Finite Group Databasebeta

← C3×#71641 #11774645

Subgroups — C3×#71641 #11774645

Order 1152.

687 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C3×#4924C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C3×#4535C212yesmaximal, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1489—31nomaximal
7#71641C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C411yescharacteristic
9C32×C4×Q8C411yescharacteristic
10C32×C4×Q8C2211yescharacteristic
11C32×C4×D4—21no—
12C32×C4×D4—21no—
13C32×C4×D4C411yescharacteristic
14C32×C4×D4C2211yescharacteristic
15C32×#117—21no—
16C32×#117C411yescharacteristic
17C2×C32×C42—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×#208—21no—
20C2×C3×#208—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)C2212yes—
23C3×#803—21no—
24C3×C4×C3⋊C8C2212yes—
25C3×C4×#41—21no—
26C3×C4×#41D311yescharacteristic
27C3×C4×#41C2×C311yescharacteristic
28C3×#423—31no—
29C3×C4×M16—31no—
30#4924C2×C311yescharacteristic, complemented
31C4×#208C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4535C2×C312yescomplemented
35D4⋊(C3⋊C8)C2×C312yescomplemented
36C32×#41—22no—
37C32×#41—22no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×D4—21no—
40C2×C32×D4C2×C411yescharacteristic
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4C2×C411yescharacteristic
50C32×C4⋊C4C2×C411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C22⋊C4—21no—
53C32×C22⋊C4—21no—
54C32×C42—21no—
55C32×C42—21no—
56C32×C42—21no—
57C32×C42C2×C411yescharacteristic
58C32×C42D411yescharacteristic
59C32×C42D411yescharacteristic
60C32×C42C2311yescharacteristic
61C3×#208—24no—
62C3×#208—42no—
63C2×C3×C3⋊C8—22no—
64C2×C3×C3⋊C8—22no—
65#1489—31noSylow
66C2×C3×#41—21no—
67C2×C3×#41Dic311yescharacteristic
68C2×C3×#41C3×C411yescharacteristic
69C2×C3×M16—61no—
70C2×C3×M16—61no—
71C3×C4×Q8—21no—
72C3×C4×Q8—21no—
73C3×C4×Q8Dic311yescharacteristic
74C3×C4×Q8C3×C411yescharacteristic
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C22×C311yescharacteristic
77C3×C4×D4—22no—
78C3×C4×D4—22no—
79C3×C4×D4—21no—
80C3×C4×D4—21no—
81C3×C4×D4—21no—
82C3×C4×D4—21no—
83C3×C4×D4—21no—
84C3×C4×D4—21no—
85C3×C4×D4Dic311yescharacteristic
86C3×C4×D4C3×C411yescharacteristic
87C3×C4×D4C2×D311yescharacteristic
88C3×C4×D4C22×C311yescharacteristic
89C3×#117—22no—
90C3×#117—21no—
91C3×#117—21no—
92C3×#117—21no—
93C3×#117Dic311yescharacteristic
94C3×#117C3×C411yescharacteristic
95C2×C3×C42—22no—
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42—21no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C22×C311yescharacteristic
101C2×#208—21no—
102C2×#208—21no—
103C3×C4⋊C8—32no—
104C3×C4⋊C8—61no—
105C3×#97—61no—
106C3×C4×C8—32no—
107C4⋊(C3⋊C8)—21no—
108C4⋊(C3⋊C8)C22×C312yes—
109#803—21no—
110C4×C3⋊C8C22×C312yes—
111C23×C32—21no—
112C23×C32C22⋊C411yescharacteristic
113C32×Q8—21no—
114C32×Q8M1612yescomplemented
115C32×D4—24no—
116C32×D4—21no—
117C32×D4M1612yescomplemented
118C2×C32×C4—24no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—22no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—42no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C22⋊C411yescharacteristic
131C2×C32×C4C22⋊C411yescharacteristic
132C2×C32×C4C22⋊C411yescharacteristic
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C3×C3⋊C8—24no—
137C3×C3⋊C8—42no—
138C4×#41C3×D311yescharacteristic
139#423—31no—
140C4×M16—31no—
141Q8⋊C8—32no—
142D4⋊C8—32no—
143C3×#41—24no—
144C3×#41—24no—
145C3×#41—22no—
146C3×#41—22no—
