Finite Group Databasebeta

← #481252

Subgroups — #481252

Order 512.

674 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60330C211yesmaximal, characteristic
2#33503C211yesmaximal, characteristic, complemented
3#33479C211yesmaximal, characteristic, complemented
4#11640C211yesmaximal, characteristic, complemented
5#11639C211yesmaximal, characteristic, complemented
6#11638C211yesmaximal, characteristic, complemented
7#11624C211yesmaximal, characteristic, complemented
8#11623C211yesmaximal, characteristic, complemented
9#11622C211yesmaximal, characteristic, complemented
10#11616C211yesmaximal, characteristic, complemented
11#11615C211yesmaximal, characteristic, complemented
12#11614C211yesmaximal, characteristic, complemented
13#11608C211yesmaximal, characteristic, complemented
14#11607C211yesmaximal, characteristic, complemented
15#11606C211yesmaximal, characteristic, complemented
16#3461C411yescharacteristic
17#2993—21no—
18#2993C411yescharacteristic
19#2993C411yescharacteristic
20#2992—21no—
21#2992—21no—
22#2989C411yescharacteristic
23#2989C411yescharacteristic
24#2985—21no—
25#2985C411yescharacteristic
26#2985C411yescharacteristic
27#2983C411yescharacteristic
28#2966—21no—
29#2966—21no—
30#2966—21no—
31#2966C2211yescharacteristic
32#2966C2211yescharacteristic
33C8×#41C2211yescharacteristic
34C8×#41C2211yescharacteristic
35#2960—21no—
36#2960C2211yescharacteristic
37#2960C2211yescharacteristic
38C2×C8×Q8C2211yescharacteristic
39#2183—21no—
40#2183—21no—
41#2169—21no—
42#2169—21no—
43#2168—21no—
44#2168—21no—
45#2168—21no—
46#2168—21no—
47#2163C2211yescharacteristic
48#2163C2211yescharacteristic
49#2162C2211yescharacteristic
50#2162C2211yescharacteristic
51#2162C2211yescharacteristic
52#2162C2211yescharacteristic
53#2150C2211yescharacteristic
54#2150C2211yescharacteristic
55C2×C4⋊C16C2211yescharacteristic
56C4×M32C2211yescharacteristic
57C4×M32C2211yescharacteristic
58C2×C4×C16C2211yescharacteristic
59Q8⋊C16C2211yescharacteristic
60Q8⋊C16C2211yescharacteristic
61Q8⋊C16C2211yescharacteristic
62Q8⋊C16C2211yescharacteristic
63Q8⋊C16C2211yescharacteristic
64Q8⋊C16C2211yescharacteristic
65Q8⋊C16C2211yescharacteristic
66Q8⋊C16C2211yescharacteristic
67Q8⋊C16C2211yescharacteristic
68Q8⋊C16C2211yescharacteristic
69Q8⋊C16C2211yescharacteristic
70Q8⋊C16C2211yescharacteristic
71D4⋊C16C2211yescharacteristic
72D4⋊C16C2211yescharacteristic
73D4⋊C16C2211yescharacteristic
74D4⋊C16C2211yescharacteristic
75#544C811yescharacteristic
76#542—21no—
77#542C811yescharacteristic
78#542C811yescharacteristic
79#541—21no—
80#541C811yescharacteristic
81#541C811yescharacteristic
82#539—21no—
83#539—21no—
84#537C811yescharacteristic
85#536C811yescharacteristic
86#536C811yescharacteristic
87#533—21no—
88#533C2×C411yescharacteristic
89#533C2×C411yescharacteristic
90#529—21no—
91#529—21no—
92#529—21no—
93#529C2×C411yescharacteristic
94#529C2×C411yescharacteristic
95C4×#41C2×C411yescharacteristic
96C4×#41C2×C411yescharacteristic
97C2×C4×Q8C2×C411yescharacteristic
98C2×M32—21no—
99C2×M32—21no—
100C2×M32—21no—
101C2×M32—21no—
102C22×C16—21no—
103C22×C16—21no—
104#446—21no—
105#446—21no—
106#446—21no—
107#446—21no—
108#446—21no—
109#446—21no—
110#446—21no—
111#446—21no—
112#446—21no—
113#446C2×C411yescharacteristic
114#446C2×C411yescharacteristic
115#446C2×C411yescharacteristic
116#446C2×C411yescharacteristic
117#446C2×C411yescharacteristic
118#446C2×C411yescharacteristic
