Finite Group Databasebeta

← #96933

Subgroups — #96933

Order 512.

964 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2860C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic, complemented
3#10795C211yesmaximal, characteristic, complemented
4C2×#1271C212yesmaximal, complemented
5C2×#1270C212yesmaximal
6C22×#126—21no—
7#2860—24no—
8#2860—24no—
9C2×#390C411yescharacteristic
10C2×#390C411yescharacteristic
11C2×#390C2211yescharacteristic
12C2×#389C411yescharacteristic
13C2×#389C411yescharacteristic
14C2×#389C2211yescharacteristic
15C2×#388—21no—
16C2×#388—21no—
17C2×#388—21no—
18C2×C43C2211yescharacteristic
19C2×#336—21no—
20C2×#336—21no—
21C2×#336—21no—
22C2×#336—21no—
23C2×#336C2212yes—
24C2×#336C2212yes—
25#1271—24no—
26#1270—24no—
27C23×D4C2×C411yescharacteristic
28C23×C8—22no—
29C23×C8—22no—
30C2×#126—28no—
31C2×#126—44no—
32C2×#126—42no—
33C2×#126—42no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C22⋊C4—21no—
41C22×C22⋊C4—21no—
42C22×C22⋊C4—21no—
43C22×C22⋊C4—21no—
44C22×C22⋊C4—21no—
45C22×C22⋊C4—21no—
46C22×C42C2×C411yescharacteristic
47C22×C42C2×C411yescharacteristic
48C22×C42D411yescharacteristic
49C22×C42D411yescharacteristic
50C22×C42D411yescharacteristic
51C22×C42D411yescharacteristic
52C22×C42C2311yescharacteristic
53#390—22no—
54#390—22no—
55#390—22no—
56#390—22no—
57#390—22no—
58#390D414yes—
59#389—22no—
60#389—22no—
61#389—22no—
62#389—22no—
63#389—22no—
64#389D414yes—
65#388—28no—
66#388—28no—
67#388—28no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C43—22no—
72C43—22no—
73#336—24no—
74#336—24no—
75#336—22no—
76#336—22no—
77#336—22no—
78#336—22no—
79#336—42no—
80#336—42no—
81C25—21no—
82C22×D4—21no—
83C22×D4—22no—
84C22×D4—22no—
85C22×D4—41no—
86C22×D4—41no—
87C22×D4—41no—
88C22×D4—41no—
89C22×D4C22⋊C412yes—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4C22⋊C411yescharacteristic
94C23×C4C22⋊C411yescharacteristic
95C23×C4C22⋊C411yescharacteristic
96C23×C4C22⋊C411yescharacteristic
97C23×C4C22×C411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C23×C4C2×D411yescharacteristic
100C22×C8—24no—
101C22×C8—24no—
102C22×C8—42no—
103C22×C8—42no—
104C22×C8—42no—
105C22×C8—42no—
106C22×C8—42no—
107C22×C8—42no—
108C22×C8—42no—
109C22×C8—42no—
110C22×C8—42no—
111C22×C8—42no—
112C22×C8—42no—
113C22×C8—42no—
114#126—416no—
115#126—416no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—24no—
119C2×C4⋊C4—24no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—42no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4C22⋊C412yes—
136C2×C4⋊C4C22⋊C412yes—
137C2×C4⋊C4C22⋊C412yes—
138C2×C22⋊C4—24no—
139C2×C22⋊C4—24no—
140C2×C22⋊C4—24no—
141C2×C22⋊C4—24no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—24no—
144C2×C22⋊C4—42no—
145C2×C22⋊C4—42no—
146C2×C22⋊C4—42no—
147C2×C22⋊C4—42no—
148C2×C22⋊C4—42no—
149C2×C22⋊C4—42no—
150C2×C22⋊C4—42no—
151C2×C22⋊C4—42no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—42no—
155C2×C22⋊C4—41no—
156C2×C22⋊C4—42no—
157C2×C22⋊C4—41no—
158C2×C42—22no—
159C2×C42—22no—
160C2×C42—22no—
161C2×C42—22no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—22no—
167C2×C42—22no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—22no—
171C2×C42—22no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42—41no—
175C2×C42—41no—
176C2×C42—41no—
177C2×C42—41no—
178C2×C42—41no—
179C2×C42—41no—
180C2×C42D812yes—
181C2×C42SD1612yes—
182C2×C42C2×D412yes—
183C2×C42C2×D412yes—
184#95—24no—
185#95—24no—
186#95—24no—
187C24—22no—
188C24—41no—
189C24—41no—
190C24—41no—
191C24—41no—
192C24—41no—
193C24—41no—
194C24—41no—
195C24—41no—
196C24—41no—
197C24—41no—
198C24—41no—
199C24—41no—
200C24—41no—
201C24—41no—
202C24C2×C22⋊C411yescharacteristic
203C2×D4—24no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—82no—
210C2×D4—82no—
211C2×D4—82no—
212C2×D4—82no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
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—21no—
234C22×C4—21no—
235C22×C4—21no—
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—22no—
250C22×C4—22no—
251C22×C4—22no—
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×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#10212yes—
271C22×C4#10212yes—
272C22×C4#10412yes—
273C22×C4#10412yes—
274C22×C4C2×C22⋊C411yescharacteristic