147C3×#41—22no—
148C3×#41—22no—
149C2×C3×Q8—21no—
150C2×C3×Q8C2×Dic311yescharacteristic
151C2×C3×Q8C2×C3×C411yescharacteristic
152C2×C3×D4—22no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4C2×Dic311yescharacteristic
157C2×C3×D4C2×C3×C411yescharacteristic
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4C2×Dic311yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4#6711yescharacteristic
173C22×C3×C4C2×C3×C411yescharacteristic
174C22×C3×C4C3×D411yescharacteristic
175C22×C3×C4C3×D411yescharacteristic
176C3×M16—64no—
177C3×M16—122no—
178C2×C3×C8—62no—
179C2×C3×C8—62no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4C2×Dic311yescharacteristic
189C3×C4⋊C4C2×Dic311yescharacteristic
190C3×C4⋊C4C2×C3×C411yescharacteristic
191C3×C4⋊C4C2×C3×C411yescharacteristic
192C3×C22⋊C4—22no—
193C3×C22⋊C4—22no—
194C3×C22⋊C4—22no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C42—22no—
202C3×C42—22no—
203C3×C42—22no—
204C3×C42—21no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42C2×Dic311yescharacteristic
215C3×C42#6711yescharacteristic
216C3×C42#6711yescharacteristic
217C3×C42C2×C3×C411yescharacteristic
218C3×C42C3×D411yescharacteristic
219C3×C42C3×D411yescharacteristic
220C3×C42C22×D311yescharacteristic
221C3×C42C23×C311yescharacteristic
222#208—24no—
223#208—42no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8—22no—
226C22×C32—21no—
227C22×C32—22no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32C2×C22⋊C411yescharacteristic
233C32×C4—21no—
234C32×C4—22no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—41no—
238C32×C4—41no—
239C32×C4#10412yes—
240C32×C4C2×M1611yescharacteristic
241C32×C4C2×M1611yescharacteristic
242C32×C4AGL(1,ℤ/8)11yescharacteristic
243C32×C4#13711yescharacteristic
244C2×#41C3×Dic311yescharacteristic
245C2×M16—61no—
246C2×M16—61no—
247C4×Q8C3×Dic311yescharacteristic
248C4×Q8C2×C3×D311yescharacteristic
249C4×D4—21no—
250C4×D4—21no—
251C4×D4C3×Dic311yescharacteristic
252C4×D4C2×C3×D311yescharacteristic
253#117—21no—
254#117C3×Dic311yescharacteristic
255C2×C42—21no—
256C2×C42C2×C3×D311yescharacteristic
257C4⋊C8—32no—
258C4⋊C8—61no—
259#97—61no—
260C4×C8—32no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3#21711yescharacteristic
266C23×C3C3×C22⋊C411yescharacteristic
267C3×Q8—22no—
268C3×Q8—21no—
269C3×Q8—21no—
270C3×Q8—22no—
271C3×Q8#20812yescomplemented
272C3×Q8C3×M1612yescomplemented
273C3×D4—28no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—22no—
277C3×D4—21no—
278C3×D4—21no—
279C3×D4—22no—
280C3×D4#20812yescomplemented
281C3×D4C3×M1612yescomplemented
282C2×C3×C4—22no—
283C2×C3×C4—28no—
284C2×C3×C4—24no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—44no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4#21711yescharacteristic
325C2×C3×C4#21711yescharacteristic
326C2×C3×C4#21711yescharacteristic
327C2×C3×C4C3×C22⋊C411yescharacteristic
328C2×C3×C4C3×C22⋊C411yescharacteristic
329C2×C3×C4C3×C22⋊C411yescharacteristic
330C2×C3×C4C22×Dic311yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C22×C3×C411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C2×C3×D411yescharacteristic
336C3×C8—64no—
337C3×C8—122no—
338C3⋊C8—24no—
339C3⋊C8—42no—
340C2×C32—41no—
341C2×C32—42no—
342C2×C32#40711yescharacteristic
343C2×C32#41711yescharacteristic
344C2×C32C2×#10411yescharacteristic
345#41—22no—
346#41—22no—
347C2×Q8C2×C3×Dic311yescharacteristic
348C2×D4—21no—
349C2×D4C2×C3×Dic311yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4C2×C3×Dic311yescharacteristic
