Finite Group Databasebeta

← C3×#71751 #11774459

Subgroups — C3×#71751 #11774459

Order 1152.

585 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
1C32×#529C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C3×#4535C212yesmaximal, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1483—31nomaximal
7#71751C311yesmaximal, characteristic, direct product factor
8C32×#126—21no—
9C32×#125C411yescharacteristic
10C32×#124C411yescharacteristic
11C32×#123—21no—
12C32×C22⋊Q8C411yescharacteristic
13C32×#121C411yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15C32×C4×D4—21no—
16C32×C4×D4C2211yescharacteristic
17C32×#117—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×#208—21no—
20C22×C3×C3⋊C8—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×#803—21no—
24C3×C4×C3⋊C8C2212yes—
25C3×#529—21no—
26C3×#529D311yescharacteristic
27C3×#529C2×C311yescharacteristic
28C2×C3×C4⋊C8—31no—
29C3×C4×M16—31no—
30C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
31C4×#208C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4535C2×C312yescomplemented
35D4⋊(C3⋊C8)C2×C312yescomplemented
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C411yescharacteristic
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C42—21no—
55C32×C42C2×C411yescharacteristic
56C32×C42D411yescharacteristic
57C32×C42D411yescharacteristic
58C32×C42C2311yescharacteristic
59C3×#208—24no—
60C2×C3×C3⋊C8—22no—
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—42no—
63#1483—31noSylow
64C2×C3×M16—61no—
65C22×C3×C8—61no—
66C3×#126—22no—
67C3×#126—21no—
68C3×#126—21no—
69C3×#125—21no—
70C3×#125Dic311yescharacteristic
71C3×#125C3×C411yescharacteristic
72C3×#124—21no—
73C3×#124Dic311yescharacteristic
74C3×#124C3×C411yescharacteristic
75C3×#123—22no—
76C3×#123—21no—
77C3×#123—21no—
78C3×C22⋊Q8—21no—
79C3×C22⋊Q8Dic311yescharacteristic
80C3×C22⋊Q8C3×C411yescharacteristic
81C3×#121—21no—
82C3×#121Dic311yescharacteristic
83C3×#121C3×C411yescharacteristic
84C3×C4×Q8—21no—
85C3×C4×Q8C2×D311yescharacteristic
86C3×C4×Q8C22×C311yescharacteristic
87C3×C4×D4—22no—
88C3×C4×D4—21no—
89C3×C4×D4—21no—
90C3×C4×D4—21no—
91C3×C4×D4C2×D311yescharacteristic
92C3×C4×D4C22×C311yescharacteristic
93C3×#117—22no—
94C3×#117—21no—
95C3×#117—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C22×C311yescharacteristic
99C2×#208—21no—
100C22×C3⋊C8—21no—
101C3×C4⋊C8—32no—
102C3×C4⋊C8—61no—
103C3×#97—61no—
104C3×C4×C8—32no—
105C4⋊(C3⋊C8)—21no—
106C4⋊(C3⋊C8)C22×C312yes—
107#803—21no—
108C4×C3⋊C8C22×C312yes—
109C23×C32—21no—
110C23×C32C22⋊C411yescharacteristic
111C32×Q8—22no—
112C32×D4—22no—
113C32×D4—42no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22⋊C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C3×C3⋊C8—24no—
130C3×C3⋊C8—42no—
131#529C3×D311yescharacteristic
132C2×C4⋊C8—31no—
133C4×M16—31no—
134Q8⋊C8—32no—
135D4⋊C8—32no—
136C2×C3×Q8—21no—
137C2×C3×Q8C2×Dic311yescharacteristic
138C2×C3×Q8C2×C3×C411yescharacteristic
139C2×C3×D4—22no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4C2×Dic311yescharacteristic
144C2×C3×D4C2×C3×C411yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4C2×Dic311yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4C2×C3×C411yescharacteristic
155C22×C3×C4C3×D411yescharacteristic
156C22×C3×C4C3×D411yescharacteristic
157C3×M16—64no—
158C2×C3×C8—62no—
159C2×C3×C8—62no—
160C2×C3×C8—122no—
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⋊C4C2×Dic311yescharacteristic
176C3×C4⋊C4C2×Dic311yescharacteristic
177C3×C4⋊C4C2×C3×C411yescharacteristic
178C3×C4⋊C4C2×C3×C411yescharacteristic
179C3×C22⋊C4—22no—
180C3×C22⋊C4—22no—
181C3×C22⋊C4—22no—
182C3×C22⋊C4—22no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—21no—
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×C42—22no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42C2×Dic311yescharacteristic
202C3×C42#6711yescharacteristic
203C3×C42#6711yescharacteristic
204C3×C42C2×C3×C411yescharacteristic
205C3×C42C3×D411yescharacteristic
206C3×C42C3×D411yescharacteristic
207C3×C42C22×D311yescharacteristic
208C3×C42C23×C311yescharacteristic
209#208—24no—
210C2×C3⋊C8—22no—
211C2×C3⋊C8—22no—
212C2×C3⋊C8—42no—
213C22×C32—21no—
214C22×C32—21no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32#10412yes—
219C22×C32C2×C22⋊C411yescharacteristic
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—41no—
226C32×C4—41no—
227C32×C4#13112yes—
228C32×C4AGL(1,ℤ/8)11yescharacteristic
229C32×C4#13711yescharacteristic
230C2×M16—61no—
231C22×C8—61no—
232#126—21no—
233#125C3×Dic311yescharacteristic
