Finite Group Databasebeta

← #101652

Subgroups — #101652

Order 512.

392 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 78 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#29244C211yesmaximal, characteristic
2#23337C211yesmaximal, characteristic
3#9883C211yesmaximal, characteristic
4#7634C211yesmaximal, characteristic
5#7610C211yesmaximal, characteristic
6#7038C211yesmaximal, characteristic
7#7034C211yesmaximal, characteristic
8C4×C22⋊Q8C2211yescharacteristic
9C2×#389C2211yescharacteristic
10#2086—21no—
11#2066—21no—
12#1985—21no—
13#1939—21no—
14#1924—21no—
15#1923—21no—
16#1920—21no—
17#1917—21no—
18#1916—21no—
19#1872C411yescharacteristic
20#1872C411yescharacteristic
21#1863—21no—
22#1853C411yescharacteristic
23#1852C411yescharacteristic
24#1817C2211yescharacteristic
25#1797C2211yescharacteristic
26#1797C2211yescharacteristic
27#1749C2211yescharacteristic
28#1728C2211yescharacteristic
29#1280—21no—
30#1280—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×#107—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
88C22×Q8C22⋊C411yescharacteristic
89C23×C4—21no—
90C23×C4—21no—
91C23×C4C22×C411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4#4111yescharacteristic
94C2×M16—22no—
95C2×M16—41no—
96C2×M16—81no—
97C2×M16—81no—
98C22×C8—21no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—21no—
103C22×C8—21no—
104C22×C8—41no—
105C22×C8—41no—
106C22⋊Q8—22no—
107C22⋊Q8—41no—
108C4×Q8—81no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—81no—
120C2×C4⋊C4—81no—
121C2×C4⋊C4—81no—
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C4⋊C4C22⋊C411yescharacteristic
124C2×C4⋊C4C22⋊C411yescharacteristic
125C2×C22⋊C4—21no—
126C2×C22⋊C4—21no—
127C2×C42—21no—
128C2×C42—21no—
129C2×C42—81no—
130C2×C42C2×D411yescharacteristic
131C2×C42C2×D411yescharacteristic
132C2×C42C2×D411yescharacteristic
133C2×C42#4111yescharacteristic
134#107—81no—
135#106—42no—
136C4⋊C8—81no—
137C4⋊C8—81no—
138C4⋊C8—81no—
139C4⋊C8—81no—
140#103—42no—
141#103—81no—
142C22⋊C8—22no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—81no—
149#97—81no—
150#97—81no—
151C4×C8—81no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—21no—
157#95—41no—
158#95—41no—
159C24C4×D411yescharacteristic
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—22no—
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—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4C2×C22⋊C411yescharacteristic
192C22×C4C4×D411yescharacteristic
193C22×C4#12011yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12111yescharacteristic
196C22×C4#12311yescharacteristic
197M16—82no—
198M16—82no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
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—41no—
211C2×C8—41no—
212C2×C8—42no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—81no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8—81no—
223C4⋊C4—21no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—42no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—82no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4#10112yes—
241C22⋊C4—42no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—41no—
250C42—41no—
251C42—41no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23#38611yescharacteristic
259C23#44311yescharacteristic
260C23#44411yescharacteristic
261Q8—42no—
262Q8—81no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—161no—
307C2×C4—161no—
308C2×C4C2×#10111yescharacteristic
309C2×C4#41311yescharacteristic
310C2×C4#45511yescharacteristic
311C2×C4#45611yescharacteristic
312C2×C4#47111yescharacteristic
313C2×C4#47211yescharacteristic
314C8—81no—
315C8—81no—
316C8—81no—
317C8—81no—
318C8—81no—
319C8—81no—
320C8—82no—
321C8—82no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22#187611yescharacteristic
333C22#188211yescharacteristic
334C22#189111yescharacteristic
335C22#190111yescharacteristic
336C22#190511yescharacteristic
337C22#190711yescharacteristic
338C22#191311yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—42no—
349C4—81no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4—161no—
354C2—41no—
355C2—41no—
356C2#905111yescharacteristic
357C2#924611yescharacteristic
358C2#926411yescharacteristic
359C2#934211yescharacteristic
360C2#935511yescharacteristic
361C2#951811yescharacteristic
362C2#953011yescharacteristic
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
#292442
#233372
#98832
#76342
#76102
#70382
#70342