Finite Group Databasebeta

← #121180

Subgroups — #121180

Order 512.

606 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#8057C211yesmaximal, characteristic
2#8020C211yesmaximal, characteristic
3#8020C211yesmaximal, characteristic
4#7982C211yesmaximal, characteristic
5#7927C211yesmaximal, characteristic
6#7925C211yesmaximal, characteristic
7C2×#1280C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14C22×#95C2211yescharacteristic
15#1298—22no—
16#1294—22no—
17#1294—22no—
18#1289C412yescomplemented
19#1289C412yescomplemented
20#1282—22no—
21#1282—22no—
22#1280—22no—
23C24×C4—21no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C22×M16—21no—
27C23×C8—21no—
28C23×C8—21no—
29C2×#117—21no—
30C2×#117—21no—
31#407—21no—
32#407—21no—
33#407—21no—
34#407—21no—
35#407—21no—
36#407—21no—
37#407—21no—
38#407Q812yes—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8C2×C412yes—
53C2×C22⋊C8D412yes—
54C2×C22⋊C8D412yes—
55#381—21no—
56#381—21no—
57#380—21no—
58#380—21no—
59#380C2×C411yescharacteristic
60#380C2×C411yescharacteristic
61#380C2×C412yes—
62#379—21no—
63#379—21no—
64C4×C22⋊C4—21no—
65C4×C22⋊C4—21no—
66C4×C22⋊C4—21no—
67C4×C22⋊C4—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95D412yes—
74C25#4111yescharacteristic
75C23×C4—24no—
76C23×C4—22no—
77C23×C4—42no—
78C23×C4—41no—
79C23×C4—41no—
80C23×C4—82no—
81C23×C4—82no—
82C23×C4—82no—
83C23×C4C22×C411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×Q811yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C23×C4#4111yescharacteristic
95C23×C4#4111yescharacteristic
96C23×C4#4111yescharacteristic
97C2×M16—22no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—82no—
102C2×M16—82no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—82no—
112C22×C8—82no—
113#117—82no—
114#117—82no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—21no—
121C2×C22⋊C4—41no—
122C2×C22⋊C4—41no—
123C2×C22⋊C4—41no—
124C2×C22⋊C4—41no—
125C2×C42—41no—
126C2×C42—41no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—22no—
134C22⋊C8—22no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143#95—22no—
144#95—21no—
145#95—21no—
146#95—22no—
147#95—22no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C24—22no—
153C24—22no—
154C24—41no—
155C24—42no—
156C24—41no—
157C24C4×D411yescharacteristic
158C24#12311yescharacteristic
159C24#12411yescharacteristic
160C24#12511yescharacteristic
161C24#12611yescharacteristic
162C24#12611yescharacteristic
163C24#12611yescharacteristic
164C22×C4—24no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—44no—
172C22×C4—44no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—81no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—82no—
187C22×C4—82no—
188C22×C4—82no—
189C22×C4—82no—
190C22×C4—88no—
191C22×C4—82no—
192C22×C4—82no—
193C22×C4—88no—
194C22×C4#11711yescharacteristic
195C22×C4#11711yescharacteristic
196C22×C4#11711yescharacteristic
197C22×C4C4×D411yescharacteristic
198C22×C4C4×D411yescharacteristic
199C22×C4C4×Q811yescharacteristic
200C22×C4#12111yescharacteristic
201C22×C4#12111yescharacteristic
202C22×C4#12111yescharacteristic
203C22×C4C22⋊Q811yescharacteristic
204C22×C4C22⋊Q811yescharacteristic
205C22×C4C22⋊Q811yescharacteristic
206C22×C4#12311yescharacteristic
207C22×C4#12311yescharacteristic
208C22×C4#12311yescharacteristic
209C22×C4#12311yescharacteristic
210C22×C4#12311yescharacteristic
211C22×C4#12411yescharacteristic
212C22×C4#12411yescharacteristic
213C22×C4#12511yescharacteristic
214C22×C4#12511yescharacteristic
215C22×C4#12611yescharacteristic
216C22×C4#12611yescharacteristic
217C22×C4#12611yescharacteristic
218C22×C4#12611yescharacteristic
219C22×C4#12611yescharacteristic
220C22×C4#12611yescharacteristic
221C22×C4#12611yescharacteristic
222M16—82no—
223M16—82no—
224M16—82no—
225M16—82no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—82no—
231C2×C8—82no—
232C2×C8—82no—
233C2×C8—82no—
234C2×C8—82no—
235C2×C8—82no—
236C2×C8—82no—
237C2×C8—82no—
238C4⋊C4—82no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—81no—
246C22⋊C4—81no—
247C22⋊C4—81no—
248C22⋊C4—81no—
249C22⋊C4—82no—
250C22⋊C4—82no—
251C42—82no—
252C42—82no—
253C23—21no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—44no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23#38711yescharacteristic
283C23#38811yescharacteristic
284C23#38811yescharacteristic
285C23#39711yescharacteristic
286C23#40011yescharacteristic
287C23#40011yescharacteristic
288C23#40111yescharacteristic
289C23#44312yes—
290C23#44412yes—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—44no—
320C2×C4—88no—
321C2×C4—82no—
322C2×C4—88no—
323C2×C4—84no—
324C2×C4—82no—
325C2×C4—84no—
326C2×C4—82no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—82no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#38311yescharacteristic
336C2×C4#38711yescharacteristic
337C2×C4#38711yescharacteristic
338C2×C4#38811yescharacteristic
339C2×C4#39611yescharacteristic
340C2×C4#39711yescharacteristic
341C2×C4#39711yescharacteristic
342C2×C4#40011yescharacteristic
343C8—82no—
344C8—82no—
345C8—82no—
346C8—82no—
347C22—24no—
348C22—24no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—44no—
372C22—41no—
373C22—42no—
374C22—41no—
375C22—42no—
376C22—44no—
377C22#144311yescharacteristic
378C22#192212yes—
379C22#192912yes—
380C22#193711yescharacteristic
381C22#193811yescharacteristic
382C22#208111yescharacteristic
383C22#208211yescharacteristic
384C22#210412yes—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—84no—
394C4—162no—
395C4—161no—
396C4—161no—
397C2—21no—
398C2—22no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2—22no—
403C2—22no—
404C2—41no—
405C2—41no—
406C2#1130811yescharacteristic
407C2#1131711yescharacteristic
408C2#1131811yescharacteristic
subgroupG/H
center, socleC22#1443
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
18. #1289C4semidirect
19. #1289C4semidirect

Maximal subgroups

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

subgroupindex
#80572
#80202
#79822
#79272
#79252
C2×#12802