Finite Group Databasebeta

← #11788334

Subgroups — #11788334

Order 1152.

507 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×M16C211yesmaximal, characteristic
2C2×#63486C211yesmaximal, characteristic
3#10588887C211yesmaximal, characteristic
4C2×#63382C212yesmaximal, complemented
5#10588234C212yesmaximal, complemented
6#72003—31nomaximal
7C23×C4×C9C2211yescharacteristic
8C22×Dic18C2211yescharacteristic
9C2×C9×M16—21no—
10C2×C9×M16—24no—
11C2×C9×M16C2212yes—
12C22×C8×C9—21no—
13C2×#3676C412yes—
14C2×C4⋊Dic9C2211yescharacteristic
15#63486—21no—
16#63486—21no—
17#63486—21no—
18#63486—21no—
19C2×Dic9⋊C4C412yes—
20C2×#3667C2212yes—
21#63389—21no—
22#63389—21no—
23#63382—24no—
24C22×C3×M16D311yescharacteristic
25C2×#924—31no—
26#5207—31no—
27C2×#824—32no—
28#4554—32no—
29C24×C9C2×C411yescharacteristic
30C22×C4×C9—22no—
31C22×C4×C9—22no—
32C22×C4×C9C2×C411yescharacteristic
33C22×C4×C9D411yescharacteristic
34C22×C4×C9D411yescharacteristic
35C22×C4×C9D411yescharacteristic
36C22×C4×C9D411yescharacteristic
37C22×C4×C9C2311yescharacteristic
38C22×Dic9C2×C412yes—
39C22×Dic9C2×C412yes—
40C2×Dic18—22no—
41C2×Dic18—21no—
42C2×Dic18—21no—
43C2×Dic18—22no—
44C9×M16—24no—
45C9×M16—22no—
46C9×M16D414yes—
47C2×C8×C9—24no—
48C2×C8×C9—22no—
49#3676—22no—
50#3676—22no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53Dic9⋊C4—22no—
54Dic9⋊C4—22no—
55#3667—22no—
56#3667—22no—
57C2×C9⋊C8—22no—
58#1901—91noSylow
59C23×C3×C4C2×D311yescharacteristic
60C22×Dic6—31no—
61C2×C3×M16—21no—
62C2×C3×M16—24no—
63C2×C3×M16C2×D312yes—
64C22×C3×C8—21no—
65C2×#217—32no—
66C2×C4⋊Dic3—31no—
67#924—61no—
68#924—61no—
69#924—61no—
70#924—61no—
71C2×Dic3⋊C4—32no—
72C2×#208—32no—
73#830—61no—
74#830—61no—
75#824—64no—
76C23×C9—22no—
77C23×C9—22no—
78C23×C9—41no—
79C23×C9C22⋊C411yescharacteristic
80C23×C9C22⋊C411yescharacteristic
81C23×C9C22×C411yescharacteristic
82C2×C4×C9—22no—
83C2×C4×C9—21no—
84C2×C4×C9—21no—
85C2×C4×C9—22no—
86C2×C4×C9—22no—
87C2×C4×C9—21no—
88C2×C4×C9—21no—
89C2×C4×C9C22⋊C411yescharacteristic
90C2×C4×C9C22⋊C411yescharacteristic
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9C2×D412yes—
93C2×C4×C9C2×D411yescharacteristic
94C2×C4×C9#4112yes—
95C2×Dic9—22no—
96C2×Dic9—22no—
97C2×Dic9—24no—
98C2×Dic9—42no—
99Dic18—41no—
100Dic18—42no—
101Dic18—41no—
102C8×C9—24no—
103C9⋊C8—42no—
104C22×M16D911yescharacteristic
105C2×C22⋊Q8—91no—
106C2×#101—92no—
107#407—91no—
108#343—92no—
109C24×C3C4×D311yescharacteristic
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4C4×D311yescharacteristic
113C22×C3×C4D1211yescharacteristic
114C22×C3×C4D1211yescharacteristic
115C22×C3×C4#6711yescharacteristic
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4C22×D311yescharacteristic
118C22×Dic3—32no—
119C22×Dic3—32no—
120C2×Dic6—61no—
121C2×Dic6—62no—
122C2×Dic6—62no—
123C2×Dic6—61no—
124C3×M16—24no—
125C3×M16—22no—
126C3×M16#6714yes—
127C2×C3×C8—24no—
128C2×C3×C8—22no—
129#217—62no—
130#217—62no—
131C4⋊Dic3—61no—
132C4⋊Dic3—61no—
133Dic3⋊C4—62no—
134Dic3⋊C4—62no—
135#208—62no—
136#208—62no—
137C2×C3⋊C8—62no—
138C22×C9—21no—
139C22×C9—21no—
140C22×C9—21no—
141C22×C9—21no—
142C22×C9—21no—
143C22×C9—21no—
144C22×C9—21no—
145C22×C9—44no—
146C22×C9#10112yescomplemented
147C22×C9C2×C22⋊C411yescharacteristic
148C22×C9C4×D412yes—
149C4×C9—21no—
150C4×C9—21no—
151C4×C9#12011yescharacteristic
152C4×C9#12112yes—
153C4×C9#12311yescharacteristic
154Dic9—42no—
155Dic9—42no—
156C22×Q8—91no—
157C23×C4C2×D911yescharacteristic
158C2×M16—21no—
159C2×M16—24no—
160C2×M16—92no—
