Finite Group Databasebeta

← #120140

Subgroups — #120140

Order 512.

862 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21940C211yesmaximal, characteristic
2#14149C211yesmaximal, characteristic
3#10854C211yesmaximal, characteristic
4#8023C211yesmaximal, characteristic
5C2×#1294C211yesmaximal, characteristic
6C2×#1294C211yesmaximal, 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
16#1852—22no—
17#1852C414yescomplemented
18#1808—22no—
19C2×#342—21no—
20C2×#342—21no—
21#1441—22no—
22#1436—22no—
23C22⋊#95—21no—
24#1294—22no—
25#1294—22no—
26#1294—22no—
27#1282—22no—
28C24×C4—21no—
29C24×C4C2311yescharacteristic
30C23×C8—21no—
31C23×C8—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4C2×C412yes—
35C22×C4⋊C4D412yes—
36C22×C22⋊C4—21no—
37C22×C22⋊C4—21no—
38C22×C22⋊C4—21no—
39C22×C22⋊C4D411yescharacteristic
40C22×C22⋊C4D411yescharacteristic
41C22×C42—21no—
42C2×#107—24no—
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⋊C8C2×C412yes—
52C2×C22⋊C8D412yes—
53C2×C22⋊C8Q812yes—
54C2×C22⋊C8Q812yes—
55#385—42no—
56#385—42no—
57#380—21no—
58#380—21no—
59#380—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65#380—21no—
66#380C2×C412yes—
67#380D412yes—
68#380Q812yes—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C2×#95—21no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—21no—
78C2×#95—21no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—21no—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—22no—
85C2×#95D412yes—
86#342—42no—
87#342—42no—
88#340—24no—
89C25C2×D411yescharacteristic
90C23×C4—22no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—22no—
94C23×C4—22no—
95C23×C4—44no—
96C23×C4—41no—
97C23×C4—41no—
98C23×C4—41no—
99C23×C4—41no—
100C23×C4—41no—
101C23×C4—41no—
102C23×C4—41no—
103C23×C4—82no—
104C23×C4—82no—
105C23×C4C22×C411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D411yescharacteristic
108C23×C4C2×D411yescharacteristic
109C23×C4C2×D411yescharacteristic
110C23×C4C2×Q811yescharacteristic
111C23×C4C2×Q811yescharacteristic
112C23×C4C2×Q811yescharacteristic
113C23×C4#4111yescharacteristic
114C23×C4#4111yescharacteristic
115C23×C4#4111yescharacteristic
116C23×C4#4111yescharacteristic
117C23×C4#4111yescharacteristic
118C23×C4#4111yescharacteristic
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—22no—
123C22×C8—41no—
124C22×C8—41no—
125C22×C8—82no—
126C22×C8—82no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—44no—
132C2×C4⋊C4—44no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—82no—
135C2×C4⋊C4—82no—
136C2×C4⋊C4—82no—
137C2×C4⋊C4—82no—
138C2×C4⋊C4C22⋊C414yes—
139C2×C22⋊C4—21no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—21no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—21no—
147C2×C22⋊C4—22no—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—21no—
150C2×C22⋊C4—21no—
151C2×C22⋊C4—22no—
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⋊C4D812yes—
168C2×C22⋊C4Q1612yes—
169C2×C42—41no—
170C2×C42—41no—
171C2×C42—82no—
172#107—84no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177C22⋊C8—22no—
178C22⋊C8—41no—
179C22⋊C8—41no—
180C22⋊C8C4⋊C414yescomplemented
181#95—22no—
182#95—22no—
183#95—22no—
184#95—22no—
185#95—22no—
186#95—44no—
187#95—44no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193#95—41no—
194#95—41no—
195#95—82no—
196C24—42no—
197C24—42no—
198C24C4×D411yescharacteristic
199C24#12011yescharacteristic
200C24#12111yescharacteristic
201C24#12111yescharacteristic
202C24C22⋊Q811yescharacteristic
203C24#12311yescharacteristic
204C24C4⋊Q811yescharacteristic
205C24C2×D811yescharacteristic
206C24C2×Q1611yescharacteristic
207C24#13511yescharacteristic
208C24#13511yescharacteristic
209C24AGL(1,ℤ/8)11yescharacteristic
210C24AGL(1,ℤ/8)11yescharacteristic
211C24#13711yescharacteristic
212C24#13711yescharacteristic
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—22no—
216C22×C4—22no—
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—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—42no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—84no—
258C22×C4—84no—
259C22×C4—84no—
260C22×C4—84no—
261C22×C4—82no—
262C22×C4—82no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4—82no—
268C22×C4—82no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—82no—
