Finite Group Databasebeta

← C3×#69143 #11796229

Subgroups — C3×#69143 #11796229

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5653C211yesmaximal, characteristic
2C3×D3×#100C211yesmaximal, characteristic, complemented
3C3×D3×#99C211yesmaximal, characteristic, complemented
4C32×#352C211yesmaximal, characteristic, complemented
5C3×#4539C211yesmaximal, characteristic, complemented
6C3×#4475C211yesmaximal, characteristic, complemented
7C3×#4471C211yesmaximal, characteristic, complemented
8C3×#2121—31nomaximal
9#69143C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4C2211yescharacteristic
11C22×C3×D12C411yescharacteristic, complemented
12C32×#123C2211yescharacteristic
13C3×#937C2211yescharacteristic
14C3×#929C411yescharacteristic, complemented
15C3×D3×M16—21no—
16C3×#895—21no—
17C3×#894—21no—
18C3×#884—21no—
19C3×#882—21no—
20C3×#882C411yescharacteristic, complemented
21C3×D3×C22⋊C4—21no—
22C3×D3×C22⋊C4C411yescharacteristic, complemented
23C32×#100C2211yescharacteristic
24C32×#99C2211yescharacteristic
25C3×#834C2211yescharacteristic
26C3×#833C2211yescharacteristic
27C3×#823—21no—
28C3×#806—21no—
29C3×#534—31no—
30#5653C2×C311yescharacteristic
31C2×C3×#100—31no—
32C2×C3×#99—31no—
33D3×#100C2×C311yescharacteristic, complemented
34D3×#99C2×C311yescharacteristic, complemented
35C3×#352—21no—
36C3×#352—31no—
37C3×#352D311yescharacteristic, complemented
38C3×#352C2×C311yescharacteristic, complemented
39C3×AΣL(1,𝔽16)—31no—
40C3×AΣL(1,𝔽16)—31no—
41#4539C2×C311yescharacteristic, complemented
42#4475C2×C311yescharacteristic, complemented
43#4471C2×C311yescharacteristic, complemented
44C23×C3×D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic, complemented
46C23×C3×D3D411yescharacteristic
47C2×C32×D4C2311yescharacteristic
48C22×C32×C4C2×C411yescharacteristic, complemented
49C2×C3×#67—21no—
50C2×C3×#67C2×C411yescharacteristic
51C2×C3×#67D411yescharacteristic
52C3×D3×D4—41no—
53C3×D3×D4—41no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—41no—
58C2×C3×D12—41no—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—41no—
62C2×C3×C4×D3D411yescharacteristic
63C32×M16—21no—
64C32×C4⋊C4—21no—
65C32×C22⋊C4—21no—
66C32×C22⋊C4—21no—
67C32×C22⋊C4C2×C411yescharacteristic, complemented
68C3×#217—21no—
69C3×#217C2×C411yescharacteristic, complemented
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×(C2×D3)⋊C4—21no—
73C3×(C2×D3)⋊C4—21no—
74C3×(C2×D3)⋊C4—41no—
75C3×Dic3⋊C4—21no—
76C3×#208—21no—
77C3×ΓL(1,𝔽25)—41no—
78C3×D3×C8—41no—
79#2121—31noSylow
80C22×C3×D4—31no—
81C22×C3×D4—31no—
82C2×D3×D4C22×C311yescharacteristic
83C22×D12C3×C411yescharacteristic, complemented
84C2×C3×M16—61no—
85C3×#123—21no—
86C3×#123—31no—
87C3×#123—61no—
88C3×#123C2×D311yescharacteristic
89C3×#123C22×C311yescharacteristic
90C3×#121—61no—
91C3×#121—61no—
92C3×#120—31no—
93C3×#120—31no—
94C3×#120—61no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—61no—
97#937C22×C311yescharacteristic
98#929C3×C411yescharacteristic, complemented
99D3×M16—21no—
100#895—21no—
101#894—21no—
102#884—21no—
103#882—21no—
104#882C3×C411yescharacteristic, complemented
105D3×C22⋊C4—21no—
106D3×C22⋊C4C3×C411yescharacteristic, complemented
107C3×#100—21no—
108C3×#100—31no—
109C3×#100—61no—
110C3×#100C2×D311yescharacteristic
111C3×#100C22×C311yescharacteristic
112C3×#99—21no—
113C3×#99—31no—
114C3×#99—61no—
115C3×#99C2×D311yescharacteristic
116C3×#99C22×C311yescharacteristic
117#834C22×C311yescharacteristic
118#833C22×C311yescharacteristic
119#823—21no—
120#806—21no—
121C23×C32C22×C411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—41no—
129C22×C3×D3—81no—
130C22×C3×D3—81no—
131C22×C3×D3—81no—
132C22×C3×D3C22⋊C411yescharacteristic
133C22×C3×D3C22⋊C411yescharacteristic
134C22×C3×D3C22⋊C411yescharacteristic
135C32×D4—41no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C2×D411yescharacteristic
141C3×#67—41no—
142C3×#67—41no—
