Finite Group Databasebeta

← #207049

Subgroups — #207049

Order 512.

930 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2864C211yesmaximal, characteristic
2C4×#432C211yesmaximal, characteristic
3C4×#423C211yesmaximal, characteristic
4#9893C214yesmaximal, complemented
5#9892C214yesmaximal, complemented
6#8033C212yesmaximal
7#8033C212yesmaximal
8C2×#432C2212yes—
9C2×#423—21no—
10C2×C4×M16C2212yes—
11#2864—21no—
12#2864—21no—
13#2864—21no—
14#2864—21no—
15#2864C412yes—
16#2864C412yes—
17#2864C2212yes—
18#2864C2212yes—
19C2×#389C411yescharacteristic
20C2×#389C411yescharacteristic
21C2×#389C411yescharacteristic
22C2×#389C411yescharacteristic
23C2×#387—21no—
24C2×#387—21no—
25C2×#387—21no—
26C2×#387—21no—
27C2×#382C2211yescharacteristic
28C2×#382C2211yescharacteristic
29C2×C43C2211yescharacteristic
30#1767—21no—
31#1767C2212yes—
32#1767C2212yes—
33C4×C4⋊C8—21no—
34C4×C4⋊C8—21no—
35C4×C4⋊C8—21no—
36#1749—21no—
37C4×C22⋊C8—21no—
38#1745C2212yes—
39#1728—21no—
40C4×#97C2212yes—
41#1295C2218yes—
42#1295C2218yes—
43C22×M16—22no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4—21no—
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C42C2×C411yescharacteristic
53C22×C42C2×C411yescharacteristic
54C22×C42D411yescharacteristic
55C22×C42D411yescharacteristic
56C22×C42D411yescharacteristic
57C22×C42D411yescharacteristic
58C22×C42C2311yescharacteristic
59#432—24no—
60#432Q818yes—
61#423—28no—
62C2×C4⋊C8—22no—
63C2×C4⋊C8—22no—
64C2×C4⋊C8—22no—
65C2×C22⋊C8—22no—
66C4×M16—28no—
67C2×#97—22no—
68C2×#97C2314yes—
69C2×#97C2314yes—
70C2×C4×C8—22no—
71C2×C4×C8—22no—
72#389—21no—
73#389—21no—
74#389—21no—
75#389—21no—
76#389—21no—
77#389—21no—
78#389—21no—
79#389—21no—
80#389C2×C412yes—
81#389C2×C412yes—
82#389C2×C412yes—
83#389C2×C412yes—
84#389C2×C412yes—
85#389C2×C412yes—
86#389C2×C412yes—
87#389C2×C412yes—
88#387—22no—
89#387—22no—
90#387—22no—
91#387—22no—
92#387—22no—
93#387—22no—
94#387—22no—
95#387—22no—
96#387—22no—
97#387—22no—
98#387—22no—
99#387—22no—
100#387—22no—
101#387—22no—
102#387—22no—
103#387—22no—
104#382—21no—
105#382—21no—
106#382—21no—
107#382—21no—
108#382C2×C412yes—
109#382C2×C412yes—
110#382C2312yes—
111#382C2312yes—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C2×#95—21no—
116C2×#95—21no—
117C2×#95—21no—
118C2×#95—21no—
119C2×#95—21no—
120C43C2×C411yescharacteristic
121C43C2×C411yescharacteristic
122C43D411yescharacteristic
123C43D411yescharacteristic
124C43D411yescharacteristic
125C43D411yescharacteristic
126C43C2311yescharacteristic
127C43C2311yescharacteristic
128#336—22no—
129#336—22no—
130#336—22no—
131#336—22no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4C22⋊C411yescharacteristic
137C23×C4C22⋊C411yescharacteristic
138C23×C4C22⋊C411yescharacteristic
139C23×C4C22⋊C411yescharacteristic
140C23×C4C22×C411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C2×M16—28no—
144C2×M16—44no—
145C2×M16—44no—
146C22×C8—24no—
147C22×C8—24no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
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—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4—42no—
166C2×C4⋊C4—42no—
167C2×C4⋊C4—42no—
168C2×C4⋊C4C22×C412yes—
169C2×C4⋊C4C22×C412yes—
170C2×C4⋊C4C22×C412yes—
171C2×C4⋊C4C22×C412yes—
172C2×C42—24no—
173C2×C42—42no—
174C2×C42—42no—
175C2×C42—42no—
176C2×C42—42no—
177C2×C42—42no—
178C2×C42C22⋊C411yescharacteristic
179C2×C42C22⋊C411yescharacteristic
180C2×C42C22⋊C411yescharacteristic
181C2×C42C22⋊C411yescharacteristic
