Finite Group Databasebeta

← C3×#10592475 #13162813

Subgroups — C3×#10592475 #13162813

Order 1728.

1328 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#3754C211yesmaximal, characteristic, complemented
3C2×C3×#3744C211yesmaximal, characteristic, complemented
4C3×#64106C211yesmaximal, characteristic, complemented
5C33×#102C211yesmaximal, characteristic, complemented
6C3×#63647C211yesmaximal, characteristic, complemented
7C3×#63636C211yesmaximal, characteristic, complemented
8#10592475C311yesmaximal, characteristic, direct product factor
9C3×#4776—34nomaximal
10C23×C3×C3⋊D3—21no—
11C2×C33×D4C2211yescharacteristic
12C2×C3×#638—21no—
13C3×D4×C3⋊D3—22no—
14C3×D4×C3⋊D3—22no—
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic, complemented
18C2×C33×C8C2211yescharacteristic, complemented
19C33×C4⋊C4C2211yescharacteristic, complemented
20C3×#3754—22no—
21C3×#3752—21no—
22C3×C4⋊(C3⋊Dic3)—21no—
23C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#3744—22no—
25C2×D4×C3⋊D3C2×C311yescharacteristic
26C2×C3×D3×D4—34no—
27C2×#3754C2×C311yescharacteristic, complemented
28C2×#3744C2×C311yescharacteristic, complemented
29#64106C2×C311yescharacteristic, complemented
30C2×C3×#214—34no—
31C2×C3×#204—34no—
32C3×#897—34no—
33C32×#102—24no—
34C32×#102D314yescomplemented
35C32×#102C2×C311yescharacteristic, complemented
36#63647C2×C311yescharacteristic, complemented
37#63636C2×C311yescharacteristic, complemented
38C3×(C2×D3)⋊C8—34no—
39C3×#809—34no—
40C23×C33—21no—
41C22×C3×C3⋊D3—24no—
42C22×C3×C3⋊D3—21no—
43C22×C3×C3⋊D3—42no—
44C22×C3×C3⋊D3—42no—
45C22×C3×C3⋊D3D411yescharacteristic
46C33×D4—21no—
47C33×D4D412yes—
48C2×C33×C4—21no—
49C2×C33×C4C2311yescharacteristic
50C3×#638—24no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3D411yescharacteristic
53C3×C4⋊(C3⋊D3)—21no—
54C3×C4⋊(C3⋊D3)D412yes—
55C3×C4×C3⋊D3—21no—
56C3×C4×C3⋊D3—21no—
57C3×#634—21no—
58C3×#634—21no—
59C33×C8—21no—
60C3×C3⋊(C3⋊C8)—21no—
61C3×#450—91no—
62#4776—34no—
63C23×C3⋊D3—21no—
64C23×C3×D3—64no—
65C2×C32×D4—24no—
66C2×C32×D4C2×D314yes—
67C2×C32×D4C22×C311yescharacteristic
68C2×#638—21no—
69D4×C3⋊D3—22no—
70D4×C3⋊D3—22no—
71C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
72C2×C4×C3⋊D3C22×C311yescharacteristic
73C2×#634C22×C311yescharacteristic, complemented
74C2×C3×#67—64no—
75C3×D3×D4—68no—
76C3×D3×D4—68no—
77C2×C3×D12—34no—
78C2×C3×C4×D3—34no—
79C2×C3×Dic6—34no—
80C2×C32×C8—24no—
81C2×C32×C8C2×D314yescomplemented
82C2×C32×C8C22×C311yescharacteristic, complemented
83C32×C4⋊C4—24no—
84C32×C4⋊C4C2×D314yescomplemented
85C32×C4⋊C4C22×C311yescharacteristic, complemented
86#3754—22no—
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
90#3744—22no—
91C3×#214—68no—
92C3×(C2×D3)⋊C4—64no—
93C3×C4⋊Dic3—64no—
94C2×C3×C3⋊C8—34no—
95C3×#204—68no—
96C22×C33—22no—
97C22×C33—41no—
98C22×C33—41no—
99C22×C33C2×D411yescharacteristic
