Finite Group Databasebeta

← #122198

Subgroups — #122198

Order 512.

639 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34948C211yesmaximal, characteristic
2#7952C211yesmaximal, characteristic
3#7952C211yesmaximal, characteristic
4C2×#1285C211yesmaximal, characteristic
5C2×#1285C211yesmaximal, characteristic
6#7930C211yesmaximal, characteristic
7#7930C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#432C2211yescharacteristic
12#2571—21no—
13#2570—22no—
14#2569—22no—
15#2552—21no—
16#2442—22no—
17#2402—22no—
18C4×#125—22no—
19#2296C412yes—
20#2285C412yes—
21#2285C2211yescharacteristic
22C4×#117C2211yescharacteristic
23C2×C4×C4⋊C4C2211yescharacteristic
24#1285—22no—
25#1285—21no—
26#1285—21no—
27#1285—22no—
28#1285—22no—
29#1282—22no—
30#1282—22no—
31C2×#125—22no—
32C2×#117C2×C411yescharacteristic
33C2×#117C2×C411yescharacteristic
34C2×#117C2×C412yes—
35C22×C4⋊C4—21no—
36C22×C42C2×C412yes—
37C22×C42C2311yescharacteristic
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#432—21no—
48#432—21no—
49#432—21no—
50#432—21no—
51#432—21no—
52#432Q812yes—
53#432Q812yes—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8Q812yes—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×#97—21no—
63C2×#97—21no—
64C2×#97—21no—
65C2×#97Q812yes—
66#400—24no—
67#400—24no—
68#398—24no—
69#398—24no—
70#389—22no—
71#389—22no—
72#389—22no—
73#389—22no—
74#387—24no—
75#387—24no—
76#385—24no—
77#384—22no—
78#384—21no—
79#382—22no—
80#382—22no—
81#382—21no—
82#380—21no—
83#380—21no—
84#380—24no—
85C4×C4⋊C4—24no—
86C4×C4⋊C4—24no—
87C4×C4⋊C4—21no—
88C4×C4⋊C4—21no—
89C4×C4⋊C4—21no—
90C4×C4⋊C4—21no—
91C4×C4⋊C4D412yes—
92C4×C4⋊C4D412yes—
93C4×C4⋊C4D411yescharacteristic
94C4×C4⋊C4D412yes—
95C4×C4⋊C4D411yescharacteristic
96C4×C22⋊C4D412yes—
97C4×C22⋊C4D412yes—
98#376—21no—
99C2×#95—21no—
100C43—21no—
101C23×C4—22no—
102C23×C4C22×C411yescharacteristic
103C23×C4C2×D411yescharacteristic
104C23×C4C2×D411yescharacteristic
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—41no—
108C22×C8—41no—
109#125—48no—
110#117—42no—
111#117—42no—
112#117—44no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—24no—
115C2×C4⋊C4—24no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—44no—
126C2×C22⋊C4—22no—
127C2×C22⋊C4C22⋊C412yes—
128C2×C22⋊C4C22⋊C412yes—
129C2×C42—21no—
130C2×C42—21no—
131C2×C42—22no—
132C2×C42—22no—
133C2×C42—22no—
134C2×C42—44no—
135C2×C42C22⋊C414yes—
136C2×C42C22⋊C412yes—
137C2×C42C22⋊C412yes—
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42C2×D411yescharacteristic
142C2×C42C2×Q811yescharacteristic
143C2×C42C2×Q811yescharacteristic
144C2×C42C2×Q811yescharacteristic
145C2×C42C2×Q811yescharacteristic
146C2×C42#4111yescharacteristic
147C2×C42#4111yescharacteristic
148C2×C42#4111yescharacteristic
149C2×C42#4111yescharacteristic
150C4⋊C8—22no—
151C4⋊C8—22no—
152C4⋊C8—22no—
153C4⋊C8—22no—
154C4⋊C8—41no—
155C4⋊C8—41no—
156C4⋊C8—41no—
157C4⋊C8—41no—
158C22⋊C8—22no—
159C22⋊C8—22no—
160C22⋊C8—41no—
161C22⋊C8—41no—
162C22⋊C8—41no—
163C22⋊C8—41no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166#97—22no—
167#97—22no—
168#97—22no—
169#97—22no—
170#97—41no—
171#97—41no—
172#97—41no—
173#97—41no—
174#95—24no—
175#95—24no—
