Finite Group Databasebeta

← C3×#79060 #11868801

Subgroups — C3×#79060 #11868801

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#235C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic, complemented
3C32×#423C211yesmaximal, characteristic, complemented
4C3×#5133C212yesmaximal
5C3×#5121C212yesmaximal, complemented
6C3×#4851C212yesmaximal, complemented
7C3×#4850C212yesmaximal, complemented
8C3×#4846C212yesmaximal, complemented
9C3×#4842C212yesmaximal, complemented
10C3×#3079—31nomaximal
11#79060C311yesmaximal, characteristic, direct product factor
12C2×C3×#235C2211yescharacteristic
13C22×C3×Dic6—21no—
14C2×C32×M16C2212yes—
15C2×C32×C42C2211yescharacteristic
16C3×C4×#67—21no—
17C3×C4×#67—21no—
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4⋊Dic3C2212yes—
21C3×C4×D12C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#872—21no—
24C3×C42×D3—21no—
25C3×#869—21no—
26C3×#869—21no—
27C3×#869C2212yes—
28C3×#869C2212yes—
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C32×C4⋊C8C2212yes—
32C32×C4⋊C8C2212yes—
33C3×#821C2214yes—
34C3×#818C2214yes—
35C3×#817C2214yes—
36C3×#816C2214yes—
37C2×C3×C4⋊Q8—31no—
38C3×C4×#41—31no—
39C4×#235C2×C311yescharacteristic
40C2×#869C2×C311yescharacteristic, complemented
41C3×#477—32no—
42C3×#476—32no—
43C3×#475—32no—
44C3×#474—32no—
45C3×#428—32no—
46C3×#423—21no—
47C3×#423D311yescharacteristic, complemented
48C3×#423C2×C311yescharacteristic, complemented
49C3×#417—32no—
50#5133C2×C312yes—
51#5121C2×C312yescomplemented
52#4851C2×C312yescomplemented
53#4850C2×C312yescomplemented
54#4846C2×C312yescomplemented
55#4842C2×C312yescomplemented
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—21no—
60C22×C3×Dic3—22no—
61C3×#235—22no—
62C3×#235Q814yescomplemented
63C2×C3×D12C2311yescharacteristic
64C2×C3×C4×D3—21no—
65C2×C3×C4×D3—21no—
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—44no—
70C2×C3×Dic6C2311yescharacteristic
71C32×M16—24no—
72C2×C32×C8C2314yes—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77C3×#217—21no—
78C3×(C2×D3)⋊C4—21no—
79C3×(C2×D3)⋊C4—21no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2314yes—
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2311yescharacteristic
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4—21no—
88C3×C4×Dic3—21no—
89C3×C4×Dic3—21no—
90C3×C4×Dic3—21no—
91#3079—31noSylow
92C2×C3×#41—31no—
93C22×C3×Q8—61no—
94C2×#235C22×C311yescharacteristic
95C22×Dic6—21no—
96C2×C3×M16—22no—
97C2×C3×M16C2×D312yes—
98C2×C3×M16C22×C312yes—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—32no—
101C3×C4⋊Q8—61no—
102C3×C4⋊Q8—61no—
103C3×C4×Q8—31no—
104C3×C4×Q8—31no—
105C3×C4×D4—31no—
106C3×C4×D4—31no—
107C3×C4×D4—61no—
108C3×C4×D4—61no—
109C3×#117—31no—
110C3×#117—61no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—61no—
113C2×C3×C42—21no—
114C2×C3×C42—61no—
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C22×C311yescharacteristic
117C4×#67—21no—
118C4×#67—21no—
119#926C22×C311yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C22×C312yes—
122C4×D12C22×C311yescharacteristic
123C4×D12C22×C311yescharacteristic
124#872—21no—
125C42×D3—21no—
126#869—21no—
127#869—21no—
128#869C22×C312yes—
129#869C22×C312yes—
130C4×Dic6C22×C311yescharacteristic
131C4×Dic6C22×C311yescharacteristic
132C3×#107—34no—
133C3×#106—34no—
134C3×C4⋊C8—22no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8C2×D312yes—
137C3×C4⋊C8C2×D312yes—
138C3×C4⋊C8C22×C312yes—
139C3×C4⋊C8C22×C312yes—
140C3×#103—34no—
141C3×#102—34no—
142#821C22×C314yes—
143#818C22×C314yes—
144#817C22×C314yes—
145#816C22×C314yes—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—21no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×Q812yes—
156C2×C32×C4#4112yes—
157C2×C32×C4C2411yescharacteristic
158C3×#67—24no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—44no—
164C3×D12—21no—
165C3×D12C2×Q812yescomplemented
166C3×C4×D3—24no—
