Finite Group Databasebeta

← C3×#79735 #11887615

Subgroups — C3×#79735 #11887615

Order 1152.

831 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5579C211yesmaximal, characteristic
2C3×Q8×D12C211yesmaximal, characteristic
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4C3×#5186C212yesmaximal, complemented
5C3×#5031C211yesmaximal, characteristic, complemented
6C3×#5021C211yesmaximal, characteristic, complemented
7C3×#4884C212yesmaximal, complemented
8C3×#4813C212yesmaximal, complemented
9C3×D3×#103C212yesmaximal, complemented
10C3×C8×D12C211yesmaximal, characteristic
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3299—31nomaximal
13#79735C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C32×Q16C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C3×#946C2212yes—
19C2×C3×#216C2212yes—
20C2×C3×D3×C8C2212yes—
21C3×#897—22no—
22C3×#897C2212yes—
23C3×#896—22no—
24C3×D3×C4⋊C4C2212yes—
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12C2211yescharacteristic
28C3×#870—21no—
29C3×#869—21no—
30C3×#869C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C32×#107C2211yescharacteristic
33C32×#103C2211yescharacteristic
34C32×#103C2211yescharacteristic
35C32×C4×C8C2211yescharacteristic
36C3×#835C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#810C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—31no—
45#5579C2×C311yescharacteristic
46Q8×D12C2×C311yescharacteristic
47C3×#487—31no—
48C3×#484—32no—
49C3×#477—31no—
50C3×#467—32no—
51C3×#462—31no—
52C3×#451—32no—
53C3×C4×Q16—21no—
54C3×C4×Q16D311yescharacteristic, complemented
55C3×C4×Q16C2×C311yescharacteristic, complemented
56C3×C8×D4—31no—
57C2×C3×#103—32no—
58#5186C2×C312yescomplemented
59#5031C2×C311yescharacteristic, complemented
60#5021C2×C311yescharacteristic, complemented
61#4884C2×C312yescomplemented
62#4813C2×C312yescomplemented
63D3×#103C2×C312yescomplemented
64C8×D12C2×C311yescharacteristic
65#4681C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×Q8C2311yescharacteristic
68C3×D3×Q8—24no—
69C3×D3×Q8—42no—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—22no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77C32×Q16—22no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C42—21no—
85C32×C42—21no—
86C32×C42C2311yescharacteristic
87C3×#216—42no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4D412yes—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3D411yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C2×C3×C3⋊C8C2312yes—
100C3×D3×C8—42no—
101#3299—31noSylow
102C22×C3×Q8—32no—
103C2×D3×Q8C22×C312yes—
104C2×C3×Q16—21no—
105C2×C3×Q16—32no—
106C2×C3×Q16C2×D311yescharacteristic
107C2×C3×Q16C22×C311yescharacteristic
108C22×C3×C8—32no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8—31no—
111C3×C4⋊Q8—61no—
112C3×#125—61no—
113C3×C22⋊Q8—32no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—62no—
116C3×C22⋊Q8—62no—
117C3×C4×Q8—21no—
118C3×C4×Q8—21no—
119C3×C4×Q8C2×D311yescharacteristic
120C3×C4×Q8C2×D311yescharacteristic
121C3×C4×Q8C22×C311yescharacteristic
122C3×C4×Q8C22×C311yescharacteristic
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C2×C3×C4⋊C4—32no—
127#946C22×C312yes—
128C2×#216C22×C312yes—
129C2×D3×C8C22×C312yes—
130#897—22no—
131#897C22×C312yes—
132#896—22no—
133D3×C4⋊C4C22×C312yes—
134C4×D12—21no—
135C4×D12—21no—
136C4×D12C22×C311yescharacteristic
137#870—21no—
138#869—21no—
139#869C22×C311yescharacteristic
140#869C22×C311yescharacteristic
141C3×#107—21no—
142C3×#107—32no—
143C3×#107C2×D311yescharacteristic
144C3×#107C22×C311yescharacteristic
145C3×C4⋊C8—31no—
146C3×#103—21no—
147C3×#103—21no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—32no—
152C3×#103C2×D311yescharacteristic
153C3×#103C2×D311yescharacteristic
154C3×#103C22×C311yescharacteristic
155C3×#103C22×C311yescharacteristic
156C3×C22⋊C8—32no—
157C3×C4×C8—21no—
