Finite Group Databasebeta

← C3×#68172 #11774542

Subgroups — C3×#68172 #11774542

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3C3×#4685C211yesmaximal, characteristic, complemented
4C32×D4⋊C8C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1486—31nomaximal
9#68172C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×D4C411yescharacteristic
11C22×C3×C4×D3—21no—
12C32×C4×D4C2211yescharacteristic
13C3×D4×Dic3C411yescharacteristic
14C3×C4×#67—21no—
15C2×C3×ΓL(1,𝔽25)—21no—
16C3×#893C411yescharacteristic
17C3×D3×C4⋊C4C411yescharacteristic
18C3×#67⋊C4—21no—
19C3×D3×C22⋊C4—21no—
20C3×C4×D12C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic, complemented
23C32×C4×C8C2211yescharacteristic, complemented
24C3×(C2×D3)⋊C8—21no—
25C3×Dic3⋊C8—21no—
26C3×Dic3⋊C8—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×C4×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×C4×D4—31no—
30C4×D3×D4C2×C311yescharacteristic
31C3×#431—31no—
32C3×#423—31no—
33#4837C2×C311yescharacteristic, complemented
34#4685C2×C311yescharacteristic, complemented
35C3×D4⋊C8—21no—
36C3×D4⋊C8—31no—
37C3×D4⋊C8—31no—
38C3×D4⋊C8—31no—
39C3×D4⋊C8D311yescharacteristic, complemented
40C3×D4⋊C8C2×C311yescharacteristic, complemented
41D4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
42#4483C2×C311yescharacteristic, complemented
43#4459C2×C311yescharacteristic, complemented
44C23×C3×D3—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C3×D3×D4—22no—
50C3×D3×D4—22no—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C22⋊C4—21no—
64C32×C42C2311yescharacteristic
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3C2×C411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C3×C4×Dic3D411yescharacteristic
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C3×ΓL(1,𝔽25)—42no—
76#1486—31noSylow
77C22×C3×D4—31no—
78C23×C3×C4—61no—
79C2×D3×D4C3×C411yescharacteristic
80C22×C4×D3—21no—
81C2×C3×M16—61no—
82C3×C4×D4—21no—
83C3×C4×D4—31no—
84C3×C4×D4—31no—
85C3×C4×D4—31no—
86C3×C4×D4—61no—
87C3×C4×D4—61no—
88C3×C4×D4C2×D311yescharacteristic
89C3×C4×D4C22×C311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—31no—
93D4×Dic3C3×C411yescharacteristic
94C4×#67—21no—
95C2×ΓL(1,𝔽25)—21no—
96#893C3×C411yescharacteristic
97D3×C4⋊C4C3×C411yescharacteristic
98#67⋊C4—21no—
99D3×C22⋊C4—21no—
100C4×D12C22×C311yescharacteristic
101C42×D3C22×C311yescharacteristic
102C3×C4⋊C8—21no—
103C3×C4⋊C8—31no—
104C3×C4⋊C8—61no—
105C3×C4⋊C8—61no—
106C3×C4⋊C8C2×D311yescharacteristic, complemented
107C3×C4⋊C8C22×C311yescharacteristic, complemented
108C3×C22⋊C8—61no—
109C3×C4×C8—21no—
110C3×C4×C8—31no—
111C3×C4×C8C2×D311yescharacteristic, complemented
112C3×C4×C8C22×C311yescharacteristic, complemented
113(C2×D3)⋊C8—21no—
114Dic3⋊C8—21no—
115Dic3⋊C8—21no—
116C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
117C4×C3⋊C8C22×C311yescharacteristic, complemented
118C23×C32—21no—
119C22×C3×D3—24no—
120C22×C3×D3—21no—
121C22×C3×D3—42no—
122C22×C3×D3—42no—
123C22×C3×D3C22⋊C411yescharacteristic
124C32×D4—21no—
125C32×D4M1612yescomplemented
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C3×#67—24no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C3×D12—21no—
139C3×D12M1612yescomplemented
140C3×C4×D3—21no—
141C3×C4×D3—21no—
142C3×C4×D3—41no—
143C3×C4×D3—42no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3—42no—
147C3×C4×D3D812yes—
148C3×C4×D3SD1612yes—
149C32×C8—41no—
150C32×C8—41no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153C2×C4×D4—31no—
154#431—31no—
155#423—31no—
156D4⋊C8—31no—
157D4⋊C8—31no—
158D4⋊C8—31no—
159D4⋊C8C3×D311yescharacteristic, complemented
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×D4—21no—
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C2×C3×D4—62no—
166C2×C3×D4—62no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×C3×C411yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4—122no—