167C3×C4×D3—42no—
168C3×C4×D3—42no—
169C3×Dic6—21no—
170C3×Dic6—44no—
171C3×Dic6—44no—
172C3×Dic6C2×Q812yescomplemented
173C32×C8—24no—
174C2×C4⋊Q8—31no—
175C4×#41—31no—
176#477—32no—
177#476—32no—
178#475—32no—
179#474—32no—
180#428—32no—
181#423C3×D311yescharacteristic, complemented
182#417—32no—
183C3×#41—34no—
184C3×#41—62no—
185C2×C3×Q8—31no—
186C2×C3×Q8—62no—
187C2×C3×Q8—62no—
188C2×C3×Q8—124no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—61no—
195C22×C3×C4—62no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4D1211yescharacteristic
199C22×C3×C4D1211yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C3×D411yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C2×#67—21no—
205C22×Dic3—22no—
206#235—22no—
207#235C3×Q814yescomplemented
208C2×D12C23×C311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×Dic6—22no—
213C2×Dic6—22no—
214C2×Dic6—44no—
215C2×Dic6C23×C311yescharacteristic
216C3×M16—24no—
217C3×M16—24no—
218C3×M16—44no—
219C2×C3×C8—24no—
220C2×C3×C8C22×D314yes—
221C2×C3×C8C23×C314yes—
222C3×C4⋊C4—34no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—62no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—61no—
238C3×C42—61no—
239C3×C42—61no—
240C3×C42D1211yescharacteristic
241C3×C42D1211yescharacteristic
242C3×C42C3×D411yescharacteristic
243C3×C42C3×D411yescharacteristic
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246C3×C42C23×C311yescharacteristic
247C3×C42C23×C311yescharacteristic
248#217—21no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251C4⋊Dic3—22no—
252C4⋊Dic3—22no—
253C4⋊Dic3—22no—
254C4⋊Dic3C23×C314yes—
255C4⋊Dic3C23×C311yescharacteristic
256C4⋊Dic3C23×C311yescharacteristic
257Dic3⋊C4—21no—
258Dic3⋊C4—21no—
259C4×Dic3—21no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32C22⋊Q812yes—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—22no—
267C2×C3×D3—41no—
268C2×C3×D3—41no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4C22⋊Q812yes—
272C32×C4AGL(1,ℤ/8)12yes—
273C32×C4#13712yes—
274C32×C4C22×Q811yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3×Dic3—22no—
277C3×Dic3—44no—
278C3×Dic3—41no—
279C3×Dic3—41no—
280C2×#41—31no—
281C22×Q8—61no—
282C2×M16C2×C3×D312yes—
283C4⋊Q8—32no—
284C4⋊Q8—32no—
285C4⋊Q8—61no—
286C4⋊Q8—61no—
287C4×Q8—31no—
288C4×Q8—31no—
289C4×D4—31no—
290C4×D4—31no—
291C4×D4—61no—
292C4×D4—61no—
293#117—31no—
294#117—61no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—61no—
297C2×C42—61no—
298C2×C42C2×C3×D311yescharacteristic
299#107—34no—
300#106—34no—
301C4⋊C8C2×C3×D312yes—
302C4⋊C8C2×C3×D312yes—
303#103—34no—
304#102—34no—
305C23×C3—21no—
306C23×C3—61no—
307C23×C3C2×D1211yescharacteristic
308C23×C3C2×C3×D411yescharacteristic
309C22×D3—21no—
310C3×Q8—32no—
311C3×Q8—61no—
312C3×Q8—124no—
313C3×Q8—124no—
314C3×D4—32no—
315C3×D4—64no—
316C3×D4—61no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—61no—
332C2×C3×C4—64no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—64no—
336C2×C3×C4—124no—
337C2×C3×C4—122no—
338C2×C3×C4—122no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4#23712yes—
345C2×C3×C4D3×Q812yes—
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C2×C3×Q812yes—
352C2×C3×C4C3×#4112yes—
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C24×C311yescharacteristic
355#67—24no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—24no—
360C2×Dic3—44no—
361D12—21no—
362D12C2×C3×Q812yescomplemented
363C4×D3—24no—
364C4×D3—42no—
365C4×D3—42no—
366Dic6—21no—
367Dic6—44no—
368Dic6—44no—
369Dic6C2×C3×Q812yescomplemented
370C3×C8—24no—
371C3×C8—24no—
372C3×C8—44no—
373C2×C32—22no—
374C2×C32C2×C22⋊Q811yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C32C2×#13711yescharacteristic
377C3×D3—42no—
378#41—34no—
379#41—62no—
380C2×Q8—31no—
381C2×Q8—62no—
382C2×Q8—62no—
383C2×Q8—124no—
384C2×D4—31no—
385C2×D4—61no—
386C22×C4—61no—
387C22×C4—62no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4C3×D1211yescharacteristic