143C3×#67—81no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3C22⋊C411yescharacteristic
147C3×D12—41no—
148C3×D12—42no—
149C3×D12—41no—
150C3×D12—41no—
151C3×D12—81no—
152C3×C4×D3—21no—
153C3×C4×D3—21no—
154C3×C4×D3—81no—
155C3×C4×D3—82no—
156C32×C8—41no—
157C3×C3⋊C8—41no—
158#534—31no—
159C2×#100—31no—
160C2×#99—31no—
161#352—31no—
162#352C3×D311yescharacteristic, complemented
163AΣL(1,𝔽16)—31no—
164AΣL(1,𝔽16)—31no—
165C24×C3—31no—
166C24×C3—31no—
167C24×C3—31no—
168C23×D3C2×C3×C411yescharacteristic
169C23×D3C2×C3×C411yescharacteristic, complemented
170C23×D3C3×D411yescharacteristic
171C2×C3×D4—21no—
172C2×C3×D4—31no—
173C2×C3×D4—31no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—121no—
180C2×C3×D4—121no—
181C2×C3×D4—121no—
182C2×C3×D4—121no—
183C2×C3×D4C22×D311yescharacteristic
184C2×C3×D4C23×C311yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—61no—
188C22×C3×C4—121no—
189C22×C3×C4C4×D311yescharacteristic, complemented
190C22×C3×C4C2×C3×C411yescharacteristic, complemented
191C2×#67—21no—
192C2×#67C2×C3×C411yescharacteristic
193C2×#67C3×D411yescharacteristic
194D3×D4—41no—
195D3×D4—41no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—41no—
200C2×D12—41no—
201C2×D12C3×D411yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—41no—
204C2×C4×D3C3×D411yescharacteristic
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—41no—
208C3×M16—61no—
209C3×M16—121no—
210C2×C3×C8—121no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—61no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—31no—
221C3×C22⋊C4—41no—
222C3×C22⋊C4—41no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C22⋊C4—61no—
227C3×C22⋊C4—61no—
228C3×C22⋊C4—121no—
229C3×C22⋊C4C4×D311yescharacteristic, complemented
230C3×C22⋊C4C2×C3×C411yescharacteristic, complemented
231#217—21no—
232#217C2×C3×C411yescharacteristic, complemented
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235(C2×D3)⋊C4—21no—
236(C2×D3)⋊C4—21no—
237(C2×D3)⋊C4—41no—
238Dic3⋊C4—21no—
239#208—21no—
240ΓL(1,𝔽25)—41no—
241D3×C8—41no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—41no—
245C22×C32—41no—
246C22×C32C2×C22⋊C411yescharacteristic
247C2×C3×D3—21no—
248C2×C3×D3—21no—
249C2×C3×D3—41no—
250C2×C3×D3—42no—
251C2×C3×D3—41no—
252C2×C3×D3—41no—
253C2×C3×D3—41no—
254C2×C3×D3—41no—
255C2×C3×D3—41no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—82no—
260C2×C3×D3#9911yescharacteristic
261C2×C3×D3#9911yescharacteristic
262C32×C4—21no—
263C32×C4—41no—
264C32×C4—41no—
265C32×C4—81no—
266C3×Dic3—21no—
267C3×Dic3—41no—
268C3×Dic3—81no—
269C22×D4—31no—
270C22×D4—31no—
271C2×M16—61no—
272#123—31no—
273#123—61no—
274#123C2×C3×D311yescharacteristic
275#121—61no—
276#121—61no—
277#120—31no—
278#120—31no—
279#120—61no—
280C2×C22⋊C4—31no—
281C2×C22⋊C4—61no—
282#100—31no—
283#100—61no—
284#100C2×C3×D311yescharacteristic
285#99—31no—
286#99—61no—
287#99C2×C3×D311yescharacteristic
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—31no—
291C23×C3—31no—
292C23×C3—31no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3—121no—
299C23×C3—241no—
300C23×C3—241no—
301C23×C3—241no—
302C23×C3C2×C4×D311yescharacteristic
303C23×C3D3×D411yescharacteristic
304C23×C3C22×C3×C411yescharacteristic
305C23×C3C2×C3×D411yescharacteristic
306C22×D3—21no—
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—21no—
311C22×D3—41no—
312C22×D3—81no—
313C22×D3—81no—
314C22×D3—81no—
315C22×D3C3×C22⋊C411yescharacteristic
316C22×D3C3×C22⋊C411yescharacteristic
317C22×D3C3×C22⋊C411yescharacteristic
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—81no—
321C3×D4—121no—
322C3×D4—121no—
323C3×D4—121no—
324C3×D4—122no—
325C3×D4—121no—
326C3×D4—121no—
327C3×D4—241no—
328C3×D4—241no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—31no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—81no—
345C2×C3×C4—81no—
346C2×C3×C4—121no—
347C2×C3×C4—241no—