100C2×C3×C3⋊D3—21no—
101C2×C3×C3⋊D3—21no—
102C2×C3×C3⋊D3—22no—
103C2×C3×C3⋊D3—48no—
104C2×C3×C3⋊D3—41no—
105C2×C3×C3⋊D3—41no—
106C2×C3×C3⋊D3SD1612yescomplemented
107C33×C4—41no—
108C33×C4C2×D411yescharacteristic
109C33×C4C2×D411yescharacteristic
110C3×C3⋊Dic3—21no—
111C3×C3⋊Dic3—41no—
112C22×C3×D4—91no—
113C2×D3×D4—34no—
114C2×C3×SD16—91no—
115C2×C3×SD16—91no—
116C3×C22⋊Q8—91no—
117C2×#214—34no—
118C2×#204—34no—
119#897—34no—
120C3×#102—24no—
121C3×#102—91no—
122C3×#102C3×D314yescomplemented
123C3×#102C3⋊D311yescharacteristic, complemented
124C3×C22⋊C8—91no—
125(C2×D3)⋊C8—34no—
126#809—34no—
127C23×C32—21no—
128C23×C32—24no—
129C23×C32—44no—
130C22×C3⋊D3—24no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3C3×D411yescharacteristic
135C22×C3×D3—34no—
136C22×C3×D3—616no—
137C22×C3×D3—64no—
138C22×C3×D3—128no—
139C22×C3×D3—128no—
140C32×D4—21no—
141C32×D4—28no—
142C32×D4—24no—
143C32×D4—44no—
144C32×D4D1218yes—
145C32×D4C3×D412yes—
146C2×C32×C4—21no—
147C2×C32×C4—24no—
148C2×C32×C4—24no—
149C2×C32×C4—44no—
150C2×C32×C4C22×D314yes—
151C2×C32×C4C23×C311yescharacteristic
152#638—24no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3C3×D411yescharacteristic
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)C3×D412yes—
157C4×C3⋊D3—21no—
158C4×C3⋊D3—21no—
159#634—21no—
160#634—21no—
161C3×#67—616no—
162C2×C3×Dic3—34no—
163C2×C3×Dic3—64no—
164C3×D12—38no—
165C3×D12—64no—
166C3×C4×D3—64no—
167C3×C4×D3—64no—
168C3×Dic6—64no—
169C3×Dic6—64no—
170C32×C8—21no—
171C32×C8—24no—
172C32×C8—44no—
173C3⋊(C3⋊C8)—21no—
174C3×C3⋊C8—64no—
175#450—91noSylow
176C2×C33—42no—
177C2×C33#12011yescharacteristic
178C2×C33C2×SD1611yescharacteristic
179C2×C33AGL(1,ℤ/8)11yescharacteristic
180C3×C3⋊D3—22no—
181C3×C3⋊D3—42no—
182C24×C3—181no—
183C23×D3—64no—
184C2×C3×Q8—91no—
185C2×C3×D4—24no—
186C2×C3×D4—91no—
187C2×C3×D4—181no—
188C2×C3×D4—182no—
189C2×C3×D4—182no—
190C2×C3×D4C2×C3×D314yes—
191C2×C3×D4C2×C3⋊D311yescharacteristic
192C22×C3×C4—91no—
193C2×#67—64no—
194D3×D4—68no—
195D3×D4—68no—
196C2×D12—34no—
197C2×C4×D3—34no—
198C2×Dic6—34no—
199C3×SD16—182no—
200C3×SD16—182no—
201C2×C3×C8—24no—
202C2×C3×C8—91no—
203C2×C3×C8C2×C3×D314yescomplemented
204C2×C3×C8C2×C3⋊D311yescharacteristic, complemented
205C3×C4⋊C4—24no—
206C3×C4⋊C4—181no—
207C3×C4⋊C4C2×C3×D314yescomplemented
208C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
209C3×C22⋊C4—181no—
210#214—68no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—64no—
213C2×C3⋊C8—34no—
214#204—68no—
215C22×C32—22no—
216C22×C32—24no—
217C22×C32—28no—
218C22×C32—48no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—44no—
222C22×C32—44no—
223C22×C32—84no—
224C22×C32—84no—
225C22×C32D3×D414yes—
226C22×C32C2×C3×D411yescharacteristic
227C2×C3⋊D3—21no—
228C2×C3⋊D3—21no—
229C2×C3⋊D3—22no—