119C8×Q8—21no—
120C8×Q8—21no—
121C8×Q8—21no—
122C8×Q8—21no—
123C8×Q8C2×C411yescharacteristic
124C8×Q8C2×C411yescharacteristic
125C8×Q8C2×C411yescharacteristic
126C8×Q8D411yescharacteristic
127C8×Q8D411yescharacteristic
128C8×Q8C2311yescharacteristic
129C8×Q8C2311yescharacteristic
130C8×Q8C2311yescharacteristic
131#436—21no—
132#436—21no—
133#436—21no—
134#436C2×C411yescharacteristic
135#436C2×C411yescharacteristic
136#435—21no—
137#435—21no—
138#435—21no—
139#435—21no—
140#435—21no—
141#435—21no—
142#435—21no—
143#435—21no—
144C8×D4—21no—
145C8×D4—21no—
146C8×D4—21no—
147C8×D4—21no—
148C8×D4C2×C411yescharacteristic
149C8×D4D411yescharacteristic
150C8×D4D411yescharacteristic
151C8×D4D411yescharacteristic
152C8×D4D411yescharacteristic
153C8×D4D411yescharacteristic
154C8×D4D411yescharacteristic
155C8×D4C2311yescharacteristic
156#433—21no—
157#433—21no—
158#433—21no—
159#433—21no—
160#433—21no—
161#433—21no—
162#433—21no—
163#433—21no—
164#432—21no—
165#432—21no—
166#432—21no—
167#432C2×C411yescharacteristic
168#432C2×C411yescharacteristic
169#431—21no—
170#431C2×C411yescharacteristic
171#431C2×C411yescharacteristic
172#431C2×C411yescharacteristic
173#431C2×C411yescharacteristic
174#424—21no—
175#424—21no—
176#424—21no—
177#424—21no—
178#423—21no—
179#423C2×C411yescharacteristic
180#423C2×C411yescharacteristic
181C2×C4⋊C8—21no—
182C2×C4⋊C8C2×C411yescharacteristic
183#405—21no—
184#405—21no—
185#405—21no—
186#405—21no—
187C2×C4×C8—21no—
188C2×C4×C8—21no—
189C2×C4×C8C2311yescharacteristic
190C2×C4×C8C2311yescharacteristic
191C2×C4×C8C2311yescharacteristic
192C4⋊C16—21no—
193C4⋊C16—21no—
194C4⋊C16—21no—
195C4⋊C16—21no—
196C4⋊C16—21no—
197C4⋊C16—21no—
198C4⋊C16C2311yescharacteristic
199C4⋊C16C2311yescharacteristic
200C4⋊C16C2311yescharacteristic
201C4⋊C16C2311yescharacteristic
202C22⋊C16—21no—
203C22⋊C16—21no—
204C22⋊C16—21no—
205C22⋊C16—21no—
206C22⋊C16—21no—
207C22⋊C16—21no—
208#346—21no—
209#346—21no—
210#346—21no—
211#346—21no—
212C4×C16—21no—
213C4×C16—21no—
214C4×C16C2311yescharacteristic
215C4×C16C2311yescharacteristic
216C4×C16C2311yescharacteristic
217C4×C16C2311yescharacteristic
218C2×#41C2×C811yescharacteristic
219C2×#41C2×C811yescharacteristic
220C22×Q8C2×C811yescharacteristic
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C2×D411yescharacteristic
229C22×C8C2×D411yescharacteristic
230C22×C8C2×D411yescharacteristic
231C22×C8C2×D411yescharacteristic
232C22×C8C2×D411yescharacteristic
233C22×C8C2×D411yescharacteristic
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8C2×C811yescharacteristic
237C4⋊Q8C2×C811yescharacteristic
238C4⋊Q8C2×C811yescharacteristic
239C4⋊Q8C2×C811yescharacteristic
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#126—21no—
248#125—21no—
249#125—21no—
250#125—21no—
251#125—21no—
252#125—21no—
253#125—21no—
254#125—21no—
255#125C2×C811yescharacteristic
256#125C2×C811yescharacteristic
257#124—21no—
258#124—21no—
259#124—21no—
260#124C2×C811yescharacteristic
261#124C2×C811yescharacteristic
262#123—21no—
263#123—21no—
264#123—21no—
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8C2×C811yescharacteristic
280C22⋊Q8C2×C811yescharacteristic
281C22⋊Q8C2×C811yescharacteristic
282C22⋊Q8C2×C811yescharacteristic
283C22⋊Q8C2×C811yescharacteristic
284C22⋊Q8C2×C811yescharacteristic
285#121—21no—
286#121—21no—
287#121—21no—
288#121C2×C811yescharacteristic
289#121C2×C811yescharacteristic
