Finite Group Databasebeta

← C3×#71639 #11774270

Subgroups — C3×#71639 #11774270

Order 1152.

683 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C3×#4535C212yesmaximal, complemented
5C3×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C3×#1477—31nomaximal
7#71639C311yesmaximal, 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
19C22×C3×C3⋊C8—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)—21no—
22C3×C4⋊(C3⋊C8)—21no—
23C3×C4⋊(C3⋊C8)C2212yes—
24C3×C4×C3⋊C8C2212yes—
25C3×C4×#41—21no—
26C3×C4×#41D311yescharacteristic
27C3×C4×#41C2×C311yescharacteristic
28C3×#431—31no—
29C2×C3×C4⋊C8—31no—
30#4925C2×C311yescharacteristic, complemented
31C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
32C3×Q8⋊C8—32no—
33C3×D4⋊C8—32no—
34#4535C2×C312yescomplemented
35D4⋊(C3⋊C8)C2×C312yescomplemented
36C32×#41—22no—
37C32×#41C814yescomplemented
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
61C2×C3×C3⋊C8—22no—
62C2×C3×C3⋊C8—22no—
63C2×C3×C3⋊C8—42no—
64#1477—31noSylow
65C2×C3×#41—21no—
66C2×C3×#41Dic311yescharacteristic
67C2×C3×#41C3×C411yescharacteristic
68C22×C3×C8—61no—
69C3×C4×Q8—21no—
70C3×C4×Q8—21no—
71C3×C4×Q8Dic311yescharacteristic
72C3×C4×Q8C3×C411yescharacteristic
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C22×C311yescharacteristic
75C3×C4×D4—22no—
76C3×C4×D4—22no—
77C3×C4×D4—21no—
78C3×C4×D4—21no—
79C3×C4×D4—21no—
80C3×C4×D4—21no—
81C3×C4×D4—21no—
82C3×C4×D4—21no—
83C3×C4×D4Dic311yescharacteristic
84C3×C4×D4C3×C411yescharacteristic
85C3×C4×D4C2×D311yescharacteristic
86C3×C4×D4C22×C311yescharacteristic
87C3×#117—22no—
88C3×#117—21no—
89C3×#117—21no—
90C3×#117—21no—
91C3×#117Dic311yescharacteristic
92C3×#117C3×C411yescharacteristic
93C2×C3×C42—22no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C22×C311yescharacteristic
99C22×C3⋊C8—21no—
100C3×C4⋊C8—32no—
101C3×C4⋊C8—61no—
102C3×C4⋊C8—61no—
103C3×C22⋊C8—61no—
104C3×C4×C8—32no—
105#830—21no—
106C4⋊(C3⋊C8)—21no—
107C4⋊(C3⋊C8)—21no—
108C4⋊(C3⋊C8)C22×C312yes—
109C4×C3⋊C8C22×C312yes—
110C23×C32—21no—
111C23×C32C22⋊C411yescharacteristic
112C32×Q8—21no—
113C32×Q8C2×C812yescomplemented
114C32×D4—24no—
115C32×D4—21no—
116C32×D4C2×C812yescomplemented
117C2×C32×C4—21no—
118C2×C32×C4—24no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—41no—
124C2×C32×C4—42no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22⋊C411yescharacteristic
129C2×C32×C4C22⋊C411yescharacteristic
130C2×C32×C4C2×C812yes—
131C2×C32×C4M1612yes—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C3×C3⋊C8—42no—
136C3×C3⋊C8—42no—
137C4×#41C3×D311yescharacteristic
138#431—31no—
139C2×C4⋊C8—31no—
140Q8⋊C8—32no—
141D4⋊C8—32no—
142C3×#41—24no—
143C3×#41—22no—
144C3×#41—22no—
145C3×#41—24no—
146C3×#41C3⋊C814yescomplemented
147C3×#41C3×C814yescomplemented
148C2×C3×Q8—21no—
149C2×C3×Q8C2×Dic311yescharacteristic
150C2×C3×Q8C2×C3×C411yescharacteristic
151C2×C3×D4—22no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4C2×Dic311yescharacteristic
156C2×C3×D4C2×C3×C411yescharacteristic
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
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×C4C2×Dic311yescharacteristic
170C22×C3×C4#6711yescharacteristic
171C22×C3×C4#6711yescharacteristic
172C22×C3×C4C2×C3×C411yescharacteristic
173C22×C3×C4C3×D411yescharacteristic
174C22×C3×C4C3×D411yescharacteristic
175C2×C3×C8—62no—
176C2×C3×C8—62no—
177C2×C3×C8—122no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4C2×Dic311yescharacteristic
