Finite Group Databasebeta

← #469839

Subgroups — #469839

Order 512.

1014 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1987C211yesmaximal, characteristic
2C2×#1928C211yesmaximal, characteristic
3#15191C211yesmaximal, characteristic
4#13936C211yesmaximal, characteristic
5#11384C211yesmaximal, characteristic
6#11322C211yesmaximal, characteristic
7#11316C212yesmaximal
8#11232C212yesmaximal
9#11190C212yesmaximal
10#11077C212yesmaximal
11#11077C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#107C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C22×C4⋊C8C2212yes—
16C22×#103C2211yescharacteristic
17C22×#103C2211yescharacteristic
18C22×#103C2212yes—
19C2×#391C2211yescharacteristic
20C2×#391C2212yes—
21C2×C4×C4⋊C4C2211yescharacteristic
22#1987—24no—
23#1928—24no—
24C2×#340C2211yescharacteristic
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#336C2211yescharacteristic
31C2×#336C2212yes—
32#1446—22no—
33#1443—22no—
34#1442—21no—
35#1442—21no—
36C4⋊#95C2212yes—
37C4⋊#95C2212yes—
38C4⋊#95C2211yescharacteristic
39C4⋊#95C2212yes—
40#1434—21no—
41#1434—21no—
42C4×#95C2211yescharacteristic
43C23×Q8—21no—
44C23×Q8C2311yescharacteristic
45C23×C8C2312yes—
46C23×C8C2311yescharacteristic
47C23×C8C2311yescharacteristic
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—42no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2311yescharacteristic
55C22×C4⋊C4C2311yescharacteristic
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2312yes—
58C22×C42—21no—
59C22×C42C2312yes—
60C22×C42C2311yescharacteristic
61C2×#107—22no—
62C2×#107—42no—
63C2×C4⋊C8—24no—
64C2×C4⋊C8—22no—
65C2×C4⋊C8—42no—
66C2×C4⋊C8—42no—
67C2×C4⋊C8—42no—
68C2×#103—22no—
69C2×#103—22no—
70C2×#103—22no—
71C2×#103—24no—
72C2×#103—22no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76#391—24no—
77#391—22no—
78#391—22no—
79#391—42no—
80C4×C4⋊C4—22no—
81C4×C4⋊C4D414yes—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—22no—
85C2×#95—21no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—21no—
89C2×#95—22no—
90C2×#95—22no—
91C2×#95—22no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95—21no—
95C2×#95D411yescharacteristic
96C2×#95D412yes—
97C2×#95D411yescharacteristic
98#340—22no—
99#340—24no—
100#340—24no—
101#340—24no—
102#340—42no—
103#340—42no—
104#336—22no—
105#336—42no—
106C22×Q8—21no—
107C22×Q8—21no—
108C22×Q8—21no—
109C22×Q8—22no—
110C22×Q8—21no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—21no—
115C22×Q8—44no—
116C22×Q8—44no—
117C22×Q8—42no—
118C22×Q8—81no—
119C22×Q8—81no—
120C22×Q8#4112yes—
121C23×C4—22no—
122C23×C4—21no—
123C23×C4—21no—
124C23×C4—21no—
125C23×C4—21no—
126C23×C4—22no—
127C23×C4C2×D412yes—
128C23×C4C2×D411yescharacteristic
129C23×C4C2×D412yes—
130C23×C4C2×D411yescharacteristic
131C23×C4C2411yescharacteristic
132C22×C8—21no—
133C22×C8—21no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—21no—
137C22×C8—22no—
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—21no—
147C22×C8—21no—
148C22×C8#4112yes—
149C4⋊Q8—28no—
150C4⋊Q8—48no—
151C4⋊Q8—44no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—44no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4C2×D412yes—
178C2×C4⋊C4C2×D412yes—
179C2×C4⋊C4#4114yes—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—24no—
189C2×C42—82no—
190C2×C42C2×D412yes—
191C2×C42#4112yes—
192#107—44no—
193C4⋊C8—44no—
194C4⋊C8—48no—
195#103—28no—
196#103—44no—
197#103—48no—
198#95—24no—
199#95—22no—
200#95—42no—
201#95—44no—
202#95—44no—
203#95—44no—
204#95—42no—
205#95—42no—
206#95—42no—
207#95—82no—
208#95—82no—
209#95—81no—
210#95—82no—
