Finite Group Databasebeta

← #102939

Subgroups — #102939

Order 512.

801 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2100C211yesmaximal, characteristic, complemented
2C2×#2094C211yesmaximal, characteristic
3#17071C211yesmaximal, characteristic
4#11371C211yesmaximal, characteristic, complemented
5C2×#1271C211yesmaximal, characteristic, complemented
6C2×#1270C211yesmaximal, characteristic
7#7025C211yesmaximal, characteristic, complemented
8C22×#106—21no—
9C22×#102—21no—
10C2×#399—21no—
11C2×#396—22no—
12C2×#390C2211yescharacteristic
13C2×#389C2211yescharacteristic
14C2×#384C2211yescharacteristic
15#2100—22no—
16#2100—22no—
17#2094—22no—
18#2094—22no—
19C2×#340—21no—
20C2×#340—21no—
21C2×#340—22no—
22C2×#336C2211yescharacteristic
23C2×#336C2211yescharacteristic
24C2×#336C2211yescharacteristic
25#1444—21no—
26#1439—21no—
27#1438—21no—
28C4⋊#95C2211yescharacteristic
29#1271—22no—
30#1270—22no—
31C23×D4D411yescharacteristic
32C23×C8—21no—
33C23×C8—21no—
34C23×C8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4—22no—
40C22×C4⋊C4D411yescharacteristic
41C22×C4⋊C4D411yescharacteristic
42C22×C4⋊C4D411yescharacteristic
43C22×C4⋊C4D412yes—
44C22×C22⋊C4—21no—
45C22×C22⋊C4—21no—
46C22×C22⋊C4—22no—
47C22×C22⋊C4—22no—
48C22×C42C2311yescharacteristic
49C2×#106—24no—
50C2×#106—44no—
51C2×#102—24no—
52C2×#102—44no—
53#399—42no—
54#399—42no—
55#396—44no—
56#396—44no—
57#390—21no—
58#390—21no—
59#390—21no—
60#390—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389—21no—
65#384—21no—
66#384—21no—
67#384—21no—
68#384D412yes—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73#340—24no—
74#340—24no—
75#340—44no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336D412yes—
81#336D412yes—
82C25—21no—
83C22×D4—21no—
84C22×D4—21no—
85C22×D4—21no—
86C22×D4—21no—
87C22×D4—21no—
88C22×D4—42no—
89C22×D4—42no—
90C22×D4Q1612yes—
91C23×C4—21no—
92C23×C4—22no—
93C23×C4—21no—
94C23×C4—21no—
95C23×C4—41no—
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C22×C8—24no—
100C22×C8—22no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—42no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—42no—
107C22×C8—41no—
108C22×C8—42no—
109C22×C8—42no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—42no—
113C22×C8—41no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—42no—
131C2×C4⋊C4—44no—
132C2×C4⋊C4—42no—
133C2×C4⋊C4—42no—
134C2×C4⋊C4—42no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—44no—
137C2×C4⋊C4—44no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—42no—
145C2×C4⋊C4—82no—
146C2×C4⋊C4SD1612yes—
147C2×C4⋊C4SD1614yes—
148C2×C22⋊C4—44no—
149C2×C22⋊C4—44no—
150C2×C22⋊C4—44no—
151C2×C22⋊C4—41no—
152C2×C22⋊C4—41no—
153C2×C22⋊C4—41no—
154C2×C22⋊C4—41no—
155C2×C22⋊C4—42no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4—41no—
158C2×C22⋊C4—42no—
159C2×C22⋊C4—41no—
160C2×C22⋊C4—41no—
161C2×C22⋊C4—82no—
162C2×C22⋊C4—82no—
163C2×C22⋊C4—82no—
164C2×C42—42no—
165C2×C42C2×D411yescharacteristic
166C2×C42C2×D411yescharacteristic
167C2×C42C2×D411yescharacteristic
168C2×C42#4111yescharacteristic
169#106—48no—
170#102—48no—
171#95—44no—
172#95—41no—
173#95—41no—
174#95—41no—
175#95—41no—
176#95—41no—
177#95—41no—
178C24—22no—
179C24—41no—
180C24—42no—
181C24—41no—
182C24—41no—
183C24—41no—
184C24—41no—
185C24—42no—
186C24—42no—
187C24—41no—
188C24—42no—
189C24#12011yescharacteristic
190C2×D4—22no—
191C2×D4—22no—
192C2×D4—44no—
193C2×D4—42no—
194C2×D4—44no—
195C2×D4—42no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—82no—
199C2×D4—82no—
200C2×D4—81no—
201C2×D4—81no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—22no—
211C22×C4—41no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—41no—
231C22×C4—42no—
232C22×C4—82no—
233C22×C4—81no—
234C22×C4—82no—
235C22×C4—81no—
236C22×C4#12011yescharacteristic
237C22×C4#12011yescharacteristic
238C22×C4#12111yescharacteristic
