Finite Group Databasebeta

← #412532

Subgroups — #412532

Order 512.

1012 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2064C212yesmaximal
2C2×#1950C211yesmaximal, characteristic
3#21172C211yesmaximal, characteristic
4#20793C211yesmaximal, characteristic
5C2×#1805C211yesmaximal, characteristic
6C2×#1801C211yesmaximal, characteristic
7C4×#419C211yesmaximal, characteristic
8#11242C212yesmaximal
9#11216C212yesmaximal
10#11062C212yesmaximal
11#10858C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C22×#108C2212yes—
14C2×#428C2212yes—
15C2×#424C2212yes—
16C2×#424C2212yes—
17C2×#423C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C2×#419C2211yescharacteristic
21C2×#419C2211yescharacteristic
22C22×#103C2212yes—
23C22×#101C2212yes—
24C2×C4×M16C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C4×#117C2211yescharacteristic
27#2064—28no—
28#1950—24no—
29#1949—22no—
30#1949—22no—
31#1843—22no—
32#1842—22no—
33#1805—22no—
34#1805—22no—
35#1801—24no—
36#1763—22no—
37C4×#103—22no—
38C2×#343C2212yes—
39C2×#343C2212yes—
40C2×#343C2212yes—
41C2×#341C2212yes—
42#1736C2212yes—
43#1736C2211yescharacteristic
44#1736C2211yescharacteristic
45C2×#340C2212yes—
46C23×Q8C2311yescharacteristic
47C22×M16C2312yes—
48C22×M16C2311yescharacteristic
49C22×M16C2312yes—
50C22×M16C2311yescharacteristic
51C23×C8C2312yes—
52C2×C4×Q8—22no—
53C2×C4×Q8—21no—
54C2×C4×Q8—21no—
55C2×C4×Q8—21no—
56C2×C4×Q8—21no—
57C2×C4×Q8—22no—
58C2×C4×Q8—22no—
59C2×C4×Q8Q814yes—
60C2×#117C2311yescharacteristic
61C2×#117C2311yescharacteristic
62C22×C4⋊C4—21no—
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C42—21no—
66C22×C42C2311yescharacteristic
67C2×#108—24no—
68C2×#108—24no—
69C2×#108—42no—
70#428—24no—
71#428—24no—
72C2×#107—22no—
73C2×#106—22no—
74#424—24no—
75#424—24no—
76#424—42no—
77#424—42no—
78#423—22no—
79#423—22no—
80#423—22no—
81#423D414yes—
82C2×C4⋊C8—22no—
83C2×C4⋊C8—21no—
84C2×C4⋊C8—21no—
85C2×C4⋊C8—22no—
86C2×C4⋊C8—24no—
87C2×C4⋊C8—24no—
88C2×C4⋊C8—21no—
89C2×C4⋊C8—21no—
90C2×C4⋊C8D412yes—
91C2×C4⋊C8D412yes—
92#419—22no—
93#419—22no—
94#419D414yes—
95#419Q814yes—
96C2×#103—22no—
97C2×#103—22no—
98C2×#103—24no—
99C2×#103—24no—
100C2×#103—42no—
101C2×#101—24no—
102C2×#101—24no—
103C2×#101—42no—
104C4×M16—22no—
105C4×M16—22no—
106C2×#97—21no—
107C2×C4×C8—21no—
108#382—21no—
109#382—21no—
110#382—21no—
111#382—21no—
112C4×C4⋊C4D412yes—
113C4×C4⋊C4D412yes—
114C4×C22⋊C4—21no—
115C4×C22⋊C4—21no—
116#376—21no—
117C2×#95—21no—
118C2×#95—21no—
119C43—21no—
120#343—24no—
121#343—24no—
122#343—42no—
123#341—24no—
124#340—24no—
125#340—24no—
126#340—22no—
127#340—22no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—21no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—21no—
136C22×Q8—21no—
137C22×Q8—21no—
138C22×Q8—21no—
139C22×Q8C2×D412yes—
140C22×Q8C2×Q812yes—
141C22×Q8C2×Q812yes—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—22no—
145C23×C4#4111yescharacteristic
146C23×C4#4111yescharacteristic
147C23×C4C2411yescharacteristic
148C2×M16—21no—
149C2×M16—21no—
150C2×M16—22no—
151C2×M16—21no—
152C2×M16—21no—
153C2×M16—22no—
154C2×M16—21no—
155C2×M16—21no—
