Finite Group Databasebeta

← #120040

Subgroups — #120040

Order 512.

606 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21955C211yesmaximal, characteristic
2#13909C211yesmaximal, characteristic
3#8030C212yesmaximal
4C2×#1285C212yesmaximal
5#7912C211yesmaximal, characteristic
6C2×#432C2212yes—
7C2×#432C2212yes—
8C2×#384C411yescharacteristic
9C2×#382C411yescharacteristic
10C2×#382C2211yescharacteristic
11C2×C4×C4⋊C4C2211yescharacteristic
12C2×C4×C4⋊C4C2211yescharacteristic
13#1940—24no—
14#1797—21no—
15#1797—21no—
16#1441—21no—
17#1441—21no—
18#1436—21no—
19#1436—21no—
20C4⋊#95C411yescharacteristic
21C4⋊#95C411yescharacteristic
22#1295—24no—
23#1285—24no—
24#1280—21no—
25#1280—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4—21no—
29C22×C4⋊C4C2×C411yescharacteristic
30C22×C4⋊C4C2×C411yescharacteristic
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C4⋊C4C2×C411yescharacteristic
33C22×C42C2×C411yescharacteristic
34C22×C42C2×C411yescharacteristic
35C22×C42D411yescharacteristic
36C22×C42D411yescharacteristic
37C22×C42C2311yescharacteristic
38#432—22no—
39#432—22no—
40#432—22no—
41#432—22no—
42#432—22no—
43#432—22no—
44#432—22no—
45#432Q814yes—
46C2×C4⋊C8—22no—
47C2×C4⋊C8—22no—
48C2×C4⋊C8—22no—
49C2×C4⋊C8—22no—
50C2×C22⋊C8—22no—
51C2×C22⋊C8—22no—
52C2×#97—22no—
53C2×#97D414yes—
54#384—42no—
55#382—22no—
56#382—22no—
57#382—42no—
58C4×C4⋊C4—22no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—22no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4D412yes—
63C4×C4⋊C4Q812yes—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72C2×#95—21no—
73C2×#95D411yescharacteristic
74C2×#95D411yescharacteristic
75#336—22no—
76#336—22no—
77C23×C4—21no—
78C23×C4—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4C22⋊C411yescharacteristic
82C23×C4C22⋊C411yescharacteristic
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22×C411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C22×C8—24no—
89C22×C8—42no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—22no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—42no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—42no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—81no—
111C2×C4⋊C4—81no—
112C2×C42—21no—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—21no—
116C2×C42—21no—
117C2×C42—21no—
118C2×C42—41no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42—81no—
123C2×C42—81no—
124C2×C42C4⋊C412yes—
125C2×C42C4⋊C412yes—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D412yes—
128C2×C42C2×Q812yes—
129C2×C42C2×Q811yescharacteristic
130C2×C42#4112yes—
131C2×C42#4111yescharacteristic
132C2×C42#4112yes—
133C2×C42#4111yescharacteristic
134C4⋊C8—24no—
135C4⋊C8—42no—
136C4⋊C8—42no—
137C4⋊C8—42no—
138C4⋊C8—82no—
139C4⋊C8—82no—
140C22⋊C8—24no—
141C22⋊C8—42no—
142C22⋊C8—42no—
143C22⋊C8—42no—
144#97—24no—
145#97—24no—
146#97—24no—
147#97—42no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—42no—
153#95—42no—
154#95—42no—
155#95—42no—
156#95—41no—
157#95—42no—
158#95—41no—
159#95—81no—
160#95—81no—
161C24C2×C22⋊C411yescharacteristic
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
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—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4#10012yes—
217C22×C4#10112yes—
218C22×C4C2×C4⋊C411yescharacteristic
219C22×C4#11711yescharacteristic
220C22×C4C4×D412yes—
221C22×C4C4×Q812yes—
222C22×C4#12011yescharacteristic
223C22×C4#12112yes—
224C22×C4#12111yescharacteristic
225C22×C4#12111yescharacteristic
226C22×C4C22⋊Q811yescharacteristic
227C22×C4C22⋊Q812yes—
228C22×C4C22⋊Q811yescharacteristic
229C22×C4#12311yescharacteristic
230C22×C4#12411yescharacteristic
231C22×C4C4⋊Q811yescharacteristic
232C2×C8—44no—
233C2×C8—44no—
234C2×C8—44no—
235C2×C8—44no—
236C2×C8—82no—
237C2×C8—82no—
238C4⋊C4—44no—
239C4⋊C4—44no—
240C4⋊C4—44no—
241C4⋊C4—44no—
242C4⋊C4—82no—
243C4⋊C4—82no—
244C4⋊C4—84no—
245C4⋊C4—84no—
246C42—42no—
247C42—42no—
248C42—42no—
249C42—42no—
250C42—42no—
251C42—42no—
252C42—81no—
253C42—81no—
254C42#12112yes—
255C42C22⋊Q812yes—
256C42C22⋊Q812yes—
257C42#12312yes—
258C42#12512yes—
259C42#12512yes—
260C42#12612yes—
261C42C4⋊Q812yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23#38011yescharacteristic
267C23#38611yescharacteristic
268C23#39111yescharacteristic
269C23C2×#10011yescharacteristic
270C23C2×#10111yescharacteristic
271C23#41311yescharacteristic
272C23#41311yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
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—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4#38712yes—
343C2×C4#38912yes—
344C2×C4#39411yescharacteristic
345C2×C4#39511yescharacteristic
346C2×C4#39612yes—
347C2×C4#39811yescharacteristic
348C2×C4#39812yes—
349C2×C4#40011yescharacteristic
350C8—84no—
351C8—84no—
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#144111yescharacteristic
365C22#180011yescharacteristic
366C22#180111yescharacteristic
367C22#188411yescharacteristic
368C22#188411yescharacteristic
369C22#190011yescharacteristic
370C22#190111yescharacteristic
371C22#191111yescharacteristic
372C22#191211yescharacteristic
373C22#199711yescharacteristic
374C22#199811yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—44no—
384C4—42no—
385C4—42no—
386C4—82no—
387C4—81no—
388C4—81no—
389C4—161no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—21no—
394C2—21no—
395C2#944711yescharacteristic
396C2#944811yescharacteristic
397C2#944911yescharacteristic
398C2#945011yescharacteristic
399C2#1120411yescharacteristic
400C2#1121211yescharacteristic
401C2#1122411yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#219552
#139092
#80302
C2×#12852
#79122