158C3×C4×C8C2×D311yescharacteristic
159C3×C4×C8C22×C311yescharacteristic
160#835C22×C312yes—
161(C2×D3)⋊C8C22×C312yes—
162#816C22×C312yes—
163#816C22×C312yes—
164#810C22×C312yes—
165#807C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C22×C3×D3C2×D412yes—
168C32×Q8—21no—
169C32×Q8—21no—
170C32×Q8—21no—
171C32×Q8#4112yes—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C2×D412yes—
182C3×D12Q1614yescomplemented
183C3×C4×D3—22no—
184C3×C4×D3—22no—
185C3×C4×D3—44no—
186C3×C4×D3—82no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×Dic6—44no—
190C3×Dic6—81no—
191C32×C8—21no—
192C32×C8—21no—
193C3×C3⋊C8—22no—
194#554—31no—
195D4×Q8—31no—
196#487—31no—
197#484—32no—
198#477—31no—
199#467—32no—
200#462—31no—
201#451—32no—
202C4×Q16C3×D311yescharacteristic, complemented
203C8×D4—31no—
204C2×#103—32no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—32no—
208C2×C3×Q8—62no—
209C2×C3×Q8—61no—
210C2×C3×Q8—64no—
211C2×C3×Q8—122no—
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×Q8C22×D311yescharacteristic
214C2×C3×Q8C23×C311yescharacteristic
215C2×C3×Q8C23×C311yescharacteristic
216C2×C3×D4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—62no—
219C22×C3×C4—62no—
220D3×Q8—24no—
221D3×Q8—42no—
222C2×D12C3×D411yescharacteristic
223C2×C4×D3—22no—
224C2×C4×D3—22no—
225C2×C4×D3C23×C312yes—
226C2×Dic6—22no—
227C2×Dic6—21no—
228C2×Dic6C23×C312yes—
229C3×Q16—24no—
230C3×Q16—22no—
231C3×Q16—22no—
232C3×Q16—122no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—32no—
236C2×C3×C8—122no—
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C23×C311yescharacteristic
240C2×C3×C8C23×C311yescharacteristic
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—32no—
249C3×C4⋊C4—41no—
250C3×C4⋊C4—41no—
251C3×C4⋊C4—62no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4C22×D311yescharacteristic
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C4⋊C4C23×C311yescharacteristic
260C3×C4⋊C4C23×C311yescharacteristic
261C3×C22⋊C4—32no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—62no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—41no—
270C3×C42—41no—
271C3×C42C22×D311yescharacteristic
272C3×C42C23×C311yescharacteristic
273#216—42no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4C3×D412yes—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—22no—
281C4⋊Dic3C3×D411yescharacteristic
282C4⋊Dic3C23×C312yes—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285C2×C3⋊C8C23×C312yes—
286D3×C8—42no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—22no—
289C2×C3×D3—22no—
290C2×C3×D3C2×Q1614yes—
291C32×C4—22no—
292C32×C4—21no—
293C32×C4—41no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C2×Q1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×Q8—32no—
303C2×Q16—32no—
304C2×Q16C2×C3×D311yescharacteristic
305C22×C8—32no—
306C4⋊Q8—31no—
307C4⋊Q8—31no—
308C4⋊Q8—61no—
309#125—61no—
310C22⋊Q8—32no—
311C22⋊Q8—32no—
312C22⋊Q8—62no—
313C22⋊Q8—62no—
314C4×Q8C2×C3×D311yescharacteristic
315C4×Q8C2×C3×D311yescharacteristic
316C4×D4—31no—
317C4×D4—61no—
318C4×D4—61no—
319C2×C4⋊C4—32no—
320#107—32no—
321#107C2×C3×D311yescharacteristic
322C4⋊C8—31no—
323#103—32no—
324#103—32no—
325#103—32no—
326#103—32no—
327#103C2×C3×D311yescharacteristic
328#103C2×C3×D311yescharacteristic
329C22⋊C8—32no—
330C4×C8C2×C3×D311yescharacteristic
331C23×C3—32no—
332C22×D3C2×C3×D412yes—
333C3×Q8—21no—
334C3×Q8—21no—
335C3×Q8—22no—
336C3×Q8—21no—
337C3×Q8—21no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×Q8—22no—
341C3×Q8—41no—
342C3×Q8—41no—
343C3×Q8—62no—
344C3×Q8—62no—
345C3×Q8—124no—
346C3×Q8—241no—
347C3×Q8#23512yes—
348C3×Q8C3×#4112yes—
349C3×D4—34no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—32no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—124no—
371C2×C3×C4—242no—
