Finite Group Databasebeta

← C3×#10588562 #13142190

Subgroups — C3×#10588562 #13142190

Order 1728.

378 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#63457C211yesmaximal, characteristic
2C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
3C3×C9×#107C211yesmaximal, characteristic, complemented
4C3×#63380C211yesmaximal, characteristic, complemented
5C3×(C2×D9)⋊C8C211yesmaximal, characteristic, complemented
6C3×#63369C211yesmaximal, characteristic, complemented
7C3×#63366C211yesmaximal, characteristic, complemented
8C3×#4882—31nomaximal
9#10588562C311yesmaximal, characteristic, direct product factor
10C2×C3×D36—21no—
11C2×C3×D36C2211yescharacteristic
12C2×C3×C4×D9—21no—
13C2×C3×C4×D9C2211yescharacteristic
14C2×C3×C8×C9C2211yescharacteristic
15C3×C9×C4⋊C4C2211yescharacteristic
16C3×C9×C4⋊C4C2211yescharacteristic
17C3×(C2×D9)⋊C4—21no—
18C3×C4⋊Dic9C2211yescharacteristic
19C3×Dic9⋊C4—21no—
20C2×C3×C9⋊C8C2211yescharacteristic
21C3×#895—31no—
22C3×D3×C4⋊C4—31no—
23C32×#107D311yescharacteristic
24C3×#821—31no—
25C3×(C2×D3)⋊C8—31no—
26C3×#809—31no—
27C3×#807—31no—
28#63457C2×C311yescharacteristic
29C4⋊C4×D9C2×C311yescharacteristic, complemented
30C9×#107—21no—
31C9×#107C2×C311yescharacteristic, complemented
32#63380C2×C311yescharacteristic, complemented
33(C2×D9)⋊C8C2×C311yescharacteristic, complemented
34#63369C2×C311yescharacteristic, complemented
35#63366C2×C311yescharacteristic, complemented
36C22×C3×D9—21no—
37C22×C3×D9D411yescharacteristic
38C2×C3×C4×C9—21no—
39C2×C3×C4×C9—21no—
40C2×C3×C4×C9C2311yescharacteristic
41C2×C3×Dic9—21no—
42C2×C3×Dic9D411yescharacteristic
43C3×D36—21no—
44C3×D36—21no—
45C3×D36—42no—
46C3×C4×D9—21no—
47C3×C4×D9—21no—
48C3×C4×D9—42no—
49C3×C8×C9—21no—
50C3×C9⋊C8—21no—
51C3×#480—91no—
52#4882—31no—
53C2×C3×D12—31no—
54C2×C3×D12—61no—
55C2×C3×C4×D3—31no—
56C2×C3×C4×D3—61no—
57C2×C32×C8C2×D311yescharacteristic
58C32×C4⋊C4C2×D311yescharacteristic
59C32×C4⋊C4C2×D311yescharacteristic
60C3×(C2×D3)⋊C4—61no—
61C3×C4⋊Dic3—31no—
62C3×Dic3⋊C4—61no—
63C2×C3×C3⋊C8—31no—
64C2×D36—21no—
65C2×D36C22×C311yescharacteristic
66C2×C4×D9—21no—
67C2×C4×D9C22×C311yescharacteristic
68C2×C8×C9—21no—
69C2×C8×C9C22×C311yescharacteristic
70C9×C4⋊C4—21no—
71C9×C4⋊C4—21no—
72C9×C4⋊C4C22×C311yescharacteristic
73C9×C4⋊C4C22×C311yescharacteristic
74(C2×D9)⋊C4—21no—
75C4⋊Dic9C22×C311yescharacteristic
76Dic9⋊C4—21no—
77C2×C9⋊C8C22×C311yescharacteristic
78C22×C3×C9C2×D411yescharacteristic
79C2×C3×D9—21no—
80C2×C3×D9—21no—
81C2×C3×D9—41no—
82C2×C3×D9—41no—
83C2×C3×D9—41no—
84C2×C3×D9D812yes—
85C3×C4×C9—41no—
86C3×C4×C9—41no—
87C3×C4×C9#4111yescharacteristic
88C3×C4×C9#4111yescharacteristic
89C3×Dic9—21no—
90C3×Dic9—41no—
91C3×#121—91no—
92C2×C3×C4⋊C4—91no—
93#895—31no—
94D3×C4⋊C4—31no—
95C3×#107—21no—
96C3×#107—91no—
97C3×#107D911yescharacteristic, complemented
98C3×#107C3×D311yescharacteristic
99C3×#102—91no—
100C3×#102—91no—
101C3×C22⋊C8—91no—
102#821—31no—
103(C2×D3)⋊C8—31no—
104#809—31no—