354C22×C4C3×#6711yescharacteristic
355C22×C4C3×#6711yescharacteristic
356M16—64no—
357M16—122no—
358C2×C8—62no—
359C2×C8—62no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4C2×C3×Dic311yescharacteristic
363C4⋊C4C2×C3×Dic311yescharacteristic
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C42—21no—
368C42—21no—
369C42—21no—
370C42C2×C3×Dic311yescharacteristic
371C42C3×#6711yescharacteristic
372C42C3×#6711yescharacteristic
373C42C22×C3×D311yescharacteristic
374C22×C3—22no—
375C22×C3—24no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3C2×#21711yescharacteristic
394C22×C3C2×C3×C22⋊C411yescharacteristic
395C3×C4—22no—
396C3×C4—24no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—22no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4#83712yes—
419C3×C4C3×#10412yes—
420C3×C4C2×#20811yescharacteristic
421C3×C4C2×#20811yescharacteristic
422C3×C4#94911yescharacteristic
423C3×C4#95111yescharacteristic
424C3×C4C2×C3×M1611yescharacteristic
425C3×C4C2×C3×M1611yescharacteristic
426C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
427C3×C4C3×#13711yescharacteristic
428C32#148911yescharacteristic, complemented, Sylow
429C23—21no—
430C23C3×#21711yescharacteristic
431Q8—21no—
432Q8C3×#20812yescomplemented
433D4—24no—
434D4—21no—
435D4C3×#20812yescomplemented
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4C3×#21711yescharacteristic
449C2×C4C3×#21711yescharacteristic
450C2×C4C3×#21711yescharacteristic
451C2×C4C22×C3×Dic311yescharacteristic
452C2×C4C2×C3×#6711yescharacteristic
453C2×C4C2×C3×#6711yescharacteristic
454C8—64no—
455C8—122no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—42no—
460C2×C3—44no—
461C2×C3—41no—
462C2×C3—42no—
463C2×C3—41no—
464C2×C3—42no—
465C2×C3#520711yescharacteristic
466C2×C3#523211yescharacteristic
467C2×C3C2×#83711yescharacteristic
468C2×C3C3×#40711yescharacteristic
469C2×C3C3×#41711yescharacteristic
470C2×C3C2×C3×#10411yescharacteristic
471C22—21no—
472C22—22no—
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22C2×C3×#21711yescharacteristic
478C4—21no—
479C4—22no—
480C4—21no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4C3×#83712yes—
485C4C2×C3×#20811yescharacteristic
486C4C2×C3×#20811yescharacteristic
487C4C3×#94911yescharacteristic
488C4C3×#95111yescharacteristic
489C3—21no—
490C3#7164111yescharacteristic, direct product factor
491C3C3×#148911yescharacteristic, complemented
492C2—41no—
493C2—42no—
494C2C3×#520711yescharacteristic
495C2C3×#523211yescharacteristic
496C2C2×C3×#83711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×#41C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C4
cosocleC3×C42C23×C3
hypercenterC3×C4×#41D3
hypocenterC3C3×#1489
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
2. C3×#4924C2semidirect
3. C3×C4×#208C2semidirect
4. C3×#4535C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71641C3direct (N × H)
30. #4924C2×C3semidirect
31. C4×#208C2×C3semidirect
34. #4535C2×C3semidirect
35. D4⋊(C3⋊C8)C2×C3semidirect
114. C32×Q8M16semidirect
117. C32×D4M16semidirect
271. C3×Q8#208semidirect
272. C3×Q8C3×M16semidirect
280. C3×D4#208semidirect
281. C3×D4C3×M16semidirect
428. C32#1489semidirect
432. Q8C3×#208semidirect
435. D4C3×#208semidirect
490. C3#71641direct (N × H)
491. C3C3×#1489semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×#49242
C3×C4×#2082
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#14893
#716413