Finite Group Databasebeta

← #134258

Subgroups — #134258

Order 512.

838 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#385C211yesmaximal, characteristic
2C2×#1326C212yesmaximal
3#8557C211yesmaximal, characteristic
4#8557C211yesmaximal, characteristic
5#7187C212yesmaximal
6C23×C42C411yescharacteristic
7C2×#385C411yescharacteristic
8C2×#385C2211yescharacteristic
9C2×C4×C4⋊C4—21no—
10C2×C4×C22⋊C4C411yescharacteristic
11C2×C4×C22⋊C4C2211yescharacteristic
12#1797—21no—
13#1797—21no—
14C2×#323C2212yes—
15C2×#323C2212yes—
16#1436—21no—
17#1436—21no—
18C22⋊#95C411yescharacteristic
19C22⋊#95C2211yescharacteristic
20C4×#95—21no—
21#1326—24no—
22#1280—21no—
23#1280—21no—
24C24×C4C2×C411yescharacteristic
25C24×C4C2×C411yescharacteristic
26C24×C4C2×C411yescharacteristic
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C22⋊C4C2×C411yescharacteristic
30C22×C22⋊C4C2×C411yescharacteristic
31C22×C22⋊C4C2×C411yescharacteristic
32C22×C22⋊C4C2311yescharacteristic
33C22×C42—21no—
34C22×C42—21no—
35C22×C42—21no—
36C22×C42—44no—
37C22×C42—41no—
38C22×C42—41no—
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C2×C4⋊C8—41no—
42C2×C4⋊C8—41no—
43C2×C22⋊C8—22no—
44C2×C22⋊C8—22no—
45#385—22no—
46#385—22no—
47#385—21no—
48#385—21no—
49#385D412yes—
50#385Q812yes—
51C4×C4⋊C4—44no—
52C4×C22⋊C4—22no—
53C4×C22⋊C4—41no—
54C4×C22⋊C4—41no—
55C4×C22⋊C4C814yescomplemented
56C2×#95—21no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95D411yescharacteristic
64C2×#95D411yescharacteristic
65#336—41no—
66#336—41no—
67#323—22no—
68#323—22no—
69#323—22no—
70#323—22no—
71C25C22×C411yescharacteristic
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4—21no—
76C23×C4—21no—
77C23×C4—22no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—42no—
82C23×C4—42no—
83C23×C4—42no—
84C23×C4—42no—
85C23×C4—42no—
86C23×C4—42no—
87C23×C4—41no—
88C23×C4—41no—
89C23×C4—41no—
90C23×C4—41no—
91C23×C4C22⋊C411yescharacteristic
92C23×C4C22⋊C411yescharacteristic
93C23×C4C22⋊C411yescharacteristic
94C23×C4C22⋊C411yescharacteristic
95C23×C4C4⋊C412yes—
96C23×C4C2×C812yes—
97C23×C4M1612yes—
98C23×C4M1612yes—
99C23×C4C2×D411yescharacteristic
100C23×C4C2×D411yescharacteristic
101C22×C8—42no—
102C22×C8—42no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—42no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—42no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C22⋊C4—21no—
113C2×C22⋊C4—21no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C22⋊C4—41no—
117C2×C22⋊C4—41no—
118C2×C22⋊C4—41no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—41no—
121C2×C22⋊C4—41no—
122C2×C22⋊C4C4⋊C412yes—
123C2×C22⋊C4C2×C812yes—
124C2×C22⋊C4C2×C812yes—
125C2×C22⋊C4M1612yes—
126C2×C22⋊C4C2×D411yescharacteristic
127C2×C22⋊C4C2×Q811yescharacteristic
128C2×C22⋊C4#4111yescharacteristic
129C2×C22⋊C4#4111yescharacteristic
130C2×C42—24no—
131C2×C42—24no—
132C2×C42—21no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—42no—
137C2×C42—42no—
138C2×C42—42no—
139C2×C42—42no—
140C2×C42—42no—
141C2×C42—42no—
142C2×C42—44no—
143C2×C42—44no—
144C2×C42—44no—
145C2×C42—41no—
146C2×C42—41no—
147C2×C42—44no—
148C2×C42—42no—
149C2×C42—42no—
150C4⋊C8—82no—
151C4⋊C8—82no—
152C22⋊C8—42no—
153C22⋊C8—42no—
154C22⋊C8—42no—
155C22⋊C8—42no—
156#95—24no—
157#95—24no—
158#95—22no—
159#95—22no—
160#95—41no—
161#95—41no—
162#95—42no—
163#95—42no—
164#95—42no—
165#95—42no—
166C24—21no—
167C24—21no—
168C24—21no—
