Finite Group Databasebeta

← #13139347

Subgroups — #13139347

Order 1728.

338 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63488C211yesmaximal, characteristic
2#11720571C211yesmaximal, characteristic
3C9×#830C211yesmaximal, characteristic
4#11720274C211yesmaximal, characteristic, complemented
5Dic9⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6Dic9⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3⋊C8×Dic9C211yesmaximal, characteristic, complemented
8#10591056—31nomaximal
9#10588400—31nomaximal
10C22×C3×C4×C9C2211yescharacteristic
11C2×C3⋊(C9⋊C8)C2211yescharacteristic
12C2×C3⋊(C9⋊C8)C2211yescharacteristic
13C3×#3676C411yescharacteristic
14C3×#3676C411yescharacteristic
15C3×C4⋊Dic9C411yescharacteristic
16C3×C4⋊Dic9C411yescharacteristic
17C3×C4×Dic9C2211yescharacteristic
18C3×C4×Dic9C2211yescharacteristic
19C2×C9×C3⋊C8C2211yescharacteristic
20C2×C9×C3⋊C8C2211yescharacteristic
21C3×#926—31no—
22#63657—31no—
23C3×#830D311yescharacteristic
24Dic3⋊(C3⋊C8)—31no—
25Dic3⋊(C3⋊C8)—31no—
26#63554—31no—
27Dic3×C3⋊C8—31no—
28#63488D311yescharacteristic
29C9×C22⋊C8—31no—
30#63389—31no—
31#63389—61no—
32#63375—31no—
33Dic9⋊C8—31no—
34Dic9⋊C8—31no—
35C8×Dic9—31no—
36C23×C3×C9C2×C411yescharacteristic
37C2×C3×C4×C9—21no—
38C2×C3×C4×C9—21no—
39C2×C3×C4×C9C2×C411yescharacteristic
40C2×C3×C4×C9C2311yescharacteristic
41C2×C3×Dic9C2×C411yescharacteristic
42C2×C3×Dic9C2×C411yescharacteristic
43C2×C3×Dic9C2×C411yescharacteristic
44C2×C3×Dic9C2×C411yescharacteristic
45C3⋊(C9⋊C8)—21no—
46C3⋊(C9⋊C8)—21no—
47C9×C3⋊C8—21no—
48C9×C3⋊C8—21no—
49#5000—91no—
50#4720—91no—
51C22×C32×C4C2×D311yescharacteristic
52C2×C3⋊(C3⋊C8)—31no—
53C2×C3⋊(C3⋊C8)—31no—
54C3×#217—31no—
55C3×#217—31no—
56C3×C4⋊Dic3—31no—
57C3×C4⋊Dic3—31no—
58C3×C4×Dic3—31no—
59C3×C4×Dic3—31no—
60C2×C3×C3⋊C8C2×D311yescharacteristic
61C2×C3×C3⋊C8C2×D311yescharacteristic
62C22×C4×C9—21no—
63C22×C4×C9C2×D311yescharacteristic
64C2×C8×C9—31no—
65C2×C8×C9—31no—
66#3676Dic311yescharacteristic
67#3676Dic311yescharacteristic
68C4⋊Dic9Dic311yescharacteristic
69C4⋊Dic9Dic311yescharacteristic
70C4×Dic9C2×D311yescharacteristic
71C4×Dic9C2×D311yescharacteristic
72C2×C9⋊C8—31no—
73C2×C9⋊C8—31no—
74C2×C9⋊C8—61no—
75C2×C9⋊C8—61no—
76C22×C3×C9—21no—
77C22×C3×C9—21no—
78C22×C3×C9—21no—
79C22×C3×C9C22×C411yescharacteristic
80C3×C4×C9—21no—
81C3×C4×C9#4111yescharacteristic
82C3×C4×C9#4111yescharacteristic
83C3×Dic9—21no—
84C3×Dic9—21no—
85C3×Dic9—21no—
86C3×Dic9—21no—
87C3×#117—91no—
88#926—31no—
89C3×C22⋊C8—31no—
90#830—91no—
91#830—91no—
92#830—181no—
93#830D911yescharacteristic
94#815—91no—
95Dic3⋊C8—91no—
96Dic3⋊C8—91no—
97C8×Dic3—91no—
98C4⋊(C3⋊C8)—91no—
99C4⋊(C3⋊C8)—91no—
100#803—91no—
101C4×C3⋊C8—91no—
