Finite Group Databasebeta

← #474358

Subgroups — #474358

Order 512.

972 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14712C211yesmaximal, characteristic
2#14687C211yesmaximal, characteristic
3#11373C212yesmaximal
4#11357C212yesmaximal
5#11357C212yesmaximal
6#11292C214yesmaximal
7#11267C212yesmaximal
8#10795C211yesmaximal, characteristic
9C2×#389—21no—
10C2×#389—21no—
11C2×#389C2212yes—
12C2×#384C2211yescharacteristic
13C2×#384C2211yescharacteristic
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#382—21no—
17C2×#382—21no—
18C2×C43C2211yescharacteristic
19C2×#340C2214yes—
20C2×#340C2214yes—
21C2×#340C2214yes—
22C2×#340C2214yes—
23C2×#336C2212yes—
24C2×#336C2212yes—
25C2×#336C2212yes—
26C4⋊#95—21no—
27C4⋊#95—21no—
28C4⋊#95—21no—
29C4⋊#95—21no—
30C4⋊#95C2212yes—
31C4⋊#95C2212yes—
32C4⋊#95C2212yes—
33C23×C8C2314yes—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4—21no—
38C22×C4⋊C4—21no—
39C22×C4⋊C4—21no—
40C22×C4⋊C4—21no—
41C22×C4⋊C4—21no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4C2312yes—
44C22×C4⋊C4C2312yes—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C42D411yescharacteristic
48C22×C42D411yescharacteristic
49C22×C42D411yescharacteristic
50C22×C42D411yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54#389—44no—
55#389—44no—
56#389—44no—
57#384—24no—
58#384—24no—
59#384—24no—
60#384—24no—
61#382—44no—
62#382—44no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95—22no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C43—24no—
71#340—28no—
72#340—44no—
73#340—44no—
74#340—44no—
75#336—24no—
76#336—24no—
77#336—42no—
78C23×C4—22no—
79C23×C4—22no—
80C23×C4—22no—
81C23×C4—22no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2411yescharacteristic
89C22×C8—24no—
90C22×C8—24no—
91C22×C8—24no—
92C22×C8—24no—
93C22×C8—24no—
94C22×C8—24no—
95C22×C8—24no—
96C2×C4⋊C4—24no—
97C2×C4⋊C4—24no—
98C2×C4⋊C4—24no—
99C2×C4⋊C4—24no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—24no—
102C2×C4⋊C4—24no—
103C2×C4⋊C4—24no—
104C2×C4⋊C4—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4—24no—
110C2×C4⋊C4—24no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—44no—
122C2×C4⋊C4—44no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4—42no—
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—42no—
137C2×C4⋊C4—42no—
138C2×C4⋊C4#4114yes—
139C2×C42—22no—
140C2×C42—22no—
141C2×C42—22no—
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—22no—
151C2×C42—22no—
152C2×C42—21no—
153C2×C42—22no—
154C2×C42—21no—
155C2×C42—41no—
156C2×C42—41no—
157C2×C42D814yes—
158C2×C42SD1614yes—
159C2×C42#4114yes—
160C2×C42#4114yes—
161#95—44no—
162#95—44no—
163#95—44no—
164#95—44no—
165#95—44no—
166#95—44no—
167#95—44no—
168C24C22×D411yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—24no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4#12312yes—
226C22×C4#12312yes—
227C22×C4#12412yes—
228C22×C4#12412yes—
229C22×C4C2×D812yes—
230C22×C4C2×D812yes—
231C22×C4C2×D812yes—
232C22×C4C2×SD1612yes—
233C22×C4C2×SD1612yes—
234C22×C4C2×SD1612yes—
235C22×C4AGL(1,ℤ/8)12yes—
236C22×C4#13712yes—
237C22×C4#13712yes—
238C22×C4#13712yes—
239C22×C4C2×#4112yes—
240C22×C4C2×#4112yes—
241C22×C4C2×#4112yes—
242C22×C4H(5,𝔽2)12yes—
