Finite Group Databasebeta

← #104032

Subgroups — #104032

Order 512.

416 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 88 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#29277C211yesmaximal, characteristic
2#29223C211yesmaximal, characteristic
3#29123C211yesmaximal, characteristic
4#9868C211yesmaximal, characteristic
5#9673C211yesmaximal, characteristic
6#7663C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8#2859C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100—21no—
12#2100—21no—
13#2100—21no—
14#2099—21no—
15#2057—21no—
16#2043—21no—
17#1993—21no—
18#1989—22no—
19#1987—21no—
20#1947—21no—
21#1933—22no—
22#1921—22no—
23#1836—21no—
24#1831C2211yescharacteristic
25#1803—21no—
26#1803—21no—
27#1767C2211yescharacteristic
28C4×C4⋊C8C2211yescharacteristic
29C4×C4⋊C8C2211yescharacteristic
30C2×Q8⋊C8—22no—
31#1279—22no—
32#1271—22no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×#125—21no—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×#107—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8D412yes—
43C2×#103—22no—
44C2×#103—22no—
45C2×#97—21no—
46C2×C4×C8—21no—
47C2×C4×C8D412yes—
48#391—21no—
49#391—21no—
50#389—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384D411yescharacteristic
59#384D411yescharacteristic
60#384D411yescharacteristic
61#384D411yescharacteristic
62#382—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C43C2311yescharacteristic
68#340—22no—
69#340—22no—
70#340—22no—
71#340—22no—
72#340—22no—
73#340—22no—
74#340—22no—
75#340—22no—
76#340—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336D412yes—
82Q8⋊C8—44no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—22no—
88C22×C8—41no—
89C4⋊Q8—21no—
90C4⋊Q8—21no—
91C4⋊Q8—21no—
92C4⋊Q8—42no—
93C4⋊Q8Q1612yes—
94#125—42no—
95#125—42no—
96C4×Q8—42no—
97C4×Q8—42no—
98C4×Q8—42no—
99C4×Q8—42no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—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⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C42—41no—
121C2×C42—41no—
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129#107—44no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—22no—
133C4⋊C8—41no—
134C4⋊C8—42no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137#103—44no—
138#103—82no—
139#97—41no—
140#97—41no—
141C4×C8—42no—
142C4×C8—42no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4#12011yescharacteristic
166C22×C4#12011yescharacteristic
167C22×C4#12011yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12711yescharacteristic
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—81no—
183C2×C8—81no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—81no—
206C4⋊C4—82no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—82no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C42—21no—
213C42—22no—
214C42—21no—
215C42—41no—
216C42—41no—
217C42—41no—
218C42—82no—
219C42—82no—
220C42C2×Q1611yescharacteristic
221C42#13511yescharacteristic
222C42#13512yes—
223C42#13711yescharacteristic
224C42#13711yescharacteristic
225C42#13712yes—
226C23#39211yescharacteristic
227Q8—44no—
228Q8—42no—
229Q8—42no—
230Q8—82no—
231Q8—81no—
232Q8—81no—
233C2×C4—21no—
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—42no—
247C2×C4—42no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4#45111yescharacteristic
265C2×C4#45111yescharacteristic
266C2×C4#45211yescharacteristic
267C2×C4#45212yes—
268C2×C4#45211yescharacteristic
269C2×C4#45311yescharacteristic
270C2×C4#45411yescharacteristic
271C2×C4#45412yes—
272C2×C4#46412yes—
273C2×C4#46711yescharacteristic
274C2×C4#47011yescharacteristic
275C2×C4#49511yescharacteristic
276C2×C4#49711yescharacteristic
277C8—82no—
278C8—82no—
279C8—82no—
280C8—82no—
281C22#200111yescharacteristic
282C22#200311yescharacteristic
283C22#200611yescharacteristic
284C22#200911yescharacteristic
285C22#201011yescharacteristic
286C22#201511yescharacteristic
287C22#201711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—22no—
295C4—21no—
296C4—21no—
297C4—41no—
298C4—82no—
299C4—82no—
300C4—161no—
301C4—161no—
302C4—161no—
303C4—161no—
304C4#163612yes—
305C4#163812yes—
306C2#1000311yescharacteristic
307C2#1000511yescharacteristic
308C2#1003511yescharacteristic
309C2#1006111yescharacteristic
310C2#1012311yescharacteristic
311C2#1020211yescharacteristic
312C2#1025811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ 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
#292772
#292232
#291232
#98682
#96732
#76632
#70222