181C2×#67—21no—
182C22×Dic3—21no—
183D3×D4—22no—
184D3×D4—22no—
185C2×D12C2×C3×C411yescharacteristic
186C2×C4×D3—21no—
187C2×C4×D3—21no—
188C2×C4×D3—21no—
189C2×C4×D3—42no—
190C2×C4×D3—42no—
191C2×C4×D3C2×C3×C411yescharacteristic
192C2×C4×D3C3×D411yescharacteristic
193C2×C4×D3C3×D411yescharacteristic
194C3×M16—122no—
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—41no—
200C2×C3×C8—41no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—31no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4C4×D311yescharacteristic
207C3×C4⋊C4C2×C3×C411yescharacteristic
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—41no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C42—21no—
215C3×C42—31no—
216C3×C42—31no—
217C3×C42—31no—
218C3×C42C22×D311yescharacteristic
219C3×C42C23×C311yescharacteristic
220#217—21no—
221(C2×D3)⋊C4—21no—
222(C2×D3)⋊C4—21no—
223C4⋊Dic3C2×C3×C411yescharacteristic
224Dic3⋊C4—21no—
225C4×Dic3C2×C3×C411yescharacteristic
226C4×Dic3C3×D411yescharacteristic
227C4×Dic3C3×D411yescharacteristic
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230ΓL(1,𝔽25)—42no—
231C22×C32—22no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32C2×C22⋊C411yescharacteristic
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—22no—
238C2×C3×D3—48no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3#10212yes—
242C32×C4—21no—
243C32×C4—41no—
244C32×C4C2×M1611yescharacteristic
245C32×C4C2×M1611yescharacteristic
246C32×C4C2×D811yescharacteristic
247C32×C4C2×SD1611yescharacteristic
248C3×Dic3—21no—
249C3×Dic3—21no—
250C3×Dic3—41no—
251C3×Dic3#10212yes—
252C22×D4—31no—
253C23×C4—61no—
254C2×M16—61no—
255C4×D4—31no—
256C4×D4—31no—
257C4×D4—31no—
258C4×D4—61no—
259C4×D4—61no—
260C4×D4C2×C3×D311yescharacteristic
261C2×C4⋊C4—31no—
262C2×C22⋊C4—61no—
263C2×C42—31no—
264C4⋊C8—31no—
265C4⋊C8—61no—
266C4⋊C8—61no—
267C4⋊C8C2×C3×D311yescharacteristic, complemented
268C22⋊C8—61no—
269C4×C8—31no—
270C4×C8C2×C3×D311yescharacteristic, complemented
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—41no—
275C23×C3—64no—
276C23×C3—61no—
277C23×C3—122no—
278C23×C3—122no—
279C22×D3—24no—
280C22×D3—21no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3C3×C22⋊C411yescharacteristic
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—22no—
287C3×D4—32no—
288C3×D4—41no—
289C3×D4—64no—
290C3×D4—61no—
291C3×D4ΓL(1,𝔽25)12yescomplemented
292C3×D4C3×M1612yescomplemented
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—32no—
300C2×C3×C4—32no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4—121no—
314C2×C3×C4—122no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4C22×C3×C411yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325#67—24no—
326C2×Dic3—21no—
327C2×Dic3—42no—
328C2×Dic3C3×C22⋊C411yescharacteristic
329C2×Dic3C3×C22⋊C411yescharacteristic
330C2×Dic3C3×C22⋊C411yescharacteristic
331D12—21no—
332D12C3×M1612yescomplemented
333C4×D3—21no—
334C4×D3—21no—
335C4×D3—41no—
336C4×D3—42no—
337C4×D3—41no—
338C4×D3—41no—
339C4×D3—42no—
340C4×D3C3×D812yes—
341C4×D3C3×SD1612yes—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—42no—
345C3×C8—41no—
346C3×C8—41no—
347C3×C8—81no—
348C3×C8—121no—
349C3×C8—121no—
350C3⋊C8—41no—
351C3⋊C8—41no—
352C2×C32—42no—
353C2×C32#40711yescharacteristic
354C2×C32C2×#10211yescharacteristic
355C2×C32#42111yescharacteristic
356C3×D3—22no—
357C3×D3—42no—
358C24—61no—
359C2×D4—31no—
360C2×D4—61no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4C3×C4×D311yescharacteristic
364C22×C4—21no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—122no—
373C22×C4—122no—
374M16—122no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—61no—
378C2×C8—61no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4C3×C4×D311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C42—31no—
