Finite Group Databasebeta

← #11779860

Subgroups — #11779860

Order 1152.

375 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 78 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#10589679C211yesmaximal, characteristic
2#10588702C211yesmaximal, characteristic, complemented
3#10588525C211yesmaximal, characteristic, complemented
4#10588376C211yesmaximal, characteristic, complemented
5C9×Q8⋊C8C211yesmaximal, characteristic, complemented
6#10588163C211yesmaximal, characteristic, complemented
7#10588136C211yesmaximal, characteristic, complemented
8#68248—31nomaximal
9C2×#3701—21no—
10C4×Q8×C9C2211yescharacteristic
11C2×#3664—21no—
12#63457—22no—
13#63457—21no—
14#63436—21no—
15#63436C2211yescharacteristic
16C4×D36—21no—
17C4×D36C2211yescharacteristic
18#63431C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C4×C8×C9C2211yescharacteristic
21#63395—21no—
22#63380—22no—
23#63376—21no—
24#63367—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5577—31no—
27#5020—31no—
28#4841—31no—
29#4694—31no—
30C3×Q8⋊C8D311yescharacteristic
31#4485—31no—
32#4459—31no—
33C2×Q8×C9D411yescharacteristic
34#3701—42no—
35#3701—42no—
36C2×D36—22no—
37C2×D36—21no—
38C2×D36—21no—
39C2×D36—22no—
40C2×D36D411yescharacteristic
41C2×D36D412yes—
42C2×C4×D9—22no—
43C2×C4×D9—21no—
44C2×Dic18—21no—
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C9×C4⋊C4—21no—
48C9×C4⋊C4D411yescharacteristic
49C42×C9—21no—
50C42×C9C2311yescharacteristic
51(C2×D9)⋊C4—22no—
52(C2×D9)⋊C4—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9—21no—
55C4⋊Dic9D411yescharacteristic
56C2×C9⋊C8—21no—
57#3664—42no—
58#1642—91noSylow
59C2×#239—61no—
60C3×C4×Q8C2×D311yescharacteristic
61C2×#204—61no—
62#895—62no—
63#895—61no—
64#874—31no—
65#874—61no—
66C4×D12—31no—
67C4×D12—61no—
68#869—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#835—61no—
72#821—62no—
73#816—61no—
74#808—61no—
75C4⋊(C3⋊C8)—31no—
76C22×D9—21no—
77C22×D9—22no—
78Q8×C9—21no—
79Q8×C9SD1612yescomplemented
80C2×C4×C9—21no—
81C2×C4×C9—21no—
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×Dic9—21no—
86C2×Dic9—41no—
87D36—21no—
88D36—21no—
89D36—42no—
90D36—44no—
91D36—41no—
92D36—41no—
93D36—41no—
94D36—41no—
95D36—82no—
96C4×D9—44no—
97C4×D9—41no—
98C4×D9—41no—
99Dic18—41no—
100Dic18—41no—
101C8×C9—41no—
102C8×C9—41no—
103C9⋊C8—41no—
104#550—91no—
105#486—91no—
106#475—91no—
107#461—91no—
108#331—91no—
109Q8⋊C8D911yescharacteristic, complemented
110D4⋊C8—91no—
111C2×C3×Q8D1211yescharacteristic
112#239—122no—
113#239—122no—
114C2×D12—31no—
115C2×D12—32no—
116C2×D12—62no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—62no—
120C2×C4×D3—62no—
121C2×C4×D3—61no—
122C2×Dic6—61no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4D1211yescharacteristic
127C3×C42—21no—
128C3×C42C22×D311yescharacteristic
129(C2×D3)⋊C4—62no—
130(C2×D3)⋊C4—61no—
131C4⋊Dic3—31no—
132C4⋊Dic3—61no—
133C4⋊Dic3—61no—
134C2×C3⋊C8—61no—
135#204—122no—
136C22×C9#12011yescharacteristic
137C2×D9—41no—
138C2×D9—42no—
139C2×D9—42no—
140C2×D9—41no—
141C2×D9—42no—
142C2×D9—41no—
143C4×C9—22no—
144C4×C9—21no—
145C4×C9—41no—
146C4×C9C2×SD1611yescharacteristic
147C4×C9#13511yescharacteristic
148C4×C9AGL(1,ℤ/8)11yescharacteristic
149C4×C9AGL(1,ℤ/8)11yescharacteristic
150Dic9—41no—
151Dic9—81no—
152C2×#41—181no—
153C2×SD16—181no—
154C4⋊Q8—91no—
155#127—91no—
156#127—181no—
157#121—182no—
