Finite Group Databasebeta

← #119262

Subgroups — #119262

Order 512.

924 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21759C211yesmaximal, characteristic
2C2×#1520C211yesmaximal, characteristic
3#14159C211yesmaximal, characteristic
4#10854C211yesmaximal, characteristic
5C2×#1294C211yesmaximal, characteristic
6C2×#1294C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C22×C22⋊Q8C2211yescharacteristic
9C22×C22⋊C8C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C2×#380C2211yescharacteristic
12C2×#380C2211yescharacteristic
13C2×C4×C22⋊C4C2211yescharacteristic
14C22×#95C2211yescharacteristic
15#1892—22no—
16#1872C414yescomplemented
17#1824—21no—
18#1787—21no—
19C2×#342—21no—
20C2×#342—21no—
21#1520—22no—
22#1520—22no—
23C2×#328—22no—
24#1446—21no—
25#1445—21no—
26#1436—22no—
27C22⋊#95—21no—
28C22⋊#95—21no—
29#1294—22no—
30#1294—22no—
31#1282—22no—
32C23×Q8D411yescharacteristic
33C24×C4—21no—
34C24×C4C2311yescharacteristic
35C23×C8—21no—
36C23×C8—21no—
37C2×C22⋊Q8—21no—
38C2×C22⋊Q8—21no—
39C2×C22⋊Q8—21no—
40C2×C22⋊Q8—21no—
41C2×C22⋊Q8—21no—
42C2×C22⋊Q8—21no—
43C2×C22⋊Q8—21no—
44C2×C22⋊Q8—21no—
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C2×C22⋊Q8C2×C412yes—
48C2×C22⋊Q8D412yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4C2×C412yes—
52C22×C4⋊C4D411yescharacteristic
53C22×C22⋊C4—21no—
54C22×C22⋊C4—21no—
55C22×C22⋊C4—21no—
56C22×C22⋊C4D411yescharacteristic
57C22×C22⋊C4D411yescharacteristic
58C22×C42—21no—
59C2×#103—24no—
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×C22⋊C8—21no—
63C2×C22⋊C8—21no—
64C2×C22⋊C8—21no—
65C2×C22⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8—21no—
68C2×C22⋊C8—21no—
69C2×C22⋊C8—21no—
70C2×C22⋊C8C2×C412yes—
71C2×C22⋊C8D412yes—
72#380—21no—
73#380—21no—
74#380—21no—
75#380—21no—
76#380—21no—
77#380—21no—
78#380—21no—
79#380D412yes—
80C4×C22⋊C4—21no—
81C4×C22⋊C4—21no—
82C4×C22⋊C4—21no—
83C4×C22⋊C4—21no—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—21no—
87C2×#95—21no—
88C2×#95—21no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95D412yes—
97#342—42no—
98#342—42no—
99#340—24no—
100#328—28no—
101C25C2×D411yescharacteristic
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—82no—
108C22×Q8C22⋊C412yes—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4—21no—
112C23×C4—21no—
113C23×C4—22no—
114C23×C4—22no—
115C23×C4—44no—
116C23×C4—41no—
117C23×C4—41no—
118C23×C4—41no—
119C23×C4—41no—
120C23×C4—41no—
121C23×C4—41no—
122C23×C4—41no—
123C23×C4—82no—
124C23×C4—82no—
125C23×C4C22×C411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2×D411yescharacteristic
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4#4111yescharacteristic
132C23×C4#4111yescharacteristic
133C23×C4#4111yescharacteristic
134C23×C4#4111yescharacteristic
135C23×C4#4111yescharacteristic
136C23×C4#4111yescharacteristic
137C23×C4#4111yescharacteristic
138C23×C4#4111yescharacteristic
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—41no—
142C22×C8—41no—
143C22×C8—41no—
144C22×C8—41no—
145C22×C8—82no—
146C22×C8—82no—
147C22⋊Q8—22no—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153C22⋊Q8—22no—
154C22⋊Q8—22no—
155C22⋊Q8—41no—
156C22⋊Q8—41no—
157C22⋊Q8—41no—
158C22⋊Q8—41no—
159C22⋊Q8—41no—
160C22⋊Q8—41no—
161C22⋊Q8—41no—
162C22⋊Q8—41no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—82no—
179C2×C4⋊C4—82no—
180C2×C4⋊C4C22⋊C412yes—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C22⋊C4—41no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C22⋊C4—41no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—41no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—41no—
205C2×C22⋊C4—41no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—41no—
208C2×C22⋊C4—41no—
209C2×C22⋊C4SD1612yes—
210C2×C22⋊C4Q1612yes—
211C2×C42—41no—
212C2×C42—41no—
213C2×C42—82no—
214#103—84no—
215C22⋊C8—22no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219C22⋊C8—41no—
220C22⋊C8—41no—
221C22⋊C8—41no—
222C22⋊C8—41no—
223#95—22no—
224#95—22no—
225#95—22no—
226#95—44no—
227#95—44no—
228#95—41no—
229#95—41no—
230#95—41no—
231#95—41no—
232#95—41no—
233#95—41no—
234#95—41no—
235#95—82no—
236#95—82no—
237C24—42no—
238C24—42no—
239C24C4×D411yescharacteristic
240C24#12011yescharacteristic
241C24#12111yescharacteristic
242C24#12111yescharacteristic
243C24#12111yescharacteristic
244C24#12311yescharacteristic
245C24#12411yescharacteristic
246C24C2×SD1611yescharacteristic
247C24C2×Q1611yescharacteristic
248C24#13511yescharacteristic
249C24#13511yescharacteristic
250C24AGL(1,ℤ/8)11yescharacteristic
251C24#13711yescharacteristic
252C24#13711yescharacteristic
253C24#13711yescharacteristic
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—44no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—82no—
260C2×Q8—82no—
261C2×Q8—82no—
262C2×Q8—82no—
263C2×Q8—82no—
