Finite Group Databasebeta

← #119856

Subgroups — #119856

Order 512.

714 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21885C211yesmaximal, characteristic
2C2×#1994C211yesmaximal, characteristic
3C2×#1550C211yesmaximal, characteristic
4#10839C211yesmaximal, characteristic
5#10832C211yesmaximal, characteristic
6#8045C211yesmaximal, characteristic
7C2×#1292C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C2×#423C2211yescharacteristic
10C2×#423C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C22×C4⋊C8C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×C43C2211yescharacteristic
15#1994—22no—
16#1994—22no—
17#1987—21no—
18#1981—21no—
19#1892—22no—
20#1803—21no—
21#1803—21no—
22C2×#339—21no—
23C2×#339—21no—
24C2×#339—21no—
25C2×#339—21no—
26C2×#336—22no—
27#1550—22no—
28#1550C414yescomplemented
29C2×#333—21no—
30C2×#332—21no—
31#1296—21no—
32#1296—21no—
33#1292—22no—
34C22×M16—21no—
35C22×M16—21no—
36C23×C8—21no—
37C23×C8D412yes—
38#533—21no—
39#533—21no—
40#533—21no—
41#533—21no—
42#533—21no—
43#533—21no—
44#533C2×C412yes—
45#533D412yes—
46C2×C4⋊Q8D411yescharacteristic
47C2×C4⋊Q8D411yescharacteristic
48C2×#125—21no—
49C2×C22⋊Q8—21no—
50C2×C22⋊Q8—21no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×#117—21no—
54C2×#117—21no—
55C22×C42—21no—
56C22×C42—21no—
57C22×C42D411yescharacteristic
58C22×C42D411yescharacteristic
59C22×C42C2311yescharacteristic
60#423—21no—
61#423—21no—
62#423—21no—
63#423—21no—
64#423—21no—
65#423—21no—
66#423C2×C412yes—
67#423D412yes—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—21no—
77C2×C4⋊C8—21no—
78C2×C4⋊C8—21no—
79C2×C4⋊C8—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8C2×C412yes—
84C2×#103—22no—
85C2×#103—22no—
86#384D411yescharacteristic
87#384D411yescharacteristic
88#382—21no—
89#380—21no—
90#380—21no—
91C4×C4⋊C4—21no—
92C4×C4⋊C4—21no—
93C43—21no—
94C43—21no—
95C43—21no—
96C43—21no—
97#340—22no—
98#340—22no—
99#339—24no—
100#339—24no—
101#339—42no—
102#339—42no—
103#336—44no—
104#333—24no—
105#332—24no—
106C22×Q8—21no—
107C22×Q8—21no—
108C23×C4—21no—
109C23×C4—21no—
110C23×C4C2×D411yescharacteristic
111C23×C4C2×D411yescharacteristic
112C23×C4#4111yescharacteristic
113C2×M16—22no—
114C2×M16—22no—
115C2×M16—41no—
116C2×M16—41no—
117C2×M16—41no—
118C2×M16—41no—
119C2×M16—41no—
120C2×M16—41no—
121C2×M16—41no—
122C2×M16—41no—
123C2×M16—41no—
124C2×M16—41no—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—22no—
128C22×C8—22no—
129C22×C8—42no—
130C22×C8—42no—
131C22×C8—42no—
132C22×C8—42no—
133C22×C8—41no—
134C22×C8—41no—
135C22×C8—41no—
136C22×C8—41no—
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139C4⋊Q8—21no—
140C4⋊Q8—21no—
141C4⋊Q8—21no—
142C4⋊Q8—21no—
143C4⋊Q8C22⋊C412yes—
144C4⋊Q8C22⋊C412yes—
145#125—22no—
146#125—22no—
147#125—41no—
148#125—41no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152C22⋊Q8—22no—
153C22⋊Q8—41no—
154C22⋊Q8—41no—
155C22⋊Q8—41no—
156C22⋊Q8—41no—
157C4×Q8—22no—
158C4×Q8—22no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×Q8—41no—
162C4×Q8—41no—
163C4×Q8—41no—
164C4×Q8—41no—
165#117—22no—
166#117—22no—
167#117—41no—
168#117—41no—
169#117—41no—
170#117—41no—
171#117—41no—
172#117—41no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—21no—
194C2×C42—21no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—41no—
200C2×C42—41no—
201C2×C42—42no—
202C2×C42—42no—
203C2×C42—41no—
204C2×C42—41no—
205C2×C42—41no—
206C2×C42—41no—
207C2×C42—41no—
208C2×C42—41no—
209C2×C42SD1612yes—
210C2×C42Q1612yes—
211C2×C42C22×C411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216C2×C42#4111yescharacteristic
217C2×C42#4111yescharacteristic
218C2×C42#4111yescharacteristic
219C2×C42#4111yescharacteristic
220C2×C42#4111yescharacteristic
221C2×C42#4111yescharacteristic
222C2×C42#4111yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—22no—
226C4⋊C8—22no—
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—41no—
230C4⋊C8—41no—
231C4⋊C8—41no—
232C4⋊C8—41no—
233C4⋊C8—41no—
234C4⋊C8—41no—
235C4⋊C8—41no—
236C4⋊C8—41no—
237C4⋊C8—41no—
238C4⋊C8—41no—
239#103—82no—
240#103—82no—
241#95—41no—
242#95—41no—
243C24#12111yescharacteristic
244C2×Q8—22no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—81no—
253C2×Q8—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4#11711yescharacteristic
279C22×C4C4×D411yescharacteristic
280C22×C4C4×D411yescharacteristic
281C22×C4#12011yescharacteristic
282C22×C4#12011yescharacteristic
283C22×C4#12111yescharacteristic
284C22×C4#12111yescharacteristic
285C22×C4#12111yescharacteristic
286C22×C4#12111yescharacteristic
287C22×C4#12311yescharacteristic
288C22×C4#12311yescharacteristic
289C22×C4#12311yescharacteristic
290C22×C4#12311yescharacteristic
