Finite Group Databasebeta

← #401949

Subgroups — #401949

Order 512.

1174 conjugacy classes of subgroups.

The subgroup lattice has 511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1865C211yesmaximal, characteristic
2C2×#1803C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4Q8×#95C211yesmaximal, characteristic
5#11357C211yesmaximal, characteristic
6#11315C212yesmaximal
7#11257C212yesmaximal
8#11255C211yesmaximal, characteristic
9#11227C211yesmaximal, characteristic
10#10789C212yesmaximal
11#10789C212yesmaximal
12C22×C4×Q8C2212yes—
13C22×C4×Q8C2211yescharacteristic
14C22×#106C2211yescharacteristic
15C22×C4⋊C8C2211yescharacteristic
16C22×#103C2211yescharacteristic
17C22×#103C2212yes—
18C22×#103C2211yescharacteristic
19C2×#389C2211yescharacteristic
20C2×#384C2211yescharacteristic
21#1865—24no—
22#1803—24no—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2211yescharacteristic
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#336C2211yescharacteristic
30C2×#336C2212yes—
31C2×#336C2212yes—
32#1442—22no—
33#1441—21no—
34#1441—21no—
35C4⋊#95—21no—
36C4⋊#95—22no—
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C4⋊#95C2212yes—
40C4⋊#95C2211yescharacteristic
41C4×#95—21no—
42C4×#95C2211yescharacteristic
43C23×Q8C2311yescharacteristic
44C23×C8C2312yes—
45C23×C8C2311yescharacteristic
46C23×C8C2311yescharacteristic
47C2×C4×Q8—24no—
48C2×C4×Q8—24no—
49C2×C4×Q8—22no—
50C2×C4×Q8—24no—
51C2×C4×Q8—24no—
52C2×C4×Q8—24no—
53C2×C4×Q8—42no—
54C2×C4×Q8—42no—
55C2×C4×Q8—42no—
56C2×C4×Q8D414yes—
57C22×C4⋊C4—22no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C4⋊C4C2311yescharacteristic
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2312yes—
67C22×C42—22no—
68C22×C42—21no—
69C22×C42C2312yes—
70C22×C42C2311yescharacteristic
71C2×#106—22no—
72C2×#106—42no—
73C2×C4⋊C8—22no—
74C2×C4⋊C8—42no—
75C2×#103—22no—
76C2×#103—22no—
77C2×#103—24no—
78C2×#103—22no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—24no—
82C2×#103Q814yes—
83#389—22no—
84#389—22no—
85#384—22no—
86#384—22no—
87C2×#95—21no—
88C2×#95—22no—
89C2×#95—21no—
90C2×#95—22no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—22no—
95C2×#95—22no—
96C2×#95D411yescharacteristic
97C2×#95D411yescharacteristic
98C2×#95D412yes—
99#340—24no—
100#340—22no—
101#340—24no—
102#340—24no—
103#340—42no—
104#340—42no—
105#336—22no—
106#336—42no—
107#336—42no—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—21no—
112C22×Q8—21no—
113C22×Q8C2×D412yes—
114C22×Q8C2×Q812yes—
115C22×Q8#4112yes—
116C22×Q8#4114yes—
117C22×Q8#4114yes—
118C23×C4—21no—
119C23×C4—21no—
120C23×C4—21no—
121C23×C4—22no—
122C23×C4—22no—
123C23×C4—21no—
124C23×C4C2×D412yes—
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D412yes—
127C23×C4C2×D411yescharacteristic
128C23×C4C2411yescharacteristic
129C22×C8—21no—
130C22×C8—22no—
131C22×C8—21no—
132C22×C8—22no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—21no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—21no—
145C22×C8C2×Q812yes—
146C4×Q8—28no—
147C4×Q8—44no—
148C4×Q8—48no—
149C4×Q8—48no—
150C4×Q8—48no—
151C4×Q8—48no—
152C4×Q8—48no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—28no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—82no—
187C2×C4⋊C4—81no—
188C2×C4⋊C4—81no—
189C2×C4⋊C4C2×D412yes—
190C2×C4⋊C4C2×Q812yes—
191C2×C4⋊C4#4114yes—
192C2×C42—22no—
193C2×C42—22no—
194C2×C42—28no—
195C2×C42—24no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42—44no—
203C2×C42—44no—
204C2×C42—44no—
205C2×C42C2×D412yes—
206C2×C42#4112yes—
207#106—44no—
208C4⋊C8—44no—
209#103—28no—
210#103—44no—
211#103—48no—
212#95—22no—
213#95—22no—
214#95—24no—
215#95—42no—
216#95—42no—
217#95—44no—
218#95—81no—
219#95—82no—
220#95—82no—
221#95—82no—
222#95—82no—
223#95—82no—
224C24C22×D411yescharacteristic
225C2×Q8—24no—