272C22×C4—82no—
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C4⋊C411yescharacteristic
275C22×C4#11711yescharacteristic
276C22×C4C4×D411yescharacteristic
277C22×C4C4×Q811yescharacteristic
278C22×C4C4×Q811yescharacteristic
279C22×C4#12111yescharacteristic
280C22×C4#12111yescharacteristic
281C22×C4#12111yescharacteristic
282C22×C4#12111yescharacteristic
283C22×C4C22⋊Q811yescharacteristic
284C22×C4C22⋊Q811yescharacteristic
285C22×C4C22⋊Q811yescharacteristic
286C22×C4C22⋊Q811yescharacteristic
287C22×C4C22⋊Q811yescharacteristic
288C22×C4C22⋊Q811yescharacteristic
289C22×C4C22⋊Q811yescharacteristic
290C22×C4#12311yescharacteristic
291C22×C4#12311yescharacteristic
292C22×C4#12411yescharacteristic
293C22×C4#12511yescharacteristic
294C22×C4#12511yescharacteristic
295C22×C4#12511yescharacteristic
296C22×C4#12511yescharacteristic
297C22×C4#12611yescharacteristic
298C22×C4#12611yescharacteristic
299C22×C4C4⋊Q811yescharacteristic
300C22×C4C4⋊Q811yescharacteristic
301C2×C8—24no—
302C2×C8—44no—
303C2×C8—42no—
304C2×C8—82no—
305C2×C8—82no—
306C2×C8—82no—
307C2×C8—82no—
308C2×C8—82no—
309C4⋊C4—44no—
310C4⋊C4—44no—
311C4⋊C4—82no—
312C4⋊C4—82no—
313C4⋊C4—88no—
314C4⋊C4—82no—
315C4⋊C4—82no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—81no—
331C22⋊C4—81no—
332C22⋊C4—81no—
333C22⋊C4—81no—
334C22⋊C4—81no—
335C22⋊C4—81no—
336C42—82no—
337C42—82no—
338C23—22no—
339C23—22no—
340C23—22no—
341C23—22no—
342C23—22no—
343C23—22no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23#38611yescharacteristic
361C23#38711yescharacteristic
362C23#38911yescharacteristic
363C23#39411yescharacteristic
364C23#39511yescharacteristic
365C23#39611yescharacteristic
366C23#39811yescharacteristic
367C23C4×D811yescharacteristic
368C23C4×Q1611yescharacteristic
369C23#44111yescharacteristic
370C23#44211yescharacteristic
371C23#44711yescharacteristic
372C23#44911yescharacteristic
373C23#45111yescharacteristic
374C23#45211yescharacteristic
375C23#45911yescharacteristic
376C23#46211yescharacteristic
377C23#46311yescharacteristic
378C23#46411yescharacteristic
379C23#46611yescharacteristic
380C23#46711yescharacteristic
381C23#46811yescharacteristic
382C23#46811yescharacteristic
383C23#47411yescharacteristic
384C23#47711yescharacteristic
385C23#47811yescharacteristic
386C23#47911yescharacteristic
387C23#48011yescharacteristic
388C23#48211yescharacteristic
389C23#48411yescharacteristic
390C23#48511yescharacteristic
391C23#49911yescharacteristic
392C23#50011yescharacteristic
393C23#50111yescharacteristic
394C23#50111yescharacteristic
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
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—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—84no—
447C2×C4—84no—
448C2×C4—84no—
449C2×C4—84no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—162no—
458C2×C4—162no—
459C2×C4—162no—
460C2×C4—162no—
461C2×C4#38011yescharacteristic
462C2×C4#38711yescharacteristic
463C2×C4#38911yescharacteristic
464C2×C4#39111yescharacteristic
465C2×C4#39611yescharacteristic
466C2×C4#39811yescharacteristic
467C2×C4#39811yescharacteristic
468C2×C4#40011yescharacteristic
469C8—44no—
470C8—82no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22#144111yescharacteristic
512C22#187811yescharacteristic
513C22#187911yescharacteristic
514C22#190612yes—
515C22#191312yes—
516C22#191811yescharacteristic
517C22#192111yescharacteristic
518C22#194211yescharacteristic
519C22#194311yescharacteristic
520C22#203311yescharacteristic
521C22#203611yescharacteristic
522C22#205711yescharacteristic
523C22#205911yescharacteristic
524C22#206711yescharacteristic
525C22#206811yescharacteristic
526C22#208311yescharacteristic
527C22#208511yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—21no—
535C4—21no—
536C4—82no—
537C4—82no—
538C4—84no—
539C4—84no—
540C4—162no—
541C4—162no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—21no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—21no—
554C2#927612yes—
555C2#927712yes—
556C2#1120511yescharacteristic
557C2#1121511yescharacteristic
558C2#1121911yescharacteristic
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
17. #1852C4semidirect
180. C22⋊C8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
#219402
#141492
#108542
#80232
C2×#12942
C2×#12822