Finite Group Databasebeta

← #11787132

Subgroups — #11787132

Order 1152.

648 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
1C23×C8×C9C211yesmaximal, characteristic, complemented
2C2×C4×#611C211yesmaximal, characteristic
3C2×#63389C211yesmaximal, characteristic, complemented
4C2×(C2×D9)⋊C8C212yesmaximal, complemented
5#10588228C212yesmaximal, complemented
6#71975—31nomaximal
7C23×C4×C9C2211yescharacteristic
8C22×#611C411yescharacteristic
9C22×C4×D9C2211yescharacteristic
10C22×C8×C9—22no—
11C22×C8×C9—24no—
12C22×C8×C9C2212yes—
13C2×#3676C411yescharacteristic
14C4×#611—22no—
15C4×#611—22no—
16C2×(C2×D9)⋊C4C411yescharacteristic
17C2×Dic9⋊C4C411yescharacteristic
18C2×C4×Dic9C2211yescharacteristic
19C22×C9⋊C8C2212yes—
20#63389—22no—
21(C2×D9)⋊C8—24no—
22C23×C3×C8D311yescharacteristic
23C2×C4×#67—31no—
24C2×#830—31no—
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×#611C814yescomplemented
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—28no—
46C2×C8×C9—22no—
47C2×C8×C9—22no—
48C2×C8×C9D414yescomplemented
49#3676—22no—
50(C2×D9)⋊C4—22no—
51Dic9⋊C4—22no—
52C4×Dic9—21no—
53C4×Dic9—21no—
54C2×C9⋊C8—22no—
55C2×C9⋊C8—22no—
56C2×C9⋊C8—22no—
57#1869—91noSylow
58C23×C3×C4C2×D311yescharacteristic
59C22×#67—31no—
60C22×C4×D3—31no—
61C22×C3×C8—22no—
62C22×C3×C8—24no—
63C22×C3×C8C2×D312yes—
64C2×#217—31no—
65C4×#67—62no—
66C4×#67—62no—
67C2×(C2×D3)⋊C4—31no—
68C2×Dic3⋊C4—31no—
69C2×C4×Dic3—31no—
70C22×C3⋊C8—32no—
71#830—62no—
72(C2×D3)⋊C8—64no—
73C23×C9—22no—
74C23×C9—22no—
75C23×C9C22⋊C412yes—
76C23×C9C2×C812yes—
77C23×C9M1612yes—
78C23×C9C22×C411yescharacteristic
79C22×D9—21no—
80C22×D9—22no—
81C22×D9—21no—
82C22×D9—22no—
83C22×D9C2×C812yescomplemented
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×Dic9C2×C812yescomplemented
101C4×D9—41no—
102C4×D9—42no—
103C4×D9—41no—
104C8×C9—24no—
105C9⋊C8—42no—
106C23×C8D911yescharacteristic, complemented
107C2×C4×D4—91no—
108C2×C22⋊C8—91no—
109C2×C22⋊C8—92no—
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—34no—
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—28no—
130C2×C3×C8—22no—
131C2×C3×C8—22no—
132C2×C3×C8#6714yes—
133#217—62no—
134(C2×D3)⋊C4—62no—
135Dic3⋊C4—62no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—62no—
141C22×C9—22no—
142C22×C9—22no—
143C22×C9—24no—
144C22×C9—24no—
145C22×C9C22⋊C814yescomplemented
146C22×C9C2×C22⋊C411yescharacteristic
147C22×C9C4×D412yes—
148C22×C9C22×C811yescharacteristic
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
166C22×C8—22no—
167C22×C8—24no—
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—182no—
177C22⋊C8—184no—
178C23×C3—22no—
179C23×C3—22no—
180C23×C3D3×C812yes—
181C23×C3ΓL(1,𝔽25)12yes—
182C23×C3(C2×D3)⋊C412yes—
183C23×C3C2×C4×D311yescharacteristic
184C22×D3—32no—
185C22×D3—61no—
186C22×D3—62no—
187C22×D3—61no—
188C22×D3—62no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—24no—
192C2×C3×C4—22no—
193C2×C3×C4(C2×D3)⋊C412yes—
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4#23512yes—
196C2×C3×C4C2×#6711yescharacteristic
197C2×C3×C4C2×#6712yes—
198#67—68no—
199C2×Dic3—32no—
200C2×Dic3—61no—
201C2×Dic3—61no—
202C2×Dic3—62no—
203C2×Dic3—61no—
