Finite Group Databasebeta

← #120820

Subgroups — #120820

Order 512.

828 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14149C211yesmaximal, 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×#380C2211yescharacteristic
12C2×#380C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×C4×C22⋊C4C2211yescharacteristic
15C22×#95C2211yescharacteristic
16C2×#342—21no—
17C2×#342—21no—
18#1441—22no—
19#1436—22no—
20C22⋊#95—21no—
21#1294—22no—
22#1294—22no—
23#1294—22no—
24#1289C414yescomplemented
25#1282—22no—
26C24×C4—21no—
27C24×C4C2311yescharacteristic
28C23×C8—21no—
29C23×C8—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4Q812yes—
34C22×C22⋊C4—21no—
35C22×C22⋊C4—21no—
36C22×C22⋊C4—21no—
37C22×C22⋊C4D411yescharacteristic
38C22×C22⋊C4D411yescharacteristic
39C22×C42—21no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—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⋊C8C2×C412yes—
51C2×C22⋊C8D412yes—
52#385—42no—
53#385—42no—
54#380—21no—
55#380—21no—
56#380—21no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380C2×C412yes—
64#380C2×C412yes—
65#380Q812yes—
66C4×C22⋊C4—21no—
67C4×C22⋊C4—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—21no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—22no—
81C2×#95D412yes—
82C2×#95D412yes—
83#342—42no—
84#342—42no—
85C25C2×D411yescharacteristic
86C23×C4—22no—
87C23×C4—21no—
88C23×C4—21no—
89C23×C4—22no—
90C23×C4—22no—
91C23×C4—44no—
92C23×C4—41no—
93C23×C4—41no—
94C23×C4—41no—
95C23×C4—41no—
96C23×C4—41no—
97C23×C4—41no—
98C23×C4—41no—
99C23×C4—82no—
100C23×C4—82no—
101C23×C4C22×C411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C23×C4C2×Q811yescharacteristic
106C23×C4C2×Q811yescharacteristic
107C23×C4#4111yescharacteristic
108C23×C4#4111yescharacteristic
109C23×C4#4111yescharacteristic
110C23×C4#4111yescharacteristic
111C23×C4#4111yescharacteristic
112C23×C4#4111yescharacteristic
113C23×C4#4111yescharacteristic
114C23×C4#4111yescharacteristic
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—82no—
122C22×C8—82no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—44no—
129C2×C4⋊C4—44no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—82no—
132C2×C4⋊C4—82no—
133C2×C4⋊C4—82no—
134C2×C4⋊C4—82no—
135C2×C22⋊C4—21no—
136C2×C22⋊C4—21no—
137C2×C22⋊C4—21no—
138C2×C22⋊C4—21no—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—22no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
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⋊C4D812yes—
164C2×C22⋊C4SD1612yes—
165C2×C42—41no—
166C2×C42—41no—
167C2×C42—82no—
168C22⋊C8—22no—
169C22⋊C8—22no—
170C22⋊C8—22no—
171C22⋊C8—22no—
172C22⋊C8—41no—
173C22⋊C8—41no—
174C22⋊C8—41no—
175C22⋊C8—41no—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—22no—
180#95—44no—
181#95—44no—
182#95—41no—
183#95—41no—
184#95—41no—
185#95—41no—
186#95—41no—
187#95—41no—
188#95—41no—
189#95—82no—
190#95C4⋊C414yes—
191C24—42no—
192C24—42no—
193C24C4×D411yescharacteristic
194C24#12011yescharacteristic
195C24#12111yescharacteristic
196C24C22⋊Q811yescharacteristic
197C24C22⋊Q811yescharacteristic
198C24#12311yescharacteristic
199C24#12411yescharacteristic
200C24C2×D811yescharacteristic
201C24C2×SD1611yescharacteristic
202C24#13511yescharacteristic
203C24#13511yescharacteristic
204C24AGL(1,ℤ/8)11yescharacteristic
205C24#13711yescharacteristic
206C24#13711yescharacteristic
207C24#13711yescharacteristic
208C22×C4—24no—
209C22×C4—24no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—44no—
230C22×C4—44no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—81no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—84no—
253C22×C4—84no—
254C22×C4—84no—
255C22×C4—84no—
256C22×C4—82no—
257C22×C4—82no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—82no—
263C22×C4—82no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4—82no—
267C22×C4—82no—
268C22×C4C2×C4⋊C411yescharacteristic
269C22×C4#11711yescharacteristic
270C22×C4#11711yescharacteristic
271C22×C4C4×D411yescharacteristic
