Finite Group Databasebeta

← #96403

Subgroups — #96403

Order 512.

1228 conjugacy classes of subgroups.

The subgroup lattice has 427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20714C211yesmaximal, characteristic
2C2×C4×C22⋊C8C211yesmaximal, characteristic
3C42×C22⋊C4C211yesmaximal, characteristic
4#7028C214yesmaximal, complemented
5C23×C42C2211yescharacteristic
6C2×#431C412yescomplemented
7C22×C22⋊C8—21no—
8C22×C4×C8—21no—
9C2×C4×C22⋊C4—21no—
10C2×C4×C22⋊C4—21no—
11C2×C4×C22⋊C4C412yes—
12C2×C43—21no—
13#1817—21no—
14#1797C412yescomplemented
15#1797C2212yes—
16#1779—21no—
17C4×C22⋊C8—21no—
18C4×C22⋊C8—21no—
19C4×C22⋊C8—21no—
20C4×C22⋊C8—21no—
21C4×C22⋊C8C412yescomplemented
22C4×C22⋊C8C2212yes—
23C2×#336C412yescomplemented
24C4×#95—21no—
25C4×#95C412yes—
26C4×#95C2212yes—
27C24×C4C2×C411yescharacteristic
28C24×C4D411yescharacteristic
29C24×C4D411yescharacteristic
30C23×C8—22no—
31C22×C22⋊C4—22no—
32C22×C42—22no—
33C22×C42—22no—
34C22×C42—22no—
35C22×C42—44no—
36C22×C42C2×C411yescharacteristic
37C22×C42C2×C411yescharacteristic
38C22×C42C2×C411yescharacteristic
39C22×C42C2×C411yescharacteristic
40C22×C42C2×C411yescharacteristic
41C22×C42D411yescharacteristic
42C22×C42D411yescharacteristic
43C22×C42D411yescharacteristic
44C22×C42D411yescharacteristic
45C22×C42Q811yescharacteristic
46C22×C42Q811yescharacteristic
47C22×C42C2311yescharacteristic
48#431—44no—
49C2×C4⋊C8C2×C414yes—
50C2×C22⋊C8—28no—
51C2×C22⋊C8—22no—
52C2×C22⋊C8—22no—
53C2×C22⋊C8—22no—
54C2×C22⋊C8—22no—
55C2×C22⋊C8—22no—
56C2×C4×C8—22no—
57C2×C4×C8—22no—
58C2×C4×C8—22no—
59C2×C4×C8—44no—
60C4×C22⋊C4—28no—
61C4×C22⋊C4—28no—
62C4×C22⋊C4—24no—
63C4×C22⋊C4C818yescomplemented
64C2×#95—22no—
65C2×#95—22no—
66C2×#95C2×C414yes—
67C43—44no—
68#336—22no—
69#336—22no—
70#336—22no—
71#336C2×C414yes—
72C25C22⋊C411yescharacteristic
73C23×C4—24no—
74C23×C4—24no—
75C23×C4—24no—
76C23×C4—24no—
77C23×C4—24no—
78C23×C4—42no—
79C23×C4—42no—
80C23×C4—42no—
81C23×C4—42no—
82C23×C4C4211yescharacteristic
83C23×C4C4211yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22⋊C411yescharacteristic
89C23×C4C22⋊C411yescharacteristic
90C23×C4C22⋊C411yescharacteristic
91C23×C4C4⋊C411yescharacteristic
92C23×C4C4⋊C411yescharacteristic
93C23×C4C4⋊C411yescharacteristic
94C23×C4C4⋊C411yescharacteristic
95C23×C4C4⋊C411yescharacteristic
96C23×C4C4⋊C411yescharacteristic
97C23×C4C2×C814yes—
98C23×C4M1614yes—
99C23×C4C22×C411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C22×C8—28no—
103C22×C8—24no—
104C22×C8—24no—
105C22×C8—44no—
106C22×C8—44no—
107C2×C22⋊C4—28no—
108C2×C22⋊C4—28no—
109C2×C22⋊C4—28no—
110C2×C42—24no—
111C2×C42—24no—
112C2×C42—24no—
113C2×C42—28no—
114C2×C42—28no—
115C2×C42—28no—
116C2×C42—42no—
117C2×C42—42no—
118C2×C42—42no—
119C2×C42—42no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—42no—
125C2×C42—44no—
126C2×C42—44no—
127C2×C42—44no—
128C2×C42—44no—
129C2×C42—44no—
130C2×C42—44no—
131C2×C42C4211yescharacteristic
132C2×C42C4211yescharacteristic
133C2×C42C22⋊C411yescharacteristic
134C2×C42C22⋊C411yescharacteristic
135C2×C42C22⋊C411yescharacteristic
136C2×C42C22⋊C411yescharacteristic
137C2×C42C4⋊C411yescharacteristic
138C2×C42C4⋊C411yescharacteristic
139C2×C42C4⋊C411yescharacteristic
140C2×C42C4⋊C411yescharacteristic
141C2×C42C4⋊C411yescharacteristic
142C2×C42C4⋊C411yescharacteristic
143C2×C42C22×C411yescharacteristic
144C2×C42C22×C411yescharacteristic
145C2×C42C2×D411yescharacteristic
146C2×C42C2×Q811yescharacteristic
147C4⋊C8—44no—
148C22⋊C8—28no—
149C22⋊C8—28no—
150C22⋊C8—44no—
151C22⋊C8—44no—
152C22⋊C8—44no—
153C4×C8—44no—
154C4×C8—44no—
155C4×C8—44no—
156#95—28no—
157#95—28no—
158#95—24no—
159#95C2×C818yescomplemented
160C24—22no—
161C24—22no—
162C24—22no—
163C24—22no—
164C24—41no—
165C24—41no—
166C24#9511yescharacteristic
167C24#9511yescharacteristic
