Finite Group Databasebeta

← #11779243

Subgroups — #11779243

Order 1152.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#10589834C211yesmaximal, characteristic, complemented
2C9×#486C211yesmaximal, characteristic, complemented
3#10588754C211yesmaximal, characteristic
4#10588752C211yesmaximal, characteristic, complemented
5#10588224C211yesmaximal, characteristic, complemented
6#10588136C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#71197—31nomaximal
9C9×C4⋊Q8C2211yescharacteristic
10C9×#127C2211yescharacteristic
11#63509—21no—
12Q8×Dic9—21no—
13C2×#3673—21no—
14C2×#3672—21no—
15#63460—22no—
16#63459—21no—
17#63454—21no—
18C4×D36C2211yescharacteristic
19C4×Dic18C2211yescharacteristic
20C9×#102—22no—
21C4×C8×C9C2211yescharacteristic
22#63392—21no—
23#63392—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5732—31no—
27C3×#486D311yescharacteristic
28#5075—31no—
29#5072—31no—
30#4547—31no—
31#4459—31no—
32#4456—31no—
33C2×Q8×C9—21no—
34C2×D4×C9—21no—
35C2×D4×C9—21no—
36C2×D4×C9—21no—
37C2×D36D411yescharacteristic
38C2×C4×D9—21no—
39C2×Dic18D411yescharacteristic
40C2×C8×C9—21no—
41C9×C4⋊C4—21no—
42C9×C4⋊C4D412yes—
43C42×C9C2311yescharacteristic
44#3673—42no—
45#3672—42no—
46(C2×D9)⋊C4—22no—
47(C2×D9)⋊C4—22no—
48(C2×D9)⋊C4—21no—
49C4⋊Dic9—22no—
50C4⋊Dic9D411yescharacteristic
51C4⋊Dic9D411yescharacteristic
52Dic9⋊C4—21no—
53C4×Dic9—22no—
54C4×Dic9—21no—
55C2×C9⋊C8—21no—
56C2×C9⋊C8—21no—
57#1628—91noSylow
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×#127C2×D311yescharacteristic
60#947—61no—
61Q8×Dic3—61no—
62C2×#214—61no—
63C2×#213—61no—
64#898—62no—
65#897—61no—
66#892—61no—
67C4×D12—31no—
68C4×Dic6—31no—
69C3×#102—22no—
70C3×C4×C8C2×D311yescharacteristic
71#832—61no—
72#832—61no—
73C4⋊(C3⋊C8)—31no—
74C4⋊(C3⋊C8)—31no—
75C23×C9—41no—
76C22×D9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79D4×C9—42no—
80D4×C9—41no—
81D4×C9—41no—
82D4×C9—41no—
83D4×C9—41no—
84C2×C4×C9—22no—
85C2×C4×C9C2×D411yescharacteristic
86C2×C4×C9C2×D411yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C2×Dic9—21no—
89C2×Dic9—21no—
90C2×Dic9—21no—
91D36—21no—
92D36—21no—
93C4×D9—41no—
94C4×D9—41no—
95Dic18—21no—
96Dic18—21no—
97C8×C9—41no—
98C9⋊C8—41no—
99C9⋊C8—41no—
100#556—91no—
101#486D911yescharacteristic, complemented
102#460—91no—
103#459—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108C2×C3×D4—21no—
109C2×C3×D4—21no—
110C2×C3×D4—21no—
111C2×D12—31no—
112C2×C4×D3—61no—
113C2×Dic6—31no—
114C2×C3×C8—21no—
115C3×C4⋊C4—21no—
116C3×C4⋊C4#6712yes—
117C3×C42C22×D311yescharacteristic
118#214—122no—
119#213—122no—
120(C2×D3)⋊C4—62no—
121(C2×D3)⋊C4—62no—
122(C2×D3)⋊C4—61no—
123C4⋊Dic3—31no—
124C4⋊Dic3—31no—
125C4⋊Dic3—62no—
126Dic3⋊C4—61no—
127C4×Dic3—62no—
128C4×Dic3—61no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C22×C9—81no—
132C22×C9—81no—
133C22×C9—81no—
134C22×C9#12011yescharacteristic
135C2×D9—41no—
136C2×D9—41no—
137C2×D9—41no—
138C4×C9—21no—
139C4×C9—42no—
140C4×C9#13511yescharacteristic
141C4×C9#13511yescharacteristic
142C4×C9AGL(1,ℤ/8)11yescharacteristic
143C4×C9AGL(1,ℤ/8)11yescharacteristic
144Dic9—41no—
145Dic9—41no—
146Dic9—41no—
147C2×SD16—181no—
148C2×D8—181no—