391C22×C4C3×D1211yescharacteristic
392C22×C4C22×C3×D311yescharacteristic
393M16—24no—
394C2×C8C22×C3×D314yes—
395C4⋊C4—34no—
396C4⋊C4—31no—
397C4⋊C4—31no—
398C4⋊C4—62no—
399C4⋊C4—62no—
400C4⋊C4—62no—
401C4⋊C4—61no—
402C4⋊C4—61no—
403C22⋊C4—61no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C42—61no—
407C42—61no—
408C42—61no—
409C42C3×D1211yescharacteristic
410C42C3×D1211yescharacteristic
411C42C22×C3×D311yescharacteristic
412C42C22×C3×D311yescharacteristic
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3—21no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—62no—
422C22×C3—121no—
423C22×C3—121no—
424C22×C3#89712yes—
425C22×C3C3×C22⋊Q812yes—
426C22×C3C22×D1211yescharacteristic
427C22×C3C22×C3×D411yescharacteristic
428C2×D3—22no—
429C2×D3—41no—
430C2×D3—41no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—62no—
443C3×C4—124no—
444C3×C4—121no—
445C3×C4—121no—
446C3×C4#89712yes—
447C3×C4#90812yes—
448C3×C4#90912yes—
449C3×C4C3×C22⋊Q812yes—
450C3×C4C3×AGL(1,ℤ/8)12yes—
451C3×C4C3×#13712yes—
452C3×C4C2×#23711yescharacteristic
453C3×C4C2×D3×Q811yescharacteristic
454C3×C4C22×C3×Q811yescharacteristic
455C3×C4C2×C3×#4111yescharacteristic
456Dic3—22no—
457Dic3—44no—
458Dic3—41no—
459Dic3—41no—
460C32#307911yescharacteristic, complemented, Sylow
461C23—61no—
462C23C2×C3×D1211yescharacteristic
463Q8—32no—
464Q8—61no—
465Q8—124no—
466Q8—124no—
467D4—32no—
468D4—64no—
469D4—61no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—61no—
473C2×C4—64no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—64no—
477C2×C4—124no—
478C2×C4—122no—
479C2×C4—122no—
480C2×C4C2×C3×D1211yescharacteristic
481C2×C4C2×C3×D1211yescharacteristic
482C2×C4C2×C3×D1211yescharacteristic
483C2×C4C2×C3×D1211yescharacteristic
484C2×C4C2×C3×D1211yescharacteristic
485C2×C4C3×#23712yes—
486C2×C4C3×D3×Q812yes—
487C2×C4C23×C3×D311yescharacteristic
488C8—24no—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3—122no—
496C2×C3C2×#89711yescharacteristic
497C2×C3C2×#90811yescharacteristic
498C2×C3C2×#90911yescharacteristic
499C2×C3C2×C3×C22⋊Q811yescharacteristic
500C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
501C2×C3C2×C3×#13711yescharacteristic
502D3—42no—
503C22—21no—
504C22—21no—
505C22—62no—
506C22—121no—
507C22—121no—
508C22C3×#89712yes—
509C22C22×C3×D1211yescharacteristic
510C4—21no—
511C4—21no—
512C4—62no—
513C4—124no—
514C4—121no—
515C4—121no—
516C4C3×#89712yes—
517C4C3×#90812yes—
518C4C3×#90912yes—
519C4C2×C3×#23711yescharacteristic
520C4C2×C3×D3×Q811yescharacteristic
521C3—21no—
522C3#7906011yescharacteristic, direct product factor
523C3C3×#307911yescharacteristic, complemented
524C2—22no—
525C2—122no—
526C2C2×C3×#89711yescharacteristic
527C2C2×C3×#90811yescharacteristic
528C2C2×C3×#90911yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#423C2
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC3×#423D3
hypocenterC3C3×#3079
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#423

Complements

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

NH ≅ G/Ntype
2. C2×C3×#869C2semidirect
3. C32×#423C2semidirect
5. C3×#5121C2semidirect
6. C3×#4851C2semidirect
7. C3×#4850C2semidirect
8. C3×#4846C2semidirect
9. C3×#4842C2semidirect
11. #79060C3direct (N × H)
40. C2×#869C2×C3semidirect
47. C3×#423D3semidirect
48. C3×#423C2×C3semidirect
51. #5121C2×C3semidirect
52. #4851C2×C3semidirect
53. #4850C2×C3semidirect
54. #4846C2×C3semidirect
55. #4842C2×C3semidirect
62. C3×#235Q8semidirect
165. C3×D12C2×Q8semidirect
172. C3×Dic6C2×Q8semidirect
181. #423C3×D3semidirect
207. #235C3×Q8semidirect
362. D12C2×C3×Q8semidirect
369. Dic6C2×C3×Q8semidirect
460. C32#3079semidirect
522. C3#79060direct (N × H)
523. C3C3×#3079semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2352
C2×C3×#8692
C32×#4232
C3×#51332
C3×#51212
C3×#48512
C3×#48502
C3×#48462
C3×#48422
C3×#30793
#790603