270#107—28no—
271#107—44no—
272#95—24no—
273#95—24no—
274#95—24no—
275#95—24no—
276#95—41no—
277#95—41no—
278#95—41no—
279#95—41no—
280#95—42no—
281#95—42no—
282#95—81no—
283#95—81no—
284#95—81no—
285#95—81no—
286#95—81no—
287#95—81no—
288#95—81no—
289#95—81no—
290#95—81no—
291#95—81no—
292#95—81no—
293#95—81no—
294C24C22×D411yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4C4×D412yes—
392C22×C4C4×D412yes—
393C22×C4C23×C411yescharacteristic
394C22×C4C2×#4111yescharacteristic
395C22×C4C2×#4111yescharacteristic
396C22×C4C2×#4111yescharacteristic
397C22×C4C2×#4111yescharacteristic
398C22×C4C2×#4111yescharacteristic
399C22×C4H(5,𝔽2)11yescharacteristic
400C22×C4H(5,𝔽2)11yescharacteristic
401C22×C4H(5,𝔽2)11yescharacteristic
402C22×C42−1+411yescharacteristic
403C22×C42−1+411yescharacteristic
404C22×C42−1+411yescharacteristic
405C22×C42−1+411yescharacteristic
406C22×C42−1+411yescharacteristic
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—41no—
434C2×C8—41no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—84no—
467C4⋊C4—84no—
468C4⋊C4—84no—
469C4⋊C4—84no—
470C4⋊C4#11714yes—
471C42—22no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—41no—
476C42—41no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42—41no—
483C42—84no—
484C42—84no—
485C23C2×C4×D411yescharacteristic
486C23#52511yescharacteristic
487C23#52511yescharacteristic
488C23#53411yescharacteristic
489C23#53611yescharacteristic
490C23#53611yescharacteristic
491C23#53711yescharacteristic
492C23#57611yescharacteristic
493C23#57611yescharacteristic
494C23#57611yescharacteristic
495C23#57711yescharacteristic
496C23#57711yescharacteristic
497C23#57811yescharacteristic
498C23#57811yescharacteristic
499C23#57811yescharacteristic
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—42no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4—81no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4C2×#11711yescharacteristic
599C2×C4C4×#4111yescharacteristic
600C2×C4#51911yescharacteristic
601C2×C4#52011yescharacteristic
602C2×C4#52011yescharacteristic
603C2×C4#52011yescharacteristic
604C2×C4#52911yescharacteristic
605C2×C4#52911yescharacteristic
606C2×C4#53811yescharacteristic
607C2×C4#53911yescharacteristic
608C2×C4#53911yescharacteristic
609C2×C4#53911yescharacteristic
610C2×C4#53911yescharacteristic
611C2×C4#53911yescharacteristic
612C2×C4#54011yescharacteristic
613C2×C4#54111yescharacteristic
614C2×C4#54111yescharacteristic
615C2×C4#54111yescharacteristic
616C2×C4#54111yescharacteristic
617C2×C4#54111yescharacteristic
618C2×C4#54111yescharacteristic
619C2×C4#54111yescharacteristic
620C2×C4#54211yescharacteristic
621C2×C4#54211yescharacteristic
622C2×C4#54211yescharacteristic
623C2×C4#54211yescharacteristic
624C2×C4#54211yescharacteristic
625C2×C4#54211yescharacteristic
626C8—42no—
627C8—42no—
628C8—81no—
629C8—81no—
630C22#229011yescharacteristic
631C22#232211yescharacteristic
632C22#232311yescharacteristic
633C22#263011yescharacteristic
634C22#263411yescharacteristic
635C22#263711yescharacteristic
636C22#263811yescharacteristic
637C22#294611yescharacteristic
638C22#294611yescharacteristic
639C22#295011yescharacteristic
640C22#295111yescharacteristic
641C22#311811yescharacteristic
642C22#311911yescharacteristic
643C22#312211yescharacteristic
644C22#312411yescharacteristic
645C22#312411yescharacteristic
646C22#312511yescharacteristic
647C22#312711yescharacteristic
648C22#312711yescharacteristic
649C22#319911yescharacteristic
650C22#320111yescharacteristic
651C22#320111yescharacteristic
652C22#320311yescharacteristic
653C22#324111yescharacteristic
654C22#324111yescharacteristic
655C22#324211yescharacteristic
656C22#324211yescharacteristic
657C22#324311yescharacteristic
658C22#324311yescharacteristic
659C22#324311yescharacteristic
660C22#324311yescharacteristic
661C22#325811yescharacteristic
662C22#325811yescharacteristic
663C22#325911yescharacteristic
664C22#326211yescharacteristic
665C4—42no—
666C4—42no—
667C4—44no—
668C4—82no—
669C4—81no—
670C4—81no—
671C4—82no—
672C4—82no—
673C4—82no—
674C4—81no—
675C4—82no—
676C4—81no—
677C4—161no—
678C4—161no—
679C4#231411yescharacteristic
680C4#232011yescharacteristic
681C4#233411yescharacteristic
682C4#233611yescharacteristic
683C4#265011yescharacteristic
684C4#265411yescharacteristic
685C4#265511yescharacteristic
686C4#265511yescharacteristic
687C2#1427011yescharacteristic
688C2#2112611yescharacteristic
689C2#2113511yescharacteristic
690C2#2208711yescharacteristic
691C2#2208811yescharacteristic
692C2#2212511yescharacteristic
693C2#2212611yescharacteristic
694C2#3002911yescharacteristic
695C2#3003111yescharacteristic
696C2#3010111yescharacteristic
697C2#3010411yescharacteristic
698C2#3015911yescharacteristic
699C2#3016111yescharacteristic
700C2#3017711yescharacteristic
701C2#3018411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
25. #1921C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19212
#142662
#137832
#113282
#113162
#113152
#112932
#112922
#112562
#112192
#109072
#108842
#108062
#107962