Finite Group Databasebeta

← C3×#68392 #11779714

Subgroups — C3×#68392 #11779714

Order 1152.

658 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic, complemented
3C3×#4846C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4483C211yesmaximal, characteristic, complemented
8C3×#1639—31nomaximal
9#68392C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C2×C3×D3×D4—21no—
12C32×#127C2211yescharacteristic
13C3×#938—21no—
14C3×#938—21no—
15C3×#937—22no—
16C2×C3×#204—21no—
17C3×C4×D12C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic, complemented
20C32×C4⋊C8C2211yescharacteristic, complemented
21C32×C4⋊C8C2211yescharacteristic, complemented
22C3×#832—22no—
23C3×#821—21no—
24C3×#818—21no—
25C3×#816—21no—
26C3×C4×C3⋊C8C2211yescharacteristic, complemented
27C3×D42—31no—
28#5717C2×C311yescharacteristic
29C3×#486—31no—
30C3×#474—31no—
31C3×#461—31no—
32#5070C2×C311yescharacteristic, complemented
33#4846C2×C311yescharacteristic, complemented
34#4841C2×C311yescharacteristic, complemented
35C3×#331—21no—
36C3×#331D311yescharacteristic, complemented
37C3×#331C2×C311yescharacteristic, complemented
38C3×D4⋊C8—31no—
39C3×D4⋊C8—31no—
40#4483C2×C311yescharacteristic, complemented
41#4483C2×C311yescharacteristic, complemented
42C23×C3×D3—22no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4D412yes—
46C2×C3×#67—22no—
47C2×C3×#67—22no—
48C3×D3×D4—42no—
49C3×D3×D4—42no—
50C3×D3×D4—42no—
51C3×D3×D4—42no—
52C2×C3×D12D411yescharacteristic
53C2×C3×D12D411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3—21no—
56C2×C3×Dic6—21no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C32×C42C2311yescharacteristic
60C3×#217—22no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C2×C3×C3⋊C8—21no—
68C3×#204—42no—
69#1639—31noSylow
70C22×C3×D4—61no—
71C22×C3×D4—61no—
72C2×D3×D4—21no—
73C2×D3×D4—21no—
74C2×C3×SD16—61no—
75C3×C4⋊Q8—31no—
76C3×#127—21no—
77C3×#127C2×D311yescharacteristic
78C3×#127C22×C311yescharacteristic
79C3×#121—61no—
80C3×#121—61no—
81C3×#120—62no—
82C3×C4×D4—31no—
83C3×C4×D4—31no—
84#938—21no—
85#938—21no—
86#937—22no—
87C2×#204—21no—
88C4×D12C22×C311yescharacteristic
89C4×D12C22×C311yescharacteristic
90#869C22×C311yescharacteristic, complemented
91C3×#107—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—21no—
94C3×C4⋊C8C2×D311yescharacteristic, complemented
95C3×C4⋊C8C2×D311yescharacteristic, complemented
96C3×C4⋊C8C22×C311yescharacteristic, complemented
97C3×C4⋊C8C22×C311yescharacteristic, complemented
98C3×#103—61no—
99C3×#102—61no—
100C3×#102—62no—
101C3×C4×C8—31no—
102#832—22no—
103#821—21no—
104#818—21no—
105#816—21no—
106C4×C3⋊C8C22×C311yescharacteristic, complemented
107C23×C32—22no—
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C22×C3×D3—44no—
111C22×C3×D3—44no—
112C22×C3×D3—82no—
113C32×D4—42no—
114C32×D4—41no—
115C32×D4—41no—
116C32×D4—41no—
117C32×D4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C3×#67—44no—
122C3×#67—44no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—41no—
126C3×D12—21no—
127C3×D12—21no—
128C3×D12D812yes—
129C3×D12SD1612yescomplemented
130C3×C4×D3—41no—
131C3×C4×D3—41no—
132C3×C4×D3—41no—
133C3×C4×D3—41no—
134C3×Dic6—41no—
135C3×Dic6—41no—
136C32×C8—41no—
137C32×C8—41no—
138C3×C3⋊C8—41no—
139D42—31no—
140#486—31no—
141#474—31no—
142#461—31no—
143#331C3×D311yescharacteristic, complemented
144D4⋊C8—31no—
145D4⋊C8—31no—
146C24×C3—62no—
147C23×D3—22no—
148C2×C3×Q8—61no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—22no—
154C2×C3×D4—31no—
155C2×C3×D4—31no—
156C2×C3×D4—41no—
157C2×C3×D4—41no—
158C2×C3×D4—62no—
159C2×C3×D4—62no—
160C2×C3×D4—122no—
161C2×C3×D4—122no—
162C2×C3×D4—122no—
163C2×C3×D4—122no—
164C2×C3×D4D1212yes—
165C2×C3×D4C3×D412yes—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C2×#67—22no—
169C2×#67—22no—
170D3×D4—42no—
171D3×D4—42no—
172D3×D4—42no—
173D3×D4—42no—
174C2×D12C3×D411yescharacteristic
175C2×D12C3×D411yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—21no—
178C2×Dic6—21no—
179C3×SD16—122no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—41no—
185C2×C3×C8—41no—
186C2×C3×C8—61no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—31no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C22⋊C4—62no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C42—21no—
195C3×C42C22×D311yescharacteristic
196C3×C42C23×C311yescharacteristic
197#217—22no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C3×D411yescharacteristic
203C4⋊Dic3C3×D411yescharacteristic
204C2×C3⋊C8—21no—
205#204—42no—
206C22×C32—42no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32#12011yescharacteristic
210C2×C3×D3—22no—
211C2×C3×D3—22no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3—41no—
