Finite Group Databasebeta

← #13139480

Subgroups — #13139480

Order 1728.

422 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#611C211yesmaximal, characteristic
2C2×C9×#208C211yesmaximal, characteristic, complemented
3C2×D9×C3⋊C8C211yesmaximal, characteristic, complemented
4#11720571C211yesmaximal, characteristic, complemented
5(C2×D9)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#11720274C211yesmaximal, characteristic, complemented
7Dic9⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10591147—31nomaximal
9#10588809—31nomaximal
10C22×C3×C4×C9C2211yescharacteristic
11C2×C3×#611C411yescharacteristic
12C2×C3×C4×D9C2211yescharacteristic
13C2×C3⋊(C9⋊C8)C2211yescharacteristic
14C2×C3⋊(C9⋊C8)C2211yescharacteristic
15C3×#3676C411yescharacteristic
16C3×(C2×D9)⋊C4C411yescharacteristic
17C3×Dic9⋊C4C411yescharacteristic
18C3×C4×Dic9C2211yescharacteristic
19C9×#208—22no—
20C2×C9×C3⋊C8C2211yescharacteristic
21C2×C9×C3⋊C8C2211yescharacteristic
22D9×C3⋊C8—22no—
23C3×C4×#67—31no—
24C2×C3×#208D311yescharacteristic
25C2×D3×C3⋊C8—31no—
26#63657—31no—
27Dic3⋊(C3⋊C8)—31no—
28(C2×D3)⋊(C3⋊C8)—31no—
29#63554—31no—
30C2×C9×M16—31no—
31C4×#611D311yescharacteristic
32C2×C8×D9—31no—
33#63389—31no—
34#63389—61no—
35(C2×D9)⋊C8—31no—
36#63375—31no—
37Dic9⋊C8—31no—
38C23×C3×C9C2×C411yescharacteristic
39C22×C3×D9C2×C411yescharacteristic
40C2×C3×C4×C9—21no—
41C2×C3×C4×C9—21no—
42C2×C3×C4×C9C2×C411yescharacteristic
43C2×C3×C4×C9C2311yescharacteristic
44C3×#611—22no—
45C2×C3×Dic9C2×C411yescharacteristic
46C2×C3×Dic9C2×C411yescharacteristic
47C2×C3×Dic9C2×C411yescharacteristic
48C3×C4×D9—21no—
49C3×C4×D9—21no—
50C3⋊(C9⋊C8)—21no—
51C3⋊(C9⋊C8)—21no—
52C9×C3⋊C8—21no—
53C9×C3⋊C8D412yescomplemented
54#5127—91no—
55#5011—91no—
56C22×C32×C4C2×D311yescharacteristic
57C2×C3×#67—31no—
58C2×C3×C4×D3—31no—
59C2×C3⋊(C3⋊C8)—31no—
60C2×C3⋊(C3⋊C8)—31no—
61C3×#217—31no—
62C3×(C2×D3)⋊C4—31no—
63C3×Dic3⋊C4—31no—
64C3×C4×Dic3—31no—
65C3×#208—22no—
66C2×C3×C3⋊C8C2×D311yescharacteristic
67C2×C3×C3⋊C8C2×D311yescharacteristic
68D3×C3⋊C8—62no—
69C22×C4×C9—21no—
70C22×C4×C9C2×D311yescharacteristic
71C2×#611Dic311yescharacteristic
72C2×C4×D9C2×D311yescharacteristic
73C9×M16—62no—
74C2×C8×C9—31no—
75C2×C8×C9—31no—
76#3676Dic311yescharacteristic
77(C2×D9)⋊C4Dic311yescharacteristic
78Dic9⋊C4Dic311yescharacteristic
79C4×Dic9C2×D311yescharacteristic
80C2×C9⋊C8—31no—
81C2×C9⋊C8—31no—
82C2×C9⋊C8—61no—
83C2×C9⋊C8—61no—
84C8×D9—62no—
85C22×C3×C9—21no—
86C22×C3×C9—21no—
87C22×C3×C9—21no—
88C22×C3×C9C22×C411yescharacteristic
89C2×C3×D9—21no—
90C2×C3×D9—21no—
91C2×C3×D9M1612yescomplemented
92C3×C4×C9—21no—
93C3×C4×C9C2×D411yescharacteristic
94C3×C4×C9#4111yescharacteristic
95C3×Dic9—21no—
96C3×Dic9—21no—
97C3×Dic9—21no—
98C2×C3×M16—31no—
99C3×C4×D4—91no—
100C4×#67—31no—
101C2×#208D911yescharacteristic, complemented
102C22×C3⋊C8—91no—
103C2×D3×C8—91no—
104#830—91no—
105#830—91no—
106#830—91no—
107#830—181no—
108(C2×D3)⋊C8—91no—
109#815—91no—
110Dic3⋊C8—91no—
111C4⋊(C3⋊C8)—91no—
112#803—91no—
113C23×C32C4×D311yescharacteristic
