Finite Group Databasebeta

← #11779857

Subgroups — #11779857

Order 1152.

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

normal subgroups only

This group has 375 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#10589655C211yesmaximal, characteristic
2#10588695C211yesmaximal, characteristic, complemented
3#10588515C211yesmaximal, characteristic, complemented
4#10588376C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic, complemented
6#10588163C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68197—31nomaximal
9C2×#3697—21no—
10C4×D4×C9C2211yescharacteristic
11#63502—21no—
12C2×#3672—21no—
13#63492—21no—
14#63455—21no—
15#63446—22no—
16#63436C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C4×C8×C9C2211yescharacteristic
21#63380—22no—
22#63377—21no—
23#63376—21no—
24#63368—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5553—31no—
27#5019—31no—
28#4851—31no—
29#4694—31no—
30C3×D4⋊C8D311yescharacteristic
31#4485—31no—
32#4456—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C2×#611—22no—
36C2×#611—22no—
37#3697—42no—
38#3697—42no—
39C2×D36—21no—
40C2×D36—21no—
41C2×D36D412yes—
42C2×C4×D9—22no—
43C2×Dic18—21no—
44C2×Dic18D411yescharacteristic
45C2×C8×C9—21no—
46C2×C8×C9—21no—
47C9×C4⋊C4D411yescharacteristic
48C9×C22⋊C4—21no—
49C42×C9C2311yescharacteristic
50#3672—42no—
51(C2×D9)⋊C4—22no—
52C4⋊Dic9—21no—
53C4⋊Dic9—21no—
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—21no—
56C4×Dic9—21no—
57C2×C9⋊C8—21no—
58#1642—91noSylow
59C2×#235—61no—
60C3×C4×D4C2×D311yescharacteristic
61#940—61no—
62C2×#214—61no—
63#930—61no—
64#893—61no—
65#884—62no—
66#874—31no—
67#869—31no—
68C4×Dic6—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#821—62no—
72#817—61no—
73#816—61no—
74#810—61no—
75C4⋊(C3⋊C8)—31no—
76C23×C9—21no—
77C22×D9—22no—
78D4×C9—21no—
79D4×C9—21no—
80C2×C4×C9—21no—
81C2×C4×C9—41no—
82C2×C4×C9—41no—
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86#611—44no—
87#611—82no—
88C2×Dic9—21no—
89C2×Dic9—21no—
90C2×Dic9—41no—
91D36—42no—
92D36—41no—
93D36—41no—
94D36—41no—
95D36—41no—
96C4×D9—44no—
97Dic18—21no—
98Dic18—41no—
99Dic18—41no—
100Dic18SD1612yescomplemented
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⋊C8—91no—
110D4⋊C8D911yescharacteristic, complemented
111C2×C3×D4D1211yescharacteristic
112C22×C3×C4—21no—
113C2×#67—62no—
114C2×#67—62no—
115#235—122no—
116#235—122no—
117C2×D12—32no—
118C2×D12—61no—
119C2×D12—61no—
120C2×C4×D3—62no—
121C2×Dic6—31no—
122C2×Dic6—61no—
123C2×C3×C8—21no—
124C2×C3×C8—21no—
125C3×C4⋊C4D1211yescharacteristic
126C3×C22⋊C4—21no—
127C3×C42C22×D311yescharacteristic
128#214—122no—
129(C2×D3)⋊C4—62no—
130C4⋊Dic3—31no—
131C4⋊Dic3—61no—
132C4⋊Dic3—61no—
133Dic3⋊C4—61no—
134C4×Dic3—61no—
135C2×C3⋊C8—61no—
136C22×C9—41no—
137C22×C9—41no—
138C22×C9—41no—
139C22×C9#12011yescharacteristic
140C2×D9—42no—
141C2×D9—42no—
142C2×D9—42no—
143C4×C9—21no—
144C4×C9—41no—
145C4×C9C2×SD1611yescharacteristic
146C4×C9#13511yescharacteristic
147C4×C9AGL(1,ℤ/8)11yescharacteristic
148C4×C9AGL(1,ℤ/8)11yescharacteristic
149Dic9—22no—
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×Q8—91no—
160C4×D4—181no—
