Finite Group Databasebeta

← C3×#69544 #11775345

Subgroups — C3×#69544 #11775345

Order 1152.

521 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×#382C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4452C212yesmaximal, complemented
5C3×#4451C212yesmaximal
6C3×#1512—31nomaximal
7#69544C311yesmaximal, characteristic, direct product factor
8C2×C32×C4⋊C4—21no—
9C2×C32×C42C2211yescharacteristic
10C3×#930C2211yescharacteristic
11C3×#929—21no—
12C3×C4×#67—21no—
13C3×#924C2211yescharacteristic
14C3×#876—21no—
15C3×#875C411yescharacteristic, complemented
16C3×C4×D12C411yescharacteristic, complemented
17C3×#872—21no—
18C3×#870C411yescharacteristic, complemented
19C3×C4×Dic6C411yescharacteristic, complemented
20C32×#95—21no—
21C32×#95C2212yes—
22C3×#830C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×#803—21no—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×#432—31no—
28C3×#382—21no—
29C3×#382D311yescharacteristic, complemented
30C3×#382C2×C311yescharacteristic, complemented
31#4926C2×C311yescharacteristic, complemented
32C3×#328—32no—
33C3×#327—32no—
34#4452C2×C312yescomplemented
35#4451C2×C312yes—
36C22×C32×C4—22no—
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—21no—
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6C2×C411yescharacteristic
44C32×C4⋊C4—42no—
45C32×C42C2×C411yescharacteristic
46C32×C42C2×C411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42D411yescharacteristic
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3C2×C411yescharacteristic
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—22no—
62#1512—31noSylow
63C3×#126—61no—
64C3×#125—31no—
65C3×#124—31no—
66C3×#123—61no—
67C3×C22⋊Q8—31no—
68C3×#121—31no—
69C3×C4×Q8—31no—
70C3×C4×D4—31no—
71C3×C4×D4—61no—
72C3×#117—61no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C42—21no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79#930C22×C311yescharacteristic
80#929—21no—
81C4×#67—21no—
82#924C22×C311yescharacteristic
83#876—21no—
84#875C3×C411yescharacteristic, complemented
85C4×D12C3×C411yescharacteristic, complemented
86#872—21no—
87#870C3×C411yescharacteristic, complemented
88C4×Dic6C3×C411yescharacteristic, complemented
89C3×C4⋊C8—61no—
90C3×C22⋊C8—32no—
91C3×#97—61no—
92C3×#95—22no—
93C3×#95—21no—
94C3×#95—21no—
95C3×#95—22no—
96C3×#95C2×D312yes—
97C3×#95C22×C312yes—
98#830C22×C312yes—
99C4⋊(C3⋊C8)—21no—
100#803—21no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4—42no—
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C3×#67—41no—
117C3×#67—41no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—41no—
122C3×C4×D3—42no—
123C3×Dic6—41no—
124C3×C3⋊C8—42no—
125#529—31no—
126#432—31no—
127#382C3×D311yescharacteristic, complemented
128#328—32no—
129#327—32no—
130C2×C3×Q8—31no—
131C2×C3×D4—31no—
132C2×C3×D4—61no—
133C22×C3×C4—24no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—61no—
140C22×C3×C4#6711yescharacteristic
141C22×C3×C4#6711yescharacteristic
142C22×C3×C4C3×D411yescharacteristic
143C22×C3×C4C3×D411yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C23×C311yescharacteristic
146C2×#67—21no—
147C2×D12C2×C3×C411yescharacteristic
148C2×C4×D3—21no—
149C2×Dic6C2×C3×C411yescharacteristic
150C2×C3×C8—62no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—44no—
154C3×C4⋊C4—42no—
155C3×C4⋊C4—42no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42C4×D311yescharacteristic
171C3×C42C4×D311yescharacteristic
172C3×C42D1211yescharacteristic
173C3×C42D1211yescharacteristic
174C3×C42C2×C3×C411yescharacteristic
175C3×C42C2×C3×C411yescharacteristic
176C3×C42C3×D411yescharacteristic
177C3×C42C3×D411yescharacteristic
178#217—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3C2×C3×C411yescharacteristic
184C4⋊Dic3C2×C3×C411yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189C4×Dic3—21no—
190C2×C3⋊C8—22no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32C2×C22⋊C411yescharacteristic
194C22×C32AGL(1,ℤ/8)11yescharacteristic
195C22×C32#13711yescharacteristic
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—41no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—82no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209#126—61no—
210#125—31no—
211#124—31no—
212#123—61no—
213C22⋊Q8—31no—
214#121—31no—
215C4×Q8—31no—
216C4×D4—31no—
217C4×D4—61no—
218#117—61no—
219C2×C4⋊C4—21no—
220C2×C42C2×C3×D311yescharacteristic
221C4⋊C8—61no—
222C22⋊C8—32no—
223#97—61no—
224#95—21no—
