Finite Group Databasebeta

← C3×#69510 #11775596

Subgroups — C3×#69510 #11775596

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#4452C214yesmaximal, complemented
5C3×#1520—31nomaximal
6#69510C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×C32×C4⋊C4—21no—
10C2×C32×C22⋊C4—21no—
11C2×C3×#217—21no—
12C2×C3×C4⋊Dic3C411yescharacteristic, complemented
13C3×#924—21no—
14C3×#924—21no—
15C3×#924C412yescomplemented
16C3×#924C2212yes—
17C2×C3×Dic3⋊C4—21no—
18C22×C3×C3⋊C8—21no—
19C32×#95C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C2×C3×C22⋊Q8—31no—
23C2×#924C2×C311yescharacteristic
24C2×C3×C22⋊C8—31no—
25C3×#380—21no—
26C3×#380D311yescharacteristic
27C3×#380C2×C311yescharacteristic
28C2×#830C2×C311yescharacteristic
29C3×#328—34no—
30#4452C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3—21no—
41C22×C3×Dic3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—42no—
44C2×C3×Dic6C2×C412yes—
45C32×C4⋊C4—42no—
46C32×C22⋊C4—42no—
47C3×#217—22no—
48C3×#217—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3C2×C412yes—
51C3×Dic3⋊C4—22no—
52C3×Dic3⋊C4—22no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—42no—
55#1520—31noSylow
56C22×C3×Q8—31no—
57C23×C3×C4—21no—
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C22×C311yescharacteristic
60C22×Dic6C3×C411yescharacteristic, complemented
61C22×C3×C8—61no—
62C3×C22⋊Q8—32no—
63C3×C22⋊Q8—32no—
64C3×C22⋊Q8—61no—
65C3×C22⋊Q8—61no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C22⋊C4—22no—
72C2×C3×C22⋊C4—21no—
73C2×C3×C22⋊C4—21no—
74C2×C3×C22⋊C4—61no—
75C2×#217—21no—
76C2×C4⋊Dic3C3×C411yescharacteristic, complemented
77#924—21no—
78#924—21no—
79#924C3×C412yescomplemented
80#924C22×C312yes—
81C2×Dic3⋊C4—21no—
82C22×C3⋊C8—21no—
83C3×C22⋊C8—32no—
84C3×C22⋊C8—61no—
85C3×#95—22no—
86C3×#95C2×D312yes—
87C3×#95C22×C312yes—
88#830—21no—
89#830C22×C312yes—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32C22⋊C411yescharacteristic
93C23×C32C22⋊C411yescharacteristic
94C23×C32SD1612yes—
95C23×C32Q1612yes—
96C23×C32C2×D411yescharacteristic
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4—42no—
105C2×C32×C4—42no—
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C3×Dic6—42no—
115C3×Dic6—42no—
116C3×C3⋊C8—42no—
117C2×C22⋊Q8—31no—
118C2×C22⋊C8—31no—
119#380C3×D311yescharacteristic
120#328—34no—
121C24×C3—21no—
122C24×C3#6711yescharacteristic
123C24×C3C3×D411yescharacteristic
124C2×C3×Q8—32no—
125C2×C3×Q8—61no—
126C2×C3×Q8—122no—
127C22×C3×C4—24no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—42no—
137C22×C3×C4—42no—
138C22×C3×C4—44no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4C4×D311yescharacteristic
142C22×C3×C4C4×D311yescharacteristic
143C22×C3×C4D1211yescharacteristic
144C22×C3×C4D1211yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C2×C3×C411yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×C3×C4C3×D411yescharacteristic
150C22×C3×C4C3×D411yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C23×C311yescharacteristic
153C22×Dic3—21no—
154C22×Dic3—21no—
155C2×Dic6—21no—
156C2×Dic6—42no—
157C2×Dic6C2×C3×C412yes—
158C2×C3×C8—62no—
159C2×C3×C8—122no—
160C3×C4⋊C4—32no—
161C3×C4⋊C4—44no—
162C3×C4⋊C4—42no—
163C3×C4⋊C4—42no—
164C3×C4⋊C4—62no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—62no—
167C3×C22⋊C4—44no—
168C3×C22⋊C4—42no—
169C3×C22⋊C4—42no—
170C3×C22⋊C4—62no—
171C3×C22⋊C4—62no—
172#217—22no—
173#217—22no—
174C4⋊Dic3—21no—
175C4⋊Dic3C2×C3×C412yes—
176Dic3⋊C4—22no—
177Dic3⋊C4—22no—
178C2×C3⋊C8—22no—
179C2×C3⋊C8—42no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32#10312yes—
189C22×C32#10312yes—
190C22×C32C2×C22⋊C411yescharacteristic
191C22×C32C2×SD1611yescharacteristic
192C22×C32C2×Q1611yescharacteristic
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—82no—
197C32×C4#9912yes—
198C3×Dic3—42no—
199C3×Dic3—42no—
200C22×Q8—31no—
201C23×C4C2×C3×D311yescharacteristic
202C22×C8—61no—
203C22⋊Q8—32no—
204C22⋊Q8—32no—
205C22⋊Q8—61no—
206C22⋊Q8—61no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—31no—
209C2×C4⋊C4—61no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—61no—
212C22⋊C8—32no—
213C22⋊C8—61no—
