Finite Group Databasebeta

← #11877024

Subgroups — #11877024

Order 1152.

537 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 150 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#10589830C211yesmaximal, characteristic
2#10589830C211yesmaximal, characteristic
3C9×#487C211yesmaximal, characteristic, complemented
4#10588765C211yesmaximal, characteristic, complemented
5#10588760C211yesmaximal, characteristic, complemented
6#10588496C214yesmaximal
7#10588469C214yesmaximal, complemented
8C4×#3663C211yesmaximal, characteristic
9#10588361C211yesmaximal, characteristic, complemented
10#81596—31nomaximal
11C9×C4⋊Q8C2211yescharacteristic
12C9×C4⋊Q8C2211yescharacteristic
13#63508—21no—
14#63508C2212yes—
15Q8×Dic9—21no—
16Q8×Dic9C2212yes—
17C2×#3674C2214yes—
18C2×#3663C2212yes—
19#63459—21no—
20#63459C2212yes—
21#63454—21no—
22#63454—21no—
23#63452—21no—
24#63452—21no—
25#63449—21no—
26#63449C2212yes—
27C42×D9C2211yescharacteristic
28#63431C2211yescharacteristic
29#63431C2211yescharacteristic
30C9×#103C2214yes—
31C4×C8×C9C2211yescharacteristic
32#63376C2214yes—
33#63375C2212yes—
34#63367C2214yes—
35C4×C9⋊C8C2211yescharacteristic
36#5728—31no—
37#5728—31no—
38C3×#487D311yescharacteristic
39#5092—31no—
40#5080—31no—
41#4816—34no—
42#4789—34no—
43C4×ΓL(1,𝔽25)—31no—
44#4681—31no—
45C2×Q8×C9—21no—
46C2×Q8×C9C2312yes—
47C2×C4×D9D411yescharacteristic
48C2×C4×D9D411yescharacteristic
49C2×C4×D9C2311yescharacteristic
50C2×Dic18—21no—
51C2×Dic18C2312yes—
52C2×C8×C9C2312yes—
53C9×C4⋊C4—21no—
54C9×C4⋊C4—21no—
55C9×C4⋊C4—21no—
56C9×C4⋊C4C2312yes—
57C42×C9C2311yescharacteristic
58#3674—28no—
59(C2×D9)⋊C4—22no—
60(C2×D9)⋊C4—22no—
61C4⋊Dic9—21no—
62C4⋊Dic9—21no—
63C4⋊Dic9—21no—
64C4⋊Dic9—22no—
65C4⋊Dic9—22no—
66C4⋊Dic9C2312yes—
67Dic9⋊C4—22no—
68Dic9⋊C4—22no—
69C4×Dic9—22no—
70C4×Dic9—22no—
71C4×Dic9D411yescharacteristic
72C4×Dic9D411yescharacteristic
73C4×Dic9C2311yescharacteristic
74C2×C9⋊C8C2312yes—
75#3663—24no—
76#3185—91noSylow
77C3×C4⋊Q8C2×D311yescharacteristic
78C3×C4⋊Q8C2×D311yescharacteristic
79#946—32no—
80#946—61no—
81Q8×Dic3—32no—
82Q8×Dic3—61no—
83C2×#216—34no—
84C2×ΓL(1,𝔽25)—32no—
85#897—32no—
86#897—61no—
87#892—61no—
88#892—61no—
89#890—61no—
90#890—61no—
91#887—32no—
92#887—61no—
93C42×D3—31no—
94#869—31no—
95#869—31no—
96C3×#103C2×D314yes—
97C3×C4×C8C2×D311yescharacteristic
98#816—34no—
99#815—32no—
100#808—34no—
101C4×C3⋊C8—31no—
102C22×D9C2×D411yescharacteristic
103Q8×C9—24no—
104Q8×C9—42no—
105C2×C4×C9—22no—
106C2×C4×C9—22no—
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2411yescharacteristic
110C2×Dic9—22no—
111C2×Dic9—22no—
112C2×Dic9C2×D411yescharacteristic
113C2×Dic9C2×D411yescharacteristic
114C2×Dic9C2×D411yescharacteristic
115C4×D9—22no—
116C4×D9—22no—
117C4×D9—22no—
118Dic18—24no—
119Dic18—42no—
120C8×C9—22no—
121C9⋊C8#4114yes—
122#533—91no—
123#533—91no—
124#498—91no—
125#494—91no—
126#487—91no—
127#487D911yescharacteristic, complemented
128#470—94no—
129#441—94no—
130C4×M16—91no—
131C2×C3×Q8—21no—
132C2×C3×Q8C22×D312yes—
133C2×C4×D3—31no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×Dic6—32no—
137C2×Dic6—61no—
138C2×C3×C8C22×D312yes—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4C22×D312yes—
143C3×C42C22×D311yescharacteristic
144#216—68no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147C4⋊Dic3—32no—
148C4⋊Dic3—62no—
149C4⋊Dic3—62no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153Dic3⋊C4—62no—