187C3×C4⋊C4C2×Dic311yescharacteristic
188C3×C4⋊C4C2×C3×C411yescharacteristic
189C3×C4⋊C4C2×C3×C411yescharacteristic
190C3×C22⋊C4—22no—
191C3×C22⋊C4—22no—
192C3×C22⋊C4—22no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—21no—
199C3×C42—22no—
200C3×C42—22no—
201C3×C42—22no—
202C3×C42—21no—
203C3×C42—21no—
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×C42C2×Dic311yescharacteristic
213C3×C42#6711yescharacteristic
214C3×C42#6711yescharacteristic
215C3×C42C2×C3×C411yescharacteristic
216C3×C42C3×D411yescharacteristic
217C3×C42C3×D411yescharacteristic
218C3×C42C22×D311yescharacteristic
219C3×C42C23×C311yescharacteristic
220C2×C3⋊C8—22no—
221C2×C3⋊C8—22no—
222C2×C3⋊C8—42no—
223C22×C32—22no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32C22⋊C812yes—
229C22×C32C2×C22⋊C411yescharacteristic
230C32×C4—22no—
231C32×C4—21no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4C22⋊C812yes—
237C32×C4C22×C811yescharacteristic
238C32×C4C2×M1611yescharacteristic
239C32×C4AGL(1,ℤ/8)11yescharacteristic
240C32×C4#13711yescharacteristic
241C2×#41C3×Dic311yescharacteristic
242C22×C8—61no—
243C4×Q8C3×Dic311yescharacteristic
244C4×Q8C2×C3×D311yescharacteristic
245C4×D4—21no—
246C4×D4—21no—
247C4×D4C3×Dic311yescharacteristic
248C4×D4C2×C3×D311yescharacteristic
249#117—21no—
250#117C3×Dic311yescharacteristic
251C2×C42—21no—
252C2×C42C2×C3×D311yescharacteristic
253C4⋊C8—32no—
254C4⋊C8—61no—
255C4⋊C8—61no—
256C22⋊C8—61no—
257C4×C8—32no—
258C23×C3—22no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3#21711yescharacteristic
263C23×C3C3×C22⋊C411yescharacteristic
264C3×Q8—22no—
265C3×Q8—21no—
266C3×Q8—21no—
267C3×Q8—22no—
268C3×Q8C2×C3⋊C812yescomplemented
269C3×Q8C2×C3×C812yescomplemented
270C3×D4—28no—
271C3×D4—22no—
272C3×D4—24no—
273C3×D4—24no—
274C3×D4—21no—
275C3×D4—21no—
276C3×D4—22no—
277C3×D4C2×C3⋊C812yescomplemented
278C3×D4C2×C3×C812yescomplemented
279C2×C3×C4—22no—
280C2×C3×C4—28no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—42no—
308C2×C3×C4—44no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4C2×C3⋊C812yes—
318C2×C3×C4#20812yes—
319C2×C3×C4#21711yescharacteristic
320C2×C3×C4#21711yescharacteristic
321C2×C3×C4#21711yescharacteristic
322C2×C3×C4C3×C22⋊C411yescharacteristic
323C2×C3×C4C3×C22⋊C411yescharacteristic
324C2×C3×C4C3×C22⋊C411yescharacteristic
325C2×C3×C4C2×C3×C812yes—
326C2×C3×C4C3×M1612yes—
327C2×C3×C4C22×Dic311yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C22×C3×C411yescharacteristic
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D411yescharacteristic
333C3×C8—122no—
334C3×C8—122no—
335C3⋊C8—42no—
336C3⋊C8—42no—
337C2×C32—22no—
338C2×C32—42no—
339C2×C32C2×C22⋊C811yescharacteristic
340C2×C32#41711yescharacteristic
341C2×C32#42111yescharacteristic
342#41—22no—
343#41C3×C3⋊C814yescomplemented
344C2×Q8C2×C3×Dic311yescharacteristic
345C2×D4—21no—
346C2×D4C2×C3×Dic311yescharacteristic
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4C2×C3×Dic311yescharacteristic
351C22×C4C3×#6711yescharacteristic
352C22×C4C3×#6711yescharacteristic
353C2×C8—62no—
354C2×C8—62no—
355C2×C8—122no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4C2×C3×Dic311yescharacteristic
359C4⋊C4C2×C3×Dic311yescharacteristic
360C22⋊C4—21no—
361C22⋊C4—21no—
362C22⋊C4—21no—
363C42—21no—
364C42—21no—
365C42—21no—
366C42C2×C3×Dic311yescharacteristic
367C42C3×#6711yescharacteristic
368C42C3×#6711yescharacteristic
369C42C22×C3×D311yescharacteristic
