Finite Group Databasebeta

← #100701

Subgroups — #100701

Order 512.

328 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 80 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#29985C211yesmaximal, characteristic
2#22831C211yesmaximal, characteristic
3#7722C211yesmaximal, characteristic
4#7682C211yesmaximal, characteristic
5#7581C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8#2862C2211yescharacteristic
9#2295C2211yescharacteristic
10#2101—21no—
11#2097—21no—
12#2058C411yescharacteristic
13#2057C411yescharacteristic
14#2024C411yescharacteristic
15#2024C411yescharacteristic
16#1985—21no—
17#1949—21no—
18#1917—21no—
19#1916—21no—
20#1840—21no—
21#1839C2211yescharacteristic
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1805—21no—
25#1771—21no—
26#1767C2211yescharacteristic
27#1746—21no—
28#1744C2211yescharacteristic
29#1272—21no—
30#1272—21no—
31#1272—21no—
32#1272—21no—
33#1272—21no—
34#1271—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C4×Q8D411yescharacteristic
38C2×#107—21no—
39C2×#106—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×#103—21no—
44C2×#103—21no—
45C2×#97—21no—
46C2×#97—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49#391—21no—
50#391—21no—
51#391—21no—
52#391—21no—
53#391C2×C411yescharacteristic
54#391D411yescharacteristic
55#389C2×C411yescharacteristic
56#389D411yescharacteristic
57#387—21no—
58#387—21no—
59#382—21no—
60#382—21no—
61C4×C4⋊C4—21no—
62C4×C4⋊C4D411yescharacteristic
63#376—21no—
64C43C2311yescharacteristic
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#336—21no—
70#336—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#336C2×C411yescharacteristic
83#336C2×C411yescharacteristic
84#336D411yescharacteristic
85#336D411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88C22×Q8—21no—
89C22×Q8—21no—
90C22×Q8C22⋊C411yescharacteristic
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—21no—
97C22×C8—41no—
98C22×C8—41no—
99C4⋊Q8—81no—
100C4⋊Q8—81no—
101C4×Q8—21no—
102C4×Q8—21no—
103C4×Q8—21no—
104C4×Q8—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4C22⋊C411yescharacteristic
113C2×C4⋊C4C22⋊C411yescharacteristic
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C42—21no—
116C2×C42—21no—
117C2×C42C22×C411yescharacteristic
118C2×C42C2×D411yescharacteristic
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124#107—81no—
125#106—81no—
126C4⋊C8—42no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131#103—81no—
132#103—81no—
133#97—42no—
134#97—41no—
135#97—41no—
136C4×C8—22no—
137C4×C8—41no—
138C4×C8—42no—
139#95—21no—
140#95—21no—
141#95—21no—
142#95—21no—
143#95—21no—
144#95—21no—
145#95—21no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—42no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—81no—
158C2×Q8—81no—
159C2×Q8—81no—
160C2×Q8—81no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4C2×C22⋊C411yescharacteristic
168C22×C4C4×D411yescharacteristic
169C22×C4C4×D411yescharacteristic
170C22×C4#12011yescharacteristic
171C22×C4#12111yescharacteristic
172C22×C4#12111yescharacteristic
173C22×C4#12311yescharacteristic
174C2×C8—22no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
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—81no—
194C2×C8—81no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—81no—
213C42—21no—
214C42—21no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42#13511yescharacteristic
225C42#13511yescharacteristic
226C42#13711yescharacteristic
227C42#13711yescharacteristic
228C23#38611yescharacteristic
229Q8—42no—
230Q8—81no—
231Q8—161no—
232Q8—161no—
233Q8—162no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4#41611yescharacteristic
270C2×C4#41911yescharacteristic
271C2×C4#44311yescharacteristic
272C2×C4#44411yescharacteristic
273C2×C4#45211yescharacteristic
274C2×C4#45211yescharacteristic
275C2×C4#48511yescharacteristic
276C2×C4#48511yescharacteristic
277C8—42no—
278C8—81no—
279C8—81no—
280C8—81no—
281C8—81no—
282C8—81no—
283C8—82no—
284C8—161no—
285C22#187311yescharacteristic
286C22#187611yescharacteristic
287C22#188111yescharacteristic
288C22#190511yescharacteristic
289C22#190611yescharacteristic
290C22#190911yescharacteristic
291C22#191411yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—81no—
304C4—81no—
305C4—81no—
306C4—81no—
307C4—161no—
308C4—161no—
309C2#899411yescharacteristic
310C2#917811yescharacteristic
311C2#919211yescharacteristic
312C2#926511yescharacteristic
313C2#928011yescharacteristic
314C2#933411yescharacteristic
315C2#936911yescharacteristic
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
#299852
#228312
#77222
#76822
#75812
#70412
#70182