Finite Group Databasebeta

← #13048771

Subgroups — #13048771

Order 1296.

464 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#66431C211yesmaximal, characteristic, complemented
3C9×#638C211yesmaximal, characteristic, complemented
4C3×#6233C211yesmaximal, characteristic, complemented
5#10619899C211yesmaximal, characteristic, complemented
6#10619897C211yesmaximal, characteristic, complemented
7#10619896C211yesmaximal, characteristic, complemented
8#89049—31nomaximal
9#88668—31nomaximal
10D9×#67—31nomaximal
11C22×C32×C9C2211yescharacteristic, complemented
12C2×C9×C3⋊D3C2211yescharacteristic, complemented
13C2×C3×C3⋊D9—22no—
14C2×C3×C3⋊D9C2211yescharacteristic
15C2×C3×C3⋊D9C2211yescharacteristic, complemented
16C2×C3×C3⋊D9C2211yescharacteristic, complemented
17#66431—22no—
18C9×C3⋊Dic3C2211yescharacteristic, complemented
19C3×C3⋊Dic9C2211yescharacteristic, complemented
20C22×C3×C3⋊D3—31no—
21C2×#1113—31no—
22C3×#638—31no—
23C3×#638D311yescharacteristic
24#6295—31no—
25#6295—31no—
26#6294—31no—
27C22×C3⋊D9D311yescharacteristic, complemented
28C22×C3×D9—31no—
29C22×C3×D9—61no—
30C2×D3×D9—31no—
31C2×D3×D9—31no—
32#6233D311yescharacteristic, complemented
33C9×#67—31no—
34C9×#67—31no—
35C9×#67—61no—
36C3×#611—31no—
37C3×#611—61no—
38#6195—31no—
39#6194—31no—
40#6192—31no—
41#6192—31no—
42(C3⋊D9)⋊C4—31no—
43Dic3×D9—31no—
44C2×C32×C9—21no—
45C2×C32×C9C2311yescharacteristic
46C9×C3⋊D3—21no—
47C3×C3⋊D9—21no—
48C3×C3⋊D9—21no—
49C3×C3⋊D9D412yescomplemented
50#3811—91no—
51D3×#67—91no—
52D3×#67—91no—
53D4×D9—91no—
54C22×C33C2×D311yescharacteristic
55C2×C3×C3⋊D3—31no—
56C2×C3×C3⋊D3—31no—
57C2×C3×C3⋊D3—31no—
58C2×C3×C3⋊D3—62no—
59C2×C3×C3⋊D3C2×D311yescharacteristic
60#1113—62no—
61C3×C3⋊Dic3—31no—
62C3×C3⋊Dic3C2×D311yescharacteristic
63C22×C3×C9—21no—
64C22×C3×C9—21no—
65C22×C3×C9—21no—
66C22×C3×C9—41no—
67C22×C3×C9C2×D311yescharacteristic, complemented
68C22×C3×C9C2×D311yescharacteristic, complemented
69C2×C3⋊D9—22no—
70C2×C3⋊D9C2×D311yescharacteristic
71C2×C3⋊D9C2×D311yescharacteristic, complemented
72C2×C3⋊D9C2×D311yescharacteristic, complemented
73C2×D3×C9—31no—
74C2×D3×C9—31no—
75C2×D3×C9—61no—
76C2×C3×D9—31no—
77C2×C3×D9—31no—
78C2×C3×D9—31no—
79C2×C3×D9—62no—
80C2×C3×D9—61no—
81C2×C3×D9—61no—
82C2×C3×D9—64no—
83C2×C3×D9—61no—
84D3×D9—62no—
85D3×D9—62no—
86C3⋊Dic9C2×D311yescharacteristic, complemented
87C9×Dic3—31no—
88C9×Dic3—31no—
89C9×Dic3—61no—
90C3×Dic9—31no—
91C3×Dic9—61no—
92C32×C9C2×D411yescharacteristic, complemented, Sylow
93C22×C3⋊D3—31no—
94C22×C3×D3—91no—
95C22×C3×D3—91no—
96C22×C3×D3—181no—
97C2×D32—91no—
98C2×D32—91no—
99C2×D32—91no—
100#638—31no—
101#638D911yescharacteristic, complemented
102C3×#67—31no—
103C3×#67—31no—
104C3×#67—61no—
105C3×#67—91no—
106C3×#67—91no—
107C3×#67—181no—
108#626—91no—
109#626—91no—
110#626—91no—
111#626—91no—
112#625—91no—
113#625—91no—
114#624—91no—
115D3×Dic3—91no—
116D3×Dic3—91no—
117C22×D9—31no—
118C22×D9—61no—
119C22×D9—91no—
120D4×C9—91no—
121#611—31no—
122#611—61no—
123#611—91no—
124D36—91no—
125C4×D9—91no—
126C2×C33—21no—
127C2×C33C22×D311yescharacteristic
128C3×C3⋊D3—21no—
