Finite Group Databasebeta

← C3×#70343 #11787794

Subgroups — C3×#70343 #11787794

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic
2C3×#5521C211yesmaximal, characteristic
3C32×#419C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1885—31nomaximal
9#70343C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#947—22no—
15C3×#947C414yescomplemented
16C2×C3×(C2×D3)⋊C4—22no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C3×#893—22no—
21C3×D3×C22⋊C4—22no—
22C3×C4×D12—22no—
23C32×#103—22no—
24C3×#835—22no—
25C3×#823—22no—
26C2×C3×#124—31no—
27C3×#518—31no—
28C2×#947C2×C311yescharacteristic
29#5521C2×C311yescharacteristic
30C3×#419—21no—
31C3×#419—31no—
32C3×#419D311yescharacteristic, complemented
33C3×#419C2×C311yescharacteristic, complemented
34C2×C3×#100—31no—
35#5225C2×C311yescharacteristic, complemented
36C2×#823C2×C311yescharacteristic
37C3×#339—31no—
38C3×#339—31no—
39#4555C2×C311yescharacteristic, complemented
40#4532C2×C311yescharacteristic, complemented
41C23×C3×D3D412yes—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yescomplemented
48C22×C32×C4—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×D12D412yes—
57C2×C3×C4×D3—24no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61C32×C4⋊C4D412yes—
62C32×C22⋊C4—21no—
63C32×C42—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—24no—
66C3×(C2×D3)⋊C4—28no—
67C3×C4⋊Dic3D412yes—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C3×C4×Dic3C2×C412yescomplemented
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8—21no—
74#1885—31noSylow
75C22×C3×Q8—21no—
76C22×C3×Q8C2×D311yescharacteristic
77C22×C3×Q8C22×C311yescharacteristic
78C22×C3×D4—31no—
79C22×D12C22×C311yescharacteristic
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C22×C311yescharacteristic
84C3×#124—34no—
85C3×#124—62no—
86C3×C4×D4—62no—
87C3×C4×D4—62no—
88C3×#117—21no—
89C3×#117—31no—
90C3×#117C2×D311yescharacteristic
91C3×#117C22×C311yescharacteristic
92C2×C3×C22⋊C4—62no—
93C2×C3×C22⋊C4—62no—
94C2×C3×C42—31no—
95#947—22no—
96#947C3×C414yescomplemented
97C2×(C2×D3)⋊C4—22no—
98#926C22×C311yescharacteristic
99C2×C4×Dic3C22×C311yescharacteristic
100C2×#208C22×C311yescharacteristic
101#893—22no—
102D3×C22⋊C4—22no—
103C4×D12—22no—
104C3×#103—24no—
105C3×#103—22no—
106C3×#103—22no—
107C3×#103—62no—
108C3×#100—62no—
109#835—22no—
110#823—22no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—44no—
115C22×C3×D3C22⋊C414yes—
116C32×Q8—22no—
117C32×Q8—22no—
118C32×Q8—41no—
119C32×Q8—41no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—22no—
137C3×C4×D3—84no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140C2×#124—31no—
141#518—31no—
142#419—31no—
143#419C3×D311yescharacteristic, complemented
144C2×#100—31no—
145#339—31no—
146#339—31no—
147C24×C3—32no—
148C23×D3C3×D412yes—
149C2×C3×Q8—21no—
150C2×C3×Q8—21no—
151C2×C3×Q8—22no—
152C2×C3×Q8—22no—
153C2×C3×Q8—21no—
154C2×C3×Q8—21no—
155C2×C3×Q8—21no—
156C2×C3×Q8—21no—
157C2×C3×Q8—21no—
158C2×C3×Q8—21no—
159C2×C3×Q8—21no—
160C2×C3×Q8—21no—
161C2×C3×Q8—22no—
162C2×C3×Q8—41no—
163C2×C3×Q8—41no—
164C2×C3×Q8—41no—
165C2×C3×Q8C4×D312yescomplemented
166C2×C3×Q8C2×C3×C412yescomplemented
167C2×C3×D4—32no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—41no—
177C22×C3×C4—64no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12C2×C3×C412yes—
187C2×D12C3×D412yes—
188C2×C4×D3—24no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—41no—
194C3×M16—41no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—22no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—61no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4#6712yes—
204C3×C4⋊C4C3×D412yes—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—41no—
208C3×C22⋊C4—68no—
209C3×C22⋊C4—64no—
210C3×C22⋊C4—61no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—32no—
214C3×C42—41no—
215C3×C42—61no—
216C3×C42—61no—
217#217—21no—
218(C2×D3)⋊C4—24no—
219(C2×D3)⋊C4—28no—
220C4⋊Dic3C3×D412yes—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C4×Dic3C2×C3×C412yescomplemented
224#208—21no—
225#208—21no—
226C2×C3⋊C8—21no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32#12311yescharacteristic
231C2×C3×D3—24no—
232C2×C3×D3—44no—
233C2×C3×D3—44no—
234C2×C3×D3—82no—
235C32×C4—42no—
236C32×C4—42no—
237C32×C4C4×D411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12111yescharacteristic
240C32×C4#12111yescharacteristic
241C3×Dic3—42no—
242C3×Dic3—42no—
243C22×Q8C2×C3×D311yescharacteristic
244C22×D4—31no—
245C2×M16—31no—
246C2×M16C2×C3×D311yescharacteristic
247#124—34no—
248#124—62no—
249C4×D4—62no—
250C4×D4—62no—
251#117—31no—
252#117C2×C3×D311yescharacteristic
253C2×C22⋊C4—62no—
254C2×C22⋊C4—62no—
255C2×C42—31no—
256#103—22no—
257#103—62no—
