Finite Group Databasebeta

← #480225

Subgroups — #480225

Order 512.

713 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60271C211yesmaximal, characteristic
2#33488C211yesmaximal, characteristic, complemented
3#33487C211yesmaximal, characteristic, complemented
4#11498C211yesmaximal, characteristic, complemented
5#11497C211yesmaximal, characteristic, complemented
6#11470C211yesmaximal, characteristic, complemented
7#11470C211yesmaximal, characteristic, complemented
8#11469C211yesmaximal, characteristic, complemented
9#11468C211yesmaximal, characteristic, complemented
10#11464C211yesmaximal, characteristic, complemented
11#11463C211yesmaximal, characteristic, complemented
12#11444C211yesmaximal, characteristic, complemented
13#11444C211yesmaximal, characteristic, complemented
14#11443C211yesmaximal, characteristic, complemented
15C2×#1323C211yesmaximal, characteristic, complemented
16#3475C411yescharacteristic
17#2994—21no—
18#2994—21no—
19#2994—21no—
20#2993—21no—
21#2992—21no—
22#2992—21no—
23#2990—21no—
24#2988—21no—
25#2962C411yescharacteristic
26#2960C2211yescharacteristic
27D4×M16C411yescharacteristic
28#2933C411yescharacteristic
29#2933C411yescharacteristic
30#2929C2211yescharacteristic
31#2929C2211yescharacteristic
32C2×C8×D4C2211yescharacteristic
33#2924C411yescharacteristic
34#2924C411yescharacteristic
35#2922C2211yescharacteristic
36#2906C411yescharacteristic
37C2×#424C2211yescharacteristic
38C2×#424C2211yescharacteristic
39#2169—21no—
40#2168—21no—
41#2168—21no—
42#2168—21no—
43#2168—21no—
44#2168—21no—
45#2168—21no—
46D4×C16—21no—
47#2163C2211yescharacteristic
48#2163C2211yescharacteristic
49#2163C2211yescharacteristic
50#2162C2211yescharacteristic
51#2112C2211yescharacteristic
52#2112C2211yescharacteristic
53#2112C2211yescharacteristic
54#2112C2211yescharacteristic
55C2×C22⋊C16C2211yescharacteristic
56C2×C22⋊C16C2211yescharacteristic
57C2×C22⋊C16C2211yescharacteristic
58C2×C22⋊C16C2211yescharacteristic
59#1323C2211yescharacteristic
60#1323C2211yescharacteristic
61#1323C2211yescharacteristic
62#1323C2211yescharacteristic
63#1323C2211yescharacteristic
64#1323C2211yescharacteristic
65#1323C2211yescharacteristic
66#1323C2211yescharacteristic
67#1323C2211yescharacteristic
68#1323C2211yescharacteristic
69#1323C2211yescharacteristic
70#1323C2211yescharacteristic
71#1315C2211yescharacteristic
72#1315C2211yescharacteristic
73#1315C2211yescharacteristic
74#1315C2211yescharacteristic
75C2×#131C2×C411yescharacteristic
76C2×#131C2×C411yescharacteristic
77C22×M16C2×C411yescharacteristic
78C22×M16C2×C411yescharacteristic
79C23×C8C2311yescharacteristic
80C23×C8C2311yescharacteristic
81#556C811yescharacteristic
82#555C811yescharacteristic
83#554C811yescharacteristic
84#553C811yescharacteristic
85#553C811yescharacteristic
86#552—21no—
87#552C811yescharacteristic
88#552C811yescharacteristic
89#551—21no—
90#551—21no—
91#547C811yescharacteristic
92#546—21no—
93#533C2×C411yescharacteristic
94#529—21no—
95#529—21no—
96#529—21no—
97#525C2×C411yescharacteristic
98#525C2×C411yescharacteristic
99C4×#41—21no—
100C4×#41C2×C411yescharacteristic
101C2×C4×D4C2×C411yescharacteristic
102C2×#117C2×C411yescharacteristic
103C2×#117C2×C411yescharacteristic
104C2×M32—21no—
105C2×M32—21no—
106C2×M32—21no—
107C2×M32—21no—
108C22×C16—21no—
109C22×C16—21no—
110C22×C16—21no—
111C22×C16—21no—
112#446—21no—
113#446—21no—
114#446—21no—
115#446—21no—
116#446—21no—
117C8×Q8—21no—
118C8×Q8—21no—
