Finite Group Databasebeta

← #95199

Subgroups — #95199

Order 512.

1032 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20715C211yesmaximal, characteristic
2#14683C211yesmaximal, characteristic
3C4×#380C211yesmaximal, characteristic
4#7035C214yesmaximal
5C23×C42C2211yescharacteristic
6C2×#432C412yescomplemented
7C2×#383—21no—
8C2×#380—21no—
9C2×C4×C4⋊C4—21no—
10C2×C4×C22⋊C4—21no—
11#1817C412yescomplemented
12#1797—21no—
13#1797—21no—
14#1779C2212yes—
15#1749—21no—
16#1749—21no—
17C4⋊#95C412yescomplemented
18#1434—21no—
19#1434—21no—
20#1434C412yescomplemented
21#1434C412yescomplemented
22C22⋊#95—21no—
23C22⋊#95—21no—
24C22⋊#95C2212yes—
25C22⋊#95C2212yes—
26C4×#95C412yescomplemented
27C24×C4D411yescharacteristic
28C24×C4D411yescharacteristic
29C24×C4C2311yescharacteristic
30C22×C4⋊C4—22no—
31C22×C22⋊C4—22no—
32C22×C22⋊C4—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#432—44no—
48C2×C4⋊C8—22no—
49C2×C22⋊C8—22no—
50C2×C22⋊C8—22no—
51C2×C22⋊C8C2×C414yes—
52C2×#97—22no—
53#383—44no—
54#380—28no—
55C4×C4⋊C4—44no—
56C4×C22⋊C4—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—22no—
71C23×C4—22no—
72C23×C4—24no—
73C23×C4—24no—
74C23×C4—24no—
75C23×C4—42no—
76C23×C4—42no—
77C23×C4—42no—
78C23×C4—42no—
79C23×C4—42no—
80C23×C4—42no—
81C23×C4—42no—
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22⋊C411yescharacteristic
88C23×C4C22⋊C411yescharacteristic
89C23×C4C22⋊C411yescharacteristic
90C23×C4C4⋊C411yescharacteristic
91C23×C4C4⋊C411yescharacteristic
92C23×C4C4⋊C411yescharacteristic
93C23×C4C4⋊C411yescharacteristic
94C23×C4C22×C411yescharacteristic
95C23×C4C22×C411yescharacteristic
96C23×C4C22×C411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×Q811yescharacteristic
100C22×C8—24no—
101C2×C4⋊C4—28no—
102C2×C4⋊C4—44no—
103C2×C4⋊C4—44no—
104C2×C22⋊C4—28no—
105C2×C22⋊C4—44no—
106C2×C22⋊C4—44no—
107C2×C22⋊C4—44no—
108C2×C22⋊C4—44no—
109C2×C22⋊C4—42no—
110C2×C22⋊C4—42no—
111C2×C42—24no—
112C2×C42—24no—
113C2×C42—24no—
114C2×C42—42no—
115C2×C42—42no—
116C2×C42—42no—
117C2×C42—42no—
118C2×C42—42no—
119C2×C42—42no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—42no—
123C2×C42—44no—
124C2×C42—44no—
125C2×C42—44no—
126C2×C42C4211yescharacteristic
127C2×C42C4211yescharacteristic
128C2×C42C4211yescharacteristic
129C2×C42C4211yescharacteristic
130C2×C42C22⋊C411yescharacteristic
131C2×C42C22⋊C411yescharacteristic
132C2×C42C22⋊C411yescharacteristic
133C2×C42C22⋊C411yescharacteristic
134C2×C42C4⋊C411yescharacteristic
135C2×C42C4⋊C411yescharacteristic
136C2×C42C4⋊C411yescharacteristic
137C2×C42C4⋊C411yescharacteristic
138C2×C42C4⋊C411yescharacteristic
139C2×C42C4⋊C411yescharacteristic
140C2×C42C4⋊C411yescharacteristic
141C2×C42C4⋊C411yescharacteristic
142C4⋊C8—44no—
143C22⋊C8—44no—
144C22⋊C8—44no—
145C22⋊C8—44no—
146#97—44no—
147#95—28no—
148#95—44no—
149#95—44no—
150#95—44no—
151#95—44no—
152#95—44no—
153#95—44no—
154#95—44no—
155#95—44no—
156#95—44no—
157C24—22no—
158C24—22no—
159C24—22no—
160C24—22no—
161C24—41no—
162C24—41no—
163C24C2×C22⋊C411yescharacteristic
164C24C2×C22⋊C411yescharacteristic
165C24C2×C4⋊C411yescharacteristic
166C24AGL(1,ℤ/8)12yes—
167C24#13712yes—
168C22×C4—21no—
169C22×C4—21no—
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—21no—
182C22×C4—21no—