129C3×C3⋊D3—32no—
130C3×C3⋊D3—61no—
131C3×C3⋊D3—61no—
132C2×C3×C9—21no—
133C2×C3×C9—22no—
134C2×C3×C9—21no—
135C2×C3×C9—21no—
136C2×C3×C9—21no—
137C2×C3×C9—21no—
138C2×C3×C9—41no—
139C2×C3×C9—41no—
140C2×C3×C9—42no—
141C2×C3×C9—41no—
142C2×C3×C9C22×D311yescharacteristic
143C2×C3×C9C22×D311yescharacteristic
144C3⋊D9—21no—
145C3⋊D9—21no—
146C3⋊D9#6712yescomplemented
147D3×C9—61no—
148D3×C9—61no—
149D3×C9—121no—
150C3×D9—32no—
151C3×D9—62no—
152C3×D9—62no—
153C3×D9—61no—
154C3×D9—61no—
155C3×D9—121no—
156C2×#67—271no—
157D3×D4—271no—
158D3×D4—271no—
159C22×C32—21no—
160C22×C32—21no—
161C22×C32—21no—
162C22×C32—41no—
163C22×C32C2×D911yescharacteristic, complemented
164C22×C32D3211yescharacteristic
165C22×C32D3211yescharacteristic
166C2×C3⋊D3—31no—
167C2×C3⋊D3—31no—
168C2×C3⋊D3—31no—
169C2×C3⋊D3—62no—
170C2×C3⋊D3C2×D911yescharacteristic, complemented
171C2×C3×D3—31no—
172C2×C3×D3—31no—
173C2×C3×D3—61no—
174C2×C3×D3—91no—
175C2×C3×D3—91no—
176C2×C3×D3—91no—
177C2×C3×D3—91no—
178C2×C3×D3—91no—
179C2×C3×D3—91no—
180C2×C3×D3—181no—
181C2×C3×D3—181no—
182C2×C3×D3—181no—
183C2×C3×D3—182no—
184C2×C3×D3—182no—
185C2×C3×D3—184no—
186D32—182no—
187D32—182no—
188D32—182no—
189C3⋊Dic3—31no—
190C3⋊Dic3C2×D911yescharacteristic, complemented
191C3×Dic3—31no—
192C3×Dic3—31no—
193C3×Dic3—61no—
194C3×Dic3—91no—
195C3×Dic3—91no—
196C3×Dic3—181no—
197C22×C9—21no—
198C22×C9—21no—
199C22×C9—41no—
200C22×C9—91no—
201C22×C9D3211yescharacteristic, complemented
202C2×D9—31no—
203C2×D9—31no—
204C2×D9—31no—
205C2×D9—61no—
206C2×D9—61no—
207C2×D9—61no—
208C2×D9—62no—
209C2×D9—64no—
210C2×D9—182no—
211C4×C9—91no—
212Dic9—31no—
213Dic9—61no—
214C33D3×D411yescharacteristic
215C3×C9—21no—
216C3×C9—21no—
217C3×C9—21no—
218C3×C9—41no—
219C3×C9D3×D411yescharacteristic, complemented
220C3×C9C2×#6711yescharacteristic, complemented
221C23×C3—271no—
222C22×D3—91no—
223C22×D3—91no—
224C22×D3—181no—
225C22×D3—271no—
226C22×D3—271no—
227C22×D3—271no—
228C3×D4—91no—
229C3×D4—271no—
230#67—31no—
231#67—31no—
232#67—61no—
233#67—91no—
234#67—91no—
235#67—181no—
236#67—271no—
237#67—271no—
238#67—271no—
239#67—271no—
240C2×Dic3—271no—
241D12—271no—
242D12—271no—
243C4×D3—271no—
244C4×D3—271no—
245C2×C32—21no—
246C2×C32—22no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32—21no—
250C2×C32—21no—
251C2×C32—21no—
252C2×C32—41no—
253C2×C32—41no—
254C2×C32—41no—
255C2×C32—42no—
256C2×C32C22×D911yescharacteristic
257C2×C32C2×D3211yescharacteristic
258C2×C32C2×D3211yescharacteristic
259C3⋊D3—21no—
260C3⋊D3—32no—
261C3⋊D3—61no—
262C3⋊D3—61no—
263C3×D3—61no—
264C3×D3—61no—
265C3×D3—92no—
266C3×D3—92no—
267C3×D3—121no—
268C3×D3—182no—
269C3×D3—182no—
270C3×D3—181no—
271C3×D3—181no—
272C3×D3—181no—
273C3×D3—181no—
274C3×D3—361no—
275C2×C9—22no—
276C2×C9—21no—
277C2×C9—21no—
278C2×C9—21no—
279C2×C9—41no—
280C2×C9—42no—
281C2×C9—41no—
282C2×C9—181no—
283C2×C9C2×D3211yescharacteristic
284D9—32no—
285D9—62no—
286D9—62no—
287D9—61no—
288D9—61no—
289D9—121no—
290C2×D4—811noSylow
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—41no—
295C22×C3—91no—
296C22×C3—271no—