168C24C22⋊C814yes—
169C24C2×C22⋊C411yescharacteristic
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—28no—
185C22×C4—28no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—28no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—48no—
206C22×C4—48no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—416no—
220C22×C4—416no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4#9511yescharacteristic
226C22×C4#9511yescharacteristic
227C22×C4#9511yescharacteristic
228C22×C4#9511yescharacteristic
229C22×C4#9511yescharacteristic
230C22×C4#9511yescharacteristic
231C22×C4C4×C812yes—
232C22×C4C4×C812yes—
233C22×C4#9712yes—
234C22×C4#9712yes—
235C22×C4C22⋊C814yes—
236C22×C4#10414yes—
237C22×C4#10414yes—
238C22×C4#10414yes—
239C22×C4C4⋊C814yes—
240C22×C4C4⋊C814yes—
241C22×C4C2×C4211yescharacteristic
242C22×C4C2×C22⋊C411yescharacteristic
243C22×C4C2×C22⋊C411yescharacteristic
244C22×C4C2×C4⋊C411yescharacteristic
245C22×C4C2×C4⋊C411yescharacteristic
246C22×C4C2×C4⋊C411yescharacteristic
247C22×C4C22×C812yes—
248C22×C4C2×M1612yes—
249C22×C4#13514yes—
250C2×C8—28no—
251C2×C8—44no—
252C2×C8—416no—
253C2×C8—44no—
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—44no—
257C22⋊C4—232no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C42—41no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—416no—
274C42—416no—
275C42—416no—
276C42#9914yes—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—28no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—28no—
293C23—44no—
294C23—44no—
295C23—44no—
296C23—44no—
297C23—44no—
298C23#33612yes—
299C23#33612yes—
300C23#33912yes—
301C23#33912yes—
302C23C2×#9511yescharacteristic
303C23C2×C22⋊C812yes—
304C23#41612yes—
305C23C2×#10412yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—28no—
321C2×C4—24no—
322C2×C4—24no—
323C2×C4—28no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—28no—
327C2×C4—28no—
328C2×C4—216no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—48no—
347C2×C4—48no—
348C2×C4—48no—
349C2×C4—48no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4#33612yes—
355C2×C4#33612yes—
356C2×C4#33912yes—
357C2×C4#33912yes—
358C2×C4#33912yes—
359C2×C4#33912yes—
360C2×C4#34212yes—
361C2×C4#34212yes—
362C2×C4#34412yes—
363C2×C4C2×C4×C811yescharacteristic
364C2×C4C2×#9711yescharacteristic
365C2×C4C2×#9912yes—
366C2×C4#41612yes—
367C2×C4C2×#10412yes—
368C2×C4C2×#10412yes—
369C2×C4C2×C4⋊C812yes—
370C2×C4#42712yes—
371C8—48no—
372C8—84no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—416no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#127614yes—
394C22#147614yes—
395C22C2×#33611yescharacteristic
396C22C2×#33911yescharacteristic
397C22C2×#33911yescharacteristic
398C22C2×#33911yescharacteristic
399C22#173511yescharacteristic
400C22C2×#34211yescharacteristic
401C22C2×#34411yescharacteristic
402C4—22no—
403C4—22no—
404C4—22no—
405C4—22no—
406C4—22no—
407C4—21no—
408C4—21no—
409C4—22no—
410C4—416no—
411C4—41no—
412C4—41no—
413C4#128214yes—
414C4#129714yes—
415C4#150114yes—
416C2—24no—
417C2—24no—
418C2—42no—
419C2C2×#127611yescharacteristic
420C2#789011yescharacteristic
421C2C2×#128211yescharacteristic
422C2#801211yescharacteristic
423C2C2×#129711yescharacteristic
424C2#806811yescharacteristic
425C2#809211yescharacteristic
subgroupG/H
centerC2×C42C22⋊C4
commutatorC2×C4C2×C4×C8
Frattini, cosocleC22×C42C23
socleC23C2×#95
prime radicalC25C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C42 ◁ C23×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #7028C2semidirect
6. C2×#431C4semidirect
14. #1797C4semidirect
21. C4×C22⋊C8C4semidirect
23. C2×#336C4semidirect
63. C4×C22⋊C4C8semidirect
159. #95C2×C8semidirect

Maximal subgroups

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

subgroupindex
#207142
C2×C4×C22⋊C82
C42×C22⋊C42
#70282