Finite Group Databasebeta

← #11805357

Subgroups — #11805357

Order 1152.

756 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63434C211yesmaximal, characteristic
2C4×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3#10588670C212yesmaximal
4#10588656C212yesmaximal, complemented
5#10588620C212yesmaximal
6#10588617C211yesmaximal, characteristic, complemented
7C4×Dic9⋊C4C212yesmaximal, complemented
8#10588347C211yesmaximal, characteristic
9#10588346C211yesmaximal, characteristic
10#10588331C211yesmaximal, characteristic, complemented
11#10588329C211yesmaximal, characteristic, complemented
12#73635—31nomaximal
13C22×C4×D9C2211yescharacteristic
14C2×C9×C4⋊C4C2212yes—
15C2×C42×C9C2212yes—
16C2×C42×C9C2211yescharacteristic
17C2×(C2×D9)⋊C4C2212yes—
18C2×(C2×D9)⋊C4C2212yes—
19C2×(C2×D9)⋊C4C2211yescharacteristic
20C2×(C2×D9)⋊C4C2211yescharacteristic
21C2×Dic9⋊C4C2212yes—
22C2×Dic9⋊C4C2212yes—
23C2×Dic9⋊C4C2211yescharacteristic
24C2×Dic9⋊C4C2211yescharacteristic
25C2×C4×Dic9C2212yes—
26C2×C4×Dic9C2212yes—
27C2×C4×Dic9C2211yescharacteristic
28#63434C418yescomplemented
29C9×#95C2211yescharacteristic
30C9×#95C2211yescharacteristic
31C9⋊#95C2211yescharacteristic
32C9⋊#95C2211yescharacteristic
33C9⋊#95C2212yes—
34C9⋊#95C2212yes—
35C9⋊#95C2212yes—
36C9⋊#95C2212yes—
37C2×#872—31no—
38C3×C4×C4⋊C4D311yescharacteristic
39#4990—32no—
40#4976—32no—
41#4940—32no—
42#4937—31no—
43C4×Dic3⋊C4—32no—
44#4667—31no—
45#4666—31no—
46#4651—31no—
47#4649—31no—
48C23×D9C2311yescharacteristic
49C22×C4×C9C2312yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2311yescharacteristic
52C22×C4×C9C2311yescharacteristic
53C22×C4×C9C2312yes—
54C22×Dic9C2312yes—
55C22×Dic9C2312yes—
56C22×Dic9C2311yescharacteristic
57C22×Dic9C2311yescharacteristic
58C22×Dic9C2311yescharacteristic
59C2×C4×D9—24no—
60C2×C4×D9C2×C414yes—
61C9×C4⋊C4—24no—
62C42×C9—42no—
63C42×C9C2×C414yes—
64(C2×D9)⋊C4—24no—
65(C2×D9)⋊C4—42no—
66(C2×D9)⋊C4C2×C414yes—
67(C2×D9)⋊C4C2×C414yes—
68Dic9⋊C4—24no—
69Dic9⋊C4—24no—
70Dic9⋊C4C2×C414yes—
71Dic9⋊C4C2×C414yes—
72C4×Dic9—24no—
73C4×Dic9—42no—
74C4×Dic9C2×C414yes—
75#2347—91noSylow
76C22×C4×D3—31no—
77C2×C3×C4⋊C4C2×D312yes—
78C2×C3×C42C2×D312yes—
79C2×C3×C42C2×D311yescharacteristic
80C2×(C2×D3)⋊C4—31no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—32no—
83C2×(C2×D3)⋊C4—32no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—32no—
87C2×Dic3⋊C4—32no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—32no—
90C2×C4×Dic3—32no—
91#872—38no—
92C3×#95C2×D311yescharacteristic
93C3×#95C2×D311yescharacteristic
94C3⋊#95—31no—
95C3⋊#95—31no—
96C3⋊#95—32no—
97C3⋊#95—32no—
98C3⋊#95—32no—
99C3⋊#95—32no—
100C23×C9C2411yescharacteristic
101C22×D9—22no—
102C22×D9—22no—
