Finite Group Databasebeta

← #384739

Subgroups — #384739

Order 512.

878 conjugacy classes of subgroups.

The subgroup lattice has 697 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1949C211yesmaximal, characteristic
2#14050C211yesmaximal, characteristic
3#13936C211yesmaximal, characteristic
4#11379C211yesmaximal, characteristic
5#11358C211yesmaximal, characteristic
6#11316C211yesmaximal, characteristic
7#11293C211yesmaximal, characteristic
8#11232C211yesmaximal, characteristic
9#11220C211yesmaximal, characteristic
10#10907C211yesmaximal, characteristic
11#10907C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic
13#10863C211yesmaximal, characteristic
14#10821C211yesmaximal, characteristic
15#10806C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×#97C2211yescharacteristic
21C2×#389C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25#1949C418yescomplemented
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×#336C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43#1443—21no—
44#1443—21no—
45#1443—21no—
46#1443—21no—
47#1436—21no—
48#1436—21no—
49C4⋊#95C2211yescharacteristic
50C4⋊#95C2211yescharacteristic
51C4⋊#95C2211yescharacteristic
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57#1434—21no—
58#1434—21no—
59C4×#95C2211yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C22×C4⋊C4—21no—
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C4⋊C4C2311yescharacteristic
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C42—21no—
74C22×C42—21no—
75C22×C42C2311yescharacteristic
76C22×C42C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C2×#107—22no—
79C2×#107—22no—
80C2×#107—41no—
81C2×#107—41no—
82C2×#107—41no—
83C2×#107C2×C414yes—
84C2×#106—41no—
85C2×#106—41no—
86C2×#106C2×C414yes—
87C2×C4⋊C8—22no—
88C2×C4⋊C8—22no—
89C2×C4⋊C8C2×C414yes—
90C2×#97—22no—
91C2×#97—22no—
92C2×#97—41no—
93#389—41no—
94#389—41no—
95#382—22no—
96#382C2×C414yes—
97C4×C4⋊C4—22no—
98C4×C4⋊C4—41no—
99C4×C4⋊C4—41no—
100C4×C4⋊C4C2×C414yes—
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×#95—21no—
120C2×#95—21no—
121C2×#95—21no—
122C2×#95D411yescharacteristic
123C2×#95D411yescharacteristic
124C2×#95D411yescharacteristic
125C2×#95D411yescharacteristic
126#340—22no—
127#340—22no—
128#340—22no—
129#340—22no—
130#340—41no—
131#340—41no—
132#340—41no—
133#340—41no—
134#340—41no—
135#340—41no—
136#340—41no—
137#340C2×C414yes—
138#340C2×C414yes—
139#336—22no—
140#336—22no—
141#336—22no—
142#336—41no—
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×C8C22×C412yes—
182C22×C8C22×C412yes—
183C22×C8#4112yes—
184C22×C8#4112yes—
185C22×C8#4112yes—
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—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4C22×C412yes—
233C2×C4⋊C4C22×C412yes—
234C2×C4⋊C4C22×C412yes—
235C2×C4⋊C4C22×C412yes—
236C2×C4⋊C4#4112yes—
237C2×C42—21no—
238C2×C42—21no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—24no—
254C2×C42—42no—
255C2×C42—81no—
256C2×C42—81no—
257C2×C42—81no—
258C2×C42—81no—
259C2×C42C22×C412yes—
260C2×C42#4112yes—
261#107—44no—
262#107—44no—
263#106—44no—
264C4⋊C8—28no—
265#97—44no—
266#95—24no—
267#95—24no—
268#95—24no—
269#95—22no—
270#95—41no—
271#95—41no—
272#95—41no—
273#95—42no—
274#95—42no—
275#95—42no—
276#95—42no—
277#95—42no—
278#95—42no—
279#95—42no—
280#95—81no—
281#95—81no—
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—
291C24C22×D411yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
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—22no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—22no—
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—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
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×C4C4×D412yes—
388C22×C4C4×D412yes—
389C22×C4#13712yes—
390C22×C4C23×C411yescharacteristic
391C22×C4C2×#4111yescharacteristic
392C22×C4C2×#4111yescharacteristic
393C22×C4C2×#4111yescharacteristic
394C22×C4C2×#4111yescharacteristic
395C22×C4C2×#4111yescharacteristic
396C22×C4H(5,𝔽2)11yescharacteristic
397C22×C4H(5,𝔽2)11yescharacteristic
398C22×C4H(5,𝔽2)11yescharacteristic
399C22×C42−1+411yescharacteristic
400C22×C42−1+411yescharacteristic
401C22×C42−1+411yescharacteristic
