Finite Group Databasebeta

← C2×C3×#4469 #11773730

Subgroups — C2×C3×#4469 #11773730

Order 1152.

757 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
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#4469C214yesmaximal, direct product factor
5C2×C3×#324—31nomaximal
6C2×#4469C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C23×C3×Dic3C411yescharacteristic
9C23×C3×Dic3C411yescharacteristic
10C22×C32×C8—21no—
11C2×C3×Dic3⋊C4—21no—
12C2×C3×Dic3⋊C4—21no—
13C2×C3×Dic3⋊C4—21no—
14C2×C3×Dic3⋊C4—21no—
15C2×C3×Dic3⋊C4C412yes—
16C2×C3×Dic3⋊C4C2212yes—
17C22×C3×C3⋊C8—21no—
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C22×C3×C4⋊C4—31no—
23C22×Dic3⋊C4C2×C311yescharacteristic
24C2×C3×C22⋊C8—21no—
25C2×C3×C22⋊C8—31no—
26C2×C3×C22⋊C8D311yescharacteristic
27C2×C3×C22⋊C8C2×C311yescharacteristic
28C2×#830C2×C311yescharacteristic
29C3×#324—34no—
30#4469C2×C314yesdirect product factor
31C24×C32C2×C411yescharacteristic
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3×Dic3—21no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—22no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—42no—
45C22×C3×Dic3C814yescomplemented
46C22×C3×Dic3C2×C412yes—
47C22×C3×Dic3C2×C412yes—
48C2×C32×C8—22no—
49C2×C32×C8—42no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—22no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—42no—
56C2×#324—31noSylow
57C23×C3×C4—21no—
58C23×C3×C4—31no—
59C23×C3×C4—31no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C22×C311yescharacteristic
62C23×Dic3C3×C411yescharacteristic
63C23×Dic3C3×C411yescharacteristic
64C22×C3×C8—22no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—61no—
68C2×C3×C4⋊C4—32no—
69C2×C3×C4⋊C4—32no—
70C2×C3×C4⋊C4—61no—
71C2×C3×C4⋊C4—61no—
72C2×C3×C4⋊C4—61no—
73C2×C3×C4⋊C4—61no—
74C2×Dic3⋊C4—21no—
75C2×Dic3⋊C4—21no—
76C2×Dic3⋊C4—21no—
77C2×Dic3⋊C4—21no—
78C2×Dic3⋊C4C3×C412yes—
79C2×Dic3⋊C4C22×C312yes—
80C22×C3⋊C8—21no—
81C3×C22⋊C8—22no—
82C3×C22⋊C8—21no—
83C3×C22⋊C8—21no—
84C3×C22⋊C8—22no—
85C3×C22⋊C8—32no—
86C3×C22⋊C8—61no—
87C3×C22⋊C8C2×D312yes—
88C3×C22⋊C8C22×C312yes—
89#830—21no—
90#830C22×C312yes—
91C23×C32—22no—
92C23×C32—22no—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22⋊C411yescharacteristic
95C23×C32C2×C812yes—
96C23×C32M1612yes—
97C23×C32C22×C411yescharacteristic
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22⋊C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3×Dic3—24no—
109C2×C3×Dic3—24no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3C2×C814yescomplemented
117C32×C8—42no—
118C3×C3⋊C8—42no—
119C22×C4⋊C4—31no—
120C2×C22⋊C8—31no—
121C2×C22⋊C8C3×D311yescharacteristic
122#324—34no—
123C24×C3—21no—
124C24×C3C4×D311yescharacteristic
125C24×C3C2×C3×C411yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—34no—
133C22×C3×C4—32no—
134C22×C3×C4—32no—
135C22×C3×C4—42no—
136C22×C3×C4—42no—
137C22×C3×C4—44no—
138C22×C3×C4—62no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×C3×C4—61no—
143C22×C3×C4—122no—
144C22×C3×C4C4×D311yescharacteristic
145C22×C3×C4D1211yescharacteristic
146C22×C3×C4D1211yescharacteristic
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4#6711yescharacteristic
149C22×C3×C4C2×C3×C411yescharacteristic
150C22×C3×C4C3×D411yescharacteristic