119C8×Q8—21no—
120#436—21no—
121#436—21no—
122#436—21no—
123#435—21no—
124#435—21no—
125#435—21no—
126#435—21no—
127#435—21no—
128#435—21no—
129#435—21no—
130#435—21no—
131#435—21no—
132#435—21no—
133C8×D4—21no—
134C8×D4—21no—
135C8×D4—21no—
136C8×D4—21no—
137C8×D4—21no—
138C8×D4—21no—
139C8×D4—21no—
140C8×D4D411yescharacteristic
141C8×D4D411yescharacteristic
142C8×D4D411yescharacteristic
143C8×D4D411yescharacteristic
144C8×D4D411yescharacteristic
145C8×D4D411yescharacteristic
146C8×D4D411yescharacteristic
147C8×D4D411yescharacteristic
148#433—21no—
149#433—21no—
150#433—21no—
151#433—21no—
152#433—21no—
153#433—21no—
154#432—21no—
155#432—21no—
156#431—21no—
157#431—21no—
158#431—21no—
159#431—21no—
160#424—21no—
161#424—21no—
162#424—21no—
163#424—21no—
164#424—21no—
165#424—21no—
166#424C2×C411yescharacteristic
167#424C2×C411yescharacteristic
168#424C2×C411yescharacteristic
169#424C2×C411yescharacteristic
170#424C2×C411yescharacteristic
171#424C2311yescharacteristic
172#424C2311yescharacteristic
173#424C2311yescharacteristic
174#423—21no—
175#423C2×C411yescharacteristic
176C2×C4⋊C8—21no—
177C2×C4⋊C8—21no—
178C2×C4⋊C8—21no—
179C2×C4⋊C8—21no—
180C2×C4⋊C8—21no—
181C2×C4⋊C8C2×C411yescharacteristic
182#408C2×C411yescharacteristic
183#408C2311yescharacteristic
184#407C2×C411yescharacteristic
185#407C2×C411yescharacteristic
186C2×C22⋊C8C2×C411yescharacteristic
187C2×C22⋊C8C2×C411yescharacteristic
188#405C2×C411yescharacteristic
189#405C2×C411yescharacteristic
190#405C2×C411yescharacteristic
191#405C2×C411yescharacteristic
192C4×M16C2×C411yescharacteristic
193C2×C4×C8C2311yescharacteristic
194C4⋊C16—21no—
195C4⋊C16—21no—
196C4⋊C16—21no—
197C4⋊C16—21no—
198C22⋊C16—21no—
199C22⋊C16—21no—
200C22⋊C16—21no—
201C22⋊C16—21no—
202C22⋊C16—21no—
203C22⋊C16—21no—
204C22⋊C16—21no—
205C22⋊C16—21no—
206C22⋊C16C2311yescharacteristic
207C22⋊C16C2311yescharacteristic
208C22⋊C16C2311yescharacteristic
209C22⋊C16C2311yescharacteristic
210C22⋊C16C2311yescharacteristic
211C22⋊C16C2311yescharacteristic
212C22⋊C16C2311yescharacteristic
213C22⋊C16C2311yescharacteristic
214#346—21no—
215#346—21no—
216#346—21no—
217C4×C16—21no—
218C2×#41—21no—
219C2×#41C22×C411yescharacteristic
220C22×D4M1611yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223#131—81no—
224#131—81no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—81no—
230C2×M16—81no—
231C2×M16C22×C411yescharacteristic
232C2×M16C22×C411yescharacteristic
233C2×M16C22×C411yescharacteristic
234C2×M16C22×C411yescharacteristic
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—81no—
240C22×C8—81no—
241C22×C8C22×C411yescharacteristic
242C22×C8C22×C411yescharacteristic
243C22×C8C22×C411yescharacteristic
244C22×C8C2×D411yescharacteristic
245C22×C8C2×D411yescharacteristic
246C22×C8C2×D411yescharacteristic
247C22×C8C2×D411yescharacteristic
248C22×C8C2×D411yescharacteristic
249C22×C8C2×D411yescharacteristic
250C22×C8C2×D411yescharacteristic
251C22×C8C2×D411yescharacteristic
252C22×C8C2411yescharacteristic
253C4⋊Q8C2×C811yescharacteristic
254C4⋊Q8C2×C811yescharacteristic
255#126—21no—
256#126—21no—
257#126—21no—
258#126—21no—
259#126—21no—
260#126—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264#125C2×C811yescharacteristic
265#125C2×C811yescharacteristic
266#124—21no—
267#124—21no—
268#124—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C22⋊Q8C2×C811yescharacteristic
283C22⋊Q8C2×C811yescharacteristic
284C22⋊Q8C2×C811yescharacteristic
