Finite Group Databasebeta

← C3×#69969 #11773992

Subgroups — C3×#69969 #11773992

Order 1152.

655 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#929C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C3×#4469C212yesmaximal, complemented
5C3×#4468C212yesmaximal, complemented
6C3×#1468—31nomaximal
7#69969C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67C411yescharacteristic
10C2×C32×M16—21no—
11C2×C3×#217C411yescharacteristic
12C3×#929—21no—
13C3×#929—21no—
14C3×#929—21no—
15C3×#929—21no—
16C2×C3×(C2×D3)⋊C4C411yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C2×C3×Dic3⋊C4C411yescharacteristic
19C2×C3×Dic3⋊C4C2211yescharacteristic
20C22×C3×C3⋊C8—21no—
21C32×C22⋊C8—21no—
22C32×C22⋊C8C2212yes—
23C3×#830—21no—
24C3×#830C2212yes—
25C2×C3×#123—31no—
26C2×#929C2×C311yescharacteristic
27C3×#407—21no—
28C3×#407D311yescharacteristic, complemented
29C3×#407C2×C311yescharacteristic, complemented
30C2×C3×C22⋊C8—31no—
31C2×#830C2×C311yescharacteristic, complemented
32C3×#324—32no—
33C3×#323—32no—
34#4469C2×C312yescomplemented
35#4468C2×C312yescomplemented
36C24×C32C2×C411yescharacteristic
37C23×C3×D3C2×C411yescharacteristic
38C22×C32×C4—42no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—42no—
48C22×C3×Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C32×M16—42no—
52C2×C32×C8—22no—
53C3×#217—21no—
54C3×#217—21no—
55C3×(C2×D3)⋊C4—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—42no—
65#1468—31noSylow
66C22×C3×D4—31no—
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C22×#67C3×C411yescharacteristic
71C2×C3×M16—22no—
72C2×C3×M16—21no—
73C2×C3×M16—21no—
74C22×C3×C8—61no—
75C3×#123—61no—
76C3×#123—61no—
77C3×#123—61no—
78C3×#123—61no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—31no—
82C2×C3×C22⋊C4—31no—
83C2×C3×C22⋊C4—31no—
84C2×#217C3×C411yescharacteristic
85#929—21no—
86#929—21no—
87#929—21no—
88#929—21no—
89C2×(C2×D3)⋊C4C3×C411yescharacteristic
90C2×(C2×D3)⋊C4C22×C311yescharacteristic
91C2×Dic3⋊C4C3×C411yescharacteristic
92C2×Dic3⋊C4C22×C311yescharacteristic
93C22×C3⋊C8—21no—
94C3×C22⋊C8—22no—
95C3×C22⋊C8—21no—
96C3×C22⋊C8—21no—
97C3×C22⋊C8—22no—
98C3×C22⋊C8—32no—
99C3×C22⋊C8—61no—
100C3×C22⋊C8C2×D312yes—
101C3×C22⋊C8C22×C312yes—
102#830—21no—
103#830C22×C312yes—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32—41no—
107C23×C32C22⋊C411yescharacteristic
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22×C411yescharacteristic
110C22×C3×D3—21no—
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C3×#67—42no—
125C3×#67—42no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C32×C8—42no—
133C3×C3⋊C8—42no—
134C2×#123—31no—
135#407C3×D311yescharacteristic, complemented
136C2×C22⋊C8—31no—
137#324—32no—
138#323—32no—
139C24×C3—21no—
140C24×C3—31no—
141C24×C3C4×D311yescharacteristic
142C24×C3C2×C3×C411yescharacteristic
143C23×D3C2×C3×C411yescharacteristic
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—122no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—42no—
157C22×C3×C4—42no—
158C22×C3×C4—44no—
159C22×C3×C4C4×D311yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4D1211yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4C2×C3×C411yescharacteristic
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C3×D411yescharacteristic
168C22×C3×C4C3×D411yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C23×C311yescharacteristic
171C2×#67—21no—
172C2×#67—21no—
173C2×#67—42no—
174C22×Dic3C2×C3×C411yescharacteristic
175C22×Dic3C2×C3×C411yescharacteristic
176C22×Dic3C2×C3×C411yescharacteristic
177C3×M16—44no—
178C3×M16—42no—
179C3×M16—42no—
180C2×C3×C8—24no—
181C2×C3×C8—22no—
182C2×C3×C8—22no—
183C2×C3×C8—62no—
184C2×C3×C8—122no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195#217—21no—
196#217—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205C2×C3⋊C8—22no—
206C2×C3⋊C8—42no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—44no—
215C22×C32#9912yes—
216C22×C32C2×C22⋊C411yescharacteristic
217C22×C32#13112yes—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C2×C3×D3—82no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C3×Dic3—41no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C22×D4—31no—
230C23×C4C2×C3×D311yescharacteristic
231C2×M16—21no—
232C22×C8—61no—
233#123—61no—
234#123—61no—
235#123—61no—
236#123—61no—
237C2×C4⋊C4—31no—
238C2×C4⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C22⋊C4—31no—
