Finite Group Databasebeta

← #476050

Subgroups — #476050

Order 512.

952 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2059C212yesmaximal
2#14283C211yesmaximal, characteristic
3#14276C211yesmaximal, characteristic
4#11357C212yesmaximal
5#11325C212yesmaximal
6#11232C212yesmaximal
7#11231C212yesmaximal
8#11207C212yesmaximal
9#10833C211yesmaximal, characteristic
10C22×#125C2211yescharacteristic
11C22×#107C2212yes—
12C22×#106C2212yes—
13C22×C4⋊C8C2211yescharacteristic
14C22×C4⋊C8C2211yescharacteristic
15C2×#389C2212yes—
16C2×#384C2211yescharacteristic
17C2×#384C2211yescharacteristic
18C2×#382C2211yescharacteristic
19C2×#376C2211yescharacteristic
20#2059—28no—
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2212yes—
29#1441—22no—
30#1441—22no—
31#1441—22no—
32#1441—22no—
33C4⋊#95C2212yes—
34C4⋊#95C2212yes—
35C4⋊#95C2212yes—
36C23×C8C2312yes—
37C23×C8C2312yes—
38C2×#125—22no—
39C2×#125—41no—
40C2×#125—41no—
41C2×#125—41no—
42C2×#125—41no—
43C2×#125D414yes—
44C22×C4⋊C4—22no—
45C22×C4⋊C4—22no—
46C22×C4⋊C4—22no—
47C22×C4⋊C4—22no—
48C22×C4⋊C4C2312yes—
49C22×C4⋊C4C2312yes—
50C22×C4⋊C4C2312yes—
51C22×C4⋊C4C2312yes—
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C22×C42C2311yescharacteristic
55C2×#107—24no—
56C2×#107—42no—
57C2×#107—42no—
58C2×#106—24no—
59C2×#106—42no—
60C2×#106—42no—
61C2×C4⋊C8—41no—
62C2×C4⋊C8—41no—
63C2×C4⋊C8—41no—
64C2×C4⋊C8—41no—
65C2×C4⋊C8Q814yes—
66C2×C4⋊C8Q814yes—
67#389—24no—
68#389—24no—
69#384—22no—
70#384—41no—
71#384—41no—
72#384Q814yes—
73#382—41no—
74#382—41no—
75#376—41no—
76#376—41no—
77C2×#95—22no—
78C2×#95—22no—
79C2×#95—22no—
80C2×#95—22no—
81C2×#95—22no—
82C2×#95—22no—
83C2×#95—22no—
84C2×#95—22no—
85C2×#95D412yes—
86C2×#95D412yes—
87#340—24no—
88#340—24no—
89#340—42no—
90#340—42no—
91#340—42no—
92#340—42no—
93#336—24no—
94#336—24no—
95C23×C4—22no—
96C23×C4—22no—
97C23×C4—22no—
98C23×C4—22no—
99C23×C4C2×D412yes—
100C23×C4C2×D412yes—
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C23×C4C2411yescharacteristic
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—22no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—22no—
116C22×C8C2×Q814yes—
117C22×C8C2×Q814yes—
118#125—44no—
119#125—44no—
120#125—44no—
121#125—44no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—28no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—28no—
146C2×C4⋊C4—44no—
147C2×C4⋊C4—44no—
148C2×C4⋊C4—44no—
149C2×C4⋊C4—44no—
150C2×C4⋊C4—82no—
151C2×C4⋊C4—82no—
152C2×C4⋊C4—82no—
153C2×C4⋊C4—82no—
154C2×C4⋊C4—82no—
155C2×C4⋊C4—82no—
156C2×C4⋊C4C2×D414yes—
157C2×C4⋊C4C2×Q814yes—
158C2×C42—21no—
159C2×C42—21no—
160C2×C42—21no—
161C2×C42—21no—
162C2×C42—21no—
163C2×C42—21no—
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—21no—
169C2×C42—21no—
170C2×C42C2×D412yes—
171C2×C42C2×Q812yes—
172C2×C42C2×Q812yes—
173C2×C42C2×Q812yes—
174C2×C42#4112yes—
175C2×C42#4112yes—
176#107—48no—
177#106—48no—
178C4⋊C8—44no—
179C4⋊C8—44no—
180#95—42no—
181#95—42no—
182#95—44no—
183#95—44no—
184#95—82no—
185#95—82no—
186#95—82no—
187#95—82no—
188#95—82no—
189#95—82no—
190C24C22×D411yescharacteristic
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
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—24no—
212C22×C4—24no—
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—42no—
226C22×C4—42no—
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#12114yes—
240C22×C4C22⋊Q814yes—
241C22×C4C4⋊Q812yes—
242C22×C4C4⋊Q812yes—
243C22×C4C22×D411yescharacteristic
244C22×C4C22×Q811yescharacteristic
245C22×C4C22×Q811yescharacteristic
246C22×C4C22×Q811yescharacteristic
247C22×C4C2×#4111yescharacteristic
