Finite Group Databasebeta

← #120862

Subgroups — #120862

Order 512.

864 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13965C211yesmaximal, characteristic
2#10854C211yesmaximal, characteristic
3#8023C211yesmaximal, characteristic
4C2×#1294C211yesmaximal, characteristic
5C2×#1294C211yesmaximal, characteristic
6C2×#1289C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C22×C22⋊C8C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C2×#385—21no—
11C2×#385—21no—
12C2×#380C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×#380C2211yescharacteristic
15C2×C4×C22⋊C4C2211yescharacteristic
16C22×#95C2211yescharacteristic
17C2×#342—21no—
18C2×#342—21no—
19#1444—22no—
20C4⋊#95—21no—
21C4⋊#95—21no—
22#1294—22no—
23#1294—22no—
24#1294—21no—
25#1294—21no—
26#1289—22no—
27#1282C414yescomplemented
28C24×C4—21no—
29C24×C4C2311yescharacteristic
30C23×C8—21no—
31C23×C8—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4—22no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4Q812yes—
37C22×C22⋊C4—21no—
38C22×C22⋊C4—21no—
39C22×C22⋊C4—21no—
40C22×C22⋊C4D411yescharacteristic
41C22×C22⋊C4D411yescharacteristic
42C22×C42—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8C2×C412yes—
54C2×C22⋊C8C2×C412yes—
55#385—42no—
56#385—42no—
57#385—42no—
58#385—42no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65#380—21no—
66#380—21no—
67#380—21no—
68#380—21no—
69#380—21no—
70#380D412yes—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4C2×C412yes—
74C4×C22⋊C4Q812yes—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—21no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—21no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95D411yescharacteristic
86C2×#95D411yescharacteristic
87C2×#95D412yes—
88#342—42no—
89#342—42no—
90C25C2×D411yescharacteristic
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—22no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—22no—
97C23×C4—44no—
98C23×C4—41no—
99C23×C4—41no—
100C23×C4—41no—
101C23×C4—41no—
102C23×C4—41no—
103C23×C4—41no—
104C23×C4—41no—
105C23×C4—82no—
106C23×C4—82no—
107C23×C4C22×C411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4C2×D411yescharacteristic
111C23×C4C2×Q811yescharacteristic
112C23×C4C2×Q811yescharacteristic
113C23×C4#4111yescharacteristic
114C23×C4#4111yescharacteristic
115C23×C4#4111yescharacteristic
116C23×C4#4111yescharacteristic
117C23×C4#4111yescharacteristic
118C23×C4#4111yescharacteristic
119C23×C4#4111yescharacteristic
120C23×C4#4111yescharacteristic
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—41no—
126C22×C8—41no—
127C22×C8—82no—
128C22×C8—82no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—44no—
133C2×C4⋊C4—44no—
134C2×C4⋊C4—44no—
135C2×C4⋊C4—44no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—82no—
140C2×C4⋊C4—82no—
141C2×C4⋊C4—82no—
142C2×C4⋊C4—82no—
143C2×C4⋊C4—82no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—41no—
159C2×C22⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—41no—
162C2×C22⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C22⋊C4—41no—
166C2×C22⋊C4—41no—
167C2×C22⋊C4—41no—
168C2×C22⋊C4C4⋊C412yes—
169C2×C22⋊C4C4⋊C412yes—
170C2×C22⋊C4D812yes—
171C2×C22⋊C4SD1612yes—
172C2×C22⋊C4SD1612yes—
173C2×C22⋊C4Q1612yes—
174C2×C42—22no—
175C2×C42—22no—
176C2×C42—82no—
177C22⋊C8—22no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181C22⋊C8—41no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C22⋊C8—41no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—21no—
189#95—21no—
190#95—22no—
191#95—22no—
192#95—21no—
193#95—21no—
194#95—44no—
195#95—44no—
196#95—41no—
197#95—41no—
198#95—41no—
199#95—41no—
200#95—41no—
201C24—42no—
202C24—42no—
203C24C2×C4⋊C411yescharacteristic
204C24#12011yescharacteristic
205C24#12111yescharacteristic
206C24C22⋊Q811yescharacteristic
207C24#12311yescharacteristic
208C24#12411yescharacteristic
209C24#12411yescharacteristic
210C24C2×D811yescharacteristic
211C24C2×SD1611yescharacteristic
212C24C2×SD1611yescharacteristic
213C24C2×Q1611yescharacteristic
214C24AGL(1,ℤ/8)11yescharacteristic
215C24AGL(1,ℤ/8)11yescharacteristic
216C24#13711yescharacteristic
217C24#13711yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—84no—
266C22×C4—84no—
267C22×C4—84no—
268C22×C4—84no—
269C22×C4—82no—
270C22×C4—82no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4—81no—
274C22×C4—81no—
