Finite Group Databasebeta

← C3×#68196 #11779717

Subgroups — C3×#68196 #11779717

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D12C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3C3×#4846C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C32×D4⋊C8C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1639—31nomaximal
9#68196C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4—21no—
11C22×C3×D12—21no—
12C32×C4×D4C2211yescharacteristic
13C2×C3×#214—21no—
14C3×#930—21no—
15C3×#895—21no—
16C3×#882—22no—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic, complemented
20C32×C4⋊C8C2211yescharacteristic, complemented
21C32×C4×C8C2211yescharacteristic, complemented
22C3×#821—22no—
23C3×#821—21no—
24C3×#818—21no—
25C3×#810—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
27C3×D42—31no—
28D4×D12C2×C311yescharacteristic
29C3×#486—31no—
30C3×#474—31no—
31C3×#461—31no—
32#5019C2×C311yescharacteristic, complemented
33#4846C2×C311yescharacteristic, complemented
34#4694C2×C311yescharacteristic, complemented
35C3×#331—31no—
36C3×D4⋊C8—21no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8D311yescharacteristic, complemented
39C3×D4⋊C8C2×C311yescharacteristic, complemented
40#4485C2×C311yescharacteristic, complemented
41#4459C2×C311yescharacteristic, complemented
42C23×C3×D3—22no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×#67—22no—
46C3×D3×D4—42no—
47C3×D3×D4—42no—
48C2×C3×D12—22no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—42no—
52C2×C3×D12—42no—
53C2×C3×D12D411yescharacteristic
54C2×C3×D12D412yes—
55C2×C3×C4×D3—21no—
56C2×C3×Dic6—21no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C32×C4⋊C4D411yescharacteristic
60C32×C22⋊C4—21no—
61C32×C42C2311yescharacteristic
62C3×#214—42no—
63C3×(C2×D3)⋊C4—22no—
64C3×(C2×D3)⋊C4—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3D411yescharacteristic
68C2×C3×C3⋊C8—21no—
69#1639—31noSylow
70C22×C3×D4—61no—
71C22×C3×D4—61no—
72C2×D3×D4—21no—
73C22×D12—21no—
74C2×C3×SD16—61no—
75C3×C4⋊Q8—31no—
76C3×#127—31no—
77C3×#121—61no—
78C3×#121—61no—
79C3×#120—62no—
80C3×C4×D4—21no—
81C3×C4×D4—31no—
82C3×C4×D4C2×D311yescharacteristic
83C3×C4×D4C22×C311yescharacteristic
84C2×#214—21no—
85#930—21no—
86#895—21no—
87#882—22no—
88#874C22×C311yescharacteristic
89C4×D12C22×C311yescharacteristic
90#869C22×C311yescharacteristic, complemented
91C3×#107—61no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic, complemented
95C3×C4⋊C8C22×C311yescharacteristic, complemented
96C3×#103—61no—
97C3×#102—61no—
98C3×#102—62no—
99C3×C4×C8—21no—
100C3×C4×C8C2×D311yescharacteristic, complemented
101C3×C4×C8C22×C311yescharacteristic, complemented
102#821—22no—
103#821—21no—
104#818—21no—
105#810—21no—
106C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
107C23×C32—21no—
108C22×C3×D3—21no—
109C22×C3×D3—22no—
110C22×C3×D3—44no—
111C22×C3×D3—44no—
112C22×C3×D3—82no—
113C32×D4—21no—
114C32×D4D812yes—
115C2×C32×C4—21no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C3×#67—44no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—41no—
124C3×D12—21no—
125C3×D12—42no—
126C3×D12—44no—
127C3×D12—41no—
128C3×D12—41no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12SD1612yescomplemented
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#331—31no—
144D4⋊C8—31no—
145D4⋊C8C3×D311yescharacteristic, complemented
146C24×C3—62no—
147C23×D3—22no—
148C2×C3×Q8—61no—
149C2×C3×D4—21no—
150C2×C3×D4—31no—
151C2×C3×D4—32no—
152C2×C3×D4—62no—
153C2×C3×D4—62no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C2×C3×D4—122no—
