Finite Group Databasebeta

← #100320

Subgroups — #100320

Order 512.

435 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33196C211yesmaximal, characteristic
2#22821C211yesmaximal, characteristic
3#9898C211yesmaximal, characteristic
4#9692C211yesmaximal, characteristic
5#8564C211yesmaximal, characteristic
6#7050C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#475—21no—
9#2868C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1988—21no—
12#1984—21no—
13#1948—21no—
14#1948C412yes—
15#1916—22no—
16#1842C2211yescharacteristic
17#1842C2211yescharacteristic
18#1842C2211yescharacteristic
19#1831—21no—
20#1803—21no—
21#1803C412yes—
22C8×C4⋊C4—21no—
23C4×C4⋊C8—21no—
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C2×#332—21no—
27C2×#332—21no—
28C2×Q8⋊C8—21no—
29#1296—22no—
30#1279—21no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37#475—42no—
38#475—42no—
39C2×#106—22no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—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⋊C8C2×C412yes—
49C2×C4⋊C8D411yescharacteristic
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D412yes—
52C2×#103—22no—
53C2×C4×C8—21no—
54C2×C4×C8—21no—
55C2×C4×C8—22no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384C2×C412yes—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4C2×C411yescharacteristic
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43—21no—
67C43C2311yescharacteristic
68#340—22no—
69#340—22no—
70#336—22no—
71#336—22no—
72#336—22no—
73#336—21no—
74#336—21no—
75#332—42no—
76#332—42no—
77Q8⋊C8—42no—
78C22×Q8—41no—
79C22×Q8C22⋊C411yescharacteristic
80C22×C8—21no—
81C22×C8—22no—
82C22×C8—21no—
83C22×C8—22no—
84C22×C8—41no—
85C22×C8—41no—
86C4⋊Q8—41no—
87C4⋊Q8—41no—
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—81no—
95C4⋊Q8—81no—
96C4×Q8—21no—
97C4×Q8—21no—
98C4×Q8—22no—
99C4×Q8—21no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—41no—
104C4×Q8D812yes—
105C4×Q8SD1612yes—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#106—44no—
132C4⋊C8—22no—
133C4⋊C8—21no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—42no—
137C4⋊C8—42no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—81no—
152C4⋊C8SD1612yes—
153#103—44no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157C4×C8—41no—
158C4×C8—82no—
159#95—21no—
160#95—21no—
161#95—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—81no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—81no—
172C2×Q8—81no—
173C2×Q8#10212yes—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—42no—
179C22×C4C2×C22⋊C411yescharacteristic
180C22×C4C4×D411yescharacteristic
181C22×C4C4×D411yescharacteristic
182C22×C4#12011yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12311yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—41no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4#10112yes—
224C4⋊C4#10212yes—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—22no—
230C42—22no—
231C42—21no—
232C42—21no—
233C42—41no—
234C42—42no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—81no—
242C42C2×D811yescharacteristic
243C42C2×SD1611yescharacteristic
244C42C2×SD1611yescharacteristic
245C42#13511yescharacteristic
246C42#13511yescharacteristic
247C42#13511yescharacteristic
248C42#13511yescharacteristic
249C42#13511yescharacteristic
250C42AGL(1,ℤ/8)11yescharacteristic
251C42#13711yescharacteristic
252C42#13711yescharacteristic
253C42#13711yescharacteristic
254C23#38611yescharacteristic
255Q8—22no—
256Q8—22no—
257Q8—41no—
258Q8—41no—
259Q8—161no—
260Q8—161no—
261Q8—161no—
262Q8—161no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4—82no—
287C2×C4C2×#10111yescharacteristic
288C2×C4#41311yescharacteristic
289C2×C4C2×#10211yescharacteristic
290C2×C4#41611yescharacteristic
291C2×C4#41611yescharacteristic
292C2×C4#41911yescharacteristic
293C2×C4C4×SD1611yescharacteristic
294C2×C4#44011yescharacteristic
295C2×C4#44811yescharacteristic
296C2×C4#44911yescharacteristic
297C2×C4#45211yescharacteristic
298C2×C4#45211yescharacteristic
299C2×C4#45511yescharacteristic
300C2×C4#45611yescharacteristic
301C2×C4#46011yescharacteristic
302C2×C4#46411yescharacteristic
303C2×C4#46511yescharacteristic
304C2×C4#46511yescharacteristic
305C2×C4#46611yescharacteristic
306C2×C4#46611yescharacteristic
307C2×C4#47111yescharacteristic
308C2×C4#47211yescharacteristic
309C2×C4#48511yescharacteristic
310C2×C4#48511yescharacteristic
311C8—42no—
312C8—82no—
313C8—82no—
314C8—82no—
315C8—81no—
316C8—161no—
317C22#187311yescharacteristic
318C22#188011yescharacteristic
319C22#188211yescharacteristic
320C22#189311yescharacteristic
321C22#190111yescharacteristic
322C22#190211yescharacteristic
323C22#190711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4—41no—
332C4—42no—
333C4—42no—
334C4—81no—
335C4—162no—
336C4#154011yescharacteristic
337C4#154411yescharacteristic
338C4#154611yescharacteristic
339C4#155411yescharacteristic
340C4#164011yescharacteristic
341C4#164311yescharacteristic
342C4#165011yescharacteristic
343C4#165311yescharacteristic
344C4#166611yescharacteristic
345C4#166811yescharacteristic
346C4#167811yescharacteristic
347C4#168211yescharacteristic
348C2#898211yescharacteristic
349C2#913011yescharacteristic
350C2#916811yescharacteristic
351C2#922211yescharacteristic
352C2#925211yescharacteristic
353C2#931611yescharacteristic
354C2#935511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#331962
#228212
#98982
#96922
#85642
#70502
#70312