154Dic3⋊C4—62no—
155C4×Dic3—31no—
156C4×Dic3—31no—
157C4×Dic3—31no—
158C4×Dic3—62no—
159C4×Dic3—62no—
160C2×C3⋊C8—32no—
161ΓL(1,𝔽25)—64no—
162C22×C9C22×D411yescharacteristic
163C2×D9—21no—
164C2×D9—21no—
165C2×D9—21no—
166C4×C9—42no—
167C4×C9—42no—
168C4×C9#13712yes—
169C4×C9#13712yes—
170C4×C9C2×#4112yes—
171Dic9—21no—
172Dic9—21no—
173Dic9—21no—
174Dic9—42no—
175Dic9—42no—
176C2×Q16—94no—
177C2×M16—92no—
178C4⋊Q8—91no—
179C4⋊Q8—91no—
180C4⋊Q8C2×D911yescharacteristic
181C4⋊Q8C2×D911yescharacteristic
182#125—181no—
183#125—181no—
184C22⋊Q8—92no—
185C22⋊Q8—92no—
186C22⋊Q8—181no—
187C22⋊Q8—181no—
188C4×Q8—92no—
189C4×Q8—92no—
190C4×Q8—181no—
191C4×Q8—181no—
192#117—181no—
193#117—181no—
194C2×C42—91no—
195#106—94no—
196#103—94no—
197#103C2×D914yes—
198#97—92no—
199C4×C8—91no—
200C4×C8C2×D911yescharacteristic
201C22×D3—31no—
202C3×Q8—24no—
203C3×Q8—42no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4C23×D311yescharacteristic
209C2×Dic3—31no—
210C2×Dic3—31no—
211C2×Dic3—31no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217Dic6—64no—
218Dic6—122no—
219C3×C8—22no—
220C3⋊C8—34no—
221C2×C9#53211yescharacteristic
222C2×C9C2×#13711yescharacteristic
223C2×C9C2×#13711yescharacteristic
224D9—41no—
225C2×Q8—21no—
226C2×Q8—92no—
227C2×Q8—181no—
228C2×Q8C22×D912yes—
229C22×C4—91no—
230C22×C4—91no—
231C22×C4—91no—
232Q16—188no—
233M16—184no—
234C2×C8—92no—
235C2×C8C22×D912yes—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—92no—
240C4⋊C4—182no—
241C4⋊C4—182no—
242C4⋊C4—182no—
243C4⋊C4—182no—
244C4⋊C4—181no—
245C4⋊C4—181no—
246C4⋊C4—181no—
247C4⋊C4C22×D912yes—
248C22⋊C4—182no—
249C22⋊C4—182no—
250C42—91no—
251C42—91no—
252C42—91no—
253C42—182no—
254C42—182no—
255C42C22×D911yescharacteristic
256C22×C3C2×D3×D411yescharacteristic
257C2×D3—61no—
258C2×D3—61no—
259C2×D3—61no—
260C3×C4—42no—
261C3×C4—42no—
262C3×C4#91512yes—
263C3×C4#91812yes—
264C3×C4D3×#4112yes—
265Dic3—61no—
266Dic3—61no—
267Dic3—61no—
268Dic3—122no—
269Dic3—122no—
270C9#318511yescharacteristic, complemented, Sylow
271C23—91no—
272Q8—24no—
273Q8—42no—
274Q8—184no—
275Q8—362no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—91no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—182no—
282C2×C4—182no—
283C2×C4—182no—
284C2×C4—182no—
285C2×C4—182no—
286C2×C4D4×D911yescharacteristic
287C2×C4D4×D911yescharacteristic
288C2×C4C23×D911yescharacteristic
289C8—22no—
290C8—94no—
291C2×C3#566811yescharacteristic
292C2×C3C2×#91511yescharacteristic
293C2×C3C2×#91811yescharacteristic
294D3—121no—
295C22—181no—
296C22—181no—
297C22—181no—
298C22C2×D4×D911yescharacteristic
299C4—42no—
300C4—42no—
301C4—181no—
302C4—181no—
303C4—181no—
304C4—362no—
305C4—362no—
306C4#6347712yes—
307C4#6348012yes—
308C4#41×D912yes—
309C3#8159611yescharacteristic
310C2—361no—
311C2#1058977011yescharacteristic
312C2C2×#6347711yescharacteristic
313C2C2×#6348011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#487C2
socleC22×C3C2×D3×D4
prime radicalC22×D9C2×D4
hypercenter#487D9
hypocenterC9#3185
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C9×#487C2semidirect
4. #10588765C2semidirect
5. #10588760C2semidirect
7. #10588469C2semidirect
9. #10588361C2semidirect
127. #487D9semidirect
270. C9#3185semidirect

Maximal subgroups

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

subgroupindex
#105898302
C9×#4872
#105887652
#105887602
#105884962
#105884692
C4×#36632
#105883612
#815963