157C2×C3×D4—122no—
158C2×C3×D4—122no—
159C2×C3×D4—122no—
160C2×C3×D4D1211yescharacteristic
161C2×C3×D4C3×D411yescharacteristic
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—41no—
165C22×C3×C4—61no—
166C2×#67—22no—
167D3×D4—42no—
168D3×D4—42no—
169C2×D12—22no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—42no—
173C2×D12—42no—
174C2×D12C3×D411yescharacteristic
175C2×D12C3×D412yes—
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C3×SD16—122no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—41no—
184C2×C3×C8—41no—
185C2×C3×C8—61no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4D1211yescharacteristic
191C3×C4⋊C4C3×D411yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—41no—
195C3×C22⋊C4—62no—
196C3×C22⋊C4—61no—
197C3×C42—21no—
198C3×C42C22×D311yescharacteristic
199C3×C42C23×C311yescharacteristic
200#214—42no—
201(C2×D3)⋊C4—22no—
202(C2×D3)⋊C4—21no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3C3×D411yescharacteristic
206C2×C3⋊C8—21no—
207C22×C32—22no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—22no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—42no—
215C2×C3×D3—42no—
216C2×C3×D3—42no—
217C2×C3×D3—88no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4C2×D811yescharacteristic
221C32×C4C2×SD1611yescharacteristic
222C32×C4AGL(1,ℤ/8)11yescharacteristic
223C32×C4AGL(1,ℤ/8)11yescharacteristic
224C3×Dic3—41no—
225C3×Dic3—81no—
226C22×D4—61no—
227C22×D4—61no—
228C2×SD16—61no—
229C4⋊Q8—31no—
230#127—31no—
231#121—61no—
232#121—61no—
233#120—62no—
234C4×D4—31no—
235C4×D4C2×C3×D311yescharacteristic
236#107—61no—
237C4⋊C8—31no—
238C4⋊C8C2×C3×D311yescharacteristic, complemented
239#103—61no—
240#102—61no—
241#102—62no—
242C4×C8C2×C3×D311yescharacteristic, complemented
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—41no—
246C23×C3—61no—
247C23×C3—62no—
248C23×C3—124no—
249C23×C3—124no—
250C23×C3—242no—
251C22×D3—21no—
252C22×D3—22no—
253C22×D3—44no—
254C22×D3—44no—
255C22×D3—82no—
256C3×Q8—121no—
257C3×Q8—121no—
258C3×D4—21no—
259C3×D4—21no—
260C3×D4—22no—
261C3×D4—32no—
262C3×D4—41no—
263C3×D4—61no—
264C3×D4—122no—
265C3×D4—124no—
266C3×D4—124no—
267C3×D4—121no—
268C3×D4—121no—
269C3×D4—121no—
270C3×D4—121no—
271C3×D4D2412yes—
272C3×D4C3×D812yes—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—61no—
284C2×C3×C4—81no—
285C2×C3×C4—81no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—121no—
289C2×C3×C4C2×D1211yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294C2×C3×C4C2×C3×D411yescharacteristic
295#67—44no—
296C2×Dic3—21no—
297C2×Dic3—41no—
298D12—21no—
299D12—42no—
300D12—44no—
301D12—41no—
302D12—41no—
303D12—41no—
304D12—41no—
305D12C3×SD1612yescomplemented
306C4×D3—41no—
307C4×D3—41no—
308Dic6—41no—
309Dic6—41no—
310C3×C8—41no—
311C3×C8—41no—
312C3×C8—42no—
313C3×C8—41no—
314C3×C8—41no—
315C3×C8—81no—
316C3×C8—121no—
317C3⋊C8—41no—
318C2×C32—42no—
319C2×C32#44711yescharacteristic
320C2×C32#45011yescharacteristic
321C2×C32#45511yescharacteristic
322C3×D3—42no—
323C3×D3—82no—
324C24—62no—
325C2×Q8—61no—
326C2×D4—31no—
327C2×D4—32no—
328C2×D4—62no—
329C2×D4—62no—
330C2×D4—61no—
331C2×D4—61no—
332C2×D4—122no—
333C2×D4—122no—
334C2×D4—122no—
335C2×D4—122no—
336C2×D4C3×D1211yescharacteristic
337C22×C4—21no—
338C22×C4—61no—
339SD16—122no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—61no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4C3×D1211yescharacteristic
347C22⋊C4—21no—
348C22⋊C4—62no—
349C22⋊C4—61no—
350C42C22×C3×D311yescharacteristic
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—21no—
