Finite Group Databasebeta

← C3×#68238 #11774642

Subgroups — C3×#68238 #11774642

Order 1152.

567 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
4C32×Q8⋊C8C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4483C211yesmaximal, characteristic, complemented
7C3×#4459C211yesmaximal, characteristic, complemented
8C3×#1489—31nomaximal
9#68238C311yesmaximal, characteristic, direct product factor
10C2×C3×#239C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C2×C3×ΓL(1,𝔽25)—21no—
14C2×C3×ΓL(1,𝔽25)—21no—
15C3×#893—21no—
16C3×#893C411yescharacteristic
17C3×#892—21no—
18C3×#892C411yescharacteristic
19C3×C4×D12—21no—
20C3×C4×D12C2211yescharacteristic
21C3×C42×D3—21no—
22C3×C42×D3C2211yescharacteristic
23C32×C4⋊C8C2211yescharacteristic
24C32×C4×C8C2211yescharacteristic
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×C4×#41—31no—
30C4×#239C2×C311yescharacteristic
31C3×#423—31no—
32C3×C4×M16—31no—
33#4837C2×C311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)C2×C311yescharacteristic, complemented
35C3×Q8⋊C8—21no—
36C3×Q8⋊C8—31no—
37C3×Q8⋊C8D311yescharacteristic, complemented
38C3×Q8⋊C8C2×C311yescharacteristic, complemented
39C3×D4⋊C8—31no—
40C3×D4⋊C8—31no—
41#4535C2×C311yescharacteristic, complemented
42#4483C2×C311yescharacteristic, complemented
43#4459C2×C311yescharacteristic, complemented
44C2×C32×Q8C2×C411yescharacteristic
45C3×#239—22no—
46C3×#239—22no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2×C411yescharacteristic
59C32×C42—21no—
60C32×C42C2311yescharacteristic
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C3×ΓL(1,𝔽25)—24no—
74C3×ΓL(1,𝔽25)—42no—
75#1489—31noSylow
76C2×C3×#41—31no—
77C2×#239C3×C411yescharacteristic
78C2×C3×M16—61no—
79C2×C3×M16—61no—
80C3×C4×Q8—21no—
81C3×C4×Q8—31no—
82C3×C4×Q8C2×D311yescharacteristic
83C3×C4×Q8C22×C311yescharacteristic
84C3×C4×D4—31no—
85C3×C4×D4—31no—
86C3×C4×D4—61no—
87C3×C4×D4—61no—
88C3×#117—31no—
89C3×#117—61no—
90C2×C3×C42—31no—
91C2×C3×C42—61no—
92Q8×Dic3C3×C411yescharacteristic
93C2×ΓL(1,𝔽25)—21no—
94C2×ΓL(1,𝔽25)—21no—
95#893—21no—
96#893C3×C411yescharacteristic
97#892—21no—
98#892C3×C411yescharacteristic
99C4×D12—21no—
100C4×D12C22×C311yescharacteristic
101C42×D3—21no—
102C42×D3C22×C311yescharacteristic
103C3×C4⋊C8—21no—
104C3×C4⋊C8—31no—
105C3×C4⋊C8—61no—
106C3×C4⋊C8C2×D311yescharacteristic
107C3×C4⋊C8C22×C311yescharacteristic
108C3×#97—61no—
109C3×C4×C8—21no—
110C3×C4×C8—31no—
111C3×C4×C8C2×D311yescharacteristic
112C3×C4×C8C22×C311yescharacteristic
113#815—21no—
114Dic3⋊C8—21no—
115C4⋊(C3⋊C8)C22×C311yescharacteristic
116C4×C3⋊C8C22×C311yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C32×Q8—21no—
120C32×Q8M1612yescomplemented
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×D12—24no—
131C3×D12—21no—
132C3×D12M1612yescomplemented
133C3×C4×D3—24no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—21no—
138C3×C4×D3—22no—
139C3×C4×D3—41no—
140C3×C4×D3—41no—
141C3×C4×D3—42no—
142C32×C8—22no—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C4×#41—31no—
147#423—31no—
148C4×M16—31no—
149Q8⋊C8—31no—
150Q8⋊C8C3×D311yescharacteristic, complemented
151D4⋊C8—31no—
152D4⋊C8—31no—
153C3×#41—62no—
154C3×#41—62no—
155C2×C3×Q8—21no—
156C2×C3×Q8C4×D311yescharacteristic
157C2×C3×Q8C2×C3×C411yescharacteristic
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166#239—22no—
167#239—22no—
168C2×D12—21no—