103C22×D9—21no—
104C22×D9—21no—
105C22×D9C22×C412yes—
106C2×C4×C9—22no—
107C2×C4×C9—22no—
108C2×C4×C9—22no—
109C2×C4×C9—22no—
110C2×C4×C9—21no—
111C2×C4×C9—21no—
112C2×C4×C9—22no—
113C2×C4×C9—22no—
114C2×C4×C9—22no—
115C2×C4×C9C22×C412yes—
116C2×C4×C9C22×C412yes—
117C2×C4×C9C22×C412yes—
118C2×C4×C9#4114yes—
119C2×Dic9—22no—
120C2×Dic9—21no—
121C2×Dic9—21no—
122C2×Dic9—22no—
123C2×Dic9—22no—
124C2×Dic9—22no—
125C2×Dic9—22no—
126C2×Dic9—22no—
127C2×Dic9—22no—
128C2×Dic9C22×C412yes—
129C2×Dic9C22×C412yes—
130C2×Dic9C22×C412yes—
131C2×Dic9#4114yes—
132C4×D9—28no—
133C2×#117—91no—
134#389—92no—
135#388—92no—
136#388—92no—
137#383—91no—
138#383—91no—
139#380—91no—
140C4×C4⋊C4—92no—
141C4×C4⋊C4—91no—
142C4×C4⋊C4D911yescharacteristic, complemented
143C4×C22⋊C4—91no—
144C23×D3—31no—
145C22×C3×C4C22×D312yes—
146C22×C3×C4C22×D311yescharacteristic
147C22×C3×C4C22×D311yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D312yes—
150C22×Dic3—31no—
151C22×Dic3—31no—
152C22×Dic3—31no—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C2×C4×D3—34no—
156C2×C4×D3—64no—
157C3×C4⋊C4—24no—
158C3×C42—42no—
159C3×C42C4×D314yes—
160(C2×D3)⋊C4—34no—
161(C2×D3)⋊C4—34no—
162(C2×D3)⋊C4—64no—
163(C2×D3)⋊C4—122no—
164Dic3⋊C4—34no—
165Dic3⋊C4—34no—
166Dic3⋊C4—64no—
167Dic3⋊C4—64no—
168C4×Dic3—34no—
169C4×Dic3—64no—
170C4×Dic3—122no—
171C22×C9C23×C411yescharacteristic
172C22×C9C2×#4112yes—
173C22×C9C2×#4112yes—
174C22×C9H(5,𝔽2)11yescharacteristic
175C22×C92−1+411yescharacteristic
176C2×D9—22no—
177C2×D9—22no—
178C2×D9—22no—
179C2×D9—42no—
180C2×D9—42no—
181C4×C9—22no—
182C4×C9—22no—
183C4×C9—22no—
184C4×C9—24no—
185C4×C9—42no—
186Dic9—22no—
187Dic9—22no—
188Dic9—42no—
189Dic9—42no—
190Dic9#11714yes—
191C23×C4—91no—
192#117—98no—
193C2×C4⋊C4—91no—
194C2×C4⋊C4—91no—
195C2×C4⋊C4—92no—
196C2×C4⋊C4—92no—
197C2×C4⋊C4C2×D912yes—
198C2×C22⋊C4—91no—
199C2×C22⋊C4—91no—
200C2×C22⋊C4—92no—
201C2×C22⋊C4—92no—
202C2×C42—91no—
203C2×C42—92no—
204C2×C42—92no—
205C2×C42C2×D912yes—
206C2×C42C2×D911yescharacteristic
207#95—91no—
208#95—91no—
209#95—92no—
210#95—92no—
211#95—92no—
212#95—92no—
213#95C2×D911yescharacteristic
214#95C2×D911yescharacteristic
215C23×C3C23×D311yescharacteristic
216C22×D3—32no—
217C22×D3—62no—
218C22×D3—61no—
219C22×D3—61no—
220C22×D3—62no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4C2×C4×D312yes—
231C2×C3×C4C2×C4×D312yes—
232C2×C3×C4C2×C4×D312yes—
233C2×C3×C4#23514yes—
234C2×Dic3—32no—
235C2×Dic3—34no—
236C2×Dic3—32no—
237C2×Dic3—32no—
238C2×Dic3—62no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C4×D3—68no—
248C2×C9C2×#11711yescharacteristic
249C2×C9C4×#4111yescharacteristic
250C2×C9#52011yescharacteristic
251C2×C9#55312yes—
252C2×C9#55612yes—