387C42—31no—
388C42—31no—
389C42C22×C3×D311yescharacteristic
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—61no—
400C22×C3—61no—
401C22×C3—62no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—128no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3C2×C3×C22⋊C411yescharacteristic
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—22no—
412C2×D3—48no—
413C2×D3—41no—
414C2×D3—41no—
415C2×D3C3×#10212yes—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—32no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4—81no—
429C3×C4—121no—
430C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
431C3×C4D3×M1611yescharacteristic
432C3×C4D3×D811yescharacteristic
433C3×C4D3×SD1611yescharacteristic
434C3×C4C2×C3×M1611yescharacteristic
435C3×C4C2×C3×M1611yescharacteristic
436C3×C4C2×C3×D811yescharacteristic
437C3×C4C2×C3×SD1611yescharacteristic
438Dic3—21no—
439Dic3—21no—
440Dic3—41no—
441Dic3C3×#10212yes—
442C32#148611yescharacteristic, complemented, Sylow
443C23—21no—
444C23—31no—
445C23—64no—
446C23—61no—
447C23—122no—
448C23—122no—
449D4—21no—
450D4—32no—
451D4—64no—
452D4—61no—
453D4C3×ΓL(1,𝔽25)12yescomplemented
454C2×C4—21no—
455C2×C4—31no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—121no—
466C2×C4—122no—
467C2×C4—122no—
468C2×C4—122no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4C2×C3×C4×D311yescharacteristic
472C2×C4C3×D3×D411yescharacteristic
473C2×C4C3×D3×D411yescharacteristic
474C8—41no—
475C8—41no—
476C8—121no—
477C8—121no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—42no—
482C2×C3—42no—
483C2×C3—62no—
484C2×C3—82no—
485C2×C3—122no—
486C2×C3#472611yescharacteristic
487C2×C3D3×#10211yescharacteristic
488C2×C3#482111yescharacteristic
489C2×C3C3×#40711yescharacteristic
490C2×C3C2×C3×#10211yescharacteristic
491C2×C3C3×#42111yescharacteristic
492D3—22no—
493D3—42no—
494C22—22no—
495C22—32no—
496C22—41no—
497C22—41no—
498C22—61no—
499C22—61no—
500C22—62no—
501C22—128no—
502C22—121no—
503C22—121no—
504C22C3×D3×C22⋊C411yescharacteristic
505C4—21no—
506C4—32no—
507C4—41no—
508C4—61no—
509C4—61no—
510C4—121no—
511C4C2×C3×ΓL(1,𝔽25)11yescharacteristic
512C4C3×D3×M1611yescharacteristic
513C4C3×D3×D811yescharacteristic
514C4C3×D3×SD1611yescharacteristic
515C3—21no—
516C3#6817211yescharacteristic, direct product factor
517C3C3×#148611yescharacteristic, complemented
518C2—42no—
519C2—62no—
520C2—122no—
521C2C3×#472611yescharacteristic
522C2C3×D3×#10211yescharacteristic
523C2C3×#482111yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×D4⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×D3×D4C4
cosocleC3×C42C23×C3
hypercenterC3×D4⋊C8D3
hypocenterC3C3×#1486
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4837C2semidirect
3. C3×#4685C2semidirect
4. C32×D4⋊C8C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. C3×#4483C2semidirect
7. C3×#4459C2semidirect
9. #68172C3direct (N × H)
22. C32×C4⋊C8C22semidirect
23. C32×C4×C8C22semidirect
27. C3×C4⋊(C3⋊C8)C22semidirect
28. C3×C4×C3⋊C8C22semidirect
33. #4837C2×C3semidirect
34. #4685C2×C3semidirect
39. C3×D4⋊C8D3semidirect
40. C3×D4⋊C8C2×C3semidirect
41. D4⋊(C3⋊C8)C2×C3semidirect
42. #4483C2×C3semidirect
43. #4459C2×C3semidirect
106. C3×C4⋊C8C2×D3semidirect
107. C3×C4⋊C8C22×C3semidirect
111. C3×C4×C8C2×D3semidirect
112. C3×C4×C8C22×C3semidirect
116. C4⋊(C3⋊C8)C22×C3semidirect
117. C4×C3⋊C8C22×C3semidirect
125. C32×D4M16semidirect
139. C3×D12M16semidirect
159. D4⋊C8C3×D3semidirect
267. C4⋊C8C2×C3×D3semidirect
270. C4×C8C2×C3×D3semidirect
291. C3×D4ΓL(1,𝔽25)semidirect
292. C3×D4C3×M16semidirect
332. D12C3×M16semidirect
442. C32#1486semidirect
453. D4C3×ΓL(1,𝔽25)semidirect
516. C3#68172direct (N × H)
517. C3C3×#1486semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
C3×#48372
C3×#46852
C32×D4⋊C82
C3×D4⋊(C3⋊C8)2
C3×#44832
C3×#44592
C3×#14863
#681723