Finite Group Databasebeta

← #11780271

Subgroups — #11780271

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
2C9×#461C211yesmaximal, characteristic
3#10588767C211yesmaximal, characteristic, complemented
4#10588760C211yesmaximal, characteristic, complemented
5D4⋊(C9⋊C8)C211yesmaximal, characteristic
6#10588161C211yesmaximal, characteristic, complemented
7#10588160C211yesmaximal, characteristic, complemented
8#71050—31nomaximal
9C22×Dic18—21no—
10C2×C9×SD16—21no—
11C9×C4⋊Q8C2211yescharacteristic
12C4×D4×C9C2211yescharacteristic
13D4×Dic9—21no—
14#63486—21no—
15#63450—21no—
16#63440—22no—
17#63431C2211yescharacteristic
18C4×Dic18C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×#103—21no—
21#63368—21no—
22#63367—22no—
23#63367—21no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26D4×Dic6—31no—
27C3×#461D311yescharacteristic
28#5094—31no—
29#5080—31no—
30D4⋊(C3⋊C8)—31no—
31#4486—31no—
32#4484—31no—
33C2×Q8×C9—21no—
34C2×D4×C9D411yescharacteristic
35C22×C4×C9—21no—
36C22×Dic9—22no—
37C2×Dic18—22no—
38C2×Dic18—21no—
39C2×Dic18—42no—
40C2×Dic18—42no—
41C2×Dic18D411yescharacteristic
42C9×SD16—42no—
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D411yescharacteristic
47C9×C22⋊C4—21no—
48C42×C9C2311yescharacteristic
49#3676—22no—
50C4⋊Dic9—21no—
51C4⋊Dic9D411yescharacteristic
52C4⋊Dic9D412yes—
53Dic9⋊C4—22no—
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C2×C9⋊C8—21no—
57C2×C9⋊C8—21no—
58#1651—91noSylow
59C22×Dic6—61no—
60C2×C3×SD16—21no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4×D4C2×D311yescharacteristic
63D4×Dic3—61no—
64#924—61no—
65#888—61no—
66#878—62no—
67#869—31no—
68C4×Dic6—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×#103—21no—
71#810—61no—
72#808—62no—
73#808—61no—
74C4⋊(C3⋊C8)—31no—
75C4×C3⋊C8—31no—
76C23×C9—21no—
77Q8×C9—41no—
78Q8×C9—41no—
79D4×C9—21no—
80D4×C9SD1612yes—
81C2×C4×C9—21no—
82C2×C4×C9—41no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9C2×D411yescharacteristic
86C2×C4×C9C2×D411yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C2×Dic9—21no—
89C2×Dic9—21no—
90C2×Dic9—22no—
91C2×Dic9—44no—
92Dic18—21no—
93Dic18—44no—
94Dic18—41no—
95Dic18—41no—
96Dic18SD1612yescomplemented
97C8×C9—41no—
98C9⋊C8—22no—
99C9⋊C8—41no—
100D4×Q8—91no—
101#498—91no—
102#475—91no—
103#461D911yescharacteristic
104#332—91no—
105Q8⋊C8—91no—
106D4⋊C8—91no—
107C2×C3×Q8—21no—
108C2×C3×D4#6711yescharacteristic
109C22×C3×C4—21no—
110C22×Dic3—62no—
111C2×Dic6—31no—
112C2×Dic6—62no—
113C2×Dic6—61no—
114C2×Dic6—122no—
115C2×Dic6—122no—
116C3×SD16—42no—
117C2×C3×C8—21no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4#6711yescharacteristic
121C3×C22⋊C4—21no—
122C3×C42C22×D311yescharacteristic
123#217—62no—
124C4⋊Dic3—31no—
125C4⋊Dic3—32no—
126C4⋊Dic3—61no—
127Dic3⋊C4—62no—
128Dic3⋊C4—61no—
129C4×Dic3—61no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—61no—
132C22×C9—22no—
133C22×C9—41no—
134C22×C9—41no—
135C22×C9#12011yescharacteristic
136C4×C9—21no—
137C4×C9—41no—
138C4×C9—81no—
139C4×C9C2×SD1611yescharacteristic
140C4×C9C2×SD1611yescharacteristic
141C4×C9AGL(1,ℤ/8)11yescharacteristic
