Finite Group Databasebeta

← C3×#69592 #11786672

Subgroups — C3×#69592 #11786672

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2C32×#384C211yesmaximal, characteristic, complemented
3C3×#4966C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1859—31nomaximal
9#69592C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4—22no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C3×C4×#67—22no—
16C3×#926C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#893—21no—
20C3×#892—21no—
21C3×D3×C4⋊C4—21no—
22C3×#887—21no—
23C3×#810—21no—
24C3×#809—21no—
25C3×#808—21no—
26C3×#807—21no—
27C3×#805C414yescomplemented
28C3×#520—31no—
29#5504C2×C311yescharacteristic
30C3×#428—31no—
31C2×C3×#104—31no—
32C3×#417—31no—
33C3×#384—21no—
34C3×#384D311yescharacteristic, complemented
35C3×#384C2×C311yescharacteristic, complemented
36#4966C2×C311yescharacteristic
37#4964C2×C311yescharacteristic, complemented
38C2×#805C2×C311yescharacteristic
39C3×#343—31no—
40C3×#339—31no—
41#4530C2×C311yescharacteristic, complemented
42#4523C2×C311yescharacteristic, complemented
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—44no—
61C32×C42—21no—
62C32×C42C2×C412yescomplemented
63C3×#217—21no—
64C3×(C2×D3)⋊C4—22no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—22no—
68C3×C4×Dic3—22no—
69C3×C4×Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#1859—31noSylow
77C2×C3×#41—31no—
78C2×#235C22×C311yescharacteristic
79C2×C3×M16—31no—
80C2×C3×M16—31no—
81C3×C4×Q8—61no—
82C3×C4×D4—61no—
83C3×C4×D4—62no—
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C22×C311yescharacteristic
95C2×C3×C4⋊C4C22×C311yescharacteristic
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C22×C311yescharacteristic
99C4×#67—22no—
100#926C22×C311yescharacteristic
101C2×#208C22×C311yescharacteristic
102C2×#208C22×C311yescharacteristic
103#893—21no—
104#892—21no—
105D3×C4⋊C4—21no—
106#887—21no—
107C3×#107—61no—
108C3×#106—61no—
109C3×#104—34no—
110C3×#103—61no—
111C3×#102—61no—
112#810—21no—
113#809—21no—
114#808—21no—
115#807—21no—
116#805C3×C414yescomplemented
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—42no—
124C2×C32×C4—42no—
125C2×C32×C4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q811yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C3×D12—21no—
138C3×D12C4⋊C412yescomplemented
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×C4×D3—82no—
142C3×Dic6—21no—
143C3×Dic6C4⋊C412yescomplemented
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146#520—31no—
147#428—31no—
148C2×#104—31no—
149#417—31no—
150#384C3×D311yescharacteristic, complemented
151#343—31no—
152#339—31no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—62no—
169C22×C3×C4—61no—
170C22×C3×C4#6712yes—
171C22×C3×C4C3×D412yes—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C311yescharacteristic
174C2×#67—21no—
175#235—21no—
176#235—21no—
177#235C2×C3×C412yes—
178#235C3×Q812yes—
179C2×D12C3×D411yescharacteristic
180C2×C4×D3—21no—
181C2×C4×D3—22no—
182C2×Dic6C3×D411yescharacteristic
183C3×M16—32no—
184C3×M16—61no—
185C3×M16—61no—
186C3×M16—61no—
187C2×C3×C8—61no—
188C2×C3×C8—61no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—31no—
199C3×C4⋊C4—41no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—44no—
204C3×C4⋊C4—44no—
205C3×C4⋊C4—48no—
206C3×C4⋊C4—62no—
207C3×C22⋊C4—62no—
208C3×C22⋊C4—61no—
209C3×C42—22no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—22no—
213C3×C42—62no—
214C3×C42—61no—
215C3×C42C4×D312yescomplemented
216C3×C42C2×C3×C412yescomplemented
217#217—21no—
218(C2×D3)⋊C4—22no—
219C4⋊Dic3C3×D411yescharacteristic
220C4⋊Dic3C3×D411yescharacteristic
221Dic3⋊C4—22no—
222C4×Dic3—22no—
223C4×Dic3—21no—
224#208—21no—
225#208—21no—
226#208—21no—
227#208C2×C3×C412yescomplemented
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C22×C32—21no—
231C22×C32—21no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32C22⋊Q811yescharacteristic
235C2×C3×D3—22no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C32×C4—24no—
239C32×C4—42no—
240C32×C4—81no—
241C32×C4C2×C4⋊C411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4#12311yescharacteristic
245C3×Dic3—22no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C2×#41—31no—
249C2×M16—31no—
250C2×M16—31no—
251C4×Q8—61no—
252C4×D4—61no—
253C4×D4—62no—
254#117—31no—
255#117—61no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4C2×C3×D311yescharacteristic
259C2×C4⋊C4C2×C3×D311yescharacteristic
260C2×C42C2×C3×D311yescharacteristic
261#107—61no—
262#106—61no—
263#104—34no—
264#103—61no—
265#102—61no—
266C23×C3—21no—
267C23×C3—61no—
268C23×C3C2×#6711yescharacteristic
269C23×C3C2×C3×D411yescharacteristic
270C22×D3—21no—
271C3×Q8—32no—
272C3×Q8—61no—
273C3×D4—32no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—61no—
277C2×C3×C4—24no—