264C22×C4—24no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—44no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—81no—
304C22×C4—81no—
305C22×C4—81no—
306C22×C4—81no—
307C22×C4—81no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—84no—
312C22×C4—84no—
313C22×C4—84no—
314C22×C4—84no—
315C22×C4—82no—
316C22×C4—82no—
317C22×C4—81no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4—82no—
322C22×C4—82no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4—82no—
326C22×C4—82no—
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4#11711yescharacteristic
329C22×C4#11711yescharacteristic
330C22×C4C4×D411yescharacteristic
331C22×C4C4×D411yescharacteristic
332C22×C4C4×D411yescharacteristic
333C22×C4#12011yescharacteristic
334C22×C4#12111yescharacteristic
335C22×C4#12111yescharacteristic
336C22×C4#12111yescharacteristic
337C22×C4#12111yescharacteristic
338C22×C4#12111yescharacteristic
339C22×C4#12311yescharacteristic
340C22×C4#12311yescharacteristic
341C22×C4#12311yescharacteristic
342C22×C4#12311yescharacteristic
343C22×C4#12311yescharacteristic
344C22×C4#12311yescharacteristic
345C22×C4#12311yescharacteristic
346C22×C4#12311yescharacteristic
347C22×C4#12311yescharacteristic
348C22×C4#12411yescharacteristic
349C22×C4#12411yescharacteristic
350C22×C4#12411yescharacteristic
351C22×C4#12611yescharacteristic
352C22×C4#12611yescharacteristic
353C22×C4#12611yescharacteristic
354C22×C4#12611yescharacteristic
355C2×C8—44no—
356C2×C8—42no—
357C2×C8—42no—
358C2×C8—82no—
359C2×C8—82no—
360C2×C8—82no—
361C2×C8—82no—
362C2×C8—82no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—44no—
366C4⋊C4—42no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—42no—
372C4⋊C4—82no—
373C4⋊C4—82no—
374C4⋊C4—82no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C22⋊C4—42no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4—81no—
390C22⋊C4—81no—
391C22⋊C4—81no—
392C22⋊C4—81no—
393C22⋊C4—81no—
394C22⋊C4—81no—
395C42—82no—
396C42—82no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23#38611yescharacteristic
420C23#38811yescharacteristic
421C23#38811yescharacteristic
422C23#39411yescharacteristic
423C23#39411yescharacteristic
424C23#39411yescharacteristic
425C23#39711yescharacteristic
426C23C4×SD1611yescharacteristic
427C23C4×Q1611yescharacteristic
428C23#44011yescharacteristic
429C23#44111yescharacteristic
430C23#44811yescharacteristic
431C23#44911yescharacteristic
432C23#45111yescharacteristic
433C23#45211yescharacteristic
434C23#46011yescharacteristic
435C23#46111yescharacteristic
436C23#46211yescharacteristic
437C23#46211yescharacteristic
438C23#46311yescharacteristic
439C23#46411yescharacteristic
440C23#46411yescharacteristic
441C23#46411yescharacteristic
442C23#46511yescharacteristic
443C23#46711yescharacteristic
444C23#46811yescharacteristic
445C23#47011yescharacteristic
446C23#48311yescharacteristic
447C23#48411yescharacteristic
448C23#48511yescharacteristic
449C23#48511yescharacteristic
450C23#48711yescharacteristic
451C23#48811yescharacteristic
452C23#48911yescharacteristic
453C23#49111yescharacteristic
454Q8—44no—
455Q8—82no—
456Q8—82no—
457Q8—82no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—82no—
508C2×C4—82no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—82no—
512C2×C4—84no—
513C2×C4—84no—
514C2×C4—84no—
515C2×C4—84no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—162no—
524C2×C4—162no—
525C2×C4—162no—
526C2×C4—162no—
527C2×C4#38111yescharacteristic
528C2×C4#38611yescharacteristic
529C2×C4#38811yescharacteristic
530C2×C4#38811yescharacteristic
531C2×C4#39411yescharacteristic
532C2×C4#39711yescharacteristic
533C2×C4#39711yescharacteristic
534C2×C4#39711yescharacteristic
535C8—82no—
536C8—82no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22#144011yescharacteristic
578C22#187811yescharacteristic
579C22#188011yescharacteristic
580C22#190612yes—
581C22#191312yes—
582C22#192711yescharacteristic
583C22#192811yescharacteristic
584C22#193311yescharacteristic
585C22#193511yescharacteristic
586C22#203511yescharacteristic
587C22#203611yescharacteristic
588C22#204211yescharacteristic
589C22#204311yescharacteristic
590C22#205511yescharacteristic
591C22#205611yescharacteristic
592C22#207211yescharacteristic
593C22#207411yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—82no—
603C4—82no—
604C4—84no—
605C4—82no—
606C4—82no—
607C4—162no—
608C4—162no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2#927612yes—
622C2#927812yes—
623C2#1117211yescharacteristic
624C2#1119011yescharacteristic
625C2#1119311yescharacteristic
subgroupG/H
center, socleC23#386
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
16. #1872C4semidirect

Maximal subgroups

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

subgroupindex
#217592
C2×#15202
#141592
#108542
C2×#12942
C2×#12822