Finite Group Databasebeta

← #474354

Subgroups — #474354

Order 512.

844 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14348C211yesmaximal, characteristic
2#14277C211yesmaximal, characteristic
3#11357C212yesmaximal
4#11325C212yesmaximal
5#11324C211yesmaximal, characteristic
6#11323C211yesmaximal, characteristic
7#11268C211yesmaximal, characteristic
8#11268C211yesmaximal, characteristic
9#11220C212yesmaximal
10#11219C212yesmaximal
11#10796C211yesmaximal, characteristic
12C22×#107C2212yes—
13C22×#106C2212yes—
14C2×#389C2211yescharacteristic
15C2×#389C2211yescharacteristic
16C2×#384C2211yescharacteristic
17C2×#384C2211yescharacteristic
18C2×#382C2211yescharacteristic
19C2×#382C2211yescharacteristic
20C2×#376C2211yescharacteristic
21C2×#340C2212yes—
22C2×#340C2212yes—
23C2×#340C2212yes—
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#336C2212yes—
28C2×#336C2212yes—
29C2×#336C2211yescharacteristic
30C2×#336C2211yescharacteristic
31#1444—22no—
32#1442—22no—
33#1442—22no—
34#1442—22no—
35C4⋊#95C2211yescharacteristic
36C4⋊#95C2211yescharacteristic
37C4⋊#95C2212yes—
38C4⋊#95C2212yes—
39C23×C8C2312yes—
40C23×C8C2312yes—
41C22×C4⋊C4—22no—
42C22×C4⋊C4—22no—
43C22×C4⋊C4—21no—
44C22×C4⋊C4—21no—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C4⋊C4C2311yescharacteristic
48C22×C4⋊C4C2311yescharacteristic
49C22×C4⋊C4C2311yescharacteristic
50C22×C4⋊C4C2311yescharacteristic
51C22×C42C2311yescharacteristic
52C22×C42C2311yescharacteristic
53C22×C42C2311yescharacteristic
54C2×#107—24no—
55C2×#107—42no—
56C2×#107—42no—
57C2×#106—24no—
58C2×#106—42no—
59C2×#106—42no—
60#389—42no—
61#389—42no—
62#384—24no—
63#384—42no—
64#382—22no—
65#382—22no—
66#382—42no—
67#376—24no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—22no—
73C2×#95—22no—
74C2×#95—22no—
75C2×#95—22no—
76C2×#95—22no—
77C2×#95—22no—
78C2×#95D412yes—
79C2×#95D412yes—
80#340—42no—
81#340—42no—
82#340—42no—
83#340—42no—
84#340—42no—
85#340—42no—
86#336—24no—
87#336—42no—
88#336Q814yes—
89#336Q814yes—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—21no—
94C23×C4—22no—
95C23×C4—22no—
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D412yes—
99C23×C4C2×D412yes—
100C23×C4C2411yescharacteristic
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
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×C8C2×Q814yes—
114C22×C8C2×Q814yes—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—44no—
142C2×C4⋊C4—42no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—44no—
145C2×C4⋊C4—82no—
146C2×C4⋊C4—82no—
147C2×C4⋊C4—82no—
148C2×C4⋊C4—82no—
149C2×C4⋊C4—82no—
150C2×C4⋊C4—82no—
151C2×C4⋊C4#4112yes—
152C2×C4⋊C4#4112yes—
153C2×C42—22no—
154C2×C42—21no—
155C2×C42—21no—
156C2×C42—22no—
157C2×C42—22no—
158C2×C42—22no—
159C2×C42—21no—
160C2×C42—22no—
161C2×C42—21no—
162C2×C42C2×Q812yes—
163C2×C42C2×Q812yes—
164C2×C42#4114yes—
165#107—48no—
166#106—48no—
167#95—28no—
168#95—24no—
169#95—24no—
170#95—44no—
171#95—42no—
172#95—42no—
173#95—82no—
174#95—82no—
175#95—82no—
176#95—82no—
177#95—82no—
178#95—82no—
179C24C22×D411yescharacteristic
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—42no—
222C22×C4—41no—
223C22×C4—41no—
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#12314yes—
237C22×C4C4⋊Q814yes—
238C22×C4C22×Q811yescharacteristic
239C22×C4C22×Q811yescharacteristic
240C22×C4C2×#4111yescharacteristic
241C22×C4C2×#4111yescharacteristic
242C22×C4C2×#4112yes—
243C22×C4H(5,𝔽2)12yes—
244C22×C4H(5,𝔽2)12yes—
245C22×C4H(5,𝔽2)11yescharacteristic
246C22×C42−1+411yescharacteristic
247C22×C42−1+412yes—
248C2×C8—24no—
249C2×C8—24no—
250C2×C8—24no—
251C2×C8—24no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—24no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—88no—
279C4⋊C4—88no—
280C4⋊C4—84no—
281C4⋊C4—84no—
282C42—24no—
283C42—24no—
284C42—24no—
285C42—24no—
286C42—42no—
287C42—42no—
288C23C2×#12311yescharacteristic
289C23#52511yescharacteristic
290C23C2×C4⋊Q811yescharacteristic
291C23#53511yescharacteristic
292C23#53511yescharacteristic
293C23#53611yescharacteristic
294C23#53711yescharacteristic
295C23#57612yes—
296C23#57712yes—
297C23#57712yes—
298C23#57812yes—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—82no—
341C2×C4—81no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—81no—
346C2×C4—81no—
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#53812yes—
358C2×C4#53812yes—
359C2×C4#54012yes—
360C2×C4#54212yes—
361C2×C4#54412yes—
362C2×C4#54412yes—
363C2×C4#55212yes—
364C2×C4#55212yes—
365C2×C4#55411yescharacteristic
366C2×C4#55411yescharacteristic
367C2×C4#55412yes—
368C2×C4#55412yes—
369C2×C4#55711yescharacteristic
370C2×C4#55711yescharacteristic
371C2×C4#56212yes—
372C2×C4#56312yes—
373C8—44no—
374C8—44no—
375C22#248411yescharacteristic
376C22#250211yescharacteristic
377C22#258411yescharacteristic
378C22#262411yescharacteristic
379C22#263111yescharacteristic
380C22#266011yescharacteristic
381C22#282011yescharacteristic
382C22#309612yes—
383C22#309712yes—
384C22#311912yes—
385C22#312012yes—
386C22#316312yes—
387C22#316412yes—
388C22#322011yescharacteristic
389C22#322111yescharacteristic
390C22#322211yescharacteristic
391C22#322311yescharacteristic
392C22#322412yes—
393C22#322512yes—
394C22#324312yes—
395C22#324412yes—
396C22#325712yes—
397C22#325812yes—
398C4—44no—
399C4—44no—
400C4—82no—
401C4—82no—
402C4—81no—
403C4—81no—
404C4—162no—
405C4—162no—
406C4—161no—
407C4—161no—
408C4#276812yes—
409C4#276812yes—
410C4#277412yes—
411C4#277412yes—
412C2#1696011yescharacteristic
413C2#2761912yes—
414C2#2795912yes—
415C2#2932412yes—
416C2#2993311yescharacteristic
417C2#2993411yescharacteristic
418C2#3005311yescharacteristic
419C2#3005411yescharacteristic
420C2#3031311yescharacteristic
421C2#3031411yescharacteristic
422C2#3283312yes—
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
#143482
#142772
#113572
#113252
#113242
#113232
#112682
#112202
#112192
#107962