402C22×C42−1+411yescharacteristic
403C22×C42−1+411yescharacteristic
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
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#11714yes—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—41no—
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—84no—
465C42—22no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—41no—
470C42—41no—
471C42—41no—
472C42—41no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42—41no—
477C42—84no—
478C42—84no—
479C23C2×C4×D411yescharacteristic
480C23#53511yescharacteristic
481C23#53711yescharacteristic
482C23#54711yescharacteristic
483C23#54711yescharacteristic
484C23#54711yescharacteristic
485C23#54811yescharacteristic
486C23C2×#13711yescharacteristic
487C23#57511yescharacteristic
488C23#57511yescharacteristic
489C23#57511yescharacteristic
490C23#57611yescharacteristic
491C23#57611yescharacteristic
492C23#57711yescharacteristic
493C23#57811yescharacteristic
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
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×C4C2×#11711yescharacteristic
593C2×C4C4×#4111yescharacteristic
594C2×C4#51811yescharacteristic
595C2×C4#51911yescharacteristic
596C2×C4#51911yescharacteristic
597C2×C4#52011yescharacteristic
598C2×C4#53911yescharacteristic
599C2×C4#53911yescharacteristic
600C2×C4#54011yescharacteristic
601C2×C4#54111yescharacteristic
602C2×C4#54111yescharacteristic
603C2×C4#54111yescharacteristic
604C2×C4#54111yescharacteristic
605C2×C4#54211yescharacteristic
606C2×C4#54211yescharacteristic
607C2×C4#54211yescharacteristic
608C2×C4#55111yescharacteristic
609C2×C4#55111yescharacteristic
610C2×C4#55211yescharacteristic
611C2×C4#55211yescharacteristic
612C2×C4#55211yescharacteristic
613C2×C4#55311yescharacteristic
614C2×C4#55311yescharacteristic
615C2×C4#55611yescharacteristic
616C2×C4#56311yescharacteristic
617C2×C4#56311yescharacteristic
618C2×C4#56311yescharacteristic
619C2×C4#56311yescharacteristic
620C8—24no—
621C8—42no—
622C8—42no—
623C8—81no—
624C22#232411yescharacteristic
625C22#234411yescharacteristic
626C22#236211yescharacteristic
627C22#271811yescharacteristic
628C22#272211yescharacteristic
629C22#272311yescharacteristic
630C22#272511yescharacteristic
631C22#294311yescharacteristic
632C22C4×#13711yescharacteristic
633C22#294611yescharacteristic
634C22#295111yescharacteristic
635C22#321511yescharacteristic
636C22#321911yescharacteristic
637C22#322011yescharacteristic
638C22#322511yescharacteristic
639C22#325211yescharacteristic
640C22#325611yescharacteristic
641C22#325711yescharacteristic
642C22#326211yescharacteristic
643C22#334611yescharacteristic
644C22#334611yescharacteristic
645C22#334711yescharacteristic
646C22#334711yescharacteristic
647C22#334911yescharacteristic
648C22#334911yescharacteristic
649C22#334911yescharacteristic
650C22#335011yescharacteristic
651C22#335111yescharacteristic
652C22#335511yescharacteristic
653C22#335511yescharacteristic
654C22#335611yescharacteristic
655C22#337011yescharacteristic
656C22#337011yescharacteristic
657C22#337111yescharacteristic
658C22#337411yescharacteristic
659C4—42no—
660C4—42no—
661C4—42no—
662C4—82no—
663C4—81no—
664C4—82no—
665C4—82no—
666C4—82no—
667C4—81no—
668C4—81no—
669C4—82no—
670C4—161no—
671C4—161no—
672C4—161no—
673C4#232011yescharacteristic
674C4#233611yescharacteristic
675C4#235311yescharacteristic
676C4#238111yescharacteristic
677C4#273811yescharacteristic
678C4#275811yescharacteristic
679C4#276611yescharacteristic
680C4#277711yescharacteristic
681C2#1438811yescharacteristic
682C2#2215611yescharacteristic
683C2#2215711yescharacteristic
684C2#2261611yescharacteristic
685C2#2262311yescharacteristic
686C2#2307111yescharacteristic
687C2#2307411yescharacteristic
688C2#3229411yescharacteristic
689C2#3230311yescharacteristic
690C2#3241611yescharacteristic
691C2#3242111yescharacteristic
692C2#3244311yescharacteristic
693C2#3245111yescharacteristic
694C2#3249111yescharacteristic
695C2#3249611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
25. #1949C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19492
#140502
#139362
#113792
#113582
#113162
#112932
#112322
#112202
#109072
#108772
#108632
#108212
#108062