Finite Group Databasebeta

← #96755

Subgroups — #96755

Order 512.

886 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14700C211yesmaximal, characteristic
2#10693C211yesmaximal, characteristic, complemented
3C4×#336C211yesmaximal, characteristic, complemented
4C2×#1270C212yesmaximal
5#7025C212yesmaximal, complemented
6C22×#97—21no—
7C22×C4×C8—21no—
8C2×#390C411yescharacteristic
9C2×#390C411yescharacteristic
10C2×#390C2211yescharacteristic
11C2×#389C411yescharacteristic
12C2×#388—21no—
13C2×#388—21no—
14C2×C43C2211yescharacteristic
15C2×#336—21no—
16C2×#336—21no—
17C2×#336C2212yes—
18C2×#336C2212yes—
19#1437—21no—
20#1437—21no—
21C4⋊#95C411yescharacteristic
22C4⋊#95C2211yescharacteristic
23#1270C418yescomplemented
24C23×D4C2×C411yescharacteristic
25C23×C8—22no—
26C23×C8—22no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C22⋊C4—21no—
32C22×C22⋊C4—21no—
33C22×C22⋊C4—21no—
34C22×C22⋊C4—21no—
35C22×C22⋊C4—21no—
36C22×C22⋊C4—21no—
37C22×C42C2×C411yescharacteristic
38C22×C42C2×C411yescharacteristic
39C22×C42D411yescharacteristic
40C22×C42D411yescharacteristic
41C22×C42D411yescharacteristic
42C22×C42D411yescharacteristic
43C22×C42C2311yescharacteristic
44C2×#97—24no—
45C2×#97—42no—
46C2×#97—42no—
47C2×C4×C8—24no—
48C2×C4×C8—42no—
49C2×C4×C8—42no—
50#390—22no—
51#390—42no—
52#390—42no—
53#390C2×C414yes—
54#389—42no—
55#388—44no—
56#388—42no—
57#388—42no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C43—42no—
64#336—24no—
65#336—24no—
66#336—22no—
67#336—22no—
68#336C2×C414yes—
69#336C2×C414yes—
70C25—21no—
71C22×D4—21no—
72C22×D4—22no—
73C22×D4—22no—
74C22×D4—41no—
75C22×D4—41no—
76C22×D4—41no—
77C22×D4—41no—
78C22×D4C4212yes—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22×C411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C22×C8—24no—
90C22×C8—24no—
91C22×C8—24no—
92C22×C8—24no—
93C22×C8—24no—
94C22×C8—24no—
95C22×C8—42no—
96C22×C8—42no—
97C22×C8—42no—
98C22×C8—42no—
99C22×C8—42no—
100C22×C8—42no—
101C22×C8—42no—
102C22×C8—42no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4C4212yes—
116C2×C22⋊C4—24no—
117C2×C22⋊C4—24no—
118C2×C22⋊C4—41no—
119C2×C22⋊C4—41no—
120C2×C22⋊C4—42no—
121C2×C22⋊C4—41no—
122C2×C22⋊C4—42no—
123C2×C22⋊C4—41no—
124C2×C22⋊C4—42no—
125C2×C22⋊C4—42no—
126C2×C22⋊C4—42no—
127C2×C22⋊C4—42no—
128C2×C22⋊C4—42no—
129C2×C22⋊C4—42no—
130C2×C22⋊C4—42no—
131C2×C22⋊C4—42no—
132C2×C22⋊C4—42no—
133C2×C22⋊C4—42no—
134C2×C22⋊C4—42no—
135C2×C22⋊C4—42no—
136C2×C42—22no—
137C2×C42—22no—
138C2×C42—22no—
139C2×C42—22no—
140C2×C42—21no—
141C2×C42—21no—
142C2×C42—22no—
143C2×C42—22no—
144C2×C42—22no—
145C2×C42—22no—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—22no—
149C2×C42—22no—
150C2×C42—41no—
151C2×C42—41no—
152C2×C42—41no—
153C2×C42—41no—
154C2×C42—41no—
155C2×C42—41no—
156C2×C42D812yes—
157C2×C42SD1612yes—
158C2×C42C22×C412yes—
159C2×C42#4112yes—
160#97—48no—
161C4×C8—48no—
162#95—42no—
163#95—42no—
164#95—42no—
165#95—41no—
166#95—41no—
167#95—42no—
168C24—22no—
169C24—41no—
170C24—41no—
171C24—41no—
172C24—41no—
173C24—41no—
174C24—41no—
175C24—41no—
176C24—41no—
177C24—41no—
178C24—41no—
179C24—41no—
180C24—41no—
181C24—41no—
182C24—41no—
183C24C2×C22⋊C411yescharacteristic
184C2×D4—24no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—82no—
191C2×D4—82no—
192C2×D4—82no—
193C2×D4—82no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
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—22no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
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—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4#9912yes—
248C22×C4#10012yes—
249C22×C4#10212yes—
250C22×C4#10212yes—
251C22×C4#10412yes—
252C22×C4#10412yes—
253C22×C4#10412yes—
254C22×C4#10412yes—
255C22×C4C2×C4211yescharacteristic
256C22×C4#11711yescharacteristic
257C22×C4C4×D412yes—
258C22×C4C4×D412yes—
259C22×C4#13112yes—
260C22×C4#13112yes—
261C22×C4C2×D811yescharacteristic
262C22×C4C2×SD1611yescharacteristic
263C22×C4#13512yes—
264C22×C4AGL(1,ℤ/8)12yes—
265C22×C4AGL(1,ℤ/8)11yescharacteristic
266C22×C4#13711yescharacteristic