214#95C2×C3×D312yes—
215C23×C3—21no—
216C23×C3—21no—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—21no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3(C2×D3)⋊C411yescharacteristic
227C23×C3(C2×D3)⋊C411yescharacteristic
228C23×C3#21412yes—
229C23×C3#21612yes—
230C23×C3C3×C22⋊C411yescharacteristic
231C23×C3C3×C22⋊C411yescharacteristic
232C23×C3C3×SD1612yes—
233C23×C3C3×Q1612yes—
234C23×C3C2×#6711yescharacteristic
235C23×C3C2×C3×D411yescharacteristic
236C3×Q8—122no—
237C3×Q8—122no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—44no—
261C2×C3×C4—44no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—42no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—122no—
272C2×C3×C4—122no—
273C2×C3×C4(C2×D3)⋊C411yescharacteristic
274C2×C3×C4(C2×D3)⋊C411yescharacteristic
275C2×C3×C4C3×C22⋊C411yescharacteristic
276C2×C3×C4C3×C22⋊C411yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4C22×C3×C411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285Dic6—42no—
286Dic6—42no—
287C3×C8—122no—
288C3⋊C8—42no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—22no—
292C2×C32—22no—
293C2×C32C2×#9911yescharacteristic
294C2×C32C2×#10311yescharacteristic
295C2×C32#42111yescharacteristic
296C24C3×#6711yescharacteristic
297C2×Q8—32no—
298C2×Q8—61no—
299C2×Q8—122no—
300C22×C4—22no—
301C22×C4—42no—
302C22×C4—61no—
303C22×C4—61no—
304C22×C4C3×C4×D311yescharacteristic
305C22×C4C3×C4×D311yescharacteristic
306C22×C4C3×D1211yescharacteristic
307C22×C4C3×D1211yescharacteristic
308C22×C4C3×#6711yescharacteristic
309C22×C4C22×C3×D311yescharacteristic
310C2×C8—62no—
311C2×C8—122no—
312C4⋊C4—32no—
313C4⋊C4—42no—
314C4⋊C4—61no—
315C4⋊C4—62no—
316C4⋊C4—62no—
317C22⋊C4—42no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3#81012yes—
350C22×C3#81012yes—
351C22×C3C3×#10312yes—
352C22×C3C3×#10312yes—
353C22×C3C2×(C2×D3)⋊C411yescharacteristic
354C22×C3C2×#21411yescharacteristic
355C22×C3C2×#21611yescharacteristic
356C22×C3C2×C3×C22⋊C411yescharacteristic
357C22×C3C2×C3×SD1611yescharacteristic
358C22×C3C2×C3×Q1611yescharacteristic
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—84no—
370C3×C4—82no—
371C3×C4—82no—
372C3×C4—122no—
373C3×C4—122no—
374C3×C4#80612yes—
375C3×C4C3×#9912yes—
376Dic3—42no—
377Dic3—42no—
378C32#152011yescharacteristic, complemented, Sylow
379C23—41no—
380C23—41no—
381C23C3×(C2×D3)⋊C411yescharacteristic
382C23C3×(C2×D3)⋊C411yescharacteristic
383C23C3×#21412yes—
384C23C3×#21612yes—
385C23C2×C3×#6711yescharacteristic
386Q8—122no—
387Q8—122no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4C3×(C2×D3)⋊C411yescharacteristic
402C2×C4C3×(C2×D3)⋊C411yescharacteristic
403C2×C4C2×C3×C4×D311yescharacteristic
404C2×C4C2×C3×D1211yescharacteristic
405C8—122no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—42no—
420C2×C3—42no—
421C2×C3C2×#80611yescharacteristic
422C2×C3C2×#81011yescharacteristic
423C2×C3#500511yescharacteristic
424C2×C3C2×C3×#9911yescharacteristic
425C2×C3C2×C3×#10311yescharacteristic
426C2×C3C3×#42111yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22C3×#81012yes—
436C22C3×#81012yes—
437C22C2×C3×(C2×D3)⋊C411yescharacteristic
438C22C2×C3×#21411yescharacteristic
439C22C2×C3×#21611yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—122no—
445C4—122no—
446C4C3×#80612yes—
447C3—21no—
448C3#6951011yescharacteristic, direct product factor
449C3C3×#152011yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—22no—
453C2—22no—
454C2C2×C3×#80611yescharacteristic
455C2C2×C3×#81011yescharacteristic
456C2C3×#500511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#380C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#380D3
hypocenterC3C3×#1520
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
4. C3×#4452C2semidirect
6. #69510C3direct (N × H)
8. C22×C3×Dic6C4semidirect
12. C2×C3×C4⋊Dic3C4semidirect
15. C3×#924C4semidirect
30. #4452C2×C3semidirect
60. C22×Dic6C3×C4semidirect
76. C2×C4⋊Dic3C3×C4semidirect
79. #924C3×C4semidirect
378. C32#1520semidirect
448. C3#69510direct (N × H)
449. C3C3×#1520semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C32×#3802
C2×C3×#8302
C3×#44522
C3×#15203
#695103