216C2×C3×D3—88no—
217C32×C4—21no—
218C32×C4C2×D811yescharacteristic
219C32×C4C2×SD1611yescharacteristic
220C32×C4AGL(1,ℤ/8)11yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3—81no—
225C22×D4—61no—
226C22×D4—61no—
227C2×SD16—61no—
228C4⋊Q8—31no—
229#127C2×C3×D311yescharacteristic
230#121—61no—
231#121—61no—
232#120—62no—
233C4×D4—31no—
234C4×D4—31no—
235#107—61no—
236C4⋊C8C2×C3×D311yescharacteristic, complemented
237C4⋊C8C2×C3×D311yescharacteristic, complemented
238#103—61no—
239#102—61no—
240#102—62no—
241C4×C8—31no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—42no—
245C23×C3—61no—
246C23×C3—61no—
247C23×C3—124no—
248C23×C3—124no—
249C23×C3—242no—
250C22×D3—21no—
251C22×D3—21no—
252C22×D3—44no—
253C22×D3—44no—
254C22×D3—82no—
255C3×Q8—121no—
256C3×Q8—121no—
257C3×D4—32no—
258C3×D4—32no—
259C3×D4—42no—
260C3×D4—42no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—41no—
264C3×D4—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—41no—
269C3×D4—61no—
270C3×D4—61no—
271C3×D4—81no—
272C3×D4—81no—
273C3×D4—81no—
274C3×D4—81no—
275C3×D4—82no—
276C3×D4—124no—
277C3×D4—124no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4C2×C3×D411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294#67—44no—
295#67—44no—
296C2×Dic3—21no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299D12—21no—
300D12—21no—
301D12C3×D812yes—
302D12C3×SD1612yescomplemented
303C4×D3—41no—
304C4×D3—41no—
305C4×D3—41no—
306C4×D3—41no—
307Dic6—41no—
308Dic6—41no—
309C3×C8—41no—
310C3×C8—41no—
311C3×C8—41no—
312C3×C8—41no—
313C3×C8—81no—
314C3×C8—81no—
315C3×C8—121no—
316C3⋊C8—41no—
317C2×C32—82no—
318C2×C32#44711yescharacteristic
319C2×C32#45011yescharacteristic
320C2×C32#45511yescharacteristic
321C3×D3—42no—
322C3×D3—42no—
323C24—62no—
324C2×Q8—61no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—31no—
328C2×D4—31no—
329C2×D4—62no—
330C2×D4—62no—
331C2×D4—122no—
332C2×D4—122no—
333C2×D4—122no—
334C2×D4—122no—
335C2×D4C3×D1212yes—
336C22×C4—61no—
337C22×C4—61no—
338SD16—122no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—61no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C22⋊C4—62no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C42C22×C3×D311yescharacteristic
350C22×C3—21no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—62no—
358C22×C3—62no—
359C22×C3—82no—
360C22×C3—82no—
361C22×C3—82no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—121no—
365C22×C3—121no—
366C22×C3—248no—
367C22×C3#88211yescharacteristic
368C22×C3C3×#12011yescharacteristic
369C2×D3—22no—
370C2×D3—22no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—88no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—41no—
383C3×C4—121no—
384C3×C4—121no—
385C3×C4—241no—
386C3×C4D3×D811yescharacteristic
387C3×C4#91111yescharacteristic
388C3×C4D3×SD1611yescharacteristic
389C3×C4#91411yescharacteristic
390C3×C4C2×C3×D811yescharacteristic
391C3×C4C2×C3×SD1611yescharacteristic
392C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
393C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
394Dic3—41no—
395Dic3—41no—
396Dic3—81no—
397C32#163911yescharacteristic, complemented, Sylow
398C23—22no—
399C23—61no—
400C23—61no—
401C23—124no—
402C23—124no—
403C23—242no—
404Q8—121no—
405Q8—121no—
406D4—32no—
407D4—32no—
408D4—42no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—61no—
414D4—61no—
415D4—124no—
416D4—124no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4C2×C3×D1211yescharacteristic
425C2×C4C3×D3×D411yescharacteristic
426C2×C4C3×D3×D411yescharacteristic
427C8—41no—
428C8—41no—
429C8—121no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—82no—
434C2×C3—82no—
435C2×C3—122no—
436C2×C3—122no—
437C2×C3—162no—
438C2×C3#474611yescharacteristic
439C2×C3#477311yescharacteristic
440C2×C3#477611yescharacteristic
441C2×C3C3×#44711yescharacteristic
442C2×C3C3×#45011yescharacteristic
443C2×C3C3×#45511yescharacteristic
444D3—42no—
445D3—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—62no—
450C22—62no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—248no—
456C22C3×#88211yescharacteristic
457C4—21no—
458C4—121no—
459C4—121no—
460C4—241no—
461C4C3×D3×D811yescharacteristic
462C4C3×#91111yescharacteristic
463C4C3×D3×SD1611yescharacteristic
464C4C3×#91411yescharacteristic
465C3—21no—
466C3#6839211yescharacteristic, direct product factor
467C3C3×#163911yescharacteristic, complemented
468C2—82no—
469C2—122no—
470C2—122no—
471C2C3×#474611yescharacteristic
472C2C3×#477311yescharacteristic
473C2C3×#477611yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC3×#5717C2
hypercenterC3×#331D3
hypocenterC3C3×#1639
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#331

