Finite Group Databasebeta

← #11779213

Subgroups — #11779213

Order 1152.

375 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 80 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
1D4×Dic18C211yesmaximal, characteristic, complemented
2#10588698C211yesmaximal, characteristic
3#10588512C211yesmaximal, characteristic, complemented
4#10588376C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic, complemented
6#10588159C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68187—31nomaximal
9C22×Dic18—21no—
10C4×D4×C9C2211yescharacteristic
11D4×Dic9—21no—
12C2×#3673—21no—
13#63486—21no—
14C2×#3664—21no—
15#63450—21no—
16#63440—22no—
17#63436C2211yescharacteristic
18#63431C2211yescharacteristic
19C4×Dic18C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21C4×C8×C9C2211yescharacteristic
22#63380—21no—
23#63380—22no—
24#63369—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26D4×Dic6—31no—
27#5015—31no—
28#4848—31no—
29#4694—31no—
30C3×D4⋊C8D311yescharacteristic
31#4482—31no—
32#4456—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C22×Dic9—22no—
36C2×D36—21no—
37C2×D36—21no—
38C2×D36—21no—
39C2×Dic18—22no—
40C2×Dic18—21no—
41C2×Dic18—42no—
42C2×Dic18—42no—
43C2×Dic18D411yescharacteristic
44C2×C8×C9—21no—
45C2×C8×C9—21no—
46C9×C4⋊C4D411yescharacteristic
47C9×C22⋊C4—21no—
48C42×C9C2311yescharacteristic
49#3676—22no—
50#3673—42no—
51C4⋊Dic9—21no—
52C4⋊Dic9D411yescharacteristic
53C4⋊Dic9D412yes—
54Dic9⋊C4—22no—
55Dic9⋊C4—21no—
56C4×Dic9—21no—
57C2×C9⋊C8—21no—
58#3664—42no—
59#1627—91noSylow
60C22×Dic6—61no—
61C3×C4×D4C2×D311yescharacteristic
62D4×Dic3—61no—
63C2×#213—61no—
64#924—61no—
65C2×#204—61no—
66#888—61no—
67#878—62no—
68#874—31no—
69#869—31no—
70C4×Dic6—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4×C8C2×D311yescharacteristic
73#821—62no—
74#821—61no—
75#809—61no—
76C4⋊(C3⋊C8)—31no—
77C23×C9—21no—
78C22×D9—41no—
79D4×C9—21no—
80D4×C9SD1612yescomplemented
81C2×C4×C9—21no—
82C2×C4×C9—41no—
83C2×C4×C9—41no—
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86C2×C4×C9C2×D411yescharacteristic
87C2×Dic9—21no—
88C2×Dic9—21no—
89C2×Dic9—22no—
90C2×Dic9—44no—
91D36—42no—
92D36—41no—
93D36—41no—
94D36—41no—
95D36—41no—
96Dic18—21no—
97Dic18—44no—
98Dic18—41no—
99Dic18—41no—
100Dic18D812yescomplemented
101C8×C9—41no—
102C8×C9—41no—
103C9⋊C8—41no—
104D4×Q8—91no—
105#486—91no—
106#460—91no—
107#459—91no—
108#332—91no—
109Q8⋊C8—91no—
110D4⋊C8D911yescharacteristic, complemented
111C2×C3×D4D1211yescharacteristic
112C22×C3×C4—21no—
113C22×Dic3—62no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×Dic6—31no—
118C2×Dic6—62no—
119C2×Dic6—61no—
120C2×Dic6—122no—
121C2×Dic6—122no—
122C2×C3×C8—21no—
123C2×C3×C8—21no—
124C3×C4⋊C4D1211yescharacteristic
125C3×C22⋊C4—21no—
126C3×C42C22×D311yescharacteristic
127#217—62no—
128#213—122no—
129C4⋊Dic3—31no—
130C4⋊Dic3—32no—
131C4⋊Dic3—61no—
132Dic3⋊C4—62no—
133Dic3⋊C4—61no—
134C4×Dic3—61no—
135C2×C3⋊C8—61no—
136#204—122no—
137C22×C9—22no—
138C22×C9—41no—
139C22×C9—41no—
140C22×C9#12011yescharacteristic
141C2×D9—81no—
142C2×D9—81no—
143C2×D9—81no—
144C4×C9—21no—
145C4×C9—41no—
146C4×C9C2×D811yescharacteristic
147C4×C9C2×SD1611yescharacteristic
148C4×C9AGL(1,ℤ/8)11yescharacteristic
149C4×C9#13711yescharacteristic
150Dic9—22no—
151Dic9—42no—
152Dic9—41no—
153C22×Q8—181no—
154C2×SD16—181no—
155C2×D8—181no—
