Finite Group Databasebeta

← #95187

Subgroups — #95187

Order 512.

1092 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20714C211yesmaximal, characteristic
2C4×#381C211yesmaximal, characteristic
3#13753C211yesmaximal, characteristic
4#7035C214yesmaximal
5C23×C42C2211yescharacteristic
6C2×#431—21no—
7C2×#381—21no—
8C2×C4×C22⋊C4—21no—
9C2×C4×C22⋊C4—21no—
10C2×#376C412yescomplemented
11#1817—21no—
12#1797—21no—
13#1797C412yescomplemented
14#1779C2212yes—
15C4×C22⋊C8—21no—
16C4×C22⋊C8C412yescomplemented
17#1434—21no—
18#1434—21no—
19#1434C412yescomplemented
20#1434C412yescomplemented
21C22⋊#95—21no—
22C22⋊#95C2212yes—
23C22⋊#95C2212yes—
24C4×#95—21no—
25C4×#95—21no—
26C4×#95C412yescomplemented
27C24×C4D411yescharacteristic
28C24×C4D411yescharacteristic
29C24×C4C2311yescharacteristic
30C22×C22⋊C4—22no—
31C22×C22⋊C4—22no—
32C22×C42—22no—
33C22×C42—22no—
34C22×C42—44no—
35C22×C42C2×C411yescharacteristic
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
47#431—44no—
48C2×C4⋊C8—22no—
49C2×C22⋊C8—22no—
50C2×C22⋊C8—22no—
51C2×C22⋊C8C2×C414yes—
52C2×C4×C8—22no—
53#381—28no—
54C4×C22⋊C4—28no—
55C4×C22⋊C4—44no—
56#376—44no—
57C2×#95—22no—
58C2×#95—22no—
59C2×#95—22no—
60C2×#95—22no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95C2×C414yes—
66C2×#95C2×C414yes—
67#336—22no—
68#336—22no—
69C25C2×D411yescharacteristic
70C23×C4—24no—
71C23×C4—24no—
72C23×C4—24no—
73C23×C4—24no—
74C23×C4—24no—
75C23×C4—24no—
76C23×C4—42no—
77C23×C4—42no—
78C23×C4—42no—
79C23×C4—42no—
80C23×C4—42no—
81C23×C4C22⋊C411yescharacteristic
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22⋊C411yescharacteristic
89C23×C4C4⋊C411yescharacteristic
90C23×C4C4⋊C411yescharacteristic
91C23×C4C4⋊C411yescharacteristic
92C23×C4C4⋊C411yescharacteristic
93C23×C4C22×C411yescharacteristic
94C23×C4C22×C411yescharacteristic
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×Q811yescharacteristic
99C22×C8—24no—
100C2×C22⋊C4—28no—
101C2×C22⋊C4—28no—
102C2×C22⋊C4—44no—
103C2×C22⋊C4—44no—
104C2×C22⋊C4—44no—
105C2×C22⋊C4—44no—
106C2×C42—24no—
107C2×C42—24no—
108C2×C42—28no—
109C2×C42—42no—
110C2×C42—42no—
111C2×C42—42no—
112C2×C42—42no—
113C2×C42—42no—
114C2×C42—42no—
115C2×C42—42no—
116C2×C42—42no—
117C2×C42—42no—
118C2×C42—42no—
119C2×C42—44no—
120C2×C42—44no—
121C2×C42—44no—
122C2×C42—44no—
123C2×C42—44no—
124C2×C42C4211yescharacteristic
125C2×C42C4211yescharacteristic
126C2×C42C4211yescharacteristic
127C2×C42C4211yescharacteristic
128C2×C42C22⋊C411yescharacteristic
129C2×C42C22⋊C411yescharacteristic
130C2×C42C22⋊C411yescharacteristic
131C2×C42C22⋊C411yescharacteristic
132C2×C42C4⋊C411yescharacteristic
133C2×C42C4⋊C411yescharacteristic
134C2×C42C4⋊C411yescharacteristic
135C2×C42C4⋊C411yescharacteristic
136C2×C42C4⋊C411yescharacteristic
137C2×C42C4⋊C411yescharacteristic
138C2×C42C4⋊C411yescharacteristic
139C2×C42C4⋊C411yescharacteristic
140C4⋊C8—44no—
141C22⋊C8—44no—
142C22⋊C8—44no—
143C22⋊C8—44no—
144C4×C8—44no—
145#95—28no—
146#95—28no—
147#95—28no—
148#95—44no—
149#95—44no—
150#95—44no—
151#95—44no—
152#95—44no—
153#95—44no—
154#95—44no—
155C24—22no—
156C24—22no—
157C24—22no—
158C24—22no—
159C24—41no—
160C24—41no—
161C24C2×C22⋊C411yescharacteristic
162C24C2×C22⋊C411yescharacteristic
