Finite Group Databasebeta

← #190834

Subgroups — #190834

Order 512.

1078 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2295C211yesmaximal, characteristic
2#20808C211yesmaximal, characteristic
3C4×#432C211yesmaximal, characteristic
4#8706C212yesmaximal
5#8568C214yesmaximal, complemented
6#8311C212yesmaximal
7#8180C214yesmaximal, complemented
8C22×C4×Q8C2211yescharacteristic
9C2×#432—21no—
10C2×#431—21no—
11#2295—21no—
12#2295—21no—
13#2295—21no—
14#2295—21no—
15#2295C412yes—
16#2295C412yes—
17#2295C2212yes—
18#2295C2212yes—
19C2×#391C411yescharacteristic
20C2×#391C411yescharacteristic
21C2×#389C411yescharacteristic
22C2×#389C411yescharacteristic
23C2×#387—21no—
24C2×#387—21no—
25C2×C4×C4⋊C4—21no—
26C2×C4×C4⋊C4C2211yescharacteristic
27C2×#376—21no—
28C2×C43C2211yescharacteristic
29#1842C2212yes—
30#1831—21no—
31#1797—21no—
32#1797C2212yes—
33#1767—21no—
34C4×C4⋊C8—21no—
35C4×C4⋊C8C2212yes—
36C4×C4⋊C8C2212yes—
37#1749—21no—
38C4×C22⋊C8C2212yes—
39#1745—21no—
40C4×#97C2212yes—
41C2×Q8⋊C8C2218yes—
42#1279C2218yes—
43C23×Q8C2×C411yescharacteristic
44C2×C4×Q8—28no—
45C2×C4×Q8—21no—
46C2×C4×Q8—21no—
47C2×C4×Q8C2×C412yes—
48C2×C4×Q8C2312yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4C2×C411yescharacteristic
53C22×C4⋊C4C2×C411yescharacteristic
54C22×C4⋊C4C2×C411yescharacteristic
55C22×C42—21no—
56C22×C42—21no—
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42D411yescharacteristic
60C22×C42D411yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42C2311yescharacteristic
64#432—28no—
65#431—44no—
66C2×C4⋊C8—22no—
67C2×C4⋊C8—22no—
68C2×C4⋊C8—22no—
69C2×C4⋊C8C2314yes—
70C2×C22⋊C8—22no—
71C2×C22⋊C8—22no—
72C2×#97—22no—
73C2×#97—22no—
74C2×C4×C8—22no—
75C2×C4×C8C2314yes—
76#391—21no—
77#391—21no—
78#391—21no—
79#391—21no—
80#391C2×C412yes—
81#391C2×C412yes—
82#391C2×C412yes—
83#391C2×C412yes—
84#389—21no—
85#389—21no—
86#389—21no—
87#389—21no—
88#389C2×C412yes—
89#389C2×C412yes—
90#389C2×C412yes—
91#389C2×C412yes—
92#387—22no—
93#387—22no—
94#387—22no—
95#387—22no—
96#387—22no—
97#387—22no—
98#387—22no—
99#387—22no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—22no—
102C4×C4⋊C4—22no—
103C4×C4⋊C4—22no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4C2×C412yes—
107C4×C4⋊C4C2312yes—
108#376—22no—
109#376—22no—
110#376—22no—
111#376—22no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C43C2×C411yescharacteristic
120C43C2×C411yescharacteristic
121C43D411yescharacteristic
122C43D411yescharacteristic
123C43D411yescharacteristic
124C43D411yescharacteristic
125C43C2311yescharacteristic
126C43C2311yescharacteristic
127#336—22no—
128#336—22no—
129#336—22no—
130#336—22no—
131Q8⋊C8—216no—
132C22×Q8—24no—
133C22×Q8—21no—
134C22×Q8—24no—
135C22×Q8—42no—
136C22×Q8C22×C412yes—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4C22⋊C411yescharacteristic
142C23×C4C22⋊C411yescharacteristic
143C23×C4C22⋊C411yescharacteristic
144C23×C4C22⋊C411yescharacteristic
145C23×C4C22×C411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C23×C4C2×D411yescharacteristic
148C22×C8—24no—
149C22×C8—24no—
150C4×Q8—28no—
151C4×Q8—28no—
152C4×Q8—24no—
153C4×Q8—24no—
154C4×Q8—24no—
155C4×Q8#4118yes—
156C2×C4⋊C4—28no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4C22×C412yes—
172C2×C4⋊C4C22×C412yes—
173C2×C4⋊C4C22×C412yes—
174C2×C42—28no—
175C2×C42—24no—
176C2×C42—22no—
177C2×C42—24no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—24no—
182C2×C42—24no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—42no—
186C2×C42—42no—
187C2×C42—42no—
188C2×C42—42no—
189C2×C42C22⋊C411yescharacteristic
190C2×C42C22⋊C411yescharacteristic
191C2×C42C22⋊C411yescharacteristic
192C2×C42C22⋊C411yescharacteristic
193C2×C42C22⋊C411yescharacteristic
194C2×C42C22⋊C411yescharacteristic
195C2×C42C22⋊C411yescharacteristic
196C2×C42C22⋊C411yescharacteristic
197C2×C42C22⋊C411yescharacteristic
198C2×C42C22⋊C411yescharacteristic
199C2×C42C22⋊C411yescharacteristic
200C2×C42C22⋊C411yescharacteristic
201C2×C42C22×C411yescharacteristic
202C2×C42C22×C411yescharacteristic
203C2×C42C22×C411yescharacteristic
204C2×C42C22×C411yescharacteristic
205C2×C42C22×C411yescharacteristic
206C2×C42C2×D411yescharacteristic
