Finite Group Databasebeta

← #120044

Subgroups — #120044

Order 512.

926 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14353C211yesmaximal, characteristic
2#14275C211yesmaximal, characteristic
3#8023C212yesmaximal
4C2×#1289C212yesmaximal
5C2×#1280C211yesmaximal, characteristic
6C22×C22⋊C8C2212yes—
7C2×#385—21no—
8C2×#380—21no—
9C2×#380—21no—
10C2×#380C2211yescharacteristic
11C2×#380C2212yes—
12C2×#380C2211yescharacteristic
13C22×#95C2211yescharacteristic
14#1444—24no—
15#1444C412yescomplemented
16#1442C412yescomplemented
17#1441—22no—
18C22⋊#95—21no—
19#1294—24no—
20#1289—24no—
21#1280—22no—
22C24×C4D411yescharacteristic
23C24×C4D411yescharacteristic
24C24×C4C2311yescharacteristic
25C23×C8—22no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4—22no—
28C22×C4⋊C4—22no—
29C22×C4⋊C4—22no—
30C22×C4⋊C4—22no—
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C4⋊C4C2×C411yescharacteristic
33C22×C22⋊C4—21no—
34C22×C22⋊C4—21no—
35C22×C22⋊C4—22no—
36C2×C22⋊C8—22no—
37C2×C22⋊C8—22no—
38C2×C22⋊C8—22no—
39C2×C22⋊C8—22no—
40C2×C22⋊C8—22no—
41C2×C22⋊C8Q814yes—
42#385—42no—
43#385—42no—
44#380—21no—
45#380—21no—
46#380—22no—
47#380—22no—
48#380—22no—
49#380—22no—
50#380—22no—
51#380—22no—
52#380—42no—
53#380—42no—
54#380—42no—
55#380—42no—
56#380D412yes—
57#380Q812yes—
58C2×#95—22no—
59C2×#95—22no—
60C2×#95—22no—
61C2×#95—22no—
62C2×#95—22no—
63C2×#95—21no—
64C2×#95—22no—
65C2×#95—22no—
66C2×#95C2×C412yes—
67C2×#95C2×C412yes—
68C2×#95D414yes—
69C2×#95D412yes—
70C25C2×D411yescharacteristic
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4—21no—
76C23×C4—21no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—22no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—24no—
83C23×C4—81no—
84C23×C4—81no—
85C23×C4—81no—
86C23×C4—81no—
87C23×C4—81no—
88C23×C4—81no—
89C23×C4C22⋊C412yes—
90C23×C4C22⋊C412yes—
91C23×C4D812yes—
92C23×C4SD1612yes—
93C23×C4SD1612yes—
94C23×C4Q1612yes—
95C23×C4C22×C411yescharacteristic
96C23×C4C2×D412yes—
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×Q811yescharacteristic
100C23×C4C2×Q812yes—
101C23×C4#4112yes—
102C23×C4#4111yescharacteristic
103C23×C4#4111yescharacteristic
104C23×C4#4112yes—
105C22×C8—24no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—82no—
109C22×C8—82no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—44no—
115C2×C4⋊C4—44no—
116C2×C4⋊C4—44no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—81no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4—82no—
122C2×C4⋊C4—82no—
123C2×C4⋊C4—82no—
124C2×C4⋊C4—82no—
125C2×C4⋊C4—82no—
126C2×C4⋊C4—82no—
127C2×C4⋊C4—82no—
128C2×C4⋊C4—82no—
129C2×C4⋊C4—81no—
130C2×C4⋊C4—81no—
131C2×C22⋊C4—22no—
132C2×C22⋊C4—22no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—41no—
137C2×C22⋊C4—41no—
138C2×C22⋊C4—42no—
139C2×C22⋊C4—41no—
140C2×C22⋊C4—42no—
141C2×C22⋊C4—42no—
142C2×C22⋊C4—41no—
143C2×C22⋊C4—42no—
144C2×C22⋊C4—41no—
145C2×C22⋊C4—41no—
146C2×C22⋊C4—42no—
147C2×C22⋊C4—42no—
148C2×C22⋊C4—41no—
149C22⋊C8—24no—
150C22⋊C8—24no—
151C22⋊C8—42no—
152C22⋊C8—42no—
153#95—22no—
154#95—24no—
155#95—24no—
156#95—24no—
157#95—24no—
158#95—44no—
159#95—44no—
160#95—44no—
161#95—42no—
162#95—82no—
163#95—82no—
164#95C4⋊C414yescomplemented
165C24—41no—
166C24—41no—
167C24—41no—
168C24—41no—
169C24C2×C22⋊C411yescharacteristic
170C24#12011yescharacteristic
171C24#12111yescharacteristic
172C24C22⋊Q811yescharacteristic
173C24#12311yescharacteristic
174C24#12411yescharacteristic
175C24C4⋊Q811yescharacteristic
176C24C2×D811yescharacteristic
177C24C2×SD1611yescharacteristic
178C24C2×SD1611yescharacteristic
179C24C2×Q1611yescharacteristic
180C24AGL(1,ℤ/8)11yescharacteristic
181C24AGL(1,ℤ/8)11yescharacteristic
182C24#13711yescharacteristic
183C24#13711yescharacteristic
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—24no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
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—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4—44no—
224C22×C4—42no—