156C2×M16—22no—
157C2×M16—21no—
158C2×M16—22no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16—22no—
162C2×M16—21no—
163C2×M16—22no—
164C2×M16—22no—
165C2×M16—22no—
166C2×M16—22no—
167C2×M16—22no—
168C2×M16—22no—
169C2×M16C2×D414yes—
170C2×M16C2×D412yes—
171C2×M16C2×Q812yes—
172C22×C8—22no—
173C22×C8—22no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—22no—
177C22×C8—22no—
178C22×C8—22no—
179C22×C8—22no—
180C22×C8—22no—
181C22×C8—22no—
182C22×C8C2×D414yes—
183C4×Q8—24no—
184C4×Q8—24no—
185C4×Q8—24no—
186C4×Q8—24no—
187C4×Q8—42no—
188C4×Q8—42no—
189C4×Q8—42no—
190C4×Q8—42no—
191#117—21no—
192#117—21no—
193#117—21no—
194#117—21no—
195#117C2×D412yes—
196#117C2×Q812yes—
197#117#4112yes—
198#117#4112yes—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—42no—
214C2×C4⋊C4C2×D412yes—
215C2×C4⋊C4C2×D412yes—
216C2×C4⋊C4C2×Q812yes—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—21no—
220C2×C42—21no—
221C2×C42—22no—
222C2×C42—24no—
223C2×C42—22no—
224C2×C42—41no—
225C2×C42—41no—
226C2×C42—42no—
227C2×C42C2×D412yes—
228C2×C42C2×D411yescharacteristic
229C2×C42C2×D411yescharacteristic
230C2×C42C2×D411yescharacteristic
231C2×C42C2×D411yescharacteristic
232C2×C42C2×Q812yes—
233C2×C42#4112yes—
234C2×C42#4112yes—
235#108—48no—
236#107—44no—
237#106—44no—
238C4⋊C8—24no—
239C4⋊C8—24no—
240C4⋊C8—24no—
241C4⋊C8—24no—
242C4⋊C8—48no—
243C4⋊C8—48no—
244C4⋊C8—42no—
245C4⋊C8—42no—
246#103—28no—
247#103—28no—
248#103—48no—
249#101—48no—
250#97—42no—
251C4×C8—42no—
252#95—22no—
253#95—22no—
254#95—41no—
255#95—41no—
256#95—41no—
257#95—41no—
258C24C2×#4111yescharacteristic
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—22no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8C4⋊Q814yes—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—41no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—82no—
305C22×C4—82no—
306C22×C4—82no—
307C22×C4#12111yescharacteristic
308C22×C4#12111yescharacteristic
309C22×C4#12111yescharacteristic
310C22×C4#12111yescharacteristic
311C22×C4C22⋊Q812yes—
312C22×C4C22⋊Q812yes—
313C22×C4#12612yes—
314C22×C4#12612yes—
315C22×C4C22×D411yescharacteristic
316C22×C4C22×D411yescharacteristic
317C22×C4C22×D411yescharacteristic
318C22×C4C22×D411yescharacteristic
319C22×C4C22×Q811yescharacteristic
320C22×C4C22×Q811yescharacteristic
321C22×C4C2×#4111yescharacteristic
322C22×C4C2×#4111yescharacteristic
323C22×C4C2×#4111yescharacteristic
324C22×C4C2×#4111yescharacteristic
325C22×C4H(5,𝔽2)11yescharacteristic
326C22×C4H(5,𝔽2)11yescharacteristic
327C22×C42−1+411yescharacteristic
328C22×C42−1+411yescharacteristic
329M16—24no—
330M16—22no—
331M16—24no—
332M16—22no—
333M16—22no—
334M16—22no—
335M16—41no—
336M16—42no—
337M16—41no—
338M16—41no—
339M16—42no—
340M16—41no—
341M16—42no—
342M16—42no—
343M16—42no—
344M16—42no—
345C2×C8—22no—
346C2×C8—24no—
347C2×C8—24no—
348C2×C8—22no—
349C2×C8—24no—
350C2×C8—24no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—41no—
356C2×C8—42no—
357C2×C8—41no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—42no—
361C2×C8—42no—
362C2×C8—42no—
363C2×C8—42no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—44no—