290C4×Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8C22⋊C411yescharacteristic
295C4×Q8C2×C811yescharacteristic
296C4×Q8C2×C811yescharacteristic
297C4×Q8C2×C811yescharacteristic
298C4×Q8M1611yescharacteristic
299C4×Q8C22×C411yescharacteristic
300C4×Q8C22×C411yescharacteristic
301C4×Q8C22×C411yescharacteristic
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4C22⋊C411yescharacteristic
307C4×D4C22⋊C411yescharacteristic
308C4×D4C22⋊C411yescharacteristic
309C4×D4C2×C811yescharacteristic
310C4×D4M1611yescharacteristic
311C4×D4M1611yescharacteristic
312C4×D4M1611yescharacteristic
313C4×D4C22×C411yescharacteristic
314#117—21no—
315#117—21no—
316#117—21no—
317#117—21no—
318#117—21no—
319#117C2×C811yescharacteristic
320#117C2×C811yescharacteristic
321#117C2×C811yescharacteristic
322#117C2×C811yescharacteristic
323C2×C4⋊C4—21no—
324C2×C4⋊C4C2×C811yescharacteristic
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C22×C411yescharacteristic
328C2×C42C22×C411yescharacteristic
329C2×C42C22×C411yescharacteristic
330M32—42no—
331M32—42no—
332M32—81no—
333M32—81no—
334C2×C16—21no—
335C2×C16—21no—
336C2×C16—21no—
337C2×C16—21no—
338C2×C16—21no—
339C2×C16—21no—
340C2×C16—21no—
341C2×C16—21no—
342C2×C16—42no—
343C2×C16—81no—
344C4⋊C8—21no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8C22⋊C411yescharacteristic
360C4⋊C8C22⋊C411yescharacteristic
361C4⋊C8C22⋊C411yescharacteristic
362C4⋊C8C22⋊C411yescharacteristic
363C4⋊C8C22⋊C411yescharacteristic
364C4⋊C8C22⋊C411yescharacteristic
365C4⋊C8C22×C411yescharacteristic
366C4⋊C8C22×C411yescharacteristic
367C4⋊C8C22×C411yescharacteristic
368C4⋊C8C22×C411yescharacteristic
369C22⋊C8—21no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8C22⋊C411yescharacteristic
377C22⋊C8C22⋊C411yescharacteristic
378C22⋊C8C22⋊C411yescharacteristic
379C22⋊C8C22⋊C411yescharacteristic
380C22⋊C8C22⋊C411yescharacteristic
381C22⋊C8C22⋊C411yescharacteristic
382#97—21no—
383#97—21no—
384#97—21no—
385#97—21no—
386#97—21no—
387#97—21no—
388#97—21no—
389#97—21no—
390C4×C8—21no—
391C4×C8—21no—
392C4×C8—21no—
393C4×C8—21no—
394C4×C8—21no—
395C4×C8—21no—
396C4×C8—21no—
397C4×C8C22×C411yescharacteristic
398C4×C8C22×C411yescharacteristic
399C4×C8C22×C411yescharacteristic
400C4×C8C2×D411yescharacteristic
401C4×C8C2×D411yescharacteristic
402C4×C8C2×D411yescharacteristic
403C4×C8C2×D411yescharacteristic
404C4×C8C2×D411yescharacteristic
405C4×C8C2×D411yescharacteristic
406C4×C8C2411yescharacteristic
407#41—42no—
408#41—42no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—42no—
413C2×Q8C22⋊C811yescharacteristic
414C2×Q8C22×C811yescharacteristic
415C2×Q8C22×C811yescharacteristic
416C2×Q8C22×C811yescharacteristic
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4C22⋊C811yescharacteristic
421C2×D4C22⋊C811yescharacteristic
422C2×D4C22⋊C811yescharacteristic
423C2×D4C22×C811yescharacteristic
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4C2×C22⋊C411yescharacteristic
430C22×C4C2×C22⋊C411yescharacteristic
431C22×C4C2×C22⋊C411yescharacteristic
432C22×C4C22×C811yescharacteristic
433C22×C4C22×C811yescharacteristic
434C22×C4C22×C811yescharacteristic
435C22×C4C2×M1611yescharacteristic
436C22×C4C2×M1611yescharacteristic
437C22×C4C2×M1611yescharacteristic
438M16—81no—
439M16—81no—
440M16—81no—
441M16—81no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8C2×C22⋊C411yescharacteristic
460C2×C8C2×C22⋊C411yescharacteristic