230C2×C3⋊D3—48no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3C3×SD1612yescomplemented
234C2×C3×D3—38no—
235C2×C3×D3—64no—
236C2×C3×D3—64no—
237C2×C3×D3—68no—
238C2×C3×D3—1232no—
239C2×C3×D3—124no—
240C2×C3×D3—124no—
241C32×C4—24no—
242C32×C4—24no—
243C32×C4—41no—
244C32×C4—44no—
245C32×C4—84no—
246C32×C4C2×D1214yes—
247C32×C4D3×D414yes—
248C32×C4C2×C3×D411yescharacteristic
249C32×C4C2×C3×D411yescharacteristic
250C3⋊Dic3—21no—
251C3⋊Dic3—41no—
252C3×Dic3—64no—
253C3×Dic3—124no—
254C22×D4—91no—
255C2×SD16—91no—
256C2×SD16—91no—
257C22⋊Q8—91no—
258#102—91no—
259#102C3×C3⋊D311yescharacteristic, complemented
260C22⋊C8—91no—
261C33#45011yescharacteristic, complemented, Sylow
262C23×C3—24no—
263C23×C3—21no—
264C23×C3—44no—
265C23×C3—91no—
266C23×C3—184no—
267C23×C3—181no—
268C23×C3—362no—
269C23×C3—362no—
270C22×D3—34no—
271C22×D3—616no—
272C22×D3—64no—
273C22×D3—128no—
274C22×D3—128no—
275C3×Q8—181no—
276C3×Q8—181no—
277C3×D4—24no—
278C3×D4—21no—
279C3×D4—28no—
280C3×D4—44no—
281C3×D4—92no—
282C3×D4—184no—
283C3×D4—181no—
284C3×D4C3×D1218yes—
285C3×D4C4⋊(C3⋊D3)12yes—
286C2×C3×C4—24no—
287C2×C3×C4—21no—
288C2×C3×C4—24no—
289C2×C3×C4—44no—
290C2×C3×C4—91no—
291C2×C3×C4—181no—
292C2×C3×C4—181no—
293C2×C3×C4—181no—
294C2×C3×C4C22×C3×D314yes—
295C2×C3×C4C22×C3⋊D311yescharacteristic
296#67—616no—
297C2×Dic3—34no—
298C2×Dic3—64no—
299D12—38no—
300D12—64no—
301C4×D3—64no—
302C4×D3—64no—
303Dic6—64no—
304Dic6—64no—
305C3×C8—24no—
306C3×C8—21no—
307C3×C8—44no—
308C3×C8—181no—
309C3⋊C8—64no—
310C2×C32—24no—
311C2×C32—24no—
312C2×C32—24no—
313C2×C32—42no—
314C2×C32—48no—
315C2×C32—88no—
316C2×C32#88214yes—
317C2×C32#91114yes—
318C2×C32D3×SD1614yes—
319C2×C32C3×#12011yescharacteristic
320C2×C32C2×C3×SD1611yescharacteristic
321C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
322C3⋊D3—22no—
323C3⋊D3—42no—
324C3×D3—68no—
325C3×D3—128no—
326C24—181no—
327C2×Q8—91no—
328C2×D4—91no—
329C2×D4—181no—
330C2×D4—182no—
331C2×D4—182no—
332C2×D4C2×C3×C3⋊D311yescharacteristic
333C22×C4—91no—
334SD16—182no—
335SD16—182no—
336C2×C8—91no—
337C2×C8C2×C3×C3⋊D311yescharacteristic, complemented
338C4⋊C4—181no—
339C4⋊C4C2×C3×C3⋊D311yescharacteristic, complemented
340C22⋊C4—181no—
341C22×C3—28no—
342C22×C3—22no—
343C22×C3—24no—
344C22×C3—48no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—84no—
350C22×C3—84no—
351C22×C3—92no—
352C22×C3—181no—
353C22×C3—181no—
354C22×C3—182no—
355C22×C3—368no—
356C22×C3—361no—
357C22×C3—361no—
358C22×C3C3×D3×D414yes—
359C22×C3D4×C3⋊D311yescharacteristic
360C2×D3—38no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—68no—
364C2×D3—1232no—
365C2×D3—124no—
366C2×D3—124no—
367C3×C4—24no—
368C3×C4—24no—
369C3×C4—44no—
370C3×C4—41no—
371C3×C4—84no—
372C3×C4—181no—
373C3×C4—361no—
374C3×C4C2×C3×D1214yes—
375C3×C4C3×D3×D414yes—
376C3×C4C2×C4⋊(C3⋊D3)11yescharacteristic
377C3×C4D4×C3⋊D311yescharacteristic
378Dic3—64no—