182C2×C42C22⋊C411yescharacteristic
183C2×C42C22⋊C411yescharacteristic
184C2×C42C22⋊C411yescharacteristic
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×C42C2×D411yescharacteristic
196C2×C42C2×D411yescharacteristic
197C2×C42C2×D411yescharacteristic
198C2×C42C2×D411yescharacteristic
199C2×C42C2×D411yescharacteristic
200C2×C42C2×D411yescharacteristic
201C2×C42C2×D411yescharacteristic
202C2×C42C2×D411yescharacteristic
203C2×C42C2×D411yescharacteristic
204C2×C42C2×D411yescharacteristic
205C2×C42C2×Q814yes—
206C2×C42#4114yes—
207C2×C42C2411yescharacteristic
208C4⋊C8—28no—
209C4⋊C8—28no—
210C4⋊C8—28no—
211C22⋊C8—28no—
212#97—24no—
213#97—28no—
214#97—44no—
215#97C2×Q818yes—
216C4×C8—44no—
217C4×C8—44no—
218#95—22no—
219#95—22no—
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—22no—
231#95—22no—
232#95—22no—
233#95—22no—
234C24C2×C22⋊C411yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4#10414yes—
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×C4C4×Q814yes—
281C22×C4C22⋊Q814yes—
282C22×C4#12412yes—
283C22×C4C4⋊Q812yes—
284C22×C4C23×C411yescharacteristic
285C22×C4C22×D411yescharacteristic
286C22×C4C22×D411yescharacteristic
287M16—416no—
288C2×C8—28no—
289C2×C8—28no—
290C2×C8—44no—
291C2×C8—44no—
292C2×C8—44no—
293C2×C8—44no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—44no—
299C4⋊C4—44no—
300C4⋊C4—44no—
301C4⋊C4—44no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—44no—
309C4⋊C4—44no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—22no—
320C42—22no—
321C42—22no—
322C42—41no—
323C42—41no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—41no—
329C42—41no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42C4×Q814yes—
335C42C22⋊Q814yes—
336C42#12412yes—
337C42C4⋊Q812yes—
338C42C22×Q812yes—
339C42C2×#4112yes—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23#39112yes—
345C23C2×#10412yes—
346C23#42112yes—
347C23C22×C22⋊C411yescharacteristic
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—28no—
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—44no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—84no—
399C2×C4—84no—
400C2×C4—84no—
401C2×C4—84no—
402C2×C4#39112yes—
403C2×C4#39112yes—
404C2×C4#39112yes—
405C2×C4#41312yes—
406C2×C4#41312yes—
407C2×C4C2×#10412yes—
408C2×C4C2×#10412yes—
409C2×C4#42112yes—
410C2×C4#42112yes—
411C2×C4C2×C4×Q812yes—
412C2×C4C2×C22⋊Q812yes—
413C2×C4C2×#12411yescharacteristic
414C2×C4C2×C4⋊Q811yescharacteristic
415C8—48no—
416C8—48no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22#198614yes—
424C22C2×#39111yescharacteristic
425C22C2×#41311yescharacteristic
426C22C2×#41311yescharacteristic
427C22C22×#10411yescharacteristic
428C22C2×#42111yescharacteristic
429C22C2×#42111yescharacteristic
430C22C2×#42111yescharacteristic
431C4—22no—
432C4—21no—
433C4—21no—
434C4—22no—
435C4—22no—
436C4—22no—
437C4—22no—
438C4—22no—
439C4—22no—
440C4—22no—
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—82no—
446C4—82no—
447C4—82no—
448C4—82no—
449C4#199814yes—
450C2—24no—
451C2#1764211yescharacteristic
452C2#1765011yescharacteristic
453C2#1766811yescharacteristic
454C2#1767011yescharacteristic
455C2C2×#198611yescharacteristic
456C2#2132911yescharacteristic
457C2C2×#199811yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
prime radicalC24C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #9893C2semidirect
5. #9892C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28642
C4×#4322
C4×#4232
#98932
#98922
#80332