105#807—31no—
106C22×C3×D3—31no—
107C22×C3×D3—61no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C22×D311yescharacteristic
111C2×C3×Dic3—31no—
112C2×C3×Dic3—61no—
113C3×D12—61no—
114C3×D12—61no—
115C3×D12—122no—
116C3×C4×D3—61no—
117C3×C4×D3—61no—
118C3×C4×D3—122no—
119C22×D9—21no—
120C22×D9C3×D411yescharacteristic
121C32×C8—21no—
122C3×C3⋊C8—61no—
123C2×C4×C9—21no—
124C2×C4×C9—21no—
125C2×C4×C9—21no—
126C2×C4×C9—41no—
127C2×C4×C9—41no—
128C2×C4×C9C23×C311yescharacteristic
129C2×Dic9—21no—
130C2×Dic9C3×D411yescharacteristic
131D36—21no—
132D36—21no—
133D36—42no—
134C4×D9—21no—
135C4×D9—21no—
136C4×D9—42no—
137C8×C9—22no—
138C8×C9—21no—
139C9⋊C8—21no—
140#480—91noSylow
141C2×C3×C9#12311yescharacteristic
142C2×C3×C9C2×D811yescharacteristic
143C2×C3×C9#13711yescharacteristic
144C3×D9—22no—
145C3×D9—81no—
146C2×C3×D4—91no—
147C2×C3×D4—181no—
148C22×C3×C4—91no—
149C22×C3×C4—181no—
150C2×D12—31no—
151C2×D12—61no—
152C2×C4×D3—31no—
153C2×C4×D3—61no—
154C2×C3×C8—21no—
155C2×C3×C8—91no—
156C2×C3×C8C2×D911yescharacteristic
157C2×C3×C8C2×C3×D311yescharacteristic
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—91no—
161C3×C4⋊C4—181no—
162C3×C4⋊C4C2×D911yescharacteristic
163C3×C4⋊C4C2×D911yescharacteristic
164C3×C4⋊C4C2×C3×D311yescharacteristic
165C3×C4⋊C4C2×C3×D311yescharacteristic
166C3×C22⋊C4—181no—
167(C2×D3)⋊C4—61no—
168C4⋊Dic3—31no—
169Dic3⋊C4—61no—
170C2×C3⋊C8—31no—
171C22×C32D3×D411yescharacteristic
172C2×C3×D3—32no—
173C2×C3×D3—61no—
174C2×C3×D3—61no—
175C2×C3×D3—121no—
176C2×C3×D3—121no—
177C2×C3×D3—121no—
178C32×C4—41no—
179C32×C4—41no—
180C32×C4#23511yescharacteristic
181C32×C4#23911yescharacteristic
182C3×Dic3—61no—
183C3×Dic3—121no—
184C22×C9—21no—
185C22×C9C2×C3×D411yescharacteristic
186C2×D9—21no—
187C2×D9—21no—
188C2×D9—41no—
189C2×D9—41no—
190C2×D9—41no—
191C2×D9C3×D812yes—
192C4×C9—21no—
193C4×C9—21no—
194C4×C9—41no—
195C4×C9—41no—
196C4×C9—81no—
197C4×C9—81no—
198C4×C9C3×#4111yescharacteristic
199C4×C9C3×#4111yescharacteristic
200Dic9—21no—
201Dic9—41no—
202#121—91no—
203C2×C4⋊C4—91no—
204#107—91no—
205#107C3×D911yescharacteristic, complemented
206#102—91no—
207#102—91no—
208C22⋊C8—91no—
209C3×C9#48011yescharacteristic, complemented, Sylow
210C23×C3—91no—
211C23×C3—181no—
212C22×D3—31no—
213C22×D3—61no—
214C3×D4—181no—
215C3×D4—181no—
216C3×D4—362no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—91no—
225C2×C3×C4—181no—
226C2×C3×C4—181no—
227C2×C3×C4—181no—
228C2×C3×C4—362no—
229C2×C3×C4C22×D911yescharacteristic
230C2×C3×C4C22×C3×D311yescharacteristic
231C2×Dic3—31no—
232C2×Dic3—61no—
233D12—61no—
234D12—61no—
235D12—122no—
236C4×D3—61no—
237C4×D3—61no—
238C4×D3—122no—
239C3×C8—22no—
240C3×C8—21no—
241C3×C8—21no—
242C3×C8—181no—
243C3⋊C8—61no—
244C2×C32#89411yescharacteristic
245C2×C32D3×D811yescharacteristic
246C2×C32#91811yescharacteristic
247C3×D3—62no—
248C3×D3—241no—
249C2×C9—21no—
250C2×C9—21no—
251C2×C9—21no—
252C2×C9C3×#12311yescharacteristic
