Finite Group Databasebeta

← #330795

Subgroups — #330795

Order 512.

519 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33256C211yesmaximal, characteristic, complemented
2#29995C211yesmaximal, characteristic
3#29995C211yesmaximal, characteristic
4#21266C211yesmaximal, characteristic
5#10656C211yesmaximal, characteristic, complemented
6#10655C211yesmaximal, characteristic, complemented
7#10654C211yesmaximal, characteristic, complemented
8#10653C211yesmaximal, characteristic, complemented
9#10622C211yesmaximal, characteristic
10#10621C211yesmaximal, characteristic
11#10619C211yesmaximal, characteristic
12#10619C211yesmaximal, characteristic
13#9906C211yesmaximal, characteristic, complemented
14#9906C211yesmaximal, characteristic, complemented
15#8784C211yesmaximal, characteristic, complemented
16C2×#433—21no—
17#2859C2211yescharacteristic
18#2859C2211yescharacteristic
19#2293C2211yescharacteristic
20#2088—21no—
21#2088—21no—
22#2087—21no—
23#2087—21no—
24#2067—21no—
25#2067—21no—
26#2065—21no—
27#2065—21no—
28#1954C2211yescharacteristic
29#1954C2211yescharacteristic
30#1948C2211yescharacteristic
31#1948C2211yescharacteristic
32#1947C2211yescharacteristic
33#1947C2211yescharacteristic
34#1941—21no—
35#1941—21no—
36#1941—21no—
37#1941—21no—
38#1939C2211yescharacteristic
39#1939C2211yescharacteristic
40#1923—21no—
41#1923—21no—
42#1844C2211yescharacteristic
43#1844C2211yescharacteristic
44#1842C2211yescharacteristic
45#1842C2211yescharacteristic
46#1834C2211yescharacteristic
47#1834C2211yescharacteristic
48#1802C2211yescharacteristic
49#1802C2211yescharacteristic
50#1802C2211yescharacteristic
51#1802C2211yescharacteristic
52#1767C2211yescharacteristic
53#1750—21no—
54C42×C8C2211yescharacteristic
55#1296C2211yescharacteristic
56#1296C2211yescharacteristic
57#1296C2211yescharacteristic
58#1296C2211yescharacteristic
59#1296C2211yescharacteristic
60#1296C2211yescharacteristic
61#1296C2211yescharacteristic
62#1296C2211yescharacteristic
63#1277C2211yescharacteristic
64#1277C2211yescharacteristic
65#1277C2211yescharacteristic
66#1277C2211yescharacteristic
67C2×#125—21no—
68C2×#125—21no—
69C2×C4×D4C2311yescharacteristic
70C2×#117—21no—
71#433—44no—
72C2×#107—21no—
73C2×#107—21no—
74C2×#106—21no—
75C2×#106—21no—
76C2×#106—21no—
77C2×#106—21no—
78C2×#106—21no—
79C2×#106—21no—
80C2×C4⋊C8—21no—
81C2×C4⋊C8—21no—
82C2×C4⋊C8—21no—
83C2×C4⋊C8—21no—
84C2×C4⋊C8—21no—
85C2×C4⋊C8—21no—
86C2×C4⋊C8C2311yescharacteristic
87C2×C4⋊C8C2311yescharacteristic
88C2×C4⋊C8C2311yescharacteristic
89C2×C4⋊C8C2311yescharacteristic
90C2×C4⋊C8C2311yescharacteristic
91C2×C4⋊C8C2311yescharacteristic
92C2×#102—21no—
93C2×#102—21no—
94C2×#102—21no—
95C2×#102—21no—
96C2×C22⋊C8—21no—
97C2×C22⋊C8—21no—
98C2×C22⋊C8—21no—
99C2×C22⋊C8—21no—
100C2×#97—21no—
101C2×C4×C8D411yescharacteristic
102C2×C4×C8D411yescharacteristic
103C2×C4×C8D411yescharacteristic
104C2×C4×C8D411yescharacteristic
105C2×C4×C8C2311yescharacteristic
106C2×C4×C8C2311yescharacteristic
107#390D411yescharacteristic
108#390D411yescharacteristic
109#389—21no—
110#389—21no—
111#389—21no—
112#389—21no—
113#389—21no—
114#389—21no—
115#389—21no—
116#389—21no—
117#389D411yescharacteristic
118#389D411yescharacteristic
119#388—21no—
120#388—21no—
121#384C2311yescharacteristic
122#384C2311yescharacteristic
123#384C2311yescharacteristic
124#384C2311yescharacteristic
125#382—21no—
126#382—21no—
127C4×C4⋊C4C2311yescharacteristic
128C4×C22⋊C4—21no—
129C43C2311yescharacteristic
130#340—21no—
131#340—21no—
132#340—21no—
133#340—21no—
134#340—21no—
135#340—21no—
136#340—21no—
137#340—21no—
138#340—21no—
139#340—21no—
140#340—21no—
141#340—21no—
142#336—21no—
143#336—21no—
144#336—21no—
145C22×D4C2×D411yescharacteristic
146C23×C4—21no—
147C22×C8—21no—
148C22×C8—21no—
149C22×C8—21no—
150C22×C8—21no—
151C22×C8—21no—
152C22×C8—21no—
153C22×C8C2×D411yescharacteristic
154C22×C8C2×D411yescharacteristic
155C22×C8C2×D411yescharacteristic
156C22×C8C2×D411yescharacteristic
157#125—82no—
158#125—82no—
159C4×D4—21no—
160C4×D4—21no—
161C4×D4—21no—
162C4×D4—21no—
163#117—42no—