291C22×C4#12311yescharacteristic
292C22×C4#12411yescharacteristic
293C22×C4#12411yescharacteristic
294C22×C4#12411yescharacteristic
295C22×C4#12611yescharacteristic
296C22×C4C2×SD1611yescharacteristic
297C22×C4C2×Q1611yescharacteristic
298C22×C4#13511yescharacteristic
299C22×C4#13511yescharacteristic
300C22×C4AGL(1,ℤ/8)11yescharacteristic
301C22×C4#13711yescharacteristic
302C22×C4#13711yescharacteristic
303C22×C4#13711yescharacteristic
304M16—42no—
305M16—42no—
306M16—42no—
307M16—42no—
308M16—81no—
309M16—81no—
310M16—81no—
311M16—81no—
312C2×C8—44no—
313C2×C8—44no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—82no—
321C2×C8—81no—
322C2×C8—81no—
323C2×C8—81no—
324C2×C8—81no—
325C2×C8—81no—
326C2×C8—81no—
327C2×C8—82no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—81no—
349C4⋊C4—81no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—81no—
353C22⋊C4—81no—
354C42—22no—
355C42—22no—
356C42—22no—
357C42—22no—
358C42—42no—
359C42—42no—
360C42—42no—
361C42—42no—
362C42—44no—
363C42—44no—
364C42—42no—
365C42—42no—
366C42—41no—
367C42—41no—
368C42—41no—
369C42—41no—
370C42—81no—
371C42—81no—
372C42C2×C22⋊C411yescharacteristic
373C42#11711yescharacteristic
374C42C4×D411yescharacteristic
375C42C4×D411yescharacteristic
376C42#12111yescharacteristic
377C42#12111yescharacteristic
378C42#12111yescharacteristic
379C42#12311yescharacteristic
380C42#12311yescharacteristic
381C42#12311yescharacteristic
382C42#12311yescharacteristic
383C42#12311yescharacteristic
384C42#12411yescharacteristic
385C42#12611yescharacteristic
386C42#12611yescharacteristic
387C42#12611yescharacteristic
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23#38811yescharacteristic
393C23#39411yescharacteristic
394C23#39411yescharacteristic
395C23#46511yescharacteristic
396C23#46711yescharacteristic
397C23#46811yescharacteristic
398C23#47011yescharacteristic
399Q8—42no—
400Q8—42no—
401Q8—82no—
402Q8—82no—
403Q8—81no—
404Q8—81no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4#38111yescharacteristic
450C2×C4#38611yescharacteristic
451C2×C4#38611yescharacteristic
452C2×C4#38811yescharacteristic
453C2×C4#38811yescharacteristic
454C2×C4#38811yescharacteristic
455C2×C4#39411yescharacteristic
456C2×C4#39411yescharacteristic
457C2×C4#39711yescharacteristic
458C2×C4#39711yescharacteristic
459C2×C4#39711yescharacteristic
460C2×C4#39711yescharacteristic
461C2×C4C4×SD1611yescharacteristic
462C2×C4C4×Q1611yescharacteristic
463C2×C4#44011yescharacteristic
464C2×C4#44111yescharacteristic
465C2×C4#44811yescharacteristic
466C2×C4#44911yescharacteristic
467C2×C4#45111yescharacteristic
468C2×C4#45211yescharacteristic
469C2×C4#45311yescharacteristic
470C2×C4#45411yescharacteristic
471C2×C4#45511yescharacteristic
472C2×C4#45611yescharacteristic
473C2×C4#46011yescharacteristic
474C2×C4#46111yescharacteristic
475C2×C4#46211yescharacteristic
476C2×C4#46211yescharacteristic
477C2×C4#46311yescharacteristic
478C2×C4#46411yescharacteristic
479C2×C4#46411yescharacteristic
480C2×C4#46411yescharacteristic
481C2×C4#48311yescharacteristic
482C2×C4#48411yescharacteristic
483C2×C4#48511yescharacteristic
484C2×C4#48511yescharacteristic
485C2×C4#48711yescharacteristic
486C2×C4#48811yescharacteristic
487C2×C4#48911yescharacteristic
488C2×C4#49111yescharacteristic
489C8—82no—
490C8—82no—
491C8—82no—
492C8—82no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22#144011yescharacteristic
506C22#193311yescharacteristic
507C22#193511yescharacteristic
508C22#203511yescharacteristic
509C22#203611yescharacteristic
510C22#203911yescharacteristic
511C22#204011yescharacteristic
512C22#205011yescharacteristic
513C22#205011yescharacteristic
514C22#205511yescharacteristic
515C22#205611yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—44no—
523C4—44no—
524C4—82no—
525C4—82no—
526C4—161no—
527C4—161no—
528C4#187811yescharacteristic
529C4#188011yescharacteristic
530C4#188211yescharacteristic
531C4#188311yescharacteristic
532C4#192711yescharacteristic
533C4#192811yescharacteristic
534C4#203711yescharacteristic
535C4#203811yescharacteristic
536C4#204211yescharacteristic
537C4#204311yescharacteristic
538C4#207211yescharacteristic
539C4#207411yescharacteristic
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2#1052011yescharacteristic
545C2#1052111yescharacteristic
546C2#1052211yescharacteristic
547C2#1052311yescharacteristic
548C2#1115111yescharacteristic
549C2#1119011yescharacteristic
550C2#1119511yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
28. #1550C4semidirect

Maximal subgroups

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

subgroupindex
#218852
C2×#19942
C2×#15502
#108392
#108322
#80452
C2×#12922