Finite Group Databasebeta

← #11792392

Subgroups — #11792392

Order 1152.

591 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 591 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C9×#575C211yesmaximal, characteristic, complemented
2#10589930C212yesmaximal, complemented
3#10588914C212yesmaximal, complemented
4#10588808C211yesmaximal, characteristic, complemented
5#10588237C211yesmaximal, characteristic, complemented
6#72118—31nomaximal
7C2×C9×#41C2212yes—
8C22×C4×D9C2211yescharacteristic
9C9×#137—22no—
10C9×AGL(1,ℤ/8)—22no—
11C9×#135—22no—
12C2×C9×M16C2211yescharacteristic
13#63508—22no—
14#63500—22no—
15#63499—22no—
16#63497—22no—
17C4×#611—24no—
18#63488C2212yes—
19C2×#3667C2211yescharacteristic
20#63396—24no—
21(C2×D9)⋊C8—22no—
22C3×#575D311yescharacteristic
23#5828—32no—
24#5236—32no—
25#5126—31no—
26#4557—31no—
27C23×D9D411yescharacteristic
28C9×#41—22no—
29C9×#41—22no—
30C9×#41—22no—
31C9×#41—22no—
32C2×Q8×C9D412yescomplemented
33C2×D4×C9—22no—
34C2×D4×C9D412yescomplemented
35C22×C4×C9—22no—
36C22×C4×C9C2311yescharacteristic
37C2×#611—24no—
38C22×Dic9D411yescharacteristic
39C2×C4×D9—22no—
40C2×C4×D9—22no—
41C2×C4×D9—21no—
42C2×C4×D9—21no—
43C9×Q16—22no—
44C9×SD16—24no—
45C9×D8—22no—
46C9×M16—22no—
47C2×C8×C9D412yescomplemented
48#3676—24no—
49#3676—22no—
50(C2×D9)⋊C4—24no—
51C4⋊Dic9—22no—
52Dic9⋊C4—24no—
53C4×Dic9D414yescomplemented
54#3667—22no—
55C2×C9⋊C8—21no—
56#2010—91noSylow
57C2×C3×#41C2×D312yes—
58C22×C4×D3—31no—
59C3×#137—22no—
60C3×AGL(1,ℤ/8)—22no—
61C3×#135—22no—
62C2×C3×M16C2×D311yescharacteristic
63#946—62no—
64#938—62no—
65#937—62no—
66#935—62no—
67C4×#67—64no—
68#926—32no—
69C2×#208—31no—
70#837—64no—
71(C2×D3)⋊C8—62no—
72C23×C9—22no—
73C23×C9C2×D411yescharacteristic
74C22×D9—22no—
75C22×D9—21no—
76C22×D9—42no—
77Q8×C9—22no—
78Q8×C9—22no—
79D4×C9—22no—
80D4×C9—22no—
81D4×C9—42no—
82D4×C9—42no—
83C2×C4×C9—22no—
84C2×C4×C9—42no—
85C2×C4×C9—42no—
86C2×C4×C9C2×D412yes—
87C2×C4×C9C2×D412yes—
88C2×C4×C9C2×D411yescharacteristic
89C2×C4×C9#4111yescharacteristic
90#611—48no—
91C2×Dic9—24no—
92C2×Dic9—22no—
93C2×Dic9—21no—
94C4×D9—41no—
95C4×D9—42no—
96C4×D9—41no—
97C8×C9—22no—
98C9⋊C8—41no—
99#575D911yescharacteristic, complemented
100#525—92no—
101#421—92no—
102#407—91no—
103H(3,ℤ/4)—91no—
104C23×D3—31no—
105C3×#41—22no—
106C3×#41—22no—
107C3×#41—22no—
108C3×#41—22no—
109C2×C3×Q8#6712yes—
110C2×C3×D4—22no—
111C2×C3×D4#6712yes—
112C22×C3×C4—22no—
113C22×C3×C4C22×D311yescharacteristic
114C2×#67—64no—
115C22×Dic3—31no—
116C2×C4×D3—62no—
117C2×C4×D3—61no—
118C2×C4×D3—61no—
119C2×C4×D3—62no—
120C3×Q16—22no—
121C3×SD16—24no—
122C3×D8—22no—
123C3×M16—22no—
124C2×C3×C8#6712yes—
125#217—64no—
126#217—62no—
127(C2×D3)⋊C4—64no—
128C4⋊Dic3—62no—
129Dic3⋊C4—64no—
130C4×Dic3—34no—
131#208—62no—
132C2×C3⋊C8—61no—
133C22×C9—41no—
134C22×C9—44no—
135C22×C9—42no—
136C22×C9#12012yes—
137C22×C9#12111yescharacteristic
138C2×D9—24no—
139C2×D9—22no—
140C2×D9—42no—
141C2×D9—41no—
142C2×D9—41no—
143C4×C9—42no—
144C4×C9#12011yescharacteristic
145C4×C9#12112yes—
146C4×C9#12711yescharacteristic
147Dic9—44no—
148Dic9—41no—
149C2×#41C2×D912yes—
150C23×C4—91no—
151#137—22no—
152AGL(1,ℤ/8)—22no—
153#135—22no—
154C2×M16—91no—
155C2×M16C2×D911yescharacteristic
