Finite Group Databasebeta

← #465193

Subgroups — #465193

Order 512.

1204 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×#2056C212yesmaximal
2C2×#2016C211yesmaximal, characteristic
3C2×#1832C211yesmaximal, characteristic
4#14274C211yesmaximal, characteristic
5#14261C211yesmaximal, characteristic
6#11268C211yesmaximal, characteristic
7#11077C212yesmaximal
8#11067C212yesmaximal
9#11052C211yesmaximal, characteristic
10#11024C212yesmaximal
11#11010C211yesmaximal, characteristic
12C23×Q16C2212yes—
13C22×C4⋊Q8C2211yescharacteristic
14C22×C4⋊C8C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#103C2212yes—
19C2×#391C2211yescharacteristic
20C2×#391C2212yes—
21C2×#391C2211yescharacteristic
22C2×#391C2211yescharacteristic
23C2×#391C2212yes—
24C2×#389C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×#376C2211yescharacteristic
27#2056—28no—
28#2016—24no—
29#1832—24no—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#336C2211yescharacteristic
34C2×#336C2212yes—
35C2×#336C2211yescharacteristic
36#1445—22no—
37#1445—22no—
38#1443—22no—
39#1442—22no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2211yescharacteristic
42C23×Q8C2311yescharacteristic
43C23×Q8C2312yes—
44C22×Q16—24no—
45C22×Q16—24no—
46C22×Q16—24no—
47C22×Q16—42no—
48C22×Q16—42no—
49C22×Q16—42no—
50C22×Q16—42no—
51C23×C8C2312yes—
52C23×C8C2312yes—
53C2×C4⋊Q8—24no—
54C2×C4⋊Q8—22no—
55C2×C4⋊Q8—22no—
56C2×C4⋊Q8—42no—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2312yes—
62C22×C4⋊C4C2311yescharacteristic
63C22×C42C2311yescharacteristic
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C2×C4⋊C8—24no—
67C2×C4⋊C8—24no—
68C2×C4⋊C8—42no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—24no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76C2×#103—42no—
77C2×#103—42no—
78C2×#103—42no—
79C2×#103—42no—
80C2×#103—42no—
81#391—22no—
82#391—24no—
83#391—22no—
84#391—22no—
85#391—24no—
86#391—42no—
87#391—42no—
88#391—42no—
89#391D414yes—
90#389—42no—
91#382—42no—
92#376—22no—
93#376—22no—
94C2×#95—22no—
95C2×#95—21no—
96C2×#95—22no—
97C2×#95—21no—
98C2×#95—21no—
99C2×#95—22no—
100C2×#95—22no—
101C2×#95—22no—
102C2×#95—24no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95D412yes—
106C2×#95D412yes—
107#340—24no—
108#340—42no—
109#340—42no—
110#336—24no—
111#336—22no—
112#336D414yes—
113C22×Q8—22no—
114C22×Q8—21no—
115C22×Q8—22no—
116C22×Q8—21no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—21no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—22no—
134C22×Q8—21no—
135C22×Q8C2×D412yes—
136C22×Q8#4114yes—
137C23×C4—22no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—22no—
142C23×C4—21no—
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D412yes—
146C23×C4C2×D412yes—
147C23×C4C2411yescharacteristic
148C2×Q16—48no—
149C2×Q16—48no—
150C2×Q16—48no—
151C2×Q16—48no—
152C2×Q16—48no—
153C2×Q16—48no—
154C2×Q16—48no—
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—22no—
165C22×C8—22no—
166C22×C8—22no—
167C22×C8—22no—
168C22×C8C2×D414yes—
169C4⋊Q8—48no—
170C4⋊Q8—48no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—28no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—82no—
193C2×C4⋊C4C2×D412yes—
194C2×C42—21no—
195C2×C42—22no—
196C2×C42—21no—
197C2×C42—22no—
198C2×C42—21no—
199C2×C42—21no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42C2×D412yes—
205C2×C42C2×D412yes—
206C2×C42#4112yes—
207C2×C42#4112yes—
208C4⋊C8—48no—
209#103—48no—
210#103—48no—
211#103—48no—
212#103—48no—
213#95—28no—
214#95—24no—
215#95—24no—
216#95—44no—
217#95—42no—
218#95—42no—
219#95—44no—