285C22⋊Q8C2×C811yescharacteristic
286#121—21no—
287#121—21no—
288#121—21no—
289#121C2×C811yescharacteristic
290#121C2×C811yescharacteristic
291#121C2×C811yescharacteristic
292#121C2×C811yescharacteristic
293#120—21no—
294#120—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8C2×C811yescharacteristic
299C4×Q8C2×C811yescharacteristic
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4C22⋊C411yescharacteristic
310C4×D4C22⋊C411yescharacteristic
311C4×D4C22⋊C411yescharacteristic
312C4×D4C22⋊C411yescharacteristic
313C4×D4C2×C811yescharacteristic
314C4×D4C2×C811yescharacteristic
315C4×D4C2×C811yescharacteristic
316C4×D4C2×C811yescharacteristic
317C4×D4C2×C811yescharacteristic
318C4×D4C2×C811yescharacteristic
319#117—21no—
320#117—21no—
321#117—21no—
322#117—21no—
323#117—21no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117C2×C811yescharacteristic
328#117C2×C811yescharacteristic
329#117C2×C811yescharacteristic
330#117C2×C811yescharacteristic
331#117C22×C411yescharacteristic
332#117C22×C411yescharacteristic
333#117C22×C411yescharacteristic
334C2×C4⋊C4C2×C811yescharacteristic
335C2×C4⋊C4C2×C811yescharacteristic
336C2×C4⋊C4C2×C811yescharacteristic
337C2×C4⋊C4C2×C811yescharacteristic
338C2×C4⋊C4M1611yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4M1611yescharacteristic
342C2×C22⋊C4M1611yescharacteristic
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42C22×C411yescharacteristic
347M32—81no—
348M32—81no—
349M32—81no—
350M32—81no—
351C2×C16—21no—
352C2×C16—21no—
353C2×C16—21no—
354C2×C16—21no—
355C2×C16—21no—
356C2×C16—21no—
357C2×C16—21no—
358C2×C16—21no—
359C2×C16—81no—
360C2×C16—81no—
361C2×C16—81no—
362C2×C16—81no—
363C4⋊C8—21no—
364C4⋊C8—21no—
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8C22⋊C411yescharacteristic
382C4⋊C8C22⋊C411yescharacteristic
383C4⋊C8C22⋊C411yescharacteristic
384C4⋊C8C22⋊C411yescharacteristic
385C22⋊C8—21no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8C22⋊C411yescharacteristic
394C22⋊C8C22⋊C411yescharacteristic
395C22⋊C8C22⋊C411yescharacteristic
396C22⋊C8C22⋊C411yescharacteristic
397C22⋊C8C22⋊C411yescharacteristic
398C22⋊C8C22⋊C411yescharacteristic
399C22⋊C8C22⋊C411yescharacteristic
400C22⋊C8C22⋊C411yescharacteristic
401#97—21no—
402#97—21no—
403#97—21no—
404#97—21no—
405#97—21no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8C2×D411yescharacteristic
412C4×C8C2×D411yescharacteristic
413C4×C8C2×D411yescharacteristic
414C4×C8C2×D411yescharacteristic
415C24C2×M1611yescharacteristic
416C24C2×M1611yescharacteristic
417#41—41no—
418#41—41no—
419#41—44no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8C22×C811yescharacteristic
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—42no—
429C2×D4C22⋊C811yescharacteristic
430C2×D4C22⋊C811yescharacteristic
431C2×D4C22⋊C811yescharacteristic
432C2×D4C22⋊C811yescharacteristic
433C2×D4C22×C811yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×C22⋊C411yescharacteristic
446C22×C4C2×C22⋊C411yescharacteristic
447C22×C4C2×C22⋊C411yescharacteristic
448C22×C4C2×C22⋊C411yescharacteristic
449C22×C4C22×C811yescharacteristic
450C22×C4C22×C811yescharacteristic
451C22×C4C22×C811yescharacteristic
452C22×C4C22×C811yescharacteristic
453C22×C4C2×M1611yescharacteristic
454C22×C4C2×M1611yescharacteristic
455C22×C4C2×M1611yescharacteristic
456C22×C4C2×M1611yescharacteristic
457C22×C4C23×C411yescharacteristic
458M16—41no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—81no—
463M16—81no—