348C2×C3×C4—242no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351#67—41no—
352#67—41no—
353#67—81no—
354C2×Dic3—21no—
355C2×Dic3—41no—
356C2×Dic3C3×C22⋊C411yescharacteristic
357D12—41no—
358D12—42no—
359D12—41no—
360D12—41no—
361D12—81no—
362C4×D3—21no—
363C4×D3—21no—
364C4×D3—81no—
365C4×D3—82no—
366C3×C8—41no—
367C3×C8—41no—
368C3×C8—81no—
369C3×C8—121no—
370C3⋊C8—41no—
371C2×C32—21no—
372C2×C32—41no—
373C2×C32—41no—
374C2×C32C2×#9911yescharacteristic
375C3×D3—21no—
376C3×D3—21no—
377C3×D3—41no—
378C3×D3—41no—
379C3×D3—81no—
380C24—31no—
381C24—31no—
382C24—31no—
383C2×D4—31no—
384C2×D4—31no—
385C2×D4—31no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—61no—
389C2×D4—61no—
390C2×D4—121no—
391C2×D4—121no—
392C2×D4—121no—
393C2×D4—121no—
394C2×D4C22×C3×D311yescharacteristic
395C22×C4—31no—
396C22×C4—61no—
397C22×C4—121no—
398C22×C4C3×C4×D311yescharacteristic, complemented
399M16—21no—
400M16—61no—
401M16—121no—
402C2×C8—121no—
403C4⋊C4—21no—
404C4⋊C4—61no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—31no—
408C22⋊C4—61no—
409C22⋊C4—61no—
410C22⋊C4—61no—
411C22⋊C4—61no—
412C22⋊C4—61no—
413C22⋊C4—121no—
414C22⋊C4C3×C4×D311yescharacteristic, complemented
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—31no—
421C22×C3—31no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—61no—
429C22×C3—61no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—122no—
438C22×C3—121no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3—241no—
442C22×C3—242no—
443C22×C3D3×C22⋊C411yescharacteristic
444C22×C3C2×C3×C22⋊C411yescharacteristic
445C2×D3—21no—
446C2×D3—21no—
447C2×D3—41no—
448C2×D3—42no—
449C2×D3—41no—
450C2×D3—41no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—81no—
455C2×D3—81no—
456C2×D3—81no—
457C2×D3—82no—
458C2×D3C3×#9911yescharacteristic
459C2×D3C3×#9911yescharacteristic
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—41no—
467C3×C4—61no—
468C3×C4—81no—
469C3×C4—81no—
470C3×C4—81no—
471C3×C4—81no—
472C3×C4—121no—
473C3×C4—161no—
474C3×C4—241no—
475Dic3—21no—
476Dic3—41no—
477Dic3—81no—
478C32#212111yescharacteristic, complemented, Sylow
479C23—31no—
480C23—31no—
481C23—31no—
482C23—61no—
483C23—61no—
484C23—61no—
485C23—61no—
486C23—61no—
487C23—121no—
488C23—241no—
489C23—241no—
490C23—241no—
491C23C2×C3×C4×D311yescharacteristic
492C23C3×D3×D411yescharacteristic
493D4—41no—
494D4—121no—
495D4—121no—
496D4—121no—
497D4—122no—
498D4—121no—
499D4—121no—
500D4—241no—
501D4—241no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—31no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—121no—
511C2×C4—241no—
512C2×C4—242no—
513C2×C4C3×D3×D411yescharacteristic
514C8—41no—
515C8—121no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—41no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—61no—
525C2×C3—61no—
526C2×C3—81no—
527C2×C3—81no—
528C2×C3—121no—
529C2×C3—121no—
530C2×C3—241no—
531C2×C3D3×#9911yescharacteristic
532C2×C3C2×C3×#9911yescharacteristic
533D3—21no—
534D3—21no—
535D3—41no—
536D3—41no—
537D3—81no—
538C22—21no—
539C22—21no—
540C22—31no—
541C22—31no—
542C22—41no—
543C22—41no—
544C22—61no—
545C22—61no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22—121no—
550C22—121no—
551C22—122no—
552C22—121no—
553C22—241no—
554C22—241no—
555C22—241no—
556C22—242no—
557C22C3×D3×C22⋊C411yescharacteristic
558C4—21no—
559C4—41no—
560C4—41no—
561C4—61no—
562C4—81no—
563C4—121no—
564C4—241no—
565C3—21no—
566C3#6914311yescharacteristic, direct product factor
567C3C3×#212111yescharacteristic, complemented
568C2—21no—
569C2—41no—
570C2—41no—
571C2—61no—
572C2—61no—
573C2—121no—
574C2—121no—
575C2—241no—
576C2C3×D3×#9911yescharacteristic
subgroupG/H
centerC2×C3D3×#99
commutatorC23×C3C22×C3×C4
FrattiniC2×D4C22×C3×D3
FittingC32×#352C2
socleC2×C32C2×#99
prime radicalC3×#5653C2
cosocleC2×C3×D4C23×C3
hypercenterC3×#352D3
hypocenterC3C3×#2121
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#352

