Finite Group Databasebeta

← #207239

Subgroups — #207239

Order 512.

990 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#36640C211yesmaximal, characteristic
2#20808C211yesmaximal, characteristic
3C4×#382C211yesmaximal, characteristic
4#9913C214yesmaximal
5#9910C214yesmaximal
6#8026C212yesmaximal
7#8026C212yesmaximal
8C2×#431C2212yes—
9#2864—21no—
10#2864—21no—
11#2859C411yescharacteristic, complemented
12#2859C411yescharacteristic, complemented
13#2859C411yescharacteristic, complemented
14#2859C411yescharacteristic, complemented
15#2851—21no—
16#2851—21no—
17#2851C2212yes—
18#2851C2212yes—
19C4×#125—21no—
20C4×#125—21no—
21C4×#125C412yescomplemented
22C4×#125C412yescomplemented
23#2296—21no—
24#2296—21no—
25#2285C2211yescharacteristic
26#2285C2211yescharacteristic
27C2×#382C2212yes—
28C2×C4×C4⋊C4—21no—
29C2×C43C2211yescharacteristic
30#1842—21no—
31#1831—21no—
32#1797C2212yes—
33#1797C2212yes—
34C4×C4⋊C8—21no—
35C4×C4⋊C8—21no—
36C4⋊#95—21no—
37#1434—21no—
38#1434C2212yes—
39C4×#95—21no—
40C4×#95C2212yes—
41#1294C2218yes—
42#1294C2218yes—
43C2×#125—21no—
44C2×#125—21no—
45C2×#125C2×C412yes—
46C2×#125C2×C412yes—
47C2×#117—21no—
48C2×#117—21no—
49C22×C4⋊C4—22no—
50C22×C42—22no—
51C22×C42D411yescharacteristic
52C22×C42D411yescharacteristic
53C22×C42D411yescharacteristic
54C22×C42D411yescharacteristic
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58#431—28no—
59C2×C4⋊C8—22no—
60C2×C4⋊C8—22no—
61C2×C4⋊C8—22no—
62C2×C22⋊C8C2314yes—
63C2×C4×C8—22no—
64#389—21no—
65#389—21no—
66#389—21no—
67#389—21no—
68#389—21no—
69#389—21no—
70#389—21no—
71#389—21no—
72#389—21no—
73#389—21no—
74#389—21no—
75#389—21no—
76#389C2×C412yes—
77#389C2×C412yes—
78#389C2×C412yes—
79#389C2×C412yes—
80#387—22no—
81#387—22no—
82#387—22no—
83#387—22no—
84#387—22no—
85#387—22no—
86#387—22no—
87#387—22no—
88#385—22no—
89#385—22no—
90#385—22no—
91#385—22no—
92#384C2×C411yescharacteristic
93#384C2×C411yescharacteristic
94#384C2×C411yescharacteristic
95#384C2×C411yescharacteristic
96#382—21no—
97#382—21no—
98#382—21no—
99#382—21no—
100#382—24no—
101#382C2×C412yes—
102#382C2×C412yes—
103#382Q818yes—
104#380—21no—
105#380—21no—
106#380C2312yes—
107#380C2312yes—
108C4×C4⋊C4—22no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4—22no—
111C4×C4⋊C4—22no—
112C4×C4⋊C4—21no—
113C4×C4⋊C4—21no—
114C4×C4⋊C4—44no—
115C4×C4⋊C4C2×C412yes—
116C4×C4⋊C4C2×C412yes—
117C2×#95—22no—
118C2×#95—22no—
119C2×#95—22no—
120C2×#95—22no—
121C2×#95C2314yes—
122C43C2×C411yescharacteristic
123C43C2×C411yescharacteristic
124C43C2×C411yescharacteristic
125C43C2×C411yescharacteristic
126C43D411yescharacteristic
127C43D411yescharacteristic
128C43D411yescharacteristic
129C43D411yescharacteristic
130#336—22no—
131#336—22no—
132C23×C4—24no—
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2411yescharacteristic
140C22×C8—24no—
141#125—44no—
142#125—44no—
143#125—44no—
144#125—44no—
145#117—44no—
146#117—42no—
147#117—42no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
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—28no—
165C2×C4⋊C4—44no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4C22×C412yes—
168C2×C4⋊C4C22×C412yes—
169C2×C4⋊C4C22×C412yes—
170C2×C4⋊C4C22×C412yes—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C42—24no—
174C2×C42—22no—
175C2×C42—22no—
176C2×C42—22no—
177C2×C42—22no—
178C2×C42—42no—
179C2×C42—42no—
180C2×C42—42no—
181C2×C42—42no—
182C2×C42—44no—
183C2×C42—44no—
184C2×C42—44no—
185C2×C42C22⋊C411yescharacteristic
186C2×C42C22⋊C411yescharacteristic
187C2×C42C22⋊C411yescharacteristic
188C2×C42C22⋊C411yescharacteristic
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×C42C22×C411yescharacteristic
207C2×C42C2×D411yescharacteristic
208C2×C42C2×D411yescharacteristic