464M16—81no—
465M16—81no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—81no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8C2×C22⋊C411yescharacteristic
487C2×C8C2×C22⋊C411yescharacteristic
488C2×C8C2×C22⋊C411yescharacteristic
489C2×C8C2×C22⋊C411yescharacteristic
490C2×C8C2×C22⋊C411yescharacteristic
491C2×C8C2×C22⋊C411yescharacteristic
492C2×C8C22×D411yescharacteristic
493C2×C8C22×D411yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4C22⋊C811yescharacteristic
511C4⋊C4C22⋊C811yescharacteristic
512C4⋊C4C22⋊C811yescharacteristic
513C4⋊C4C22⋊C811yescharacteristic
514C4⋊C4C22×C811yescharacteristic
515C4⋊C4C22×C811yescharacteristic
516C4⋊C4C22×C811yescharacteristic
517C4⋊C4C22×C811yescharacteristic
518C4⋊C4C22×C811yescharacteristic
519C4⋊C4C22×C811yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4C22⋊C811yescharacteristic
538C22⋊C4C22⋊C811yescharacteristic
539C22⋊C4C22⋊C811yescharacteristic
540C22⋊C4C22⋊C811yescharacteristic
541C22⋊C4C22⋊C811yescharacteristic
542C22⋊C4C22⋊C811yescharacteristic
543C22⋊C4C22⋊C811yescharacteristic
544C22⋊C4C22⋊C811yescharacteristic
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42C2×C22⋊C411yescharacteristic
555C42C2×C22⋊C411yescharacteristic
556C42C22×C811yescharacteristic
557C42C22×C811yescharacteristic
558C16—41no—
559C16—41no—
560C16—41no—
561C16—41no—
562C16—41no—
563C16—41no—
564C16—41no—
565C16—41no—
566C23—22no—
567C23—21no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C2×C22⋊C811yescharacteristic
574C23C2×C22⋊C811yescharacteristic
575C23C2×C22⋊C811yescharacteristic
576C23C2×C22⋊C811yescharacteristic
577C23C22×M1611yescharacteristic
578Q8—41no—
579Q8—42no—
580Q8—81no—
581D4—22no—
582D4—22no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—81no—
590D4—81no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4C2×C22⋊C811yescharacteristic
625C2×C4C2×C22⋊C811yescharacteristic
626C2×C4C2×C22⋊C811yescharacteristic
627C2×C4C2×C22⋊C811yescharacteristic
628C2×C4C2×C22⋊C811yescharacteristic
629C2×C4C2×C22⋊C811yescharacteristic
630C2×C4C2×C22⋊C811yescharacteristic
631C2×C4C2×C22⋊C811yescharacteristic
632C2×C4C22×C22⋊C411yescharacteristic
633C2×C4C23×C811yescharacteristic
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—21no—
642C8—41no—
643C8—41no—
644C8—41no—
645C8—41no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—82no—
664C22—82no—
665C22#211712yes—
666C22C22×C22⋊C811yescharacteristic
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4#288311yescharacteristic
684C4#288911yescharacteristic
685C2—22no—
686C2—41no—
687C2—41no—
688C2—41no—
689C2—41no—
690C2—81no—
691C2#1735111yescharacteristic
692C2C2×#211711yescharacteristic
693C2#3334011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊C4
commutatorC2×C4C23×C8
Frattini, cosocleC22×C8C24
socleC22C22×C22⋊C8
prime radical#3475C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C8×D4 ◁ G
LECSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33488C2semidirect
3. #33487C2semidirect
4. #11498C2semidirect
5. #11497C2semidirect
6. #11470C2semidirect
7. #11470C2semidirect
8. #11469C2semidirect
9. #11468C2semidirect
10. #11464C2semidirect
11. #11463C2semidirect
12. #11444C2semidirect
13. #11444C2semidirect
14. #11443C2semidirect
15. C2×#1323C2semidirect

Maximal subgroups

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

subgroupindex
#602712
#334882
#334872
#114982
#114972
#114702
#114692
#114682
#114642
#114632
#114442
#114432
C2×#13232