220#95—44no—
221#95—42no—
222#95—48no—
223#95—44no—
224#95—82no—
225#95—82no—
226C24C22×D411yescharacteristic
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—22no—
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—24no—
236C2×Q8—24no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×Q8—42no—
244C2×Q8—41no—
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—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—42no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—42no—
329C22×C4#12114yes—
330C22×C4#12114yes—
331C22×C4C22×D411yescharacteristic
332C22×C4C22×D411yescharacteristic
333C22×C4C2×#4112yes—
334C22×C4C2×#4111yescharacteristic
335C22×C4C2×#4111yescharacteristic
336C22×C4H(5,𝔽2)12yes—
337C22×C4H(5,𝔽2)12yes—
338C22×C4H(5,𝔽2)12yes—
339C22×C4H(5,𝔽2)11yescharacteristic
340C22×C42−1+411yescharacteristic
341Q16—432no—
342C2×C8—24no—
343C2×C8—24no—
344C2×C8—24no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C2×C8—42no—
350C2×C8—42no—
351C2×C8—42no—
352C2×C8—42no—
353C2×C8—42no—
354C2×C8—42no—
355C2×C8—42no—
356C4⋊C4—24no—
357C4⋊C4—416no—
358C4⋊C4—42no—
359C4⋊C4—42no—
360C4⋊C4—42no—
361C4⋊C4—42no—
362C4⋊C4—42no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—42no—
367C4⋊C4—84no—
368C42—22no—
369C42—24no—
370C42—22no—
371C42—22no—
372C42—24no—
373C42—22no—
374C42—42no—
375C42—42no—
376C23C2×#12111yescharacteristic
377C23C2×#12111yescharacteristic
378C23#52511yescharacteristic
379C23#53511yescharacteristic
380C23#53511yescharacteristic
381C23#53511yescharacteristic
382C23#53711yescharacteristic
383C23#57712yes—
384C23#57812yes—
385C23#57812yes—
386C23#57812yes—
387Q8—44no—
388Q8—44no—
389Q8—44no—
390Q8—44no—
391Q8—44no—
392Q8—44no—
393Q8—82no—
394Q8—82no—
395Q8—82no—
396Q8—82no—
397Q8—82no—
398Q8—82no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—44no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
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—82no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—82no—
459C2×C4#53512yes—
460C2×C4#53512yes—
461C2×C4#53812yes—
462C2×C4#53912yes—
463C2×C4#54012yes—
464C2×C4#54012yes—
465C2×C4D4211yescharacteristic
466C2×C4#54612yes—
467C2×C4#54612yes—
468C2×C4#54711yescharacteristic
469C2×C4#54811yescharacteristic
470C2×C4#55112yes—
471C2×C4#55312yes—
472C2×C4#55311yescharacteristic
473C2×C4H(3,𝔽4)12yes—
474C2×C4#56212yes—
475C8—44no—
476C8—82no—
477C22#241111yescharacteristic
478C22#241611yescharacteristic
479C22#253511yescharacteristic
480C22#261911yescharacteristic
481C22#261911yescharacteristic
482C22#263611yescharacteristic
483C22#281911yescharacteristic
484C22#304412yes—
485C22#304612yes—
486C22#305912yes—
487C22#306312yes—
488C22#312112yes—
489C22#312712yes—
490C22#322211yescharacteristic
491C22#322311yescharacteristic
492C22#322311yescharacteristic
493C22#322311yescharacteristic
494C22#322312yes—
495C22#322312yes—
496C22#322512yes—
497C22#322512yes—
498C22#325812yes—
499C22#326112yes—
500C4—44no—
501C4—44no—
502C4—82no—
503C4—81no—
504C4—81no—
505C4—82no—
506C4—84no—
507C4—161no—
508C4—162no—
509C4—161no—
510C4#267012yes—
511C4#270612yes—
512C4#271112yes—
513C4#275312yes—
514C2#1651611yescharacteristic
515C2#2451412yes—
516C2#2476412yes—
517C2#2817011yescharacteristic
518C2#2817311yescharacteristic
519C2#2980512yes—
520C2#2981211yescharacteristic
521C2#2981711yescharacteristic
522C2#3014012yes—
523C2#3281311yescharacteristic
524C2#3281611yescharacteristic
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×#20562
C2×#20162
C2×#18322
#142742
#142612
#112682
#110772
#110672
#110522
#110242
#110102