161C2×M16C2×D912yes—
162C22×C8—21no—
163C22⋊Q8—181no—
164C22⋊Q8—181no—
165C22⋊Q8—181no—
166C22⋊Q8—181no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—91no—
169C2×C22⋊C4—92no—
170#101—184no—
171C22⋊C8—181no—
172C22⋊C8—181no—
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—41no—
176C23×C3(C2×D3)⋊C411yescharacteristic
177C23×C3(C2×D3)⋊C411yescharacteristic
178C23×C3C2×C4×D311yescharacteristic
179C2×C3×C4—22no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4(C2×D3)⋊C411yescharacteristic
187C2×C3×C4(C2×D3)⋊C411yescharacteristic
188C2×C3×C4C2×D1211yescharacteristic
189C2×C3×C4#23512yes—
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×#6712yes—
192C2×Dic3—62no—
193C2×Dic3—62no—
194C2×Dic3—64no—
195C2×Dic3—122no—
196Dic6—121no—
197Dic6—122no—
198Dic6—121no—
199C3×C8—24no—
200C3⋊C8—122no—
201C2×C9—22no—
202C2×C9—22no—
203C2×C9—41no—
204C2×C9#38611yescharacteristic
205C2×C9C2×#10111yescharacteristic
206C2×C9#41311yescharacteristic
207C24C4×D911yescharacteristic
208C2×Q8—181no—
209C2×Q8—182no—
210C2×Q8—182no—
211C2×Q8—181no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—92no—
215C22×C4—92no—
216C22×C4C4×D911yescharacteristic
217C22×C4D3611yescharacteristic
218C22×C4D3611yescharacteristic
219C22×C4#61111yescharacteristic
220C22×C4#61111yescharacteristic
221C22×C4C22×D911yescharacteristic
222M16—24no—
223M16—22no—
224M16—182no—
225M16—182no—
226M16#61114yes—
227C2×C8—24no—
228C2×C8—22no—
229C2×C8—182no—
230C4⋊C4—182no—
231C4⋊C4—182no—
232C4⋊C4—181no—
233C4⋊C4—181no—
234C22⋊C4—182no—
235C22⋊C4—182no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—44no—
244C22×C3#82412yes—
245C22×C3C2×(C2×D3)⋊C411yescharacteristic
246C22×C3C4×#6712yes—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4#92911yescharacteristic
250C3×C4#93012yes—
251C3×C4#95311yescharacteristic
252Dic3—122no—
253Dic3—122no—
254C9#190111yescharacteristic, complemented, Sylow
255C23—22no—
256C23—22no—
257C23—41no—
258C23(C2×D9)⋊C411yescharacteristic
259C23(C2×D9)⋊C411yescharacteristic
260C23C2×C4×D911yescharacteristic
261Q8—361no—
262Q8—362no—
263Q8—361no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—184no—
274C2×C4—362no—
275C2×C4(C2×D9)⋊C411yescharacteristic
276C2×C4(C2×D9)⋊C411yescharacteristic
277C2×C4C2×D3611yescharacteristic
278C2×C4#369712yes—
279C2×C4C2×#61111yescharacteristic
280C2×C4C2×#61112yes—
281C8—24no—
282C8—362no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—41no—
286C2×C3#513211yescharacteristic
287C2×C3C2×#82411yescharacteristic
288C2×C3#521311yescharacteristic
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—44no—
297C22#6338212yescomplemented
298C22C2×(C2×D9)⋊C411yescharacteristic
299C22C4×#61112yes—
300C4—21no—
301C4—21no—
302C4—362no—
303C4—362no—
304C4#6349111yescharacteristic
305C4#6349212yes—
306C4#6351511yescharacteristic
307C3#7200311yescharacteristic
308C2—22no—
309C2—22no—
310C2—41no—
311C2C2×#6338211yescharacteristic
312C2#1058881411yescharacteristic
313C2#1058889311yescharacteristic
subgroupG/H
centerC22C2×(C2×D9)⋊C4
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC22×C9×M16C2
socleC22×C3C2×(C2×D3)⋊C4
prime radicalC24×C3C4×D3
cosocleC22×C4×C9C23
hypercenterC22×M16D9
hypocenterC9#1901
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
4. C2×#63382C2semidirect
5. #10588234C2semidirect
146. C22×C9#101semidirect
254. C9#1901semidirect
297. C22#63382semidirect

Maximal subgroups

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

subgroupindex
C22×C9×M162
C2×#634862
#105888872
C2×#633822
#105882342
#720033