Finite Group Databasebeta

← #121519

Subgroups — #121519

Order 512.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21976C211yesmaximal, characteristic
2#17818C211yesmaximal, characteristic
3C2×#1573C211yesmaximal, characteristic
4#8089C211yesmaximal, characteristic
5#7930C211yesmaximal, characteristic
6#7924C211yesmaximal, characteristic
7#7879C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C22×C4⋊C8C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1940—22no—
16#1850—22no—
17#1842—21no—
18#1831—21no—
19#1573—22no—
20#1573—22no—
21#1573—21no—
22#1573—21no—
23#1573—21no—
24#1573—21no—
25#1568—22no—
26C2×#335—21no—
27C2×#334—21no—
28#1302—22no—
29#1282—22no—
30#1282C412yes—
31#1282C412yes—
32#1277—22no—
33C23×C8—21no—
34C2×#117Q812yes—
35C22×C42C2311yescharacteristic
36#432—21no—
37#432—21no—
38#432—21no—
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432—21no—
46#432—21no—
47#432Q812yes—
48#431—21no—
49#431—21no—
50#431—21no—
51#431—21no—
52#431—21no—
53#431—21no—
54#431D412yes—
55#431Q812yes—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8—21no—
63C2×C4⋊C8—24no—
64C2×C4⋊C8D411yescharacteristic
65C2×C4⋊C8D411yescharacteristic
66C2×C4⋊C8D411yescharacteristic
67C2×C4⋊C8D411yescharacteristic
68C2×C4⋊C8D412yes—
69C2×C4⋊C8Q812yes—
70C2×C22⋊C8—21no—
71C2×C22⋊C8—21no—
72C2×C22⋊C8—21no—
73C2×C22⋊C8C2×C412yes—
74C2×C22⋊C8C2×C412yes—
75C2×#97—21no—
76C2×#97—21no—
77C2×#97—21no—
78C2×C4×C8—21no—
79C2×C4×C8D412yes—
80C4×C4⋊C4—21no—
81C4×C4⋊C4—21no—
82C4×C22⋊C4C2×C411yescharacteristic
83C4×C22⋊C4C2×C411yescharacteristic
84C4×C22⋊C4D412yes—
85#376—21no—
86C43—21no—
87#336—24no—
88#335—24no—
89#335—22no—
90#335—22no—
91#334—24no—
92#334—22no—
93#334—22no—
94C23×C4C22×C411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4C2×Q811yescharacteristic
97C22×C8—22no—
98C22×C8—22no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—82no—
107C22×C8C4⋊C414yes—
108#117—24no—
109#117—42no—
110C2×C4⋊C4—22no—
111C2×C22⋊C4C4⋊C412yes—
112C2×C22⋊C4C4⋊C412yes—
113C2×C42—21no—
114C2×C42—21no—
115C2×C42—22no—
116C2×C42—22no—
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×Q811yescharacteristic
123C2×C42C2×Q811yescharacteristic
124C2×C42C2×Q811yescharacteristic
125C2×C42#4111yescharacteristic
126C2×C42#4111yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129C4⋊C8—21no—
130C4⋊C8—22no—
131C4⋊C8—21no—
132C4⋊C8—21no—
133C4⋊C8—21no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—22no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—84no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—22no—
151C22⋊C8—22no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—41no—
157C22⋊C8C4⋊C414yes—
158#97—22no—
159#97—41no—
160#97—41no—
161#97—41no—
162#97—41no—
163#97—41no—
164C4×C8—22no—
165C4×C8—22no—
166C4×C8—22no—
167C4×C8—22no—
168#95—21no—
169#95—21no—
170#95—22no—
171C24C2×C4⋊C411yescharacteristic
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—41no—
179C22×C4C2×C4⋊C411yescharacteristic
180C22×C4C2×C4⋊C411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4C4×D411yescharacteristic
183C22×C4C4×D411yescharacteristic
184C22×C4C4×Q811yescharacteristic
185C22×C4#12011yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4C22⋊Q811yescharacteristic
188C22×C4C22⋊Q811yescharacteristic
189C22×C4C22⋊Q811yescharacteristic
190C22×C4#12311yescharacteristic
191C22×C4#12511yescharacteristic
192C22×C4#12711yescharacteristic
193C22×C4C4⋊Q811yescharacteristic
194C22×C4C4⋊Q811yescharacteristic
195C22×C4C4⋊Q811yescharacteristic
196C22×C4C4⋊Q811yescharacteristic
197C2×C8—24no—
198C2×C8—24no—
199C2×C8—44no—
200C2×C8—44no—
201C2×C8—42no—
202C2×C8—44no—
203C2×C8—42no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—81no—
211C2×C8—81no—
212C2×C8—82no—
213C2×C8—82no—
214C2×C8—81no—
215C2×C8—81no—
216C4⋊C4—44no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—22no—
220C22⋊C4#10814yes—
221C42—44no—
222C42—42no—
223C42—42no—
224C42—42no—
225C42—42no—
226C42#12011yescharacteristic
227C42#12011yescharacteristic
228C42#12111yescharacteristic
229C42#12111yescharacteristic
230C42C22⋊Q811yescharacteristic
231C42C22⋊Q811yescharacteristic
232C42C22⋊Q811yescharacteristic
233C42C22⋊Q811yescharacteristic
234C42C22⋊Q811yescharacteristic
235C42C22⋊Q811yescharacteristic
236C42#12311yescharacteristic
237C42#12311yescharacteristic
238C42#12511yescharacteristic
239C42#12511yescharacteristic
240C42C4⋊Q811yescharacteristic
241C42C4⋊Q811yescharacteristic
242C23—41no—
243C23—41no—
244C23#38411yescharacteristic
245C23#38511yescharacteristic
246C23#38911yescharacteristic
247C23C2×#10812yes—
248C23#43012yes—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—24no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4#38511yescharacteristic
279C2×C4#38511yescharacteristic
280C2×C4#38911yescharacteristic
281C2×C4#38911yescharacteristic
282C2×C4#39211yescharacteristic
283C2×C4#39511yescharacteristic
284C2×C4#39511yescharacteristic
285C2×C4#39511yescharacteristic
286C2×C4#39811yescharacteristic
287C2×C4#39811yescharacteristic
288C2×C4#39811yescharacteristic
289C2×C4#39911yescharacteristic
290C8—44no—
291C8—44no—
292C8—82no—
293C8—81no—
294C8—82no—
295C8—81no—
296C8—81no—
297C8—81no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—42no—
305C22—42no—
306C22#144411yescharacteristic
307C22#184811yescharacteristic
308C22#184911yescharacteristic
309C22#185512yes—
310C22#195012yes—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—44no—
322C4—82no—
323C4#186812yes—
324C4#200811yescharacteristic
325C4#200911yescharacteristic
326C2—22no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2#1132611yescharacteristic
331C2#1133311yescharacteristic
332C2#1134511yescharacteristic
subgroupG/H
centerC2×C4#392
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
socleC22#1444
prime radicalC24C2×C4⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ 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
#219762
#178182
C2×#15732
#80892
#79302
#79242
#78792