Finite Group Databasebeta

← #99121

Subgroups — #99121

Order 512.

590 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14688C211yesmaximal, characteristic
2#10795C211yesmaximal, characteristic
3#10795C211yesmaximal, characteristic
4#7025C212yesmaximal
5#7025C212yesmaximal
6C2×#383—21no—
7C2×C43C2211yescharacteristic
8C2×#336—21no—
9C2×#336—21no—
10C2×#336—21no—
11C2×#336—21no—
12C2×#336C2212yes—
13C2×#336C2212yes—
14C4⋊#95C411yescharacteristic
15C4⋊#95C411yescharacteristic
16C4⋊#95C411yescharacteristic
17C4⋊#95C411yescharacteristic
18C4⋊#95C2211yescharacteristic
19C4⋊#95C2211yescharacteristic
20#1434—21no—
21#1434—21no—
22#1434—21no—
23C23×C8—22no—
24C23×C8—22no—
25C22×C4⋊C4C2×C411yescharacteristic
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C411yescharacteristic
28C22×C4⋊C4C2×C411yescharacteristic
29C22×C42C2×C411yescharacteristic
30C22×C42C2×C411yescharacteristic
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42C2311yescharacteristic
36#383—44no—
37C2×#95—21no—
38C2×#95—21no—
39C2×#95—21no—
40C2×#95—21no—
41C2×#95—21no—
42C2×#95—21no—
43C2×#95—21no—
44C2×#95—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C43—24no—
50#336—24no—
51#336—24no—
52#336—24no—
53#336—24no—
54#336—42no—
55#336—42no—
56C23×C4—21no—
57C23×C4—21no—
58C23×C4—21no—
59C23×C4—21no—
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22⋊C411yescharacteristic
63C23×C4C22⋊C411yescharacteristic
64C23×C4C22×C411yescharacteristic
65C23×C4C2×D411yescharacteristic
66C23×C4C2×D411yescharacteristic
67C22×C8—24no—
68C22×C8—24no—
69C22×C8—42no—
70C22×C8—42no—
71C22×C8—42no—
72C22×C8—42no—
73C22×C8—42no—
74C22×C8—42no—
75C22×C8—42no—
76C22×C8—42no—
77C22×C8—42no—
78C22×C8—42no—
79C22×C8—42no—
80C22×C8—42no—
81C2×C4⋊C4—22no—
82C2×C4⋊C4—22no—
83C2×C4⋊C4—22no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—41no—
93C2×C42—22no—
94C2×C42—22no—
95C2×C42—22no—
96C2×C42—22no—
97C2×C42—22no—
98C2×C42—22no—
99C2×C42—22no—
100C2×C42—22no—
101C2×C42—22no—
102C2×C42—22no—
103C2×C42—22no—
104C2×C42—22no—
105C2×C42—21no—
106C2×C42—21no—
107C2×C42—41no—
108C2×C42—41no—
109C2×C42—41no—
110C2×C42—41no—
111C2×C42—41no—
112C2×C42—41no—
113C2×C42SD1612yes—
114C2×C42Q1612yes—
115C2×C42#4114yes—
116#95—42no—
117#95—42no—
118#95—42no—
119#95—42no—
120#95—42no—
121#95—42no—
122#95—42no—
123#95—42no—
124#95—42no—
125#95—41no—
126#95—42no—
127#95—42no—
128#95—41no—
129C24C2×C22⋊C411yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4#10312yes—
195C22×C4#10312yes—
196C22×C4#10412yes—
197C22×C4#10412yes—
198C22×C4#11712yes—
199C22×C4#12312yes—
200C22×C4#12312yes—
201C22×C4#13112yes—
202C22×C4#13112yes—
203C22×C4C2×SD1611yescharacteristic
204C22×C4C2×Q1611yescharacteristic
205C22×C4#13512yes—
206C22×C4AGL(1,ℤ/8)12yes—
207C22×C4AGL(1,ℤ/8)11yescharacteristic
208C22×C4#13711yescharacteristic
209C2×C8—44no—
210C2×C8—44no—
211C2×C8—44no—
212C2×C8—44no—
213C2×C8—44no—
214C2×C8—44no—
215C2×C8—82no—
216C2×C8—82no—
217C2×C8—82no—
218C2×C8—82no—
219C2×C8—82no—
220C2×C8—82no—
221C2×C8—82no—
222C2×C8—82no—
223C4⋊C4—82no—
224C4⋊C4—82no—
225C4⋊C4—82no—
226C4⋊C4—82no—
227C42—24no—
228C42—24no—
229C42—44no—
230C42—44no—
231C42—44no—
232C42—44no—
233C42—44no—
234C42—42no—
235C42—42no—
236C23#38111yescharacteristic
237C23#40811yescharacteristic
238C23#40811yescharacteristic
239C23#41011yescharacteristic
240C23#41011yescharacteristic
241C23#41311yescharacteristic
242C23#41311yescharacteristic
243C23C2×#10311yescharacteristic
244C23#41611yescharacteristic
245C23#41711yescharacteristic
246C23#41811yescharacteristic
247C23C2×#10411yescharacteristic
248C23C2×#10411yescharacteristic
249C23#42111yescharacteristic
250C23#42111yescharacteristic
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4#43314yes—
330C2×C4#48112yes—
331C2×C4#48212yes—
332C2×C4#48412yes—
333C2×C4#48512yes—
334C8—84no—
335C8—84no—
336C22#147311yescharacteristic
337C22#147311yescharacteristic
338C22#147311yescharacteristic
339C22#147311yescharacteristic
340C22#148111yescharacteristic
341C22#148211yescharacteristic
342C22#148311yescharacteristic
343C22#148411yescharacteristic
344C22#149311yescharacteristic
345C22#149411yescharacteristic
346C22#149511yescharacteristic
347C22#149611yescharacteristic
348C22#150011yescharacteristic
349C22#150311yescharacteristic
350C22#150511yescharacteristic
351C22#150911yescharacteristic
352C22#151211yescharacteristic
353C22#151411yescharacteristic
354C22#151811yescharacteristic
355C22#152111yescharacteristic
356C22#152411yescharacteristic
357C22#152911yescharacteristic
358C22#153211yescharacteristic
359C22#153511yescharacteristic
360C22#154211yescharacteristic
361C22#155011yescharacteristic
362C22#155311yescharacteristic
363C22#155711yescharacteristic
364C22#181811yescharacteristic
365C22#182011yescharacteristic
366C22#182211yescharacteristic
367C22#182411yescharacteristic
368C22#182511yescharacteristic
369C22#182611yescharacteristic
370C22#182611yescharacteristic
371C4—24no—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—42no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—161no—
381C4—161no—
382C4—161no—
383C4—161no—
384C2#766911yescharacteristic
385C2#767311yescharacteristic
386C2#768911yescharacteristic
387C2#769211yescharacteristic
388C2#770611yescharacteristic
389C2#771211yescharacteristic
390C2#772611yescharacteristic
391C2#773311yescharacteristic
392C2#870511yescharacteristic
393C2#871011yescharacteristic
394C2#871111yescharacteristic
395C2#871411yescharacteristic
396C2#871711yescharacteristic
397C2#872011yescharacteristic
398C2#872711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C2×C22⋊C4
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#146882
#107952
#70252