Finite Group Databasebeta

← #101516

Subgroups — #101516

Order 512.

351 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 76 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#29391C211yesmaximal, characteristic
2#22021C211yesmaximal, characteristic
3#9677C211yesmaximal, characteristic
4#7638C211yesmaximal, characteristic
5#7630C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7023C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2084C411yescharacteristic
11#2072C411yescharacteristic
12#2057C411yescharacteristic
13#2024C411yescharacteristic
14#1985—21no—
15#1940—21no—
16#1928—21no—
17#1919—21no—
18#1918—21no—
19#1916—21no—
20#1916—21no—
21#1865—21no—
22#1840—21no—
23#1839C2211yescharacteristic
24#1832—21no—
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27#1745C2211yescharacteristic
28#1745C2211yescharacteristic
29C2×Q8⋊C8—21no—
30C2×Q8⋊C8—21no—
31#1272—21no—
32#1271—21no—
33#1271—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4×Q8—21no—
37C2×C4×Q8D411yescharacteristic
38C2×#107—21no—
39C2×#106—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×#103—21no—
45C2×#103—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×#97—21no—
49C2×C4×C8D411yescharacteristic
50C2×C4×C8D411yescharacteristic
51#391—21no—
52#391C2×C411yescharacteristic
53#391D411yescharacteristic
54#389—21no—
55#389—21no—
56#389C2×C411yescharacteristic
57#389D411yescharacteristic
58#387—21no—
59#387—21no—
60#384C2×C411yescharacteristic
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65#376—21no—
66C43C2311yescharacteristic
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—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#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88Q8⋊C8—42no—
89Q8⋊C8—42no—
90C22×Q8—21no—
91C22×Q8C22⋊C411yescharacteristic
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—21no—
98C22×C8—41no—
99C22×C8—41no—
100C4⋊Q8—42no—
101C4×Q8—41no—
102C4×Q8—41no—
103C4×Q8—41no—
104C4×Q8—41no—
105C4×Q8—41no—
106C4×Q8—41no—
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—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—41no—
122C2×C42C22×C411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42#4111yescharacteristic
128C2×C42#4111yescharacteristic
129#107—42no—
130#106—42no—
131C4⋊C8—22no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—81no—
136C4⋊C8—81no—
137#103—42no—
138#103—42no—
139#97—22no—
140#97—41no—
141#97—41no—
142#97—41no—
143#97—81no—
144C4×C8—41no—
145C4×C8—41no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—41no—
154#95—41no—
155C2×Q8—22no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—41no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4C2×C22⋊C411yescharacteristic
172C22×C4C4×D411yescharacteristic
173C22×C4C4×D411yescharacteristic
174C22×C4#12011yescharacteristic
175C22×C4#12111yescharacteristic
176C22×C4#12111yescharacteristic
177C22×C4#12311yescharacteristic
178C2×C8—42no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—42no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—42no—
234C42—41no—
235C42—41no—
236C42—81no—
237C42—81no—
238C23#38611yescharacteristic
239Q8—42no—
240Q8—42no—
241Q8—42no—
242Q8—81no—
243Q8—81no—
244Q8—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
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—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4#42111yescharacteristic
281C2×C4#42111yescharacteristic
282C2×C4#44311yescharacteristic
283C2×C4#44411yescharacteristic
284C2×C4#45311yescharacteristic
285C2×C4#45411yescharacteristic
286C2×C4#47111yescharacteristic
287C2×C4#47311yescharacteristic
288C8—81no—
289C8—81no—
290C8—81no—
291C8—81no—
292C8—81no—
293C8—81no—
294C8—82no—
295C8—82no—
296C22#187611yescharacteristic
297C22#188311yescharacteristic
298C22#189111yescharacteristic
299C22#189711yescharacteristic
300C22#190511yescharacteristic
301C22#190811yescharacteristic
302C22#190911yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—81no—
315C4—81no—
316C4—82no—
317C4—81no—
318C4—81no—
319C4—161no—
320C2#905211yescharacteristic
321C2#921411yescharacteristic
322C2#928011yescharacteristic
323C2#933011yescharacteristic
324C2#937711yescharacteristic
325C2#949311yescharacteristic
326C2#952811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#293912
#220212
#96772
#76382
#76302
#70432
#70232