169C2×D12C2×C3×C411yescharacteristic
170C2×C4×D3—21no—
171C2×C4×D3—21no—
172C2×C4×D3—21no—
173C2×C4×D3C2×C3×C411yescharacteristic
174C2×C4×D3C3×D411yescharacteristic
175C2×C4×D3C3×D411yescharacteristic
176C3×M16—64no—
177C3×M16—122no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—41no—
183C2×C3×C8—41no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—31no—
190C3×C4⋊C4—41no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4C4×D311yescharacteristic
193C3×C4⋊C4C2×C3×C411yescharacteristic
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—31no—
201C3×C42—31no—
202C3×C42—31no—
203C3×C42—41no—
204C3×C42—61no—
205C3×C42—61no—
206C3×C42C22×D311yescharacteristic
207C3×C42C23×C311yescharacteristic
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210(C2×D3)⋊C4—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3C2×C3×C411yescharacteristic
213C4×Dic3—21no—
214C4×Dic3—21no—
215C4×Dic3C2×C3×C411yescharacteristic
216C4×Dic3C3×D411yescharacteristic
217C4×Dic3C3×D411yescharacteristic
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220ΓL(1,𝔽25)—24no—
221ΓL(1,𝔽25)—42no—
222C22×C32C2×C22⋊C411yescharacteristic
223C2×C3×D3—21no—
224C2×C3×D3—22no—
225C2×C3×D3—21no—
226C2×C3×D3—21no—
227C2×C3×D3—41no—
228C2×C3×D3—41no—
229C32×C4—22no—
230C32×C4—21no—
231C32×C4—41no—
232C32×C4C2×M1611yescharacteristic
233C32×C4C2×M1611yescharacteristic
234C32×C4AGL(1,ℤ/8)11yescharacteristic
235C32×C4#13711yescharacteristic
236C3×Dic3—21no—
237C3×Dic3—21no—
238C3×Dic3—41no—
239C3×Dic3#10412yes—
240C2×#41—31no—
241C2×M16—61no—
242C2×M16—61no—
243C4×Q8—31no—
244C4×Q8C2×C3×D311yescharacteristic
245C4×D4—31no—
246C4×D4—31no—
247C4×D4—61no—
248C4×D4—61no—
249#117—31no—
250#117—61no—
251C2×C42—31no—
252C2×C42—61no—
253C4⋊C8—31no—
254C4⋊C8—61no—
255C4⋊C8C2×C3×D311yescharacteristic
256#97—61no—
257C4×C8—31no—
258C4×C8C2×C3×D311yescharacteristic
259C23×C3—31no—
260C23×C3—61no—
261C22×D3—21no—
262C22×D3C3×C22⋊C411yescharacteristic
263C3×Q8—21no—
264C3×Q8—21no—
265C3×Q8—22no—
266C3×Q8—41no—
267C3×Q8ΓL(1,𝔽25)12yescomplemented
268C3×Q8C3×M1612yescomplemented
269C3×D4—32no—
270C3×D4—64no—
271C3×D4—61no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—62no—
285C2×C3×C4—64no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—122no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4C22×C3×C411yescharacteristic
298C2×C3×C4C2×C3×D411yescharacteristic
299C2×C3×C4C2×C3×D411yescharacteristic
300C2×Dic3—21no—
301C2×Dic3C3×C22⋊C411yescharacteristic
302C2×Dic3C3×C22⋊C411yescharacteristic
303C2×Dic3C3×C22⋊C411yescharacteristic
304D12—24no—
305D12—21no—
306D12C3×M1612yescomplemented
307C4×D3—24no—
308C4×D3—21no—
309C4×D3—21no—
310C4×D3—21no—
311C4×D3—21no—
312C4×D3—22no—
313C4×D3—41no—
314C4×D3—41no—
315C4×D3—42no—
316C3×C8—22no—
317C3×C8—22no—
318C3×C8—42no—
319C3×C8—41no—
320C3×C8—41no—
321C3×C8—62no—
322C3×C8—81no—
323C3×C8—121no—
324C3⋊C8—22no—
325C3⋊C8—41no—
326C2×C32#40711yescharacteristic
327C2×C32#41711yescharacteristic
328C2×C32C2×#10411yescharacteristic
329C3×D3—41no—
330C3×D3—42no—
331#41—62no—
332#41—62no—
333C2×Q8C3×C4×D311yescharacteristic
334C2×D4—31no—
335C2×D4—61no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—61no—
342M16—64no—
343M16—122no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—61no—
347C2×C8—61no—
348C4⋊C4—21no—
349C4⋊C4—31no—
350C4⋊C4—61no—
351C4⋊C4C3×C4×D311yescharacteristic
