Finite Group Databasebeta

← C3×#68280 #11775342

Subgroups — C3×#68280 #11775342

Order 1152.

489 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3C3×#4650C211yesmaximal, characteristic, complemented
4C32×#327C211yesmaximal, characteristic
5C3×#4537C211yesmaximal, characteristic
6C3×#4467C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1512—31nomaximal
9#68280C311yesmaximal, characteristic, direct product factor
10C32×#121C2211yescharacteristic
11C3×#936C411yescharacteristic, complemented
12C3×#935—21no—
13C3×D4×Dic3—21no—
14C3×D4×Dic3C411yescharacteristic, complemented
15C3×#924C2211yescharacteristic
16C2×C3×Dic3⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C3×#890C411yescharacteristic, complemented
19C3×#887C411yescharacteristic, complemented
20C3×#879—21no—
21C3×#877—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#815—21no—
28C3×Dic3⋊C8—21no—
29C3×#529—31no—
30#5600C2×C311yescharacteristic
31C3×#432—31no—
32C3×#382—31no—
33#4719C2×C311yescharacteristic, complemented
34#4650C2×C311yescharacteristic, complemented
35C3×#328—31no—
36C3×#328—31no—
37C3×#327—21no—
38C3×#327—31no—
39C3×#327D311yescharacteristic
40C3×#327C2×C311yescharacteristic
41#4537C2×C311yescharacteristic
42#4467C2×C311yescharacteristic, complemented
43#4452C2×C311yescharacteristic, complemented
44C2×C32×D4—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6C2×C411yescharacteristic
53C2×C32×C8—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—42no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72#1512—31noSylow
73C3×#126—61no—
74C3×#125—31no—
75C3×#124—31no—
76C3×#123—61no—
77C3×C22⋊Q8—31no—
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C22×C311yescharacteristic
81C3×C4×Q8—31no—
82C3×C4×D4—31no—
83C3×C4×D4—61no—
84C3×#117—61no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C42—31no—
87#936C3×C411yescharacteristic, complemented
88#935—21no—
89D4×Dic3—21no—
90D4×Dic3C3×C411yescharacteristic, complemented
91#924C22×C311yescharacteristic
92C2×Dic3⋊C4—21no—
93C2×C4×Dic3C22×C311yescharacteristic
94#890C3×C411yescharacteristic, complemented
95#887C3×C411yescharacteristic, complemented
96#879—21no—
97#877—21no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C22×C311yescharacteristic
103C3×#97—61no—
104C3×#95—21no—
105C3×#95—31no—
106C3×#95—61no—
107C3×#95C2×D311yescharacteristic
108C3×#95C22×C311yescharacteristic
109C3⋊#95—21no—
110C3⋊#95C22×C311yescharacteristic
111#830C22×C311yescharacteristic
112#815—21no—
113Dic3⋊C8—21no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C32×D4—41no—
117C32×D4—41no—
118C32×D4—41no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C3×Dic6—41no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#529—31no—
143#432—31no—
144#382—31no—
145#328—31no—
146#328—31no—
147#327—31no—
148#327C3×D311yescharacteristic
149C2×C3×Q8—31no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—41no—
154C2×C3×D4C4×D311yescharacteristic
155C2×C3×D4C2×C3×C411yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—41no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3C3×D411yescharacteristic
169C22×Dic3C3×D411yescharacteristic
170C2×Dic6C2×C3×C411yescharacteristic
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—41no—
174C2×C3×C8—61no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—122no—
182C3×C4⋊C4C4×D311yescharacteristic
183C3×C4⋊C4C2×C3×C411yescharacteristic
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—41no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—61no—
196#217—21no—
197#217—21no—
198#217—21no—
199#217—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3C2×C3×C411yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—42no—
206C4×Dic3—21no—
207C4×Dic3C2×C3×C411yescharacteristic
208C4×Dic3C2×C3×C411yescharacteristic
209C4×Dic3C3×D411yescharacteristic
210C4×Dic3C3×D411yescharacteristic
211C2×C3⋊C8—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—81no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—61no—
232#125—31no—
233#124—31no—
234#123—61no—
235C22⋊Q8—31no—
236#121C2×C3×D311yescharacteristic
237C4×Q8—31no—
238C4×D4—31no—
239C4×D4—61no—
240#117—61no—
241C2×C4⋊C4—61no—
242C2×C42—31no—
243C4⋊C8—61no—
244C22⋊C8—31no—
245C22⋊C8C2×C3×D311yescharacteristic