164#117—42no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—41no—
183C2×C4⋊C4C2×D411yescharacteristic
184C2×C4⋊C4C2×D411yescharacteristic
185C2×C4⋊C4C2×D411yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C42—21no—
192C2×C42C2×D411yescharacteristic
193C2×C42C2×D411yescharacteristic
194C2×C42C2×D411yescharacteristic
195C2×C42C2×D411yescharacteristic
196C2×C42#4111yescharacteristic
197C2×C42#4111yescharacteristic
198C2×C42C2411yescharacteristic
199#107—81no—
200#107—81no—
201#106—42no—
202#106—42no—
203#106—42no—
204#106—42no—
205#106—81no—
206#106—81no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—42no—
220C4⋊C8—42no—
221C4⋊C8—81no—
222C4⋊C8—81no—
223C4⋊C8—81no—
224C4⋊C8—81no—
225#102—81no—
226#102—81no—
227#102—81no—
228#102—81no—
229C22⋊C8—42no—
230C22⋊C8—42no—
231C22⋊C8—42no—
232C22⋊C8—42no—
233#97—42no—
234C4×C8—22no—
235C4×C8—22no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—41no—
241C4×C8—41no—
242#95—21no—
243#95—21no—
244#95—21no—
245#95—41no—
246#95—41no—
247#95—41no—
248#95—41no—
249C24—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4#12111yescharacteristic
270C22×C4#12111yescharacteristic
271C22×C4#12111yescharacteristic
272C22×C4#12111yescharacteristic
273C22×C4C22×D411yescharacteristic
274C22×C4C22×D411yescharacteristic
275C22×C4C2×#4111yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8#13512yes—
305C2×C8AGL(1,ℤ/8)12yes—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—42no—
313C4⋊C4—42no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—81no—
331C4⋊C4—81no—
332C4⋊C4—81no—
333C4⋊C4—81no—
334C4⋊C4—82no—
335C4⋊C4—82no—
336C4⋊C4—82no—
337C4⋊C4—82no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42—22no—
353C42—22no—
354C42—41no—
355C42—41no—
356C422−1+411yescharacteristic
357C422−1+411yescharacteristic
358C422−1+411yescharacteristic
359C422−1+411yescharacteristic
360C23—41no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23C2×#12111yescharacteristic
368D4—41no—
369D4—41no—
370D4—41no—
371D4—41no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4#47112yes—
410C2×C4#47112yes—
411C2×C4#53611yescharacteristic
412C2×C4#53611yescharacteristic
413C2×C4#53611yescharacteristic
414C2×C4#53611yescharacteristic
415C2×C4#54111yescharacteristic
416C2×C4#54111yescharacteristic
417C2×C4C2×#13511yescharacteristic
418C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
419C2×C4#57511yescharacteristic
420C2×C4#57511yescharacteristic
421C2×C4#57611yescharacteristic
422C2×C4#57711yescharacteristic
423C2×C4#57711yescharacteristic
424C2×C4#57811yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—81no—
430C8—81no—
431C8—81no—
432C8—81no—
433C8—81no—
434C8—81no—
435C22—81no—
436C22—81no—
437C22—81no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22#262111yescharacteristic
443C22#303511yescharacteristic
444C22#303611yescharacteristic
445C22#306011yescharacteristic
446C22#306111yescharacteristic
447C22C2×#47111yescharacteristic
448C22C2×#47111yescharacteristic
449C4—22no—
450C4—22no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4—81no—
456C4—81no—
457C4—81no—
458C4—161no—
459C4—161no—
460C4—161no—
461C4—161no—
462C4#322811yescharacteristic
463C4#323211yescharacteristic
464C4#323411yescharacteristic
465C4#324011yescharacteristic
466C4#324111yescharacteristic
467C4#324111yescharacteristic
468C4#324211yescharacteristic
469C4#324211yescharacteristic
470C2—161no—
471C2#1922111yescharacteristic
472C2#1922911yescharacteristic
473C2#1933111yescharacteristic
474C2#1933911yescharacteristic
475C2#2987011yescharacteristic
476C2#2988211yescharacteristic
477C2#2988711yescharacteristic
subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC2×C42C24
prime radicalC22×D4C2×D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #33256C2semidirect
5. #10656C2semidirect
6. #10655C2semidirect
7. #10654C2semidirect
8. #10653C2semidirect
13. #9906C2semidirect
14. #9906C2semidirect
15. #8784C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#332562
#299952
#212662
#106562
#106552
#106542
#106532
#106222
#106212
#106192
#99062
#87842