267C2×C8—28no—
268C2×C8—28no—
269C2×C8—44no—
270C2×C8—44no—
271C2×C8—44no—
272C2×C8—44no—
273C2×C8—44no—
274C2×C8—44no—
275C2×C8—44no—
276C2×C8—44no—
277C2×C8—44no—
278C2×C8—44no—
279C2×C8—44no—
280C2×C8—44no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—82no—
284C4⋊C4—82no—
285C4⋊C4—84no—
286C22⋊C4—44no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—44no—
290C22⋊C4—84no—
291C22⋊C4—84no—
292C22⋊C4—84no—
293C22⋊C4—84no—
294C42—24no—
295C42—24no—
296C42—24no—
297C42—24no—
298C42—42no—
299C42—42no—
300C42—44no—
301C42—44no—
302C42—44no—
303C42—44no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—81no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—81no—
329C23—81no—
330C23—81no—
331C23—81no—
332C23—81no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23—81no—
338C23—81no—
339C23C4×C22⋊C411yescharacteristic
340C23#40811yescharacteristic
341C23#40811yescharacteristic
342C23C2×#9911yescharacteristic
343C23#41011yescharacteristic
344C23C2×#10011yescharacteristic
345C23#41311yescharacteristic
346C23C2×#10211yescharacteristic
347C23#41611yescharacteristic
348C23#41711yescharacteristic
349C23#41811yescharacteristic
350C23C2×#10411yescharacteristic
351C23C2×#10411yescharacteristic
352C23C2×#10411yescharacteristic
353C23C2×#10411yescharacteristic
354D4—84no—
355D4—84no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—81no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
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—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4#32714yes—
428C2×C4#32914yes—
429C2×C4#40512yes—
430C2×C4#43312yes—
431C2×C4C4×D812yes—
432C2×C4C4×SD1612yes—
433C2×C4#44012yes—
434C2×C4#44212yes—
435C8—48no—
436C8—48no—
437C22—82no—
438C22—82no—
439C22—82no—
440C22—82no—
441C22—82no—
442C22—82no—
443C22—82no—
444C22—161no—
445C22—161no—
446C22—161no—
447C22—161no—
448C22—161no—
449C22—161no—
450C22—161no—
451C22—161no—
452C22#146811yescharacteristic
453C22#146911yescharacteristic
454C22#147111yescharacteristic
455C22#147311yescharacteristic
456C22#148311yescharacteristic
457C22#148311yescharacteristic
458C22#148411yescharacteristic
459C22#148411yescharacteristic
460C22#149211yescharacteristic
461C22#149211yescharacteristic
462C22#149411yescharacteristic
463C22#149411yescharacteristic
464C22C2×#32711yescharacteristic
465C22#150011yescharacteristic
466C22#150111yescharacteristic
467C22#150211yescharacteristic
468C22#150411yescharacteristic
469C22#150511yescharacteristic
470C22#150711yescharacteristic
471C22#150911yescharacteristic
472C22C2×#32911yescharacteristic
473C22#152411yescharacteristic
474C22#152411yescharacteristic
475C22#152511yescharacteristic
476C22#154511yescharacteristic
477C22#154711yescharacteristic
478C22#155111yescharacteristic
479C22#155311yescharacteristic
480C22#175011yescharacteristic
481C22C4×#9911yescharacteristic
482C22C4×#10011yescharacteristic
483C22C4×#10411yescharacteristic
484C22C4×#10411yescharacteristic
485C22C4×#10211yescharacteristic
486C22#176211yescharacteristic
487C4—24no—
488C4—22no—
489C4—22no—
490C4—22no—
491C4—22no—
492C4—22no—
493C4—22no—
494C4—24no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—161no—
499C4—161no—
500C2—162no—
501C2#767411yescharacteristic
502C2#767611yescharacteristic
503C2#767811yescharacteristic
504C2#767911yescharacteristic
505C2#768411yescharacteristic
506C2#768611yescharacteristic
507C2#769011yescharacteristic
508C2#769211yescharacteristic
509C2#815511yescharacteristic
510C2#817711yescharacteristic
511C2#818111yescharacteristic
512C2C4×#32711yescharacteristic
513C2#821811yescharacteristic
514C2C4×#32911yescharacteristic
515C2#823411yescharacteristic
subgroupG/H
center, socleC24C2×C22⋊C4
commutatorC22×C4C2×C42
Frattini, cosocleC22×C42C23
prime radicalC23×D4C2×C4
LCSG ▷ C22×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. #10693C2semidirect
3. C4×#336C2semidirect
5. #7025C2semidirect
23. #1270C4semidirect

Maximal subgroups

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

subgroupindex
#147002
#106932
C4×#3362
C2×#12702
#70252