Finite Group Databasebeta

← C3×#71756 #11775351

Subgroups — C3×#71756 #11775351

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4C3×#4538C212yesmaximal, complemented
5C3×#4537C212yesmaximal
6C3×#1512—31nomaximal
7#71756C311yesmaximal, characteristic, direct product factor
8C32×#126—21no—
9C32×#125C411yescharacteristic, complemented
10C32×#124C411yescharacteristic, complemented
11C32×#123—21no—
12C32×C22⋊Q8C2211yescharacteristic
13C32×#121C2211yescharacteristic
14C32×C4×Q8C411yescharacteristic, complemented
15C32×C4×D4—21no—
16C32×C4×D4C411yescharacteristic, complemented
17C32×#117—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yes—
22C3×#830C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×#803—21no—
25C3×#529—21no—
26C3×#529D311yescharacteristic
27C3×#529C2×C311yescharacteristic
28C3×#432—31no—
29C3×#382—31no—
30#4936C2×C311yescharacteristic, complemented
31#4926C2×C311yescharacteristic, complemented
32C3×#328—32no—
33C3×#327—32no—
34#4538C2×C312yescomplemented
35#4537C2×C312yes—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3×Dic3—22no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C4⋊C4C2×C411yescharacteristic
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42—21no—
56C32×C42C2×C411yescharacteristic
57C32×C42C2×C411yescharacteristic
58C32×C42D411yescharacteristic
59C32×C42D411yescharacteristic
60C3×C4⋊Dic3—42no—
61C2×C3×C3⋊C8—22no—
62#1512—31noSylow
63C3×#126—22no—
64C3×#126—21no—
65C3×#126—21no—
66C3×#125—21no—
67C3×#125Dic311yescharacteristic, complemented
68C3×#125C3×C411yescharacteristic, complemented
69C3×#124—21no—
70C3×#124Dic311yescharacteristic, complemented
71C3×#124C3×C411yescharacteristic, complemented
72C3×#123—22no—
73C3×#123—21no—
74C3×#123—21no—
75C3×C22⋊Q8—21no—
76C3×C22⋊Q8C2×D311yescharacteristic
77C3×C22⋊Q8C22×C311yescharacteristic
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C22×C311yescharacteristic
81C3×C4×Q8—21no—
82C3×C4×Q8Dic311yescharacteristic, complemented
83C3×C4×Q8C3×C411yescharacteristic, complemented
84C3×C4×D4—22no—
85C3×C4×D4—21no—
86C3×C4×D4—21no—
87C3×C4×D4—21no—
88C3×C4×D4Dic311yescharacteristic, complemented
89C3×C4×D4C3×C411yescharacteristic, complemented
90C3×#117—22no—
91C3×#117—21no—
92C3×#117—21no—
93C2×C3×C4⋊C4—61no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C22×C311yescharacteristic
97C2×C4⋊Dic3—21no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—32no—
100C3×#97—61no—
101C3×#95—32no—
102C3×#95—61no—
103C3⋊#95—21no—
104C3⋊#95C22×C312yes—
105#830C22×C312yes—
106C4⋊(C3⋊C8)—21no—
107#803—21no—
108C23×C32—21no—
109C23×C32C2×D411yescharacteristic
110C32×Q8—41no—
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—41no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—42no—
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22⋊C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3×Dic3—42no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—42no—
131C3×C3⋊C8—42no—
132#529C3×D311yescharacteristic
133#432—31no—
134#382—31no—
135#328—32no—
136#327—32no—
137C2×C3×Q8—21no—
138C2×C3×Q8C2×Dic311yescharacteristic
139C2×C3×Q8C2×C3×C411yescharacteristic
140C2×C3×D4—22no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4C2×Dic311yescharacteristic
145C2×C3×D4C2×C3×C411yescharacteristic
146C22×C3×C4—22no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—62no—
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4C3×D411yescharacteristic
156C22×C3×C4C3×D411yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C23×C311yescharacteristic
159C22×Dic3—22no—
160C2×C3×C8—62no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—122no—
176C3×C4⋊C4C2×Dic311yescharacteristic
177C3×C4⋊C4C2×Dic311yescharacteristic
178C3×C4⋊C4C2×C3×C411yescharacteristic
179C3×C4⋊C4C2×C3×C411yescharacteristic
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—21no—
191C3×C22⋊C4—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C42—22no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42—21no—
202C3×C42C2×Dic311yescharacteristic
203C3×C42C2×Dic311yescharacteristic
204C3×C42#6711yescharacteristic
205C3×C42#6711yescharacteristic
206C3×C42C2×C3×C411yescharacteristic
207C3×C42C2×C3×C411yescharacteristic
208C3×C42C3×D411yescharacteristic
209C3×C42C3×D411yescharacteristic
210C4⋊Dic3—42no—
211C2×C3⋊C8—22no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—41no—
227C32×C4—41no—
228C32×C4—41no—
229C3×Dic3—82no—
230#126—21no—
231#125C3×Dic311yescharacteristic, complemented
232#124C3×Dic311yescharacteristic, complemented
233#123—21no—
234C22⋊Q8C2×C3×D311yescharacteristic
235#121C2×C3×D311yescharacteristic
