Finite Group Databasebeta

← #120561

Subgroups — #120561

Order 512.

522 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21351C211yesmaximal, characteristic
2C2×C4×#108C211yesmaximal, characteristic
3#8035C212yesmaximal
4C2×#1291C212yesmaximal
5#7875C211yesmaximal, characteristic
6C2×#432C2212yes—
7C2×#432C2211yescharacteristic
8C22×#108—21no—
9C2×C4×M16C2212yes—
10C22×C4×C8C2211yescharacteristic
11#2283C2211yescharacteristic
12#1939C411yescharacteristic
13#1939C411yescharacteristic
14#1939C411yescharacteristic
15#1939C411yescharacteristic
16#1850—21no—
17#1850—21no—
18C4×#108—24no—
19#1768—21no—
20#1768—21no—
21C2×#341—21no—
22#1295—22no—
23#1295—22no—
24#1291—24no—
25#1277—21no—
26#1277—21no—
27C22×M16—22no—
28C23×C8D411yescharacteristic
29C23×C8D411yescharacteristic
30C22×C42C2311yescharacteristic
31#432—22no—
32#432—22no—
33#432—22no—
34#432—22no—
35#432—22no—
36#432Q814yes—
37C2×#108—24no—
38C2×#108—24no—
39C2×#108—24no—
40C2×C4⋊C8—22no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8C2×C411yescharacteristic
46C2×C4⋊C8C2×C411yescharacteristic
47C2×C22⋊C8—22no—
48C2×C22⋊C8—21no—
49C4×M16—22no—
50C4×M16—22no—
51C4×M16—22no—
52C4×M16D414yes—
53C2×#97—22no—
54C2×#97—22no—
55C2×#97—21no—
56C2×C4×C8—22no—
57C2×C4×C8—22no—
58C2×C4×C8—22no—
59C2×C4×C8C2×C411yescharacteristic
60C2×C4×C8C2×C411yescharacteristic
61C2×C4×C8D411yescharacteristic
62C2×C4×C8D411yescharacteristic
63#383—21no—
64#382D411yescharacteristic
65#382D411yescharacteristic
66#381—21no—
67#380Q811yescharacteristic
68#380Q811yescharacteristic
69C4×C4⋊C4C2×C411yescharacteristic
70C4×C4⋊C4C2×C411yescharacteristic
71C4×C22⋊C4—21no—
72#376—21no—
73#341—24no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78C23×C4C2×D411yescharacteristic
79C23×C4C2×Q811yescharacteristic
80C23×C4#4111yescharacteristic
81C2×M16—24no—
82C2×M16—24no—
83C2×M16—24no—
84C2×M16—42no—
85C2×M16—42no—
86C2×M16—42no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—42no—
98C22×C8—42no—
99C22×C8C22⋊C411yescharacteristic
100C22×C8C22⋊C411yescharacteristic
101C22×C8C22⋊C411yescharacteristic
102C22×C8C22⋊C411yescharacteristic
103C2×C4⋊C4C4⋊C411yescharacteristic
104C2×C4⋊C4C4⋊C411yescharacteristic
105C2×C4⋊C4C4⋊C411yescharacteristic
106C2×C4⋊C4C4⋊C411yescharacteristic
107C2×C22⋊C4—21no—
108C2×C22⋊C4—21no—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42C22×C411yescharacteristic
112C2×C42C2×D412yes—
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×Q812yes—
116C2×C42#4112yes—
117C2×C42#4112yes—
118C2×C42#4111yescharacteristic
119#108—216no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—24no—
123C4⋊C8—42no—
124C4⋊C8—42no—
125C4⋊C8—42no—
126C4⋊C8—42no—
127C4⋊C8—42no—
128C22⋊C8—24no—
129C22⋊C8—41no—
130C22⋊C8—41no—
131C22⋊C8—42no—
132#97—24no—
133#97—24no—
134#97—42no—
135#97—42no—
136#97—42no—
137C4×C8—22no—
138C4×C8—22no—
139C4×C8—22no—
140C4×C8—22no—
141C4×C8—24no—
142C4×C8—42no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—21no—
151C24C22⋊Q811yescharacteristic
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—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4C2×C22⋊C411yescharacteristic
165C22×C4C2×C4⋊C411yescharacteristic
166C22×C4#11711yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4C22⋊Q811yescharacteristic
171C22×C4C22⋊Q812yes—
172C22×C4#12311yescharacteristic
173C22×C4#12411yescharacteristic
174C22×C4#12512yes—
175C22×C4#12612yes—
176C22×C4C4⋊Q811yescharacteristic
177C22×C4C4⋊Q812yes—
178M16—28no—
179M16—44no—
180M16—44no—
181M16—44no—
182C2×C8—24no—
183C2×C8—24no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—21no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—44no—
197C2×C8—44no—
198C2×C8—44no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—44no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—82no—
207C2×C8—82no—
208C2×C8#10412yes—
209C2×C8#10412yes—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42C4×D412yes—
221C42C4×Q812yes—
222C42#12112yes—
223C42#12112yes—
224C42C22⋊Q812yes—
225C42C22⋊Q812yes—
226C42#12312yes—
227C42#12512yes—
228C23—21no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23#38011yescharacteristic
235C23#39511yescharacteristic
236C23#40011yescharacteristic
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4#38611yescharacteristic
272C2×C4#38712yes—
273C2×C4#38912yes—
274C2×C4#39111yescharacteristic
275C2×C4#39411yescharacteristic
276C2×C4#39612yes—
277C2×C4#39812yes—
278C2×C4#39811yescharacteristic
279C2×C4C2×#10411yescharacteristic
280C2×C4C2×#10411yescharacteristic
281C2×C4#42111yescharacteristic
282C2×C4#42111yescharacteristic
283C8—22no—
284C8—22no—
285C8—48no—
286C8—41no—
287C8—41no—
288C8—84no—
289C8—81no—
290C8—81no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22#144111yescharacteristic
302C22#180611yescharacteristic
303C22#180611yescharacteristic
304C22#181311yescharacteristic
305C22#181311yescharacteristic
306C22#181411yescharacteristic
307C22#181411yescharacteristic
308C4—21no—
309C4—21no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—81no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4#189611yescharacteristic
319C4#189711yescharacteristic
320C4#198611yescharacteristic
321C4#198611yescharacteristic
322C2—41no—
323C2—41no—
324C2#869011yescharacteristic
325C2#869111yescharacteristic
326C2#869211yescharacteristic
327C2#869311yescharacteristic
328C2#1122611yescharacteristic
329C2#1123011yescharacteristic
330C2#1124011yescharacteristic
subgroupG/H
center, socleC23#380
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C22⋊Q8
LCSG ▷ C2×C42 ▷ 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
#213512
C2×C4×#1082
#80352
C2×#12912
#78752