297C22×C3—271no—
298C22×C3—271no—
299C22×C3—542no—
300C22×C3D3×D911yescharacteristic, complemented
301C22×C3D3×D911yescharacteristic, complemented
302C22×C3#111311yescharacteristic
303C2×D3—31no—
304C2×D3—31no—
305C2×D3—61no—
306C2×D3—91no—
307C2×D3—91no—
308C2×D3—91no—
309C2×D3—91no—
310C2×D3—91no—
311C2×D3—91no—
312C2×D3—181no—
313C2×D3—181no—
314C2×D3—181no—
315C2×D3—182no—
316C2×D3—182no—
317C2×D3—184no—
318C2×D3—542no—
319C2×D3—542no—
320C2×D3—542no—
321C3×C4—91no—
322C3×C4—271no—
323Dic3—31no—
324Dic3—31no—
325Dic3—61no—
326Dic3—91no—
327Dic3—91no—
328Dic3—181no—
329C32—21no—
330C32—21no—
331C32—21no—
332C32—41no—
333C32D4×D911yescharacteristic, complemented
334C32D3×#6711yescharacteristic
335C32#381111yescharacteristic
336C9—21no—
337C9—21no—
338C9—41no—
339C9D3×#6711yescharacteristic, complemented
340C23—271no—
341C23—811no—
342D4—91no—
343D4—271no—
344D4—811no—
345D4—811no—
346C2×C4—811no—
347C2×C3—22no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—41no—
355C2×C3—41no—
356C2×C3—42no—
357C2×C3—41no—
358C2×C3—181no—
359C2×C3—272no—
360C2×C3—541no—
361C2×C3—541no—
362C2×C3C2×D3×D911yescharacteristic
363C2×C3C2×D3×D911yescharacteristic
364C2×C3C2×#111311yescharacteristic
365D3—61no—
366D3—61no—
367D3—92no—
368D3—92no—
369D3—121no—
370D3—182no—
371D3—182no—
372D3—181no—
373D3—181no—
374D3—181no—
375D3—181no—
376D3—361no—
377C22—91no—
378C22—271no—
379C22—271no—
380C22—271no—
381C22—542no—
382C22—1622no—
383C22#6643111yescharacteristic, complemented
384C4—91no—
385C4—271no—
386C3—21no—
387C3—21no—
388C3—21no—
389C3—41no—
390C3D9×#6711yescharacteristic, complemented
391C3#8866811yescharacteristic, complemented
392C3#8904911yescharacteristic
393C2—21no—
394C2—181no—
395C2—272no—
396C2—541no—
397C2—541no—
398C2C2×#6643111yescharacteristic
subgroupG/H
centerC2C2×#66431
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×#1113
FittingC22×C32×C9C22
socleC2×C33C22×D3
hypercenterC22#66431
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊D9C2semidirect
2. C2×#66431C2semidirect
3. C9×#638C2semidirect
4. C3×#6233C2semidirect
5. #10619899C2semidirect
6. #10619897C2semidirect
7. #10619896C2semidirect
11. C22×C32×C9C22semidirect
12. C2×C9×C3⋊D3C22semidirect
15. C2×C3×C3⋊D9C22semidirect
16. C2×C3×C3⋊D9C22semidirect
18. C9×C3⋊Dic3C22semidirect
19. C3×C3⋊Dic9C22semidirect
27. C22×C3⋊D9D3semidirect
32. #6233D3semidirect
49. C3×C3⋊D9D4semidirect
67. C22×C3×C9C2×D3semidirect
68. C22×C3×C9C2×D3semidirect
71. C2×C3⋊D9C2×D3semidirect
72. C2×C3⋊D9C2×D3semidirect
86. C3⋊Dic9C2×D3semidirect
92. C32×C9C2×D4semidirect
101. #638D9semidirect
146. C3⋊D9#67semidirect
163. C22×C32C2×D9semidirect
170. C2×C3⋊D3C2×D9semidirect
190. C3⋊Dic3C2×D9semidirect
201. C22×C9D32semidirect
219. C3×C9D3×D4semidirect
220. C3×C9C2×#67semidirect
300. C22×C3D3×D9semidirect
301. C22×C3D3×D9semidirect
333. C32D4×D9semidirect
339. C9D3×#67semidirect
383. C22#66431semidirect
390. C3D9×#67semidirect
391. C3#88668semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊D92
C2×#664312
C9×#6382
C3×#62332
#106198992
#106198972
#106198962
#890493
#886683
D9×#673