Finite Group Databasebeta

← #120015

Subgroups — #120015

Order 512.

902 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21934C211yesmaximal, characteristic
2#14130C211yesmaximal, characteristic
3#10727C212yesmaximal
4C2×#1305C212yesmaximal
5#7911C211yesmaximal, characteristic
6C23×C4⋊C4C2211yescharacteristic
7C2×#407C2212yes—
8C2×#407C2212yes—
9C2×#389—21no—
10C2×#385C412yes—
11C2×#380C2211yescharacteristic
12C2×C4×C22⋊C4C2211yescharacteristic
13#1851—24no—
14#1797—21no—
15#1797—21no—
16C2×#343—24no—
17#1444—21no—
18#1442—21no—
19C4⋊#95—21no—
20C22⋊#95C412yes—
21#1305—24no—
22#1280—21no—
23#1280—21no—
24C24×C4C2×C412yes—
25C24×C4C2311yescharacteristic
26C22×M16—22no—
27C22×M16D414yes—
28C22×C4⋊C4—21no—
29C22×C4⋊C4—22no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—22no—
33C22×C4⋊C4—22no—
34C22×C4⋊C4—44no—
35C22×C22⋊C4C2×C411yescharacteristic
36C22×C22⋊C4C2×C411yescharacteristic
37C22×C22⋊C4C2×C412yes—
38C22×C42D411yescharacteristic
39C22×C42D411yescharacteristic
40C2×C4⋊C8—22no—
41C2×C4⋊C8—22no—
42#407—22no—
43#407—22no—
44#407—22no—
45#407—22no—
46#407—22no—
47#407—22no—
48#407—22no—
49#407Q814yes—
50C2×C22⋊C8—22no—
51C2×C22⋊C8—22no—
52C2×C22⋊C8—22no—
53C2×C22⋊C8—22no—
54#389—44no—
55#385—44no—
56#380—21no—
57#380—21no—
58#380D412yes—
59#380Q812yes—
60C4×C22⋊C4—22no—
61C4×C22⋊C4—22no—
62C2×#95—21no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95—22no—
66C2×#95D411yescharacteristic
67C2×#95D411yescharacteristic
68#343—48no—
69#336—22no—
70#336—22no—
71C25C22×C411yescharacteristic
72C23×C4—22no—
73C23×C4—22no—
74C23×C4—24no—
75C23×C4—42no—
76C23×C4—42no—
77C23×C4—44no—
78C23×C4—42no—
79C23×C4—42no—
80C23×C4—82no—
81C23×C4C22⋊C411yescharacteristic
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C2×D412yes—
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×Q812yes—
90C23×C4C2×Q811yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4112yes—
94C23×C4#4112yes—
95C2×M16—24no—
96C2×M16—24no—
97C2×M16—24no—
98C2×M16—42no—
99C2×M16—44no—
100C2×M16—44no—
101C2×M16—44no—
102C2×M16—44no—
103C22×C8—24no—
104C22×C8—42no—
105C2×C4⋊C4—28no—
106C2×C4⋊C4—24no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—44no—
111C2×C4⋊C4—48no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—44no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—44no—
119C2×C4⋊C4—44no—
120C2×C4⋊C4—82no—
121C2×C22⋊C4—22no—
122C2×C22⋊C4—22no—
123C2×C22⋊C4—22no—
124C2×C22⋊C4—22no—
125C2×C22⋊C4—22no—
126C2×C22⋊C4—41no—
127C2×C22⋊C4—41no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—42no—
130C2×C22⋊C4C4⋊C414yes—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—42no—
136C2×C42—42no—
137C4⋊C8—82no—
138C4⋊C8—82no—
139C22⋊C8—24no—
140C22⋊C8—24no—
141C22⋊C8—42no—
142C22⋊C8—42no—
143C22⋊C8—42no—
144C22⋊C8—42no—
145C22⋊C8—42no—
146C22⋊C8—42no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95—44no—
152#95—44no—
153#95—82no—
154C24—21no—
155C24—21no—
156C24—21no—
157C24—21no—
158C24—41no—
159C24—41no—
160C24—41no—
161C24—41no—
162C24C2×C22⋊C411yescharacteristic
163C24C2×C4⋊C411yescharacteristic
164C24#11711yescharacteristic
165C24C4×D412yes—
166C24C4×Q812yes—
167C22×C4—22no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—24no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—24no—