114C22×C3×D3—31no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C4×D311yescharacteristic
118C2×C32×C4C22×D311yescharacteristic
119C3×#67—62no—
120C2×C3×Dic3—31no—
121C2×C3×Dic3—31no—
122C2×C3×Dic3—31no—
123C3×C4×D3—61no—
124C3×C4×D3—61no—
125C23×C9—21no—
126C23×C9C2×Dic311yescharacteristic
127C22×D9C2×Dic311yescharacteristic
128C3⋊(C3⋊C8)—61no—
129C3⋊(C3⋊C8)—61no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8#6712yes—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—21no—
135C2×C4×C9—21no—
136C2×C4×C9—41no—
137C2×C4×C9—41no—
138C2×C4×C9C2×Dic311yescharacteristic
139C2×C4×C9C22×D311yescharacteristic
140#611—22no—
141C2×Dic9C2×Dic311yescharacteristic
142C2×Dic9C2×Dic311yescharacteristic
143C2×Dic9C2×Dic311yescharacteristic
144C4×D9—21no—
145C4×D9—21no—
146C8×C9—32no—
147C8×C9—61no—
148C9⋊C8—61no—
149C9⋊C8—61no—
150C9⋊C8—121no—
151C9⋊C8—121no—
152#435—271noSylow
153C2×C3×C9—41no—
154C2×C3×C9C4×D411yescharacteristic
155C2×C3×C9C2×M1611yescharacteristic
156C2×C3×C9#13111yescharacteristic
157C3×D9—22no—
158C2×C3×D4—91no—
159C22×C3×C4—21no—
160C22×C3×C4—91no—
161C22×C3×C4C2×D911yescharacteristic
162C22×C3×C4D3211yescharacteristic
163C2×#67—31no—
164C2×C4×D3—31no—
165C3×M16—62no—
166C2×C3×C8—31no—
167C2×C3×C8—31no—
168C3×C4⋊C4—91no—
169C3×C22⋊C4—91no—
170C3×C22⋊C4—91no—
171C3×C42—91no—
172#217—31no—
173(C2×D3)⋊C4—31no—
174Dic3⋊C4—31no—
175C4×Dic3—31no—
176#208—22no—
177C2×C3⋊C8—91no—
178C2×C3⋊C8—91no—
179C2×C3⋊C8—91no—
180C2×C3⋊C8—91no—
181C2×C3⋊C8—181no—
182C2×C3⋊C8—181no—
183C2×C3⋊C8—182no—
184C2×C3⋊C8C2×D911yescharacteristic
185C2×C3⋊C8C2×D911yescharacteristic
186D3×C8—182no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32C2×C4×D311yescharacteristic
191C2×C3×D3—32no—
192C2×C3×D3—61no—
193C2×C3×D3—61no—
194C32×C4—21no—
195C32×C4#23511yescharacteristic
196C32×C4C2×#6711yescharacteristic
197C3×Dic3—61no—
198C3×Dic3—61no—
199C3×Dic3—61no—
200C22×C9—22no—
201C22×C9—21no—
202C22×C9—21no—
203C22×C9—21no—
204C22×C9—21no—
205C22×C9—41no—
206C22×C9—41no—
207C22×C9C22×Dic311yescharacteristic
208C2×D9—21no—
209C2×D9—21no—
210C2×D9#20812yescomplemented
211C4×C9—21no—
212C4×C9—21no—
213C4×C9—21no—
214C4×C9—41no—
215C4×C9D3×D411yescharacteristic
216C4×C9#23711yescharacteristic
217Dic9—21no—
218Dic9—21no—
219Dic9—21no—
220C2×M16—31no—
221C22×C8—271no—
222C4×D4—91no—
223C4⋊C8—271no—
224C22⋊C8—271no—
225C22⋊C8—271no—
226#97—271no—
227C3×C9#43511yescharacteristic, complemented, Sylow
228C23×C3—21no—
229C23×C3—91no—
230C23×C3C4×D911yescharacteristic
231C23×C3D3×Dic311yescharacteristic
232C22×D3—31no—
233C3×D4—182no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—91no—
243C2×C3×C4—91no—
244C2×C3×C4—91no—
245C2×C3×C4—181no—
246C2×C3×C4—181no—
247C2×C3×C4C4×D911yescharacteristic
248C2×C3×C4C22×D911yescharacteristic
249C2×C3×C4D3×Dic311yescharacteristic
250C2×C3×C4C2×D3211yescharacteristic
251#67—62no—
252C2×Dic3—31no—
253C2×Dic3—31no—
254C2×Dic3—31no—
255C4×D3—61no—
256C4×D3—61no—
257C3×C8—32no—
258C3×C8—61no—
259C3⋊C8—21no—
260C3⋊C8—181no—
261C3⋊C8—181no—
262C3⋊C8—181no—
