Finite Group Databasebeta

← #99920

Subgroups — #99920

Order 512.

464 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23237C211yesmaximal, characteristic
2#22078C211yesmaximal, characteristic
3#9650C211yesmaximal, characteristic
4#7589C211yesmaximal, characteristic
5C2×#1271C211yesmaximal, characteristic
6#7029C211yesmaximal, characteristic
7#7016C211yesmaximal, characteristic
8C2×#483C411yescharacteristic
9C4×C22⋊Q8C2211yescharacteristic
10C2×#389C2211yescharacteristic
11#1984—21no—
12#1941—21no—
13#1933—21no—
14#1919—21no—
15#1916—21no—
16#1916—21no—
17#1872C411yescharacteristic
18#1865—21no—
19#1853C411yescharacteristic
20#1850—21no—
21#1823C411yescharacteristic
22#1797C2211yescharacteristic
23C8×C4⋊C4—21no—
24C8×C22⋊C4—21no—
25C4×C22⋊C8C2211yescharacteristic
26C4×C22⋊C8C2211yescharacteristic
27C2×#336C2211yescharacteristic
28C2×#336C2211yescharacteristic
29C2×#324—21no—
30C2×#324—21no—
31#1272—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C23×C8—21no—
36C23×C8—21no—
37C2×C22⋊Q8C2×C411yescharacteristic
38C2×C4×Q8D411yescharacteristic
39C22×C4⋊C4—21no—
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C4⋊C4C2×C411yescharacteristic
42C22×C42C2311yescharacteristic
43#483—22no—
44#483C814yescomplemented
45C2×#106—21no—
46C2×#106—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8C2×C411yescharacteristic
54C2×C22⋊C8C2×C411yescharacteristic
55C2×C22⋊C8D411yescharacteristic
56C2×C22⋊C8D411yescharacteristic
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60C2×C4×C8—21no—
61#391D411yescharacteristic
62#389—21no—
63#389—21no—
64#389—21no—
65#389—21no—
66#389D411yescharacteristic
67#387—21no—
68#385—21no—
69#380C2×C411yescharacteristic
70C4×C4⋊C4—21no—
71C4×C4⋊C4D411yescharacteristic
72C4×C22⋊C4—21no—
73C2×#95—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#340—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336D411yescharacteristic
89#336D411yescharacteristic
90#324—42no—
91#324—42no—
92C22×Q8C22⋊C411yescharacteristic
93C23×C4—21no—
94C23×C4—21no—
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D411yescharacteristic
97C23×C4#4111yescharacteristic
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—22no—
105C22×C8—42no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—81no—
112C22×C8—81no—
113C22×C8—81no—
114C22⋊Q8—21no—
115C22⋊Q8—21no—
116C22⋊Q8C2×C812yes—
117C22⋊Q8M1612yes—
118C4×Q8—81no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—81no—
136C2×C4⋊C4C22⋊C411yescharacteristic
137C2×C4⋊C4C22⋊C411yescharacteristic
138C2×C4⋊C4C22⋊C411yescharacteristic
139C2×C4⋊C4C2×C812yes—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C42—21no—
143C2×C42—21no—
144C2×C42—81no—
145C2×C42C2×D411yescharacteristic
146C2×C42C2×D411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42#4111yescharacteristic
149#106—24no—
150#106—81no—
151C4⋊C8—42no—
152C4⋊C8—81no—
153C4⋊C8—81no—
154#103—24no—
155#103—81no—
156C22⋊C8—21no—
157C22⋊C8—21no—
158C22⋊C8—21no—
159C22⋊C8—21no—
160C22⋊C8—21no—
161C22⋊C8—21no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164C22⋊C8C2×C812yes—
165C22⋊C8SD1612yes—
166C4×C8—42no—
167C4×C8—81no—
168C4×C8—81no—
169C4×C8—81no—
170#95—21no—
171#95—21no—
172#95—21no—
173#95—21no—
174#95—21no—
175#95—41no—
176#95—41no—
177C24C4×D411yescharacteristic
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8C22⋊C812yes—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4C2×C22⋊C411yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4#12011yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4#12311yescharacteristic
213C22×C4C22×C811yescharacteristic
214C22×C4C2×M1611yescharacteristic
215C22×C4#13111yescharacteristic
216C22×C4#13111yescharacteristic
217C22×C4C2×SD1611yescharacteristic
218C22×C4#13511yescharacteristic
219C22×C4AGL(1,ℤ/8)11yescharacteristic
220C22×C4#13711yescharacteristic
221C2×C8—22no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—82no—
241C2×C8—82no—
242C2×C8—81no—
243C2×C8—82no—
244C2×C8—81no—
245C2×C8—82no—
246C2×C8—81no—
247C2×C8—81no—
248C2×C8—81no—
249C4⋊C4—21no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4C22⋊C812yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C42—41no—
274C42—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42—41no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23#38611yescharacteristic
286C23C8×D411yescharacteristic
287C23#43511yescharacteristic
288C23C4×SD1611yescharacteristic
289C23#44011yescharacteristic
290C23#44311yescharacteristic
291C23#44411yescharacteristic
292Q8—42no—
293Q8—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—161no—
342C2×C4—161no—
343C2×C4C2×C22⋊C811yescharacteristic
344C2×C4#40811yescharacteristic
345C2×C4C8×D411yescharacteristic
346C2×C4#43511yescharacteristic
347C2×C4#44811yescharacteristic
348C2×C4#44911yescharacteristic
349C2×C4#46011yescharacteristic
350C2×C4#46411yescharacteristic
351C2×C4#47111yescharacteristic
352C2×C4#47311yescharacteristic
353C8—42no—
354C8—42no—
355C8—42no—
356C8—81no—
357C8—81no—
358C8—81no—
359C8—82no—
360C8—161no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22C8×SD1611yescharacteristic
374C22SD16⋊C811yescharacteristic
375C22#158311yescharacteristic
376C22#158811yescharacteristic
377C22#186911yescharacteristic
378C22#187611yescharacteristic
379C22#188011yescharacteristic
380C22#190611yescharacteristic
381C22#190811yescharacteristic
382C22#191311yescharacteristic
383C22#191511yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—42no—
396C4—42no—
397C4—81no—
398C4—81no—
399C4—82no—
400C4—161no—
401C2—21no—
402C2—21no—
403C2—21no—
404C2—21no—
405C2#894811yescharacteristic
406C2#909611yescharacteristic
407C2#910811yescharacteristic
408C2#926311yescharacteristic
409C2#926611yescharacteristic
410C2#927211yescharacteristic
411C2#927811yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC22×C4C22×C8
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
44. #483C8semidirect

Maximal subgroups

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

subgroupindex
#232372
#220782
#96502
#75892
C2×#12712
#70292
#70162