Finite Group Databasebeta

← #445734

Subgroups — #445734

Order 512.

1042 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15152C211yesmaximal, characteristic
2#14155C211yesmaximal, characteristic
3#11190C212yesmaximal
4#11190C212yesmaximal
5#11050C212yesmaximal
6#11010C212yesmaximal
7#10928C212yesmaximal
8#10875C211yesmaximal, characteristic
9#10806C212yesmaximal
10C22×C4⋊Q8C2211yescharacteristic
11C22×#103C2212yes—
12C22×#103C2212yes—
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#97C2211yescharacteristic
16C2×#400—21no—
17C2×#391C2212yes—
18C2×#391C2212yes—
19C2×#384C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C4⋊C4C2211yescharacteristic
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#336C2212yes—
27C2×#336C2212yes—
28C2×#336C2211yescharacteristic
29#1445—21no—
30#1445—21no—
31#1445—21no—
32#1442—21no—
33#1441—21no—
34C4⋊#95—21no—
35C4⋊#95—21no—
36C4⋊#95C2212yes—
37C4⋊#95C2212yes—
38C4⋊#95C2211yescharacteristic
39C23×Q8C2312yes—
40C23×C8C2312yes—
41C23×C8C2312yes—
42C2×C4⋊Q8—24no—
43C2×C4⋊Q8—24no—
44C2×C4⋊Q8—41no—
45C2×C4⋊Q8—41no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4—21no—
49C22×C4⋊C4—21no—
50C22×C4⋊C4D411yescharacteristic
51C22×C4⋊C4D411yescharacteristic
52C22×C4⋊C4C2312yes—
53C22×C4⋊C4C2312yes—
54C22×C4⋊C4C2312yes—
55C22×C42—21no—
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58C22×C42C2311yescharacteristic
59C2×#103—24no—
60C2×#103—24no—
61C2×#103—24no—
62C2×#103—24no—
63C2×#103—42no—
64C2×#103—42no—
65C2×#103—42no—
66C2×#103—42no—
67C2×#103—42no—
68C2×#103—42no—
69C2×#103—42no—
70C2×#103—42no—
71C2×#97—41no—
72C2×#97—42no—
73#400—44no—
74#391—24no—
75#391—24no—
76#391—42no—
77#391—42no—
78#384—41no—
79#384—41no—
80C4×C4⋊C4—24no—
81C4×C4⋊C4—41no—
82C4×C4⋊C4—41no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95—21no—
86C2×#95—22no—
87C2×#95—22no—
88C2×#95—22no—
89C2×#95—22no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—22no—
93C2×#95—22no—
94C2×#95D411yescharacteristic
95C2×#95D411yescharacteristic
96#340—24no—
97#340—24no—
98#340—42no—
99#340—42no—
100#336—24no—
101#336—41no—
102#336—42no—
103C22×Q8—22no—
104C22×Q8—22no—
105C22×Q8—22no—
106C22×Q8—22no—
107C22×Q8—22no—
108C22×Q8—22no—
109C22×Q8—22no—
110C22×Q8—22no—
111C22×Q8—22no—
112C22×Q8—22no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8#4114yes—
117C23×C4—22no—
118C23×C4—22no—
119C23×C4—22no—
120C23×C4—22no—
121C23×C4C2×D411yescharacteristic
122C23×C4C2×D411yescharacteristic
123C23×C4C2×D411yescharacteristic
124C23×C4C2×D411yescharacteristic
125C23×C4C2×D411yescharacteristic
126C23×C4C2×D411yescharacteristic
127C23×C4C2411yescharacteristic
128C22×C8—22no—
129C22×C8—22no—
130C22×C8—22no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8—22no—
134C22×C8—22no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8—22no—
138C22×C8—22no—
139C22×C8—22no—
140C22×C8—22no—
141C22×C8#4114yes—
142C4⋊Q8—48no—
143C4⋊Q8—48no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—42no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—82no—
178C2×C4⋊C4#4114yes—
179C2×C42—22no—
180C2×C42—21no—
181C2×C42—21no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—21no—
185C2×C42—22no—
186C2×C42—21no—
187C2×C42—21no—
188C2×C42—21no—
189C2×C42—22no—
190C2×C42—42no—
191C2×C42—42no—
192C2×C42—42no—
193C2×C42#4114yes—
194#103—48no—
195#103—48no—
196#103—48no—
197#103—48no—
198#97—44no—
199#95—41no—
200#95—41no—
201#95—44no—
202#95—44no—
203#95—44no—
204#95—44no—
205#95—42no—
206#95—44no—
207#95—42no—
208#95—44no—
209#95—42no—
210#95—82no—