176#95—24no—
177#95—24no—
178#95—22no—
179#95—21no—
180#95—21no—
181#95—22no—
182#95—22no—
183#95—22no—
184#95—22no—
185C24C2×C22⋊C411yescharacteristic
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—42no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4—81no—
197C22×C4—82no—
198C22×C4C2×C22⋊C411yescharacteristic
199C22×C4C2×C22⋊C411yescharacteristic
200C22×C4C4×Q811yescharacteristic
201C22×C4C4×Q811yescharacteristic
202C22×C4C4×Q811yescharacteristic
203C22×C4C4×Q811yescharacteristic
204C22×C4#12011yescharacteristic
205C22×C4#12011yescharacteristic
206C22×C4#12011yescharacteristic
207C22×C4#12011yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4C22⋊Q811yescharacteristic
210C22×C4C22⋊Q811yescharacteristic
211C22×C4C22⋊Q811yescharacteristic
212C22×C4#12411yescharacteristic
213C22×C4#12411yescharacteristic
214C22×C4C4⋊Q811yescharacteristic
215C22×C4C4⋊Q811yescharacteristic
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—82no—
221C2×C8—82no—
222C2×C8—82no—
223C2×C8—82no—
224C4⋊C4—24no—
225C4⋊C4—42no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—44no—
230C4⋊C4—44no—
231C4⋊C4—48no—
232C4⋊C4—48no—
233C4⋊C4—82no—
234C4⋊C4—84no—
235C4⋊C4—84no—
236C22⋊C4—24no—
237C22⋊C4—24no—
238C22⋊C4—44no—
239C42—42no—
240C42—42no—
241C42—44no—
242C42—44no—
243C42—42no—
244C42—42no—
245C42—44no—
246C42—82no—
247C42C22⋊Q811yescharacteristic
248C42C22⋊Q811yescharacteristic
249C42C22⋊Q811yescharacteristic
250C42C22⋊Q811yescharacteristic
251C42C22⋊Q811yescharacteristic
252C42C22⋊Q811yescharacteristic
253C42C22⋊Q811yescharacteristic
254C42C22⋊Q811yescharacteristic
255C42#12411yescharacteristic
256C42#12411yescharacteristic
257C42#12411yescharacteristic
258C42#12411yescharacteristic
259C42C4⋊Q811yescharacteristic
260C42C4⋊Q811yescharacteristic
261C42C4⋊Q811yescharacteristic
262C42C4⋊Q811yescharacteristic
263C23—41no—
264C23—41no—
265C23#37911yescharacteristic
266C23#39111yescharacteristic
267C23#39111yescharacteristic
268C23#41312yes—
269C23#41312yes—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—24no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4—88no—
306C2×C4#39111yescharacteristic
307C2×C4#39111yescharacteristic
308C2×C4#39111yescharacteristic
309C2×C4#39111yescharacteristic
310C2×C4#39311yescharacteristic
311C2×C4#39311yescharacteristic
312C2×C4#39311yescharacteristic
313C2×C4#39311yescharacteristic
314C2×C4#39511yescharacteristic
315C2×C4#39511yescharacteristic
316C2×C4#39511yescharacteristic
317C2×C4#39511yescharacteristic
318C8—82no—
319C8—82no—
320C8—82no—
321C8—82no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—42no—
329C22—42no—
330C22#144611yescharacteristic
331C22#178511yescharacteristic
332C22#178511yescharacteristic
333C22#199812yes—
334C22#199812yes—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—44no—
347C4—82no—
348C4—82no—
349C4—84no—
350C4—82no—
351C4#203112yes—
352C2—21no—
353C2—21no—
354C2—22no—
355C2—22no—
356C2#1138311yescharacteristic
357C2#1138711yescharacteristic
358C2#1138911yescharacteristic
subgroupG/H
center, socleC22#1446
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ 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
#349482
#79522
C2×#12852
#79302