225#95C2×C3×D312yes—
226C23×C3—21no—
227C23×C3—61no—
228C23×C3C2×#6711yescharacteristic
229C23×C3C2×C3×D411yescharacteristic
230C22×D3—21no—
231C3×Q8—121no—
232C3×D4—121no—
233C3×D4—121no—
234C3×D4—121no—
235C2×C3×C4—22no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—42no—
252C2×C3×C4—42no—
253C2×C3×C4—44no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4—42no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—122no—
266C2×C3×C4(C2×D3)⋊C411yescharacteristic
267C2×C3×C4(C2×D3)⋊C411yescharacteristic
268C2×C3×C4(C2×D3)⋊C411yescharacteristic
269C2×C3×C4(C2×D3)⋊C411yescharacteristic
270C2×C3×C4C3×C22⋊C411yescharacteristic
271C2×C3×C4C3×C22⋊C411yescharacteristic
272C2×C3×C4C3×C22⋊C411yescharacteristic
273C2×C3×C4C3×C22⋊C411yescharacteristic
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4C2×D1211yescharacteristic
276C2×C3×C4C22×C3×C411yescharacteristic
277C2×C3×C4C2×C3×D411yescharacteristic
278#67—41no—
279#67—41no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283D12—41no—
284C4×D3—42no—
285Dic6—41no—
286C3×C8—122no—
287C3⋊C8—42no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32#41011yescharacteristic
291C2×C32#41711yescharacteristic
292C2×C32#42111yescharacteristic
293C3×D3—81no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—22no—
298C22×C4—61no—
299C22×C4C3×#6711yescharacteristic
300C22×C4C3×#6711yescharacteristic
301C22×C4C22×C3×D311yescharacteristic
302C2×C8—62no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—42no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4—61no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C42—61no—
316C42C3×C4×D311yescharacteristic
317C42C3×C4×D311yescharacteristic
318C42C3×D1211yescharacteristic
319C42C3×D1211yescharacteristic
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—121no—
330C22×C3—121no—
331C22×C3—121no—
332C22×C3C2×(C2×D3)⋊C411yescharacteristic
333C22×C3#93211yescharacteristic
334C22×C3#94211yescharacteristic
335C22×C3C2×C3×C22⋊C411yescharacteristic
336C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
337C22×C3C3×#13711yescharacteristic
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—41no—
359C3×C4—84no—
360C3×C4—82no—
361C3×C4—82no—
362C3×C4—121no—
363C3×C4—121no—
364C3×C4—121no—
365Dic3—41no—
366Dic3—41no—
367Dic3—41no—
368C32#151211yescharacteristic, complemented, Sylow
369C23—61no—
370C23C2×C3×#6711yescharacteristic
371Q8—121no—
372D4—121no—
373D4—121no—
374D4—121no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—61no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—122no—
386C2×C4C3×(C2×D3)⋊C411yescharacteristic
387C2×C4C3×(C2×D3)⋊C411yescharacteristic
388C2×C4C3×(C2×D3)⋊C411yescharacteristic
389C2×C4C3×(C2×D3)⋊C411yescharacteristic
390C2×C4C2×C3×C4×D311yescharacteristic
391C2×C4C2×C3×D1211yescharacteristic
392C8—122no—
393C2×C3—22no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—241no—
403C2×C3#496611yescharacteristic
404C2×C3#500511yescharacteristic
405C2×C3#500611yescharacteristic
406C2×C3C3×#41011yescharacteristic
407C2×C3C3×#41711yescharacteristic
408C2×C3C3×#42111yescharacteristic
409D3—81no—
410C22—21no—
411C22—21no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22C2×C3×(C2×D3)⋊C411yescharacteristic
416C22C3×#93211yescharacteristic
417C22C3×#94211yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—21no—
424C4—82no—
425C4—121no—
426C4—121no—
427C4—121no—
428C3—21no—
429C3#6954411yescharacteristic, direct product factor
430C3C3×#151211yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2—241no—
434C2C3×#496611yescharacteristic
435C2C3×#500511yescharacteristic
436C2C3×#500611yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#382C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#382D3
hypocenterC3C3×#1512
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
2. C32×#382C2semidirect
3. C3×#4926C2semidirect
4. C3×#4452C2semidirect
7. #69544C3direct (N × H)
15. C3×#875C4semidirect
16. C3×C4×D12C4semidirect
18. C3×#870C4semidirect
19. C3×C4×Dic6C4semidirect
29. C3×#382D3semidirect
30. C3×#382C2×C3semidirect
31. #4926C2×C3semidirect
34. #4452C2×C3semidirect
84. #875C3×C4semidirect
85. C4×D12C3×C4semidirect
87. #870C3×C4semidirect
88. C4×Dic6C3×C4semidirect
127. #382C3×D3semidirect
368. C32#1512semidirect
429. C3#69544direct (N × H)
430. C3C3×#1512semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×#3822
C3×#49262
C3×#44522
C3×#44512
C3×#15123
#695443