Finite Group Databasebeta

← #121476

Subgroups — #121476

Order 512.

612 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21986C211yesmaximal, characteristic
2#20764C211yesmaximal, characteristic
3#14348C211yesmaximal, characteristic
4C2×#1300C211yesmaximal, characteristic
5#8040C211yesmaximal, characteristic
6#8033C211yesmaximal, characteristic
7#8022C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×C4×M16C2211yescharacteristic
11#2285C2211yescharacteristic
12C2×#384C2211yescharacteristic
13C2×#382C2211yescharacteristic
14C2×#376C2211yescharacteristic
15#1949—22no—
16#1853—21no—
17#1852—21no—
18#1847—21no—
19#1836—22no—
20#1836—21no—
21#1834—21no—
22#1834—21no—
23#1736—22no—
24#1442—22no—
25#1442—22no—
26C4⋊#95—21no—
27C4⋊#95—21no—
28#1300C414yescomplemented
29#1296—22no—
30#1295—22no—
31#1294—22no—
32C22×M16—21no—
33C2×#117—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432—21no—
46#432C2×C412yes—
47#432Q812yes—
48#432Q812yes—
49C2×#107—22no—
50C2×#106—22no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8D412yes—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C4×M16—21no—
56C4×M16—21no—
57C4×M16C2×C412yes—
58C4×M16Q812yes—
59C2×#97—21no—
60C2×#97—21no—
61C2×#97D412yes—
62C2×C4×C8—21no—
63#384—21no—
64#384—21no—
65#384—21no—
66#384—21no—
67#384D411yescharacteristic
68#384D411yescharacteristic
69#382—21no—
70#382—21no—
71#382—21no—
72#382—21no—
73#382—21no—
74#380—21no—
75#380—21no—
76C4×C4⋊C4—21no—
77C4×C4⋊C4—21no—
78#376—21no—
79#376—21no—
80#376C2×C412yes—
81#376Q812yes—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95—24no—
86C2×#95—24no—
87C2×#95D412yes—
88#340—24no—
89#340—24no—
90#340—22no—
91#340—22no—
92C23×C4—22no—
93C23×C4—22no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4C2×D411yescharacteristic
97C23×C4C2×D411yescharacteristic
98C23×C4C2×D411yescharacteristic
99C2×M16—22no—
100C2×M16—22no—
101C2×M16—42no—
102C2×M16—42no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—41no—
106#117—44no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—44no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—42no—
122C2×C4⋊C4—44no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—82no—
128C2×C22⋊C4—41no—
129C2×C42—22no—
130C2×C42—22no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42—41no—
134C2×C42C22×C411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42C2×Q811yescharacteristic
139C2×C42C2×Q811yescharacteristic
140C2×C42C2×Q811yescharacteristic
141C2×C42C2×Q811yescharacteristic
142C2×C42#4111yescharacteristic
143C2×C42#4111yescharacteristic
144C2×C42#4111yescharacteristic
145C2×C42#4111yescharacteristic
146#107—82no—
147#106—82no—
148C4⋊C8—22no—
149C4⋊C8—22no—
150C4⋊C8—41no—
151C4⋊C8C4⋊C414yes—
152C22⋊C8—22no—
153C22⋊C8—22no—
154C22⋊C8—22no—
155C22⋊C8—41no—
156#97—22no—
157#97—22no—
158#97—22no—
159#97—22no—
160#97—41no—
161#97C4⋊C414yes—
162C4×C8—22no—
163C4×C8—22no—
164#95—22no—
165#95—22no—
166#95—22no—
167#95—41no—
168#95—41no—
169#95—41no—
170#95—41no—
171#95—41no—
172#95—41no—
173#95—84no—
174#95—84no—
175#95C4⋊C414yes—
176C24#12011yescharacteristic
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—24no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—44no—
192C22×C4—44no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—42no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—44no—
204C22×C4C2×C4⋊C411yescharacteristic
205C22×C4C4×D411yescharacteristic
206C22×C4C4×D411yescharacteristic
207C22×C4#12011yescharacteristic
208C22×C4#12011yescharacteristic
209C22×C4#12111yescharacteristic
210C22×C4#12111yescharacteristic
211C22×C4#12111yescharacteristic
212C22×C4C22⋊Q811yescharacteristic
213C22×C4C22⋊Q811yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4#12311yescharacteristic
218C22×C4#12711yescharacteristic
219C22×C4C4⋊Q811yescharacteristic
220C22×C4C4⋊Q811yescharacteristic
221C22×C4C4⋊Q811yescharacteristic
222M16—44no—
223M16—44no—
224C2×C8—24no—
225C2×C8—24no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—81no—
232C2×C8—81no—
233C4⋊C4—44no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—82no—
245C4⋊C4—82no—
246C4⋊C4—82no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C22⋊C4—82no—
250C42—44no—
251C42—44no—
252C42—82no—
253C42C2×C4⋊C411yescharacteristic
254C42C2×C4⋊C411yescharacteristic
255C42C4×D411yescharacteristic
256C42C4×Q811yescharacteristic
257C42C22⋊Q811yescharacteristic
258C42C22⋊Q811yescharacteristic
259C42C22⋊Q811yescharacteristic
260C42C22⋊Q811yescharacteristic
261C42#12311yescharacteristic
262C42#12311yescharacteristic
263C42#12511yescharacteristic
264C42#12511yescharacteristic
265C42#12511yescharacteristic
266C42C4⋊Q811yescharacteristic
267C42C4⋊Q811yescharacteristic
268C42C4⋊Q811yescharacteristic
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23#38511yescharacteristic
274C23#39211yescharacteristic
275C23#39511yescharacteristic
276C23#45412yes—
277C23#45512yes—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4—82no—
307C2×C4—84no—
308C2×C4—88no—
309C2×C4—84no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—82no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4#38411yescharacteristic
326C2×C4#38511yescharacteristic
327C2×C4#38511yescharacteristic
328C2×C4#38911yescharacteristic
329C2×C4#38911yescharacteristic
330C2×C4#38911yescharacteristic
331C2×C4#39511yescharacteristic
332C2×C4#39511yescharacteristic
333C2×C4#39811yescharacteristic
334C2×C4#39811yescharacteristic
335C2×C4#39811yescharacteristic
336C2×C4#39911yescharacteristic
337C2×C4#45412yes—
338C2×C4#45512yes—
339C8—44no—
340C8—44no—
341C8—82no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22#144411yescharacteristic
351C22#186012yes—
352C22#200311yescharacteristic
353C22#200311yescharacteristic
354C22#200411yescharacteristic
355C22#200411yescharacteristic
356C22#200811yescharacteristic
357C22#200911yescharacteristic
358C22#206112yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—84no—
370C4—161no—
371C4—161no—
372C4—161no—
373C4—162no—
374C4—161no—
375C4#186012yes—
376C4#206112yes—
377C2—22no—
378C2—22no—
379C2#1009211yescharacteristic
380C2#1009511yescharacteristic
381C2#1009711yescharacteristic
382C2#1009811yescharacteristic
383C2#1133311yescharacteristic
384C2#1133911yescharacteristic
385C2#1133911yescharacteristic
subgroupG/H
center, socleC23#392
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
28. #1300C4semidirect

Maximal subgroups

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

subgroupindex
#219862
#207642
#143482
C2×#13002
#80402
#80332
#80222