Finite Group Databasebeta

← C3×#69003 #11786733

Subgroups — C3×#69003 #11786733

Order 1152.

621 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2C2×C3×#825C211yesmaximal, characteristic
3C3×#5133C211yesmaximal, characteristic
4C3×#5121C211yesmaximal, characteristic, complemented
5C3×#4977C211yesmaximal, characteristic, complemented
6C32×#343C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8C3×#1860—31nomaximal
9#69003C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C3×C4×#67—22no—
15C3×#926C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C3×#893—21no—
19C3×#892—21no—
20C3×D3×C4⋊C4—21no—
21C3×#887—21no—
22C3×C3⋊#95—22no—
23C3×#825C414yescomplemented
24C3×#821—21no—
25C3×#818—21no—
26C3×#817—21no—
27C3×#816—21no—
28C3×#520—31no—
29#5504C2×C311yescharacteristic
30C3×#428—31no—
31C2×C3×#104—31no—
32C3×#417—31no—
33C3×#382—31no—
34C2×#825C2×C311yescharacteristic
35#5133C2×C311yescharacteristic
36#5121C2×C311yescharacteristic, complemented
37#4977C2×C311yescharacteristic, complemented
38C3×#343—21no—
39C3×#343D311yescharacteristic, complemented
40C3×#343C2×C311yescharacteristic, complemented
41C3×#339—31no—
42#4555C2×C311yescharacteristic, complemented
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—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×M16—21no—
57C32×M16—21no—
58C32×M16—21no—
59C32×M16C2×C412yescomplemented
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3—22no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3C2×C412yescomplemented
75#1860—31noSylow
76C2×C3×#41—31no—
77C2×#235C22×C311yescharacteristic
78C2×C3×M16—21no—
79C2×C3×M16—21no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C2×D311yescharacteristic
82C2×C3×M16C22×C311yescharacteristic
83C2×C3×M16C22×C311yescharacteristic
84C3×C4×Q8—61no—
85C3×C4×D4—61no—
86C3×C4×D4—62no—
87C3×#117—31no—
88C3×#117—61no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C22×C311yescharacteristic
94C2×C3×C42—31no—
95C4×#67—22no—
96#926C22×C311yescharacteristic
97C2×C4⋊Dic3C22×C311yescharacteristic
98C2×C4×Dic3C22×C311yescharacteristic
99#893—21no—
100#892—21no—
101D3×C4⋊C4—21no—
102#887—21no—
103C3×#107—61no—
104C3×#106—61no—
105C3×#104—34no—
106C3×#103—61no—
107C3×#102—61no—
108C3×#95—62no—
109C3⋊#95—22no—
110#825C3×C414yescomplemented
111#821—21no—
112#818—21no—
113#817—21no—
114#816—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—22no—
118C2×C32×C4—42no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q811yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C3×#67—22no—
126C3×#67—22no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—41no—
135C3×D12—21no—
136C3×D12C4⋊C412yes—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×C4×D3—82no—
140C3×Dic6—21no—
141C3×Dic6C4⋊C412yes—
142C32×C8—22no—
143C32×C8—41no—
144#520—31no—
145#428—31no—
146C2×#104—31no—
147#417—31no—
148#382—31no—
149#343C3×D311yescharacteristic, complemented
150#339—31no—
151C3×#41—32no—
152C3×#41—32no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—31no—
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—62no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4D1212yes—
165C22×C3×C4C3×D412yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C23×C311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170C22×Dic3—21no—
171#235—21no—
172#235—21no—
173#235C2×C3×C412yes—
174#235C3×Q812yes—
175C2×D12C3×D411yescharacteristic
176C2×C4×D3—21no—
177C2×C4×D3—22no—
178C2×Dic6C3×D411yescharacteristic
179C3×M16—21no—
180C3×M16—21no—
181C3×M16—22no—
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—22no—
187C3×M16—41no—
