Finite Group Databasebeta

← #391929

Subgroups — #391929

Order 512.

1042 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic
2#20752C211yesmaximal, characteristic
3C4×#382C211yesmaximal, characteristic
4#11370C212yesmaximal
5#11359C212yesmaximal
6#11226C214yesmaximal
7#11209C214yesmaximal
8C2×#423C2212yes—
9#2864C412yescomplemented
10#2864C412yescomplemented
11#2859C411yescharacteristic, complemented
12#2859C411yescharacteristic, complemented
13#2859C411yescharacteristic, complemented
14#2859C411yescharacteristic, complemented
15#2851—21no—
16#2851—21no—
17#2851—21no—
18#2851—21no—
19C4×#125—21no—
20C4×#125—21no—
21C4×#125—21no—
22C4×#125—21no—
23#2296C2212yes—
24#2296C2212yes—
25#2285C2211yescharacteristic
26#2285C2211yescharacteristic
27C2×#382—21no—
28C2×C4×C4⋊C4C2212yes—
29C2×C43C2211yescharacteristic
30#1831—21no—
31#1831—21no—
32#1831—21no—
33#1831—21no—
34C2×#339C2218yes—
35C2×#339C2218yes—
36#1728C2212yes—
37#1728C2212yes—
38C4⋊#95—21no—
39#1434—21no—
40#1434—21no—
41C4×#95C2212yes—
42C4×#95C2212yes—
43C22×M16C2314yes—
44C2×#125—21no—
45C2×#125—21no—
46C2×#125—21no—
47C2×#125—21no—
48C2×#117C2312yes—
49C2×#117C2312yes—
50C22×C4⋊C4—22no—
51C22×C42D411yescharacteristic
52C22×C42D411yescharacteristic
53C22×C42D411yescharacteristic
54C22×C42D411yescharacteristic
55C22×C42C2314yes—
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58C22×C42C2311yescharacteristic
59#423—44no—
60C2×C4⋊C8—22no—
61C2×C4⋊C8—22no—
62#389—21no—
63#389—21no—
64#389—21no—
65#389—21no—
66#389—21no—
67#389—21no—
68#389—21no—
69#389—21no—
70#389C2×C412yes—
71#389C2×C412yes—
72#389C2×C412yes—
73#389C2×C412yes—
74#389C2×C412yes—
75#389C2×C412yes—
76#389C2×C412yes—
77#389C2×C412yes—
78#387—22no—
79#387—22no—
80#387—22no—
81#387—22no—
82#387—22no—
83#387—22no—
84#387—22no—
85#387—22no—
86#385—22no—
87#385—22no—
88#385—22no—
89#385—22no—
90#384C2×C411yescharacteristic
91#384C2×C411yescharacteristic
92#384C2×C411yescharacteristic
93#384C2×C411yescharacteristic
94#382—28no—
95#382—21no—
96#382—21no—
97#382—21no—
98#382—21no—
99#382C2×C412yes—
100#382C2×C412yes—
101#380—21no—
102#380—21no—
103#380—21no—
104#380—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C4×C4⋊C4—21no—
108C4×C4⋊C4—21no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4—22no—
111C4×C4⋊C4—22no—
112C4×C4⋊C4—22no—
113C4×C4⋊C4—44no—
114C2×#95—22no—
115C2×#95—22no—
116C2×#95—22no—
117C2×#95—22no—
118C2×#95—22no—
119C43C2×C411yescharacteristic
120C43C2×C411yescharacteristic
121C43C2×C411yescharacteristic
122C43C2×C411yescharacteristic
123C43D411yescharacteristic
124C43D411yescharacteristic
125C43D411yescharacteristic
126C43D411yescharacteristic
127#339—48no—
128#339—48no—
129#336—22no—
130#336—22no—
131#336—22no—
132#336—22no—
133C23×C4—24no—
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2×D411yescharacteristic
140C23×C4C2411yescharacteristic
141C2×M16—24no—
142C2×M16—28no—
143C2×M16—28no—
144C2×M16—24no—
145C22×C8—24no—
146#125—44no—
147#125—44no—
148#125—44no—
149#125—44no—
150#117—24no—
151#117—24no—
152#117—24no—
153#117—24no—
154C2×C4⋊C4—28no—
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—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—44no—
173C2×C4⋊C4C22×C412yes—
174C2×C4⋊C4C22×C412yes—
175C2×C4⋊C4C22×C412yes—
176C2×C4⋊C4C22×C412yes—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—24no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—24no—
185C2×C42—22no—
186C2×C42—22no—
187C2×C42—24no—
188C2×C42—28no—
189C2×C42—28no—
190C2×C42—24no—
191C2×C42—42no—
192C2×C42—42no—
193C2×C42—42no—
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×C42C22⋊C411yescharacteristic
207C2×C42C22⋊C411yescharacteristic
208C2×C42C22⋊C411yescharacteristic
209C2×C42C22⋊C411yescharacteristic
210C2×C42C22×C411yescharacteristic
211C2×C42C22×C411yescharacteristic
212C2×C42C22×C411yescharacteristic
213C2×C42C22×C411yescharacteristic
214C2×C42C22×C411yescharacteristic
215C2×C42C22×C411yescharacteristic
216C2×C42C2×D411yescharacteristic
217C2×C42C2×D411yescharacteristic
