Finite Group Databasebeta

← #11785304

Subgroups — #11785304

Order 1152.

468 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589624C211yesmaximal, characteristic
2C2×#63384C211yesmaximal, characteristic
3#10588802C211yesmaximal, characteristic, complemented
4C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
5C2×#63364C211yesmaximal, characteristic
6C9×#339C211yesmaximal, characteristic, complemented
7#10588208C211yesmaximal, characteristic, complemented
8#68770—31nomaximal
9C2×#3697C2211yescharacteristic
10C2×C9×M16C2211yescharacteristic
11C9×#117C2211yescharacteristic
12C2×C42×C9C2211yescharacteristic
13C2×Dic9⋊C4—21no—
14C2×C4×Dic9C2211yescharacteristic
15C2×C4×Dic9C2211yescharacteristic
16C2×#3667C2211yescharacteristic
17#63455C411yescharacteristic, complemented
18#63455C411yescharacteristic, complemented
19#63449C411yescharacteristic, complemented
20#63449C411yescharacteristic, complemented
21#611⋊C4—21no—
22#611⋊C4—21no—
23#63434—21no—
24C42×D9—21no—
25C9⋊#95—21no—
26#63384—22no—
27Dic9⋊C8—21no—
28Dic9⋊C8—21no—
29#63364—22no—
30#5522—31no—
31C2×#825—31no—
32#5118—31no—
33C4×Dic3⋊C4—31no—
34C2×#805—31no—
35C3×#339D311yescharacteristic
36#4532—31no—
37C22×C4×C9—21no—
38C22×C4×C9C2311yescharacteristic
39C2×#611—21no—
40C22×Dic9—21no—
41C22×Dic9D411yescharacteristic
42C22×Dic9D411yescharacteristic
43#3697—21no—
44#3697—21no—
45#3697D412yes—
46#3697Q812yes—
47C2×D36C2×C411yescharacteristic
48C2×C4×D9—21no—
49C2×C4×D9—21no—
50C2×C4×D9—21no—
51C2×Dic18C2×C411yescharacteristic
52C9×M16—21no—
53C9×M16—21no—
54C2×C8×C9—21no—
55C9×C4⋊C4C2×C411yescharacteristic
56C9×C4⋊C4C2×C411yescharacteristic
57C9×C22⋊C4—21no—
58C42×C9—21no—
59C42×C9—21no—
60C42×C9—21no—
61(C2×D9)⋊C4—21no—
62(C2×D9)⋊C4—21no—
63Dic9⋊C4—24no—
64Dic9⋊C4—21no—
65Dic9⋊C4—21no—
66C4×Dic9—21no—
67C4×Dic9—21no—
68C4×Dic9—21no—
69C4×Dic9—21no—
70C4×Dic9C2×C411yescharacteristic
71C4×Dic9C2×C411yescharacteristic
72C4×Dic9D411yescharacteristic
73C4×Dic9D411yescharacteristic
74#3667—21no—
75#3667—21no—
76C2×C9⋊C8—21no—
77#1806—91noSylow
78C2×#235—31no—
79C2×C3×M16C2×D311yescharacteristic
80C3×#117C2×D311yescharacteristic
81C2×C3×C42C2×D311yescharacteristic
82C2×Dic3⋊C4—61no—
83C2×C4×Dic3—31no—
84C2×C4×Dic3—31no—
85C2×#208—31no—
86#893—31no—
87#893—31no—
88#887—31no—
89#887—31no—
90#67⋊C4—61no—
91#67⋊C4—61no—
92#872—61no—
93C42×D3—61no—
94C3⋊#95—61no—
95#825—62no—
96Dic3⋊C8—61no—
97Dic3⋊C8—61no—
98#805—62no—
99C23×C9C2×D411yescharacteristic
100C22×D9—21no—
101C2×C4×C9—22no—
102C2×C4×C9—21no—
103C2×C4×C9—21no—
104C2×C4×C9—41no—
105C2×C4×C9—41no—
106C2×C4×C9C22×C411yescharacteristic
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×Q811yescharacteristic
110C2×C4×C9#4111yescharacteristic
111C2×C4×C9#4111yescharacteristic
112#611—22no—
113#611—22no—
114C2×Dic9—21no—
115C2×Dic9—22no—
116C2×Dic9—22no—
117C2×Dic9—41no—
118C2×Dic9—41no—
119C2×Dic9—41no—
120C2×Dic9C22⋊C411yescharacteristic
121C2×Dic9C22⋊C411yescharacteristic
122C2×Dic9C22⋊C411yescharacteristic