225C22×C4—44no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—44no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—81no—
237C22×C4—81no—
238C22×C4—82no—
239C22×C4—82no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—82no—
243C22×C4—82no—
244C22×C4—82no—
245C22×C4—82no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—82no—
251C22×C4—82no—
252C22×C4—82no—
253C22×C4—82no—
254C22×C4#10214yes—
255C22×C4#10314yes—
256C22×C4C2×C4⋊C411yescharacteristic
257C22×C4#11711yescharacteristic
258C22×C4C4×D412yes—
259C22×C4C4×Q812yes—
260C22×C4#12112yes—
261C22×C4#12112yes—
262C22×C4#12111yescharacteristic
263C22×C4C22⋊Q812yes—
264C22×C4C22⋊Q812yes—
265C22×C4C22⋊Q812yes—
266C22×C4C22⋊Q811yescharacteristic
267C22×C4#12312yes—
268C22×C4#12512yes—
269C22×C4#12512yes—
270C22×C4#12612yes—
271C22×C4C4⋊Q812yes—
272C2×C8—44no—
273C2×C8—82no—
274C2×C8—82no—
275C2×C8—84no—
276C2×C8—84no—
277C4⋊C4—82no—
278C4⋊C4—82no—
279C4⋊C4—82no—
280C4⋊C4—82no—
281C4⋊C4—84no—
282C4⋊C4—84no—
283C4⋊C4—88no—
284C4⋊C4—88no—
285C4⋊C4—88no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—82no—
293C22⋊C4—82no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C22⋊C4—82no—
297C22⋊C4—82no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#38011yescharacteristic
335C23#38611yescharacteristic
336C23#39111yescharacteristic
337C23#39411yescharacteristic
338C23#39511yescharacteristic
339C23#39811yescharacteristic
340C23#40011yescharacteristic
341C23C2×#10211yescharacteristic
342C23C2×#10311yescharacteristic
343C23#41711yescharacteristic
344C23#41711yescharacteristic
345C23#44711yescharacteristic
346C23#44811yescharacteristic
347C23#45011yescharacteristic
348C23#45111yescharacteristic
349C23#45911yescharacteristic
350C23#46011yescharacteristic
351C23#46111yescharacteristic
352C23#46211yescharacteristic
353C23#47411yescharacteristic
354C23#47511yescharacteristic
355C23#47611yescharacteristic
356C23#47711yescharacteristic
357C23#48011yescharacteristic
358C23#48111yescharacteristic
359C23#48311yescharacteristic
360C23#48411yescharacteristic
361C23#48611yescharacteristic
362C23#48711yescharacteristic
363C23#49011yescharacteristic
364C23#49111yescharacteristic
365C23#49811yescharacteristic
366C23#50011yescharacteristic
367C23#50111yescharacteristic
368C23#50111yescharacteristic
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—82no—
403C2×C4—82no—
404C2×C4—82no—
405C2×C4—82no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4—82no—
412C2×C4—84no—
413C2×C4—84no—
414C2×C4—84no—
415C2×C4—82no—
416C2×C4—84no—
417C2×C4—84no—
418C2×C4—84no—
419C2×C4—82no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—84no—
429C2×C4#38712yes—
430C2×C4#38912yes—
431C2×C4#39612yes—
432C2×C4#39812yes—
433C8—84no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22#144111yescharacteristic
487C22#180211yescharacteristic
488C22#180311yescharacteristic
489C22#187211yescharacteristic
490C22#187411yescharacteristic
491C22#191111yescharacteristic
492C22#191211yescharacteristic
493C22#191311yescharacteristic
494C22#191311yescharacteristic
495C22#199011yescharacteristic
496C22#199211yescharacteristic
497C22#204111yescharacteristic
498C22#204311yescharacteristic
499C22#205711yescharacteristic
500C22#205811yescharacteristic
501C22#208311yescharacteristic
502C22#208411yescharacteristic
503C22#209911yescharacteristic
504C22#210011yescharacteristic
505C4—22no—
506C4—22no—
507C4—22no—
508C4—22no—
509C4—44no—
510C4—44no—
511C4—84no—
512C4—164no—
513C4—161no—
514C4—161no—
515C2—21no—
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2—21no—
525C2—21no—
526C2—21no—
527C2#919911yescharacteristic
528C2#920011yescharacteristic
529C2#920311yescharacteristic
530C2#920411yescharacteristic
531C2#1120511yescharacteristic
532C2#1120711yescharacteristic
533C2#1122411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
15. #1444C4semidirect
16. #1442C4semidirect
164. #95C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
#143532
#142752
#80232
C2×#12892
C2×#12802