278C2×C3×C4—24no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—44no—
298C2×C3×C4—44no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—242no—
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×Q811yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×C3×C4C22×C3×C411yescharacteristic
317C2×C3×C4C2×C3×D411yescharacteristic
318C2×C3×C4C2×C3×D411yescharacteristic
319C2×C3×C4C2×C3×Q811yescharacteristic
320C2×C3×C4C3×#4111yescharacteristic
321C2×C3×C4C3×#4111yescharacteristic
322#67—22no—
323#67—22no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327D12—21no—
328D12C3×C4⋊C412yescomplemented
329C4×D3—22no—
330C4×D3—22no—
331C4×D3—82no—
332Dic6—21no—
333Dic6C3×C4⋊C412yescomplemented
334C3×C8—62no—
335C3×C8—121no—
336C3⋊C8—22no—
337C3⋊C8—41no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32#38511yescharacteristic
341C2×C32#45311yescharacteristic
342C2×C32#45611yescharacteristic
343C3×D3—42no—
344#41—32no—
345#41—32no—
346#41—61no—
347#41—61no—
348C2×Q8—31no—
349C2×D4—31no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—62no—
354C22×C4—61no—
355C22×C4C3×#6712yes—
356C22×C4C22×C3×D311yescharacteristic
357M16—32no—
358M16—61no—
359M16—61no—
360M16—61no—
361C2×C8—61no—
362C2×C8—61no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—31no—
368C4⋊C4—31no—
369C4⋊C4—44no—
370C4⋊C4—62no—
371C22⋊C4—62no—
372C22⋊C4—61no—
373C42—21no—
374C42—62no—
375C42—61no—
376C42C3×C4×D312yescomplemented
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—62no—
387C22×C3—121no—
388C22×C3—121no—
389C22×C3C4×#6711yescharacteristic
390C22×C3#93711yescharacteristic
391C22×C3#94611yescharacteristic
392C22×C3C3×C4×D411yescharacteristic
393C22×C3C3×#12011yescharacteristic
394C22×C3C3×C22⋊Q811yescharacteristic
395C2×D3—22no—
396C2×D3—41no—
397C2×D3—41no—
398C3×C4—28no—
399C3×C4—24no—
400C3×C4—24no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—62no—
408C3×C4—82no—
409C3×C4—82no—
410C3×C4—81no—
411C3×C4—81no—
412C3×C4—121no—
413C3×C4—121no—
414C3×C4D3×C4⋊C411yescharacteristic
415C3×C4#89311yescharacteristic
416C3×C4#89411yescharacteristic
417C3×C4#89611yescharacteristic
418C3×C4C2×C3×C4⋊C411yescharacteristic
419C3×C4C3×C4×D411yescharacteristic
420C3×C4C3×C22⋊Q811yescharacteristic
421C3×C4C3×#12311yescharacteristic
422Dic3—22no—
423Dic3—41no—
424Dic3—41no—
425C32#185911yescharacteristic, complemented, Sylow
426C23—61no—
427C23C2×C3×#6711yescharacteristic
428Q8—32no—
429Q8—61no—
430D4—32no—
431D4—62no—
432D4—62no—
433D4—61no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—61no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—242no—
447C2×C4C2×C3×C4×D311yescharacteristic
448C2×C4C3×#23511yescharacteristic
449C2×C4C3×D3×D411yescharacteristic
450C2×C4C3×D3×D411yescharacteristic
451C2×C4C3×D3×Q811yescharacteristic
452C2×C4C3×#23911yescharacteristic
453C8—62no—
454C8—121no—
455C2×C3—22no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—122no—
465C2×C3#498911yescharacteristic
466C2×C3#507711yescharacteristic
467C2×C3#509511yescharacteristic
468C2×C3C3×#38511yescharacteristic
469C2×C3C3×#45311yescharacteristic
470C2×C3C3×#45611yescharacteristic
471D3—42no—
472C22—21no—
473C22—21no—
474C22—62no—
475C22—121no—
476C22—121no—
477C22C3×C4×#6711yescharacteristic
478C22C3×#93711yescharacteristic
479C22C3×#94611yescharacteristic
480C4—24no—
481C4—42no—
482C4—62no—
483C4—81no—
484C4—121no—
485C4—121no—
486C4C3×D3×C4⋊C411yescharacteristic
487C4C3×#89311yescharacteristic
488C4C3×#89411yescharacteristic
489C4C3×#89611yescharacteristic
490C3—21no—
491C3#6959211yescharacteristic, direct product factor
492C3C3×#185911yescharacteristic, complemented
493C2—21no—
494C2—21no—
495C2—122no—
496C2C3×#498911yescharacteristic
497C2C3×#507711yescharacteristic
498C2C3×#509511yescharacteristic
subgroupG/H
centerC22×C3#937
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#384C2
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#384D3
hypocenterC3C3×#1859
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
2. C32×#384C2semidirect
4. C3×#4964C2semidirect
6. C3×#4530C2semidirect
7. C3×#4523C2semidirect
9. #69592C3direct (N × H)
27. C3×#805C4semidirect
34. C3×#384D3semidirect
35. C3×#384C2×C3semidirect
37. #4964C2×C3semidirect
41. #4530C2×C3semidirect
42. #4523C2×C3semidirect
62. C32×C42C2×C4semidirect
73. C3×#208C2×C4semidirect
116. #805C3×C4semidirect
138. C3×D12C4⋊C4semidirect
143. C3×Dic6C4⋊C4semidirect
150. #384C3×D3semidirect
215. C3×C42C4×D3semidirect
216. C3×C42C2×C3×C4semidirect
227. #208C2×C3×C4semidirect
328. D12C3×C4⋊C4semidirect
333. Dic6C3×C4⋊C4semidirect
376. C42C3×C4×D3semidirect
425. C32#1859semidirect
491. C3#69592direct (N × H)
492. C3C3×#1859semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C32×#3842
C3×#49662
C3×#49642
C2×C3×#8052
C3×#45302
C3×#45232
C3×#18593
#695923