Finite Group Databasebeta

← #384465

Subgroups — #384465

Order 512.

916 conjugacy classes of subgroups.

The subgroup lattice has 705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1989C211yesmaximal, characteristic
2#14054C211yesmaximal, characteristic
3#13936C211yesmaximal, characteristic
4#11385C211yesmaximal, characteristic
5#11316C211yesmaximal, characteristic
6#11316C211yesmaximal, characteristic
7#11292C211yesmaximal, characteristic
8#11257C211yesmaximal, characteristic
9#11231C211yesmaximal, characteristic
10#10908C211yesmaximal, characteristic
11#10881C211yesmaximal, characteristic
12#10877C211yesmaximal, characteristic
13#10821C211yesmaximal, characteristic
14#10806C211yesmaximal, characteristic
15#10806C211yesmaximal, characteristic
16C22×#125C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×#97C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×C4×C4⋊C4C2211yescharacteristic
23#1989C418yescomplemented
24C2×#340C2211yescharacteristic
25C2×#340C2211yescharacteristic
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#1445—21no—
44#1443—21no—
45#1443—21no—
46#1441—21no—
47#1436—21no—
48C4⋊#95—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
64C2×#125—22no—
65C2×#125—22no—
66C2×#125—22no—
67C2×#125—41no—
68C2×#125—41no—
69C2×#125C2×C414yes—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4—21no—
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C42—21no—
82C22×C42—21no—
83C22×C42C2311yescharacteristic
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C2×#106—22no—
87C2×#106—41no—
88C2×#106—41no—
89C2×C4⋊C8—41no—
90C2×C4⋊C8—41no—
91C2×C4⋊C8C2×C414yes—
92C2×#97—22no—
93C2×#97—41no—
94C2×#97—41no—
95#389—22no—
96#389—41no—
97C4×C4⋊C4—22no—
98C4×C4⋊C4—22no—
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×#95D411yescharacteristic
121C2×#95D411yescharacteristic
122C2×#95D411yescharacteristic
123C2×#95D411yescharacteristic
124#340—22no—
125#340—22no—
126#340—22no—
127#340—22no—
128#340—22no—
129#340—41no—
130#340—41no—
131#340—41no—
132#340—41no—
133#340—41no—
134#340—41no—
135#340C2×C414yes—
136#340C2×C414yes—
137#340C2×C414yes—
138#340C2×C414yes—
139#336—22no—
140#336—22no—
141#336—41no—
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×C8—21no—
182C22×C8—21no—
183C22×C8C22×C412yes—
184C22×C8C22×C412yes—
185C22×C8#4112yes—
186#125—28no—
187#125—44no—
188#125—44no—
189#125—44no—
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—24no—
210C2×C4⋊C4—24no—
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—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—42no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—42no—
239C2×C4⋊C4—81no—
240C2×C4⋊C4C22×C412yes—
241C2×C4⋊C4C22×C412yes—
242C2×C4⋊C4C22×C412yes—
243C2×C4⋊C4C22×C412yes—
244C2×C4⋊C4#4112yes—
245C2×C4⋊C4#4112yes—
246C2×C4⋊C4#4112yes—
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—21no—
263C2×C42—24no—
264C2×C42—42no—
265C2×C42—42no—
266C2×C42—81no—
267C2×C42—81no—
268C2×C42—81no—
269C2×C42C22×C412yes—
270C2×C42#4112yes—
271#106—44no—
272C4⋊C8—44no—
273#97—44no—
274#95—24no—
275#95—22no—
276#95—41no—
277#95—41no—
278#95—41no—
279#95—42no—
280#95—42no—
281#95—42no—
282#95—42no—
283#95—42no—
284#95—42no—
285#95—42no—
286#95—81no—
287#95—81no—
288#95—81no—
289#95—81no—
290#95—81no—
291#95—81no—
292#95—81no—
293#95—81no—
294#95—81no—
295#95—81no—
296#95—81no—
297C24C22×D411yescharacteristic
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
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—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
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—22no—
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—21no—
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×C4—41no—
392C22×C4—41no—
393C22×C4C4×D412yes—
394C22×C4C4×D412yes—
395C22×C4#13712yes—
396C22×C4C23×C411yescharacteristic
397C22×C4C2×#4111yescharacteristic
398C22×C4C2×#4111yescharacteristic
399C22×C4C2×#4111yescharacteristic
400C22×C4C2×#4111yescharacteristic
401C22×C4C2×#4111yescharacteristic
402C22×C4H(5,𝔽2)11yescharacteristic
403C22×C4H(5,𝔽2)11yescharacteristic
404C22×C4H(5,𝔽2)11yescharacteristic
405C22×C42−1+411yescharacteristic
406C22×C42−1+411yescharacteristic
407C22×C42−1+411yescharacteristic
408C22×C42−1+411yescharacteristic
409C22×C42−1+411yescharacteristic
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
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—
