Finite Group Databasebeta

← #11780192

Subgroups — #11780192

Order 1152.

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

normal subgroups only

This group has 351 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
2#10588690C211yesmaximal, characteristic
3#10588513C211yesmaximal, characteristic, complemented
4#10588362C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic
6#10588159C211yesmaximal, characteristic, complemented
7#10588133C211yesmaximal, characteristic, complemented
8#68192—31nomaximal
9C22×Dic18—21no—
10C4×D4×C9C2211yescharacteristic
11D4×Dic9—21no—
12#63486—21no—
13C2×Dic36—21no—
14#63450—21no—
15#63440—22no—
16#63431C2211yescharacteristic
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C4×C8×C9C2211yescharacteristic
21#63392—21no—
22#63378—22no—
23#63376—21no—
24#63366—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26D4×Dic6—31no—
27#5007—31no—
28#4849—31no—
29#4682—31no—
30C3×D4⋊C8D311yescharacteristic
31#4482—31no—
32#4456—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C22×Dic9—22no—
36C2×Dic18—22no—
37C2×Dic18—21no—
38C2×Dic18—21no—
39C2×Dic18—42no—
40C2×Dic18—42no—
41C2×Dic18D411yescharacteristic
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C9×C4⋊C4D411yescharacteristic
45C9×C22⋊C4—21no—
46C42×C9C2311yescharacteristic
47#3676—22no—
48C4⋊Dic9—21no—
49C4⋊Dic9—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9D411yescharacteristic
52C4⋊Dic9D412yes—
53Dic9⋊C4—22no—
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C2×C9⋊C8—21no—
57Dic36—42no—
58#1649—91noSylow
59C22×Dic6—61no—
60C3×C4×D4C2×D311yescharacteristic
61D4×Dic3—61no—
62#924—61no—
63C2×Dic12—61no—
64#888—61no—
65#878—62no—
66#869—31no—
67#869—31no—
68C4×Dic6—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#832—61no—
72#818—62no—
73#816—61no—
74#807—61no—
75C4⋊(C3⋊C8)—31no—
76C23×C9—21no—
77D4×C9—21no—
78D4×C9Q1612yescomplemented
79C2×C4×C9—21no—
80C2×C4×C9—41no—
81C2×C4×C9—41no—
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×Dic9—21no—
86C2×Dic9—21no—
87C2×Dic9—22no—
88C2×Dic9—44no—
89C2×Dic9—41no—
90Dic18—21no—
91Dic18—44no—
92Dic18—41no—
93Dic18—41no—
94Dic18—41no—
95Dic18—41no—
96Dic18D812yes—
97C8×C9—22no—
98C8×C9—41no—
99C9⋊C8—41no—
100D4×Q8—91no—
101#500—91no—
102#474—91no—
103#462—91no—
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8D911yescharacteristic
107C2×C3×D4D1211yescharacteristic
108C22×C3×C4—21no—
109C22×Dic3—62no—
110C2×Dic6—31no—
111C2×Dic6—62no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—122no—
115C2×Dic6—122no—
116C2×C3×C8—21no—
117C2×C3×C8—21no—
118C3×C4⋊C4D1211yescharacteristic
119C3×C22⋊C4—21no—
120C3×C42C22×D311yescharacteristic
121#217—62no—
122C4⋊Dic3—31no—
123C4⋊Dic3—32no—
124C4⋊Dic3—61no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127Dic3⋊C4—62no—
128Dic3⋊C4—61no—
129C4×Dic3—61no—
130C2×C3⋊C8—61no—
131Dic12—122no—
132C22×C9—22no—
133C22×C9—41no—
134C22×C9—41no—
135C22×C9#12011yescharacteristic
136C4×C9—21no—
137C4×C9—41no—
138C4×C9C2×D811yescharacteristic
139C4×C9C2×Q1611yescharacteristic
140C4×C9AGL(1,ℤ/8)11yescharacteristic
141C4×C9#13711yescharacteristic
142Dic9—22no—
143Dic9—42no—
144Dic9—41no—
145Dic9—81no—