211#95—82no—
212#95—82no—
213#95Q1614yes—
214C24C22×D411yescharacteristic
215C2×Q8—22no—
216C2×Q8—24no—
217C2×Q8—22no—
218C2×Q8—24no—
219C2×Q8—48no—
220C2×Q8—41no—
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—84no—
235C2×Q8—84no—
236C2×Q8—88no—
237C2×Q8—88no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—24no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4#12112yes—
292C22×C4#12112yes—
293C22×C4C2×Q1614yes—
294C22×C4C2×Q1612yes—
295C22×C4#13712yes—
296C22×C4C22×D411yescharacteristic
297C22×C4C2×#4111yescharacteristic
298C22×C4C2×#4111yescharacteristic
299C22×C4C2×#4112yes—
300C22×C4C2×#4111yescharacteristic
301C22×C4H(5,𝔽2)12yes—
302C22×C4H(5,𝔽2)12yes—
303C22×C42−1+411yescharacteristic
304C22×C42−1+411yescharacteristic
305C22×C42−1+412yes—
306C2×C8—22no—
307C2×C8—24no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—42no—
311C2×C8—42no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—41no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C4⋊C4—22no—
324C4⋊C4—24no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—24no—
329C4⋊C4—48no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—42no—
341C4⋊C4—42no—
342C42—22no—
343C42—22no—
344C42—24no—
345C42—42no—
346C42—42no—
347C42—42no—
348C42—42no—
349C42—84no—
350C23C2×#12111yescharacteristic
351C23#53712yes—
352C23#54612yes—
353C23#54711yescharacteristic
354C23#54811yescharacteristic
355C23C22×Q1611yescharacteristic
356C23C2×#13711yescharacteristic
357C23#57512yes—
358C23#57611yescharacteristic
359C23#57712yes—
360C23#57711yescharacteristic
361Q8—42no—
362Q8—42no—
363Q8—44no—
364Q8—816no—
365Q8—81no—
366Q8—81no—
367Q8—82no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—44no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—81no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4#46214yes—
426C2×C4#52511yescharacteristic
427C2×C4#52511yescharacteristic
428C2×C4#53511yescharacteristic
429C2×C4#53511yescharacteristic
430C2×C4#53611yescharacteristic
431C2×C4#53611yescharacteristic
432C2×C4#53812yes—
433C2×C4#53812yes—
434C2×C4#54212yes—
435C2×C4#54212yes—
436C2×C4#54212yes—
437C2×C4#55112yes—
438C2×C4#55212yes—
439C2×C4#55211yescharacteristic
440C2×C4#55612yes—
441C2×C4#55611yescharacteristic
442C2×C4#56312yes—
443C2×C4#56312yes—
444C8—42no—
445C8—82no—
446C8—81no—
447C22#241111yescharacteristic
448C22#241511yescharacteristic
449C22#262011yescharacteristic
450C22#270212yes—
451C22#271512yes—
452C22C2×#46211yescharacteristic
453C22#304011yescharacteristic
454C22#304211yescharacteristic
455C22#304511yescharacteristic
456C22#324912yes—
457C22#325212yes—
458C22#325712yes—
459C22#326312yes—
460C22#329912yes—
461C22#331912yes—
462C22#332012yes—
463C22#332312yes—
464C22#333811yescharacteristic
465C22#335012yes—
466C22#335611yescharacteristic
467C22#336311yescharacteristic
468C22#337112yes—
469C22#337511yescharacteristic
470C4—24no—
471C4—42no—
472C4—44no—
473C4—82no—
474C4—82no—
475C4—82no—
476C4—84no—
477C4—82no—
478C4—162no—
479C4—161no—
480C4#259911yescharacteristic
481C4#263111yescharacteristic
482C4#263211yescharacteristic
483C4#275912yes—
484C4#276412yes—
485C4#282111yescharacteristic
486C2#1666511yescharacteristic
487C2#2448211yescharacteristic
488C2#2449511yescharacteristic
489C2#2468211yescharacteristic
490C2#2469711yescharacteristic
491C2#2983011yescharacteristic
492C2#2983811yescharacteristic
493C2#3180812yes—
494C2#3183312yes—
495C2#3220012yes—
496C2#3221412yes—
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×#19872
C2×#19282
#151912
#139362
#113842
#113222
#113162
#112322
#111902
#110772