Finite Group Databasebeta

← #101625

Subgroups — #101625

Order 512.

391 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 391 conjugacy classes of subgroups — too many to draw. Only its 84 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#27613C211yesmaximal, characteristic
2#22628C211yesmaximal, characteristic
3#9654C211yesmaximal, characteristic
4#8727C211yesmaximal, characteristic
5#7641C211yesmaximal, characteristic
6#7044C211yesmaximal, characteristic
7#7033C211yesmaximal, characteristic
8C2×#389C2211yescharacteristic
9#2285C2211yescharacteristic
10#2100—21no—
11#2084—21no—
12#1940—21no—
13#1919—21no—
14#1919—21no—
15#1917—21no—
16#1916—21no—
17#1853C411yescharacteristic
18#1853C411yescharacteristic
19#1823C411yescharacteristic
20#1823C411yescharacteristic
21#1817C2211yescharacteristic
22#1798—21no—
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1797C2211yescharacteristic
26#1771—21no—
27#1750—21no—
28#1749C2211yescharacteristic
29C2×#324—21no—
30C2×#324—21no—
31#1296—21no—
32#1296—21no—
33#1271—21no—
34#1271—21no—
35C2×#117—21no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C4⋊C4C2×C411yescharacteristic
39C22×C42C2311yescharacteristic
40C2×#106—21no—
41C2×#106—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8C2×C411yescharacteristic
51C2×C22⋊C8C2×C411yescharacteristic
52C2×C22⋊C8D411yescharacteristic
53C2×C22⋊C8D411yescharacteristic
54C2×#97—21no—
55C2×#97—21no—
56C2×C4×C8—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384D411yescharacteristic
62#384D411yescharacteristic
63#382—21no—
64#380—21no—
65#380C2×C411yescharacteristic
66#380C2×C411yescharacteristic
67C4×C4⋊C4—21no—
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C2×#95—21no—
71#340—21no—
72#340—21no—
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#336D411yescharacteristic
87#336D411yescharacteristic
88#324—42no—
89#324—42no—
90C23×C4—21no—
91C23×C4—21no—
92C23×C4C22×C411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C23×C4#4111yescharacteristic
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—41no—
102C22×C8—41no—
103#117—81no—
104#117—81no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—42no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C4⋊C4C22⋊C411yescharacteristic
126C2×C22⋊C4—21no—
127C2×C22⋊C4—21no—
128C2×C42—21no—
129C2×C42—21no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136#106—42no—
137#106—42no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—81no—
145C4⋊C8—81no—
146C22⋊C8—21no—
147C22⋊C8—21no—
148C22⋊C8—21no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—81no—
156C22⋊C8SD1612yes—
157#97—41no—
158#97—41no—
159#97—81no—
160C4×C8—81no—
161#95—21no—
162#95—21no—
163#95—21no—
164#95—21no—
165#95—41no—
166#95—41no—
167C24C4×D411yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—81no—
193C22×C4—81no—
194C22×C4C2×C22⋊C411yescharacteristic
195C22×C4C4×D411yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12311yescharacteristic
200C22×C4C2×SD1611yescharacteristic
201C22×C4#13511yescharacteristic
202C22×C4AGL(1,ℤ/8)11yescharacteristic
203C22×C4#13711yescharacteristic
204C2×C8—22no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
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—41no—
221C2×C8—41no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C22⋊C4—81no—
249C22⋊C4—81no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42—41no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23#38611yescharacteristic
267C23C4×SD1611yescharacteristic
268C23#44011yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
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—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—161no—
314C2×C4—161no—
315C2×C4#41011yescharacteristic
316C2×C4#41011yescharacteristic
317C2×C4#44811yescharacteristic
318C2×C4#44911yescharacteristic
319C2×C4#46011yescharacteristic
320C2×C4#46411yescharacteristic
321C2×C4#47111yescharacteristic
322C2×C4#47311yescharacteristic
323C8—42no—
324C8—81no—
325C8—81no—
326C8—81no—
327C8—81no—
328C8—81no—
329C8—161no—
330C8—161no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#188011yescharacteristic
342C22#188111yescharacteristic
343C22#189111yescharacteristic
344C22#189911yescharacteristic
345C22#190411yescharacteristic
346C22#190811yescharacteristic
347C22#191511yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—81no—
359C4—81no—
360C4—82no—
361C4—81no—
362C4—81no—
363C4—161no—
364C2—41no—
365C2—41no—
366C2#905011yescharacteristic
367C2#926111yescharacteristic
368C2#927211yescharacteristic
369C2#933511yescharacteristic
370C2#934611yescharacteristic
371C2#951411yescharacteristic
372C2#952711yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C4×D4
LCSG ▷ C23×C4 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#276132
#226282
#96542
#87272
#76412
#70442
#70332