239C22×C4#12111yescharacteristic
240C22×C4#12111yescharacteristic
241C22×C4#12711yescharacteristic
242C22×C4C2×SD1611yescharacteristic
243C22×C4C2×SD1612yes—
244C22×C4C2×Q1611yescharacteristic
245C22×C4#13511yescharacteristic
246C22×C4#13511yescharacteristic
247C22×C4AGL(1,ℤ/8)11yescharacteristic
248C22×C4AGL(1,ℤ/8)12yes—
249C22×C4#13711yescharacteristic
250C22×C4#13711yescharacteristic
251C22×C4#13711yescharacteristic
252C2×C8—24no—
253C2×C8—44no—
254C2×C8—44no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—44no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—82no—
263C2×C8—82no—
264C2×C8—82no—
265C2×C8—81no—
266C2×C8—81no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—44no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—44no—
274C4⋊C4—44no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—82no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C4⋊C4—82no—
282C4⋊C4—82no—
283C4⋊C4—82no—
284C4⋊C4—88no—
285C4⋊C4—82no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C22⋊C4—88no—
289C22⋊C4—88no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C22⋊C4—82no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—41no—
298C42—41no—
299C42—41no—
300C42—41no—
301C23—44no—
302C23—42no—
303C23—44no—
304C23—42no—
305C23—42no—
306C23—82no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23—82no—
312C23—82no—
313C23—81no—
314C23—82no—
315C23—81no—
316C23—82no—
317C23—82no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23—81no—
324C23#39211yescharacteristic
325C23#45012yes—
326C23#45011yescharacteristic
327C23#45111yescharacteristic
328C23#45211yescharacteristic
329C23#45211yescharacteristic
330C23#45311yescharacteristic
331C23#45312yes—
332C23#45412yes—
333C23#45411yescharacteristic
334C23#45812yes—
335D4—44no—
336D4—82no—
337D4—82no—
338D4—82no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—81no—
380C2×C4—82no—
381C2×C4—81no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—162no—
389C2×C4—162no—
390C2×C4#44811yescharacteristic
391C2×C4#44911yescharacteristic
392C2×C4#45111yescharacteristic
393C2×C4#45211yescharacteristic
394C2×C4#46012yes—
395C2×C4#46511yescharacteristic
396C2×C4#46711yescharacteristic
397C2×C4#46811yescharacteristic
398C2×C4#47011yescharacteristic
399C2×C4#49211yescharacteristic
400C2×C4#49611yescharacteristic
401C8—44no—
402C8—82no—
403C8—82no—
404C22—82no—
405C22—84no—
406C22—84no—
407C22—82no—
408C22—82no—
409C22—161no—
410C22—161no—
411C22—162no—
412C22—162no—
413C22—161no—
414C22—161no—
415C22#161312yes—
416C22#161412yes—
417C22#161512yes—
418C22#161612yes—
419C22#161612yes—
420C22#161812yes—
421C22#162912yes—
422C22#163112yes—
423C22#163111yescharacteristic
424C22#163211yescharacteristic
425C22#163512yes—
426C22#163712yes—
427C22#163711yescharacteristic
428C22#163811yescharacteristic
429C22#165612yes—
430C22#165712yes—
431C22#200011yescharacteristic
432C22#200111yescharacteristic
433C22#200211yescharacteristic
434C22#200311yescharacteristic
435C22#200611yescharacteristic
436C22#201411yescharacteristic
437C22#202211yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—21no—
447C4—22no—
448C4—21no—
449C4—82no—
450C4—84no—
451C4—161no—
452C4—162no—
453C4—161no—
454C2—162no—
455C2#782312yes—
456C2#782512yes—
457C2#782612yes—
458C2#782812yes—
459C2#992111yescharacteristic
460C2#992811yescharacteristic
461C2#996811yescharacteristic
462C2#1005411yescharacteristic
463C2#1006011yescharacteristic
464C2#1007911yescharacteristic
465C2#1023611yescharacteristic
subgroupG/H
center, socleC24#120
commutator, Frattini, cosocleC22×C42C23
prime radicalC23×D4D4
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2100C2semidirect
4. #11371C2semidirect
5. C2×#1271C2semidirect
7. #7025C2semidirect

Maximal subgroups

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

subgroupindex
C2×#21002
C2×#20942
#170712
#113712
C2×#12712
C2×#12702
#70252