Finite Group Databasebeta

← #120018

Subgroups — #120018

Order 512.

784 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21934C211yesmaximal, characteristic
2#14149C211yesmaximal, characteristic
3C2×#1305C212yesmaximal
4#7911C211yesmaximal, characteristic
5#7909C212yesmaximal
6C2×#407C2212yes—
7C2×#407C2212yes—
8C2×#385C411yescharacteristic
9C2×#385C411yescharacteristic
10C2×#380C2211yescharacteristic
11C2×C4×C22⋊C4C2211yescharacteristic
12C22×#95C2211yescharacteristic
13#1851—24no—
14#1797—21no—
15#1797—21no—
16#1441—21no—
17#1441—21no—
18#1436—21no—
19#1436—21no—
20C22⋊#95C411yescharacteristic
21C22⋊#95C411yescharacteristic
22#1305—24no—
23#1280—24no—
24#1280—21no—
25#1280—21no—
26C24×C4C2×C411yescharacteristic
27C24×C4C2×C411yescharacteristic
28C24×C4C2311yescharacteristic
29C22×M16—22no—
30C22×M16—22no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—21no—
34C22×C22⋊C4C2×C411yescharacteristic
35C22×C22⋊C4C2×C411yescharacteristic
36C22×C22⋊C4C2×C411yescharacteristic
37C22×C22⋊C4C2×C411yescharacteristic
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⋊C8D414yes—
54#385—42no—
55#385—42no—
56#380—21no—
57#380—21no—
58#380D412yes—
59#380Q812yes—
60C4×C22⋊C4—22no—
61C4×C22⋊C4—22no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—22no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—22no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75#336—22no—
76#336—22no—
77C25C22×C411yescharacteristic
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—22no—
83C23×C4—22no—
84C23×C4—42no—
85C23×C4—42no—
86C23×C4—41no—
87C23×C4—41no—
88C23×C4—41no—
89C23×C4—41no—
90C23×C4—81no—
91C23×C4—81no—
92C23×C4—81no—
93C23×C4—81no—
94C23×C4C22⋊C411yescharacteristic
95C23×C4C22⋊C411yescharacteristic
96C23×C4C22⋊C411yescharacteristic
97C23×C4C22⋊C411yescharacteristic
98C23×C4C2×D412yes—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×Q812yes—
103C23×C4C2×Q811yescharacteristic
104C23×C4#4112yes—
105C23×C4#4111yescharacteristic
106C23×C4#4111yescharacteristic
107C23×C4#4112yes—
108C2×M16—24no—
109C2×M16—42no—
110C2×M16—42no—
111C2×M16—42no—
112C2×M16—82no—
113C2×M16—82no—
114C2×M16—82no—
115C2×M16—82no—
116C22×C8—24no—
117C22×C8—42no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—81no—
125C2×C4⋊C4—81no—
126C2×C4⋊C4—81no—
127C2×C4⋊C4—81no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—22no—
133C2×C22⋊C4—22no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C22⋊C4—41no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4C4⋊C412yes—
141C2×C22⋊C4C4⋊C412yes—
142C2×C42—21no—
143C2×C42—21no—
144C2×C42—21no—
145C2×C42—21no—
146C2×C42—81no—
147C2×C42—81no—
148C4⋊C8—82no—
149C4⋊C8—82no—
150C22⋊C8—24no—
151C22⋊C8—24no—
152C22⋊C8—24no—
153C22⋊C8—24no—
154C22⋊C8—42no—
155C22⋊C8—42no—
156C22⋊C8—42no—
157C22⋊C8—42no—
158#95—22no—
159#95—22no—
160#95—22no—
161#95—22no—
162#95—42no—
163#95—42no—
164#95—42no—
165#95—42no—
166#95—41no—
167#95—42no—
168#95—41no—
169#95—81no—
170#95—81no—
171C24—21no—
172C24—21no—
173C24—21no—
174C24—21no—
175C24—41no—
176C24—41no—
177C24—41no—
178C24—41no—
179C24C2×C22⋊C411yescharacteristic
180C24C2×C4⋊C411yescharacteristic
181C24#11711yescharacteristic
182C24C4×D412yes—
183C24C4×Q812yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—24no—
197C22×C4—24no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
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—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4—82no—
245C22×C4—81no—
246C22×C4—81no—
247C22×C4—82no—
248C22×C4—84no—
249C22×C4—84no—
250C22×C4—84no—
251C22×C4—84no—
252C22×C4—82no—
253C22×C4—82no—
254C22×C4—82no—
255C22×C4—82no—
256C22×C4#10012yes—
257C22×C4#10112yes—
258C22×C4#12011yescharacteristic
259C22×C4#12112yes—
260C22×C4#12112yes—
261C22×C4#12111yescharacteristic
262C22×C4#12111yescharacteristic
263C22×C4C22⋊Q812yes—
264C22×C4C22⋊Q811yescharacteristic
265C22×C4C22⋊Q812yes—
266C22×C4C22⋊Q812yes—
267C22×C4C22⋊Q811yescharacteristic
268C22×C4#12311yescharacteristic
269C22×C4#12312yes—
270C22×C4#12411yescharacteristic
271C22×C4#12512yes—
272C22×C4#12512yes—
273C22×C4#12612yes—
274C22×C4C4⋊Q812yes—
275C22×C4C4⋊Q811yescharacteristic
276M16—84no—
277M16—84no—
278M16—84no—
279M16—84no—
280C2×C8—44no—
281C2×C8—44no—
282C2×C8—44no—
283C2×C8—44no—
284C2×C8—82no—
285C2×C8—82no—
286C4⋊C4—82no—
287C4⋊C4—82no—
288C4⋊C4—84no—
289C4⋊C4—84no—
290C22⋊C4—44no—
291C22⋊C4—44no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C42—42no—
297C42—42no—
298C42—81no—
299C42—81no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—42no—
319C23—41no—
320C23—41no—
321C23—42no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23#38011yescharacteristic
331C23#38611yescharacteristic
332C23#38712yes—
333C23#38912yes—
334C23#39111yescharacteristic
335C23C2×#10011yescharacteristic
336C23C2×#10111yescharacteristic
337C23#41311yescharacteristic
338C23#41311yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—84no—
411C2×C4—84no—
412C2×C4#39411yescharacteristic
413C2×C4#39511yescharacteristic
414C2×C4#39612yes—
415C2×C4#39812yes—
416C2×C4#39811yescharacteristic
417C2×C4#40011yescharacteristic
418C8—84no—
419C8—84no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—44no—
443C22—44no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22#144111yescharacteristic
449C22#180011yescharacteristic
450C22#180111yescharacteristic
451C22#189111yescharacteristic
452C22#189111yescharacteristic
453C22#190011yescharacteristic
454C22#190111yescharacteristic
455C22#191311yescharacteristic
456C22#191311yescharacteristic
457C22#199711yescharacteristic
458C22#199811yescharacteristic
459C4—21no—
460C4—22no—
461C4—21no—
462C4—21no—
463C4—22no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—82no—
468C4—82no—
469C4—82no—
470C4—81no—
471C4—82no—
472C4—81no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2—21no—
477C2—42no—
478C2—42no—
479C2#951511yescharacteristic
480C2#951611yescharacteristic
481C2#951711yescharacteristic
482C2#951811yescharacteristic
483C2#1120411yescharacteristic
484C2#1120511yescharacteristic
485C2#1122311yescharacteristic
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
#141492
C2×#13052
#79112
#79092