Finite Group Databasebeta

← #99674

Subgroups — #99674

Order 512.

402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23816C211yesmaximal, characteristic
2#23249C211yesmaximal, characteristic
3#9869C211yesmaximal, characteristic
4#9677C211yesmaximal, characteristic
5C4×#333C211yesmaximal, characteristic
6#7027C211yesmaximal, characteristic
7#7027C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2100—21no—
11#2072C411yescharacteristic
12#2072C411yescharacteristic
13#2043—21no—
14#2024C411yescharacteristic
15#2024C411yescharacteristic
16#1985—21no—
17#1984—21no—
18#1940—21no—
19#1940—21no—
20#1771—21no—
21#1771—21no—
22#1767C2211yescharacteristic
23#1767C2211yescharacteristic
24C4×C4⋊C8C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26C4×#103—21no—
27C4×#103—21no—
28#1744C2211yescharacteristic
29C2×#333—21no—
30C2×Q8⋊C8—21no—
31C2×Q8⋊C8—21no—
32#1296—21no—
33#1279—21no—
34#1279—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4×Q8—21no—
38C2×C4×Q8D411yescharacteristic
39C2×C4×Q8D411yescharacteristic
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×#103—21no—
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×#97—21no—
53C2×#97—21no—
54C2×#97—21no—
55C2×C4×C8—21no—
56C2×C4×C8—21no—
57C2×C4×C8—21no—
58C2×C4×C8—21no—
59#391—21no—
60#391C2×C411yescharacteristic
61#391C2×C411yescharacteristic
62#389—21no—
63#389—21no—
64#389—21no—
65#389—21no—
66#384C2×C411yescharacteristic
67#384D411yescharacteristic
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C43C2311yescharacteristic
73#340—21no—
74#340—21no—
75#340—21no—
76#340—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336—21no—
85#336—21no—
86#336C2×C411yescharacteristic
87#336C2×C411yescharacteristic
88#333—24no—
89Q8⋊C8—42no—
90Q8⋊C8—42no—
91C22×Q8—21no—
92C22×Q8C22⋊C411yescharacteristic
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—22no—
103C4⋊Q8—41no—
104C4⋊Q8—42no—
105C4×Q8—41no—
106C4×Q8—41no—
107C4×Q8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110C4×Q8—41no—
111C4×Q8—41no—
112C4×Q8—41no—
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—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—41no—
130C2×C42C22×C411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—21no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—21no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—81no—
148C4⋊C8—81no—
149C4⋊C8SD1612yes—
150C4⋊C8Q1612yes—
151#103—42no—
152#103—42no—
153#103—42no—
154#103—42no—
155#97—41no—
156#97—41no—
157#97—41no—
158#97—41no—
159#97—81no—
160C4×C8—41no—
161C4×C8—41no—
162C4×C8—41no—
163C4×C8—41no—
164C4×C8—41no—
165C4×C8—41no—
166C4×C8—81no—
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—21no—
176C2×Q8—21no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8#10412yes—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4C2×C22⋊C411yescharacteristic
194C22×C4C4×D411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12311yescharacteristic
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8—81no—
223C2×C8—81no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—81no—
255C42—81no—
256C42C2×SD1611yescharacteristic
257C42C2×Q1611yescharacteristic
258C42#13511yescharacteristic
259C42#13511yescharacteristic
260C42AGL(1,ℤ/8)11yescharacteristic
261C42#13711yescharacteristic
262C42#13711yescharacteristic
263C42#13711yescharacteristic
264C23#38611yescharacteristic
265Q8—42no—
266Q8—42no—
267Q8—42no—
268Q8—42no—
269Q8—81no—
270Q8—81no—
271Q8—81no—
272Q8—81no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4C2×#10411yescharacteristic
305C2×C4#42111yescharacteristic
306C2×C4C4×SD1611yescharacteristic
307C2×C4C4×Q1611yescharacteristic
308C2×C4#44011yescharacteristic
309C2×C4#44111yescharacteristic
310C2×C4#44811yescharacteristic
311C2×C4#44911yescharacteristic
312C2×C4#45111yescharacteristic
313C2×C4#45211yescharacteristic
314C2×C4#45511yescharacteristic
315C2×C4#45511yescharacteristic
316C2×C4#46011yescharacteristic
317C2×C4#46211yescharacteristic
318C2×C4#46411yescharacteristic
319C2×C4#46411yescharacteristic
320C8—42no—
321C8—42no—
322C8—81no—
323C8—81no—
324C8—82no—
325C8—82no—
326C8—81no—
327C8—81no—
328C22#187111yescharacteristic
329C22#187811yescharacteristic
330C22#188011yescharacteristic
331C22#188111yescharacteristic
332C22#188111yescharacteristic
333C22#188511yescharacteristic
334C22#189111yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—42no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4—82no—
351C4—161no—
352C4#164311yescharacteristic
353C4#164411yescharacteristic
354C4#164511yescharacteristic
355C4#164611yescharacteristic
356C2#899011yescharacteristic
357C2#899211yescharacteristic
358C2#900511yescharacteristic
359C2#902911yescharacteristic
360C2#904811yescharacteristic
361C2#905011yescharacteristic
362C2#906011yescharacteristic
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
#238162
#232492
#98692
#96772
C4×#3332
#70272