156#123—182no—
157C22⋊Q8—182no—
158#121—182no—
159#120—182no—
160C4×D4—184no—
161#117—92no—
162#104—184no—
163C22⋊C8—182no—
164C23×C3—22no—
165C23×C3D3×D411yescharacteristic
166C22×D3—62no—
167C22×D3—61no—
168C22×D3—122no—
169C3×Q8—22no—
170C3×Q8—22no—
171C3×D4—22no—
172C3×D4—22no—
173C3×D4—42no—
174C3×D4—42no—
175C2×C3×C4—22no—
176C2×C3×C4—42no—
177C2×C3×C4—42no—
178C2×C3×C4D3×D412yes—
179C2×C3×C4#23711yescharacteristic
180C2×C3×C4C2×#6712yes—
181C2×C3×C4C2×#6711yescharacteristic
182#67—128no—
183C2×Dic3—64no—
184C2×Dic3—62no—
185C2×Dic3—61no—
186C4×D3—122no—
187C4×D3—121no—
188C4×D3—121no—
189C3×C8—22no—
190C3⋊C8—121no—
191C2×C9—22no—
192C2×C9—21no—
193C2×C9—82no—
194C2×C9#39211yescharacteristic
195D9—42no—
196C24—91no—
197#41—22no—
198#41—22no—
199#41—22no—
200#41—22no—
201C2×Q8#61112yescomplemented
202C2×D4—22no—
203C2×D4—184no—
204C2×D4#61112yescomplemented
205C22×C4—22no—
206C22×C4—91no—
207C22×C4—182no—
208C22×C4—181no—
209C22×C4—181no—
210C22×C4—182no—
211C22×C4C22×D911yescharacteristic
212Q16—22no—
213SD16—24no—
214D8—22no—
215M16—22no—
216M16—182no—
217C2×C8—181no—
218C2×C8#61112yescomplemented
219C4⋊C4—184no—
220C4⋊C4—182no—
221C22⋊C4—184no—
222C22⋊C4—184no—
223C22⋊C4—182no—
224C42—94no—
225C22×C3—41no—
226C22×C3—44no—
227C22×C3—42no—
228C22×C3#93712yes—
229C22×C3#93811yescharacteristic
230C2×D3—64no—
231C2×D3—62no—
232C2×D3—122no—
233C2×D3—121no—
234C2×D3—121no—
235C3×C4—42no—
236C3×C4#93912yes—
237C3×C4#94011yescharacteristic
238C3×C4#95311yescharacteristic
239Dic3—124no—
240Dic3—121no—
241C9#201011yescharacteristic, complemented, Sylow
242C23—22no—
243C23—182no—
244C23—181no—
245C23—362no—
246C23D4×D911yescharacteristic
247Q8—22no—
248Q8—22no—
249D4—22no—
250D4—22no—
251D4—42no—
252D4—42no—
253D4—368no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—184no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—362no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4D4×D912yes—
264C2×C4#369911yescharacteristic
265C2×C4C2×#61112yes—
266C2×C4C2×#61111yescharacteristic
267C8—22no—
268C8—361no—
269C2×C3—22no—
270C2×C3—21no—
271C2×C3—82no—
272C2×C3#522311yescharacteristic
273D3—122no—
274C22—41no—
275C22—44no—
276C22—42no—
277C22—184no—
278C22—182no—
279C22—362no—
280C22—361no—
281C22—361no—
282C22#6349912yes—
283C22#6350011yescharacteristic
284C4—42no—
285C4—364no—
286C4—361no—
287C4#6350112yes—
288C4#6350211yescharacteristic
289C4#6351511yescharacteristic
290C3#7211811yescharacteristic
291C2—22no—
292C2—21no—
293C2—82no—
294C2—362no—
295C2#1058890311yescharacteristic
subgroupG/H
centerC4#63502
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#575C2
socleC2×C3#5223
hypercenter#575D9
hypocenterC9#2010
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C9×#575C2semidirect
2. #10589930C2semidirect
3. #10588914C2semidirect
4. #10588808C2semidirect
5. #10588237C2semidirect
32. C2×Q8×C9D4semidirect
34. C2×D4×C9D4semidirect
47. C2×C8×C9D4semidirect
53. C4×Dic9D4semidirect
99. #575D9semidirect
201. C2×Q8#611semidirect
204. C2×D4#611semidirect
218. C2×C8#611semidirect
241. C9#2010semidirect

Maximal subgroups

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

subgroupindex
C9×#5752
#105899302
#105889142
#105888082
#105882372
#721183