258#100—62no—
259C23×C3—21no—
260C23×C3—34no—
261C23×C3—62no—
262C23×C3—62no—
263C23×C3—124no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×C3×D411yescharacteristic
266C22×D3—22no—
267C22×D3—22no—
268C22×D3—44no—
269C22×D3C3×C22⋊C414yes—
270C3×Q8—24no—
271C3×Q8—22no—
272C3×Q8—22no—
273C3×Q8—22no—
274C3×Q8—22no—
275C3×Q8—42no—
276C3×Q8—42no—
277C3×Q8—42no—
278C3×Q8—41no—
279C3×Q8—41no—
280C3×Q8—41no—
281C3×Q8—41no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—122no—
307C2×C3×C4—244no—
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C22×C3×C411yescharacteristic
315C2×C3×C4C2×C3×D411yescharacteristic
316C2×C3×C4C2×C3×D411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C3×#4111yescharacteristic
319C2×C3×C4C3×#4111yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—42no—
323D12—22no—
324D12—22no—
325D12—22no—
326D12—22no—
327C4×D3—84no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—121no—
332C3⋊C8—41no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32#38611yescharacteristic
336C2×C32#45512yes—
337C3×D3—44no—
338C24—32no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8C3×C4×D312yescomplemented
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—64no—
353C22×C4—61no—
354C22×C4C22×C3×D311yescharacteristic
355M16—21no—
356M16—21no—
357M16—61no—
358M16—61no—
359C2×C8—21no—
360C2×C8—61no—
361C4⋊C4—32no—
362C4⋊C4C3×#6712yes—
363C22⋊C4—21no—
364C22⋊C4—68no—
365C22⋊C4—64no—
366C22⋊C4—61no—
367C42—21no—
368C42—32no—
369C42—61no—
370C42—61no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—42no—
377C22×C3—64no—
378C22×C3—124no—
379C22×C3—124no—
380C22×C3—242no—
381C22×C3D3×C22⋊C411yescharacteristic
382C22×C3#88311yescharacteristic
383C22×C3#93711yescharacteristic
384C22×C3C2×C3×C22⋊C411yescharacteristic
385C22×C3C3×#12011yescharacteristic
386C22×C3C3×#12311yescharacteristic
387C2×D3—24no—
388C2×D3—44no—
389C2×D3—44no—
390C2×D3—82no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—44no—
396C3×C4—42no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—82no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4#67⋊C411yescharacteristic
404C3×C4#88411yescharacteristic
405C3×C4C4×#6711yescharacteristic
406C3×C4#93811yescharacteristic
407C3×C4C3×C4×D411yescharacteristic
408C3×C4C3×C4×D411yescharacteristic
409C3×C4C3×#12111yescharacteristic
410C3×C4C3×#12111yescharacteristic
411Dic3—42no—
412Dic3—42no—
413C32#188511yescharacteristic, complemented, Sylow
414C23—34no—
415C23—62no—
416C23—62no—
417C23—124no—
418C23C3×D3×D411yescharacteristic
419Q8—22no—
420Q8—22no—
421Q8—41no—
422Q8—41no—
423D4—62no—
424D4—62no—
425D4—62no—
426D4—62no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—122no—
434C2×C4—244no—
435C2×C4C2×C3×C4×D311yescharacteristic
436C2×C4C3×#23511yescharacteristic
437C2×C4C3×D3×D411yescharacteristic
438C2×C4C3×D3×D411yescharacteristic
439C2×C4C3×#23711yescharacteristic
440C2×C4C2×C3×#6711yescharacteristic
441C8—41no—
442C8—121no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—22no—
448C2×C3—21no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—124no—
452C2×C3#495611yescharacteristic
453C2×C3#520212yes—
454C2×C3C3×#38611yescharacteristic
455C2×C3C3×#45512yes—
456D3—44no—
457C22—22no—
458C22—64no—
459C22—124no—
460C22—124no—
461C22—242no—
462C22C3×D3×C22⋊C411yescharacteristic
463C22C3×#88311yescharacteristic
464C22C3×#93711yescharacteristic
465C4—42no—
466C4—42no—
467C4—122no—
468C4—122no—
469C4C3×#67⋊C411yescharacteristic
470C4C3×#88411yescharacteristic
471C4C3×C4×#6711yescharacteristic
472C4C3×#93811yescharacteristic
473C3—21no—
474C3#7034311yescharacteristic, direct product factor
475C3C3×#188511yescharacteristic, complemented
476C2—21no—
477C2—21no—
478C2—124no—
479C2C3×#495611yescharacteristic
480C2C3×#520212yes—
subgroupG/H
centerC22×C3#937
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#419C2
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#419D3
hypocenterC3C3×#1885
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
3. C32×#419C2semidirect
4. C3×#5225C2semidirect
6. C3×#4555C2semidirect
7. C3×#4532C2semidirect
9. #70343C3direct (N × H)
15. C3×#947C4semidirect
32. C3×#419D3semidirect
33. C3×#419C2×C3semidirect
35. #5225C2×C3semidirect
39. #4555C2×C3semidirect
40. #4532C2×C3semidirect
47. C2×C32×Q8C2×C4semidirect
70. C3×C4×Dic3C2×C4semidirect
96. #947C3×C4semidirect
143. #419C3×D3semidirect
165. C2×C3×Q8C4×D3semidirect
166. C2×C3×Q8C2×C3×C4semidirect
223. C4×Dic3C2×C3×C4semidirect
344. C2×Q8C3×C4×D3semidirect
413. C32#1885semidirect
474. C3#70343direct (N × H)
475. C3C3×#1885semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C3×#55212
C32×#4192
C3×#52252
C2×C3×#8232
C3×#45552
C3×#45322
C3×#18853
#703433