Finite Group Databasebeta

← C3×#71921 #11779853

Subgroups — C3×#71921 #11779853

Order 1152.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#550C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×#5020C211yesmaximal, characteristic, complemented
4C3×#5019C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6C3×#4535C211yesmaximal, characteristic, complemented
7C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#1642—31nomaximal
9#71921C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—21no—
11C32×#127—21no—
12C32×#127C2211yescharacteristic
13C32×#121—22no—
14C32×#121—21no—
15C32×C4×Q8C2211yescharacteristic
16C32×C4×D4—21no—
17C32×C4×D4C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#835—21no—
21C3×#832—22no—
22C3×#810—21no—
23C3×#808—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#550—21no—
28C3×#550D311yescharacteristic
29C3×#550C2×C311yescharacteristic
30C3×#486—31no—
31C3×#475—31no—
32C3×#461—31no—
33#5070C2×C311yescharacteristic, complemented
34#5020C2×C311yescharacteristic, complemented
35#5019C2×C311yescharacteristic, complemented
36C3×#331—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39#4544C2×C311yescharacteristic, complemented
40#4535C2×C311yescharacteristic, complemented
41D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
42C32×#41—42no—
43C32×#41—42no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4—22no—
46C2×C32×D4—22no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C2×C32×D4D412yes—
51C22×C32×C4—22no—
52C22×C32×C4—21no—
53C2×C3×Dic6—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—22no—
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C32×C42C2311yescharacteristic
61C3×#214—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67#1642—31noSylow
68C2×C3×#41—22no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×SD16—61no—
72C3×C4⋊Q8—31no—
73C3×#127—22no—
74C3×#127—21no—
75C3×#127—21no—
76C3×#127—21no—
77C3×#127C2×D311yescharacteristic
78C3×#127C22×C311yescharacteristic
79C3×#121—24no—
80C3×#121—22no—
81C3×#121—22no—
82C3×#121—22no—
83C3×#121—21no—
84C3×#121—21no—
85C3×C4×Q8—21no—
86C3×C4×Q8C2×D311yescharacteristic
87C3×C4×Q8C22×C311yescharacteristic
88C3×C4×D4—22no—
89C3×C4×D4—21no—
90C3×C4×D4—21no—
91C3×C4×D4—21no—
92C3×C4×D4C2×D311yescharacteristic
93C3×C4×D4C22×C311yescharacteristic
94C2×#214—21no—
95#869C22×C311yescharacteristic
96C3×#106—61no—
97C3×C4⋊C8—31no—
98C3×C4⋊C8—31no—
99C3×#103—61no—
100C3×#103—61no—
101C3×#102—62no—
102C3×C4×C8—31no—
103#835—21no—
104#832—22no—
105#810—21no—
106#808—21no—
107C4⋊(C3⋊C8)C22×C311yescharacteristic
108C4⋊(C3⋊C8)C22×C311yescharacteristic
109C4×C3⋊C8C22×C311yescharacteristic
110C23×C32—21no—
111C23×C32—22no—
112C32×Q8—21no—
113C32×Q8SD1612yescomplemented
114C32×D4—21no—
115C32×D4—21no—
116C32×D4—44no—
117C32×D4—41no—
118C32×D4—41no—
119C32×D4—41no—
120C32×D4—41no—
121C32×D4—42no—
122C32×D4—82no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—44no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3×Dic3—41no—
133C3×Dic6—41no—
134C3×Dic6—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137C3×C3⋊C8—41no—
138#550C3×D311yescharacteristic
139#486—31no—
140#475—31no—
141#461—31no—
142#331—31no—
143Q8⋊C8—31no—
144D4⋊C8—31no—
145C3×#41—44no—
146C3×#41—42no—
147C3×#41—42no—
148C3×#41—44no—
149C3×#41—42no—
150C3×#41—42no—
151C2×C3×Q8—21no—
152C2×C3×Q8—61no—
153C2×C3×Q8#6711yescharacteristic
154C2×C3×Q8C3×D411yescharacteristic
155C2×C3×D4—22no—
156C2×C3×D4—24no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—24no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—22no—
169C2×C3×D4#6711yescharacteristic
170C2×C3×D4#6712yes—
171C2×C3×D4C3×D411yescharacteristic
172C2×C3×D4C3×D412yes—
173C22×C3×C4—24no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C2×Dic6—21no—
180C3×SD16—122no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4#6711yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4C3×D411yescharacteristic
194C3×C4⋊C4C3×D411yescharacteristic
195C3×C22⋊C4—24no—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—22no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—21no—
201C3×C42—22no—
202C3×C42—21no—
203C3×C42—21no—
204C3×C42—21no—
205C3×C42C22×D311yescharacteristic
206C3×C42C23×C311yescharacteristic
207#214—42no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C22×C32—41no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—41no—
217C22×C32—42no—
218C22×C32—41no—
219C22×C32#12011yescharacteristic
220C32×C4—22no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4C2×SD1611yescharacteristic
225C32×C4#13511yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4AGL(1,ℤ/8)11yescharacteristic
228C3×Dic3—81no—
229C2×#41—21no—
230C2×SD16—61no—
231C4⋊Q8—31no—
232#127—21no—
233#127C2×C3×D311yescharacteristic
234#121—22no—
235#121—21no—
236C4×Q8C2×C3×D311yescharacteristic
237C4×D4—21no—
238C4×D4C2×C3×D311yescharacteristic
239#106—61no—
240C4⋊C8—31no—
241C4⋊C8—31no—
