Finite Group Databasebeta

← #11787162

Subgroups — #11787162

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#611C211yesmaximal, characteristic
2C22×#3667C211yesmaximal, characteristic, complemented
3C2×C9×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×(C2×D9)⋊C8C212yesmaximal, complemented
5#10588228C212yesmaximal, complemented
6#69953—31nomaximal
7C23×C4×C9C2211yescharacteristic
8C22×#611C411yescharacteristic
9C22×C4×D9C2211yescharacteristic
10C22×C8×C9C2212yes—
11C2×#3676C411yescharacteristic
12C4×#611—22no—
13C4×#611—22no—
14C2×(C2×D9)⋊C4C411yescharacteristic
15C2×Dic9⋊C4C411yescharacteristic
16C2×C4×Dic9C2211yescharacteristic
17C2×#3667—22no—
18C2×#3667—24no—
19C22×C9⋊C8C2212yes—
20C9×C22⋊C8—22no—
21(C2×D9)⋊C8—24no—
22C2×C4×#67—31no—
23C22×#208—31no—
24C2×C3×C22⋊C8D311yescharacteristic
25C2×(C2×D3)⋊C8—32no—
26#4550—32no—
27C24×C9C2×C411yescharacteristic
28C23×D9C2×C411yescharacteristic
29C22×C4×C9—22no—
30C22×C4×C9—22no—
31C22×C4×C9C2×C411yescharacteristic
32C22×C4×C9D412yes—
33C22×C4×C9D412yes—
34C22×C4×C9C2311yescharacteristic
35C2×#611—22no—
36C2×#611—22no—
37C2×#611—22no—
38C22×Dic9C2×C411yescharacteristic
39C22×Dic9C2×C411yescharacteristic
40C22×Dic9C2×C411yescharacteristic
41C2×C4×D9—21no—
42C2×C4×D9—21no—
43C2×C4×D9—22no—
44C2×C4×D9—22no—
45C2×C8×C9—22no—
46C2×C8×C9—22no—
47C2×C8×C9—22no—
48#3676—22no—
49(C2×D9)⋊C4—22no—
50Dic9⋊C4—22no—
51C4×Dic9—21no—
52C4×Dic9—21no—
53#3667—28no—
54C2×C9⋊C8—22no—
55C2×C9⋊C8—22no—
56C2×C9⋊C8D414yescomplemented
57#1870—91noSylow
58C23×C3×C4C2×D311yescharacteristic
59C22×#67—31no—
60C22×C4×D3—31no—
61C22×C3×C8C2×D312yes—
62C2×#217—31no—
63C4×#67—62no—
64C4×#67—62no—
65C2×(C2×D3)⋊C4—31no—
66C2×Dic3⋊C4—31no—
67C2×C4×Dic3—31no—
68C2×#208—64no—
69C2×#208—62no—
70C22×C3⋊C8—32no—
71C3×C22⋊C8—22no—
72(C2×D3)⋊C8—64no—
73C23×C9—22no—
74C23×C9—21no—
75C23×C9—21no—
76C23×C9—22no—
77C23×C9C22⋊C412yes—
78C23×C9C22×C411yescharacteristic
79C22×D9—21no—
80C22×D9—22no—
81C22×D9—21no—
82C22×D9—22no—
83C22×D9M1612yescomplemented
84C2×C4×C9—22no—
85C2×C4×C9—22no—
86C2×C4×C9—24no—
87C2×C4×C9—22no—
88C2×C4×C9C22⋊C412yes—
89C2×C4×C9C2×D411yescharacteristic
90C2×C4×C9C2×D412yes—
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9#4112yes—
93#611—28no—
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—22no—
99C2×Dic9—22no—
100C2×Dic9M1612yescomplemented
101C4×D9—41no—
102C4×D9—42no—
103C4×D9—41no—
104C8×C9—42no—
105C9⋊C8—24no—
106C22×M16—91no—
107C2×C4×D4—91no—
108C2×C22⋊C8—92no—
109C2×C22⋊C8D911yescharacteristic, complemented
110#336—92no—
111C24×C3C4×D311yescharacteristic
112C23×D3—31no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4D1212yes—
117C22×C3×C4#6712yes—
118C22×C3×C4C22×D311yescharacteristic
119C2×#67—62no—
120C2×#67—62no—
121C2×#67—62no—
122C22×Dic3—31no—
123C22×Dic3—31no—
124C22×Dic3—31no—
125C2×C4×D3—61no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—61no—
129C2×C3×C8—22no—
130C2×C3×C8—22no—
131C2×C3×C8—22no—
132#217—62no—
133(C2×D3)⋊C4—62no—
134Dic3⋊C4—62no—
135C4×Dic3—61no—
136C4×Dic3—61no—
137#208—68no—
138C2×C3⋊C8—34no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C22×C9—22no—
142C22×C9—22no—
143C22×C9—22no—
144C22×C9—42no—
145C22×C9—42no—
146C22×C9C2×C22⋊C411yescharacteristic
147C22×C9C4×D412yes—
148C22×C9C2×M1611yescharacteristic
149C22×C9C2×M1611yescharacteristic
150C22×C9#13112yes—
151C2×D9—22no—
152C2×D9—24no—
153C2×D9—41no—
154C2×D9—41no—
155C2×D9—42no—
156C4×C9—22no—
157C4×C9#12011yescharacteristic
158C4×C9#12112yes—
159C4×C9#12311yescharacteristic
160Dic9—22no—
161Dic9—41no—
162Dic9—41no—
163C22×D4—91no—
164C23×C4—91no—
165C23×C4C2×D911yescharacteristic
166C2×M16—184no—
167C2×M16—182no—
168C22×C8—92no—
169C22×C8C2×D912yes—
170C4×D4—182no—
171C4×D4—182no—
