Finite Group Databasebeta

← #100508

Subgroups — #100508

Order 512.

409 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33202C211yesmaximal, characteristic
2#22736C211yesmaximal, characteristic
3#8566C211yesmaximal, characteristic
4#7662C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8C2×#477C411yescharacteristic
9C2×#475C411yescharacteristic
10C2×#446—21no—
11#2862C2211yescharacteristic
12C42×Q8C2211yescharacteristic
13#1988C411yescharacteristic
14#1987C411yescharacteristic
15#1949—21no—
16#1949—21no—
17#1940—22no—
18#1939—21no—
19#1842C2211yescharacteristic
20#1831—21no—
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1805—21no—
24#1805—21no—
25#1767—21no—
26C4×C4⋊C8C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28C2×Q8⋊C8—21no—
29#1279—21no—
30#1272—21no—
31#1272—21no—
32#1272—22no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4⋊Q8C2×C411yescharacteristic
35C2×C4×Q8C2×C411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38#477—42no—
39#475—42no—
40#446—42no—
41#446—42no—
42C2×#107—21no—
43C2×#106—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—22no—
46C2×C4⋊C8—22no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8C2×C411yescharacteristic
53C2×C4⋊C8C2×C411yescharacteristic
54C2×#103—21no—
55C2×#103—21no—
56C2×#97—22no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59#391—21no—
60#391—21no—
61#391—21no—
62#391—21no—
63#382—21no—
64#382—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4C2×C411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C4×C4⋊C4D411yescharacteristic
71C43—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—22no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D411yescharacteristic
83#336D412yes—
84#336D411yescharacteristic
85Q8⋊C8—42no—
86C22×Q8—21no—
87C22×Q8—21no—
88C22×Q8C22⋊C411yescharacteristic
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—22no—
94C22×C8—41no—
95C22×C8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4×Q8—21no—
101C4×Q8—21no—
102C4×Q8—22no—
103C4×Q8—21no—
104C4×Q8—21no—
105C4×Q8—21no—
106C4×Q8—21no—
107C4×Q8—41no—
108C4×Q8SD1612yes—
109C4×Q8Q1612yes—
110C2×C4⋊C4—21no—
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⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42—21no—
125C2×C42—21no—
126C2×C42C22×C411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133#107—42no—
134#106—42no—
135C4⋊C8—22no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—44no—
140C4⋊C8—42no—
141C4⋊C8—44no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150#103—42no—
151#103—42no—
152#97—44no—
153C4×C8—41no—
154C4×C8—41no—
155C4×C8—41no—
156C4×C8—41no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—42no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—81no—
173C2×Q8—81no—
174C2×Q8—81no—
175C2×Q8—81no—
176C2×Q8#10312yes—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4C2×C22⋊C411yescharacteristic
184C22×C4C4×D411yescharacteristic
185C22×C4C4×D411yescharacteristic
186C22×C4#12011yescharacteristic
187C22×C4#12111yescharacteristic
188C22×C4#12111yescharacteristic
189C22×C4#12311yescharacteristic
190C2×C8—22no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—42no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—81no—
207C2×C8—81no—
208C2×C8—81no—
209C2×C8—81no—
210C2×C8—81no—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4#10012yes—
227C4⋊C4#10312yes—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—22no—
233C42—22no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—42no—
238C42—42no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—81no—
244C42C2×SD1611yescharacteristic
245C42C2×Q1611yescharacteristic
246C42AGL(1,ℤ/8)11yescharacteristic
247C42AGL(1,ℤ/8)11yescharacteristic
248C42#13711yescharacteristic
249C42#13711yescharacteristic
250C42#13711yescharacteristic
251C42#13711yescharacteristic
252C23#38611yescharacteristic
253Q8—22no—
254Q8—22no—
255Q8—41no—
256Q8—41no—
257Q8—161no—
258Q8—161no—
259Q8—162no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
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—21no—
274C2×C4—22no—
275C2×C4—21no—
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—41no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4C2×#10011yescharacteristic
292C2×C4#41311yescharacteristic
293C2×C4C2×#10311yescharacteristic
294C2×C4#41711yescharacteristic
295C2×C4#41711yescharacteristic
296C2×C4#41911yescharacteristic
297C2×C4#44311yescharacteristic
298C2×C4#44411yescharacteristic
299C2×C4#45011yescharacteristic
300C2×C4#45111yescharacteristic
301C2×C4#46811yescharacteristic
302C2×C4#46811yescharacteristic
303C2×C4#47011yescharacteristic
304C2×C4#47011yescharacteristic
305C2×C4#48311yescharacteristic
306C2×C4#48411yescharacteristic
307C8—42no—
308C8—81no—
309C8—82no—
310C8—82no—
311C8—81no—
312C8—81no—
313C8—161no—
314C22#187211yescharacteristic
315C22#187611yescharacteristic
316C22#188111yescharacteristic
317C22#189411yescharacteristic
318C22#190011yescharacteristic
319C22#190511yescharacteristic
320C22#190611yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—41no—
333C4—42no—
334C4—42no—
335C4—81no—
336C4—161no—
337C4—161no—
338C4#154811yescharacteristic
339C4#155011yescharacteristic
340C4#155911yescharacteristic
341C4#156011yescharacteristic
342C2#899311yescharacteristic
343C2#913511yescharacteristic
344C2#917611yescharacteristic
345C2#920911yescharacteristic
346C2#924411yescharacteristic
347C2#930811yescharacteristic
348C2#934911yescharacteristic
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
#332022
#227362
#85662
#76622
#70402
#70312