243C22×C4H(5,𝔽2)11yescharacteristic
244C22×C42−1+412yes—
245C22×C42−1+412yes—
246C22×C42−1+411yescharacteristic
247C2×C8—44no—
248C2×C8—44no—
249C2×C8—44no—
250C2×C8—44no—
251C2×C8—44no—
252C2×C8—44no—
253C2×C8—44no—
254C4⋊C4—28no—
255C4⋊C4—48no—
256C4⋊C4—48no—
257C4⋊C4—44no—
258C4⋊C4—44no—
259C4⋊C4—44no—
260C4⋊C4—44no—
261C4⋊C4—44no—
262C4⋊C4—44no—
263C4⋊C4—44no—
264C4⋊C4—84no—
265C4⋊C4—84no—
266C4⋊C4—88no—
267C4⋊C4—84no—
268C4⋊C4—84no—
269C4⋊C4—84no—
270C4⋊C4—84no—
271C42—28no—
272C42—28no—
273C42—28no—
274C42—28no—
275C42—44no—
276C42—44no—
277C42—42no—
278C42—42no—
279C23C2×#12311yescharacteristic
280C23#52511yescharacteristic
281C23C2×#12411yescharacteristic
282C23#53511yescharacteristic
283C23#53611yescharacteristic
284C23#53611yescharacteristic
285C23#53711yescharacteristic
286C23C22×D811yescharacteristic
287C23C22×SD1611yescharacteristic
288C23C2×AGL(1,ℤ/8)11yescharacteristic
289C23C2×#13711yescharacteristic
290C23C2×#13711yescharacteristic
291C23C2×#13711yescharacteristic
292C23#57511yescharacteristic
293C23#57511yescharacteristic
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4#48014yes—
361C2×C4#48314yes—
362C2×C4#48614yes—
363C2×C4#48914yes—
364C2×C4#53914yes—
365C2×C4#54012yes—
366C2×C4#54212yes—
367C2×C4#54214yes—
368C2×C4#55214yes—
369C2×C4#55214yes—
370C2×C4#55612yes—
371C2×C4#55912yes—
372C2×C4#56312yes—
373C2×C4#56412yes—
374C8—84no—
375C22#248411yescharacteristic
376C22#250311yescharacteristic
377C22#259211yescharacteristic
378C22#262411yescharacteristic
379C22#263311yescharacteristic
380C22#264011yescharacteristic
381C22#282211yescharacteristic
382C22C2×#48011yescharacteristic
383C22C2×#48311yescharacteristic
384C22#309411yescharacteristic
385C22#309511yescharacteristic
386C22#310011yescharacteristic
387C22#310311yescharacteristic
388C22#311011yescharacteristic
389C22#311311yescharacteristic
390C22C2×#48611yescharacteristic
391C22C2×#48911yescharacteristic
392C22#313911yescharacteristic
393C22#314011yescharacteristic
394C22#320511yescharacteristic
395C22#320611yescharacteristic
396C22#321611yescharacteristic
397C22#321611yescharacteristic
398C22#322611yescharacteristic
399C22#322611yescharacteristic
400C22#322711yescharacteristic
401C22#322911yescharacteristic
402C22#323411yescharacteristic
403C22#323611yescharacteristic
404C22#323611yescharacteristic
405C22#323611yescharacteristic
406C22#324511yescharacteristic
407C22#324611yescharacteristic
408C22#325411yescharacteristic
409C22#325511yescharacteristic
410C4—24no—
411C4—24no—
412C4—24no—
413C4—24no—
414C4—42no—
415C4—42no—
416C4—84no—
417C4—162no—
418C4—162no—
419C4—162no—
420C4#276714yes—
421C4#277314yes—
422C2#1696111yescharacteristic
423C2#2761011yescharacteristic
424C2#2761111yescharacteristic
425C2#2796011yescharacteristic
426C2#2796911yescharacteristic
427C2#2934611yescharacteristic
428C2#2935511yescharacteristic
429C2#2992011yescharacteristic
430C2#2992211yescharacteristic
431C2#3007511yescharacteristic
432C2#3007811yescharacteristic
433C2#3020311yescharacteristic
434C2#3021411yescharacteristic
435C2#3284811yescharacteristic
436C2#3284911yescharacteristic
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
#147122
#146872
#113732
#113572
#112922
#112672
#107952