Finite Group Databasebeta

← C3×#69986 #11788330

Subgroups — C3×#69986 #11788330

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic
3C32×#407C211yesmaximal, characteristic
4C2×C3×#824C212yesmaximal, complemented
5C3×#4554C212yesmaximal, complemented
6C3×#1901—31nomaximal
7#69986C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×Dic6C2211yescharacteristic
10C2×C32×M16C2212yes—
11C2×C3×#217C412yes—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C3×#924—21no—
14C3×#924—21no—
15C3×#924—21no—
16C3×#924—21no—
17C2×C3×Dic3⋊C4C412yes—
18C2×C3×#208—21no—
19C2×C3×#208—24no—
20C2×C3×#208C2212yes—
21C22×C3×C3⋊C8—21no—
22C32×C22⋊C8—21no—
23C32×C22⋊C8—21no—
24C3×#824—24no—
25C22×C3×M16—31no—
26C2×C3×C22⋊Q8—31no—
27C2×#924C2×C311yescharacteristic
28C22×#208C2×C311yescharacteristic
29C2×C3×#101—32no—
30C3×#407—21no—
31C3×#407D311yescharacteristic
32C3×#407C2×C311yescharacteristic
33C2×#824C2×C312yescomplemented
34C3×#343—32no—
35#4554C2×C312yescomplemented
36C24×C32C2×C411yescharacteristic
37C22×C32×C4—22no—
38C22×C32×C4—22no—
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3×Dic3C2×C412yes—
46C22×C3×Dic3C2×C412yes—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C2×C3×Dic6—22no—
50C2×C3×Dic6—22no—
51C32×M16—22no—
52C32×M16—22no—
53C2×C32×C8—22no—
54C3×#217—22no—
55C3×#217—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—22no—
60C3×#208—24no—
61C3×#208—22no—
62C3×#208D414yes—
63C2×C3×C3⋊C8—24no—
64C2×C3×C3⋊C8—22no—
65#1901—31noSylow
66C22×C3×Q8—31no—
67C23×C3×C4—21no—
68C23×C3×C4C2×D311yescharacteristic
69C23×C3×C4C22×C311yescharacteristic
70C22×Dic6C22×C311yescharacteristic
71C2×C3×M16—22no—
72C2×C3×M16—32no—
73C2×C3×M16—64no—
74C2×C3×M16—61no—
75C2×C3×M16C2×D312yes—
76C2×C3×M16C22×C312yes—
77C22×C3×C8—61no—
78C3×C22⋊Q8—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8—61no—
82C2×C3×C4⋊C4—32no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—32no—
85C2×#217C3×C412yes—
86C2×C4⋊Dic3C22×C311yescharacteristic
87#924—21no—
88#924—21no—
89#924—21no—
90#924—21no—
91C2×Dic3⋊C4C3×C412yes—
92C2×#208—21no—
93C2×#208—24no—
94C2×#208C22×C312yes—
95C22×C3⋊C8—21no—
96C3×#101—64no—
97C3×C22⋊C8—22no—
98C3×C22⋊C8—22no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—21no—
101C3×C22⋊C8—21no—
102C3×C22⋊C8—21no—
103#824—24no—
104C23×C32—22no—
105C23×C32—22no—
106C23×C32—41no—
107C23×C32C22⋊C411yescharacteristic
108C23×C32C22⋊C411yescharacteristic
109C23×C32C22×C411yescharacteristic
110C2×C32×C4—22no—
111C2×C32×C4—21no—
112C2×C32×C4—21no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4112yes—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—22no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—42no—
127C3×Dic6—41no—
128C3×Dic6—42no—
129C3×Dic6—41no—
130C32×C8—42no—
131C3×C3⋊C8—24no—
132C22×M16—31no—
133C2×C22⋊Q8—31no—
134C2×#101—32no—
135#407C3×D311yescharacteristic
136#343—32no—
137C24×C3—21no—
138C24×C3C4×D311yescharacteristic
139C24×C3C2×C3×C411yescharacteristic
140C2×C3×Q8—61no—
141C2×C3×Q8—62no—
142C2×C3×Q8—62no—
143C2×C3×Q8—61no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—42no—