176C22×C4—24no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—28no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—44no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—44no—
190C22×C4—41no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4—42no—
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—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—44no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—88no—
216C22×C4—88no—
217C22×C4—84no—
218C22×C4—84no—
219C22×C4#10012yes—
220C22×C4#10112yes—
221C22×C4#12011yescharacteristic
222C22×C4#12112yes—
223C22×C4#12111yescharacteristic
224C22×C4#12112yes—
225C22×C4#12111yescharacteristic
226C22×C4C22⋊Q812yes—
227C22×C4C22⋊Q811yescharacteristic
228C22×C4C22⋊Q812yes—
229C22×C4C22⋊Q812yes—
230C22×C4C22⋊Q811yescharacteristic
231C22×C4#12312yes—
232C22×C4#12311yescharacteristic
233C22×C4#12411yescharacteristic
234C22×C4#12512yes—
235C22×C4#12512yes—
236C22×C4#12612yes—
237C22×C4C4⋊Q812yes—
238C22×C4C4⋊Q811yescharacteristic
239M16—48no—
240M16—48no—
241M16—84no—
242M16—84no—
243C2×C8—44no—
244C2×C8—44no—
245C2×C8—44no—
246C2×C8—44no—
247C2×C8—82no—
248C2×C8—82no—
249C4⋊C4—44no—
250C4⋊C4—44no—
251C4⋊C4—44no—
252C4⋊C4—48no—
253C4⋊C4—44no—
254C4⋊C4—88no—
255C22⋊C4—44no—
256C22⋊C4—44no—
257C22⋊C4—44no—
258C22⋊C4—44no—
259C42—42no—
260C42—42no—
261C42—81no—
262C42—81no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—22no—
277C23—22no—
278C23—22no—
279C23—41no—
280C23—41no—
281C23—42no—
282C23—41no—
283C23—41no—
284C23—42no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23#38011yescharacteristic
294C23#38611yescharacteristic
295C23#38712yes—
296C23#38912yes—
297C23#39111yescharacteristic
298C23C2×#10011yescharacteristic
299C23C2×#10111yescharacteristic
300C23#41311yescharacteristic
301C23#41311yescharacteristic
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—88no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—88no—
357C2×C4#39411yescharacteristic
358C2×C4#39511yescharacteristic
359C2×C4#39612yes—
360C2×C4#39811yescharacteristic
361C2×C4#39812yes—
362C2×C4#40011yescharacteristic
363C2×C4B(4,𝔽2)12yes—
364C2×C4#45812yes—
365C8—84no—
366C8—84no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—44no—
390C22—44no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—42no—
395C22#144111yescharacteristic
396C22#180011yescharacteristic
397C22#180111yescharacteristic
398C22#188911yescharacteristic
399C22#189011yescharacteristic
400C22#190011yescharacteristic
401C22#190111yescharacteristic
402C22#191411yescharacteristic
403C22#191511yescharacteristic
404C22#199711yescharacteristic
405C22#199811yescharacteristic
406C4—22no—
407C4—21no—
408C4—22no—
409C4—21no—
410C4—42no—
411C4—42no—
412C4—84no—
413C4—84no—
414C4—81no—
415C4—81no—
416C4#204412yes—
417C4#206212yes—
418C2—21no—
419C2—21no—
420C2—21no—
421C2—21no—
422C2—42no—
423C2—42no—
424C2#950311yescharacteristic
425C2#950611yescharacteristic
426C2#950811yescharacteristic
427C2#950911yescharacteristic
428C2#1120411yescharacteristic
429C2#1120611yescharacteristic
430C2#1122211yescharacteristic
subgroupG/H
center, socleC23#386
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#219342
#141302
#107272
C2×#13052
#79112