Finite Group Databasebeta

← #101669

Subgroups — #101669

Order 512.

373 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 373 conjugacy classes of subgroups — too many to draw. Only its 74 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#27616C211yesmaximal, characteristic
2#22635C211yesmaximal, characteristic
3#9883C211yesmaximal, characteristic
4#8720C211yesmaximal, characteristic
5#7627C211yesmaximal, characteristic
6#7046C211yesmaximal, characteristic
7#7033C211yesmaximal, characteristic
8C2×#389C2211yescharacteristic
9#2283C2211yescharacteristic
10#2101—21no—
11#2085—21no—
12#1940—21no—
13#1924—21no—
14#1923—21no—
15#1921—21no—
16#1920—21no—
17#1853C411yescharacteristic
18#1852C411yescharacteristic
19#1832—21no—
20#1823C411yescharacteristic
21#1823C411yescharacteristic
22#1817C2211yescharacteristic
23#1797C2211yescharacteristic
24#1771—21no—
25#1749C2211yescharacteristic
26#1749C2211yescharacteristic
27#1749C2211yescharacteristic
28#1746—21no—
29#1295—21no—
30#1295—21no—
31#1280—21no—
32#1280—21no—
33#1271—21no—
34#1271—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4C2×C411yescharacteristic
37C22×C4⋊C4C2×C411yescharacteristic
38C22×C42C2311yescharacteristic
39C2×#107—21no—
40C2×#106—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C22⋊C8—21no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8C2×C411yescharacteristic
48C2×C22⋊C8C2×C411yescharacteristic
49C2×C22⋊C8D411yescharacteristic
50C2×C22⋊C8D411yescharacteristic
51C2×#97—21no—
52C2×#97—21no—
53C2×#97—21no—
54C2×#97—21no—
55C2×C4×C8—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#383—21no—
61#382D411yescharacteristic
62#382D411yescharacteristic
63#381—21no—
64#380C2×C411yescharacteristic
65#380C2×C411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C4×C4⋊C4D411yescharacteristic
68C4×C22⋊C4—21no—
69#376—21no—
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
88C23×C4—21no—
89C23×C4—21no—
90C23×C4C22×C411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4#4111yescharacteristic
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—21no—
99C22×C8—41no—
100C22×C8—41no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—82no—
111C2×C4⋊C4C22⋊C411yescharacteristic
112C2×C4⋊C4C22⋊C411yescharacteristic
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42—21no—
118C2×C42—21no—
119C2×C42—41no—
120C2×C42—41no—
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42#4111yescharacteristic
125#107—42no—
126#106—42no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—81no—
130C4⋊C8—81no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—42no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140#97—41no—
141#97—41no—
142#97—41no—
143#97—41no—
144#97—41no—
145#97—41no—
146#97—42no—
147C4×C8—42no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—21no—
154#95—21no—
155#95—21no—
156#95—41no—
157#95—41no—
158C24C4×D411yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4C2×C22⋊C411yescharacteristic
186C22×C4C4×D411yescharacteristic
187C22×C4#12011yescharacteristic
188C22×C4#12111yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4#12311yescharacteristic
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
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—81no—
212C2×C8—81no—
213C2×C8—81no—
214C2×C8—81no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—81no—
226C4⋊C4—82no—
227C4⋊C4—82no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—81no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—41no—
236C42—41no—
237C42—41no—
238C42—41no—
239C42—41no—
240C42—41no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23#38611yescharacteristic
248C23#44311yescharacteristic
249C23#44411yescharacteristic
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—82no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—161no—
293C2×C4—161no—
294C2×C4#41011yescharacteristic
295C2×C4#41011yescharacteristic
296C2×C4#45511yescharacteristic
297C2×C4#45611yescharacteristic
298C8—42no—
299C8—81no—
300C8—81no—
301C8—81no—
302C8—81no—
303C8—81no—
304C8—82no—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22#187611yescharacteristic
317C22#188211yescharacteristic
318C22#189111yescharacteristic
319C22#189911yescharacteristic
320C22#190311yescharacteristic
321C22#190611yescharacteristic
322C22#191511yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4—82no—
334C4—81no—
335C4—81no—
336C4—161no—
337C2—41no—
338C2—41no—
339C2#905111yescharacteristic
340C2#924211yescharacteristic
341C2#926611yescharacteristic
342C2#933811yescharacteristic
343C2#936311yescharacteristic
344C2#951411yescharacteristic
345C2#953211yescharacteristic
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
#276162
#226352
#98832
#87202
#76272
#70462
#70332