Finite Group Databasebeta

← #13159508

Subgroups — #13159508

Order 1728.

884 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D3×C3⋊Dic3C211yesmaximal, characteristic
2C8×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C3×#63641C211yesmaximal, characteristic, complemented
4C32×(C2×D3)⋊C8C211yesmaximal, characteristic
5#11722051C211yesmaximal, characteristic, complemented
6(C2×D3)⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
7#11722018C211yesmaximal, characteristic, complemented
8#10592417—31nomaximal
9#10590656—34nomaximal
10C2×C32×C4×D3C2211yescharacteristic
11C2×D3×C3⋊Dic3C411yescharacteristic
12C2×D3×C3⋊Dic3C411yescharacteristic
13C2×C33×C8C2211yescharacteristic
14C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C3×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C32×C3⋊C8C2211yescharacteristic
19Dic3×C3⋊Dic3C411yescharacteristic
20Dic3×C3⋊Dic3C411yescharacteristic
21C2×C4×C3⋊Dic3—31no—
22C4×D3×Dic3—34no—
23C32×C22⋊C8—31no—
24#63657—31no—
25#63641—31no—
26#63641D311yescharacteristic, complemented
27C8×C3⋊Dic3—31no—
28C8×C3⋊Dic3—31no—
29C8×C3⋊Dic3—34no—
30C8×C3⋊Dic3—64no—
31C3×(C2×D3)⋊C8D314yes—
32C3×Dic3⋊C8—34no—
33Dic3⋊(C3⋊C8)—34no—
34(C2×D3)⋊(C3⋊C8)—34no—
35#63553—34no—
36C22×C32×D3C2×C411yescharacteristic
37C2×C33×C4C2311yescharacteristic
38C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
39C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic
40C2×C3×C3⋊Dic3C2×C411yescharacteristic
41C2×C3×C3⋊Dic3C2×C411yescharacteristic
42C2×C32×Dic3C2×C411yescharacteristic
43C32×C4×D3—21no—
44C32×C4×D3—21no—
45D3×C3⋊Dic3—22no—
46D3×C3⋊Dic3C814yescomplemented
47C33×C8—21no—
48C3⋊(C3⋊(C3⋊C8))—21no—
49C3×C3⋊(C3⋊C8)—21no—
50C32×C3⋊C8—21no—
51#4833—91no—
52#4718—94no—
53C22×C32×C4—31no—
54C22×C3⋊Dic3—31no—
55C22×C3⋊Dic3—31no—
56C2×C3×C4×D3C2×D314yes—
57C2×D3×Dic3—34no—
58C2×D3×Dic3—34no—
59C2×C32×C8—24no—
60C2×C32×C8—31no—
61C2×C32×C8C2×D314yes—
62C2×C32×C8C2×D311yescharacteristic
63C4×C3⋊Dic3—31no—
64C4×C3⋊Dic3—34no—
65C4×C3⋊Dic3—31no—
66C4×C3⋊Dic3—31no—
67C4×C3⋊Dic3—64no—
68C4×C3⋊Dic3C2×D311yescharacteristic
69C2×C3⋊(C3⋊C8)—31no—
70C2×C3⋊(C3⋊C8)—34no—
71C2×C3⋊(C3⋊C8)—64no—
72C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
73C3×C4×Dic3—34no—
74C2×C3×C3⋊C8—34no—
75C2×C3×C3⋊C8C2×D314yes—
76Dic32—34no—
77Dic32—34no—
78C22×C33C22×C411yescharacteristic
79C2×C32×D3—21no—
80C2×C32×D3—21no—
81C2×C32×D3C2×C812yes—
82C33×C4#4111yescharacteristic
83C33×C4#4111yescharacteristic
84C3⋊(C3⋊Dic3)C2×C812yes—
85C3⋊(C3⋊Dic3)M1612yes—
86C3×C3⋊Dic3—21no—
87C3×C3⋊Dic3C2×C812yes—
88C32×Dic3—21no—
89C2×C4×Dic3—94no—
90C42×D3—91no—
91C3×C4⋊C8—91no—
92C3×C22⋊C8—34no—
93#830—94no—
94(C2×D3)⋊C8—91no—
95(C2×D3)⋊C8C3⋊D311yescharacteristic
96Dic3⋊C8—34no—
97Dic3⋊C8—94no—
98C8×Dic3—94no—
99C8×Dic3—94no—