151C22×C3×C4C3×D411yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C22×C3×C4C3×D411yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C23×C311yescharacteristic
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—22no—
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—42no—
162C22×Dic3C3×C814yescomplemented
163C22×Dic3C2×C3×C412yes—
164C22×Dic3C2×C3×C412yes—
165C2×C3×C8—24no—
166C2×C3×C8—22no—
167C2×C3×C8—22no—
168C2×C3×C8—44no—
169C2×C3×C8—42no—
170C2×C3×C8—42no—
171C2×C3×C8—62no—
172C2×C3×C8—122no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—62no—
176C3×C4⋊C4—62no—
177Dic3⋊C4—22no—
178Dic3⋊C4—22no—
179Dic3⋊C4—22no—
180Dic3⋊C4—22no—
181C2×C3⋊C8—22no—
182C2×C3⋊C8—42no—
183C22×C32—24no—
184C22×C32—24no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32C22⋊C812yes—
190C22×C32C22⋊C812yes—
191C22×C32#9912yes—
192C22×C32#10112yes—
193C22×C32C2×C22⋊C411yescharacteristic
194C22×C32C22×C811yescharacteristic
195C22×C32C2×M1611yescharacteristic
196C32×C4—21no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C3×Dic3—24no—
201C3×Dic3—42no—
202C23×C4—31no—
203C23×C4—31no—
204C23×C4C2×C3×D311yescharacteristic
205C22×C8—21no—
206C22×C8—61no—
207C2×C4⋊C4—32no—
208C2×C4⋊C4—32no—
209C2×C4⋊C4—61no—
210C2×C4⋊C4—61no—
211C2×C4⋊C4—61no—
212C2×C4⋊C4—61no—
213C22⋊C8—21no—
214C22⋊C8—32no—
215C22⋊C8—61no—
216C22⋊C8C2×C3×D312yes—
217C23×C3—22no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—42no—
227C23×C3—42no—
228C23×C3D3×C812yes—
229C23×C3ΓL(1,𝔽25)12yes—
230C23×C3(C2×D3)⋊C411yescharacteristic
231C23×C3(C2×D3)⋊C411yescharacteristic
232C23×C3C3×C22⋊C411yescharacteristic
233C23×C3C3×C22⋊C411yescharacteristic
234C23×C3C2×C3×C812yes—
235C23×C3C3×M1612yes—
236C23×C3C2×C4×D311yescharacteristic
237C23×C3C22×C3×C411yescharacteristic
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—34no—
248C2×C3×C4—42no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
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—42no—
261C2×C3×C4—64no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—122no—
267C2×C3×C4—122no—
268C2×C3×C4—122no—
269C2×C3×C4(C2×D3)⋊C411yescharacteristic
270C2×C3×C4(C2×D3)⋊C411yescharacteristic
271C2×C3×C4C3×C22⋊C411yescharacteristic
272C2×C3×C4C3×C22⋊C411yescharacteristic
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×C3×D411yescharacteristic
276C2×C3×C4C2×C3×D411yescharacteristic
277C2×Dic3—24no—
278C2×Dic3—24no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—22no—
282C2×Dic3—42no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C2×Dic3C2×C3×C814yescomplemented
286C3×C8—44no—
287C3×C8—42no—
288C3×C8—42no—
289C3×C8—122no—
290C3⋊C8—42no—
291C2×C32—22no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32#32414yescomplemented
295C2×C32C2×C22⋊C811yescharacteristic
296C2×C32C2×#9911yescharacteristic
297C2×C32C2×#10111yescharacteristic
298C24C3×C4×D311yescharacteristic
299C22×C4—34no—
300C22×C4—32no—
301C22×C4—32no—
302C22×C4—42no—
303C22×C4—62no—
304C22×C4—61no—
305C22×C4—61no—
306C22×C4—61no—
307C22×C4—61no—
308C22×C4—122no—
309C22×C4C3×C4×D311yescharacteristic
310C22×C4C3×D1211yescharacteristic
311C22×C4C3×D1211yescharacteristic
312C22×C4C3×#6711yescharacteristic
313C22×C4C3×#6711yescharacteristic