102C23×C32C4×D311yescharacteristic
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4C4×D311yescharacteristic
106C2×C32×C4C22×D311yescharacteristic
107C2×C3×Dic3—31no—
108C2×C3×Dic3—31no—
109C2×C3×Dic3—31no—
110C2×C3×Dic3—31no—
111C23×C9—21no—
112C23×C9C2×Dic311yescharacteristic
113C3⋊(C3⋊C8)—61no—
114C3⋊(C3⋊C8)—61no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—21no—
117C2×C4×C9—21no—
118C2×C4×C9—21no—
119C2×C4×C9—21no—
120C2×C4×C9—21no—
121C2×C4×C9—41no—
122C2×C4×C9—41no—
123C2×C4×C9C2×Dic311yescharacteristic
124C2×C4×C9C22×D311yescharacteristic
125C2×Dic9C2×Dic311yescharacteristic
126C2×Dic9C2×Dic311yescharacteristic
127C2×Dic9C2×Dic311yescharacteristic
128C2×Dic9C2×Dic311yescharacteristic
129C8×C9—61no—
130C8×C9—61no—
131C9⋊C8—61no—
132C9⋊C8—61no—
133C9⋊C8—121no—
134C9⋊C8—121no—
135#433—271noSylow
136C2×C3×C9—41no—
137C2×C3×C9#11711yescharacteristic
138C2×C3×C9#13111yescharacteristic
139C2×C3×C9#13111yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4C2×D911yescharacteristic
142C22×C3×C4D3211yescharacteristic
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C3×C4⋊C4—91no—
146C3×C4⋊C4—91no—
147C3×C22⋊C4—91no—
148C3×C22⋊C4—91no—
149C3×C42—91no—
150C3×C42—91no—
151#217—31no—
152#217—31no—
153C4⋊Dic3—31no—
154C4⋊Dic3—31no—
155C4×Dic3—31no—
156C4×Dic3—31no—
157C2×C3⋊C8—91no—
158C2×C3⋊C8—91no—
159C2×C3⋊C8—91no—
160C2×C3⋊C8—91no—
161C2×C3⋊C8—181no—
162C2×C3⋊C8—181no—
163C2×C3⋊C8C2×D911yescharacteristic
164C2×C3⋊C8C2×D911yescharacteristic
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32C2×C4×D311yescharacteristic
169C32×C4—21no—
170C32×C4#23711yescharacteristic
171C32×C4#23711yescharacteristic
172C3×Dic3—61no—
173C3×Dic3—61no—
174C3×Dic3—61no—
175C3×Dic3—61no—
176C22×C9—22no—
177C22×C9—21no—
178C22×C9—21no—
179C22×C9—21no—
180C22×C9—21no—
181C22×C9—41no—
182C22×C9—41no—
183C22×C9C22×Dic311yescharacteristic
184C4×C9—21no—
185C4×C9—21no—
186C4×C9—21no—
187C4×C9—41no—
188C4×C9#23511yescharacteristic
189C4×C9#23511yescharacteristic
190Dic9—21no—
191Dic9—21no—
192Dic9—21no—
193Dic9—21no—
194#117—91no—
195C4⋊C8—271no—
196C4⋊C8—271no—
197C22⋊C8—31no—
198C22⋊C8—271no—
199#97—271no—
200C4×C8—271no—
201C3×C9#43311yescharacteristic, complemented, Sylow
202C23×C3—21no—
203C23×C3C4×D911yescharacteristic
204C23×C3D3×Dic311yescharacteristic
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—91no—
214C2×C3×C4—91no—
215C2×C3×C4—91no—
216C2×C3×C4—91no—
217C2×C3×C4C4×D911yescharacteristic
218C2×C3×C4C22×D911yescharacteristic
219C2×C3×C4D3×Dic311yescharacteristic
220C2×C3×C4C2×D3211yescharacteristic
221C2×Dic3—31no—
222C2×Dic3—31no—
223C2×Dic3—31no—
224C2×Dic3—31no—
225C3×C8—61no—
226C3×C8—61no—
227C3⋊C8—21no—
228C3⋊C8—21no—
229C3⋊C8—181no—
230C3⋊C8—181no—