100C8×Dic3—91no—
101C8×Dic3—91no—
102C8×Dic3—184no—
103C4⋊(C3⋊C8)—91no—
104C23×C32—31no—
105C22×C3×D3C4×D314yes—
106C2×C32×C4—24no—
107C2×C32×C4—31no—
108C2×C32×C4—61no—
109C2×C32×C4—61no—
110C2×C32×C4C22×D314yes—
111C2×C32×C4C22×D311yescharacteristic
112C2×C3⋊Dic3—31no—
113C2×C3⋊Dic3—31no—
114C2×C3⋊Dic3—34no—
115C2×C3⋊Dic3—34no—
116C2×C3⋊Dic3—34no—
117C2×C3⋊Dic3—64no—
118C2×C3⋊Dic3—64no—
119C2×C3⋊Dic3—62no—
120C2×C3⋊Dic3C4×D311yescharacteristic
121C2×C3⋊Dic3C4×D311yescharacteristic
122C2×C3×Dic3—34no—
123C2×C3×Dic3—34no—
124C2×C3×Dic3C4×D314yes—
125C3×C4×D3—24no—
126C3×C4×D3—24no—
127D3×Dic3—316no—
128D3×Dic3—68no—
129C32×C8—28no—
130C32×C8—24no—
131C32×C8—21no—
132C32×C8—61no—
133C3⋊(C3⋊C8)—21no—
134C3⋊(C3⋊C8)—68no—
135C3⋊(C3⋊C8)—64no—
136C3⋊(C3⋊C8)—61no—
137C3×C3⋊C8—24no—
138C3×C3⋊C8—64no—
139#431—271noSylow
140C2×C33#11711yescharacteristic
141C2×C33C22×C811yescharacteristic
142C2×C33C2×M1611yescharacteristic
143C32×D3—22no—
144C22×C3×C4—34no—
145C22×Dic3—94no—
146C22×Dic3—94no—
147C2×C4×D3—91no—
148C2×C4×D3—91no—
149C2×C4×D3C2×C3⋊D311yescharacteristic
150C2×C3×C8—24no—
151C2×C3×C8—34no—
152C2×C3×C8—91no—
153C2×C3×C8D3214yes—
154C2×C3×C8C2×C3⋊D311yescharacteristic
155C3×C42—91no—
156C4×Dic3—34no—
157C4×Dic3—94no—
158C4×Dic3—94no—
159C4×Dic3—94no—
160C4×Dic3—91no—
161C4×Dic3—91no—
162C4×Dic3—91no—
163C4×Dic3—184no—
164C2×C3⋊C8—34no—
165C2×C3⋊C8—94no—
166C2×C3⋊C8—91no—
167C2×C3⋊C8—184no—
168C2×C3⋊C8C2×C3⋊D311yescharacteristic
169C22×C32—24no—
170C22×C32—32no—
171C22×C32—61no—
172C22×C32—61no—
173C22×C32C2×C4×D314yes—
174C22×C32C2×C4×D311yescharacteristic
175C2×C3×D3—24no—
176C2×C3×D3—24no—
177C2×C3×D3D3×C818yes—
178C32×C4—24no—
179C32×C4—24no—
180C32×C4—61no—
181C32×C4#23714yes—
182C32×C4#23714yes—
183C32×C4#23711yescharacteristic
184C32×C4#23911yescharacteristic
185C3⋊Dic3—21no—
186C3⋊Dic3—32no—
187C3⋊Dic3—32no—
188C3⋊Dic3—38no—
189C3⋊Dic3—38no—
190C3⋊Dic3—68no—
191C3⋊Dic3—68no—
192C3⋊Dic3D3×C812yes—
193C3×Dic3—24no—
194C3×Dic3—38no—
195C3×Dic3—64no—
196C2×C42—271no—
197C4⋊C8—91no—
198C4⋊C8—271no—
199C22⋊C8—31no—
200C22⋊C8—271no—
201C4×C8—271no—
202C4×C8—271no—
203C33#43111yescharacteristic, complemented, Sylow
204C23×C3—34no—
205C22×D3C4×C3⋊D311yescharacteristic
206C2×C3×C4—24no—
207C2×C3×C4—34no—
208C2×C3×C4—64no—
209C2×C3×C4—64no—
210C2×C3×C4—91no—
211C2×C3×C4—91no—
212C2×C3×C4C2×D3214yes—
213C2×C3×C4C22×C3⋊D311yescharacteristic
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—916no—
217C2×Dic3—94no—
218C2×Dic3—94no—
219C2×Dic3—91no—
220C2×Dic3—91no—
221C2×Dic3—184no—
222C2×Dic3—184no—
223C2×Dic3—188no—
224C2×Dic3C4×C3⋊D311yescharacteristic
225C4×D3—21no—
226C4×D3—21no—
227C4×D3—94no—
228C4×D3—182no—
229C3×C8—28no—
230C3×C8—24no—
231C3×C8—21no—
232C3×C8—64no—
233C3×C8—181no—
234C3⋊C8—21no—