253C2×C9C2×C3×D811yescharacteristic
254C2×C9C3×#13711yescharacteristic
255D9—22no—
256D9—81no—
257C2×D4—91no—
258C2×D4—181no—
259C22×C4—91no—
260C22×C4—181no—
261C2×C8—91no—
262C2×C8C2×C3×D911yescharacteristic
263C4⋊C4—91no—
264C4⋊C4—181no—
265C4⋊C4C2×C3×D911yescharacteristic
266C4⋊C4C2×C3×D911yescharacteristic
267C22⋊C4—181no—
268C22×C3—21no—
269C22×C3—92no—
270C22×C3—181no—
271C22×C3—181no—
272C22×C3—361no—
273C22×C3—361no—
274C22×C3—361no—
275C22×C3D4×D911yescharacteristic
276C22×C3C3×D3×D411yescharacteristic
277C2×D3—32no—
278C2×D3—61no—
279C2×D3—61no—
280C2×D3—121no—
281C2×D3—121no—
282C2×D3—121no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—81no—
290C3×C4—81no—
291C3×C4—181no—
292C3×C4—361no—
293C3×C4#369711yescharacteristic
294C3×C4#370111yescharacteristic
295C3×C4C3×#23511yescharacteristic
296C3×C4C3×#23911yescharacteristic
297Dic3—61no—
298Dic3—121no—
299C32#488211yescharacteristic
300C9—21no—
301C9C3×#48011yescharacteristic, complemented
302C23—91no—
303C23—181no—
304D4—181no—
305D4—181no—
306D4—362no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—91no—
310C2×C4—181no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—362no—
314C2×C4C22×C3×D911yescharacteristic
315C8—21no—
316C8—181no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—182no—
321C2×C3—721no—
322C2×C3#6345611yescharacteristic
323C2×C3D8×D911yescharacteristic
324C2×C3#6348011yescharacteristic
325C2×C3C3×#89411yescharacteristic
326C2×C3C3×D3×D811yescharacteristic
327C2×C3C3×#91811yescharacteristic
328D3—62no—
329D3—241no—
330C22—92no—
331C22—181no—
332C22—181no—
333C22—361no—
334C22—361no—
335C22—361no—
336C22C3×D4×D911yescharacteristic
337C4—41no—
338C4—41no—
339C4—181no—
340C4—361no—
341C4C3×#369711yescharacteristic
342C4C3×#370111yescharacteristic
343C3—21no—
344C3#1058856211yescharacteristic, direct product factor
345C3C3×#488211yescharacteristic
346C2—182no—
347C2—721no—
348C2C3×#6345611yescharacteristic
349C2C3×D8×D911yescharacteristic
350C2C3×#6348011yescharacteristic
subgroupG/H
centerC22×C3D4×D9
commutator, cosocleC2×C4×C9C23×C3
FrattiniC2×C3×C4C22×C3×D3
FittingC3×C9×#107C2
socleC22×C32D3×D4
prime radicalC3×#63457C2
hypercenterC3×#107D9
hypocenterC9C3×#480
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#107

Complements

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

NH ≅ G/Ntype
2. C3×C4⋊C4×D9C2semidirect
3. C3×C9×#107C2semidirect
4. C3×#63380C2semidirect
5. C3×(C2×D9)⋊C8C2semidirect
6. C3×#63369C2semidirect
7. C3×#63366C2semidirect
9. #10588562C3direct (N × H)
29. C4⋊C4×D9C2×C3semidirect
31. C9×#107C2×C3semidirect
32. #63380C2×C3semidirect
33. (C2×D9)⋊C8C2×C3semidirect
34. #63369C2×C3semidirect
35. #63366C2×C3semidirect
97. C3×#107D9semidirect
205. #107C3×D9semidirect
209. C3×C9#480semidirect
301. C9C3×#480semidirect
344. C3#10588562direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#634572
C3×C4⋊C4×D92
C3×C9×#1072
C3×#633802
C3×(C2×D9)⋊C82
C3×#633692
C3×#633662
C3×#48823
#105885623