207C2×C42C2×D411yescharacteristic
208C2×C42C2×D411yescharacteristic
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42C2×D411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×D411yescharacteristic
214C2×C42C2×D411yescharacteristic
215C2×C42C2×D411yescharacteristic
216C2×C42C2411yescharacteristic
217C4⋊C8—28no—
218C4⋊C8—28no—
219C4⋊C8—44no—
220C4⋊C8—44no—
221C22⋊C8—28no—
222C22⋊C8—44no—
223#97—28no—
224#97—44no—
225C4×C8—28no—
226C4×C8—44no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—22no—
231#95—22no—
232#95—22no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—22no—
237#95—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241C24C2×C22⋊C411yescharacteristic
242C2×Q8—24no—
243C2×Q8—22no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8—416no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8#11714yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
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—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
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#10414yes—
285C22×C4C2×C22⋊C411yescharacteristic
286C22×C4C2×C22⋊C411yescharacteristic
287C22×C4C2×C22⋊C411yescharacteristic
288C22×C4C2×C22⋊C411yescharacteristic
289C22×C4C2×C22⋊C411yescharacteristic
290C22×C4C2×C22⋊C411yescharacteristic
291C22×C4C2×C22⋊C411yescharacteristic
292C22×C4C2×C22⋊C411yescharacteristic
293C22×C4C2×C22⋊C411yescharacteristic
294C22×C4C2×C22⋊C411yescharacteristic
295C22×C4C2×C22⋊C411yescharacteristic
296C22×C4#13114yes—
297C22×C4AGL(1,ℤ/8)12yes—
298C22×C4#13712yes—
299C22×C4C23×C411yescharacteristic
300C22×C4C22×D411yescharacteristic
301C22×C4C22×D411yescharacteristic
302C2×C8—28no—
303C2×C8—44no—
304C2×C8—44no—
305C2×C8—44no—
306C2×C8—44no—
307C2×C8—44no—
308C4⋊C4—24no—
309C4⋊C4—28no—
310C4⋊C4—22no—
311C4⋊C4—28no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—42no—
315C4⋊C4—44no—
316C4⋊C4—42no—
317C4⋊C4—44no—
318C4⋊C4—44no—
319C4⋊C4—44no—
320C4⋊C4#11714yes—
321C42—28no—
322C42—22no—
323C42—28no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—21no—
331C42—21no—
332C42—21no—
333C42—21no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42—41no—
349C42—41no—
350C42—41no—
351C42—42no—
352C42—42no—
353C42—44no—
354C42#13714yes—
355C42C2×#4114yes—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23#40812yes—
361C23#41712yes—
362C23C2×#10412yes—
363C23C22×C22⋊C411yescharacteristic
364Q8—28no—
365Q8—48no—
366Q8—44no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
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—28no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—28no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—48no—
406C2×C4—48no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4#40812yes—
420C2×C4#41712yes—
421C2×C4#41912yes—
422C2×C4#41912yes—
423C2×C4C2×#10412yes—
424C2×C4C2×#10412yes—
425C2×C4#42112yes—
426C2×C4C2×#11712yes—
427C2×C4#52512yes—
428C2×C4#52512yes—
429C2×C4C2×#13112yes—
430C2×C4#56812yes—
431C2×C4C2×AGL(1,ℤ/8)11yescharacteristic
432C2×C4C2×#13712yes—
433C2×C4C2×#13711yescharacteristic
434C8—48no—
435C8—84no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—22no—
442C22#148314yes—
443C22#228011yescharacteristic
444C22C2×#40811yescharacteristic
445C22#287911yescharacteristic
446C22C2×#41911yescharacteristic
447C22C2×#41711yescharacteristic
448C22C22×#10411yescharacteristic
449C22C2×#42111yescharacteristic
450C4—22no—
451C4—22no—
452C4—22no—
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—44no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—44no—
464C4—82no—
465C4—82no—
466C4#292414yes—
467C4#311212yes—
468C4#311312yes—
469C2—24no—
470C2C2×#148311yescharacteristic
471C2#1746411yescharacteristic
472C2#1749211yescharacteristic
473C2#1750111yescharacteristic
474C2#2071711yescharacteristic
475C2#2074011yescharacteristic
476C2#2074711yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23C22×C22⋊C4
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
5. #8568C2semidirect
7. #8180C2semidirect

Maximal subgroups

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

subgroupindex
C2×#22952
#208082
C4×#4322
#87062
#85682
#83112
#81802