Finite Group Databasebeta

← #97545

Subgroups — #97545

Order 512.

853 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2806C211yesmaximal, characteristic
2#11207C211yesmaximal, characteristic
3#11050C211yesmaximal, characteristic
4#11050C211yesmaximal, characteristic
5C2×#1272C211yesmaximal, characteristic
6C2×#1272C211yesmaximal, characteristic
7C2×#1271C211yesmaximal, characteristic
8C22×#103—21no—
9C22×#103—21no—
10#2806—22no—
11#2806—22no—
12#2806—22no—
13#2806C414yescomplemented
14C2×#398—21no—
15C2×#398—21no—
16C2×#395—21no—
17C2×#391—21no—
18C2×#391C2211yescharacteristic
19C2×#391C2211yescharacteristic
20C2×#389—21no—
21C2×#389C2211yescharacteristic
22C2×#387—21no—
23C2×#384C2211yescharacteristic
24C2×#340—21no—
25C2×#340—21no—
26C2×#340—21no—
27C2×#340—21no—
28C2×#336C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1272—22no—
32#1272—22no—
33#1271—22no—
34C23×Q8D411yescharacteristic
35C23×Q8D411yescharacteristic
36C23×C8—21no—
37C23×C8—21no—
38C23×C8—21no—
39C22×C4⋊C4—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—21no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4D411yescharacteristic
48C22×C4⋊C4D411yescharacteristic
49C22×C4⋊C4D411yescharacteristic
50C22×C4⋊C4D411yescharacteristic
51C22×C42—21no—
52C22×C42C2311yescharacteristic
53C2×#103—42no—
54C2×#103—42no—
55C2×#103—42no—
56C2×#103—42no—
57C2×#103—42no—
58C2×#103—42no—
59#398—24no—
60#398—24no—
61#398—24no—
62#398—24no—
63#395—24no—
64#395—24no—
65#391—24no—
66#391—24no—
67#391—21no—
68#391—21no—
69#391—21no—
70#391—21no—
71#391C2×C412yes—
72#391C2×C412yes—
73#391D412yes—
74#391D412yes—
75#389—24no—
76#389—24no—
77#389—21no—
78#389—21no—
79#389C2×C412yes—
80#389D412yes—
81#387—24no—
82#387—24no—
83#384—42no—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—21no—
87C2×#95—21no—
88C2×#95—21no—
89C2×#95—21no—
90C2×#95—21no—
91C2×#95—21no—
92#340—42no—
93#340—42no—
94#340—42no—
95#340—42no—
96#336—21no—
97#336—21no—
98#336—21no—
99#336—21no—
100#336—21no—
101#336—21no—
102C22×Q8—21no—
103C22×Q8—21no—
104C22×Q8—21no—
105C22×Q8—21no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—21no—
110C22×Q8—41no—
111C22×Q8—41no—
112C22×Q8—41no—
113C22×Q8—41no—
114C22×Q8—41no—
115C22×Q8—41no—
116C22×Q8—41no—
117C22×Q8—41no—
118C22×Q8C22⋊C412yes—
119C22×Q8C22⋊C412yes—
120C22×Q8SD1612yes—
121C22×Q8Q1612yes—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—41no—
129C23×C4C2×D411yescharacteristic
130C23×C4C2×D411yescharacteristic
131C23×C4C2×D411yescharacteristic
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—41no—
136C22×C8—41no—
137C22×C8—41no—
138C22×C8—41no—
139C22×C8—41no—
140C22×C8—41no—
141C22×C8—41no—
142C22×C8—41no—
143C22×C8—41no—
144C22×C8—41no—
145C22×C8—41no—
146C22×C8—41no—
147C22×C8—41no—
148C22×C8—41no—
149C22×C8—41no—
150C22×C8—41no—
151C22×C8—41no—
152C22×C8—41no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4—41no—
173C2×C4⋊C4—41no—
174C2×C4⋊C4—41no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—41no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—41no—
193C2×C4⋊C4—81no—
194C2×C4⋊C4—81no—
195C2×C4⋊C4—81no—
196C2×C4⋊C4—81no—
197C2×C4⋊C4—81no—
198C2×C4⋊C4—81no—
199C2×C4⋊C4—81no—
200C2×C4⋊C4—81no—
201C2×C4⋊C4C22⋊C412yes—
202C2×C4⋊C4C22⋊C412yes—
203C2×C4⋊C4C22⋊C412yes—
204C2×C4⋊C4C22⋊C412yes—
205C2×C4⋊C4SD1612yes—
206C2×C4⋊C4Q1612yes—
207C2×C42—24no—
208C2×C42—41no—
209C2×C42—41no—
210C2×C42—81no—
211C2×C42—81no—
212C2×C42C22×C411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216#103—48no—
217#103—48no—
218#95—24no—
219#95—24no—
220#95—24no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95—22no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—22no—
231C24#12011yescharacteristic
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—42no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—81no—
252C2×Q8—81no—
253C2×Q8—81no—
254C2×Q8—81no—
255C2×Q8—81no—
256C2×Q8—81no—
257C2×Q8—81no—
258C2×Q8—81no—
259C2×Q8—81no—
260C2×Q8—81no—
261C2×Q8—81no—
262C2×Q8—81no—
263C2×Q8#10314yescomplemented
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—81no—
320C22×C4—81no—
321C22×C4—81no—
322C22×C4—81no—
323C22×C4—81no—
324C22×C4—81no—
325C22×C4C2×C22⋊C411yescharacteristic
