Finite Group Databasebeta

← #11775109

Subgroups — #11775109

Order 1152.

501 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#525C211yesmaximal, characteristic
2C2×C9⋊#95C211yesmaximal, characteristic, complemented
3#10588887C211yesmaximal, characteristic, complemented
4#10588215C212yesmaximal, complemented
5#10588214C212yesmaximal, complemented
6#71708—31nomaximal
7C2×C9×#41C411yescharacteristic, complemented
8C23×C4×C9C2211yescharacteristic
9C23×Dic9—21no—
10C9×#123—21no—
11C9×C22⋊Q8C411yescharacteristic, complemented
12C9×C22⋊Q8C2211yescharacteristic
13C9×#121C411yescharacteristic, complemented
14C9×#121C2211yescharacteristic
15C9×#120—21no—
16C4×D4×C9—21no—
17C4×D4×C9—21no—
18C9×#117C411yescharacteristic, complemented
19C2×#3667—21no—
20C9⋊#95—21no—
21C9⋊#95C2212yes—
22#63389—21no—
23#63389C2212yes—
24C3×#525D311yescharacteristic
25C2×C3⋊#95—31no—
26#5207—31no—
27#4538—32no—
28#4537—32no—
29C24×C9D411yescharacteristic
30C9×#41—42no—
31C2×Q8×C9C2×C411yescharacteristic, complemented
32C2×D4×C9—21no—
33C2×D4×C9—21no—
34C2×D4×C9—21no—
35C2×D4×C9C2×C411yescharacteristic, complemented
36C22×C4×C9—21no—
37C22×C4×C9—42no—
38C22×C4×C9C2×C411yescharacteristic
39C22×C4×C9C2×C411yescharacteristic
40C22×C4×C9D411yescharacteristic
41C22×C4×C9D411yescharacteristic
42C22×C4×C9D411yescharacteristic
43C22×C4×C9C2311yescharacteristic
44C22×Dic9—24no—
45C22×Dic9—22no—
46C22×Dic9—42no—
47C22×Dic9—42no—
48C9×C4⋊C4—21no—
49C9×C4⋊C4—21no—
50C9×C4⋊C4C2×C411yescharacteristic, complemented
51C9×C4⋊C4C2×C411yescharacteristic, complemented
52C9×C22⋊C4—21no—
53C9×C22⋊C4—21no—
54C9×C22⋊C4—21no—
55C9×C22⋊C4—21no—
56C9×C22⋊C4—21no—
57C42×C9—21no—
58#3667—42no—
59C2×C9⋊C8—22no—
60#1504—91noSylow
61C2×C3×#41Dic311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C23×Dic3—61no—
64C3×#123—21no—
65C3×C22⋊Q8Dic311yescharacteristic
66C3×C22⋊Q8C2×D311yescharacteristic
67C3×#121Dic311yescharacteristic
68C3×#121C2×D311yescharacteristic
69C3×#120—21no—
70C3×C4×D4—21no—
71C3×C4×D4—21no—
72C3×#117Dic311yescharacteristic
73C2×#208—61no—
74C3⋊#95—32no—
75C3⋊#95—61no—
76#830—32no—
77#830—61no—
78C23×C9—22no—
79C23×C9—22no—
80C23×C9—21no—
81C23×C9—21no—
82C23×C9—21no—
83C23×C9C22⋊C411yescharacteristic
84C23×C9C22⋊C411yescharacteristic
85C23×C9C2×D411yescharacteristic
86Q8×C9—41no—
87D4×C9—41no—
88D4×C9—42no—
89D4×C9—42no—
90D4×C9—41no—
91D4×C9—41no—
92C2×C4×C9—22no—
93C2×C4×C9—22no—
94C2×C4×C9—21no—
95C2×C4×C9—21no—
96C2×C4×C9—21no—
97C2×C4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9—41no—
100C2×C4×C9—41no—
101C2×C4×C9—42no—
102C2×C4×C9C22⋊C411yescharacteristic
103C2×C4×C9C22⋊C411yescharacteristic
104C2×C4×C9C22×C411yescharacteristic
105C2×C4×C9C2×D411yescharacteristic
106C2×Dic9—24no—
107C2×Dic9—48no—
108C2×Dic9—42no—
109C2×Dic9—42no—
110C9⋊C8—42no—
111#525D911yescharacteristic
112#407—91no—
113C2×#95—91no—
114#328—92no—
115#327—92no—
116C24×C3#6711yescharacteristic
117C3×#41—42no—
118C2×C3×Q8C2×Dic311yescharacteristic
119C2×C3×D4—21no—
120C2×C3×D4—21no—
121C2×C3×D4—21no—
122C2×C3×D4C2×Dic311yescharacteristic
123C22×C3×C4—21no—
124C22×C3×C4—42no—
125C22×C3×C4C2×Dic311yescharacteristic
126C22×C3×C4C2×Dic311yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—64no—
132C22×Dic3—62no—
133C22×Dic3—122no—
134C22×Dic3—122no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—21no—
137C3×C4⋊C4C2×Dic311yescharacteristic
138C3×C4⋊C4C2×Dic311yescharacteristic
139C3×C22⋊C4—21no—
140C3×C22⋊C4—21no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—21no—
143C3×C22⋊C4—21no—
144C3×C42—21no—
145#208—122no—
146C2×C3⋊C8—62no—
147C22×C9—24no—
148C22×C9—24no—
149C22×C9—21no—
150C22×C9—21no—
151C22×C9—21no—
152C22×C9—21no—
153C22×C9—21no—
154C22×C9—21no—
155C22×C9—41no—
156C22×C9—41no—
157C22×C9—41no—
158C22×C9#9912yes—
159C22×C9#10412yes—
160C22×C9C2×C22⋊C411yescharacteristic
161C22×C9AGL(1,ℤ/8)11yescharacteristic
162C22×C9#13711yescharacteristic
163C4×C9—21no—
164C4×C9—21no—
165C4×C9—21no—
166C4×C9—21no—
167C4×C9—41no—
168C4×C9—41no—
169C4×C9—41no—
170Dic9—44no—
171C2×#41Dic911yescharacteristic, complemented
172C23×C4—181no—
173C23×C4C2×D911yescharacteristic
174C2×M16—181no—
175#123—21no—