161C4×D4C2×D911yescharacteristic
162#106—181no—
163C4⋊C8—91no—
164C4⋊C8C2×D911yescharacteristic
165#103—181no—
166#103—181no—
167#102—182no—
168C4×C8C2×D911yescharacteristic
169C23×C3—21no—
170C22×D3—62no—
171C3×D4—21no—
172C3×D4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4C2×D1211yescharacteristic
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179#67—124no—
180#67—242no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—121no—
184D12—122no—
185D12—121no—
186D12—121no—
187D12—121no—
188D12—121no—
189C4×D3—124no—
190Dic6—32no—
191Dic6—61no—
192Dic6—121no—
193Dic6—121no—
194C3×C8—41no—
195C3×C8—41no—
196C3⋊C8—121no—
197C2×C9—81no—
198C2×C9#44911yescharacteristic
199C2×C9#45011yescharacteristic
200C2×C9#45511yescharacteristic
201D9—82no—
202#41—362no—
203#41—362no—
204C2×Q8—91no—
205C2×Q8—181no—
206C2×D4—92no—
207C2×D4—182no—
208C2×D4—182no—
209C2×D4—181no—
210C2×D4—181no—
211C2×D4D3611yescharacteristic
212C22×C4—21no—
213C22×C4—182no—
214SD16—362no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—181no—
218C4⋊C4—91no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4D3611yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—182no—
225C42—181no—
226C42C22×D911yescharacteristic
227C22×C3—41no—
228C22×C3—41no—
229C22×C3—41no—
230C22×C3#88211yescharacteristic
231C2×D3—122no—
232C2×D3—122no—
233C2×D3—122no—
234C3×C4—21no—
235C3×C4—41no—
236C3×C4#90411yescharacteristic
237C3×C4#90811yescharacteristic
238C3×C4#91111yescharacteristic
239C3×C4D3×SD1611yescharacteristic
240Dic3—62no—
241Dic3—121no—
242Dic3—241no—
243C9#164211yescharacteristic, complemented, Sylow
244C23—21no—
245C23—182no—
246Q8—92no—
247Q8—181no—
248Q8—361no—
249Q8—361no—
250D4—21no—
251D4—21no—
252D4—362no—
253D4—364no—
254D4—361no—
255D4—361no—
256D4—361no—
257D4—361no—
258D4—722no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—364no—
265C2×C4—361no—
266C2×C4C2×D3611yescharacteristic
267C2×C4D4×D911yescharacteristic
268C2×C4D4×D911yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C2×C3—81no—
273C2×C3#473411yescharacteristic
274C2×C3#477611yescharacteristic
275C2×C3#482511yescharacteristic
276D3—242no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—362no—
281C22—362no—
282C22—362no—
283C22#6344411yescharacteristic
284C4—21no—
285C4—41no—
286C4—182no—
287C4—361no—
288C4—721no—
289C4#6346711yescharacteristic
290C4#6347011yescharacteristic
291C4#6347311yescharacteristic
292C4SD16×D911yescharacteristic
293C3#6819711yescharacteristic
294C2—81no—
295C2—722no—
296C2#1058841611yescharacteristic
297C2#1058845611yescharacteristic
298C2#1058850511yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radical#10589655C2
hypercenterD4⋊C8D9
hypocenterC9#1642
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. #10588695C2semidirect
3. #10588515C2semidirect
4. #10588376C2semidirect
5. C9×D4⋊C8C2semidirect
6. #10588163C2semidirect
7. #10588133C2semidirect
100. Dic18SD16semidirect
110. D4⋊C8D9semidirect
243. C9#1642semidirect

Maximal subgroups

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

subgroupindex
#105896552
#105886952
#105885152
#105883762
C9×D4⋊C82
#105881632
#105881332
#681973