231C3⋊C8—181no—
232C3⋊C8—181no—
233C3⋊C8—361no—
234C3⋊C8—361no—
235C2×C32—41no—
236C2×C32#87711yescharacteristic
237C2×C32#90111yescharacteristic
238C2×C32#90711yescharacteristic
239C2×C9—21no—
240C2×C9—21no—
241C2×C9—21no—
242C2×C9—42no—
243C2×C9—41no—
244C2×C9#92611yescharacteristic
245C2×C9#94811yescharacteristic
246C2×C9#94811yescharacteristic
247C22×C4D3×D911yescharacteristic
248C2×C8—31no—
249C2×C8—31no—
250C2×C8—271no—
251C2×C8—271no—
252C4⋊C4—91no—
253C4⋊C4—91no—
254C22⋊C4—91no—
255C22⋊C4—91no—
256C42—91no—
257C42—91no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3C2×C4×D911yescharacteristic
269C22×C3C2×D3×Dic311yescharacteristic
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—41no—
275C3×C4—181no—
276C3×C4—181no—
277C3×C4—181no—
278C3×C4—181no—
279C3×C4#369911yescharacteristic
280C3×C4#369911yescharacteristic
281C3×C4#380411yescharacteristic
282C3×C4#380411yescharacteristic
283Dic3—61no—
284Dic3—61no—
285Dic3—61no—
286Dic3—61no—
287C32#472011yescharacteristic
288C9—21no—
289C9#500011yescharacteristic, complemented
290C23Dic3×D911yescharacteristic
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—91no—
294C2×C4—91no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4Dic3×D911yescharacteristic
298C2×C4C2×D3×D911yescharacteristic
299C8—61no—
300C8—61no—
301C8—541no—
302C8—541no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—42no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3#6343911yescharacteristic
310C2×C3#6346411yescharacteristic
311C2×C3#6346911yescharacteristic
312C2×C3#6381411yescharacteristic
313C2×C3#6381511yescharacteristic
314C2×C3#6395511yescharacteristic
315C22—21no—
316C22—21no—
317C22—21no—
318C22C2×Dic3×D911yescharacteristic
319C4—21no—
320C4—181no—
321C4—181no—
322C4—181no—
323C4—181no—
324C4#8866211yescharacteristic
325C4#8866211yescharacteristic
326C3—21no—
327C3#1058840011yescharacteristic, complemented
328C3#1059105611yescharacteristic
329C2—41no—
330C2#1172085811yescharacteristic
331C2#1172085911yescharacteristic
332C2#1172124511yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC22×C3×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC22×C3×C4×C9C22
socleC22×C32C2×C4×D3
prime radicalC23×C32C4×D3
cosocleC2×C3×C4×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9#433
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
4. #11720274C2semidirect
5. Dic9⋊(C3⋊C8)C2semidirect
6. Dic9⋊(C3⋊C8)C2semidirect
7. C3⋊C8×Dic9C2semidirect
201. C3×C9#433semidirect
289. C9#5000semidirect
327. C3#10588400semidirect

Maximal subgroups

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

subgroupindex
C3×#634882
#117205712
C9×#8302
#117202742
Dic9⋊(C3⋊C8)2
C3⋊C8×Dic92
#105910563
#105884003