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C42—21no—
356C42—31no—
357C42—31no—
358C42—31no—
359C42—61no—
360C42—61no—
361C42C22×C3×D311yescharacteristic
362C22×C3—21no—
363C22×C3—62no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—61no—
367C22×C3—121no—
368C22×C3—121no—
369C22×C3D3×C22⋊C411yescharacteristic
370C22×C3C2×C3×C22⋊C411yescharacteristic
371C2×D3—21no—
372C2×D3—22no—
373C2×D3—21no—
374C2×D3—21no—
375C2×D3—41no—
376C2×D3—41no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—32no—
386C3×C4—41no—
387C3×C4—42no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—61no—
391C3×C4—61no—
392C3×C4—81no—
393C3×C4—121no—
394C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
395C3×C4D3×M1611yescharacteristic
396C3×C4#91411yescharacteristic
397C3×C4#91811yescharacteristic
398C3×C4C2×C3×M1611yescharacteristic
399C3×C4C2×C3×M1611yescharacteristic
400C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
401C3×C4C3×#13711yescharacteristic
402Dic3—21no—
403Dic3—21no—
404Dic3—41no—
405Dic3C3×#10412yes—
406C32#148911yescharacteristic, complemented, Sylow
407C23—31no—
408C23—61no—
409Q8—21no—
410Q8C3×ΓL(1,𝔽25)12yescomplemented
411D4—32no—
412D4—64no—
413D4—61no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—62no—
420C2×C4—64no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—122no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4C2×C3×C4×D311yescharacteristic
430C2×C4C3×D3×D411yescharacteristic
431C2×C4C3×D3×D411yescharacteristic
432C8—22no—
433C8—41no—
434C8—62no—
435C8—121no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—121no—
440C2×C3—122no—
441C2×C3#472611yescharacteristic
442C2×C3#480311yescharacteristic
443C2×C3D3×#10411yescharacteristic
444C2×C3C3×#40711yescharacteristic
445C2×C3C3×#41711yescharacteristic
446C2×C3C2×C3×#10411yescharacteristic
447D3—41no—
448D3—42no—
449C22—62no—
450C22—61no—
451C22—61no—
452C22—61no—
453C22—121no—
454C22—121no—
455C22C3×D3×C22⋊C411yescharacteristic
456C4—22no—
457C4—21no—
458C4—32no—
459C4—41no—
460C4—61no—
461C4—61no—
462C4—121no—
463C4C2×C3×ΓL(1,𝔽25)11yescharacteristic
464C4C3×D3×M1611yescharacteristic
465C4C3×#91411yescharacteristic
466C4C3×#91811yescharacteristic
467C3—21no—
468C3#6823811yescharacteristic, direct product factor
469C3C3×#148911yescharacteristic, complemented
470C2—121no—
471C2—122no—
472C2C3×#472611yescharacteristic
473C2C3×#480311yescharacteristic
474C2C3×D3×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#239C4
cosocleC3×C42C23×C3
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1489
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4837C2semidirect
3. C3×C4×ΓL(1,𝔽25)C2semidirect
4. C32×Q8⋊C8C2semidirect
5. C3×#4535C2semidirect
6. C3×#4483C2semidirect
7. C3×#4459C2semidirect
9. #68238C3direct (N × H)
33. #4837C2×C3semidirect
34. C4×ΓL(1,𝔽25)C2×C3semidirect
37. C3×Q8⋊C8D3semidirect
38. C3×Q8⋊C8C2×C3semidirect
41. #4535C2×C3semidirect
42. #4483C2×C3semidirect
43. #4459C2×C3semidirect
120. C32×Q8M16semidirect
132. C3×D12M16semidirect
150. Q8⋊C8C3×D3semidirect
267. C3×Q8ΓL(1,𝔽25)semidirect
268. C3×Q8C3×M16semidirect
306. D12C3×M16semidirect
406. C32#1489semidirect
410. Q8C3×ΓL(1,𝔽25)semidirect
468. C3#68238direct (N × H)
469. C3C3×#1489semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C3×#48372
C3×C4×ΓL(1,𝔽25)2
C32×Q8⋊C82
C3×#45352
C3×#44832
C3×#44592
C3×#14893
#682383