176C22⋊Q8Dic911yescharacteristic, complemented
177C22⋊Q8C2×D911yescharacteristic
178#121Dic911yescharacteristic, complemented
179#121C2×D911yescharacteristic
180#120—21no—
181C4×D4—21no—
182C4×D4—21no—
183#117Dic911yescharacteristic, complemented
184C22⋊C8—92no—
185C22⋊C8—181no—
186#95—92no—
187#95—181no—
188C23×C3—22no—
189C23×C3—22no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3#21711yescharacteristic
194C23×C3#21711yescharacteristic
195C23×C3C2×#6711yescharacteristic
196C3×Q8—41no—
197C3×D4—41no—
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—41no—
201C3×D4—41no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—42no—
212C2×C3×C4#21711yescharacteristic
213C2×C3×C4#21711yescharacteristic
214C2×C3×C4C22×Dic311yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—64no—
217C2×Dic3—128no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C3⋊C8—122no—
221C2×C9—21no—
222C2×C9—22no—
223C2×C9—22no—
224C2×C9—21no—
225C2×C9—81no—
226C2×C9C2×#9911yescharacteristic
227C2×C9#41711yescharacteristic
228C2×C9C2×#10411yescharacteristic
229C24#61111yescharacteristic
230#41—42no—
231C2×Q8C2×Dic911yescharacteristic, complemented
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C2×Dic911yescharacteristic, complemented
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—184no—
239C22×C4—182no—
240C22×C4—362no—
241C22×C4—362no—
242C22×C4C2×Dic911yescharacteristic
243C22×C4C2×Dic911yescharacteristic
244C22×C4#61111yescharacteristic
245C22×C4#61111yescharacteristic
246C22×C4#61111yescharacteristic
247C22×C4C22×D911yescharacteristic
248M16—362no—
249C2×C8—182no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4C2×Dic911yescharacteristic, complemented
253C4⋊C4C2×Dic911yescharacteristic, complemented
254C22⋊C4—21no—
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C42—21no—
260C22×C3—24no—
261C22×C3—24no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3#83412yes—
272C22×C3#83712yes—
273C22×C3#94911yescharacteristic
274C22×C3#95111yescharacteristic
275C22×C3C2×#21711yescharacteristic
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283Dic3—124no—
284C9#150411yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—21no—
290C23#367611yescharacteristic
291C23#367611yescharacteristic
292C23C2×#61111yescharacteristic
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297D4—42no—
298D4—42no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—184no—
310C2×C4—368no—
311C2×C4—362no—
312C2×C4—362no—
313C2×C4#367611yescharacteristic
314C2×C4#367611yescharacteristic
315C2×C4C22×Dic911yescharacteristic
316C2×C4C2×#61111yescharacteristic
317C8—362no—
318C2×C3—21no—
319C2×C3—22no—
320C2×C3—22no—
321C2×C3—21no—
322C2×C3—81no—
323C2×C3C2×#83411yescharacteristic
324C2×C3#523211yescharacteristic
325C2×C3C2×#83711yescharacteristic
326C22—24no—
327C22—24no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22#6339312yes—
338C22#6339612yes—
339C22#6351111yescharacteristic
340C22#6351211yescharacteristic
341C22C2×#367611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—364no—
350C3#7170811yescharacteristic
351C2—21no—
352C2—21no—
353C2—22no—
354C2—22no—
355C2—81no—
356C2C2×#6339311yescharacteristic
357C2C2×#6339611yescharacteristic
358C2#1058891611yescharacteristic
subgroupG/H
centerC22C2×#3676
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#525C2
socleC22×C3C2×#217
prime radicalC3×#525D3
cosocleC22×C4×C9C23
hypercenter#525D9
hypocenterC9#1504
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. C2×C9⋊#95C2semidirect
3. #10588887C2semidirect
4. #10588215C2semidirect
5. #10588214C2semidirect
7. C2×C9×#41C4semidirect
11. C9×C22⋊Q8C4semidirect
13. C9×#121C4semidirect
18. C9×#117C4semidirect
31. C2×Q8×C9C2×C4semidirect
35. C2×D4×C9C2×C4semidirect
50. C9×C4⋊C4C2×C4semidirect
51. C9×C4⋊C4C2×C4semidirect
171. C2×#41Dic9semidirect
176. C22⋊Q8Dic9semidirect
178. #121Dic9semidirect
183. #117Dic9semidirect
231. C2×Q8C2×Dic9semidirect
235. C2×D4C2×Dic9semidirect
252. C4⋊C4C2×Dic9semidirect
253. C4⋊C4C2×Dic9semidirect
284. C9#1504semidirect

Maximal subgroups

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

subgroupindex
C9×#5252
C2×C9⋊#952
#105888872
#105882152
#105882142
#717083