235C3⋊C8—64no—
236C3⋊C8—188no—
237C3⋊C8—184no—
238C3⋊C8—181no—
239C2×C32—24no—
240C2×C32—24no—
241C2×C32—24no—
242C2×C32—62no—
243C2×C32#87714yes—
244C2×C32#89211yescharacteristic
245C2×C32C2×D3×C814yes—
246C2×C32C2×D3×C811yescharacteristic
247C2×C32D3×M1614yes—
248C2×C32D3×M1611yescharacteristic
249C3×D3—28no—
250C22×C4—31no—
251C22×C4—271no—
252C22×C4—271no—
253C2×C8—31no—
254C2×C8—91no—
255C2×C8—271no—
256C2×C8D3×C3⋊D311yescharacteristic
257C42—91no—
258C42—271no—
259C42—271no—
260C42—271no—
261C22×C3—24no—
262C22×C3—38no—
263C22×C3—64no—
264C22×C3—64no—
265C22×C3C4×D3214yes—
266C22×C3C2×C4×C3⋊D311yescharacteristic
267C2×D3—21no—
268C2×D3—21no—
269C2×D3C8×C3⋊D312yes—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—64no—
273C3×C4—92no—
274C3×C4—181no—
275C3×C4#379614yes—
276C3×C4#380514yes—
277C3×C4#383011yescharacteristic
278C3×C4#383011yescharacteristic
279Dic3—21no—
280Dic3—38no—
281Dic3—64no—
282Dic3—98no—
283Dic3—98no—
284Dic3—92no—
285Dic3—92no—
286Dic3—188no—
287Dic3—188no—
288C32—24no—
289C32#471814yescomplemented
290C32#483311yescharacteristic, complemented
291C23—31no—
292C2×C4—31no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—91no—
296C2×C4—91no—
297C2×C4—274no—
298C2×C4—271no—
299C2×C4—271no—
300C2×C4—542no—
301C2×C4C2×D3×C3⋊D311yescharacteristic
302C8—21no—
303C8—61no—
304C8—181no—
305C8—541no—
306C2×C3—24no—
307C2×C3—24no—
308C2×C3—24no—
309C2×C3—68no—
310C2×C3D32×C814yes—
311C2×C3#6379114yes—
312C2×C3#6387814yes—
313C2×C3#6408611yescharacteristic
314C2×C3C2×C8×C3⋊D311yescharacteristic
315C2×C3M16×C3⋊D311yescharacteristic
316D3—22no—
317C22—32no—
318C22—61no—
319C22—61no—
320C22C4×D3×C3⋊D311yescharacteristic
321C4—61no—
322C4—92no—
323C4—181no—
324C4—272no—
325C4—272no—
326C4#8901511yescharacteristic
327C4#8902911yescharacteristic
328C3—24no—
329C3#1059065614yescomplemented
330C3#1059241711yescharacteristic, complemented
331C2—62no—
332C2D3×C8×C3⋊D311yescharacteristic
333C2#1172331211yescharacteristic
334C2#1172346011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×D3×C3⋊D3
commutatorC2×C33C22×C8
FittingC2×C33×C8C22
socleC22×C33C22×C4
prime radicalC22×C32×D3C2×C4
cosocleC2×C33×C4C23
hypercenterC2×C8D3×C3⋊D3
hypocenterC33#431
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C8×C3⋊(C3⋊Dic3)C2semidirect
3. C3×#63641C2semidirect
5. #11722051C2semidirect
7. #11722018C2semidirect
26. #63641D3semidirect
46. D3×C3⋊Dic3C8semidirect
203. C33#431semidirect
289. C32#4718semidirect
290. C32#4833semidirect
329. C3#10590656semidirect
330. C3#10592417semidirect

Maximal subgroups

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

subgroupindex
C4×D3×C3⋊Dic32
C8×C3⋊(C3⋊Dic3)2
C3×#636412
C32×(C2×D3)⋊C82
#117220512
(C2×D3)⋊(C3⋊(C3⋊C8))2
#117220182
#105924173
#105906563