Finite Group Databasebeta

← #11873477

Subgroups — #11873477

Order 1152.

600 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 154 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, complemented
2#10589827C211yesmaximal, characteristic
3C9×#487C211yesmaximal, characteristic, complemented
4#10588773C211yesmaximal, characteristic, complemented
5#10588759C211yesmaximal, characteristic, complemented
6#10588484C214yesmaximal, complemented
7#10588480C214yesmaximal, complemented
8#10588376C211yesmaximal, characteristic, complemented
9C4×C8×D9C211yesmaximal, characteristic, complemented
10#81598—31nomaximal
11C2×#3701C2212yes—
12C9×C4⋊Q8C2211yescharacteristic
13C9×C4⋊Q8C2211yescharacteristic
14#63509C2212yes—
15#63508—21no—
16Q8×Dic9—21no—
17C2×C8×D9C2212yes—
18#63459—21no—
19#63457—21no—
20#63457—21no—
21#63455—21no—
22#63455—21no—
23#63454C2212yes—
24#63452C2212yes—
25#63449—21no—
26#63436C2211yescharacteristic
27C42×D9C2211yescharacteristic
28#63431C2211yescharacteristic
29C9×#103C2214yes—
30C4×C8×C9C2211yescharacteristic
31#63395C2214yes—
32#63380C2214yes—
33C8×Dic9C2212yes—
34#63369C2214yes—
35C4×C9⋊C8C2211yescharacteristic
36#5728—31no—
37#5725—31no—
38C3×#487D311yescharacteristic
39#5088—31no—
40#5079—31no—
41#4804—34no—
42#4800—34no—
43#4694—31no—
44C4×D3×C8—31no—
45C2×Q8×C9—21no—
46C2×Q8×C9C2312yes—
47#3701—28no—
48C2×D36—22no—
49C2×D36—21no—
50C2×D36—21no—
51C2×D36C2312yes—
52C2×C4×D9—22no—
53C2×C4×D9D411yescharacteristic
54C2×C4×D9D411yescharacteristic
55C2×C4×D9C2311yescharacteristic
56C2×Dic18—21no—
57C2×C8×C9C2312yes—
58C9×C4⋊C4—21no—
59C9×C4⋊C4—21no—
60C9×C4⋊C4—21no—
61C9×C4⋊C4C2312yes—
62C42×C9C2311yescharacteristic
63(C2×D9)⋊C4—22no—
64(C2×D9)⋊C4—22no—
65(C2×D9)⋊C4—22no—
66C4⋊Dic9—21no—
67C4⋊Dic9—22no—
68C4⋊Dic9C2312yes—
69Dic9⋊C4—22no—
70C4×Dic9—22no—
71C4×Dic9D411yescharacteristic
72C4×Dic9D411yescharacteristic
73C4×Dic9C2311yescharacteristic
74C2×C9⋊C8C2312yes—
75C8×D9—24no—
76#3131—91noSylow
77C2×#239—32no—
78C3×C4⋊Q8C2×D311yescharacteristic
79C3×C4⋊Q8C2×D311yescharacteristic
80#947—32no—
81#946—61no—
82Q8×Dic3—61no—
83C2×D3×C8—32no—
84#897—61no—
85#895—61no—
86#895—61no—
87#893—61no—
88#893—61no—
89#892—32no—
90#890—32no—
91#887—61no—
92#874—31no—
93C42×D3—31no—
94#869—31no—
95C3×#103C2×D314yes—
96C3×C4×C8C2×D311yescharacteristic
97#835—34no—
98#821—34no—
99C8×Dic3—32no—
100#809—34no—
101C4×C3⋊C8—31no—
102C22×D9—22no—
103C22×D9C2×D411yescharacteristic
104Q8×C9—24no—
105Q8×C9—42no—
106C2×C4×C9—22no—
107C2×C4×C9—22no—
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9C2411yescharacteristic
111C2×Dic9—22no—
112C2×Dic9C2×D411yescharacteristic
113C2×Dic9C2×D411yescharacteristic
114C2×Dic9C2×D411yescharacteristic
115D36—24no—
116D36—44no—
117D36—42no—
118D36—42no—
119C4×D9—22no—
120C4×D9—22no—
121C4×D9—44no—
122C4×D9#4114yes—
123Dic18—42no—
124C8×C9—22no—
125C9⋊C8—22no—
126#533—91no—
127#532—91no—
128#488—94no—
129#487—91no—
130#487D911yescharacteristic, complemented
131#486—91no—
132#486—91no—
133#416—94no—
134C2×C4×C8—91no—
135C2×C3×Q8—21no—
136C2×C3×Q8C22×D312yes—
137#239—68no—
138C2×D12—32no—
139C2×D12—62no—
140C2×D12—61no—
141C2×D12—61no—
142C2×C4×D3—31no—
143C2×C4×D3—31no—
144C2×C4×D3—31no—
145C2×C4×D3—62no—
146C2×Dic6—61no—
147C2×C3×C8C22×D312yes—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4C22×D312yes—
152C3×C42C22×D311yescharacteristic
153(C2×D3)⋊C4—62no—
154(C2×D3)⋊C4—62no—
155(C2×D3)⋊C4—62no—
156C4⋊Dic3—32no—
157C4⋊Dic3—62no—
158C4⋊Dic3—61no—
159Dic3⋊C4—62no—
160C4×Dic3—31no—
161C4×Dic3—31no—
162C4×Dic3—31no—
163C4×Dic3—62no—
164C2×C3⋊C8—32no—
165D3×C8—64no—
166C22×C9C22×D411yescharacteristic
167C2×D9—21no—