275C22×C4C2×C22⋊C411yescharacteristic
276C22×C4#12012yes—
277C22×C4#12012yes—
278C22×C4#13112yes—
279C22×C4#13112yes—
280C22×C4C2×D811yescharacteristic
281C22×C4C2×SD1611yescharacteristic
282C22×C4#13512yes—
283C22×C4AGL(1,ℤ/8)12yes—
284C22×C4AGL(1,ℤ/8)11yescharacteristic
285C22×C4#13711yescharacteristic
286C2×C8—44no—
287C2×C8—44no—
288C2×C8—44no—
289C2×C8—44no—
290C2×C8—44no—
291C2×C8—44no—
292C2×C8—82no—
293C2×C8—82no—
294C2×C8—82no—
295C2×C8—82no—
296C2×C8—82no—
297C2×C8—82no—
298C2×C8—82no—
299C2×C8—82no—
300C4⋊C4—24no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—48no—
306C4⋊C4—48no—
307C4⋊C4—42no—
308C4⋊C4—44no—
309C4⋊C4—44no—
310C22⋊C4—48no—
311C22⋊C4—48no—
312C22⋊C4—48no—
313C22⋊C4—48no—
314C22⋊C4—44no—
315C22⋊C4—44no—
316C22⋊C4—44no—
317C22⋊C4—44no—
318C42—24no—
319C42—24no—
320C42—42no—
321C42—42no—
322C42—44no—
323C42—44no—
324C42—42no—
325C42—42no—
326C42—42no—
327C42—42no—
328C42—42no—
329C42—42no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—81no—
339C23—81no—
340C23—81no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23—81no—
348C23—81no—
349C23—81no—
350C23—81no—
351C23—81no—
352C23—81no—
353C23—81no—
354C23—81no—
355C23—81no—
356C23—81no—
357C23—81no—
358C23—81no—
359C23—81no—
360C23—81no—
361C23—81no—
362C23—81no—
363C23—81no—
364C23—81no—
365C23#37911yescharacteristic
366C23#40811yescharacteristic
367C23#40811yescharacteristic
368C23#41011yescharacteristic
369C23#41011yescharacteristic
370C23#41311yescharacteristic
371C23#41311yescharacteristic
372C23C2×#10211yescharacteristic
373C23#41611yescharacteristic
374C23#41711yescharacteristic
375C23#41811yescharacteristic
376C23C2×#10411yescharacteristic
377C23C2×#10411yescharacteristic
378C23#42111yescharacteristic
379C23#42111yescharacteristic
380D4—84no—
381D4—84no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
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—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4#40812yes—
456C2×C4#40812yes—
457C2×C4#44712yes—
458C2×C4#44912yes—
459C2×C4#45012yes—
460C2×C4#45212yes—
461C8—84no—
462C8—84no—
463C22—82no—
464C22—82no—
465C22—82no—
466C22—82no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—161no—
471C22—161no—
472C22—161no—
473C22—161no—
474C22—161no—
475C22—161no—
476C22—161no—
477C22—161no—
478C22#147311yescharacteristic
479C22#147311yescharacteristic
480C22#147311yescharacteristic
481C22#147311yescharacteristic
482C22#148011yescharacteristic
483C22#148211yescharacteristic
484C22#148311yescharacteristic
485C22#148411yescharacteristic
486C22#149211yescharacteristic
487C22#149411yescharacteristic
488C22#149511yescharacteristic
489C22#149611yescharacteristic
490C22#150011yescharacteristic
491C22#150211yescharacteristic
492C22#150511yescharacteristic
493C22#150911yescharacteristic
494C22#151211yescharacteristic
495C22#151411yescharacteristic
496C22#151711yescharacteristic
497C22#152111yescharacteristic
498C22#152411yescharacteristic
499C22#152911yescharacteristic
500C22#153211yescharacteristic
501C22#153511yescharacteristic
502C22#154011yescharacteristic
503C22#154711yescharacteristic
504C22#155311yescharacteristic
505C22#155711yescharacteristic
506C22#178011yescharacteristic
507C22#178211yescharacteristic
508C22#178511yescharacteristic
509C22#178611yescharacteristic
510C22#178811yescharacteristic
511C22#178911yescharacteristic
512C22#178911yescharacteristic
513C4—22no—
514C4—22no—
515C4—22no—
516C4—22no—
517C4—22no—
518C4—22no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—42no—
523C4—82no—
524C4—82no—
525C4—82no—
526C2—162no—
527C2#766611yescharacteristic
528C2#767211yescharacteristic
529C2#768611yescharacteristic
530C2#769211yescharacteristic
531C2#770611yescharacteristic
532C2#771211yescharacteristic
533C2#772611yescharacteristic
534C2#773211yescharacteristic
535C2#830911yescharacteristic
536C2#831311yescharacteristic
537C2#831511yescharacteristic
538C2#833011yescharacteristic
539C2#833211yescharacteristic
540C2#833611yescharacteristic
541C2#834111yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC23×D4C2×C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #10795C2semidirect
3. #10795C2semidirect
4. C2×#1271C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28602
#107952
C2×#12712
C2×#12702