204C2×Dic3—61no—
205C2×Dic3—62no—
206C4×D3—121no—
207C4×D3—122no—
208C4×D3—121no—
209C3×C8—24no—
210C3⋊C8—122no—
211C2×C9—24no—
212C2×C9#38611yescharacteristic
213C2×C9C2×C22⋊C811yescharacteristic
214C2×C9#40811yescharacteristic
215C2×C9C8×D412yes—
216C2×C9#43512yes—
217D9—42no—
218C24—91no—
219C24C4×D911yescharacteristic
220C2×D4—94no—
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
236C2×C8—28no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—182no—
240C2×C8—182no—
241C2×C8—182no—
242C2×C8#61114yescomplemented
243C4⋊C4—182no—
244C22⋊C4—182no—
245C22⋊C4—182no—
246C42—181no—
247C42—181no—
248C22×C3—22no—
249C22×C3—24no—
250C22×C3—22no—
251C22×C3—24no—
252C22×C3(C2×D3)⋊C814yes—
253C22×C3C2×D3×C811yescharacteristic
254C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
255C22×C3#90112yes—
256C22×C3C2×(C2×D3)⋊C411yescharacteristic
257C22×C3C4×#6712yes—
258C2×D3—62no—
259C2×D3—64no—
260C2×D3—121no—
261C2×D3—121no—
262C2×D3—122no—
263C3×C4—22no—
264C3×C4#92911yescharacteristic
265C3×C4#93012yes—
266C3×C4#95311yescharacteristic
267Dic3—62no—
268Dic3—121no—
269Dic3—121no—
270C9#186911yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—92no—
274C23—181no—
275C23—182no—
276C23—181no—
277C23—182no—
278C23C8×D912yes—
279C23#366312yes—
280C23(C2×D9)⋊C412yes—
281C23C2×C4×D911yescharacteristic
282D4—188no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—24no—
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—361no—
295C2×C4—362no—
296C2×C4—361no—
297C2×C4(C2×D9)⋊C412yes—
298C2×C4C2×D3611yescharacteristic
299C2×C4#369712yes—
300C2×C4C2×#61111yescharacteristic
301C2×C4C2×#61112yes—
302C8—24no—
303C8—362no—
304C2×C3—24no—
305C2×C3C2×(C2×D3)⋊C811yescharacteristic
306C2×C3C8×#6712yes—
307C2×C3#511011yescharacteristic
308C2×C3#511112yes—
309C2×C3#521311yescharacteristic
310D3—122no—
311C22—24no—
312C22—22no—
313C22—24no—
314C22—22no—
315C22—182no—
316C22—184no—
317C22—361no—
318C22—362no—
319C22—361no—
320C22(C2×D9)⋊C814yescomplemented
321C22C2×C8×D911yescharacteristic
322C22C2×#366311yescharacteristic
323C22#6346412yes—
324C22C2×(C2×D9)⋊C411yescharacteristic
325C22C4×#61112yes—
326C4—22no—
327C4—182no—
328C4—361no—
329C4—361no—
330C4#6349111yescharacteristic
331C4#6349212yes—
332C4#6351511yescharacteristic
333C3#7197511yescharacteristic
334C2—24no—
335C2—362no—
336C2C2×(C2×D9)⋊C811yescharacteristic
337C2C8×#61112yes—
338C2#1058879111yescharacteristic
339C2#1058879212yes—
340C2#1058889311yescharacteristic
subgroupG/H
centerC22×C4C22×D9
commutatorC22×C9C22×C8
FrattiniC22×C3×C4C22×D3
FittingC23×C8×C9C2
socleC23×C3C2×C4×D3
prime radicalC22×#611C4
cosocleC22×C4×C9C23
hypercenterC23×C8D9
hypocenterC9#1869
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. C23×C8×C9C2semidirect
3. C2×#63389C2semidirect
4. C2×(C2×D9)⋊C8C2semidirect
5. #10588228C2semidirect
37. C2×#611C8semidirect
48. C2×C8×C9D4semidirect
83. C22×D9C2×C8semidirect
100. C2×Dic9C2×C8semidirect
106. C23×C8D9semidirect
145. C22×C9C22⋊C8semidirect
242. C2×C8#611semidirect
270. C9#1869semidirect
320. C22(C2×D9)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C23×C8×C92
C2×C4×#6112
C2×#633892
C2×(C2×D9)⋊C82
#105882282
#719753