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—24no—
230C2×Q8—24no—
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—24no—
234C2×Q8—22no—
235C2×Q8—24no—
236C2×Q8—22no—
237C2×Q8—24no—
238C2×Q8C22⋊Q814yes—
239C2×Q8#12314yes—
240C2×Q8#12414yes—
241C2×Q8#12518yes—
242C2×Q8#12618yes—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—21no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—41no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4#12112yes—
299C22×C4#12112yes—
300C22×C4#13512yes—
301C22×C4#13714yes—
302C22×C4#13712yes—
303C22×C4C22×D411yescharacteristic
304C22×C4C22×Q811yescharacteristic
305C22×C4C2×#4111yescharacteristic
306C22×C4C2×#4112yes—
307C22×C4C2×#4112yes—
308C22×C4C2×#4111yescharacteristic
309C22×C4C2×#4112yes—
310C22×C4H(5,𝔽2)12yes—
311C22×C4H(5,𝔽2)11yescharacteristic
312C22×C42−1+411yescharacteristic
313C2×C8—22no—
314C2×C8—24no—
315C2×C8—41no—
316C2×C8—41no—
317C2×C8—42no—
318C2×C8—41no—
319C2×C8—42no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—42no—
323C2×C8—41no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—24no—
334C4⋊C4—24no—
335C4⋊C4—22no—
336C4⋊C4—48no—
337C4⋊C4—416no—
338C4⋊C4—42no—
339C4⋊C4—41no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—41no—
349C4⋊C4—42no—
350C4⋊C4—84no—
351C4⋊C4—84no—
352C4⋊C4—84no—
353C42—22no—
354C42—22no—
355C42—24no—
356C42—48no—
357C42—416no—
358C42—42no—
359C42—42no—
360C42—42no—
361C42—42no—
362C23C2×#12111yescharacteristic
363C23#52512yes—
364C23#54611yescharacteristic
365C23#54612yes—
366C23D4×Q811yescharacteristic
367C23C2×#13511yescharacteristic
368C23C2×#13711yescharacteristic
369C23C2×#13712yes—
370C23#57611yescharacteristic
371C23#57711yescharacteristic
372C23#57712yes—
373Q8—24no—
374Q8—24no—
375Q8—28no—
376Q8—24no—
377Q8—28no—
378Q8#40018yes—
379C2×C4—24no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—28no—
384C2×C4—28no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—81no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—81no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4#46414yes—
439C2×C4C2×C22⋊Q811yescharacteristic
440C2×C4C2×#12311yescharacteristic
441C2×C4C2×#12411yescharacteristic
442C2×C4C2×#12512yes—
443C2×C4C2×#12612yes—
444C2×C4#52912yes—
445C2×C4#53211yescharacteristic
446C2×C4#53411yescharacteristic
447C2×C4#53711yescharacteristic
448C2×C4#53812yes—
449C2×C4#53912yes—
450C2×C4#55112yes—
451C2×C4#55112yes—
452C2×C4#55112yes—
453C2×C4#55211yescharacteristic
454C2×C4#55212yes—
455C2×C4#55412yes—
456C2×C4#55411yescharacteristic
457C8—42no—
458C8—82no—
459C8—81no—
460C22#241211yescharacteristic
461C22#241711yescharacteristic
462C22#247312yes—
463C22#248012yes—
464C22#285011yescharacteristic
465C22C2×#46411yescharacteristic
466C22#303911yescharacteristic
467C22#304311yescharacteristic
468C22#304511yescharacteristic
469C22#310712yes—
470C22#311312yes—
471C22#311912yes—
472C22#312612yes—
473C22#330112yes—
474C22#330511yescharacteristic
475C22#331612yes—
476C22#331612yes—
477C22#332012yes—
478C22#332911yescharacteristic
479C22#333312yes—
480C22#338111yescharacteristic
481C22#338511yescharacteristic
482C22#338712yes—
483C4—24no—
484C4—28no—
485C4—44no—
486C4—42no—
487C4—82no—
488C4—84no—
489C4—82no—
490C4—82no—
491C4—162no—
492C4—161no—
493C4C2×#40011yescharacteristic
494C4#249312yes—
495C4#249811yescharacteristic
496C4#250512yes—
497C4#256411yescharacteristic
498C4#263911yescharacteristic
499C2#1482611yescharacteristic
500C2#2453311yescharacteristic
501C2#2454611yescharacteristic
502C2#2481411yescharacteristic
503C2#2483111yescharacteristic
504C2#2730512yes—
505C2#2731312yes—
506C2#2752912yes—
507C2#2753712yes—
508C2#3303311yescharacteristic
509C2#3303911yescharacteristic
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×#18652
C2×#18032
#151972
Q8×#952
#113572
#113152
#112572
#112552
#112272
#107892