246#97—61no—
247#95—31no—
248#95—61no—
249#95C2×C3×D311yescharacteristic
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3D3×D411yescharacteristic
255C23×C3C2×C3×D411yescharacteristic
256C3×Q8—121no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—81no—
264C3×D4—81no—
265C3×D4—81no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—42no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—81no—
289C2×C3×C4—81no—
290C2×C3×C4—81no—
291C2×C3×C4—121no—
292C2×C3×C4—122no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4C22×C3×C411yescharacteristic
299C2×C3×C4C2×C3×D411yescharacteristic
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—21no—
304C2×Dic3—41no—
305C2×Dic3—42no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3C3×C22⋊C411yescharacteristic
310C2×Dic3C3×C22⋊C411yescharacteristic
311C2×Dic3C3×C22⋊C411yescharacteristic
312C2×Dic3C3×C22⋊C411yescharacteristic
313Dic6—41no—
314C3×C8—41no—
315C3×C8—41no—
316C3×C8—81no—
317C3×C8—121no—
318C3⋊C8—41no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—81no—
322C2×C32#41011yescharacteristic
323C2×C32#41711yescharacteristic
324C2×C32#42111yescharacteristic
325C2×Q8—31no—
326C2×D4—21no—
327C2×D4C3×C4×D311yescharacteristic
328C22×C4—21no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—61no—
332C22×C4—61no—
333C22×C4C22×C3×D311yescharacteristic
334C2×C8—21no—
335C2×C8—61no—
336C4⋊C4—31no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—122no—
342C4⋊C4C3×C4×D311yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C42—31no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—61no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3—81no—
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3#91111yescharacteristic
373C22×C3#91511yescharacteristic
374C22×C3C2×C3×C22⋊C411yescharacteristic
375C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
376C22×C3C3×#13711yescharacteristic
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—81no—
390C3×C4—81no—
391C3×C4—81no—
392C3×C4—82no—
393C3×C4—121no—
394C3×C4—121no—
395C3×C4—241no—
396Dic3—21no—
397Dic3—21no—
398Dic3—21no—
399Dic3—21no—
400Dic3—41no—
401Dic3—41no—
402Dic3—81no—
403C32#151211yescharacteristic, complemented, Sylow
404C23—21no—
405C23C3×D3×D411yescharacteristic
406Q8—121no—
407D4—41no—
408D4—41no—
409D4—41no—
410C2×C4—21no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—121no—
424C2×C4—122no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4C2×C3×C4×D311yescharacteristic
429C2×C4C3×D3×D411yescharacteristic
430C8—41no—
431C8—121no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—81no—
442C2×C3—81no—
443C2×C3—161no—
444C2×C3#474011yescharacteristic
445C2×C3#477111yescharacteristic
446C2×C3#482111yescharacteristic
447C2×C3C3×#41011yescharacteristic
448C2×C3C3×#41711yescharacteristic
449C2×C3C3×#42111yescharacteristic
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22C3×D3×C22⋊C411yescharacteristic
456C22C3×#91111yescharacteristic
457C22C3×#91511yescharacteristic
458C4—21no—
459C4—21no—
460C4—41no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4—81no—
466C4—121no—
467C4—121no—
468C4—241no—
469C3—21no—
470C3#6828011yescharacteristic, direct product factor
471C3C3×#151211yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—81no—
475C2C3×#474011yescharacteristic
476C2C3×#477111yescharacteristic
477C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#327C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#327D3
hypocenterC3C3×#1512
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#327

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. C3×#4650C2semidirect
6. C3×#4467C2semidirect
7. C3×#4452C2semidirect
9. #68280C3direct (N × H)
11. C3×#936C4semidirect
14. C3×D4×Dic3C4semidirect
18. C3×#890C4semidirect
19. C3×#887C4semidirect
33. #4719C2×C3semidirect
34. #4650C2×C3semidirect
42. #4467C2×C3semidirect
43. #4452C2×C3semidirect
87. #936C3×C4semidirect
90. D4×Dic3C3×C4semidirect
94. #890C3×C4semidirect
95. #887C3×C4semidirect
403. C32#1512semidirect
470. C3#68280direct (N × H)
471. C3C3×#1512semidirect

Maximal subgroups

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

subgroupindex
C3×#56002
C3×#47192
C3×#46502
C32×#3272
C3×#45372
C3×#44672
C3×#44522
C3×#15123
#682803