Finite Group Databasebeta

← #477688

Subgroups — #477688

Order 512.

826 conjugacy classes of subgroups.

The subgroup lattice has 409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2101C212yesmaximal
2#15221C212yesmaximal
3#11377C211yesmaximal, characteristic
4#11346C211yesmaximal, characteristic
5#11328C212yesmaximal
6#11315C212yesmaximal
7#11268C212yesmaximal
8#11256C211yesmaximal, characteristic
9#11219C212yesmaximal
10C22×#107C2211yescharacteristic
11C22×#107C2211yescharacteristic
12C2×#389C2212yes—
13C2×#389C2212yes—
14C2×#382C2212yes—
15C2×C4×C4⋊C4C2211yescharacteristic
16#2101—28no—
17C2×#340C2212yes—
18C2×#340C2212yes—
19C2×#340C2212yes—
20C2×#340C2212yes—
21C2×#340C2212yes—
22C2×#340C2211yescharacteristic
23C2×#340C2212yes—
24C2×#340C2211yescharacteristic
25C2×#336C2212yes—
26C2×#336C2212yes—
27C2×#336C2211yescharacteristic
28C2×#336C2211yescharacteristic
29#1445—22no—
30#1444—22no—
31#1442—22no—
32#1442—22no—
33C4⋊#95C2212yes—
34C4⋊#95C2212yes—
35C4⋊#95C2212yes—
36C23×C8C2312yes—
37C23×C8C2311yescharacteristic
38C23×C8C2311yescharacteristic
39C22×C4⋊C4—22no—
40C22×C4⋊C4—22no—
41C22×C4⋊C4D411yescharacteristic
42C22×C4⋊C4D411yescharacteristic
43C22×C4⋊C4C2312yes—
44C22×C4⋊C4C2312yes—
45C22×C4⋊C4C2312yes—
46C22×C4⋊C4C2312yes—
47C22×C42C2311yescharacteristic
48C22×C42C2312yes—
49C2×#107—22no—
50C2×#107—24no—
51C2×#107—41no—
52C2×#107—41no—
53C2×#107—41no—
54#389—24no—
55#389—42no—
56#389—42no—
57#389—42no—
58#382—24no—
59#382—42no—
60C4×C4⋊C4—41no—
61C4×C4⋊C4—41no—
62C2×#95—22no—
63C2×#95—22no—
64C2×#95—22no—
65C2×#95—22no—
66C2×#95—22no—
67C2×#95—22no—
68C2×#95—22no—
69C2×#95—22no—
70C2×#95—22no—
71C2×#95—22no—
72C2×#95D412yes—
73#340—24no—
74#340—24no—
75#340—24no—
76#340—24no—
77#340—24no—
78#340—42no—
79#340—41no—
80#340D414yes—
81#336—24no—
82#336—24no—
83#336—41no—
84#336—41no—
85C23×C4—22no—
86C23×C4—22no—
87C23×C4—22no—
88C23×C4—22no—
89C23×C4C2×D412yes—
90C23×C4C2×D412yes—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2411yescharacteristic
94C22×C8—22no—
95C22×C8—22no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—22no—
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×C8C2×D412yes—
110C22×C8#4112yes—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
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—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—41no—
135C2×C4⋊C4—42no—
136C2×C4⋊C4—41no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—44no—
139C2×C4⋊C4—44no—
140C2×C4⋊C4—44no—
141C2×C4⋊C4—82no—
142C2×C4⋊C4—82no—
143C2×C4⋊C4—82no—
144C2×C4⋊C4C2×D414yes—
145C2×C4⋊C4#4114yes—
146C2×C42—22no—
147C2×C42—22no—
148C2×C42—21no—
149C2×C42—21no—
150C2×C42—22no—
151C2×C42—22no—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42—22no—
155C2×C42—22no—
156#107—44no—
157#107—44no—
158#95—42no—
159#95—44no—
160#95—44no—
161#95—44no—
162#95—44no—
163#95—44no—
164#95—44no—
165#95—44no—
166#95—82no—
167#95—82no—
168#95—82no—
169C24C22×D411yescharacteristic
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—24no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
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—22no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—42no—
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#13512yes—
222C22×C4C22×D411yescharacteristic
223C22×C4C2×#4111yescharacteristic
224C22×C4C2×#4112yes—
225C22×C4H(5,𝔽2)11yescharacteristic
226C22×C4H(5,𝔽2)11yescharacteristic
227C22×C4H(5,𝔽2)11yescharacteristic
228C22×C42−1+412yes—
229C22×C42−1+412yes—
230C22×C42−1+411yescharacteristic
231C22×C42−1+412yes—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—24no—
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—42no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—44no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—88no—
268C4⋊C4—88no—
269C42—42no—
270C42—42no—
271C42—42no—
272C42—42no—
273C42—41no—
274C42—41no—
275C42—42no—
276C23#53411yescharacteristic
277C23#53612yes—
278C23D4211yescharacteristic
279C23#54711yescharacteristic
280C23#54812yes—
281C23C2×#13511yescharacteristic
282C23#57512yes—
283C23#57511yescharacteristic
284C23#57612yes—
285C23#57811yescharacteristic
286C23#57811yescharacteristic
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4#53612yes—
340C2×C4#53711yescharacteristic
341C2×C4#53811yescharacteristic
342C2×C4#53912yes—
343C2×C4#54112yes—
344C2×C4#54112yes—
345C2×C4#54212yes—
346C2×C4#54712yes—
347C2×C4#55011yescharacteristic
348C2×C4#55111yescharacteristic
349C2×C4#55212yes—
350C2×C4#56211yescharacteristic
351C2×C4#56311yescharacteristic
352C2×C4#56311yescharacteristic
353C2×C4#56312yes—
354C2×C4#56311yescharacteristic
355C2×C4#56312yes—
356C2×C4#56412yes—
357C8—42no—
358C8—42no—
359C8—82no—
360C22#267412yes—
361C22#268211yescharacteristic
362C22#271912yes—
363C22#272811yescharacteristic
364C22#281711yescharacteristic
365C22#319111yescharacteristic
366C22#319711yescharacteristic
367C22#319911yescharacteristic
368C22#320211yescharacteristic
369C22#323212yes—
370C22#324012yes—
371C22#324312yes—
372C22#324312yes—
373C22#326812yes—
374C22#327711yescharacteristic
375C22#328311yescharacteristic
376C22#334211yescharacteristic
377C22#334712yes—
378C22#335211yescharacteristic
379C22#336112yes—
380C22#337012yes—
381C22#337712yes—
382C22#337712yes—
383C4—42no—
384C4—81no—
385C4—84no—
386C4—84no—
387C4—82no—
388C4—82no—
389C4—162no—
390C4—162no—
391C4#272112yes—
392C4#272211yescharacteristic
393C4#276411yescharacteristic
394C4#282211yescharacteristic
395C4#283311yescharacteristic
396C4#283912yes—
397C2#1712011yescharacteristic
398C2#3081112yes—
399C2#3082212yes—
400C2#3119311yescharacteristic
401C2#3120711yescharacteristic
402C2#3232312yes—
403C2#3232712yes—
404C2#3254511yescharacteristic
405C2#3256211yescharacteristic
406C2#3279111yescharacteristic
407C2#3279211yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#21012
#152212
#113772
#113462
#113282
#113152
#112682
#112562
#112192