326C22×C4C2×C22⋊C411yescharacteristic
327C22×C4C2×C22⋊C411yescharacteristic
328C22×C4#12011yescharacteristic
329C22×C4#12011yescharacteristic
330C22×C4#12011yescharacteristic
331C22×C4C2×SD1611yescharacteristic
332C22×C4C2×SD1611yescharacteristic
333C22×C4C2×Q1611yescharacteristic
334C22×C4C2×Q1611yescharacteristic
335C22×C4#13511yescharacteristic
336C22×C4#13511yescharacteristic
337C22×C4AGL(1,ℤ/8)11yescharacteristic
338C22×C4#13711yescharacteristic
339C22×C4#13711yescharacteristic
340C22×C4#13711yescharacteristic
341C22×C4#13711yescharacteristic
342C22×C4#13711yescharacteristic
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—81no—
353C2×C8—81no—
354C2×C8—81no—
355C2×C8—81no—
356C2×C8—81no—
357C2×C8—81no—
358C2×C8—81no—
359C2×C8—81no—
360C2×C8—81no—
361C2×C8—81no—
362C2×C8—81no—
363C2×C8—81no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—42no—
380C4⋊C4—81no—
381C4⋊C4—81no—
382C4⋊C4—81no—
383C4⋊C4—81no—
384C4⋊C4—81no—
385C4⋊C4—81no—
386C4⋊C4—81no—
387C4⋊C4—81no—
388C4⋊C4—81no—
389C4⋊C4—84no—
390C4⋊C4—84no—
391C4⋊C4—84no—
392C4⋊C4—84no—
393C4⋊C4#10314yescomplemented
394C42—41no—
395C42—41no—
396C42—41no—
397C42—41no—
398C42—84no—
399C23#37911yescharacteristic
400C23#44811yescharacteristic
401C23#44811yescharacteristic
402C23#44911yescharacteristic
403C23#45111yescharacteristic
404C23#45111yescharacteristic
405C23#45211yescharacteristic
406C23#45311yescharacteristic
407C23#45311yescharacteristic
408C23#45411yescharacteristic
409C23#45511yescharacteristic
410C23#45511yescharacteristic
411C23#45611yescharacteristic
412C23B(4,𝔽2)11yescharacteristic
413C23#45811yescharacteristic
414Q8—44no—
415Q8—44no—
416Q8—82no—
417Q8—82no—
418Q8—82no—
419Q8—82no—
420Q8—82no—
421Q8—82no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—161no—
504C2×C4—161no—
505C2×C4—161no—
506C2×C4—161no—
507C2×C4C2×#10311yescharacteristic
508C2×C4C2×#10311yescharacteristic
509C2×C4#41611yescharacteristic
510C2×C4#41711yescharacteristic
511C2×C4#41911yescharacteristic
512C2×C4#41911yescharacteristic
513C2×C4#44811yescharacteristic
514C2×C4#44811yescharacteristic
515C2×C4#44911yescharacteristic
516C2×C4#45111yescharacteristic
517C2×C4#45111yescharacteristic
518C2×C4#45211yescharacteristic
519C8—82no—
520C8—82no—
521C8—82no—
522C22#159611yescharacteristic
523C22#159911yescharacteristic
524C22#160011yescharacteristic
525C22#160211yescharacteristic
526C22#160511yescharacteristic
527C22#160611yescharacteristic
528C22#160811yescharacteristic
529C22#161111yescharacteristic
530C22#161211yescharacteristic
531C22#161411yescharacteristic
532C22#161711yescharacteristic
533C22#161811yescharacteristic
534C22#162211yescharacteristic
535C22#162311yescharacteristic
536C22#162611yescharacteristic
537C22#163211yescharacteristic
538C22#163311yescharacteristic
539C22#163611yescharacteristic
540C22#164311yescharacteristic
541C22#164411yescharacteristic
542C22#164511yescharacteristic
543C22#164511yescharacteristic
544C22#164811yescharacteristic
545C22#165311yescharacteristic
546C22#165611yescharacteristic
547C22#166111yescharacteristic
548C22#166111yescharacteristic
549C22#166211yescharacteristic
550C22#178711yescharacteristic
551C22#178711yescharacteristic
552C22#178811yescharacteristic
553C22#179011yescharacteristic
554C22#179211yescharacteristic
555C22#179211yescharacteristic
556C22#179311yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—44no—
570C4—44no—
571C4—82no—
572C4—82no—
573C4—82no—
574C4—82no—
575C4—162no—
576C2#774811yescharacteristic
577C2#776111yescharacteristic
578C2#776911yescharacteristic
579C2#778411yescharacteristic
580C2#780911yescharacteristic
581C2#781411yescharacteristic
582C2#781611yescharacteristic
583C2#783611yescharacteristic
584C2#840511yescharacteristic
585C2#840611yescharacteristic
586C2#840811yescharacteristic
587C2#844811yescharacteristic
588C2#845011yescharacteristic
589C2#845111yescharacteristic
590C2#850811yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
13. #2806C4semidirect
263. C2×Q8#103semidirect
393. C4⋊C4#103semidirect

Maximal subgroups

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

subgroupindex
C2×#28062
#112072
#110502
C2×#12722
C2×#12712