158#121—181no—
159C4×Q8C2×D911yescharacteristic
160C4×D4—91no—
161C4×D4—181no—
162#106—181no—
163C4⋊C8—91no—
164C4⋊C8C2×D911yescharacteristic
165#103—181no—
166#103—181no—
167#102—182no—
168C4×C8C2×D911yescharacteristic
169C22×D3—61no—
170C22×D3—62no—
171C3×Q8—21no—
172C3×Q8#20412yes—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4C2×D1211yescharacteristic
176C2×C3×C4D3×D411yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×Dic3—61no—
179C2×Dic3—121no—
180D12—61no—
181D12—61no—
182D12—122no—
183D12—124no—
184D12—121no—
185D12—121no—
186D12—121no—
187D12—121no—
188D12—242no—
189C4×D3—124no—
190C4×D3—121no—
191C4×D3—121no—
192Dic6—121no—
193Dic6—121no—
194C3×C8—41no—
195C3×C8—41no—
196C3⋊C8—121no—
197C2×C9#44911yescharacteristic
198C2×C9#45011yescharacteristic
199C2×C9#45511yescharacteristic
200D9—81no—
201D9—82no—
202#41—362no—
203#41—362no—
204C2×Q8—181no—
205C2×Q8D3611yescharacteristic
206C2×D4—91no—
207C2×D4—92no—
208C2×D4—182no—
209C2×D4—182no—
210C2×D4—181no—
211C2×D4—181no—
212C22×C4—182no—
213C22×C4—181no—
214SD16—362no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—181no—
218C4⋊C4—21no—
219C4⋊C4—91no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4D3611yescharacteristic
223C22⋊C4—182no—
224C22⋊C4—181no—
225C42—21no—
226C42C22×D911yescharacteristic
227C22×C3#88211yescharacteristic
228C2×D3—122no—
229C2×D3—121no—
230C2×D3—121no—
231C2×D3—122no—
232C2×D3—122no—
233C2×D3—121no—
234C3×C4—22no—
235C3×C4—21no—
236C3×C4—41no—
237C3×C4C2×#20411yescharacteristic
238C3×C4#90811yescharacteristic
239C3×C4#91411yescharacteristic
240C3×C4#91911yescharacteristic
241Dic3—121no—
242Dic3—241no—
243C9#164211yescharacteristic, complemented, Sylow
244C23—181no—
245C23—182no—
246Q8—21no—
247Q8—361no—
248Q8—361no—
249Q8#366412yescomplemented
250D4—181no—
251D4—181no—
252D4—362no—
253D4—364no—
254D4—361no—
255D4—361no—
256D4—361no—
257D4—361no—
258D4—722no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—181no—
262C2×C4—364no—
263C2×C4—361no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4C2×D3611yescharacteristic
267C2×C4D4×D911yescharacteristic
268C2×C4D4×D911yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C2×C3#473111yescharacteristic
273C2×C3#481011yescharacteristic
274C2×C3#482511yescharacteristic
275D3—241no—
276D3—242no—
277C22—361no—
278C22—362no—
279C22—362no—
280C22—361no—
281C22—362no—
282C22—361no—
283C22#6344411yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—361no—
288C4—721no—
289C4C2×#366411yescharacteristic
290C4#6347011yescharacteristic
291C4#6347611yescharacteristic
292C4#6348111yescharacteristic
293C3#6824811yescharacteristic
294C2—721no—
295C2—722no—
296C2#1058841311yescharacteristic
297C2#1058849011yescharacteristic
298C2#1058850511yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×Q8⋊C8C2
socleC22×C3#882
prime radical#10589679C2
hypercenterQ8⋊C8D9
hypocenterC9#1642
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #10588702C2semidirect
3. #10588525C2semidirect
4. #10588376C2semidirect
5. C9×Q8⋊C8C2semidirect
6. #10588163C2semidirect
7. #10588136C2semidirect
79. Q8×C9SD16semidirect
109. Q8⋊C8D9semidirect
243. C9#1642semidirect
249. Q8#3664semidirect

Maximal subgroups

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

subgroupindex
#105896792
#105887022
#105885252
#105883762
C9×Q8⋊C82
#105881632
#105881362
#682483