163C24C2×C4⋊C411yescharacteristic
164C24#13514yes—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
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—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
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—28no—
199C22×C4—28no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
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—416no—
219C22×C4—416no—
220C22×C4—416no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—44no—
225C22×C4—44no—
226C22×C4—44no—
227C22×C4—44no—
228C22×C4—44no—
229C22×C4—44no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4#9511yescharacteristic
234C22×C4#9511yescharacteristic
235C22×C4#9511yescharacteristic
236C22×C4#9511yescharacteristic
237C22×C4#9511yescharacteristic
238C22×C4#9511yescharacteristic
239C22×C4#9511yescharacteristic
240C22×C4#9511yescharacteristic
241C22×C4#9914yes—
242C22×C4#10414yes—
243C22×C4#10414yes—
244C22×C4C2×C4211yescharacteristic
245C22×C4C2×C22⋊C411yescharacteristic
246C22×C4C2×C4⋊C411yescharacteristic
247C22×C4C2×C4⋊C411yescharacteristic
248C2×C8—44no—
249C2×C8—44no—
250C2×C8—44no—
251C22⋊C4—416no—
252C22⋊C4—416no—
253C42—22no—
254C42—22no—
255C42—22no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—41no—
269C42—416no—
270C42—88no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—28no—
286C23—28no—
287C23—44no—
288C23—44no—
289C23—44no—
290C23—44no—
291C23—44no—
292C23C2×#9511yescharacteristic
293C23C2×#9912yes—
294C23#41012yes—
295C23#41612yes—
296C23#41612yes—
297C23C2×#10412yes—
298C23C2×#10412yes—
299C23#42712yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—28no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—44no—
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—84no—
353C2×C4—84no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—84no—
358C2×C4—84no—
359C2×C4—84no—
360C2×C4H(3,ℤ/4)12yes—
361C2×C4#33912yes—
362C2×C4#33912yes—
363C2×C4#33912yes—
364C2×C4#33912yes—
365C2×C4#34212yes—
366C2×C4#34212yes—
367C2×C4#41012yes—
368C8—84no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—416no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22#150014yes—
390C22#150114yes—
391C22C2×H(3,ℤ/4)11yescharacteristic
392C22C2×#33911yescharacteristic
393C22C2×#33911yescharacteristic
394C22#173511yescharacteristic
395C22C2×#34211yescharacteristic
396C22#174011yescharacteristic
397C22#174011yescharacteristic
398C4—22no—
399C4—22no—
400C4—22no—
401C4—22no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—88no—
410C4—88no—
411C4#128414yes—
412C2—24no—
413C2—24no—
414C2—42no—
415C2C2×#128411yescharacteristic
416C2#794011yescharacteristic
417C2#798011yescharacteristic
418C2#801211yescharacteristic
419C2#801311yescharacteristic
420C2#804811yescharacteristic
421C2#810011yescharacteristic
subgroupG/H
centerC22×C4#95
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23C2×#95
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
10. C2×#376C4semidirect
13. #1797C4semidirect
16. C4×C22⋊C8C4semidirect
19. #1434C4semidirect
20. #1434C4semidirect
26. C4×#95C4semidirect

Maximal subgroups

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

subgroupindex
#207142
C4×#3812
#137532
#70352