Finite Group Databasebeta

← #190481

Subgroups — #190481

Order 512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2274C211yesmaximal, characteristic
2#21916C212yesmaximal, complemented
3#8701C212yesmaximal, complemented
4#8560C212yesmaximal, complemented
5#8557C212yesmaximal
6#8300C212yesmaximal
7#8153C212yesmaximal, complemented
8#8152C212yesmaximal
9C22×#117C411yescharacteristic
10C22×#117C2211yescharacteristic
11C23×C4⋊C4C411yescharacteristic
12#2274—28no—
13C2×C4×C4⋊C4C411yescharacteristic
14C2×C4×C4⋊C4C411yescharacteristic
15C2×C4×C4⋊C4C411yescharacteristic
16C2×C4×C4⋊C4C411yescharacteristic
17C2×C4×C4⋊C4C2211yescharacteristic
18C2×C4×C4⋊C4C2211yescharacteristic
19C2×C4×C4⋊C4C2211yescharacteristic
20C2×C4×C4⋊C4C2211yescharacteristic
21C2×C4×C22⋊C4C411yescharacteristic
22C2×C4×C22⋊C4C411yescharacteristic
23C2×C4×C22⋊C4C2211yescharacteristic
24C2×C4×C22⋊C4C2211yescharacteristic
25#1917—28no—
26#1817C2214yes—
27#1797C2214yes—
28#1749C2214yes—
29C2×#324C2214yes—
30C2×#323C2214yes—
31#1280C2214yes—
32#1280C2214yes—
33C24×C4C2×C411yescharacteristic
34C24×C4C2×C411yescharacteristic
35C24×C4C2×C411yescharacteristic
36C2×#117—24no—
37C2×#117—24no—
38C2×#117—24no—
39C2×#117—24no—
40C2×#117—24no—
41C2×#117—24no—
42C22×C4⋊C4—24no—
43C22×C4⋊C4—24no—
44C22×C4⋊C4—24no—
45C22×C4⋊C4C2×C411yescharacteristic
46C22×C4⋊C4C2×C411yescharacteristic
47C22×C4⋊C4C2×C411yescharacteristic
48C22×C4⋊C4C2×C411yescharacteristic
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2×C411yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C22⋊C4C2×C411yescharacteristic
54C22×C22⋊C4C2×C411yescharacteristic
55C22×C22⋊C4C2×C411yescharacteristic
56C22×C22⋊C4C2311yescharacteristic
57C22×C42C2×C411yescharacteristic
58C22×C42C2×C411yescharacteristic
59C22×C42C2×C411yescharacteristic
60C22×C42C2×C411yescharacteristic
61C22×C42C2×C411yescharacteristic
62C22×C42C2×C411yescharacteristic
63C22×C42C2×C411yescharacteristic
64C22×C42C2×C411yescharacteristic
65C22×C42C2×C411yescharacteristic
66C22×C42C2311yescharacteristic
67C22×C42C2311yescharacteristic
68C22×C42C2311yescharacteristic
69C2×C4⋊C8—24no—
70C2×C22⋊C8C2318yes—
71C2×#97—24no—
72C4×C4⋊C4—24no—
73C4×C4⋊C4—24no—
74C4×C4⋊C4—24no—
75C4×C4⋊C4—24no—
76C4×C4⋊C4—24no—
77C4×C4⋊C4—24no—
78C4×C4⋊C4—24no—
79C4×C4⋊C4D418yes—
80C4×C22⋊C4—24no—
81C4×C22⋊C4—24no—
82C4×C22⋊C4—24no—
83C4×C22⋊C4—24no—
84C2×#95C2×C411yescharacteristic
85C2×#95C2×C411yescharacteristic
86C2×#95C2×C411yescharacteristic
87C2×#95C2×C411yescharacteristic
88C2×#95C2×C411yescharacteristic
89C2×#95C2×C411yescharacteristic
90C2×#95C2311yescharacteristic
91C2×#95C2311yescharacteristic
92#336—24no—
93#336—28no—
94#336—24no—
95#324—28no—
96#323—28no—
97C25C22×C411yescharacteristic
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—22no—
101C23×C4—22no—
102C23×C4—22no—
103C23×C4—22no—
104C23×C4—22no—
105C23×C4—22no—
106C23×C4—22no—
107C23×C4—22no—
108C23×C4—22no—
109C23×C4—81no—
110C23×C4—81no—
111C23×C4—81no—
112C23×C4—81no—
113C23×C4M1614yes—
114C23×C4M1614yes—
115C23×C4C22×C411yescharacteristic
116C23×C4C22×C411yescharacteristic
117C23×C4C22×C411yescharacteristic
118C23×C4C22×C411yescharacteristic
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C411yescharacteristic
121C23×C4C22×C411yescharacteristic
122C23×C4C22×C411yescharacteristic
123C23×C4C22×C411yescharacteristic
124C23×C4C22×C411yescharacteristic
125C23×C4C22×C411yescharacteristic
126C23×C4C22×C411yescharacteristic
127C23×C4C22×C411yescharacteristic
128C23×C4C2411yescharacteristic
129C22×C8—28no—
130#117—232no—
131#117—232no—
132C2×C4⋊C4—232no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4C22⋊C414yes—
153C2×C4⋊C4C22⋊C414yes—
154C2×C4⋊C4M1614yes—
155C2×C4⋊C4M1614yes—
156C2×C4⋊C4#4114yes—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—22no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4—22no—