Complements

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

NH ≅ G/Ntype
2. C3×#5070C2semidirect
3. C3×#4846C2semidirect
4. C3×#4841C2semidirect
5. C32×#331C2semidirect
6. C3×#4483C2semidirect
7. C3×#4483C2semidirect
9. #68392C3direct (N × H)
19. C3×#869C22semidirect
20. C32×C4⋊C8C22semidirect
21. C32×C4⋊C8C22semidirect
26. C3×C4×C3⋊C8C22semidirect
32. #5070C2×C3semidirect
33. #4846C2×C3semidirect
34. #4841C2×C3semidirect
36. C3×#331D3semidirect
37. C3×#331C2×C3semidirect
40. #4483C2×C3semidirect
41. #4483C2×C3semidirect
90. #869C22×C3semidirect
94. C3×C4⋊C8C2×D3semidirect
95. C3×C4⋊C8C2×D3semidirect
96. C3×C4⋊C8C22×C3semidirect
97. C3×C4⋊C8C22×C3semidirect
106. C4×C3⋊C8C22×C3semidirect
129. C3×D12SD16semidirect
143. #331C3×D3semidirect
236. C4⋊C8C2×C3×D3semidirect
237. C4⋊C8C2×C3×D3semidirect
302. D12C3×SD16semidirect
397. C32#1639semidirect
466. C3#68392direct (N × H)
467. C3C3×#1639semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
C3×#50702
C3×#48462
C3×#48412
C32×#3312
C3×#44832
C3×#16393
#683923