146C22×Q8—181no—
147C2×Q16—181no—
148C4⋊Q8—91no—
149C4⋊Q8—91no—
150C4⋊Q8—181no—
151C22⋊Q8—182no—
152C22⋊Q8—181no—
153C4×Q8—91no—
154C4×D4—181no—
155C4×D4C2×D911yescharacteristic
156#107—182no—
157#107—181no—
158C4⋊C8—91no—
159C4⋊C8C2×D911yescharacteristic
160#103—181no—
161#102—181no—
162C4×C8C2×D911yescharacteristic
163C23×C3—21no—
164C3×D4—21no—
165C3×D4Dic1212yes—
166C2×C3×C4—21no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4C2×D1211yescharacteristic
170C2×C3×C4D3×D411yescharacteristic
171C2×C3×C4D3×D411yescharacteristic
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—62no—
175C2×Dic3—124no—
176C2×Dic3—121no—
177Dic6—32no—
178Dic6—61no—
179Dic6—124no—
180Dic6—121no—
181Dic6—121no—
182Dic6—121no—
183Dic6—121no—
184C3×C8—22no—
185C3×C8—41no—
186C3⋊C8—121no—
187C2×C9—42no—
188C2×C9#44711yescharacteristic
189C2×C9#45111yescharacteristic
190C2×C9#45611yescharacteristic
191C2×Q8—91no—
192C2×Q8—182no—
193C2×Q8—181no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4D3611yescharacteristic
198C22×C4—21no—
199C22×C4—182no—
200Q16—362no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—181no—
204C4⋊C4—91no—
205C4⋊C4—92no—
206C4⋊C4—182no—
207C4⋊C4—181no—
208C4⋊C4—181no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4D3611yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—182no—
214C42—181no—
215C42C22×D911yescharacteristic
216C22×C3—22no—
217C22×C3—41no—
218C22×C3—41no—
219C22×C3#88211yescharacteristic
220C3×C4—21no—
221C3×C4—41no—
222C3×C4C2×Dic1211yescharacteristic
223C3×C4#90911yescharacteristic
224C3×C4D3×D811yescharacteristic
225C3×C4#91411yescharacteristic
226Dic3—62no—
227Dic3—122no—
228Dic3—121no—
229Dic3—241no—
230C9#164911yescharacteristic, complemented, Sylow
231C23—21no—
232Q8—92no—
233Q8—181no—
234Q8—364no—
235Q8—361no—
236Q8—361no—
237Q8—361no—
238Q8—361no—
239D4—21no—
240D4Dic3612yescomplemented
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—181no—
245C2×C4—181no—
246C2×C4—182no—
247C2×C4—364no—
248C2×C4—361no—
249C2×C4C2×D3611yescharacteristic
250C2×C4D4×D911yescharacteristic
251C2×C4D4×D911yescharacteristic
252C8—22no—
253C8—41no—
254C8—361no—
255C2×C3—42no—
256C2×C3#473911yescharacteristic
257C2×C3#477311yescharacteristic
258C2×C3#482611yescharacteristic
259C22—22no—
260C22—41no—
261C22—41no—
262C22#6344411yescharacteristic
263C4—21no—
264C4—41no—
265C4—182no—
266C4—362no—
267C4—361no—
268C4—721no—
269C4C2×Dic3611yescharacteristic
270C4#6347111yescharacteristic
271C4D8×D911yescharacteristic
272C4#6347611yescharacteristic
273C3#6819211yescharacteristic
274C2—42no—
275C2#1058840511yescharacteristic
276C2#1058845311yescharacteristic
277C2#1058850611yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radicalC2×C3×D4D12
hypercenterD4⋊C8D9
hypocenterC9#1649
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
3. #10588513C2semidirect
4. #10588362C2semidirect
6. #10588159C2semidirect
7. #10588133C2semidirect
78. D4×C9Q16semidirect
230. C9#1649semidirect
240. D4Dic36semidirect

Maximal subgroups

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

subgroupindex
D4×Dic182
#105886902
#105885132
#105883622
C9×D4⋊C82
#105881592
#105881332
#681923