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—41no—
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—22no—
449C4⋊C4—48no—
450C4⋊C4—48no—
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—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—84no—
472C4⋊C4#11714yes—
473C42—22no—
474C42—22no—
475C42—22no—
476C42—22no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42—41no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42—41no—
485C42—84no—
486C42—84no—
487C23C2×C4×D411yescharacteristic
488C23#53611yescharacteristic
489C23#53711yescharacteristic
490C23#54611yescharacteristic
491C23#54611yescharacteristic
492C23#54711yescharacteristic
493C23#54811yescharacteristic
494C23C2×#13711yescharacteristic
495C23#57511yescharacteristic
496C23#57511yescharacteristic
497C23#57511yescharacteristic
498C23#57611yescharacteristic
499C23#57711yescharacteristic
500C23#57711yescharacteristic
501C23#57711yescharacteristic
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
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—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×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—81no—
599C2×C4—81no—
600C2×C4C2×#11711yescharacteristic
601C2×C4C4×#4111yescharacteristic
602C2×C4#51811yescharacteristic
603C2×C4#51911yescharacteristic
604C2×C4#51911yescharacteristic
605C2×C4#52011yescharacteristic
606C2×C4#53811yescharacteristic
607C2×C4#53811yescharacteristic
608C2×C4#54111yescharacteristic
609C2×C4#54111yescharacteristic
610C2×C4#54111yescharacteristic
611C2×C4#54211yescharacteristic
612C2×C4#54211yescharacteristic
613C2×C4#54211yescharacteristic
614C2×C4#54211yescharacteristic
615C2×C4#54211yescharacteristic
616C2×C4#55111yescharacteristic
617C2×C4#55111yescharacteristic
618C2×C4#55211yescharacteristic
619C2×C4#55211yescharacteristic
620C2×C4#55211yescharacteristic
621C2×C4#55611yescharacteristic
622C2×C4#55611yescharacteristic
623C2×C4#55611yescharacteristic
624C2×C4#56311yescharacteristic
625C2×C4#56311yescharacteristic
626C2×C4#56311yescharacteristic
627C2×C4#56311yescharacteristic
628C8—42no—
629C8—42no—
630C8—42no—
631C8—81no—
632C22#232311yescharacteristic
633C22#234211yescharacteristic
634C22#236211yescharacteristic
635C22#269811yescharacteristic
636C22#270211yescharacteristic
637C22#271511yescharacteristic
638C22#271611yescharacteristic
639C22#294311yescharacteristic
640C22C4×#13711yescharacteristic
641C22#294611yescharacteristic
642C22#295211yescharacteristic
643C22#323611yescharacteristic
644C22#324011yescharacteristic
645C22#324111yescharacteristic
646C22#324411yescharacteristic
647C22#325211yescharacteristic
648C22#325611yescharacteristic
649C22#325711yescharacteristic
650C22#326011yescharacteristic
651C22#330711yescharacteristic
652C22#331411yescharacteristic
653C22#331711yescharacteristic
654C22#331711yescharacteristic
655C22#332111yescharacteristic
656C22#332111yescharacteristic
657C22#332211yescharacteristic
658C22#333111yescharacteristic
659C22#334411yescharacteristic
660C22#335011yescharacteristic
661C22#335111yescharacteristic
662C22#335511yescharacteristic
663C22#337011yescharacteristic
664C22#337111yescharacteristic
665C22#337111yescharacteristic
666C22#337211yescharacteristic
667C4—42no—
668C4—42no—
669C4—44no—
670C4—42no—
671C4—82no—
672C4—82no—
673C4—82no—
674C4—82no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4—161no—
679C4—161no—
680C4—161no—
681C4#232011yescharacteristic
682C4#233711yescharacteristic
683C4#235611yescharacteristic
684C4#238111yescharacteristic
685C4#275811yescharacteristic
686C4#275911yescharacteristic
687C4#276211yescharacteristic
688C4#276411yescharacteristic
689C2#1438011yescharacteristic
690C2#2212111yescharacteristic
691C2#2212211yescharacteristic
692C2#2256511yescharacteristic
693C2#2257811yescharacteristic
694C2#2307111yescharacteristic
695C2#2307811yescharacteristic
696C2#3170511yescharacteristic
697C2#3171011yescharacteristic
698C2#3182111yescharacteristic
699C2#3182611yescharacteristic
700C2#3221511yescharacteristic
701C2#3222311yescharacteristic
702C2#3224711yescharacteristic
703C2#3225511yescharacteristic
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
23. #1989C4semidirect

Maximal subgroups

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

subgroupindex
C2×#19892
#140542
#139362
#113852
#113162
#112922
#112572
#112312
#109082
#108812
#108772
#108212
#108062