379Dic3—124no—
380C32—24no—
381C32#477614yescomplemented
382C32C3×#45011yescharacteristic, complemented
383C23—21no—
384C23—91no—
385C23—184no—
386C23—181no—
387C23—362no—
388C23—362no—
389Q8—181no—
390Q8—181no—
391D4—21no—
392D4—92no—
393D4—184no—
394D4—181no—
395D4C3×C4⋊(C3⋊D3)12yes—
396C2×C4—21no—
397C2×C4—91no—
398C2×C4—181no—
399C2×C4—181no—
400C2×C4—181no—
401C2×C4C22×C3×C3⋊D311yescharacteristic
402C8—21no—
403C8—181no—
404C2×C3—24no—
405C2×C3—24no—
406C2×C3—24no—
407C2×C3—48no—
408C2×C3—42no—
409C2×C3—88no—
410C2×C3—182no—
411C2×C3—362no—
412C2×C3C3×#88214yes—
413C2×C3C3×#91114yes—
414C2×C3C3×D3×SD1614yes—
415C2×C3#6409111yescharacteristic
416C2×C3#6412011yescharacteristic
417C2×C3SD16×C3⋊D311yescharacteristic
418D3—68no—
419D3—128no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—92no—
424C22—181no—
425C22—181no—
426C22—182no—
427C22—368no—
428C22—361no—
429C22—361no—
430C22C3×D4×C3⋊D311yescharacteristic
431C4—41no—
432C4—181no—
433C4—361no—
434C4C2×C3×C4⋊(C3⋊D3)11yescharacteristic
435C4C3×D4×C3⋊D311yescharacteristic
436C3—24no—
437C3C3×#477614yescomplemented
438C3#1059247511yescharacteristic, direct product factor
439C2—42no—
440C2—182no—
441C2—362no—
442C2C3×#6409111yescharacteristic
443C2C3×#6412011yescharacteristic
444C2C3×SD16×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C3D4×C3⋊D3
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C22×C3×C3⋊D3
FittingC33×#102C2
socleC22×C33C2×D4
prime radicalC2×C3×D4×C3⋊D3C2
hypercenterC3×#102C3⋊D3
hypocenterC32C3×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3754C2semidirect
3. C2×C3×#3744C2semidirect
4. C3×#64106C2semidirect
5. C33×#102C2semidirect
6. C3×#63647C2semidirect
7. C3×#63636C2semidirect
8. #10592475C3direct (N × H)
17. C2×C3×#634C22semidirect
18. C2×C33×C8C22semidirect
19. C33×C4⋊C4C22semidirect
23. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. C2×#3754C2×C3semidirect
28. C2×#3744C2×C3semidirect
29. #64106C2×C3semidirect
34. C32×#102D3semidirect
35. C32×#102C2×C3semidirect
36. #63647C2×C3semidirect
37. #63636C2×C3semidirect
73. C2×#634C22×C3semidirect
81. C2×C32×C8C2×D3semidirect
82. C2×C32×C8C22×C3semidirect
84. C32×C4⋊C4C2×D3semidirect
85. C32×C4⋊C4C22×C3semidirect
89. C2×C3⋊(C3⋊C8)C22×C3semidirect
106. C2×C3×C3⋊D3SD16semidirect
122. C3×#102C3×D3semidirect
123. C3×#102C3⋊D3semidirect
203. C2×C3×C8C2×C3×D3semidirect
204. C2×C3×C8C2×C3⋊D3semidirect
207. C3×C4⋊C4C2×C3×D3semidirect
208. C3×C4⋊C4C2×C3⋊D3semidirect
233. C2×C3⋊D3C3×SD16semidirect
259. #102C3×C3⋊D3semidirect
261. C33#450semidirect
337. C2×C8C2×C3×C3⋊D3semidirect
339. C4⋊C4C2×C3×C3⋊D3semidirect
381. C32#4776semidirect
382. C32C3×#450semidirect
437. C3C3×#4776semidirect
438. C3#10592475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3×#37542
C2×C3×#37442
C3×#641062
C33×#1022
C3×#636472
C3×#636362
#105924753
C3×#47763