164C2×C22⋊C4—22no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4#4114yes—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—22no—
173C2×C42—22no—
174C2×C42—22no—
175C2×C42—22no—
176C2×C42—22no—
177C2×C42—22no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—81no—
187C2×C42—81no—
188C2×C42—81no—
189C2×C42—81no—
190C2×C42—81no—
191C2×C42—81no—
192C2×C42—81no—
193C2×C42—81no—
194C2×C42C2×D414yes—
195C2×C42C2×D414yes—
196C2×C42C2×D414yes—
197C4⋊C8—84no—
198C22⋊C8—28no—
199C22⋊C8—28no—
200#97—84no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95C22⋊C414yes—
208#95C22⋊C414yes—
209C24—21no—
210C24—21no—
211C24—21no—
212C24—21no—
213C24—41no—
214C24—41no—
215C24—41no—
216C24—41no—
217C24#11712yes—
218C24C2×M1612yes—
219C24C2×M1612yes—
220C24C23×C411yescharacteristic
221C22×C4—28no—
222C22×C4—28no—
223C22×C4—28no—
224C22×C4—28no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—28no—
234C22×C4—28no—
235C22×C4—28no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—82no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4—84no—
287C22×C4—84no—
288C22×C4—84no—
289C22×C4—84no—
290C22×C4C2×C22⋊C412yes—
291C22×C4C2×C22⋊C412yes—
292C22×C4C2×C22⋊C412yes—
293C22×C4C2×C22⋊C412yes—
294C22×C4C2×C22⋊C412yes—
295C22×C4C2×C22⋊C412yes—
296C22×C4#11712yes—
297C22×C4#11712yes—
298C22×C4#11712yes—
299C22×C4C2×M1612yes—
300C22×C4C2×M1612yes—
301C22×C4C2×M1612yes—
302C22×C4C2×M1612yes—
303C22×C4C2×M1612yes—
304C22×C4C2×M1612yes—
305C22×C4C2×M1612yes—
306C22×C4C2×M1612yes—
307C22×C4C2×M1612yes—
308C22×C4C2×M1612yes—
309C22×C4C22×D412yes—
310C22×C4C2×#4112yes—
311C22×C4C2×#4112yes—
312C2×C8—48no—
313C2×C8—48no—
314C2×C8—48no—
315C4⋊C4—28no—
316C4⋊C4—28no—
317C4⋊C4—28no—
318C4⋊C4—28no—
319C4⋊C4—28no—
320C4⋊C4—28no—
321C4⋊C4—28no—
322C4⋊C4—28no—
323C22⋊C4—28no—
324C22⋊C4—28no—
325C22⋊C4—28no—
326C22⋊C4—28no—
327C42—28no—
328C42—28no—
329C42—28no—
330C42—28no—
331C42—44no—
332C42—44no—
333C42—82no—
334C42—82no—
335C42—82no—
336C42—82no—
337C42—82no—
338C42—82no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23#43214yes—
366C23C22×C22⋊C411yescharacteristic
367C23C2×#11711yescharacteristic
368C23C2×#11711yescharacteristic
369C23C22×M1611yescharacteristic
370C23C22×M1611yescharacteristic
371C23C22×M1611yescharacteristic
372C23C22×M1611yescharacteristic
373C2×C4—232no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—88no—
445C2×C4—88no—
446C2×C4#40714yes—
447C2×C4#40714yes—
448C2×C4#43214yes—
449C2×C4#52514yes—
450C8—88no—
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—24no—
464C22—44no—
465C22—44no—
466C22—44no—
467C22—44no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22#228011yescharacteristic
475C22C2×#40711yescharacteristic
476C22C2×#40711yescharacteristic
477C22#288311yescharacteristic
478C22#288411yescharacteristic
479C22#288811yescharacteristic
480C22#288911yescharacteristic
481C22C2×#43211yescharacteristic
482C22C2×#43211yescharacteristic
483C22#292011yescharacteristic
484C22#292011yescharacteristic
485C4—24no—
486C4—24no—
487C4—24no—
488C4—24no—
489C4—42no—
490C4—42no—
491C4—42no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C2—21no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—44no—
504C2#1736711yescharacteristic
505C2#1737011yescharacteristic
506C2#1737111yescharacteristic
507C2#1737211yescharacteristic
508C2#2071511yescharacteristic
509C2#2072511yescharacteristic
510C2#2073111yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC24C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #21916C2semidirect
3. #8701C2semidirect
4. #8560C2semidirect
7. #8153C2semidirect

Maximal subgroups

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

subgroupindex
C2×#22742
#219162
#87012
#85602
#85572
#83002
#81532
#81522