Finite Group Databasebeta

← #471520

Subgroups — #471520

Order 512.

1152 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2074C211yesmaximal, characteristic
2C2×#2016C211yesmaximal, characteristic
3#14274C211yesmaximal, characteristic
4#14261C211yesmaximal, characteristic
5#11358C211yesmaximal, characteristic
6#11190C212yesmaximal
7#11067C212yesmaximal
8#11024C212yesmaximal
9#11024C212yesmaximal
10#11010C211yesmaximal, characteristic
11#10796C211yesmaximal, characteristic
12C23×Q16C2212yes—
13C22×C4⋊Q8C2211yescharacteristic
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C2×#391C2211yescharacteristic
19C2×#391C2211yescharacteristic
20C2×#391C2211yescharacteristic
21C2×#391C2212yes—
22C2×#391C2212yes—
23C2×#389C2211yescharacteristic
24C2×#382C2211yescharacteristic
25C2×#376C2211yescharacteristic
26#2074—24no—
27#2016—24no—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#336C2211yescharacteristic
32C2×#336C2212yes—
33C2×#336C2211yescharacteristic
34C2×#336C2212yes—
35#1445—22no—
36#1445—22no—
37#1443—22no—
38#1442—22no—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C23×Q8C2311yescharacteristic
42C23×Q8C2312yes—
43C22×Q16—24no—
44C22×Q16—24no—
45C22×Q16—24no—
46C22×Q16—42no—
47C22×Q16—42no—
48C22×Q16—42no—
49C22×Q16—42no—
50C23×C8C2312yes—
51C23×C8C2312yes—
52C2×C4⋊Q8—24no—
53C2×C4⋊Q8—22no—
54C2×C4⋊Q8—22no—
55C2×C4⋊Q8—42no—
56C22×C4⋊C4—22no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2312yes—
61C22×C4⋊C4C2311yescharacteristic
62C22×C42C2311yescharacteristic
63C22×C42C2311yescharacteristic
64C22×C42C2311yescharacteristic
65C2×#103—24no—
66C2×#103—24no—
67C2×#103—24no—
68C2×#103—24no—
69C2×#103—42no—
70C2×#103—42no—
71C2×#103—42no—
72C2×#103—42no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76C2×#103—42no—
77#391—22no—
78#391—42no—
79#391—42no—
80#391—42no—
81#391—42no—
82#391—42no—
83#391—42no—
84#391D414yes—
85#389—42no—
86#382—22no—
87#382—22no—
88#376—42no—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—22no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95—22no—
97C2×#95—24no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95D412yes—
101C2×#95D412yes—
102#340—24no—
103#340—42no—
104#340—42no—
105#336—24no—
106#336—22no—
107#336—22no—
108#336—42no—
109C22×Q8—22no—
110C22×Q8—21no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—21no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—21no—
129C22×Q8—21no—
130C22×Q8—22no—
131C22×Q8C2×D412yes—
132C22×Q8#4114yes—
133C23×C4—22no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—22no—
138C23×C4—21no—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D412yes—
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D412yes—
143C23×C4C2411yescharacteristic
144C2×Q16—48no—
145C2×Q16—48no—
146C2×Q16—48no—
147C2×Q16—48no—
148C2×Q16—48no—
149C2×Q16—48no—
150C2×Q16—48no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8#4114yes—
165C4⋊Q8—48no—
166C4⋊Q8—48no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—28no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—82no—
189C2×C4⋊C4C2×D412yes—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×D412yes—
201C2×C42#4112yes—
202#103—48no—
203#103—48no—
204#103—48no—
205#103—48no—
206#95—28no—
207#95—42no—
208#95—42no—
209#95—42no—
210#95—44no—
211#95—42no—
212#95—48no—
213#95—44no—
214#95—44no—
215#95—42no—
216#95—44no—
217#95—82no—
218#95—82no—
219C24C22×D411yescharacteristic
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—24no—
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
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—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4#12114yes—
324C22×C4C22×D411yescharacteristic
325C22×C4C2×#4112yes—
326C22×C4C2×#4112yes—
327C22×C4C2×#4111yescharacteristic
328C22×C4H(5,𝔽2)11yescharacteristic
329C22×C4H(5,𝔽2)11yescharacteristic
330C22×C4H(5,𝔽2)11yescharacteristic
331C22×C4H(5,𝔽2)11yescharacteristic
332C22×C4H(5,𝔽2)12yes—
333C22×C4H(5,𝔽2)12yes—
334Q16—432no—
335C2×C8—24no—
336C2×C8—24no—
337C2×C8—24no—
338C2×C8—42no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—42no—
342C2×C8—42no—
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C4⋊C4—24no—
350C4⋊C4—416no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4—42no—
357C4⋊C4—42no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—84no—
361C42—24no—
362C42—24no—
363C42—42no—
364C42—42no—
365C42—42no—
366C42—42no—
367C23C2×#12111yescharacteristic
368C23#52511yescharacteristic
369C23#53211yescharacteristic
370C23#53411yescharacteristic
371C23#53511yescharacteristic
372C23#53511yescharacteristic
373C23#53511yescharacteristic
374C23#57712yes—
375C23#57812yes—
376C23#57812yes—
377C23#57812yes—
378Q8—44no—
379Q8—44no—
380Q8—44no—
381Q8—44no—
382Q8—44no—
383Q8—44no—
384Q8—82no—
385Q8—82no—
386Q8—82no—
387Q8—82no—
388Q8—82no—
389Q8—82no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—44no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—81no—
423C2×C4—82no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—82no—
431C2×C4—81no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—82no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—81no—
450C2×C4#53511yescharacteristic
451C2×C4#53511yescharacteristic
452C2×C4#53812yes—
453C2×C4#53812yes—
454C2×C4#53812yes—
455C2×C4#54012yes—
456C2×C4#54011yescharacteristic
457C2×C4#54011yescharacteristic
458C2×C4#54612yes—
459C2×C4#54612yes—
460C2×C4#55112yes—
461C2×C4#55112yes—
462C2×C4#55312yes—
463C2×C4#55912yes—
464C2×C4#56012yes—
465C2×C4#56012yes—
466C8—44no—
467C8—82no—
468C22#253411yescharacteristic
469C22#254411yescharacteristic
470C22#260311yescharacteristic
471C22#261911yescharacteristic
472C22#263111yescharacteristic
473C22#266111yescharacteristic
474C22#281511yescharacteristic
475C22#304412yes—
476C22#304612yes—
477C22#312112yes—
478C22#312712yes—
479C22#317712yes—
480C22#317812yes—
481C22#320112yes—
482C22#320212yes—
483C22#322211yescharacteristic
484C22#322312yes—
485C22#322311yescharacteristic
486C22#322311yescharacteristic
487C22#322312yes—
488C22#322311yescharacteristic
489C22#322512yes—
490C22#322512yes—
491C4—44no—
492C4—81no—
493C4—82no—
494C4—84no—
495C4—82no—
496C4—82no—
497C4—81no—
498C4—161no—
499C4—162no—
500C4—161no—
501C4#268512yes—
502C4#270312yes—
503C4#275212yes—
504C4#279712yes—
505C2#1679911yescharacteristic
506C2#2813212yes—
507C2#2862511yescharacteristic
508C2#2862911yescharacteristic
509C2#2950912yes—
510C2#2980512yes—
511C2#3005011yescharacteristic
512C2#3005211yescharacteristic
513C2#3033112yes—
514C2#3276711yescharacteristic
515C2#3276811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#20742
C2×#20162
#142742
#142612
#113582
#111902
#110672
#110242
#110102
#107962