142C4×C9#13711yescharacteristic
143Dic9—22no—
144Dic9—42no—
145Dic9—41no—
146C22×Q8—181no—
147C2×SD16—21no—
148C4⋊Q8—91no—
149C4⋊Q8—181no—
150C4⋊Q8C2×D911yescharacteristic
151C22⋊Q8—182no—
152C22⋊Q8—181no—
153C4×Q8—91no—
154C4×D4—181no—
155C4×D4C2×D911yescharacteristic
156#106—181no—
157#106—182no—
158C4⋊C8—91no—
159C4⋊C8C2×D911yescharacteristic
160#103—21no—
161#103—181no—
162C4×C8—91no—
163C23×C3—21no—
164C3×Q8—41no—
165C3×Q8—41no—
166C3×D4—21no—
167C3×D4#21412yes—
168C2×C3×C4—21no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4D3×D411yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174C2×C3×C4C2×#6711yescharacteristic
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—62no—
178C2×Dic3—124no—
179Dic6—32no—
180Dic6—61no—
181Dic6—124no—
182Dic6—121no—
183Dic6—121no—
184C3×C8—41no—
185C3⋊C8—62no—
186C3⋊C8—121no—
187C2×C9—42no—
188C2×C9#44811yescharacteristic
189C2×C9#45011yescharacteristic
190C2×C9#45611yescharacteristic
191C2×Q8—21no—
192C2×Q8—91no—
193C2×Q8—182no—
194C2×Q8—181no—
195C2×Q8—362no—
196C2×Q8—362no—
197C2×D4#61111yescharacteristic
198C22×C4—21no—
199C22×C4—182no—
200SD16—42no—
201C2×C8—21no—
202C2×C8—181no—
203C2×C8—181no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—91no—
207C4⋊C4—92no—
208C4⋊C4—182no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4#61111yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—182no—
214C42—181no—
215C42C22×D911yescharacteristic
216C22×C3—22no—
217C22×C3—41no—
218C22×C3—41no—
219C22×C3#93711yescharacteristic
220C3×C4—21no—
221C3×C4—41no—
222C3×C4—81no—
223C3×C4D3×SD1611yescharacteristic
224C3×C4#91411yescharacteristic
225C3×C4C2×#21411yescharacteristic
226C3×C4#95111yescharacteristic
227Dic3—62no—
228Dic3—122no—
229Dic3—121no—
230C9#165111yescharacteristic, complemented, Sylow
231C23—21no—
232Q8—41no—
233Q8—41no—
234Q8—92no—
235Q8—181no—
236Q8—364no—
237Q8—361no—
238Q8—361no—
239D4—21no—
240D4#367212yes—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—181no—
246C2×C4—181no—
247C2×C4—182no—
248C2×C4—364no—
249C2×C4D4×D911yescharacteristic
250C2×C4D4×D911yescharacteristic
251C2×C4C2×#61111yescharacteristic
252C8—41no—
253C8—182no—
254C8—361no—
255C2×C3—42no—
256C2×C3#504011yescharacteristic
257C2×C3#516911yescharacteristic
258C2×C3#520511yescharacteristic
259C22—22no—
260C22—41no—
261C22—41no—
262C22#6349911yescharacteristic
263C4—21no—
264C4—41no—
265C4—81no—
266C4—182no—
267C4—362no—
268C4—361no—
269C4SD16×D911yescharacteristic
270C4#6347611yescharacteristic
271C4C2×#367211yescharacteristic
272C4#6351111yescharacteristic
273C3#7105011yescharacteristic
274C2—42no—
275C2#1058871611yescharacteristic
276C2#1058884911yescharacteristic
277C2#1058888511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#461C2
socleC22×C3#937
prime radicalC2×C3×D4#67
hypercenter#461D9
hypocenterC9#1651
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
3. #10588767C2semidirect
4. #10588760C2semidirect
6. #10588161C2semidirect
7. #10588160C2semidirect
96. Dic18SD16semidirect
230. C9#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic182
C9×#4612
#105887672
#105887602
D4⋊(C9⋊C8)2
#105881612
#105881602
#710503