Finite Group Databasebeta

← #472038

Subgroups — #472038

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2097C212yesmaximal
2C2×#2084C211yesmaximal, characteristic
3C2×#2083C211yesmaximal, characteristic
4C2×#2043C211yesmaximal, characteristic
5C2×#2043C211yesmaximal, characteristic
6#14714C211yesmaximal, characteristic
7#14707C211yesmaximal, characteristic
8#11124C212yesmaximal
9#11122C212yesmaximal
10#11052C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2212yes—
14C22×#106C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#103C2212yes—
19C2×#391C2212yes—
20C2×#391C2212yes—
21C2×#389C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#384C2211yescharacteristic
24C2×#382C2211yescharacteristic
25C2×#382C2211yescharacteristic
26C2×C43C2211yescharacteristic
27#2097—28no—
28#2084—24no—
29#2083—24no—
30#2043—24no—
31#2043—24no—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#336C2212yes—
35C2×#336C2212yes—
36C2×#336C2211yescharacteristic
37C2×#336C2211yescharacteristic
38#1436—22no—
39#1436—22no—
40C4⋊#95—22no—
41C4⋊#95—22no—
42C4⋊#95C2211yescharacteristic
43C4⋊#95C2211yescharacteristic
44C23×Q8C2312yes—
45C23×C8C2312yes—
46C23×C8C2312yes—
47C2×C4⋊Q8—24no—
48C2×C4⋊Q8—22no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—42no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2311yescharacteristic
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C42D412yes—
63C22×C42D412yes—
64C22×C42C2311yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C2×#107—24no—
68C2×#107—24no—
69C2×#107—42no—
70C2×#106—24no—
71C2×#106—24no—
72C2×#106—42no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—42no—
82C2×#103—42no—
83C2×#103—42no—
84C2×#103—42no—
85#391—24no—
86#391—24no—
87#391—42no—
88#391—42no—
89#389—22no—
90#389—22no—
91#389—22no—
92#389—22no—
93#384—22no—
94#384—22no—
95#382—22no—
96#382—42no—
97#382D414yes—
98C2×#95—22no—
99C2×#95—24no—
100C2×#95—24no—
101C2×#95—22no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—21no—
105C2×#95—21no—
106C43—42no—
107#340—24no—
108#340—24no—
109#336—24no—
110#336—42no—
111#336D414yes—
112#336D414yes—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8#4114yes—
127C23×C4—22no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—22no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4C2×D412yes—
134C23×C4C2×D412yes—
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2411yescharacteristic
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8C2×D414yes—
151C22×C8C2×D414yes—
152C4⋊Q8—48no—
153C4⋊Q8—48no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4C2×D412yes—
193C2×C4⋊C4C2×D412yes—
194C2×C42—22no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—24no—
201C2×C42—22no—
202C2×C42—21no—
203C2×C42—21no—
204C2×C42—22no—
205C2×C42—42no—
206C2×C42—42no—
207C2×C42—42no—
208C2×C42C2×D412yes—
209C2×C42C2×D412yes—
210C2×C42C2×D412yes—
211C2×C42#4112yes—
212#107—48no—
213#106—48no—
214#103—48no—
215#103—48no—
216#103—48no—
217#103—48no—
218#95—28no—
219#95—44no—
220#95—44no—
221#95—48no—
222#95—48no—
223#95—42no—
224#95—42no—
225#95—44no—
226C24C22×D411yescharacteristic
227C2×Q8—24no—
228C2×Q8—24no—
229C2×Q8—24no—
230C2×Q8—24no—
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—42no—
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—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
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—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—42no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—42no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—42no—
299C22×C4—42no—
300C22×C4—44no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—44no—
305C22×C4#12114yes—
306C22×C4#12712yes—
307C22×C4#12712yes—
308C22×C4#13514yes—
309C22×C4#13714yes—
310C22×C4#13714yes—
311C22×C4C22×D411yescharacteristic
312C22×C4C22×D411yescharacteristic
313C22×C4C22×D411yescharacteristic
314C22×C4C2×#4112yes—
315C22×C4C2×#4111yescharacteristic
316C22×C4H(5,𝔽2)12yes—
317C22×C4H(5,𝔽2)11yescharacteristic
318C22×C4H(5,𝔽2)11yescharacteristic
319C22×C42−1+412yes—
320C22×C42−1+412yes—
321C2×C8—24no—
322C2×C8—24no—
323C2×C8—24no—
324C2×C8—24no—
325C2×C8—24no—
326C2×C8—24no—
327C2×C8—42no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—42no—
331C2×C8—42no—
332C2×C8—42no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—48no—
340C4⋊C4—48no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4—84no—
354C4⋊C4—84no—
355C4⋊C4—84no—
356C4⋊C4—84no—
357C42—24no—
358C42—24no—
359C42—24no—
360C42—24no—
361C42—48no—
362C42—48no—
363C42—42no—
364C42—42no—
365C23C2×#12111yescharacteristic
366C23#52511yescharacteristic
367C23C2×#12711yescharacteristic
368C23#53411yescharacteristic
369C23#53511yescharacteristic
370C23#53611yescharacteristic
371C23#53611yescharacteristic
372C23C2×#13512yes—
373C23C2×#13712yes—
374C23C2×#13712yes—
375C23#57512yes—
376Q8—44no—
377Q8—44no—
378Q8—44no—
379Q8—44no—
380Q8—82no—
381Q8—82no—
382Q8—82no—
383Q8—82no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—84no—
434C2×C4—84no—
435C2×C4—81no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4#49514yes—
439C2×C4#49714yes—
440C2×C4#53612yes—
441C2×C4#53612yes—
442C2×C4#53712yes—
443C2×C4#53912yes—
444C2×C4#53912yes—
445C2×C4#53912yes—
446C2×C4D4211yescharacteristic
447C2×C4D4211yescharacteristic
448C2×C4#54612yes—
449C2×C4#54612yes—
450C2×C4#54812yes—
451C2×C4#55011yescharacteristic
452C2×C4#55011yescharacteristic
453C2×C4#55212yes—
454C2×C4#56212yes—
455C2×C4#56212yes—
456C8—44no—
457C8—44no—
458C22#253611yescharacteristic
459C22#253911yescharacteristic
460C22#254111yescharacteristic
461C22#261811yescharacteristic
462C22#263311yescharacteristic
463C22#265811yescharacteristic
464C22#281611yescharacteristic
465C22#303512yes—
466C22#303912yes—
467C22#310812yes—
468C22#311712yes—
469C22C2×#49511yescharacteristic
470C22C2×#49711yescharacteristic
471C22#315211yescharacteristic
472C22#315311yescharacteristic
473C22#319012yes—
474C22#319612yes—
475C22#321212yes—
476C22#321812yes—
477C22#323112yes—
478C22#323112yes—
479C22#323612yes—
480C22#323712yes—
481C4—24no—
482C4—24no—
483C4—44no—
484C4—44no—
485C4—82no—
486C4—82no—
487C4—84no—
488C4—162no—
489C4—161no—
490C4—161no—
491C4#268112yes—
492C4#268112yes—
493C4#269412yes—
494C4#269412yes—
495C2#1681111yescharacteristic
496C2#2820912yes—
497C2#2830611yescharacteristic
498C2#2831511yescharacteristic
499C2#2843911yescharacteristic
500C2#2844911yescharacteristic
501C2#2975912yes—
502C2#3008012yes—
503C2#3028111yescharacteristic
504C2#3028411yescharacteristic
505C2#3277712yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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×#20972
C2×#20842
C2×#20832
C2×#20432
#147142
#147072
#111242
#111222
#110522
#107952