354C22×C3—42no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—62no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—121no—
363C22×C3—121no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3—122no—
367C22×C3—248no—
368C22×C3#88211yescharacteristic
369C22×C3C3×#12011yescharacteristic
370C2×D3—22no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—42no—
374C2×D3—42no—
375C2×D3—42no—
376C2×D3—88no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—81no—
387C3×C4—121no—
388C3×C4—241no—
389C3×C4C2×D2411yescharacteristic
390C3×C4#90811yescharacteristic
391C3×C4#91111yescharacteristic
392C3×C4D3×SD1611yescharacteristic
393C3×C4C2×C3×D811yescharacteristic
394C3×C4C2×C3×SD1611yescharacteristic
395C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
396C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
397Dic3—41no—
398Dic3—81no—
399C32#163911yescharacteristic, complemented, Sylow
400C23—21no—
401C23—61no—
402C23—62no—
403C23—124no—
404C23—124no—
405C23—242no—
406Q8—121no—
407Q8—121no—
408D4—21no—
409D4—32no—
410D4—61no—
411D4—122no—
412D4—124no—
413D4—124no—
414D4—121no—
415D4—121no—
416D4—121no—
417D4—121no—
418D4C3×D2412yes—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—61no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4C2×C3×D1211yescharacteristic
427C2×C4C3×D3×D411yescharacteristic
428C2×C4C3×D3×D411yescharacteristic
429C8—41no—
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—42no—
436C2×C3—42no—
437C2×C3—82no—
438C2×C3—122no—
439C2×C3—242no—
440C2×C3#473211yescharacteristic
441C2×C3#477611yescharacteristic
442C2×C3#482511yescharacteristic
443C2×C3C3×#44711yescharacteristic
444C2×C3C3×#45011yescharacteristic
445C2×C3C3×#45511yescharacteristic
446D3—42no—
447D3—82no—
448C22—22no—
449C22—41no—
450C22—41no—
451C22—62no—
452C22—121no—
453C22—121no—
454C22—122no—
455C22—122no—
456C22—122no—
457C22—248no—
458C22C3×#88211yescharacteristic
459C4—21no—
460C4—41no—
461C4—121no—
462C4—241no—
463C4C2×C3×D2411yescharacteristic
464C4C3×#90811yescharacteristic
465C4C3×#91111yescharacteristic
466C4C3×D3×SD1611yescharacteristic
467C3—21no—
468C3#6819611yescharacteristic, direct product factor
469C3C3×#163911yescharacteristic, complemented
470C2—42no—
471C2—122no—
472C2—242no—
473C2C3×#473211yescharacteristic
474C2C3×#477611yescharacteristic
475C2C3×#482511yescharacteristic
subgroupG/H
centerC22×C3#882
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32#120
prime radicalC3×D4×D12C2
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1639
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5019C2semidirect
3. C3×#4846C2semidirect
4. C3×#4694C2semidirect
5. C32×D4⋊C8C2semidirect
6. C3×#4485C2semidirect
7. C3×#4459C2semidirect
9. #68196C3direct (N × H)
19. C3×#869C22semidirect
20. C32×C4⋊C8C22semidirect
21. C32×C4×C8C22semidirect
26. C3×C4⋊(C3⋊C8)C22semidirect
32. #5019C2×C3semidirect
33. #4846C2×C3semidirect
34. #4694C2×C3semidirect
38. C3×D4⋊C8D3semidirect
39. C3×D4⋊C8C2×C3semidirect
40. #4485C2×C3semidirect
41. #4459C2×C3semidirect
90. #869C22×C3semidirect
94. C3×C4⋊C8C2×D3semidirect
95. C3×C4⋊C8C22×C3semidirect
100. C3×C4×C8C2×D3semidirect
101. C3×C4×C8C22×C3semidirect
106. C4⋊(C3⋊C8)C22×C3semidirect
131. C3×D12SD16semidirect
145. D4⋊C8C3×D3semidirect
238. C4⋊C8C2×C3×D3semidirect
242. C4×C8C2×C3×D3semidirect
305. D12C3×SD16semidirect
399. C32#1639semidirect
468. C3#68196direct (N × H)
469. C3C3×#1639semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
C3×#50192
C3×#48462
C3×#46942
C32×D4⋊C82
C3×#44852
C3×#44592
C3×#16393
#681963