253D9—42no—
254C24—91no—
255C22×C4—91no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—94no—
259C22×C4—92no—
260C22×C4—92no—
261C22×C4—184no—
262C22×C4C22×D912yes—
263C22×C4C22×D911yescharacteristic
264C22×C4C22×D911yescharacteristic
265C22×C4C22×D911yescharacteristic
266C22×C4C22×D912yes—
267C4⋊C4—24no—
268C4⋊C4—94no—
269C4⋊C4—94no—
270C4⋊C4—184no—
271C4⋊C4—184no—
272C22⋊C4—94no—
273C22⋊C4—94no—
274C22⋊C4—184no—
275C22⋊C4—362no—
276C42—42no—
277C42—94no—
278C42—184no—
279C42—362no—
280C42C4×D914yes—
281C22×C3C22×C4×D311yescharacteristic
282C22×C3C2×#23512yes—
283C22×C3#100411yescharacteristic
284C22×C3#100711yescharacteristic
285C22×C3D3×#4112yes—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—122no—
290C2×D3—122no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—24no—
295C3×C4—42no—
296Dic3—34no—
297Dic3—62no—
298Dic3—62no—
299Dic3—122no—
300Dic3—122no—
301C9#234711yescharacteristic, complemented, Sylow
302C23—92no—
303C23—182no—
304C23—181no—
305C23—181no—
306C23—182no—
307C23C23×D911yescharacteristic
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—92no—
318C2×C4—94no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—188no—
322C2×C4—182no—
323C2×C4—181no—
324C2×C4—181no—
325C2×C4—182no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4C2×C4×D912yes—
332C2×C4C2×C4×D912yes—
333C2×C4C2×C4×D912yes—
334C2×C4#369714yes—
335C2×C3C4×#23511yescharacteristic
336C2×C3#550411yescharacteristic
337C2×C3D3×#11711yescharacteristic
338C2×C3#554012yes—
339C2×C3#556812yes—
340D3—122no—
341C22—182no—
342C22—182no—
343C22—182no—
344C22—362no—
345C22—362no—
346C22C22×C4×D911yescharacteristic
347C22C2×#369712yes—
348C22#6371011yescharacteristic
349C22#6371311yescharacteristic
350C22#41×D912yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—42no—
356C4—94no—
357C4—182no—
358C4—182no—
359C4—362no—
360C4—362no—
361C3#7363511yescharacteristic
362C2—362no—
363C2C4×#369711yescharacteristic
364C2#1058960611yescharacteristic
365C2D9×#11711yescharacteristic
366C2#1058964212yes—
367C2#1058967012yes—
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC4×C9×C4⋊C4C2
prime radicalC23×D9C23
cosocleC23×C9C24
hypercenterC4×C4⋊C4D9
hypocenterC9#2347
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C9×C4⋊C4C2semidirect
4. #10588656C2semidirect
6. #10588617C2semidirect
7. C4×Dic9⋊C4C2semidirect
10. #10588331C2semidirect
11. #10588329C2semidirect
28. #63434C4semidirect
142. C4×C4⋊C4D9semidirect
301. C9#2347semidirect

Maximal subgroups

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

subgroupindex
C2×#634342
C4×C9×C4⋊C42
#105886702
#105886562
#105886202
#105886172
C4×Dic9⋊C42
#105883472
#105883462
#105883312
#105883292
#736353