Finite Group Databasebeta

← #469739

Subgroups — #469739

Order 512.

1208 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
1C2×#1981C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3#15190C211yesmaximal, characteristic
4#13936C211yesmaximal, characteristic
5#11255C211yesmaximal, characteristic
6#11190C212yesmaximal
7#11124C212yesmaximal
8#11077C211yesmaximal, characteristic
9#11010C212yesmaximal
10#11010C212yesmaximal
11#11010C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×C4⋊Q8C2212yes—
14C22×#107C2211yescharacteristic
15C22×C4⋊C8C2211yescharacteristic
16C22×#103C2211yescharacteristic
17C22×#103C2211yescharacteristic
18C22×#103C2212yes—
19C22×#103C2212yes—
20C22×#103C2212yes—
21C22×#103C2212yes—
22C22×#103C2212yes—
23C2×#391C2211yescharacteristic
24C2×#391C2212yes—
25C2×C4×C4⋊C4C2211yescharacteristic
26#1981—24no—
27#1928—24no—
28C2×#340C2211yescharacteristic
29C2×#340C2212yes—
30C2×#336C2211yescharacteristic
31C2×#336C2212yes—
32C2×#336C2212yes—
33#1444—21no—
34#1444—22no—
35#1444—21no—
36#1443—22no—
37C4⋊#95C2211yescharacteristic
38C4⋊#95C2212yes—
39C4⋊#95C2212yes—
40#1434—21no—
41#1434—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2312yes—
44C23×Q8C2311yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—24no—
50C2×C4⋊Q8—24no—
51C2×C4⋊Q8—22no—
52C2×C4⋊Q8—22no—
53C2×C4⋊Q8—42no—
54C2×C4⋊Q8—42no—
55C2×C4⋊Q8—42no—
56C2×C4⋊Q8—42no—
57C2×C4⋊Q8—42no—
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4C2312yes—
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C42—21no—
67C22×C42C2312yes—
68C22×C42C2311yescharacteristic
69C2×#107—22no—
70C2×#107—42no—
71C2×C4⋊C8—22no—
72C2×C4⋊C8—42no—
73C2×#103—22no—
74C2×#103—22no—
75C2×#103—22no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—22no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—42no—
82C2×#103—42no—
83C2×#103—42no—
84C2×#103—42no—
85C2×#103—42no—
86C2×#103—42no—
87C2×#103—42no—
88C2×#103—42no—
89C2×#103—42no—
90C2×#103—42no—
91C2×#103—42no—
92C2×#103—42no—
93#391—22no—
94#391—22no—
95#391—42no—
96#391—42no—
97C4×C4⋊C4—22no—
98C4×C4⋊C4D414yes—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—21no—
105C2×#95—21no—
106C2×#95—22no—
107C2×#95—22no—
108C2×#95—22no—
109C2×#95—21no—
110C2×#95D411yescharacteristic
111C2×#95D412yes—
112C2×#95D411yescharacteristic
113#340—22no—
114#340—42no—
115#336—22no—
116#336—42no—
117#336—42no—
118C22×Q8—22no—
119C22×Q8—21no—
120C22×Q8—22no—
121C22×Q8—21no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—21no—
127C22×Q8—21no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—22no—
137C22×Q8—22no—
138C22×Q8—22no—
139C22×Q8—21no—
140C22×Q8#4112yes—
141C22×Q8#4114yes—
142C23×C4—21no—
143C23×C4—22no—
144C23×C4—21no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4—22no—
148C23×C4C2×D411yescharacteristic
149C23×C4C2×D412yes—
150C23×C4C2×D412yes—
151C23×C4C2×D411yescharacteristic
152C23×C4C2411yescharacteristic
153C22×C8—21no—
154C22×C8—21no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—21no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—21no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—22no—
165C22×C8—22no—
166C22×C8—22no—
167C22×C8—21no—
168C22×C8—22no—
169C22×C8#4112yes—
170C4⋊Q8—28no—
171C4⋊Q8—48no—
172C4⋊Q8—44no—
173C4⋊Q8—48no—
174C4⋊Q8—48no—
175C4⋊Q8—48no—
176C4⋊Q8—48no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—44no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4—44no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4C2×D412yes—
206C2×C4⋊C4C2×D412yes—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—24no—
216C2×C42—82no—
217C2×C42C2×D412yes—
218C2×C42#4112yes—
219#107—44no—
220C4⋊C8—44no—
221#103—28no—
222#103—48no—
223#103—48no—
224#103—44no—
225#103—48no—
226#103—48no—
227#103—48no—
228#95—24no—
229#95—24no—
230#95—22no—
231#95—44no—
232#95—44no—
233#95—42no—
234#95—42no—
235#95—44no—
236#95—42no—
237#95—82no—
238#95—82no—
239#95—82no—
240#95—81no—
241#95Q1614yes—
242C24C22×D411yescharacteristic