169C24—21no—
170C24—41no—
171C24—41no—
172C24—41no—
173C24—41no—
174C24C2×C22⋊C411yescharacteristic
175C24C2×C4⋊C411yescharacteristic
176C24#11711yescharacteristic
177C24C22×C811yescharacteristic
178C24C2×M1611yescharacteristic
179C24C2×M1611yescharacteristic
180C24C2×M1611yescharacteristic
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
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—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—48no—
212C22×C4—44no—
213C22×C4—44no—
214C22×C4—44no—
215C22×C4—44no—
216C22×C4—44no—
217C22×C4—44no—
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—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—48no—
231C22×C4—48no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C22⋊C812yes—
263C22×C4C22⋊C812yes—
264C22×C4#9911yescharacteristic
265C22×C4#9911yescharacteristic
266C22×C4#10112yes—
267C22×C4#12111yescharacteristic
268C22×C4#12111yescharacteristic
269C22×C4C22⋊Q811yescharacteristic
270C22×C4C22⋊Q811yescharacteristic
271C2×C8—82no—
272C2×C8—82no—
273C2×C8—82no—
274C2×C8—82no—
275C2×C8—82no—
276C2×C8—82no—
277C4⋊C4—44no—
278C4⋊C4—44no—
279C4⋊C4—48no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4C4⋊C814yescomplemented
292C42—48no—
293C42—44no—
294C42—48no—
295C42—42no—
296C42—44no—
297C42—42no—
298C42—81no—
299C42—81no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
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—42no—
329C23—42no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23#38011yescharacteristic
339C23C2×C22⋊C811yescharacteristic
340C23#40711yescharacteristic
341C23C2×#9911yescharacteristic
342C23#41011yescharacteristic
343C23C2×#10111yescharacteristic
344C23#41311yescharacteristic
345C23C2×C4⋊C811yescharacteristic
346C23#42311yescharacteristic
347C23#43111yescharacteristic
348C23#43211yescharacteristic
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
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—44no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—44no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4#32412yes—
423C2×C4#32412yes—
424C2×C4AΣL(1,𝔽16)12yes—
425C2×C4#35212yes—
426C8—162no—
427C8—162no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22C2×#32411yescharacteristic
467C22#145811yescharacteristic
468C22#146511yescharacteristic
469C22#146711yescharacteristic
470C22#179711yescharacteristic
471C22#179911yescharacteristic
472C22#180111yescharacteristic
473C22C2×AΣL(1,𝔽16)11yescharacteristic
474C22C2×#35211yescharacteristic
475C22#212011yescharacteristic
476C22#212011yescharacteristic
477C4—22no—
478C4—44no—
479C4—44no—
480C4—42no—
481C4—41no—
482C4—44no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—82no—
487C4—81no—
488C4—81no—
489C4#132614yescomplemented
490C2—21no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—41no—
495C2—41no—
496C2—41no—
497C2—41no—
498C2#855811yescharacteristic
499C2C2×#132611yescharacteristic
500C2#1145211yescharacteristic
501C2#1152511yescharacteristic
502C2#1152611yescharacteristic
503C2#1279311yescharacteristic
504C2#1279411yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC24C22×C8
Frattini, cosocleC22×C22⋊C4C23
prime radicalC25C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
55. C4×C22⋊C4C8semidirect
291. C22⋊C4C4⋊C8semidirect
489. C4#1326semidirect

Maximal subgroups

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

subgroupindex
C4×#3852
C2×#13262
#85572
#71872