272C22×C4C4×D411yescharacteristic
273C22×C4C4×Q811yescharacteristic
274C22×C4#12111yescharacteristic
275C22×C4#12111yescharacteristic
276C22×C4C22⋊Q811yescharacteristic
277C22×C4C22⋊Q811yescharacteristic
278C22×C4C22⋊Q811yescharacteristic
279C22×C4#12311yescharacteristic
280C22×C4#12311yescharacteristic
281C22×C4#12311yescharacteristic
282C22×C4#12311yescharacteristic
283C22×C4#12411yescharacteristic
284C22×C4#12411yescharacteristic
285C22×C4#12411yescharacteristic
286C22×C4#12511yescharacteristic
287C22×C4#12511yescharacteristic
288C22×C4#12511yescharacteristic
289C22×C4#12511yescharacteristic
290C22×C4#12511yescharacteristic
291C22×C4#12611yescharacteristic
292C22×C4#12611yescharacteristic
293C22×C4#12611yescharacteristic
294C22×C4#12611yescharacteristic
295C22×C4C4⋊Q811yescharacteristic
296C2×C8—42no—
297C2×C8—42no—
298C2×C8—82no—
299C2×C8—82no—
300C2×C8—82no—
301C2×C8—82no—
302C2×C8—82no—
303C2×C8—82no—
304C4⋊C4—82no—
305C4⋊C4—82no—
306C4⋊C4—82no—
307C4⋊C4—82no—
308C4⋊C4—88no—
309C4⋊C4—82no—
310C4⋊C4—82no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C22⋊C4—81no—
330C22⋊C4—81no—
331C42—82no—
332C42—82no—
333C23—22no—
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—41no—
350C23—41no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23#38511yescharacteristic
356C23#38711yescharacteristic
357C23#38811yescharacteristic
358C23#39311yescharacteristic
359C23#39411yescharacteristic
360C23#39811yescharacteristic
361C23#40011yescharacteristic
362C23C4×D811yescharacteristic
363C23C4×SD1611yescharacteristic
364C23#44011yescharacteristic
365C23#44111yescharacteristic
366C23#44711yescharacteristic
367C23#44811yescharacteristic
368C23#45211yescharacteristic
369C23#45211yescharacteristic
370C23#46511yescharacteristic
371C23#46611yescharacteristic
372C23#46811yescharacteristic
373C23#47011yescharacteristic
374C23#47411yescharacteristic
375C23#47411yescharacteristic
376C23#47511yescharacteristic
377C23#47611yescharacteristic
378C23#47811yescharacteristic
379C23#47911yescharacteristic
380C23#47911yescharacteristic
381C23#47911yescharacteristic
382C23#48011yescharacteristic
383C23#48211yescharacteristic
384C23#48311yescharacteristic
385C23#48511yescharacteristic
386C23#48611yescharacteristic
387C23#48811yescharacteristic
388C23#48911yescharacteristic
389C23#49111yescharacteristic
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
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—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—84no—
442C2×C4—84no—
443C2×C4—84no—
444C2×C4—84no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—162no—
453C2×C4—162no—
454C2×C4—162no—
455C2×C4—162no—
456C2×C4#38211yescharacteristic
457C2×C4#38711yescharacteristic
458C2×C4#38811yescharacteristic
459C2×C4#38911yescharacteristic
460C2×C4#39711yescharacteristic
461C2×C4#39811yescharacteristic
462C2×C4#40011yescharacteristic
463C2×C4#40011yescharacteristic
464C8—82no—
465C8—82no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22#144211yescharacteristic
507C22#186211yescharacteristic
508C22#186511yescharacteristic
509C22#191811yescharacteristic
510C22#192011yescharacteristic
511C22#193411yescharacteristic
512C22#193511yescharacteristic
513C22#202311yescharacteristic
514C22#202611yescharacteristic
515C22#203112yes—
516C22#203212yes—
517C22#203311yescharacteristic
518C22#203511yescharacteristic
519C22#208611yescharacteristic
520C22#208811yescharacteristic
521C22#209911yescharacteristic
522C22#210111yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—82no—
532C4—84no—
533C4—82no—
534C4—84no—
535C4—162no—
536C4—162no—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2#1037412yes—
550C2#1037712yes—
551C2#1127911yescharacteristic
552C2#1128211yescharacteristic
553C2#1129211yescharacteristic
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
24. #1289C4semidirect

Maximal subgroups

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

subgroupindex
#141492
#108542
#80232
C2×#12942
C2×#12892
C2×#12822