234#124C3×Dic311yescharacteristic
235#123—21no—
236C22⋊Q8C3×Dic311yescharacteristic
237#121C3×Dic311yescharacteristic
238C4×Q8C2×C3×D311yescharacteristic
239C4×D4—21no—
240C4×D4C2×C3×D311yescharacteristic
241#117—21no—
242C2×C42C2×C3×D311yescharacteristic
243C4⋊C8—32no—
244C4⋊C8—61no—
245#97—61no—
246C4×C8—32no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3#21711yescharacteristic
252C23×C3C3×C22⋊C411yescharacteristic
253C3×Q8—22no—
254C3×Q8—22no—
255C3×Q8—42no—
256C3×D4—22no—
257C3×D4—22no—
258C3×D4—42no—
259C3×D4—44no—
260C3×D4—42no—
261C3×D4—42no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
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—21no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4#21711yescharacteristic
296C2×C3×C4#21711yescharacteristic
297C2×C3×C4#21711yescharacteristic
298C2×C3×C4C3×C22⋊C411yescharacteristic
299C2×C3×C4C3×C22⋊C411yescharacteristic
300C2×C3×C4C3×C22⋊C411yescharacteristic
301C2×C3×C4C22×Dic311yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304C2×C3×C4C22×C3×C411yescharacteristic
305C2×C3×C4C2×C3×D411yescharacteristic
306C2×C3×C4C2×C3×D411yescharacteristic
307C3×C8—64no—
308C3×C8—122no—
309C3⋊C8—24no—
310C3⋊C8—42no—
311C2×C32—22no—
312C2×C32—81no—
313C2×C32#40811yescharacteristic
314C2×C32#41711yescharacteristic
315C2×C32C2×#10411yescharacteristic
316C2×Q8C2×C3×Dic311yescharacteristic
317C2×D4—21no—
318C2×D4C2×C3×Dic311yescharacteristic
319C22×C4—21no—
320C22×C4C2×C3×Dic311yescharacteristic
321C22×C4C3×#6711yescharacteristic
322C22×C4C3×#6711yescharacteristic
323M16—64no—
324C2×C8—62no—
325C2×C8—62no—
326C2×C8—122no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4C2×C3×Dic311yescharacteristic
332C4⋊C4C2×C3×Dic311yescharacteristic
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C42—21no—
339C42C2×C3×Dic311yescharacteristic
340C42C3×#6711yescharacteristic
341C42C3×#6711yescharacteristic
342C42C22×C3×D311yescharacteristic
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—22no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3#83712yes—
361C22×C3C3×#10412yes—
362C22×C3C2×#21711yescharacteristic
363C22×C3C2×C3×C22⋊C411yescharacteristic
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—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—42no—
380C3×C4—42no—
381C3×C4—42no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4#94812yes—
389C3×C4#94911yescharacteristic
390C3×C4#95111yescharacteristic
391C3×C4C3×#13112yes—
392C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
393C3×C4C3×#13711yescharacteristic
394C32#148311yescharacteristic, complemented, Sylow
395C23—21no—
396C23C3×#21711yescharacteristic
397Q8—22no—
398D4—22no—
399D4—42no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4C3×#21711yescharacteristic
410C2×C4C3×#21711yescharacteristic
411C2×C4C3×#21711yescharacteristic
412C2×C4C22×C3×Dic311yescharacteristic
413C2×C4C2×C3×#6711yescharacteristic
414C2×C4C2×C3×#6711yescharacteristic
415C8—64no—
416C8—122no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—42no—
423C2×C3—82no—
424C2×C3—81no—
425C2×C3—81no—
426C2×C3#523211yescharacteristic
427C2×C3#523411yescharacteristic
428C2×C3C2×#83711yescharacteristic
429C2×C3C3×#40811yescharacteristic
430C2×C3C3×#41711yescharacteristic
431C2×C3C2×C3×#10411yescharacteristic
432C22—21no—
433C22—21no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22C3×#83712yes—
438C22C2×C3×#21711yescharacteristic
439C4—21no—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4C3×#94812yes—
447C4C3×#94911yescharacteristic
448C4C3×#95111yescharacteristic
449C3—21no—
450C3#7175111yescharacteristic, direct product factor
451C3C3×#148311yescharacteristic, complemented
452C2—22no—
453C2—81no—
454C2C3×#523211yescharacteristic
455C2C3×#523411yescharacteristic
456C2C2×C3×#83711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#529C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C4
cosocleC3×C42C23×C3
hypercenterC3×#529D3
hypocenterC3C3×#1483
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#529

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4⋊(C3⋊C8)C2semidirect
3. C3×C4×#208C2semidirect
4. C3×#4535C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71751C3direct (N × H)
30. C2×C4⋊(C3⋊C8)C2×C3semidirect
31. C4×#208C2×C3semidirect
34. #4535C2×C3semidirect
35. D4⋊(C3⋊C8)C2×C3semidirect
394. C32#1483semidirect
450. C3#71751direct (N × H)
451. C3C3×#1483semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C2×C3×C4⋊(C3⋊C8)2
C3×C4×#2082
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#14833
#717513