Finite Group Databasebeta

← #101641

Subgroups — #101641

Order 512.

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

normal subgroups only

This group has 404 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#29240C211yesmaximal, characteristic
2#23240C211yesmaximal, characteristic
3#9654C211yesmaximal, characteristic
4#7648C211yesmaximal, characteristic
5#7610C211yesmaximal, characteristic
6#7045C211yesmaximal, characteristic
7#7033C211yesmaximal, characteristic
8C4×C22⋊Q8C2211yescharacteristic
9C2×#389C2211yescharacteristic
10#2088—21no—
11#2066—21no—
12#1985—21no—
13#1919—21no—
14#1917—21no—
15#1916—21no—
16#1872C411yescharacteristic
17#1872C411yescharacteristic
18#1865—21no—
19#1853C411yescharacteristic
20#1853C411yescharacteristic
21#1851—21no—
22#1817C2211yescharacteristic
23#1797C2211yescharacteristic
24#1797C2211yescharacteristic
25#1770—21no—
26#1753—21no—
27#1749C2211yescharacteristic
28#1728C2211yescharacteristic
29C2×#324—21no—
30C2×#324—21no—
31#1272—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C22×M16—21no—
36C2×C22⋊Q8C2×C411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38C22×C4⋊C4—21no—
39C22×C4⋊C4C2×C411yescharacteristic
40C22×C4⋊C4C2×C411yescharacteristic
41C22×C42C2311yescharacteristic
42C2×#106—21no—
43C2×#106—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×#103—21no—
49C2×#103—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8C2×C411yescharacteristic
53C2×C22⋊C8C2×C411yescharacteristic
54C2×C22⋊C8D411yescharacteristic
55C2×C22⋊C8D411yescharacteristic
56C2×#97—21no—
57C2×#97—21no—
58C2×C4×C8—21no—
59#391D411yescharacteristic
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389D411yescharacteristic
65#387—21no—
66#385—21no—
67#380C2×C411yescharacteristic
68C4×C4⋊C4—21no—
69C4×C4⋊C4D411yescharacteristic
70C4×C22⋊C4—21no—
71C2×#95—21no—
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#336—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—
90C22×Q8C22⋊C411yescharacteristic
91C23×C4—21no—
92C23×C4—21no—
93C23×C4C22×C411yescharacteristic
94C23×C4C2×D411yescharacteristic
95C23×C4#4111yescharacteristic
96C2×M16—42no—
97C2×M16—41no—
98C2×M16—41no—
99C2×M16—81no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—21no—
105C22×C8—21no—
106C22×C8—41no—
107C22×C8—41no—
108C22⋊Q8—22no—
109C22⋊Q8—41no—
110C4×Q8—81no—
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⋊C4—21no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—81no—
126C2×C4⋊C4C22⋊C411yescharacteristic
127C2×C4⋊C4C22⋊C411yescharacteristic
128C2×C4⋊C4C22⋊C411yescharacteristic
129C2×C22⋊C4—21no—
130C2×C22⋊C4—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—81no—
134C2×C42C2×D411yescharacteristic
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42#4111yescharacteristic
138#106—42no—
139#106—81no—
140C4⋊C8—42no—
141C4⋊C8—81no—
142C4⋊C8—81no—
143C4⋊C8—81no—
144#103—42no—
145#103—81no—
146C22⋊C8—21no—
147C22⋊C8—21no—
148C22⋊C8—21no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—81no—
154C22⋊C8SD1612yes—
155#97—81no—
156#97—81no—
157C4×C8—42no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162#95—21no—
163#95—41no—
164#95—41no—
165C24C4×D411yescharacteristic
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—41no—
169C2×Q8—41no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—22no—
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—41no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4C2×C22⋊C411yescharacteristic
196C22×C4C4×D411yescharacteristic
197C22×C4#12011yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4#12311yescharacteristic
201C22×C4C2×SD1611yescharacteristic
202C22×C4#13511yescharacteristic
203C22×C4AGL(1,ℤ/8)11yescharacteristic
204C22×C4#13711yescharacteristic
205M16—82no—
206M16—82no—
207C2×C8—22no—
208C2×C8—22no—
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—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C2×C8—81no—
230C2×C8—81no—
231C4⋊C4—21no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—42no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4#10112yes—
249C22⋊C4—42no—
250C22⋊C4—81no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—41no—
255C42—41no—
256C42—41no—
257C42—41no—
258C42—41no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23#38611yescharacteristic
266C23C4×SD1611yescharacteristic
267C23#44011yescharacteristic
268Q8—42no—
269Q8—81no—
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—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—161no—
315C2×C4—161no—
316C2×C4C2×#10111yescharacteristic
317C2×C4#41311yescharacteristic
318C2×C4#44811yescharacteristic
319C2×C4#44911yescharacteristic
320C2×C4#46011yescharacteristic
321C2×C4#46411yescharacteristic
322C8—42no—
323C8—42no—
324C8—81no—
325C8—81no—
326C8—81no—
327C8—81no—
328C8—161no—
329C8—161no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#188011yescharacteristic
341C22#188111yescharacteristic
342C22#189111yescharacteristic
343C22#190111yescharacteristic
344C22#190211yescharacteristic
345C22#190611yescharacteristic
346C22#191311yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—42no—
357C4—81no—
358C4—81no—
359C4—82no—
360C4—81no—
361C4—161no—
362C2—41no—
363C2—41no—
364C2#905011yescharacteristic
365C2#925211yescharacteristic
366C2#927811yescharacteristic
367C2#933111yescharacteristic
368C2#935111yescharacteristic
369C2#951811yescharacteristic
370C2#953111yescharacteristic
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
#292402
#232402
#96542
#76482
#76102
#70452
#70332