242#103—61no—
243#103—61no—
244#102—62no—
245C4×C8—31no—
246C23×C3—24no—
247C23×C3—22no—
248C23×C3—21no—
249C23×C3—22no—
250C23×C3—21no—
251C23×C3—22no—
252C3×Q8—22no—
253C3×Q8—21no—
254C3×Q8—21no—
255C3×Q8—22no—
256C3×Q8—121no—
257C3×Q8—121no—
258C3×Q8#21412yescomplemented
259C3×Q8C3×SD1612yescomplemented
260C3×D4—21no—
261C3×D4—21no—
262C3×D4—21no—
263C3×D4—21no—
264C3×D4—41no—
265C3×D4—41no—
266C3×D4—42no—
267C3×D4—42no—
268C3×D4—42no—
269C3×D4—42no—
270C3×D4—48no—
271C3×D4—44no—
272C3×D4—44no—
273C3×D4—42no—
274C3×D4—42no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—41no—
281C3×D4—41no—
282C3×D4—41no—
283C3×D4—82no—
284C3×D4—84no—
285C3×D4—82no—
286C3×D4—82no—
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—48no—
300C2×C3×C4—44no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—121no—
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×C3×D411yescharacteristic
313C2×C3×C4C2×C3×D411yescharacteristic
314C2×C3×C4C2×C3×D411yescharacteristic
315C2×Dic3—41no—
316Dic6—41no—
317Dic6—41no—
318C3×C8—121no—
319C3×C8—121no—
320C3×C8—121no—
321C3⋊C8—41no—
322C3⋊C8—41no—
323C3⋊C8—41no—
324C2×C32—81no—
325C2×C32—82no—
326C2×C32#44911yescharacteristic
327C2×C32#45011yescharacteristic
328C2×C32#45511yescharacteristic
329#41—42no—
330#41—42no—
331C2×Q8—61no—
332C2×Q8C3×#6711yescharacteristic
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4C3×#6711yescharacteristic
338C2×D4C3×#6712yes—
339C22×C4—22no—
340C22×C4—21no—
341SD16—122no—
342C2×C8—61no—
343C2×C8—61no—
344C2×C8—61no—
345C4⋊C4—21no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4C3×#6711yescharacteristic
349C4⋊C4C3×#6711yescharacteristic
350C22⋊C4—22no—
351C22⋊C4—21no—
352C42—21no—
353C42C22×C3×D311yescharacteristic
354C22×C3—21no—
355C22×C3—44no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—44no—
359C22×C3—44no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—42no—
365C22×C3—42no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—41no—
371C22×C3—42no—
372C22×C3—41no—
373C22×C3#95311yescharacteristic
374C22×C3C3×#12011yescharacteristic
375C3×C4—24no—
376C3×C4—22no—
377C3×C4—21no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—41no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—241no—
392C3×C4#93211yescharacteristic
393C3×C4C2×#21411yescharacteristic
394C3×C4#94911yescharacteristic
395C3×C4#95011yescharacteristic
396C3×C4C2×C3×SD1611yescharacteristic
397C3×C4C3×#13511yescharacteristic
398C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
399C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
400Dic3—81no—
401C32#164211yescharacteristic, complemented, Sylow
402C23—21no—
403C23—22no—
404Q8—21no—
405Q8—121no—
406Q8—121no—
407Q8C3×#21412yescomplemented
408D4—21no—
409D4—21no—
410D4—42no—
411D4—44no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—82no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—44no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—121no—
424C2×C4C2×C3×#6711yescharacteristic
425C2×C4C2×C3×#6711yescharacteristic
426C2×C4C2×C3×#6711yescharacteristic
427C8—121no—
428C8—121no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—82no—
434C2×C3—84no—
435C2×C3—81no—
436C2×C3—82no—
437C2×C3—81no—
438C2×C3—82no—
439C2×C3#521811yescharacteristic
440C2×C3#523811yescharacteristic
441C2×C3#524211yescharacteristic
442C2×C3C3×#44911yescharacteristic
443C2×C3C3×#45011yescharacteristic
444C2×C3C3×#45511yescharacteristic
445C22—42no—
446C22—41no—
447C22—41no—
448C22—42no—
449C22—42no—
450C22—41no—
451C22C3×#95311yescharacteristic
452C4—22no—
453C4—21no—
454C4—41no—
455C4—41no—
456C4—241no—
457C4C3×#93211yescharacteristic
458C4C2×C3×#21411yescharacteristic
459C4C3×#94911yescharacteristic
460C4C3×#95011yescharacteristic
461C3—21no—
462C3#7192111yescharacteristic, direct product factor
463C3C3×#164211yescharacteristic, complemented
464C2—81no—
465C2—82no—
466C2C3×#521811yescharacteristic
467C2C3×#523811yescharacteristic
468C2C3×#524211yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
Fitting, prime radicalC32×#550C2
socleC22×C32#120
hypercenterC3×#550D3
hypocenterC3C3×#1642
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#550

Complements

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

NH ≅ G/Ntype
2. C3×#5070C2semidirect
3. C3×#5020C2semidirect
4. C3×#5019C2semidirect
5. C3×#4544C2semidirect
6. C3×#4535C2semidirect
7. C3×D4⋊(C3⋊C8)C2semidirect
9. #71921C3direct (N × H)
33. #5070C2×C3semidirect
34. #5020C2×C3semidirect
35. #5019C2×C3semidirect
39. #4544C2×C3semidirect
40. #4535C2×C3semidirect
41. D4⋊(C3⋊C8)C2×C3semidirect
113. C32×Q8SD16semidirect
258. C3×Q8#214semidirect
259. C3×Q8C3×SD16semidirect
401. C32#1642semidirect
407. Q8C3×#214semidirect
462. C3#71921direct (N × H)
463. C3C3×#1642semidirect

Maximal subgroups

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

subgroupindex
C32×#5502
C3×#50702
C3×#50202
C3×#50192
C3×#45442
C3×#45352
C3×D4⋊(C3⋊C8)2
C3×#16423
#719213