Finite Group Databasebeta

← #11779528

Subgroups — #11779528

Order 1152.

351 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 74 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#10589653C211yesmaximal, characteristic
2#10588691C211yesmaximal, characteristic, complemented
3#10588526C211yesmaximal, characteristic, complemented
4#10588361C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic, complemented
6#10588159C211yesmaximal, characteristic, complemented
7#10588136C211yesmaximal, characteristic, complemented
8#68181—31nomaximal
9C2×#3697—21no—
10C4×D4×C9C2211yescharacteristic
11#63500—21no—
12#63486—21no—
13C4⋊C4×D9—21no—
14#63445—22no—
15C4×D36C2211yescharacteristic
16#63431C2211yescharacteristic
17#63431C2211yescharacteristic
18C9×C4⋊C8C2211yescharacteristic
19C4×C8×C9C2211yescharacteristic
20#63392—21no—
21#63380—21no—
22#63377—21no—
23#63376—22no—
24#63367—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5551—31no—
27#5008—31no—
28#4842—31no—
29#4681—31no—
30C3×D4⋊C8D311yescharacteristic
31#4482—31no—
32#4459—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C2×#611—22no—
36#3697—42no—
37#3697—42no—
38C2×D36D411yescharacteristic
39C2×C4×D9—22no—
40C2×C4×D9—21no—
41C2×Dic18—21no—
42C2×Dic18—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C9×C4⋊C4D411yescharacteristic
46C9×C22⋊C4—21no—
47C42×C9C2311yescharacteristic
48#3676—22no—
49(C2×D9)⋊C4—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D412yes—
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—22no—
56C2×C9⋊C8—21no—
57#1635—91noSylow
58C2×#235—61no—
59C3×C4×D4C2×D311yescharacteristic
60#938—61no—
61#924—61no—
62D3×C4⋊C4—61no—
63#883—62no—
64C4×D12—31no—
65#869—31no—
66#869—31no—
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4×C8C2×D311yescharacteristic
69#832—61no—
70#821—61no—
71#817—61no—
72#816—62no—
73#808—61no—
74C4⋊(C3⋊C8)—31no—
75C23×C9—21no—
76C22×D9—21no—
77D4×C9—21no—
78D4×C9—21no—
79C2×C4×C9—21no—
80C2×C4×C9—41no—
81C2×C4×C9—41no—
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85#611—44no—
86C2×Dic9—21no—
87C2×Dic9—22no—
88C2×Dic9—41no—
89D36—21no—
90D36SD1612yes—
91C4×D9—44no—
92C4×D9—41no—
93C4×D9—41no—
94Dic18—41no—
95Dic18—41no—
96Dic18—42no—
97C8×C9—41no—
98C8×C9—41no—
99C9⋊C8—41no—
100#547—91no—
101#487—91no—
102#476—91no—
103#476—91no—
104#332—91no—
105D4⋊C8—91no—
106D4⋊C8D911yescharacteristic, complemented
107C2×C3×D4D1211yescharacteristic
108C22×C3×C4—21no—
109C2×#67—62no—
110#235—122no—
111#235—122no—
112C2×D12—31no—
113C2×C4×D3—62no—
114C2×C4×D3—61no—
115C2×Dic6—61no—
116C2×Dic6—61no—
117C2×C3×C8—21no—
118C2×C3×C8—21no—
119C3×C4⋊C4D1211yescharacteristic
120C3×C22⋊C4—21no—
121C3×C42C22×D311yescharacteristic
122#217—62no—
123(C2×D3)⋊C4—61no—
124C4⋊Dic3—32no—
125C4⋊Dic3—31no—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129Dic3⋊C4—62no—
130C2×C3⋊C8—61no—
131C22×C9—41no—
132C22×C9—41no—
133C22×C9—41no—
134C22×C9#12011yescharacteristic
135C2×D9—22no—
136C2×D9—41no—
137C2×D9—41no—
138C4×C9—21no—
139C4×C9—41no—
140C4×C9C2×SD1611yescharacteristic
141C4×C9#13511yescharacteristic
142C4×C9AGL(1,ℤ/8)11yescharacteristic
143C4×C9#13711yescharacteristic
144Dic9—42no—
145Dic9—41no—
146Dic9—81no—
