Finite Group Databasebeta

← #100748

Subgroups — #100748

Order 512.

375 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 96 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#29213C211yesmaximal, characteristic
2#23369C211yesmaximal, characteristic
3#9903C211yesmaximal, characteristic
4#9702C211yesmaximal, characteristic
5#8580C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7049C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2058C412yes—
11#2057C412yes—
12#1992—21no—
13#1948—21no—
14#1947—21no—
15#1939—21no—
16#1939—21no—
17#1916—21no—
18#1916—21no—
19#1916—21no—
20#1916—21no—
21#1847—21no—
22#1831C2211yescharacteristic
23#1831C2211yescharacteristic
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26#1767C2211yescharacteristic
27C2×#333—21no—
28C2×#333—21no—
29C2×#330—21no—
30#1296—21no—
31#1296—21no—
32#1295—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8C2×C412yes—
36C2×#125D411yescharacteristic
37C2×#107—22no—
38C2×#106—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C4⋊C8D411yescharacteristic
48C2×#97—21no—
49C2×#97—21no—
50C2×#97—21no—
51C2×C4×C8—21no—
52C2×C4×C8—21no—
53#389C2×C411yescharacteristic
54#389C2×C411yescharacteristic
55#387—21no—
56#387—21no—
57#384—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#382D411yescharacteristic
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4D411yescharacteristic
65C4×C4⋊C4D411yescharacteristic
66C43C2311yescharacteristic
67#340—22no—
68#340—22no—
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#336C2×C412yes—
80#333—42no—
81#333—42no—
82#330—42no—
83C22×Q8—22no—
84C22×C8—22no—
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—41no—
90C22×C8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—82no—
96C4⋊Q8—82no—
97#125—21no—
98#125—21no—
99#125SD1612yes—
100#125Q1612yes—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C22⋊C411yescharacteristic
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—82no—
125#106—82no—
126C4⋊C8—22no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—81no—
137C4⋊C8—81no—
138#97—41no—
139#97—41no—
140#97—41no—
141#97—41no—
142#97—41no—
143#97—41no—
144C4×C8—81no—
145C4×C8—81no—
146#95—21no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—21no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—82no—
155C2×Q8—82no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—42no—
161C22×C4C2×C22⋊C411yescharacteristic
162C22×C4C4×D411yescharacteristic
163C22×C4C4×D411yescharacteristic
164C22×C4#12011yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12311yescharacteristic
168C2×C8—24no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C4⋊C4—82no—
205C4⋊C4—82no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4#10312yes—
209C4⋊C4#10312yes—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—41no—
217C42—41no—
218C42—41no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42C2×SD1611yescharacteristic
224C42C2×Q1611yescharacteristic
225C42#13511yescharacteristic
226C42#13511yescharacteristic
227C23#38611yescharacteristic
228Q8—162no—
229Q8—162no—
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—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4C2×#10311yescharacteristic
261C2×C4#41611yescharacteristic
262C2×C4#45311yescharacteristic
263C2×C4#45411yescharacteristic
264C2×C4#45511yescharacteristic
265C2×C4#45611yescharacteristic
266C2×C4#45611yescharacteristic
267C2×C4#45611yescharacteristic
268C2×C4#46511yescharacteristic
269C2×C4#46511yescharacteristic
270C2×C4#46711yescharacteristic
271C2×C4#46711yescharacteristic
272C8—44no—
273C8—82no—
274C8—82no—
275C8—81no—
276C8—81no—
277C8—81no—
278C8—81no—
279C22#188211yescharacteristic
280C22#188311yescharacteristic
281C22#188611yescharacteristic
282C22#189211yescharacteristic
283C22#190211yescharacteristic
284C22#190311yescharacteristic
285C22#191411yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—42no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—162no—
300C4#166011yescharacteristic
301C4#166111yescharacteristic
302C4#166311yescharacteristic
303C4#166411yescharacteristic
304C2#900011yescharacteristic
305C2#931511yescharacteristic
306C2#931711yescharacteristic
307C2#933711yescharacteristic
308C2#934011yescharacteristic
309C2#939211yescharacteristic
310C2#942011yescharacteristic
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
#292132
#233692
#99032
#97022
#85802
#70492