314C22×C4C22×C3×D311yescharacteristic
315C2×C8—22no—
316C2×C8—42no—
317C2×C8—62no—
318C2×C8—122no—
319C4⋊C4—62no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—24no—
328C22×C3—24no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—44no—
345C22×C3—44no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3#80612yes—
349C22×C3(C2×D3)⋊C812yes—
350C22×C3(C2×D3)⋊C812yes—
351C22×C3#82412yes—
352C22×C3C3×C22⋊C812yes—
353C22×C3C3×C22⋊C812yes—
354C22×C3C3×#9912yes—
355C22×C3C3×#10112yes—
356C22×C3C2×D3×C811yescharacteristic
357C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
358C22×C3C2×(C2×D3)⋊C411yescharacteristic
359C22×C3C2×C3×C22⋊C411yescharacteristic
360C22×C3C22×C3×C811yescharacteristic
361C22×C3C2×C3×M1611yescharacteristic
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—64no—
375C3×C4—122no—
376Dic3—24no—
377Dic3—42no—
378C32C2×#32411yescharacteristic, complemented, Sylow
379C23—22no—
380C23—22no—
381C23C3×D3×C812yes—
382C23C3×ΓL(1,𝔽25)12yes—
383C23C3×(C2×D3)⋊C411yescharacteristic
384C23C3×(C2×D3)⋊C411yescharacteristic
385C23C2×C3×C4×D311yescharacteristic
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—34no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—64no—
396C2×C4—64no—
397C2×C4—62no—
398C2×C4—122no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4C3×(C2×D3)⋊C411yescharacteristic
402C2×C4C3×(C2×D3)⋊C411yescharacteristic
403C2×C4C2×C3×D1211yescharacteristic
404C2×C4C2×C3×#6711yescharacteristic
405C8—42no—
406C8—122no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—24no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3—42no—
420C2×C3#446914yesdirect product factor
421C2×C3C3×#32414yescomplemented
422C2×C3C2×#80611yescharacteristic
423C2×C3C2×(C2×D3)⋊C811yescharacteristic
424C2×C3C2×#82411yescharacteristic
425C2×C3C2×C3×C22⋊C811yescharacteristic
426C2×C3C2×C3×#9911yescharacteristic
427C2×C3C2×C3×#10111yescharacteristic
428C22—24no—
429C22—24no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22C3×#80612yes—
435C22C3×(C2×D3)⋊C812yes—
436C22C3×(C2×D3)⋊C812yes—
437C22C3×#82412yes—
438C22C2×C3×D3×C811yescharacteristic
439C22C2×C3×ΓL(1,𝔽25)11yescharacteristic
440C22C2×C3×(C2×D3)⋊C411yescharacteristic
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—64no—
446C4—122no—
447C3—21no—
448C3C2×#446911yescharacteristic, direct product factor
449C3C2×C3×#32411yescharacteristic, complemented
450C2—21no—
451C2—21no—
452C2—22no—
453C2C3×#446914yesdirect product factor
454C2C2×C3×#80611yescharacteristic
455C2C2×C3×(C2×D3)⋊C811yescharacteristic
456C2C2×C3×#82411yescharacteristic
subgroupG/H
centerC23×C3(C2×D3)⋊C4
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C2×C3×#324
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4469C2direct (N × H)
6. C2×#4469C3direct (N × H)
30. #4469C2×C3direct (N × H)
45. C22×C3×Dic3C8semidirect
116. C2×C3×Dic3C2×C8semidirect
162. C22×Dic3C3×C8semidirect
285. C2×Dic3C2×C3×C8semidirect
294. C2×C32#324semidirect
378. C32C2×#324semidirect
420. C2×C3#4469direct (N × H)
421. C2×C3C3×#324semidirect
448. C3C2×#4469direct (N × H)
449. C3C2×C3×#324semidirect
453. C2C3×#4469direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×C32×C22⋊C82
C2×C3×#8302
C3×#44692
C2×C3×#3243
C2×#44693