242C22⋊C8—21no—
243C22⋊C8—32no—
244C22⋊C8—61no—
245C22⋊C8C2×C3×D312yes—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3—41no—
256C23×C3—41no—
257C23×C3—42no—
258C23×C3—61no—
259C23×C3—62no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3(C2×D3)⋊C411yescharacteristic
263C23×C3(C2×D3)⋊C411yescharacteristic
264C23×C3C3×C22⋊C411yescharacteristic
265C23×C3C3×C22⋊C411yescharacteristic
266C23×C3C2×C4×D311yescharacteristic
267C23×C3C22×C3×C411yescharacteristic
268C22×D3—21no—
269C22×D3—22no—
270C22×D3—41no—
271C22×D3—41no—
272C3×D4—122no—
273C3×D4—122no—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—62no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4(C2×D3)⋊C411yescharacteristic
303C2×C3×C4(C2×D3)⋊C411yescharacteristic
304C2×C3×C4C3×C22⋊C411yescharacteristic
305C2×C3×C4C3×C22⋊C411yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×C3×D411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310#67—42no—
311#67—42no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—22no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C3×C8—44no—
319C3×C8—42no—
320C3×C8—42no—
321C3×C8—122no—
322C3⋊C8—42no—
323C2×C32—22no—
324C2×C32—22no—
325C2×C32—41no—
326C2×C32#40811yescharacteristic
327C2×C32C2×#9911yescharacteristic
328C2×C32#41311yescharacteristic
329C3×D3—81no—
330C24—31no—
331C24C3×C4×D311yescharacteristic
332C2×D4—61no—
333C2×D4—61no—
334C2×D4—122no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—42no—
339C22×C4C3×C4×D311yescharacteristic
340C22×C4C3×D1211yescharacteristic
341C22×C4C3×D1211yescharacteristic
342C22×C4C3×#6711yescharacteristic
343C22×C4C3×#6711yescharacteristic
344C22×C4C22×C3×D311yescharacteristic
345M16—42no—
346C2×C8—22no—
347C2×C8—62no—
348C2×C8—122no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C22⋊C4—61no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—44no—
384C22×C3—44no—
385C22×C3—48no—
386C22×C3—121no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3—242no—
390C22×C3#80612yes—
391C22×C3C3×#9912yes—
392C22×C3#90712yes—
393C22×C3C2×(C2×D3)⋊C411yescharacteristic
394C22×C3C2×C3×C22⋊C411yescharacteristic
395C22×C3C3×#13112yes—
396C2×D3—41no—
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—82no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—121no—
413C3×C4—121no—
414C3×C4—121no—
415Dic3—41no—
416Dic3—41no—
417Dic3—41no—
418C32#146811yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—41no—
422C23—61no—
423C23—62no—
424C23—121no—
425C23—121no—
426C23C3×(C2×D3)⋊C411yescharacteristic
427C23C3×(C2×D3)⋊C411yescharacteristic
428C23C2×C3×C4×D311yescharacteristic
429D4—122no—
430D4—122no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—62no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4C3×(C2×D3)⋊C411yescharacteristic
444C2×C4C3×(C2×D3)⋊C411yescharacteristic
445C2×C4C2×C3×D1211yescharacteristic
446C2×C4C2×C3×#6711yescharacteristic
447C8—42no—
448C8—122no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—42no—
457C2×C3—42no—
458C2×C3—42no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3C2×#80611yescharacteristic
463C2×C3#512911yescharacteristic
464C2×C3#513211yescharacteristic
465C2×C3C3×#40811yescharacteristic
466C2×C3C2×C3×#9911yescharacteristic
467C2×C3C3×#41311yescharacteristic
468D3—81no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22—242no—
481C22C3×#80612yes—
482C22C3×#90712yes—
483C22C2×C3×(C2×D3)⋊C411yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—121no—
489C4—121no—
490C4—121no—
491C3—21no—
492C3#6996911yescharacteristic, direct product factor
493C3C3×#146811yescharacteristic, complemented
494C2—22no—
495C2—22no—
496C2—41no—
497C2—241no—
498C2C2×C3×#80611yescharacteristic
499C2C3×#512911yescharacteristic
500C2C3×#513211yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#67C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1468
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. C2×C3×#830C2semidirect
4. C3×#4469C2semidirect
5. C3×#4468C2semidirect
7. #69969C3direct (N × H)
28. C3×#407D3semidirect
29. C3×#407C2×C3semidirect
31. C2×#830C2×C3semidirect
34. #4469C2×C3semidirect
35. #4468C2×C3semidirect
135. #407C3×D3semidirect
418. C32#1468semidirect
492. C3#69969direct (N × H)
493. C3C3×#1468semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9292
C32×#4072
C2×C3×#8302
C3×#44692
C3×#44682
C3×#14683
#699693