371C4⋊C4—44no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—42no—
376C4⋊C4#12114yes—
377C4⋊C4C22⋊Q814yes—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C42—22no—
383C42—22no—
384C42—22no—
385C42—22no—
386C42—44no—
387C42—44no—
388C42—44no—
389C42—82no—
390C42#12112yes—
391C42#12112yes—
392C42#12112yes—
393C42#12112yes—
394C42C22⋊Q812yes—
395C42C22⋊Q812yes—
396C42C22⋊Q812yes—
397C42C22⋊Q812yes—
398C23—22no—
399C23—22no—
400C23C2×#12111yescharacteristic
401C23C2×C22⋊Q811yescharacteristic
402C23C2×#12611yescharacteristic
403C23#54711yescharacteristic
404C23#55211yescharacteristic
405C23#55311yescharacteristic
406C23#55411yescharacteristic
407Q8—24no—
408Q8—24no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
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—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—162no—
444C2×C4—162no—
445C2×C4#39612yes—
446C2×C4#39612yes—
447C2×C4#39612yes—
448C2×C4#39612yes—
449C2×C4C2×#12111yescharacteristic
450C2×C4C2×#12111yescharacteristic
451C2×C4C2×#12111yescharacteristic
452C2×C4C2×C22⋊Q811yescharacteristic
453C2×C4C2×C22⋊Q811yescharacteristic
454C2×C4C2×C22⋊Q811yescharacteristic
455C2×C4C2×C4⋊Q811yescharacteristic
456C2×C4#53211yescharacteristic
457C2×C4#53311yescharacteristic
458C2×C4#53311yescharacteristic
459C2×C4#53711yescharacteristic
460C2×C4#53711yescharacteristic
461C2×C4#54011yescharacteristic
462C2×C4#54111yescharacteristic
463C2×C4#54411yescharacteristic
464C2×C4#54411yescharacteristic
465C2×C4D4211yescharacteristic
466C2×C4D4211yescharacteristic
467C2×C4#54611yescharacteristic
468C2×C4#54711yescharacteristic
469C2×C4#54711yescharacteristic
470C2×C4#54811yescharacteristic
471C2×C4D4×Q811yescharacteristic
472C2×C4D4×Q811yescharacteristic
473C2×C4#55011yescharacteristic
474C2×C4#55411yescharacteristic
475C2×C4#55511yescharacteristic
476C2×C4#55611yescharacteristic
477C8—44no—
478C8—42no—
479C8—44no—
480C8—42no—
481C8—82no—
482C22—22no—
483C22—22no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—22no—
489C22—22no—
490C22C2×#39611yescharacteristic
491C22#241611yescharacteristic
492C22#241711yescharacteristic
493C22#244011yescharacteristic
494C22#244111yescharacteristic
495C22#249611yescharacteristic
496C22#249711yescharacteristic
497C22#306712yes—
498C22#306912yes—
499C4—22no—
500C4—22no—
501C4—22no—
502C4—22no—
503C4—44no—
504C4—44no—
505C4—44no—
506C4—82no—
507C4—162no—
508C4#242811yescharacteristic
509C4#242911yescharacteristic
510C4#243911yescharacteristic
511C4#244011yescharacteristic
512C4#253711yescharacteristic
513C4#253811yescharacteristic
514C4#262911yescharacteristic
515C4#285711yescharacteristic
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2#1513111yescharacteristic
521C2#2360111yescharacteristic
522C2#2360311yescharacteristic
523C2#2477512yes—
524C2#2486012yes—
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC23×C4C24
prime radicalC24C2×#41
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ 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×#20642
C2×#19502
#211722
#207932
C2×#18052
C2×#18012
C4×#4192
#112422
#112162
#110622
#108582