275C22×C4—82no—
276C22×C4—82no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4—82no—
280C22×C4—82no—
281C22×C4#11711yescharacteristic
282C22×C4#11711yescharacteristic
283C22×C4C4×D411yescharacteristic
284C22×C4C4×D411yescharacteristic
285C22×C4C4×D411yescharacteristic
286C22×C4C4×Q811yescharacteristic
287C22×C4#12111yescharacteristic
288C22×C4#12111yescharacteristic
289C22×C4C22⋊Q811yescharacteristic
290C22×C4C22⋊Q811yescharacteristic
291C22×C4C22⋊Q811yescharacteristic
292C22×C4C22⋊Q811yescharacteristic
293C22×C4#12311yescharacteristic
294C22×C4#12311yescharacteristic
295C22×C4#12311yescharacteristic
296C22×C4#12311yescharacteristic
297C22×C4#12411yescharacteristic
298C22×C4#12411yescharacteristic
299C22×C4#12511yescharacteristic
300C22×C4#12511yescharacteristic
301C22×C4#12511yescharacteristic
302C22×C4#12511yescharacteristic
303C22×C4#12511yescharacteristic
304C22×C4#12611yescharacteristic
305C22×C4#12611yescharacteristic
306C22×C4#12611yescharacteristic
307C22×C4#12611yescharacteristic
308C22×C4C4⋊Q811yescharacteristic
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—82no—
312C2×C8—82no—
313C2×C8—82no—
314C2×C8—82no—
315C2×C8—82no—
316C2×C8—82no—
317C4⋊C4—82no—
318C4⋊C4—82no—
319C4⋊C4—88no—
320C4⋊C4—88no—
321C4⋊C4—82no—
322C4⋊C4—82no—
323C4⋊C4—82no—
324C4⋊C4—82no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—42no—
332C22⋊C4—42no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C22⋊C4—81no—
337C22⋊C4—81no—
338C22⋊C4—81no—
339C22⋊C4—81no—
340C22⋊C4—81no—
341C22⋊C4—81no—
342C22⋊C4—81no—
343C22⋊C4#10614yes—
344C22⋊C4#10714yes—
345C42—82no—
346C42—82no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23#38211yescharacteristic
370C23#38511yescharacteristic
371C23#38911yescharacteristic
372C23#39311yescharacteristic
373C23#39411yescharacteristic
374C23#39711yescharacteristic
375C23#40011yescharacteristic
376C23C2×#10611yescharacteristic
377C23C2×#10711yescharacteristic
378C23#42811yescharacteristic
379C23#42811yescharacteristic
380C23#44711yescharacteristic
381C23#44811yescharacteristic
382C23#45011yescharacteristic
383C23#45111yescharacteristic
384C23#45911yescharacteristic
385C23#46011yescharacteristic
386C23#46111yescharacteristic
387C23#46211yescharacteristic
388C23#47411yescharacteristic
389C23#47511yescharacteristic
390C23#47611yescharacteristic
391C23#47711yescharacteristic
392C23#48011yescharacteristic
393C23#48111yescharacteristic
394C23#48311yescharacteristic
395C23#48411yescharacteristic
396C23#48611yescharacteristic
397C23#48611yescharacteristic
398C23#48711yescharacteristic
399C23#48711yescharacteristic
400C23#48911yescharacteristic
401C23#48911yescharacteristic
402C23#49011yescharacteristic
403C23#49111yescharacteristic
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—84no—
449C2×C4—84no—
450C2×C4—84no—
451C2×C4—84no—
452C2×C4—82no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—162no—
470C2×C4—162no—
471C2×C4—162no—
472C2×C4—162no—
473C2×C4#38711yescharacteristic
474C2×C4#38711yescharacteristic
475C2×C4#38811yescharacteristic
476C2×C4#38811yescharacteristic
477C2×C4#39811yescharacteristic
478C2×C4#39811yescharacteristic
479C2×C4#40011yescharacteristic
480C2×C4#40011yescharacteristic
481C8—82no—
482C8—82no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22#144211yescharacteristic
524C22#183411yescharacteristic
525C22#183611yescharacteristic
526C22#185211yescharacteristic
527C22#185311yescharacteristic
528C22#194711yescharacteristic
529C22#194811yescharacteristic
530C22#202311yescharacteristic
531C22#202411yescharacteristic
532C22#203112yes—
533C22#203212yes—
534C22#204111yescharacteristic
535C22#204311yescharacteristic
536C22#207111yescharacteristic
537C22#207211yescharacteristic
538C22#209911yescharacteristic
539C22#210011yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—44no—
549C4—44no—
550C4—84no—
551C4—161no—
552C4—161no—
553C4—162no—
554C4—162no—
555C2—21no—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—21no—
566C2—21no—
567C2#1037412yes—
568C2#1037512yes—
569C2#1126311yescharacteristic
570C2#1126711yescharacteristic
571C2#1127911yescharacteristic
subgroupG/H
center, socleC23#393
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
27. #1282C4semidirect

Maximal subgroups

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

subgroupindex
#139652
#108542
#80232
C2×#12942
C2×#12892
C2×#12822