Complements

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

NH ≅ G/Ntype
2. C3×D3×#100C2semidirect
3. C3×D3×#99C2semidirect
4. C32×#352C2semidirect
5. C3×#4539C2semidirect
6. C3×#4475C2semidirect
7. C3×#4471C2semidirect
9. #69143C3direct (N × H)
11. C22×C3×D12C4semidirect
14. C3×#929C4semidirect
20. C3×#882C4semidirect
22. C3×D3×C22⋊C4C4semidirect
33. D3×#100C2×C3semidirect
34. D3×#99C2×C3semidirect
37. C3×#352D3semidirect
38. C3×#352C2×C3semidirect
41. #4539C2×C3semidirect
42. #4475C2×C3semidirect
43. #4471C2×C3semidirect
45. C23×C3×D3C2×C4semidirect
48. C22×C32×C4C2×C4semidirect
67. C32×C22⋊C4C2×C4semidirect
69. C3×#217C2×C4semidirect
83. C22×D12C3×C4semidirect
98. #929C3×C4semidirect
104. #882C3×C4semidirect
106. D3×C22⋊C4C3×C4semidirect
162. #352C3×D3semidirect
169. C23×D3C2×C3×C4semidirect
189. C22×C3×C4C4×D3semidirect
190. C22×C3×C4C2×C3×C4semidirect
229. C3×C22⋊C4C4×D3semidirect
230. C3×C22⋊C4C2×C3×C4semidirect
232. #217C2×C3×C4semidirect
398. C22×C4C3×C4×D3semidirect
414. C22⋊C4C3×C4×D3semidirect
478. C32#2121semidirect
566. C3#69143direct (N × H)
567. C3C3×#2121semidirect

Maximal subgroups

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

subgroupindex
C3×#56532
C3×D3×#1002
C3×D3×#992
C32×#3522
C3×#45392
C3×#44752
C3×#44712
C3×#21213
#691433