211#95—82no—
212C24C22×D411yescharacteristic
213C2×Q8—24no—
214C2×Q8—24no—
215C2×Q8—24no—
216C2×Q8—24no—
217C2×Q8—24no—
218C2×Q8—24no—
219C2×Q8—42no—
220C2×Q8—42no—
221C2×Q8—42no—
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—42no—
240C2×Q8—42no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—24no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4#12412yes—
296C22×C4#12412yes—
297C22×C4AGL(1,ℤ/8)12yes—
298C22×C4#13712yes—
299C22×C4#13712yes—
300C22×C4#13712yes—
301C22×C4C2×#4112yes—
302C22×C4C2×#4112yes—
303C22×C4C2×#4112yes—
304C22×C4C2×#4112yes—
305C22×C4H(5,𝔽2)12yes—
306C22×C4H(5,𝔽2)11yescharacteristic
307C22×C4H(5,𝔽2)12yes—
308C22×C4H(5,𝔽2)11yescharacteristic
309C2×C8—24no—
310C2×C8—24no—
311C2×C8—24no—
312C2×C8—42no—
313C2×C8—42no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—42no—
319C2×C8—42no—
320C2×C8—42no—
321C2×C8—42no—
322C2×C8—42no—
323C4⋊C4—24no—
324C4⋊C4—24no—
325C4⋊C4—44no—
326C4⋊C4—44no—
327C4⋊C4—48no—
328C4⋊C4—48no—
329C4⋊C4—42no—
330C4⋊C4—42no—
331C4⋊C4—42no—
332C4⋊C4—42no—
333C4⋊C4—42no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—42no—
338C4⋊C4—42no—
339C4⋊C4—84no—
340C4⋊C4—84no—
341C42—24no—
342C42—24no—
343C42—42no—
344C42—42no—
345C42—41no—
346C42—41no—
347C42—41no—
348C42—41no—
349C42—84no—
350C23#52511yescharacteristic
351C23C2×#12411yescharacteristic
352C23#53411yescharacteristic
353C23#54612yes—
354C23#55012yes—
355C23C2×AGL(1,ℤ/8)11yescharacteristic
356C23C2×#13711yescharacteristic
357C23C2×#13711yescharacteristic
358C23C2×#13711yescharacteristic
359C23#57712yes—
360C23#57812yes—
361Q8—44no—
362Q8—44no—
363Q8—44no—
364Q8—44no—
365Q8—82no—
366Q8—82no—
367Q8—82no—
368Q8—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—42no—
405C2×C4—42no—
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—82no—
416C2×C4—82no—
417C2×C4—82no—
418C2×C4—82no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—82no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4#48914yes—
429C2×C4#52912yes—
430C2×C4#52912yes—
431C2×C4#53812yes—
432C2×C4#53812yes—
433C2×C4#54012yes—
434C2×C4#54012yes—
435C2×C4#55112yes—
436C2×C4#55112yes—
437C2×C4#55112yes—
438C2×C4#55312yes—
439C2×C4#55312yes—
440C2×C4#55312yes—
441C2×C4#55511yescharacteristic
442C2×C4#55911yescharacteristic
443C2×C4#56011yescharacteristic
444C2×C4H(3,𝔽4)11yescharacteristic
445C8—44no—
446C8—82no—
447C22#246712yes—
448C22#249012yes—
449C22#256111yescharacteristic
450C22#270911yescharacteristic
451C22#273311yescharacteristic
452C22#311211yescharacteristic
453C22#311311yescharacteristic
454C22#312112yes—
455C22C2×#48911yescharacteristic
456C22#313712yes—
457C22#313911yescharacteristic
458C22#319311yescharacteristic
459C22#319511yescharacteristic
460C22#320011yescharacteristic
461C22#320211yescharacteristic
462C22#331212yes—
463C22#332012yes—
464C22#333012yes—
465C22#333112yes—
466C22#339712yes—
467C22#339812yes—
468C22#339812yes—
469C22#340012yes—
470C4—24no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—84no—
477C4—84no—
478C4—162no—
479C4—162no—
480C4#252612yes—
481C4#259712yes—
482C4#274912yes—
483C4#275312yes—
484C2#1582011yescharacteristic
485C2#2708312yes—
486C2#2708512yes—
487C2#2775612yes—
488C2#2776212yes—
489C2#2911111yescharacteristic
490C2#2911811yescharacteristic
491C2#3203711yescharacteristic
492C2#3203911yescharacteristic
493C2#3267911yescharacteristic
494C2#3268011yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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
#151522
#141552
#111902
#110502
#110102
#109282
#108752
#108062