243C2×Q8—22no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8—24no—
247C2×Q8—24no—
248C2×Q8—24no—
249C2×Q8—24no—
250C2×Q8—24no—
251C2×Q8—22no—
252C2×Q8—24no—
253C2×Q8—42no—
254C2×Q8—41no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—41no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—41no—
267C2×Q8—42no—
268C2×Q8—41no—
269C2×Q8—42no—
270C2×Q8—41no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8—42no—
288C2×Q8—42no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—41no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—41no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4#12112yes—
342C22×C4#12112yes—
343C22×C4C2×Q1614yes—
344C22×C4C2×Q1612yes—
345C22×C4#13714yes—
346C22×C4#13712yes—
347C22×C4C22×D411yescharacteristic
348C22×C4C2×#4112yes—
349C22×C4C2×#4111yescharacteristic
350C22×C4C2×#4111yescharacteristic
351C22×C4C2×#4111yescharacteristic
352C22×C4H(5,𝔽2)12yes—
353C22×C4H(5,𝔽2)12yes—
354C22×C4H(5,𝔽2)11yescharacteristic
355C22×C4H(5,𝔽2)11yescharacteristic
356C22×C4H(5,𝔽2)12yes—
357C2×C8—22no—
358C2×C8—24no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8—41no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—41no—
366C2×C8—42no—
367C2×C8—41no—
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—42no—
373C2×C8—42no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—48no—
379C4⋊C4—48no—
380C4⋊C4—416no—
381C4⋊C4—416no—
382C4⋊C4—42no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C42—22no—
393C42—22no—
394C42—24no—
395C42—42no—
396C42—42no—
397C42—42no—
398C42—42no—
399C42—84no—
400C23C2×#12111yescharacteristic
401C23#53512yes—
402C23#54611yescharacteristic
403C23#54612yes—
404C23#55011yescharacteristic
405C23C22×Q1611yescharacteristic
406C23C2×#13711yescharacteristic
407C23C2×#13712yes—
408C23#57711yescharacteristic
409C23#57712yes—
410C23#57811yescharacteristic
411Q8—42no—
412Q8—44no—
413Q8—42no—
414Q8—44no—
415Q8—44no—
416Q8—44no—
417Q8—44no—
418Q8—82no—
419Q8—81no—
420Q8—82no—
421Q8—81no—
422Q8—82no—
423Q8—82no—
424Q8—82no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—81no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—81no—
463C2×C4—82no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—81no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4#46214yes—
483C2×C4#52511yescharacteristic
484C2×C4#52511yescharacteristic
485C2×C4#53511yescharacteristic
486C2×C4#53511yescharacteristic
487C2×C4#53511yescharacteristic
488C2×C4#53511yescharacteristic
489C2×C4#53812yes—
490C2×C4#53812yes—
491C2×C4#53812yes—
492C2×C4#53812yes—
493C2×C4#54012yes—
494C2×C4#55112yes—
495C2×C4#55112yes—
496C2×C4#55312yes—
497C2×C4#55311yescharacteristic
498C2×C4#55511yescharacteristic
499C2×C4#56012yes—
500C2×C4#56012yes—
501C8—42no—
502C8—82no—
503C8—81no—
504C22#241111yescharacteristic
505C22#241411yescharacteristic
506C22#261911yescharacteristic
507C22#268512yes—
508C22#271412yes—
509C22C2×#46211yescharacteristic
510C22#303911yescharacteristic
511C22#304211yescharacteristic
512C22#304611yescharacteristic
513C22#320912yes—
514C22#321812yes—
515C22#322112yes—
516C22#322512yes—
517C22#329911yescharacteristic
518C22#329912yes—
519C22#331212yes—
520C22#332012yes—
521C22#332012yes—
522C22#332811yescharacteristic
523C22#332912yes—
524C22#339511yescharacteristic
525C22#340011yescharacteristic
526C22#340012yes—
527C4—24no—
528C4—44no—
529C4—44no—
530C4—42no—
531C4—84no—
532C4—82no—
533C4—82no—
534C4—82no—
535C4—161no—
536C4—162no—
537C4#259811yescharacteristic
538C4#263111yescharacteristic
539C4#263111yescharacteristic
540C4#274912yes—
541C4#275612yes—
542C4#281811yescharacteristic
543C2#1666211yescharacteristic
544C2#2448211yescharacteristic
545C2#2449811yescharacteristic
546C2#2463211yescharacteristic
547C2#2464611yescharacteristic
548C2#2979911yescharacteristic
549C2#2980411yescharacteristic
550C2#3129212yes—
551C2#3131212yes—
552C2#3216812yes—
553C2#3218212yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#19812
C2×#19282
#151902
#139362
#112552
#111902
#111242
#110772
#110102