Finite Group Databasebeta

← #104031

Subgroups — #104031

Order 512.

472 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 92 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#29211C211yesmaximal, characteristic
3#28373C211yesmaximal, characteristic
4#9868C211yesmaximal, characteristic
5#9673C211yesmaximal, characteristic
6#7662C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#477—21no—
9C2×#462—21no—
10#2862C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12C4×C4⋊Q8C2211yescharacteristic
13#2100—21no—
14#2095—21no—
15#2058—21no—
16#2057—21no—
17#2057—21no—
18#2016—21no—
19#1993—21no—
20#1987—21no—
21#1969—22no—
22#1949—22no—
23#1947—21no—
24#1921—22no—
25#1847—21no—
26#1831C2211yescharacteristic
27#1767C2211yescharacteristic
28C4×C4⋊C8C2211yescharacteristic
29C4×C4⋊C8C2211yescharacteristic
30C2×Q8⋊C8—22no—
31#1279—22no—
32#1272—22no—
33C22×Q16—22no—
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D411yescharacteristic
36C2×C4⋊Q8D411yescharacteristic
37C2×C4⋊Q8D411yescharacteristic
38C2×C4×Q8—21no—
39C2×C4×Q8—21no—
40#477—44no—
41#462—44no—
42C2×#107—22no—
43C2×#107—22no—
44C2×#107—22no—
45C2×#106—22no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8D412yes—
50C2×#103—22no—
51C2×#103—22no—
52C2×#97—21no—
53C2×C4×C8—21no—
54C2×C4×C8D412yes—
55#391—21no—
56#391—21no—
57#391—21no—
58#391—21no—
59#391—21no—
60#391—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389—21no—
65#384D411yescharacteristic
66#384D411yescharacteristic
67#382—21no—
68#382—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C43C2311yescharacteristic
74#340—22no—
75#340—22no—
76#340—22no—
77#340—22no—
78#340—22no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336D412yes—
84Q8⋊C8—44no—
85C22×Q8—21no—
86C22×Q8—21no—
87C22×Q8—21no—
88C22×Q8—21no—
89C2×Q16—44no—
90C2×Q16—44no—
91C2×Q16—82no—
92C22×C8—22no—
93C22×C8—22no—
94C22×C8—22no—
95C22×C8—41no—
96C4⋊Q8—21no—
97C4⋊Q8—21no—
98C4⋊Q8—21no—
99C4⋊Q8—42no—
100C4⋊Q8—42no—
101C4⋊Q8—42no—
102C4⋊Q8Q1612yescomplemented
103C4×Q8—42no—
104C4×Q8—42no—
105C4×Q8—42no—
106C4×Q8—42no—
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—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132#107—44no—
133#107—44no—
134#107—82no—
135#106—82no—
136C4⋊C8—24no—
137C4⋊C8—22no—
138C4⋊C8—22no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8Q1614yescomplemented
143#103—44no—
144#103—44no—
145#97—41no—
146#97—41no—
147C4×C8—42no—
148C4×C8—42no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157C2×Q8—22no—
158C2×Q8—22no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—42no—
166C2×Q8—42no—
167C2×Q8—41no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—81no—
173C2×Q8—81no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4#12011yescharacteristic
181C22×C4#12011yescharacteristic
182C22×C4#12011yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#12711yescharacteristic
187Q16—88no—
188C2×C8—24no—
189C2×C8—24no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—81no—
199C2×C8—81no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—81no—
219C4⋊C4—82no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C42—21no—
223C42—22no—
224C42—21no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42—82no—
229C42—82no—
230C42C2×Q1611yescharacteristic
231C42C2×Q1612yes—
232C42#13511yescharacteristic
233C42#13711yescharacteristic
234C42#13711yescharacteristic
235C42#13712yes—
236C23#39211yescharacteristic
237Q8—42no—
238Q8—44no—
239Q8—42no—
240Q8—82no—
241Q8—81no—
242Q8—81no—
243Q8—82no—
244Q8—82no—
245Q8—162no—
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—42no—
260C2×C4—42no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4#45111yescharacteristic
278C2×C4#45112yes—
279C2×C4#45111yescharacteristic
280C2×C4#45211yescharacteristic
281C2×C4#45211yescharacteristic
282C2×C4#45311yescharacteristic
283C2×C4#45312yes—
284C2×C4#45411yescharacteristic
285C2×C4#46212yes—
286C2×C4#46711yescharacteristic
287C2×C4#47011yescharacteristic
288C2×C4#49411yescharacteristic
289C2×C4#49711yescharacteristic
290C8—44no—
291C8—44no—
292C8—82no—
293C8—82no—
294C22#200111yescharacteristic
295C22#200211yescharacteristic
296C22#200611yescharacteristic
297C22#200911yescharacteristic
298C22#201011yescharacteristic
299C22#201611yescharacteristic
300C22#201711yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—22no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—82no—
312C4—82no—
313C4—161no—
314C4—161no—
315C4—161no—
316C4—161no—
317C4#163212yes—
318C4#163312yes—
319C2#1000311yescharacteristic
320C2#1000411yescharacteristic
321C2#1003711yescharacteristic
322C2#1005711yescharacteristic
323C2#1012111yescharacteristic
324C2#1020311yescharacteristic
325C2#1025811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
102. C4⋊Q8Q16semidirect
142. C4⋊C8Q16semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#292772
#292112
#283732
#98682
#96732
#76622
#70222