Finite Group Databasebeta

← #468891

Subgroups — #468891

Order 512.

1012 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2864C211yesmaximal, characteristic
2C2×#2101C212yesmaximal
3#14707C211yesmaximal, characteristic
4#11293C212yesmaximal
5#11292C212yesmaximal
6#11208C212yesmaximal
7#11208C211yesmaximal, characteristic
8#11208C211yesmaximal, characteristic
9#11208C211yesmaximal, characteristic
10#11208C211yesmaximal, characteristic
11#10795C211yesmaximal, characteristic
12#2864—28no—
13C2×#389C2212yes—
14C2×#389C2211yescharacteristic
15C2×#389C2211yescharacteristic
16C2×#389C2212yes—
17C2×#387—22no—
18C2×#387—22no—
19C2×#382C2211yescharacteristic
20C2×#382C2211yescharacteristic
21C2×#382C2211yescharacteristic
22C2×#382C2211yescharacteristic
23C2×C43C2211yescharacteristic
24#2101—28no—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#336C2212yes—
34C2×#336C2211yescharacteristic
35C2×#336C2211yescharacteristic
36C2×#336C2212yes—
37#1436—22no—
38#1436—22no—
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C23×C8C2312yes—
42C23×C8C2312yes—
43C22×C4⋊C4—22no—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—21no—
46C22×C4⋊C4—21no—
47C22×C4⋊C4C2311yescharacteristic
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2311yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C42D412yes—
54C22×C42D412yes—
55C22×C42C2311yescharacteristic
56C22×C42C2311yescharacteristic
57C22×C42C2311yescharacteristic
58#389—24no—
59#389—24no—
60#389—24no—
61#389—22no—
62#389—22no—
63#389—22no—
64#389—22no—
65#389D418yes—
66#387—216no—
67#387—216no—
68#382—24no—
69#382—24no—
70#382—22no—
71#382—22no—
72#382—24no—
73C2×#95—22no—
74C2×#95—21no—
75C2×#95—21no—
76C2×#95—21no—
77C2×#95—21no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—21no—
84C2×#95—21no—
85C43—24no—
86#340—24no—
87#340—24no—
88#340—24no—
89#340—24no—
90#340—24no—
91#340—24no—
92#340—42no—
93#340—42no—
94#336—24no—
95#336—22no—
96#336—22no—
97#336—42no—
98C23×C4—22no—
99C23×C4—22no—
100C23×C4—21no—
101C23×C4—21no—
102C23×C4—21no—
103C23×C4—21no—
104C23×C4C2×D412yes—
105C23×C4C2×D411yescharacteristic
106C23×C4C2×D411yescharacteristic
107C23×C4C2×D412yes—
108C23×C4C2411yescharacteristic
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8—22no—
117C22×C8—22no—
118C22×C8—22no—
119C22×C8—22no—
120C22×C8—22no—
121C22×C8—22no—
122C22×C8—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—28no—
140C2×C4⋊C4—28no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—44no—
154C2×C4⋊C4—44no—
155C2×C4⋊C4—44no—
156C2×C4⋊C4—44no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—42no—
160C2×C4⋊C4—42no—
161C2×C4⋊C4C2×D414yes—
162C2×C4⋊C4C2×D414yes—
163C2×C4⋊C4#4112yes—
164C2×C4⋊C4#4112yes—
165C2×C42—22no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—22no—
169C2×C42—22no—
170C2×C42—24no—
171C2×C42—24no—
172C2×C42—24no—
173C2×C42—22no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—22no—
177C2×C42—42no—
178C2×C42—42no—
179C2×C42—42no—
180C2×C42C2×D414yes—
181C2×C42#4112yes—
182C2×C42#4112yes—
183#95—28no—
184#95—24no—
185#95—24no—
186#95—24no—
187#95—24no—
188#95—28no—
189#95—28no—
190#95—44no—
191#95—44no—
192#95—42no—
193#95—42no—
194#95—44no—
195C24C22×D411yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—42no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4#12014yes—
251C22×C4#12412yes—
252C22×C4#12412yes—
253C22×C4#13514yes—
254C22×C4C22×D412yes—
255C22×C4C2×#4111yescharacteristic
256C22×C4C2×#4111yescharacteristic
257C22×C4C2×#4111yescharacteristic
258C22×C4C2×#4111yescharacteristic
259C22×C4H(5,𝔽2)11yescharacteristic
260C22×C42−1+411yescharacteristic
261C22×C42−1+412yes—
262C22×C42−1+412yes—
263C22×C42−1+412yes—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—24no—
279C4⋊C4—24no—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—416no—
287C4⋊C4—416no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—84no—
301C4⋊C4—84no—
302C42—24no—
303C42—24no—
304C42—24no—
305C42—24no—
306C42—48no—
307C42—48no—
308C42—42no—
309C42—42no—
310C23C2×#12011yescharacteristic
311C23#52511yescharacteristic
312C23C2×#12411yescharacteristic
313C23#53611yescharacteristic
314C23#53611yescharacteristic
315C23#53611yescharacteristic
316C23#53711yescharacteristic
317C23C2×#13512yes—
318C23#57512yes—
319C23#57512yes—
320C23#57512yes—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4#53612yes—
380C2×C4#53712yes—
381C2×C4#54112yes—
382C2×C4#54112yes—
383C2×C4#54112yes—
384C2×C4#54112yes—
385C2×C4#54712yes—
386C2×C4#54712yes—
387C2×C4#54812yes—
388C2×C4#54812yes—
389C2×C4#55211yescharacteristic
390C2×C4#55211yescharacteristic
391C2×C4#55311yescharacteristic
392C2×C4#55311yescharacteristic
393C2×C4#56312yes—
394C2×C4#56412yes—
395C8—82no—
396C8—82no—
397C22#240611yescharacteristic
398C22#243611yescharacteristic
399C22#256211yescharacteristic
400C22#261611yescharacteristic
401C22#263411yescharacteristic
402C22#264211yescharacteristic
403C22#282211yescharacteristic
404C22#300212yes—
405C22#300512yes—
406C22#310212yes—
407C22#311112yes—
408C22#313111yescharacteristic
409C22#313511yescharacteristic
410C22#314011yescharacteristic
411C22#314011yescharacteristic
412C22#323212yes—
413C22#323312yes—
414C22#323312yes—
415C22#324012yes—
416C22#324012yes—
417C22#324012yes—
418C22#325012yes—
419C22#325612yes—
420C4—44no—
421C4—42no—
422C4—42no—
423C4—44no—
424C4—84no—
425C4—82no—
426C4—82no—
427C4—84no—
428C4—161no—
429C4—161no—
430C4#271912yes—
431C4#271912yes—
432C4#272512yes—
433C4#272512yes—
434C2#1663411yescharacteristic
435C2#2406812yes—
436C2#2590611yescharacteristic
437C2#2590911yescharacteristic
438C2#2912511yescharacteristic
439C2#2912811yescharacteristic
440C2#2969312yes—
441C2#3009712yes—
442C2#3023111yescharacteristic
443C2#3023411yescharacteristic
444C2#3285112yes—
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#28642
C2×#21012
#147072
#112932
#112922
#112082
#107952