Finite Group Databasebeta

← #102015

Subgroups — #102015

Order 512.

418 conjugacy classes of subgroups.

The subgroup lattice has 319 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#498C211yesmaximal, characteristic
2#9864C211yesmaximal, characteristic
3#9673C211yesmaximal, characteristic
4C4×#334C211yesmaximal, characteristic
5#8261C211yesmaximal, characteristic
6#7571C211yesmaximal, characteristic
7#7570C211yesmaximal, characteristic
8C2×#498C411yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#1990C411yescharacteristic
12#1990C411yescharacteristic
13#1941—21no—
14#1941—21no—
15#1844C411yescharacteristic
16C4×#106—21no—
17C4×#106—21no—
18C4×C4⋊C8C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×C4⋊C8C2211yescharacteristic
21C4×C4⋊C8C2211yescharacteristic
22C42×C8C2211yescharacteristic
23C2×#334—21no—
24C2×Q8⋊C8—22no—
25C2×#322—21no—
26#1279—22no—
27#1277—21no—
28#1273—21no—
29#1272—22no—
30#1271—22no—
31C2×C4⋊Q8C2×C411yescharacteristic
32C2×C4⋊Q8C2×C411yescharacteristic
33C2×C4×Q8—21no—
34C2×C4×Q8—21no—
35#498—22no—
36#498—22no—
37C2×#106—21no—
38C2×#106—21no—
39C2×#106—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D412yes—
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49C2×C4×C8C2×C411yescharacteristic
50C2×C4×C8C2×C411yescharacteristic
51C2×C4×C8D411yescharacteristic
52C2×C4×C8D411yescharacteristic
53C2×C4×C8D411yescharacteristic
54C2×C4×C8D411yescharacteristic
55#391—21no—
56#391—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384C2×C411yescharacteristic
62#384C2×C411yescharacteristic
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336D412yes—
76#334—24no—
77Q8⋊C8—44no—
78#322—42no—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—41no—
84C22×C8—41no—
85C22×C8C22⋊C411yescharacteristic
86C22×C8C22⋊C411yescharacteristic
87C22×C8C22⋊C411yescharacteristic
88C22×C8C22⋊C411yescharacteristic
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—21no—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8M1612yes—
96C4⋊Q8M1612yes—
97C4×Q8—42no—
98C4×Q8—42no—
99C4×Q8—82no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C42—41no—
113C2×C42—41no—
114C2×C42C22×C411yescharacteristic
115C2×C42C2×D411yescharacteristic
116C2×C42C2×D411yescharacteristic
117C2×C42C2×D411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42#4111yescharacteristic
120C2×C42#4111yescharacteristic
121#106—24no—
122#106—24no—
123#106—42no—
124#106—42no—
125C4⋊C8—22no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—42no—
131C4⋊C8SD1614yes—
132C4×C8—22no—
133C4×C8—21no—
134C4×C8—21no—
135C4×C8—21no—
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—41no—
145C4×C8—41no—
146C4×C8SD1612yes—
147C4×C8Q1612yes—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—81no—
159C2×Q8—81no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4C2×C22⋊C411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12411yescharacteristic
170C22×C4#12711yescharacteristic
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C2×C8#10312yes—
193C2×C8#10312yes—
194C2×C8#10412yes—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—82no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C42—21no—
215C42—21no—
216C42—22no—
217C42—22no—
218C42—41no—
219C42—82no—
220C42—82no—
221C42C2×M1611yescharacteristic
222C42C2×M1611yescharacteristic
223C42#13111yescharacteristic
224C42#13111yescharacteristic
225C42C2×SD1611yescharacteristic
226C42C2×SD1612yes—
227C42C2×Q1611yescharacteristic
228C42#13512yes—
229C42#13711yescharacteristic
230C42#13711yescharacteristic
231C23#39011yescharacteristic
232Q8—44no—
233Q8—82no—
234Q8—82no—
235Q8—82no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4#40711yescharacteristic
258C2×C4#40811yescharacteristic
259C2×C4C2×#10311yescharacteristic
260C2×C4#41911yescharacteristic
261C2×C4C2×#10411yescharacteristic
262C2×C4#42111yescharacteristic
263C2×C4#43511yescharacteristic
264C2×C4#43511yescharacteristic
265C2×C4#43511yescharacteristic
266C2×C4#43511yescharacteristic
267C2×C4C4×SD1612yes—
268C2×C4#44412yes—
269C2×C4#46111yescharacteristic
270C2×C4#46111yescharacteristic
271C2×C4#46211yescharacteristic
272C2×C4#46211yescharacteristic
273C2×C4#46512yes—
274C2×C4#47112yes—
275C2×C4#49211yescharacteristic
276C2×C4#49511yescharacteristic
277C8—22no—
278C8—22no—
279C8—22no—
280C8—44no—
281C8—41no—
282C8—82no—
283C8—82no—
284C8—82no—
285C22#195511yescharacteristic
286C22#196811yescharacteristic
287C22#197511yescharacteristic
288C22#197611yescharacteristic
289C22#197711yescharacteristic
290C22#198011yescharacteristic
291C22#198111yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—41no—
299C4—82no—
300C4—82no—
301C4—161no—
302C4—161no—
303C4#148711yescharacteristic
304C4#149111yescharacteristic
305C4#149311yescharacteristic
306C4#149711yescharacteristic
307C4#158212yes—
308C4#158312yes—
309C4#167112yes—
310C4#167212yes—
311C2#966111yescharacteristic
312C2#967211yescharacteristic
313C2#967711yescharacteristic
314C2#971711yescharacteristic
315C2#972811yescharacteristic
316C2#972911yescharacteristic
317C2#975211yescharacteristic
subgroupG/H
centerC22×C4#121
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#390
LCSG ▷ C2×C42 ▷ C22 ▷ 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
C4×#4982
#98642
#96732
C4×#3342
#82612
#75712
#75702