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—24no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—21no—
378C22×C3—22no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3#83012yes—
388C22×C3C3×C22⋊C812yes—
389C22×C3C2×#21711yescharacteristic
390C22×C3C2×C3×C22⋊C411yescharacteristic
391C3×C4—24no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—22no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—22no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—42no—
409C3×C4—42no—
410C3×C4—41no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—41no—
414C3×C4#83012yes—
415C3×C4C3×C22⋊C812yes—
416C3×C4C22×C3⋊C811yescharacteristic
417C3×C4C2×#20811yescharacteristic
418C3×C4#94911yescharacteristic
419C3×C4#95111yescharacteristic
420C3×C4C22×C3×C811yescharacteristic
421C3×C4C2×C3×M1611yescharacteristic
422C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
423C3×C4C3×#13711yescharacteristic
424C32#147711yescharacteristic, complemented, Sylow
425C23—21no—
426C23C3×#21711yescharacteristic
427Q8—21no—
428Q8C2×C3×C3⋊C812yescomplemented
429D4—24no—
430D4—21no—
431D4C2×C3×C3⋊C812yescomplemented
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4C2×C3×C3⋊C812yes—
443C2×C4C3×#20812yes—
444C2×C4C3×#21711yescharacteristic
445C2×C4C3×#21711yescharacteristic
446C2×C4C3×#21711yescharacteristic
447C2×C4C22×C3×Dic311yescharacteristic
448C2×C4C2×C3×#6711yescharacteristic
449C2×C4C2×C3×#6711yescharacteristic
450C8—122no—
451C8—122no—
452C2×C3—22no—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—42no—
458C2×C3—44no—
459C2×C3—42no—
460C2×C3—42no—
461C2×C3C2×#83011yescharacteristic
462C2×C3#523211yescharacteristic
463C2×C3#523611yescharacteristic
464C2×C3C2×C3×C22⋊C811yescharacteristic
465C2×C3C3×#41711yescharacteristic
466C2×C3C3×#42111yescharacteristic
467C22—21no—
468C22—21no—
469C22—22no—
470C22—41no—
471C22—41no—
472C22C3×#83012yes—
473C22C2×C3×#21711yescharacteristic
474C4—22no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—41no—
479C4—41no—
480C4C3×#83012yes—
481C4C22×C3×C3⋊C811yescharacteristic
482C4C2×C3×#20811yescharacteristic
483C4C3×#94911yescharacteristic
484C4C3×#95111yescharacteristic
485C3—21no—
486C3#7163911yescharacteristic, direct product factor
487C3C3×#147711yescharacteristic, complemented
488C2—22no—
489C2—42no—
490C2C2×C3×#83011yescharacteristic
491C2C3×#523211yescharacteristic
492C2C3×#523611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC3×C4C22×C3×C8
FrattiniC42C22×C3×D3
FittingC32×C4×#41C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C4
cosocleC3×C42C23×C3
hypercenterC3×C4×#41D3
hypocenterC3C3×#1477
LCSG ▷ 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×#4925C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C3×#4535C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
7. #71639C3direct (N × H)
30. #4925C2×C3semidirect
31. C2×C4⋊(C3⋊C8)C2×C3semidirect
34. #4535C2×C3semidirect
35. D4⋊(C3⋊C8)C2×C3semidirect
37. C32×#41C8semidirect
113. C32×Q8C2×C8semidirect
116. C32×D4C2×C8semidirect
146. C3×#41C3⋊C8semidirect
147. C3×#41C3×C8semidirect
268. C3×Q8C2×C3⋊C8semidirect
269. C3×Q8C2×C3×C8semidirect
277. C3×D4C2×C3⋊C8semidirect
278. C3×D4C2×C3×C8semidirect
343. #41C3×C3⋊C8semidirect
424. C32#1477semidirect
428. Q8C2×C3×C3⋊C8semidirect
431. D4C2×C3×C3⋊C8semidirect
486. C3#71639direct (N × H)
487. C3C3×#1477semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C3×#49252
C2×C3×C4⋊(C3⋊C8)2
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#14773
#716393