123C2×Dic9C22⋊C411yescharacteristic
124D36—21no—
125D36C4⋊C412yescomplemented
126C4×D9—22no—
127C4×D9—22no—
128C4×D9—42no—
129C4×D9—42no—
130Dic18—21no—
131Dic18C4⋊C412yescomplemented
132C8×C9—41no—
133C9⋊C8—41no—
134C4×#41—91no—
135#423—91no—
136C2×#104—91no—
137C2×#104—91no—
138C4×C4⋊C4—91no—
139#339—91no—
140#339D911yescharacteristic, complemented
141C22×C3×C4—21no—
142C22×C3×C4C22×D311yescharacteristic
143C2×#67—61no—
144C22×Dic3—31no—
145C22×Dic3—31no—
146C22×Dic3—61no—
147#235—32no—
148#235—32no—
149#235—61no—
150#235—61no—
151C2×D12—31no—
152C2×C4×D3—61no—
153C2×C4×D3—61no—
154C2×C4×D3—61no—
155C2×Dic6—31no—
156C3×M16—21no—
157C3×M16—21no—
158C2×C3×C8—21no—
159C3×C4⋊C4C4×D311yescharacteristic
160C3×C4⋊C4C4×D311yescharacteristic
161C3×C22⋊C4—21no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167Dic3⋊C4—61no—
168Dic3⋊C4—61no—
169Dic3⋊C4—64no—
170C4×Dic3—31no—
171C4×Dic3—31no—
172C4×Dic3—31no—
173C4×Dic3—31no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—61no—
177C4×Dic3—61no—
178#208—61no—
179#208—61no—
180C2×C3⋊C8—61no—
181C22×C9—21no—
182C22×C9—21no—
183C22×C9C2×C22⋊C411yescharacteristic
184C22×C9#12111yescharacteristic
185C22×C9C22⋊Q811yescharacteristic
186C2×D9—22no—
187C2×D9—41no—
188C2×D9—41no—
189C4×C9—42no—
190C4×C9—41no—
191C4×C9—41no—
192C4×C9C2×C4⋊C411yescharacteristic
193C4×C9#11711yescharacteristic
194C4×C9#12111yescharacteristic
195C4×C9C22⋊Q811yescharacteristic
196Dic9—22no—
197Dic9—21no—
198Dic9—21no—
199Dic9—21no—
200Dic9—42no—
201Dic9#10412yescomplemented
202C2×#41—91no—
203C2×M16—91no—
204C2×M16C2×D911yescharacteristic
205C4×Q8—91no—
206C4×Q8—91no—
207C4×D4—91no—
208C4×D4—91no—
209C4×D4—181no—
210C4×D4—181no—
211#117—181no—
212#117C2×D911yescharacteristic
213C2×C4⋊C4—181no—
214C2×C42—91no—
215C2×C42—91no—
216C2×C42—181no—
217C2×C42C2×D911yescharacteristic
218C4⋊C8—181no—
219C4⋊C8—181no—
220#104—182no—
221#104—182no—
222#95—181no—
223C23×C3D3×D411yescharacteristic
224C22×D3—61no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4C2×C4×D311yescharacteristic
231C2×C3×C4#23511yescharacteristic
232C2×C3×C4#23511yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4D3×Q811yescharacteristic
236#67—62no—
237#67—62no—
238C2×Dic3—31no—
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—62no—
243C2×Dic3—61no—
244C2×Dic3—62no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248D12—32no—
249D12—61no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—122no—
253C4×D3—122no—
254Dic6—32no—
255Dic6—61no—
256C3×C8—41no—
257C3⋊C8—121no—
258C2×C9—21no—
259C2×C9—21no—
260C2×C9#38011yescharacteristic
261C2×C9C2×#10411yescharacteristic
262C2×C9#42111yescharacteristic
263D9—42no—
264#41—92no—
265#41—92no—
266#41—181no—
267#41—181no—
268C2×Q8—91no—
269C2×D4—91no—
270C2×D4—181no—
271C22×C4—21no—
272C22×C4—91no—
273C22×C4—91no—
274C22×C4—181no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4C22×D911yescharacteristic
279M16—21no—
280M16—21no—
281M16—181no—
282M16—181no—
