Finite Group Databasebeta

← #99683

Subgroups — #99683

Order 512.

405 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#23776C211yesmaximal, characteristic
2#22723C211yesmaximal, characteristic
3#9874C211yesmaximal, characteristic
4#9677C211yesmaximal, characteristic
5#7562C211yesmaximal, characteristic
6#7031C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C2×#446—21no—
9C4×C4⋊Q8C2211yescharacteristic
10#2295C2211yescharacteristic
11#2099C411yescharacteristic
12#2096C411yescharacteristic
13#2088—21no—
14#2066—21no—
15#2058C411yescharacteristic
16#2024C411yescharacteristic
17#1940—21no—
18#1940—21no—
19#1939—21no—
20#1843—21no—
21#1842C2211yescharacteristic
22C4×#106—21no—
23#1768—21no—
24#1767C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C4×#103—21no—
28#1744C2211yescharacteristic
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1279—21no—
33#1272—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8D411yescharacteristic
38#446—42no—
39#446—42no—
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×C4⋊C8D411yescharacteristic
53C2×C4⋊C8D411yescharacteristic
54C2×#103—21no—
55C2×#103—21no—
56C2×#97—21no—
57C2×#97—21no—
58C2×C4×C8—21no—
59C2×C4×C8—21no—
60C2×C4×C8—21no—
61C2×C4×C8—21no—
62#391—21no—
63#391C2×C411yescharacteristic
64#391D411yescharacteristic
65#389—21no—
66#389—21no—
67#389C2×C411yescharacteristic
68#389D411yescharacteristic
69#387—21no—
70#387—21no—
71#384C2×C411yescharacteristic
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74C4×C4⋊C4—21no—
75C4×C4⋊C4D411yescharacteristic
76#376—21no—
77C43C2311yescharacteristic
78#340—21no—
79#340—21no—
80#340—21no—
81#340—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336—21no—
87#336—21no—
88#336C2×C411yescharacteristic
89#336C2×C411yescharacteristic
90Q8⋊C8—42no—
91Q8⋊C8—42no—
92C22×Q8—21no—
93C22×Q8C22⋊C411yescharacteristic
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—41no—
101C22×C8—41no—
102C4⋊Q8—42no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8SD1612yes—
110C4×Q8Q1612yes—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—41no—
126C2×C42C22×C411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133#106—42no—
134#106—42no—
135C4⋊C8—22no—
136C4⋊C8—21no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—42no—
143C4⋊C8—42no—
144C4⋊C8—42no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—81no—
150C4⋊C8—81no—
151C4⋊C8SD1612yes—
152#103—42no—
153#103—42no—
154#97—42no—
155#97—41no—
156#97—41no—
157C4×C8—22no—
158C4×C8—41no—
159C4×C8—42no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—41no—
163C4×C8—41no—
164#95—21no—
165#95—21no—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—41no—
172#95—41no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8#10312yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4C2×C22⋊C411yescharacteristic
190C22×C4C4×D411yescharacteristic
191C22×C4C4×D411yescharacteristic
192C22×C4#12011yescharacteristic
193C22×C4#12111yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12311yescharacteristic
196C2×C8—22no—
197C2×C8—22no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—42no—
203C2×C8—41no—
204C2×C8—42no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C4⋊C4—21no—
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4#10312yes—
241C42—21no—
242C42—21no—
243C42—22no—
244C42—22no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—81no—
253C42—81no—
254C42C2×SD1611yescharacteristic
255C42C2×SD1611yescharacteristic
256C42C2×Q1611yescharacteristic
257C42#13511yescharacteristic
258C42AGL(1,ℤ/8)11yescharacteristic
259C42AGL(1,ℤ/8)11yescharacteristic
260C42#13711yescharacteristic
261C42#13711yescharacteristic
262C23#38611yescharacteristic
263Q8—42no—
264Q8—42no—
265Q8—42no—
266Q8—81no—
267Q8—81no—
268Q8—81no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4C2×#10311yescharacteristic
301C2×C4#41711yescharacteristic
302C2×C4C4×SD1611yescharacteristic
303C2×C4#44011yescharacteristic
304C2×C4#44311yescharacteristic
305C2×C4#44411yescharacteristic
306C2×C4#44811yescharacteristic
307C2×C4#44911yescharacteristic
308C2×C4#45011yescharacteristic
309C2×C4#45111yescharacteristic
310C2×C4#45511yescharacteristic
311C2×C4#45611yescharacteristic
312C2×C4#46011yescharacteristic
313C2×C4#46411yescharacteristic
314C2×C4#48311yescharacteristic
315C2×C4#48411yescharacteristic
316C8—42no—
317C8—42no—
318C8—81no—
319C8—82no—
320C8—82no—
321C8—81no—
322C8—81no—
323C8—81no—
324C22#187211yescharacteristic
325C22#187611yescharacteristic
326C22#188011yescharacteristic
327C22#188111yescharacteristic
328C22#188211yescharacteristic
329C22#188411yescharacteristic
330C22#189111yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—42no—
344C4—81no—
345C4—82no—
346C4—81no—
347C4—161no—
348C4#164211yescharacteristic
349C4#164511yescharacteristic
350C4#164811yescharacteristic
351C4#165111yescharacteristic
352C2#898311yescharacteristic
353C2#899311yescharacteristic
354C2#899811yescharacteristic
355C2#903311yescharacteristic
356C2#905011yescharacteristic
357C2#905111yescharacteristic
358C2#905411yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#386
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#237762
#227232
#98742
#96772
#75622
#70312
#70272