149C4⋊Q8C2×D911yescharacteristic
150#127C2×D911yescharacteristic
151#126—182no—
152#124—181no—
153C22⋊Q8—181no—
154C4×Q8—91no—
155C4×Q8—181no—
156C4×D4—91no—
157#117—181no—
158C4⋊C8—91no—
159C4⋊C8—91no—
160#102—22no—
161#102—181no—
162#102—181no—
163C4×C8C2×D911yescharacteristic
164C23×C3—41no—
165C22×D3—61no—
166C3×Q8—41no—
167C3×Q8—41no—
168C3×D4—42no—
169C3×D4—41no—
170C3×D4—41no—
171C3×D4—41no—
172C3×D4—41no—
173C2×C3×C4—22no—
174C2×C3×C4D3×D411yescharacteristic
175C2×C3×C4D3×D411yescharacteristic
176C2×C3×C4C2×#6711yescharacteristic
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180D12—61no—
181D12—61no—
182C4×D3—121no—
183C4×D3—121no—
184Dic6—61no—
185Dic6—61no—
186C3×C8—41no—
187C3⋊C8—121no—
188C3⋊C8—121no—
189C2×C9—161no—
190C2×C9#44911yescharacteristic
191C2×C9#44911yescharacteristic
192C2×C9#45411yescharacteristic
193D9—81no—
194C2×Q8—21no—
195C2×Q8—91no—
196C2×D4—21no—
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—91no—
200C22×C4—181no—
201SD16—362no—
202D8—362no—
203C2×C8—21no—
204C2×C8—181no—
205C2×C8—181no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—91no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4#61112yes—
212C22⋊C4—182no—
213C22⋊C4—182no—
214C22⋊C4—181no—
215C42—182no—
216C42—181no—
217C42C22×D911yescharacteristic
218C22×C3—81no—
219C22×C3—81no—
220C22×C3—81no—
221C22×C3#93711yescharacteristic
222C2×D3—121no—
223C2×D3—121no—
224C2×D3—121no—
225C3×C4—21no—
226C3×C4—42no—
227C3×C4#91111yescharacteristic
228C3×C4#91211yescharacteristic
229C3×C4#91411yescharacteristic
230C3×C4#91611yescharacteristic
231Dic3—121no—
232Dic3—121no—
233Dic3—121no—
234C9#162811yescharacteristic, complemented, Sylow
235C23—41no—
236C23—181no—
237Q8—41no—
238Q8—41no—
239Q8—181no—
240Q8—181no—
241D4—42no—
242D4—41no—
243D4—41no—
244D4—41no—
245D4—41no—
246D4—181no—
247D4—181no—
248C2×C4—22no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4D4×D911yescharacteristic
255C2×C4D4×D911yescharacteristic
256C2×C4C2×#61111yescharacteristic
257C8—41no—
258C8—361no—
259C8—361no—
260C2×C3—161no—
261C2×C3#506211yescharacteristic
262C2×C3#515811yescharacteristic
263C2×C3#517211yescharacteristic
264D3—241no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—361no—
269C22—361no—
270C22—361no—
271C22#6349911yescharacteristic
272C4—21no—
273C4—42no—
274C4—361no—
275C4—361no—
276C4—361no—
277C4#6347311yescharacteristic
278C4#6347411yescharacteristic
279C4#6347611yescharacteristic
280C4#6347811yescharacteristic
281C3#7119711yescharacteristic
282C2—161no—
283C2—721no—
284C2#1058874211yescharacteristic
285C2#1058883811yescharacteristic
286C2#1058885211yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#486C2
socleC22×C3#937
prime radical#10588754C2
hypercenter#486D9
hypocenterC9#1628
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #10589834C2semidirect
2. C9×#486C2semidirect
4. #10588752C2semidirect
5. #10588224C2semidirect
6. #10588136C2semidirect
7. #10588133C2semidirect
101. #486D9semidirect
234. C9#1628semidirect

Maximal subgroups

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

subgroupindex
#105898342
C9×#4862
#105887542
#105887522
#105882242
#105881362
#105881332
#711973