168C2×D9—21no—
169C2×D9—42no—
170C2×D9—42no—
171C2×D9—42no—
172C2×D9#12412yes—
173C4×C9—42no—
174C4×C9—42no—
175C4×C9#13512yes—
176C4×C9#13512yes—
177C4×C9C2×#4112yes—
178Dic9—21no—
179Dic9—21no—
180Dic9—42no—
181Dic9#12412yes—
182C2×#41—92no—
183C22×C8—92no—
184C4⋊Q8—91no—
185C4⋊Q8C2×D911yescharacteristic
186C4⋊Q8C2×D911yescharacteristic
187#127—91no—
188#125—92no—
189#124—92no—
190C22⋊Q8—181no—
191C22⋊Q8—181no—
192#121—181no—
193#121—181no—
194C4×Q8—181no—
195C4×Q8—181no—
196C4×D4—181no—
197C4×D4—181no—
198#117—92no—
199C2×C42—91no—
200#103—94no—
201#103C2×D914yes—
202#102—94no—
203#102—94no—
204C4×C8—92no—
205C4×C8—91no—
206C4×C8C2×D911yescharacteristic
207C22×D3—31no—
208C22×D3—62no—
209C3×Q8—24no—
210C3×Q8—42no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4D3×D411yescharacteristic
215C2×C3×C4C23×D311yescharacteristic
216C2×Dic3—31no—
217C2×Dic3—31no—
218C2×Dic3—31no—
219C2×Dic3—62no—
220D12—64no—
221D12—124no—
222D12—122no—
223D12—122no—
224C4×D3—34no—
225C4×D3—62no—
226C4×D3—62no—
227C4×D3—124no—
228Dic6—122no—
229C3×C8—22no—
230C3⋊C8—62no—
231C2×C9C2×#12411yescharacteristic
232C2×C9C2×#13511yescharacteristic
233C2×C9C2×#13511yescharacteristic
234D9—22no—
235D9—82no—
236#41—188no—
237C2×Q8—21no—
238C2×Q8—181no—
239C2×Q8C22×D912yes—
240C2×D4—92no—
241C2×D4—182no—
242C2×D4—181no—
243C2×D4—181no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—182no—
248C2×C8—92no—
249C2×C8—184no—
250C2×C8C22×D912yes—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—92no—
255C4⋊C4—182no—
256C4⋊C4—182no—
257C4⋊C4—181no—
258C4⋊C4C22×D912yes—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C22⋊C4—182no—
262C42—91no—
263C42—91no—
264C42—91no—
265C42—182no—
266C42C22×D911yescharacteristic
267C22×C3C2×D3×D411yescharacteristic
268C2×D3—32no—
269C2×D3—61no—
270C2×D3—61no—
271C2×D3—122no—
272C2×D3—122no—
273C2×D3—122no—
274C3×C4—42no—
275C3×C4—42no—
276C3×C4#91612yes—
277C3×C4#91912yes—
278C3×C4D3×#4112yes—
279Dic3—32no—
280Dic3—61no—
281Dic3—61no—
282Dic3—122no—
283C9#313111yescharacteristic, complemented, Sylow
284C23—91no—
285C23—182no—
286Q8—24no—
287Q8—42no—
288Q8—362no—
289D4—184no—
290D4—364no—
291D4—362no—
292D4—362no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—91no—
296C2×C4—94no—
297C2×C4—91no—
298C2×C4—91no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—182no—
302C2×C4—364no—
303C2×C4D4×D911yescharacteristic
304C2×C4D4×D911yescharacteristic
305C2×C4C23×D911yescharacteristic
306C8—22no—
307C8—182no—
308C2×C3D3×#12411yescharacteristic
309C2×C3C2×#91611yescharacteristic
310C2×C3C2×#91911yescharacteristic
311D3—62no—
312D3—242no—
313C22—92no—
314C22—181no—
315C22—181no—
316C22—362no—
317C22—362no—
318C22—362no—
319C22C2×D4×D911yescharacteristic
320C4—42no—
321C4—42no—
322C4—92no—
323C4—181no—
324C4—181no—
325C4—362no—
326C4#6347812yes—
327C4#6348112yes—
328C4#41×D912yes—
329C3#8159811yescharacteristic
330C2—182no—
331C2—722no—
332C2D9×#12411yescharacteristic
333C2C2×#6347811yescharacteristic
334C2C2×#6348111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#487C2
socleC22×C3C2×D3×D4
prime radical#10589827C2
hypercenter#487D9
hypocenterC9#3131
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
1. #10589830C2semidirect
3. C9×#487C2semidirect
4. #10588773C2semidirect
5. #10588759C2semidirect
6. #10588484C2semidirect
7. #10588480C2semidirect
8. #10588376C2semidirect
9. C4×C8×D9C2semidirect
130. #487D9semidirect
283. C9#3131semidirect

Maximal subgroups

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

subgroupindex
#105898302
#105898272
C9×#4872
#105887732
#105887592
#105884842
#105884802
#105883762
C4×C8×D92
#815983