248C22×C4C2×#4111yescharacteristic
249C22×C4H(5,𝔽2)11yescharacteristic
250C22×C4H(5,𝔽2)11yescharacteristic
251C22×C4H(5,𝔽2)11yescharacteristic
252C22×C4H(5,𝔽2)11yescharacteristic
253C22×C4H(5,𝔽2)11yescharacteristic
254C22×C42−1+411yescharacteristic
255C22×C42−1+411yescharacteristic
256C22×C42−1+411yescharacteristic
257C2×C8—24no—
258C2×C8—24no—
259C2×C8—24no—
260C2×C8—24no—
261C2×C8—24no—
262C2×C8—24no—
263C2×C8—42no—
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C2×C8—42no—
271C4⋊C4—24no—
272C4⋊C4—24no—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—416no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C4⋊C4—88no—
289C4⋊C4—88no—
290C4⋊C4—88no—
291C42—22no—
292C42—22no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—22no—
297C42—22no—
298C42—22no—
299C42—22no—
300C42—22no—
301C42—22no—
302C42—22no—
303C23C2×#12111yescharacteristic
304C23C2×C22⋊Q811yescharacteristic
305C23C2×C4⋊Q811yescharacteristic
306C23#53411yescharacteristic
307C23#53511yescharacteristic
308C23#53611yescharacteristic
309C23#53711yescharacteristic
310C23#57612yes—
311C23#57712yes—
312C23#57712yes—
313C23#57812yes—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—24no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
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—82no—
361C2×C4—82no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4#53411yescharacteristic
367C2×C4#53411yescharacteristic
368C2×C4#53811yescharacteristic
369C2×C4#53811yescharacteristic
370C2×C4#53911yescharacteristic
371C2×C4#53911yescharacteristic
372C2×C4#54311yescharacteristic
373C2×C4#54311yescharacteristic
374C2×C4#54411yescharacteristic
375C2×C4#54411yescharacteristic
376C2×C4#54411yescharacteristic
377C2×C4#54411yescharacteristic
378C2×C4D4×Q811yescharacteristic
379C2×C4D4×Q811yescharacteristic
380C2×C4D4×Q811yescharacteristic
381C2×C4#55011yescharacteristic
382C2×C4#55411yescharacteristic
383C2×C4#55411yescharacteristic
384C2×C4#55411yescharacteristic
385C2×C4#55611yescharacteristic
386C2×C4#55711yescharacteristic
387C2×C4#55711yescharacteristic
388C2×C4Q8211yescharacteristic
389C2×C4Q8211yescharacteristic
390C2×C4#56211yescharacteristic
391C2×C4#56211yescharacteristic
392C2×C4#56311yescharacteristic
393C2×C4#56311yescharacteristic
394C8—44no—
395C8—44no—
396C22#253811yescharacteristic
397C22#254611yescharacteristic
398C22#256711yescharacteristic
399C22#261711yescharacteristic
400C22#262711yescharacteristic
401C22#265911yescharacteristic
402C22#282011yescharacteristic
403C22#304512yes—
404C22#304612yes—
405C22#308112yes—
406C22#308212yes—
407C22#316312yes—
408C22#316412yes—
409C22#320312yes—
410C22#320412yes—
411C22#322412yes—
412C22#322512yes—
413C22#324112yes—
414C22#324212yes—
415C22#325911yescharacteristic
416C22#326011yescharacteristic
417C22#326011yescharacteristic
418C22#326111yescharacteristic
419C4—44no—
420C4—44no—
421C4—42no—
422C4—42no—
423C4—84no—
424C4—84no—
425C4—162no—
426C4—162no—
427C4#273211yescharacteristic
428C4#273211yescharacteristic
429C4#273411yescharacteristic
430C4#273411yescharacteristic
431C4#280511yescharacteristic
432C4#280511yescharacteristic
433C4#280611yescharacteristic
434C4#280611yescharacteristic
435C2#1707811yescharacteristic
436C2#2829211yescharacteristic
437C2#2829411yescharacteristic
438C2#2869812yes—
439C2#2921712yes—
440C2#2972912yes—
441C2#2997812yes—
442C2#3030111yescharacteristic
443C2#3030311yescharacteristic
444C2#3282711yescharacteristic
445C2#3282811yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#20592
#142832
#142762
#113572
#113252
#112322
#112312
#112072
#108332