147C2×#41—181no—
148C4⋊Q8—91no—
149C4⋊Q8—91no—
150#123—182no—
151C22⋊Q8—181no—
152#121—181no—
153C4×D4—91no—
154C4×D4C2×D911yescharacteristic
155C2×C4⋊C4—181no—
156#106—181no—
157#106—181no—
158C4⋊C8—91no—
159C4⋊C8C2×D911yescharacteristic
160#103—182no—
161#102—181no—
162#102—181no—
163C4×C8C2×D911yescharacteristic
164C23×C3—21no—
165C22×D3—61no—
166C3×D4—21no—
167C3×D4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4C2×D1211yescharacteristic
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174#67—124no—
175C2×Dic3—61no—
176C2×Dic3—62no—
177C2×Dic3—121no—
178D12—32no—
179D12—61no—
180C4×D3—124no—
181C4×D3—121no—
182C4×D3—121no—
183Dic6—121no—
184Dic6—121no—
185Dic6—122no—
186C3×C8—41no—
187C3×C8—41no—
188C3⋊C8—121no—
189C2×C9—81no—
190C2×C9#45011yescharacteristic
191C2×C9#45211yescharacteristic
192C2×C9#45411yescharacteristic
193D9—42no—
194#41—362no—
195#41—362no—
196C2×Q8—181no—
197C2×Q8—181no—
198C2×D4—91no—
199C2×D4—182no—
200C2×D4D3611yescharacteristic
201C22×C4—21no—
202C22×C4—182no—
203C22×C4—181no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—181no—
207C4⋊C4—92no—
208C4⋊C4—91no—
209C4⋊C4—182no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4D3611yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—182no—
216C22⋊C4—181no—
217C42C22×D911yescharacteristic
218C22×C3—41no—
219C22×C3—41no—
220C22×C3—41no—
221C22×C3#88211yescharacteristic
222C2×D3—62no—
223C2×D3—121no—
224C2×D3—121no—
225C3×C4—21no—
226C3×C4—41no—
227C3×C4#90411yescharacteristic
228C3×C4#90911yescharacteristic
229C3×C4#91111yescharacteristic
230C3×C4D3×SD1611yescharacteristic
231Dic3—121no—
232Dic3—122no—
233Dic3—241no—
234C9#163511yescharacteristic, complemented, Sylow
235C23—21no—
236C23—181no—
237Q8—362no—
238Q8—361no—
239Q8—361no—
240D4—21no—
241D4—21no—
242D4—92no—
243D4—181no—
244D4—364no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—181no—
249C2×C4—182no—
250C2×C4—364no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4C2×D3611yescharacteristic
255C2×C4D4×D911yescharacteristic
256C2×C4D4×D911yescharacteristic
257C8—41no—
258C8—41no—
259C8—361no—
260C2×C3—81no—
261C2×C3#473311yescharacteristic
262C2×C3#477611yescharacteristic
263C2×C3#482711yescharacteristic
264D3—122no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—182no—
269C22—361no—
270C22—361no—
271C22#6344411yescharacteristic
272C4—21no—
273C4—41no—
274C4—362no—
275C4—361no—
276C4—721no—
277C4#6346711yescharacteristic
278C4#6347111yescharacteristic
279C4#6347311yescharacteristic
280C4SD16×D911yescharacteristic
281C3#6818111yescharacteristic
282C2—81no—
283C2—362no—
284C2#1058841511yescharacteristic
285C2#1058845611yescharacteristic
286C2#1058850711yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radical#10589653C2
hypercenterD4⋊C8D9
hypocenterC9#1635
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10588691C2semidirect
3. #10588526C2semidirect
4. #10588361C2semidirect
5. C9×D4⋊C8C2semidirect
6. #10588159C2semidirect
7. #10588136C2semidirect
106. D4⋊C8D9semidirect
234. C9#1635semidirect

Maximal subgroups

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

subgroupindex
#105896532
#105886912
#105885262
#105883612
C9×D4⋊C82
#105881592
#105881362
#681813