461C2×C8C2×C22⋊C411yescharacteristic
462C2×C8C2×C22⋊C411yescharacteristic
463C2×C8C2×C22⋊C411yescharacteristic
464C2×C8C2×C22⋊C411yescharacteristic
465C2×C8C22×D411yescharacteristic
466C2×C8C22×D411yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4C22⋊C811yescharacteristic
491C4⋊C4C22⋊C811yescharacteristic
492C4⋊C4C22⋊C811yescharacteristic
493C4⋊C4C22⋊C811yescharacteristic
494C4⋊C4C22⋊C811yescharacteristic
495C4⋊C4C22⋊C811yescharacteristic
496C4⋊C4C22×C811yescharacteristic
497C4⋊C4C22×C811yescharacteristic
498C4⋊C4C22×C811yescharacteristic
499C4⋊C4C22×C811yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4C22⋊C811yescharacteristic
516C22⋊C4C22⋊C811yescharacteristic
517C22⋊C4C22⋊C811yescharacteristic
518C22⋊C4C22⋊C811yescharacteristic
519C22⋊C4C22⋊C811yescharacteristic
520C22⋊C4C22⋊C811yescharacteristic
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42C2×C22⋊C411yescharacteristic
529C42C2×C22⋊C411yescharacteristic
530C42C2×C22⋊C411yescharacteristic
531C42C22×C811yescharacteristic
532C42C22×C811yescharacteristic
533C42C22×C811yescharacteristic
534C42C2×M1611yescharacteristic
535C42C2×M1611yescharacteristic
536C42C2×M1611yescharacteristic
537C42C23×C411yescharacteristic
538C16—22no—
539C16—41no—
540C16—41no—
541C16—41no—
542C16—41no—
543C16—41no—
544C16—41no—
545C16—41no—
546C23—21no—
547C23C2×C22⋊C811yescharacteristic
548C23C2×C22⋊C811yescharacteristic
549C23C2×C22⋊C811yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—42no—
555Q8—81no—
556Q8—81no—
557D4—22no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—42no—
562D4—81no—
563D4—81no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—81no—
588C2×C4—81no—
589C2×C4C2×C22⋊C811yescharacteristic
590C2×C4C2×C22⋊C811yescharacteristic
591C2×C4C2×C22⋊C811yescharacteristic
592C2×C4C2×C22⋊C811yescharacteristic
593C2×C4C2×C22⋊C811yescharacteristic
594C2×C4C2×C22⋊C811yescharacteristic
595C2×C4C2×C22⋊C811yescharacteristic
596C2×C4C2×C22⋊C811yescharacteristic
597C2×C4C2×C22⋊C811yescharacteristic
598C2×C4C22×C22⋊C411yescharacteristic
599C2×C4C23×C811yescharacteristic
600C2×C4C22×M1611yescharacteristic
601C8—21no—
602C8—21no—
603C8—21no—
604C8—21no—
605C8—21no—
606C8—21no—
607C8—21no—
608C8—41no—
609C8—41no—
610C8—41no—
611C8—41no—
612C8#57711yescharacteristic
613C8#57811yescharacteristic
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22C22×C22⋊C811yescharacteristic
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4#289811yescharacteristic
645C4#290111yescharacteristic
646C4#340712yes—
647C2—41no—
648C2—41no—
649C2—41no—
650C2—81no—
651C2#1743911yescharacteristic
652C2#3333311yescharacteristic
653C2#3334011yescharacteristic
subgroupG/H
centerC2×C8C22×D4
commutatorC2×C4C23×C8
Frattini, cosocleC4×C8C24
socleC22C22×C22⋊C8
prime radical#537C8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C8 ◁ C8×#41 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33503C2semidirect
3. #33479C2semidirect
4. #11640C2semidirect
5. #11639C2semidirect
6. #11638C2semidirect
7. #11624C2semidirect
8. #11623C2semidirect
9. #11622C2semidirect
10. #11616C2semidirect
11. #11615C2semidirect
12. #11614C2semidirect
13. #11608C2semidirect
14. #11607C2semidirect
15. #11606C2semidirect

Maximal subgroups

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

subgroupindex
#603302
#335032
#334792
#116402
#116392
#116382
#116242
#116232
#116222
#116162
#116152
#116142
#116082
#116072
#116062