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—22no—
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—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—48no—
225C22×C4—416no—
226C22×C4—48no—
227C22×C4—416no—
228C22×C4—44no—
229C22×C4—44no—
230C22×C4—44no—
231C22×C4—44no—
232C22×C4—44no—
233C22×C4—44no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4—44no—
238C22×C4—44no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4#9511yescharacteristic
242C22×C4#9511yescharacteristic
243C22×C4#9511yescharacteristic
244C22×C4#9511yescharacteristic
245C22×C4#9511yescharacteristic
246C22×C4#9511yescharacteristic
247C22×C4#9511yescharacteristic
248C22×C4#9511yescharacteristic
249C22×C4#10414yes—
250C22×C4C2×C4211yescharacteristic
251C22×C4C2×C22⋊C411yescharacteristic
252C22×C4C2×C4⋊C411yescharacteristic
253C22×C4C2×C4⋊C411yescharacteristic
254C2×C8—44no—
255C2×C8—44no—
256C2×C8—44no—
257C4⋊C4—416no—
258C22⋊C4—416no—
259C22⋊C4—84no—
260C22⋊C4—84no—
261C42—22no—
262C42—22no—
263C42—22no—
264C42—22no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—22no—
269C42—22no—
270C42—41no—
271C42—41no—
272C42—41no—
273C42—41no—
274C42—41no—
275C42—41no—
276C42—88no—
277C42#9914yes—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—24no—
293C23—24no—
294C23—24no—
295C23—24no—
296C23—42no—
297C23—42no—
298C23—44no—
299C23—44no—
300C23—44no—
301C23—44no—
302C23C2×#9511yescharacteristic
303C23#41012yes—
304C23#41012yes—
305C23#41712yes—
306C23#41811yescharacteristic
307C23#41911yescharacteristic
308C23C2×#10412yes—
309C23#42112yes—
310C23#42812yes—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—24no—
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—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—48no—
362C2×C4—48no—
363C2×C4—48no—
364C2×C4—84no—
365C2×C4—84no—
366C2×C4—84no—
367C2×C4—84no—
368C2×C4—84no—
369C2×C4—84no—
370C2×C4—84no—
371C2×C4—84no—
372C2×C4—84no—
373C2×C4—84no—
374C2×C4—84no—
375C2×C4H(3,ℤ/4)12yes—
376C2×C4#33912yes—
377C2×C4#33912yes—
378C2×C4#34212yes—
379C2×C4#34212yes—
380C2×C4C2×#9912yes—
381C8—84no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—48no—
400C22—48no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22#150914yes—
406C22#151412yes—
407C22#151512yes—
408C22C2×H(3,ℤ/4)11yescharacteristic
409C22C2×#33911yescharacteristic
410C22#173311yescharacteristic
411C22#173611yescharacteristic
412C22C2×#34211yescharacteristic
413C22#174011yescharacteristic
414C22#174011yescharacteristic
415C4—22no—
416C4—22no—
417C4—22no—
418C4—22no—
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—88no—
428C4—164no—
429C2—22no—
430C2—24no—
431C2—22no—
432C2—42no—
433C2#794011yescharacteristic
434C2#794411yescharacteristic
435C2#798311yescharacteristic
436C2#801811yescharacteristic
437C2#802111yescharacteristic
438C2#805111yescharacteristic
439C2#810011yescharacteristic
subgroupG/H
center, socleC23C2×#95
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C24×C4 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
6. C2×#432C4semidirect
11. #1817C4semidirect
17. C4⋊#95C4semidirect
20. #1434C4semidirect
21. #1434C4semidirect
26. C4×#95C4semidirect

Maximal subgroups

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

subgroupindex
#207152
#146832
C4×#3802
#70352