157C22×C3×C4—42no—
158C22×C3×C4C4×D311yescharacteristic
159C22×C3×C4D1211yescharacteristic
160C22×C3×C4D1211yescharacteristic
161C22×C3×C4#6711yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4C2×C3×C411yescharacteristic
164C22×C3×C4C3×D411yescharacteristic
165C22×C3×C4C3×D411yescharacteristic
166C22×C3×C4C3×D411yescharacteristic
167C22×C3×C4C3×D411yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C311yescharacteristic
170C22×Dic3C2×C3×C412yes—
171C22×Dic3C2×C3×C412yes—
172C2×Dic6—22no—
173C2×Dic6—21no—
174C2×Dic6—21no—
175C2×Dic6—22no—
176C3×M16—22no—
177C3×M16—22no—
178C3×M16—22no—
179C3×M16—22no—
180C3×M16—34no—
181C3×M16—42no—
182C3×M16—42no—
183C3×M16—64no—
184C3×M16—62no—
185C2×C3×C8—24no—
186C2×C3×C8—22no—
187C2×C3×C8—22no—
188C2×C3×C8—64no—
189C2×C3×C8—62no—
190C3×C4⋊C4—62no—
191C3×C4⋊C4—62no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C22⋊C4—62no—
195C3×C22⋊C4—62no—
196#217—22no—
197#217—22no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200Dic3⋊C4—22no—
201Dic3⋊C4—22no—
202#208—24no—
203#208—22no—
204#208C3×D414yes—
205C2×C3⋊C8—24no—
206C2×C3⋊C8—22no—
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#10112yescomplemented
216C22×C32C2×C22⋊C411yescharacteristic
217C22×C32C4×D412yes—
218C32×C4—21no—
219C32×C4—21no—
220C32×C4#12011yescharacteristic
221C32×C4#12112yes—
222C32×C4#12311yescharacteristic
223C3×Dic3—42no—
224C3×Dic3—42no—
225C22×Q8—31no—
226C23×C4C2×C3×D311yescharacteristic
227C2×M16—32no—
228C2×M16—64no—
229C2×M16—61no—
230C2×M16C2×C3×D312yes—
231C22×C8—61no—
232C22⋊Q8—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235C22⋊Q8—61no—
236C2×C4⋊C4—32no—
237C2×C4⋊C4—31no—
238C2×C22⋊C4—32no—
239#101—64no—
240C22⋊C8—21no—
241C22⋊C8—21no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—22no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—42no—
250C23×C3—42no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—42no—
254C23×C3(C2×D3)⋊C411yescharacteristic
255C23×C3(C2×D3)⋊C411yescharacteristic
256C23×C3C3×C22⋊C411yescharacteristic
257C23×C3C3×C22⋊C411yescharacteristic
258C23×C3C2×C4×D311yescharacteristic
259C23×C3C22×C3×C411yescharacteristic
260C3×Q8—121no—
261C3×Q8—121no—
262C3×Q8—122no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—64no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—122no—
294C2×C3×C4(C2×D3)⋊C411yescharacteristic
295C2×C3×C4(C2×D3)⋊C411yescharacteristic
296C2×C3×C4C3×C22⋊C411yescharacteristic
297C2×C3×C4C3×C22⋊C411yescharacteristic
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4D3×D412yes—
300C2×C3×C4#23712yes—
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D412yes—
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C3×#4112yes—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—24no—
309C2×Dic3—42no—
310Dic6—41no—
311Dic6—42no—
312Dic6—41no—
313C3×C8—44no—
314C3×C8—42no—
315C3×C8—42no—
316C3×C8—64no—
317C3⋊C8—24no—
318C2×C32—22no—
319C2×C32—22no—
320C2×C32—41no—
321C2×C32#38611yescharacteristic
322C2×C32C2×#10111yescharacteristic
323C2×C32#41311yescharacteristic
324C24C3×C4×D311yescharacteristic
325C2×Q8—61no—
326C2×Q8—62no—