218C2×C42C2×D411yescharacteristic
219C2×C42C2×D411yescharacteristic
220C2×C42C2×D411yescharacteristic
221C2×C42C2×D411yescharacteristic
222C4⋊C8—44no—
223C4⋊C8—44no—
224#95—28no—
225#95—28no—
226#95—22no—
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—44no—
239#95—44no—
240#95—44no—
241C24C22×D411yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—28no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—44no—
268C22×C4—44no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4—44no—
272C22×C4—44no—
273C22×C4C2×C22⋊C411yescharacteristic
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4C2×C22⋊C411yescharacteristic
277C22×C4C2×C22⋊C411yescharacteristic
278C22×C4C2×C22⋊C411yescharacteristic
279C22×C4C2×C22⋊C411yescharacteristic
280C22×C4C2×C22⋊C411yescharacteristic
281C22×C4C2×C22⋊C411yescharacteristic
282C22×C4C2×C22⋊C411yescharacteristic
283C22×C4C2×C22⋊C411yescharacteristic
284C22×C4C2×C22⋊C411yescharacteristic
285C22×C4C23×C411yescharacteristic
286C22×C4C22×D411yescharacteristic
287C22×C4H(5,𝔽2)12yes—
288C22×C4H(5,𝔽2)12yes—
289C22×C42−1+414yes—
290C22×C42−1+412yes—
291C22×C42−1+412yes—
292M16—48no—
293M16—48no—
294C2×C8—44no—
295C2×C8—44no—
296C2×C8—44no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—416no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—44no—
309C4⋊C4—44no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—44no—
313C4⋊C4—44no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—44no—
317C4⋊C4—44no—
318C22⋊C4—42no—
319C22⋊C4—42no—
320C22⋊C4—44no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—21no—
328C42—21no—
329C42—22no—
330C42—22no—
331C42—21no—
332C42—21no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C42—22no—
338C42—22no—
339C42—22no—
340C42—22no—
341C42—22no—
342C42—22no—
343C42—22no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42—41no—
348C42—41no—
349C42—41no—
350C42—42no—
351C42—42no—
352C42—44no—
353C42—48no—
354C42—48no—
355C42#10414yes—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23C22×C22⋊C411yescharacteristic
361C23#53511yescharacteristic
362C23#53612yes—
363C23#53611yescharacteristic
364C23#53712yes—
365C2×C4—24no—
366C2×C4—24no—
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—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
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—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—48no—
404C2×C4—48no—
405C2×C4—48no—
406C2×C4—42no—
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—42no—
418C2×C4—84no—
419C2×C4—84no—
420C2×C4—84no—
421C2×C4—84no—
422C2×C4C2×#10412yes—
423C2×C4C2×#10412yes—
424C2×C4C2×#10412yes—
425C2×C4#42112yes—
426C2×C4#42112yes—
427C2×C4#42112yes—
428C2×C4#51912yes—
429C2×C4#52012yes—
430C2×C4#52012yes—
431C2×C4#53511yescharacteristic
432C2×C4#53612yes—
433C2×C4#53611yescharacteristic
434C2×C4#53712yes—
435C2×C4#56214yes—
436C2×C4#56314yes—
437C2×C4#56314yes—
438C2×C4#56414yes—
439C8—84no—
440C22—22no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22#231011yescharacteristic
449C22#231111yescharacteristic
450C22#231111yescharacteristic
451C22#282012yes—
452C22#282212yes—
453C22C22×#10411yescharacteristic
454C22C2×#42111yescharacteristic
455C22C2×#42111yescharacteristic
456C22C2×#42111yescharacteristic
457C4—22no—
458C4—22no—
459C4—22no—
460C4—22no—
461C4—22no—
462C4—22no—
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—88no—
470C4—82no—
471C4—82no—
472C4—82no—
473C4—82no—
474C4#238214yes—
475C4#282012yes—
476C4#282212yes—
477C2—22no—
478C2—22no—
479C2#1466411yescharacteristic
480C2#2184411yescharacteristic
481C2#2184511yescharacteristic
482C2#2185611yescharacteristic
483C2#2185711yescharacteristic
484C2#2189911yescharacteristic
485C2#2190011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
9. #2864C4semidirect
10. #2864C4semidirect
11. #2859C4semidirect
12. #2859C4semidirect
13. #2859C4semidirect
14. #2859C4semidirect

Maximal subgroups

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

subgroupindex
#366402
#207522
C4×#3822
#113702
#113592
#112262
#112092