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C2×C3×D411yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C24×C311yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3C2×C3×D412yes—
381D12C3×Q1614yescomplemented
382C4×D3—22no—
383C4×D3—22no—
384C4×D3—44no—
385C4×D3—82no—
386Dic6—22no—
387Dic6—22no—
388Dic6—44no—
389Dic6—81no—
390C3×C8—22no—
391C3×C8—21no—
392C3×C8—21no—
393C3×C8—21no—
394C3×C8—21no—
395C3×C8—41no—
396C3×C8—62no—
397C3⋊C8—22no—
398C2×C32#54611yescharacteristic
399C2×C32C22×Q1611yescharacteristic
400C2×C32#57711yescharacteristic
401C3×D3—24no—
402C2×Q8—32no—
403C2×Q8—62no—
404C2×Q8—61no—
405C2×Q8—64no—
406C2×Q8—122no—
407C2×Q8C22×C3×D311yescharacteristic
408C2×Q8C22×C3×D311yescharacteristic
409C2×D4—31no—
410C22×C4—32no—
411C22×C4—62no—
412C22×C4—62no—
413Q16—22no—
414Q16—122no—
415C2×C8—32no—
416C2×C8—122no—
417C2×C8C22×C3×D311yescharacteristic
418C2×C8C22×C3×D311yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—31no—
422C4⋊C4—32no—
423C4⋊C4—62no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4C22×C3×D311yescharacteristic
430C4⋊C4C22×C3×D311yescharacteristic
431C22⋊C4—32no—
432C22⋊C4—62no—
433C22⋊C4—62no—
434C42—21no—
435C42—21no—
436C42C22×C3×D311yescharacteristic
437C22×C3—21no—
438C22×C3—34no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×C3×D411yescharacteristic
443C2×D3—22no—
444C2×D3—22no—
445C2×D3C2×C3×Q1614yes—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—41no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—62no—
463C3×C4—81no—
464C3×C4—81no—
465C3×C4—122no—
466C3×C4—122no—
467C3×C4D3×Q1612yes—
468C3×C4C2×C3×Q1612yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4#100911yescharacteristic
471C3×C4C2×C3×#4111yescharacteristic
472C3×C4C3×H(5,𝔽2)11yescharacteristic
473Dic3—22no—
474Dic3—42no—
475Dic3—42no—
476C32#329911yescharacteristic, complemented, Sylow
477C23—32no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—62no—
482Q8—62no—
483Q8—124no—
484Q8—241no—
485Q8C3×#23512yes—
486D4—34no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—32no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—124no—
497C2×C4—242no—
498C2×C4C3×D3×D411yescharacteristic
499C2×C4C3×D3×D411yescharacteristic
500C2×C4C23×C3×D311yescharacteristic
501C8—21no—
502C8—21no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—64no—
508C2×C3#555011yescharacteristic
509C2×C3C2×D3×Q1611yescharacteristic
510C2×C3#577011yescharacteristic
511C2×C3C3×#54611yescharacteristic
512C2×C3C22×C3×Q1611yescharacteristic
513C2×C3C3×#57711yescharacteristic
514D3—24no—
515C22—34no—
516C22—62no—
517C22—62no—
518C22C2×C3×D3×D411yescharacteristic
519C4—21no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—62no—
525C4—122no—
526C4—122no—
527C4C3×D3×Q1612yes—
528C4C2×C3×#23511yescharacteristic
529C4C3×#100911yescharacteristic
530C3—21no—
531C3#7973511yescharacteristic, direct product factor
532C3C3×#329911yescharacteristic, complemented
533C2—64no—
534C2C3×#555011yescharacteristic
535C2C2×C3×D3×Q1611yescharacteristic
536C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×C4×Q16D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C32×C4×Q16C2semidirect
4. C3×#5186C2semidirect
5. C3×#5031C2semidirect
6. C3×#5021C2semidirect
7. C3×#4884C2semidirect
8. C3×#4813C2semidirect
9. C3×D3×#103C2semidirect
11. C3×#4681C2semidirect
13. #79735C3direct (N × H)
54. C3×C4×Q16D3semidirect
55. C3×C4×Q16C2×C3semidirect
58. #5186C2×C3semidirect
59. #5031C2×C3semidirect
60. #5021C2×C3semidirect
61. #4884C2×C3semidirect
62. #4813C2×C3semidirect
63. D3×#103C2×C3semidirect
65. #4681C2×C3semidirect
182. C3×D12Q16semidirect
202. C4×Q16C3×D3semidirect
381. D12C3×Q16semidirect
476. C32#3299semidirect
531. C3#79735direct (N × H)
532. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×Q8×D122
C32×C4×Q162
C3×#51862
C3×#50312
C3×#50212
C3×#48842
C3×#48132
C3×D3×#1032
C3×C8×D122
C3×#46812
C3×#32993
#797353