327C2×Q8—62no—
328C2×Q8—61no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4C3×C4×D311yescharacteristic
334C22×C4C3×D1211yescharacteristic
335C22×C4C3×D1211yescharacteristic
336C22×C4C3×#6711yescharacteristic
337C22×C4C3×#6711yescharacteristic
338C22×C4C22×C3×D311yescharacteristic
339M16—22no—
340M16—22no—
341M16—34no—
342M16—64no—
343M16—62no—
344C2×C8—22no—
345C2×C8—64no—
346C2×C8—62no—
347C4⋊C4—62no—
348C4⋊C4—62no—
349C4⋊C4—61no—
350C4⋊C4—61no—
351C22⋊C4—62no—
352C22⋊C4—62no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—44no—
378C22×C3—44no—
379C22×C3—48no—
380C22×C3#82412yescomplemented
381C22×C3C3×#10112yescomplemented
382C22×C3#67⋊C412yes—
383C22×C3C2×(C2×D3)⋊C411yescharacteristic
384C22×C3C2×C3×C22⋊C411yescharacteristic
385C22×C3C3×C4×D412yes—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4#88211yescharacteristic
398C3×C4#88611yescharacteristic
399C3×C4#93912yes—
400C3×C4C3×#12011yescharacteristic
401C3×C4C3×#12112yes—
402C3×C4C3×#12311yescharacteristic
403Dic3—42no—
404Dic3—42no—
405C32#190111yescharacteristic, complemented, Sylow
406C23—22no—
407C23—22no—
408C23—41no—
409C23C3×(C2×D3)⋊C411yescharacteristic
410C23C3×(C2×D3)⋊C411yescharacteristic
411C23C2×C3×C4×D311yescharacteristic
412Q8—121no—
413Q8—121no—
414Q8—122no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—64no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—122no—
426C2×C4C3×(C2×D3)⋊C411yescharacteristic
427C2×C4C3×(C2×D3)⋊C411yescharacteristic
428C2×C4C2×C3×D1211yescharacteristic
429C2×C4C3×D3×D412yes—
430C2×C4C3×#23712yes—
431C2×C4C2×C3×#6711yescharacteristic
432C8—42no—
433C8—64no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—22no—
437C2×C3—22no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—42no—
442C2×C3—42no—
443C2×C3—42no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3#495811yescharacteristic
447C2×C3#513211yescharacteristic
448C2×C3C2×#82411yescharacteristic
449C2×C3C3×#38611yescharacteristic
450C2×C3C2×C3×#10111yescharacteristic
451C2×C3C3×#41311yescharacteristic
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—44no—
460C22C3×#82412yescomplemented
461C22C3×#67⋊C412yes—
462C22C2×C3×(C2×D3)⋊C411yescharacteristic
463C4—21no—
464C4—21no—
465C4—122no—
466C4—122no—
467C4C3×#88211yescharacteristic
468C4C3×#88611yescharacteristic
469C4C3×#93912yes—
470C3—21no—
471C3#6998611yescharacteristic, direct product factor
472C3C3×#190111yescharacteristic, complemented
473C2—22no—
474C2—22no—
475C2—41no—
476C2C3×#495811yescharacteristic
477C2C3×#513211yescharacteristic
478C2C2×C3×#82411yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1901
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
4. C2×C3×#824C2semidirect
5. C3×#4554C2semidirect
7. #69986C3direct (N × H)
33. C2×#824C2×C3semidirect
35. #4554C2×C3semidirect
215. C22×C32#101semidirect
380. C22×C3#824semidirect
381. C22×C3C3×#101semidirect
405. C32#1901semidirect
460. C22C3×#824semidirect
471. C3#69986direct (N × H)
472. C3C3×#1901semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C22×C3×#2082
C32×#4072
C2×C3×#8242
C3×#45542
C3×#19013
#699863