209C2×C42C2×D411yescharacteristic
210C2×C42C2×D411yescharacteristic
211C2×C42C2×D411yescharacteristic
212C2×C42C2×D411yescharacteristic
213C2×C42C2×Q814yes—
214C2×C42#4114yes—
215C4⋊C8—44no—
216C4⋊C8—44no—
217C4⋊C8—44no—
218C22⋊C8—28no—
219C4×C8—44no—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225#95—22no—
226#95—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95—28no—
231#95—22no—
232#95—22no—
233#95—24no—
234#95—44no—
235#95—44no—
236#95—44no—
237#95C2×Q818yes—
238C24C22×D411yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—28no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—44no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4—44no—
267C22×C4—44no—
268C22×C4C2×C22⋊C411yescharacteristic
269C22×C4C2×C22⋊C411yescharacteristic
270C22×C4C2×C22⋊C411yescharacteristic
271C22×C4C2×C22⋊C411yescharacteristic
272C22×C4C2×C22⋊C411yescharacteristic
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×C4C22⋊Q814yes—
281C22×C4C22⋊Q814yes—
282C22×C4#13514yes—
283C22×C4AGL(1,ℤ/8)12yes—
284C22×C4#13712yes—
285C22×C4C23×C411yescharacteristic
286C22×C4C22×D411yescharacteristic
287C22×C4C22×Q812yes—
288C22×C4C2×#4112yes—
289C2×C8—44no—
290C2×C8—44no—
291C2×C8—44no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—44no—
301C4⋊C4—44no—
302C4⋊C4—44no—
303C4⋊C4—44no—
304C4⋊C4—44no—
305C4⋊C4—44no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—44no—
311C4⋊C4—44no—
312C4⋊C4—416no—
313C22⋊C4—44no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—22no—
331C42—22no—
332C42—41no—
333C42—41no—
334C42—41no—
335C42—41no—
336C42—41no—
337C42—41no—
338C42—41no—
339C42—41no—
340C42—44no—
341C42—44no—
342C42—88no—
343C42C4×Q814yes—
344C42C4×Q814yes—
345C42#12412yes—
346C42#12412yes—
347C42C4⋊Q812yes—
348C42C4⋊Q812yes—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23C22×C22⋊C411yescharacteristic
354C23C2×C22⋊Q812yes—
355C23C2×#13512yes—
356C23C2×AGL(1,ℤ/8)11yescharacteristic
357C23C2×#13711yescharacteristic
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
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—44no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—48no—
396C2×C4—48no—
397C2×C4—48no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4—84no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4#39112yes—
415C2×C4#39112yes—
416C2×C4#39112yes—
417C2×C4#39112yes—
418C2×C4#41012yes—
419C2×C4#41012yes—
420C2×C4#41612yes—
421C2×C4#41612yes—
422C2×C4#41712yes—
423C2×C4#41712yes—
424C2×C4#42112yes—
425C2×C4#42112yes—
426C2×C4#47818yes—
427C2×C4#47918yes—
428C2×C4C2×C4×Q812yes—
429C2×C4C2×#12411yescharacteristic
430C2×C4C2×C4⋊Q811yescharacteristic
431C8—84no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22C2×#39111yescharacteristic
441C22C2×#41011yescharacteristic
442C22C2×#41011yescharacteristic
443C22C2×#41611yescharacteristic
444C22C2×#41711yescharacteristic
445C22C2×#42111yescharacteristic
446C22C2×#42111yescharacteristic
447C22C2×#47812yes—
448C22C2×#47912yes—
449C4—22no—
450C4—22no—
451C4—21no—
452C4—22no—
453C4—21no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—88no—
463C4—82no—
464C4—82no—
465C4—82no—
466C4—82no—
467C4#198914yes—
468C4#198914yes—
469C2—22no—
470C2—22no—
471C2#1757111yescharacteristic
472C2#1757311yescharacteristic
473C2#1758511yescharacteristic
474C2#1758811yescharacteristic
475C2C2×#198911yescharacteristic
476C2#2132911yescharacteristic
477C2#2133211yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
11. #2859C4semidirect
12. #2859C4semidirect
13. #2859C4semidirect
14. #2859C4semidirect
21. C4×#125C4semidirect
22. C4×#125C4semidirect

Maximal subgroups

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

subgroupindex
#366402
#208082
C4×#3822
#99132
#99102
#80262