172C2×C4⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4—91no—
175C2×C42—91no—
176C22⋊C8—22no—
177C22⋊C8—184no—
178C23×C3—22no—
179C23×C3—22no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3(C2×D3)⋊C412yes—
183C23×C3C2×C4×D311yescharacteristic
184C22×D3—32no—
185C22×D3—62no—
186C22×D3—62no—
187C22×D3—61no—
188C22×D3—61no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—24no—
193C2×C3×C4(C2×D3)⋊C412yes—
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4D3×D412yes—
196C2×C3×C4#23712yes—
197C2×C3×C4C2×#6711yescharacteristic
198#67—68no—
199C2×Dic3—32no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—62no—
203C2×Dic3—62no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C4×D3—121no—
207C4×D3—121no—
208C4×D3—122no—
209C3×C8—42no—
210C3⋊C8—64no—
211C2×C9—42no—
212C2×C9#38611yescharacteristic
213C2×C9#40711yescharacteristic
214C2×C9#40811yescharacteristic
215C2×C9#43512yes—
216C2×C9#43612yes—
217D9—42no—
218C24—91no—
219C24C4×D911yescharacteristic
220C2×D4—182no—
221C2×D4—182no—
222C2×D4—182no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—91no—
228C22×C4—181no—
229C22×C4—182no—
230C22×C4—182no—
231C22×C4—181no—
232C22×C4C4×D911yescharacteristic
233C22×C4D3612yes—
234C22×C4#61112yes—
235C22×C4C22×D911yescharacteristic
236M16—188no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—94no—
241C2×C8—182no—
242C2×C8—182no—
243C4⋊C4—182no—
244C22⋊C4—182no—
245C22⋊C4—182no—
246C42—181no—
247C42—181no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—42no—
252C22×C3—42no—
253C22×C3#67⋊C412yes—
254C22×C3#90112yes—
255C22×C3D3×M1611yescharacteristic
256C22×C3D3×M1611yescharacteristic
257C22×C3C2×(C2×D3)⋊C411yescharacteristic
258C2×D3—62no—
259C2×D3—64no—
260C2×D3—121no—
261C2×D3—122no—
262C2×D3—121no—
263C3×C4—22no—
264C3×C4#88211yescharacteristic
265C3×C4#88611yescharacteristic
266C3×C4#93912yes—
267Dic3—62no—
268Dic3—121no—
269Dic3—121no—
270C9#187011yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23—92no—
276C23—181no—
277C23—182no—
278C23—182no—
279C23—181no—
280C23(C2×D9)⋊C412yes—
281C23C2×C4×D911yescharacteristic
282D4—188no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—92no—
288C2×C4—181no—
289C2×C4—181no—
290C2×C4—181no—
291C2×C4—181no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—362no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4(C2×D9)⋊C412yes—
298C2×C4C2×D3611yescharacteristic
299C2×C4D4×D912yes—
300C2×C4#369912yes—
301C2×C4C2×#61111yescharacteristic
302C8—42no—
303C8—184no—
304C2×C3—42no—
305C2×C3#472812yes—
306C2×C3#472912yes—
307C2×C3#495811yescharacteristic
308C2×C3#511011yescharacteristic
309C2×C3#512611yescharacteristic
310D3—122no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—182no—
317C22—184no—
318C22—361no—
319C22—361no—
320C22—362no—
321C22#611⋊C412yes—
322C22#6346412yes—
323C22M16×D911yescharacteristic
324C22M16×D911yescharacteristic
325C22C2×(C2×D9)⋊C411yescharacteristic
326C4—22no—
327C4—182no—
328C4—361no—
329C4—361no—
330C4#6344411yescharacteristic
331C4#6344811yescharacteristic
332C4#6350112yes—
333C3#6995311yescharacteristic
334C2—42no—
335C2—362no—
336C2#1058841012yes—
337C2#1058841112yes—
338C2#1058863811yescharacteristic
339C2#1058879111yescharacteristic
340C2#1058880811yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×C22⋊C8C2
socleC23×C3C2×C4×D3
prime radicalC22×#611C4
cosocleC22×C4×C9C23
hypercenterC2×C22⋊C8D9
hypocenterC9#1870
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#3667C2semidirect
3. C2×C9×C22⋊C8C2semidirect
4. C2×(C2×D9)⋊C8C2semidirect
5. #10588228C2semidirect
56. C2×C9⋊C8D4semidirect
83. C22×D9M16semidirect
100. C2×Dic9M16semidirect
109. C2×C22⋊C8D9semidirect
270. C9#1870semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C22×#36672
C2×C9×C22⋊C82
C2×(C2×D9)⋊C82
#105882282
#699533