283C2×C8—21no—
284C2×C8—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C4⋊C4—184no—
288C4⋊C4C4×D911yescharacteristic
289C4⋊C4C4×D911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—181no—
292C22⋊C4—181no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—91no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—181no—
301C42—181no—
302C42—181no—
303C42—181no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3D3×C22⋊C411yescharacteristic
307C22×C3#88411yescharacteristic
308C22×C3#89611yescharacteristic
309C2×D3—62no—
310C2×D3—121no—
311C2×D3—121no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4#87211yescharacteristic
316C3×C4#88411yescharacteristic
317C3×C4D3×C4⋊C411yescharacteristic
318C3×C4#89611yescharacteristic
319Dic3—32no—
320Dic3—62no—
321Dic3—61no—
322Dic3—61no—
323Dic3—61no—
324Dic3—122no—
325C9#180611yescharacteristic, complemented, Sylow
326C23—181no—
327C23D4×D911yescharacteristic
328Q8—92no—
329Q8—181no—
330D4—92no—
331D4—182no—
332D4—182no—
333D4—181no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—91no—
340C2×C4—91no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—182no—
344C2×C4—181no—
345C2×C4—182no—
346C2×C4—182no—
347C2×C4—182no—
348C2×C4—362no—
349C2×C4—362no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4C2×C4×D911yescharacteristic
354C2×C4#369711yescharacteristic
355C2×C4#369711yescharacteristic
356C2×C4D4×D911yescharacteristic
357C2×C4D4×D911yescharacteristic
358C2×C4Q8×D911yescharacteristic
359C8—41no—
360C8—361no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3#466711yescharacteristic
364C2×C3D3×#10411yescharacteristic
365C2×C3#482111yescharacteristic
366D3—122no—
367C22—21no—
368C22—21no—
369C22—182no—
370C22—361no—
371C22—361no—
372C22C22⋊C4×D911yescharacteristic
373C22#6344611yescharacteristic
374C22#6345811yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—92no—
379C4—181no—
380C4—181no—
381C4—181no—
382C4—182no—
383C4—362no—
384C4#6343411yescharacteristic
385C4#6344611yescharacteristic
386C4C4⋊C4×D911yescharacteristic
387C4#6345811yescharacteristic
388C3#6877011yescharacteristic
389C2—21no—
390C2—21no—
391C2—362no—
392C2#1058834711yescharacteristic
393C2D9×#10411yescharacteristic
394C2#1058850111yescharacteristic
subgroupG/H
centerC2×C4D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#339C2
socleC22×C3D3×C22⋊C4
prime radicalC2×#3697C22
cosocleC22×C4×C9C23
hypercenter#339D9
hypocenterC9#1806
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
3. #10588802C2semidirect
4. C4×Dic9⋊C4C2semidirect
6. C9×#339C2semidirect
7. #10588208C2semidirect
17. #63455C4semidirect
18. #63455C4semidirect
19. #63449C4semidirect
20. #63449C4semidirect
125. D36C4⋊C4semidirect
131. Dic18C4⋊C4semidirect
140. #339D9semidirect
201. Dic9#104semidirect
325. C9#1806semidirect

Maximal subgroups

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

subgroupindex
#105896242
C2×#633842
#105888022
C4×Dic9⋊C42
C2×#633642
C9×#3392
#105882082
#687703