Finite Group Databasebeta

← #104995

Subgroups — #104995

Order 512.

384 conjugacy classes of subgroups.

The subgroup lattice has 335 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#28283C211yesmaximal, characteristic
2#9870C211yesmaximal, characteristic
3#9637C211yesmaximal, characteristic
4#8784C211yesmaximal, characteristic
5#8586C211yesmaximal, characteristic
6#8586C211yesmaximal, characteristic
7#7050C211yesmaximal, characteristic
8C2×#475—21no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2066—22no—
12#1981—21no—
13#1948—21no—
14#1842C2211yescharacteristic
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17#1842C2211yescharacteristic
18#1803—21no—
19C42×C8C2211yescharacteristic
20C2×#332—21no—
21C2×#332—21no—
22C2×Q8⋊C8—21no—
23C2×Q8⋊C8—21no—
24#1296—21no—
25#1296—21no—
26#1279—21no—
27#1279—21no—
28#1277—22no—
29C2×C4⋊Q8D411yescharacteristic
30C2×C4⋊Q8D411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8—21no—
33#475—42no—
34#475—42no—
35C2×#106—22no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
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⋊C8D412yes—
48C2×#103—22no—
49C2×#103—22no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52C2×C4×C8D411yescharacteristic
53C2×C4×C8D411yescharacteristic
54#391—21no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#384D411yescharacteristic
61#384D411yescharacteristic
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C43C2311yescharacteristic
67#340—22no—
68#332—42no—
69#332—42no—
70Q8⋊C8—42no—
71Q8⋊C8—42no—
72C22×Q8—21no—
73C22×Q8—21no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—22no—
77C22×C8—41no—
78C22×C8—41no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8D812yes—
87C4⋊Q8SD1612yes—
88C4×Q8—41no—
89C4×Q8—41no—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
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—41no—
107C2×C4⋊C4—41no—
108C2×C42—41no—
109C2×C42—41no—
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116C2×C42#4111yescharacteristic
117#106—44no—
118C4⋊C8—42no—
119C4⋊C8—42no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—81no—
137C4⋊C8—81no—
138#103—44no—
139#103—82no—
140C4×C8—21no—
141C4×C8—21no—
142C4×C8—21no—
143C4×C8—41no—
144C4×C8—41no—
145C4×C8—42no—
146C4×C8SD1612yes—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12311yescharacteristic
172C22×C4#12311yescharacteristic
173C22×C4#12411yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—42no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
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—41no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C4⋊C4—81no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—41no—
221C42—81no—
222C42—81no—
223C42—81no—
224C42—81no—
225C42C2×D811yescharacteristic
226C42C2×SD1611yescharacteristic
227C42C2×SD1611yescharacteristic
228C42#13511yescharacteristic
229C42#13511yescharacteristic
230C42#13511yescharacteristic
231C42AGL(1,ℤ/8)11yescharacteristic
232C42AGL(1,ℤ/8)11yescharacteristic
233C42#13711yescharacteristic
234C42#13711yescharacteristic
235C42#13711yescharacteristic
236C42#13711yescharacteristic
237C23#39411yescharacteristic
238Q8—42no—
239Q8—42no—
240Q8—42no—
241Q8—42no—
242Q8—81no—
243Q8—81no—
244Q8—81no—
245Q8—81no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4#44711yescharacteristic
268C2×C4#44811yescharacteristic
269C2×C4#45211yescharacteristic
270C2×C4#45211yescharacteristic
271C2×C4#45411yescharacteristic
272C2×C4#45511yescharacteristic
273C2×C4#46011yescharacteristic
274C2×C4#46111yescharacteristic
275C2×C4#46311yescharacteristic
276C2×C4#46411yescharacteristic
277C2×C4#46511yescharacteristic
278C2×C4#46511yescharacteristic
279C2×C4#46611yescharacteristic
280C2×C4#46811yescharacteristic
281C2×C4#46811yescharacteristic
282C2×C4#47011yescharacteristic
283C2×C4#47111yescharacteristic
284C2×C4#47111yescharacteristic
285C2×C4#47311yescharacteristic
286C2×C4#47311yescharacteristic
287C2×C4#48011yescharacteristic
288C2×C4#48211yescharacteristic
289C2×C4#48311yescharacteristic
290C2×C4#48511yescharacteristic
291C8—42no—
292C8—42no—
293C8—82no—
294C8—161no—
295C8—161no—
296C8—161no—
297C22#203311yescharacteristic
298C22#203511yescharacteristic
299C22#204011yescharacteristic
300C22#205011yescharacteristic
301C22#205211yescharacteristic
302C22#205211yescharacteristic
303C22#205511yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4—161no—
314C4—161no—
315C4#162711yescharacteristic
316C4#163811yescharacteristic
317C4#164111yescharacteristic
318C4#164311yescharacteristic
319C4#166611yescharacteristic
320C4#167311yescharacteristic
321C4#168011yescharacteristic
322C4#168111yescharacteristic
323C4#169011yescharacteristic
324C4#169111yescharacteristic
325C4#169911yescharacteristic
326C4#170411yescharacteristic
327C2#1043311yescharacteristic
328C2#1045811yescharacteristic
329C2#1046211yescharacteristic
330C2#1047611yescharacteristic
331C2#1048611yescharacteristic
332C2#1052111yescharacteristic
333C2#1053511yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ 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
#282832
#98702
#96372
#87842
#85862
#70502