263C3⋊C8—181no—
264C3⋊C8—361no—
265C3⋊C8—361no—
266C3⋊C8#61112yescomplemented
267C2×C32—41no—
268C2×C32D3×M1611yescharacteristic
269C2×C32#90711yescharacteristic
270C2×C32C4×#6711yescharacteristic
271C3×D3—62no—
272C2×C9—21no—
273C2×C9—21no—
274C2×C9—21no—
275C2×C9—42no—
276C2×C9—41no—
277C2×C9C2×#20811yescharacteristic
278C2×C9D4×Dic311yescharacteristic
279C2×C9#94811yescharacteristic
280D9—22no—
281C2×D4—91no—
282C22×C4—91no—
283C22×C4D3×D911yescharacteristic
284M16—62no—
285C2×C8—31no—
286C2×C8—31no—
287C2×C8—271no—
288C2×C8—271no—
289C2×C8—542no—
290C4⋊C4—91no—
291C22⋊C4—91no—
292C22⋊C4—91no—
293C42—91no—
294C22×C3—22no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—92no—
305C22×C3—181no—
306C22×C3—181no—
307C22×C3C2×C4×D911yescharacteristic
308C22×C3C2×D3×Dic311yescharacteristic
309C2×D3—32no—
310C2×D3—61no—
311C2×D3—61no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—181no—
318C3×C4—181no—
319C3×C4—181no—
320C3×C4#369711yescharacteristic
321C3×C4C2×#61111yescharacteristic
322C3×C4#380411yescharacteristic
323C3×C4D3×#6711yescharacteristic
324Dic3—61no—
325Dic3—61no—
326Dic3—61no—
327C32#512711yescharacteristic
328C9—21no—
329C9#501111yescharacteristic, complemented
330C23—91no—
331C23Dic3×D911yescharacteristic
332D4—182no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—91no—
336C2×C4—91no—
337C2×C4—91no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4Dic3×D911yescharacteristic
341C2×C4C2×D3×D911yescharacteristic
342C8—32no—
343C8—61no—
344C8—541no—
345C8—541no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—42no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—182no—
353C2×C3M16×D911yescharacteristic
354C2×C3#6346911yescharacteristic
355C2×C3C4×#61111yescharacteristic
356C2×C3D3×#20811yescharacteristic
357C2×C3#6381511yescharacteristic
358C2×C3Dic3×#6711yescharacteristic
359D3—62no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—92no—
364C22—181no—
365C22—181no—
366C22C2×Dic3×D911yescharacteristic
367C4—21no—
368C4—181no—
369C4—181no—
370C4—181no—
371C4#8865811yescharacteristic
372C4D3×#61111yescharacteristic
373C3—21no—
374C3#1058880911yescharacteristic, complemented
375C3#1059114711yescharacteristic
376C2—41no—
377C2—182no—
378C2D9×#20811yescharacteristic
379C2#1172085911yescharacteristic
380C2Dic3×#61111yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC22×C3×C4×C9C22
socleC22×C32C2×C4×D3
prime radicalC2×C3×#611C4
cosocleC2×C3×C4×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#435
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C9×#208C2semidirect
3. C2×D9×C3⋊C8C2semidirect
4. #11720571C2semidirect
5. (C2×D9)⋊(C3⋊C8)C2semidirect
6. #11720274C2semidirect
7. Dic9⋊(C3⋊C8)C2semidirect
53. C9×C3⋊C8D4semidirect
91. C2×C3×D9M16semidirect
101. C2×#208D9semidirect
210. C2×D9#208semidirect
227. C3×C9#435semidirect
266. C3⋊C8#611semidirect
329. C9#5011semidirect
374. C3#10588809semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6112
C2×C9×#2082
C2×D9×C3⋊C82
#117205712
(C2×D9)⋊(C3⋊C8)2
#117202742
Dic9⋊(C3⋊C8)2
#105911473
#105888093