156C4⋊Q8—91no—
157C4⋊Q8—181no—
158#127—91no—
159C22⋊Q8—182no—
160C22⋊Q8—181no—
161C4×Q8—91no—
162C4×D4—181no—
163C4×D4C2×D911yescharacteristic
164C4⋊C8—91no—
165C4⋊C8C2×D911yescharacteristic
166#102—181no—
167#102—182no—
168#102—181no—
169C4×C8C2×D911yescharacteristic
170C23×C3—21no—
171C22×D3—121no—
172C3×D4—21no—
173C3×D4#20412yes—
174C2×C3×C4—21no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4C2×D1211yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179C2×C3×C4D3×D411yescharacteristic
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—124no—
184D12—122no—
185D12—121no—
186D12—121no—
187D12—121no—
188D12—121no—
189Dic6—32no—
190Dic6—61no—
191Dic6—124no—
192Dic6—121no—
193Dic6—121no—
194C3×C8—41no—
195C3×C8—41no—
196C3⋊C8—121no—
197C2×C9—42no—
198C2×C9#44711yescharacteristic
199C2×C9#44811yescharacteristic
200C2×C9#45411yescharacteristic
201D9—161no—
202C2×Q8—91no—
203C2×Q8—182no—
204C2×Q8—181no—
205C2×Q8—362no—
206C2×Q8—362no—
207C2×D4—181no—
208C2×D4—181no—
209C2×D4—181no—
210C2×D4D3611yescharacteristic
211C22×C4—21no—
212C22×C4—182no—
213SD16—362no—
214D8—362no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—181no—
218C4⋊C4—91no—
219C4⋊C4—92no—
220C4⋊C4—182no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4D3611yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—182no—
226C42—181no—
227C42C22×D911yescharacteristic
228C22×C3—22no—
229C22×C3—41no—
230C22×C3—41no—
231C22×C3#88211yescharacteristic
232C2×D3—241no—
233C2×D3—241no—
234C2×D3—241no—
235C3×C4—21no—
236C3×C4—41no—
237C3×C4C2×#20411yescharacteristic
238C3×C4#90911yescharacteristic
239C3×C4D3×D811yescharacteristic
240C3×C4#91411yescharacteristic
241Dic3—62no—
242Dic3—122no—
243Dic3—121no—
244C9#162711yescharacteristic, complemented, Sylow
245C23—21no—
246C23—361no—
247Q8—92no—
248Q8—181no—
249Q8—364no—
250Q8—361no—
251Q8—361no—
252D4—21no—
253D4—362no—
254D4—361no—
255D4—361no—
256D4—361no—
257D4—361no—
258D4#366412yescomplemented
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—182no—
265C2×C4—364no—
266C2×C4C2×D3611yescharacteristic
267C2×C4D4×D911yescharacteristic
268C2×C4D4×D911yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C2×C3—42no—
273C2×C3#473811yescharacteristic
274C2×C3#477311yescharacteristic
275C2×C3#482711yescharacteristic
276D3—481no—
277C22—22no—
278C22—41no—
279C22—41no—
280C22—721no—
281C22—721no—
282C22—721no—
283C22#6344411yescharacteristic
284C4—21no—
285C4—41no—
286C4—182no—
287C4—362no—
288C4—361no—
289C4C2×#366411yescharacteristic
290C4#6347111yescharacteristic
291C4D8×D911yescharacteristic
292C4#6347611yescharacteristic
293C3#6818711yescharacteristic
294C2—42no—
295C2—1441no—
296C2#1058840411yescharacteristic
297C2#1058845311yescharacteristic
298C2#1058850711yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radical#10588698C2
hypercenterD4⋊C8D9
hypocenterC9#1627
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
1. D4×Dic18C2semidirect
3. #10588512C2semidirect
4. #10588376C2semidirect
5. C9×D4⋊C8C2semidirect
6. #10588159C2semidirect
7. #10588133C2semidirect
80. D4×C9SD16semidirect
100. Dic18D8semidirect
110. D4⋊C8D9semidirect
244. C9#1627semidirect
258. D4#3664semidirect

Maximal subgroups

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

subgroupindex
D4×Dic182
#105886982
#105885122
#105883762
C9×D4⋊C82
#105881592
#105881332
#681873