236C4×Q8C3×Dic311yescharacteristic, complemented
237C4×D4—21no—
238C4×D4C3×Dic311yescharacteristic, complemented
239#117—21no—
240C2×C4⋊C4—61no—
241C2×C42C2×C3×D311yescharacteristic
242C4⋊C8—61no—
243C22⋊C8—32no—
244#97—61no—
245#95—32no—
246#95—61no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3C2×#6711yescharacteristic
252C23×C3C2×C3×D411yescharacteristic
253C3×Q8—41no—
254C3×Q8—41no—
255C3×Q8—42no—
256C3×D4—41no—
257C3×D4—41no—
258C3×D4—42no—
259C3×D4—42no—
260C3×D4—42no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—41no—
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—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
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—42no—
291C2×C3×C4—42no—
292C2×C3×C4—44no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×C3×C4#21711yescharacteristic
299C2×C3×C4#21711yescharacteristic
300C2×C3×C4#21711yescharacteristic
301C2×C3×C4#21711yescharacteristic
302C2×C3×C4C3×C22⋊C411yescharacteristic
303C2×C3×C4C3×C22⋊C411yescharacteristic
304C2×C3×C4C3×C22⋊C411yescharacteristic
305C2×C3×C4C3×C22⋊C411yescharacteristic
306C2×C3×C4C22×Dic311yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C22×C3×C411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C3×C8—122no—
314C3⋊C8—42no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32—81no—
318C2×C32#41011yescharacteristic
319C2×C32#41711yescharacteristic
320C2×C32#42111yescharacteristic
321C2×Q8C2×C3×Dic311yescharacteristic
322C2×D4—21no—
323C2×D4C2×C3×Dic311yescharacteristic
324C22×C4—21no—
325C22×C4—62no—
326C22×C4C3×#6711yescharacteristic
327C22×C4C3×#6711yescharacteristic
328C22×C4C22×C3×D311yescharacteristic
329C2×C8—62no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—122no—
335C4⋊C4C2×C3×Dic311yescharacteristic
336C4⋊C4C2×C3×Dic311yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C42—21no—
343C42C2×C3×Dic311yescharacteristic
344C42C2×C3×Dic311yescharacteristic
345C42C3×#6711yescharacteristic
346C42C3×#6711yescharacteristic
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3#94911yescharacteristic
366C22×C3#95111yescharacteristic
367C22×C3C2×#21711yescharacteristic
368C22×C3C2×C3×C22⋊C411yescharacteristic
369C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
370C22×C3C3×#13711yescharacteristic
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—41no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—41no—
398C3×C4—242no—
399Dic3—82no—
400C32#151211yescharacteristic, complemented, Sylow
401C23—21no—
402C23C2×C3×#6711yescharacteristic
403Q8—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4C3×#21711yescharacteristic
419C2×C4C3×#21711yescharacteristic
420C2×C4C3×#21711yescharacteristic
421C2×C4C3×#21711yescharacteristic
422C2×C4C22×C3×Dic311yescharacteristic
423C2×C4C2×C3×#6711yescharacteristic
424C8—122no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3—82no—
435C2×C3—81no—
436C2×C3—81no—
437C2×C3#523211yescharacteristic
438C2×C3#523611yescharacteristic
439C2×C3#524011yescharacteristic
440C2×C3C3×#41011yescharacteristic
441C2×C3C3×#41711yescharacteristic
442C2×C3C3×#42111yescharacteristic
443C22—21no—
444C22—21no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22C3×#94911yescharacteristic
449C22C3×#95111yescharacteristic
450C22C2×C3×#21711yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—242no—
461C3—21no—
462C3#7175611yescharacteristic, direct product factor
463C3C3×#151211yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—81no—
467C2C3×#523211yescharacteristic
468C2C3×#523611yescharacteristic
469C2C3×#524011yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#529C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#529D3
hypocenterC3C3×#1512
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#529

Complements

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

NH ≅ G/Ntype
2. C3×#4936C2semidirect
3. C3×#4926C2semidirect
4. C3×#4538C2semidirect
7. #71756C3direct (N × H)
9. C32×#125C4semidirect
10. C32×#124C4semidirect
14. C32×C4×Q8C4semidirect
16. C32×C4×D4C4semidirect
30. #4936C2×C3semidirect
31. #4926C2×C3semidirect
34. #4538C2×C3semidirect
67. C3×#125Dic3semidirect
68. C3×#125C3×C4semidirect
70. C3×#124Dic3semidirect
71. C3×#124C3×C4semidirect
82. C3×C4×Q8Dic3semidirect
83. C3×C4×Q8C3×C4semidirect
88. C3×C4×D4Dic3semidirect
89. C3×C4×D4C3×C4semidirect
231. #125C3×Dic3semidirect
232. #124C3×Dic3semidirect
236. C4×Q8C3×Dic3semidirect
238. C4×D4C3×Dic3semidirect
400. C32#1512semidirect
462. C3#71756direct (N × H)
463. C3C3×#1512semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C3×#49362
C3×#49262
C3×#45382
C3×#45372
C3×#15123
#717563