Finite Group Databasebeta

← #101512

Subgroups — #101512

Order 512.

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

normal subgroups only

This group has 341 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#29395C211yesmaximal, characteristic
2#22021C211yesmaximal, characteristic
3#9869C211yesmaximal, characteristic
4#7639C211yesmaximal, characteristic
5#7630C211yesmaximal, characteristic
6#7043C211yesmaximal, characteristic
7#7023C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2083C411yescharacteristic
11#2072C411yescharacteristic
12#2058C411yescharacteristic
13#2024C411yescharacteristic
14#1985—21no—
15#1940—21no—
16#1927—21no—
17#1920—21no—
18#1918—21no—
19#1916—22no—
20#1863—21no—
21#1840—21no—
22#1839C2211yescharacteristic
23#1832—21no—
24#1767C2211yescharacteristic
25C4×C4⋊C8C2211yescharacteristic
26#1745C2211yescharacteristic
27#1745C2211yescharacteristic
28#1279—22no—
29#1272—21no—
30#1272—21no—
31#1272—21no—
32#1271—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8D411yescharacteristic
36C2×#107—21no—
37C2×#106—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—22no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×C4×C8D412yes—
47#391—21no—
48#391C2×C411yescharacteristic
49#391D411yescharacteristic
50#389—21no—
51#389—21no—
52#389C2×C411yescharacteristic
53#389D411yescharacteristic
54#387—21no—
55#387—21no—
56#384C2×C411yescharacteristic
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4D411yescharacteristic
61#376—21no—
62C43C2311yescharacteristic
63#340—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#336—22no—
68#336—22no—
69#336—22no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336C2×C411yescharacteristic
78#336C2×C411yescharacteristic
79#336D411yescharacteristic
80#336D411yescharacteristic
81C22×Q8—21no—
82C22×Q8C22⋊C411yescharacteristic
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—22no—
87C22×C8—21no—
88C22×C8—41no—
89C22×C8—41no—
90C4⋊Q8—42no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—81no—
94C4×Q8—81no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4C22⋊C411yescharacteristic
105C2×C4⋊C4C22⋊C411yescharacteristic
106C2×C4⋊C4C22⋊C411yescharacteristic
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—41no—
110C2×C42C22×C411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42#4111yescharacteristic
116C2×C42#4111yescharacteristic
117#107—42no—
118#106—42no—
119C4⋊C8—22no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—82no—
124#103—42no—
125#103—42no—
126#97—22no—
127#97—41no—
128#97—41no—
129#97—41no—
130#97—81no—
131C4×C8—42no—
132#95—21no—
133#95—21no—
134#95—21no—
135#95—21no—
136#95—21no—
137#95—21no—
138#95—21no—
139#95—41no—
140#95—41no—
141C2×Q8—22no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—81no—
148C2×Q8—81no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4C2×C22⋊C411yescharacteristic
156C22×C4C4×D411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4#12011yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12311yescharacteristic
162C2×C8—42no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—41no—
211C42—41no—
212C42—41no—
213C42—42no—
214C42—41no—
215C42—41no—
216C42—81no—
217C42—81no—
218C23#38611yescharacteristic
219Q8—42no—
220Q8—81no—
221Q8—82no—
222Q8—82no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4#42111yescharacteristic
259C2×C4#42111yescharacteristic
260C2×C4#44311yescharacteristic
261C2×C4#44411yescharacteristic
262C2×C4#45511yescharacteristic
263C2×C4#45611yescharacteristic
264C2×C4#47111yescharacteristic
265C2×C4#47211yescharacteristic
266C8—81no—
267C8—81no—
268C8—81no—
269C8—82no—
270C8—81no—
271C8—82no—
272C8—82no—
273C22#187611yescharacteristic
274C22#188211yescharacteristic
275C22#189111yescharacteristic
276C22#189711yescharacteristic
277C22#190511yescharacteristic
278C22#190711yescharacteristic
279C22#190911yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—81no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—81no—
296C4—161no—
297C2#905111yescharacteristic
298C2#921311yescharacteristic
299C2#928011yescharacteristic
300C2#932811yescharacteristic
301C2#937511yescharacteristic
302C2#949311yescharacteristic
303C2#953011yescharacteristic
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
#293952
#220212
#98692
#76392
#76302
#70432
#70232