188C3×M16—41no—
189C3×M16C4×D312yescomplemented
190C3×M16C2×C3×C412yescomplemented
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—41no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—31no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—62no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—62no—
209C3×C22⋊C4—61no—
210C3×C42—32no—
211C3×C42—62no—
212C3×C42—61no—
213C3×C42—61no—
214#217—21no—
215(C2×D3)⋊C4—22no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3C3×D411yescharacteristic
219C4⋊Dic3C3×D411yescharacteristic
220Dic3⋊C4—22no—
221C4×Dic3—22no—
222C4×Dic3—21no—
223C4×Dic3—21no—
224C4×Dic3C2×C3×C412yescomplemented
225C22×C32—21no—
226C22×C32—21no—
227C22×C32C4×D411yescharacteristic
228C22×C32#12011yescharacteristic
229C22×C32C22⋊Q811yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—42no—
234C32×C4C2×C4⋊C411yescharacteristic
235C32×C4C4×D411yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4#12311yescharacteristic
238C3×Dic3—22no—
239C3×Dic3—42no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C3×Dic3—81no—
243C2×#41—31no—
244C2×M16C2×C3×D311yescharacteristic
245C2×M16C2×C3×D311yescharacteristic
246C4×Q8—61no—
247C4×D4—61no—
248C4×D4—62no—
249#117—31no—
250#117—61no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4C2×C3×D311yescharacteristic
254C2×C42—31no—
255#107—61no—
256#106—61no—
257#104—34no—
258#103—61no—
259#102—61no—
260#95—62no—
261C23×C3—21no—
262C23×C3—61no—
263C23×C3C2×D1211yescharacteristic
264C23×C3C2×C3×D411yescharacteristic
265C22×D3—21no—
266C3×Q8—32no—
267C3×Q8—61no—
268C3×D4—32no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—61no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—82no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—122no—
293C2×C3×C4—121no—
294C2×C3×C4—242no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4C22×C3×C411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×Q811yescharacteristic
305C2×C3×C4C3×#4111yescharacteristic
306C2×C3×C4C3×#4111yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—21no—
310C2×Dic3—22no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—42no—
316C2×Dic3—41no—
317D12—21no—
318D12C3×C4⋊C412yes—
319C4×D3—22no—
320C4×D3—22no—
321C4×D3—82no—
322Dic6—21no—
323Dic6C3×C4⋊C412yes—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—42no—
327C3×C8—42no—
328C3×C8—41no—
329C3×C8—41no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32#38511yescharacteristic
333C2×C32#45411yescharacteristic
334C2×C32#45511yescharacteristic
335C3×D3—42no—
336#41—32no—
337#41—32no—
338#41—61no—
339#41—61no—
340C2×Q8—31no—
341C2×D4—31no—
342C2×D4—61no—
343C22×C4—62no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4C3×D1212yes—
348C22×C4C22×C3×D311yescharacteristic
349M16—21no—
350M16—21no—
351M16—21no—
352M16C3×C4×D312yescomplemented
353C2×C8—21no—
354C2×C8—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—31no—
358C4⋊C4—31no—
359C4⋊C4—62no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C22⋊C4—62no—
363C22⋊C4—61no—
364C42—32no—
365C42—62no—
366C42—61no—
367C42—61no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—62no—
378C22×C3—121no—
379C22×C3—121no—
380C22×C3C4×D1211yescharacteristic
381C22×C3#88211yescharacteristic
382C22×C3#89711yescharacteristic
383C22×C3C3×C4×D411yescharacteristic
384C22×C3C3×#12011yescharacteristic
385C22×C3C3×C22⋊Q811yescharacteristic
386C2×D3—22no—
387C2×D3—41no—
388C2×D3—41no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—62no—
396C3×C4—82no—
397C3×C4—122no—
398C3×C4—121no—
399C3×C4—121no—
400C3×C4—241no—
401C3×C4#67⋊C411yescharacteristic
402C3×C4#88311yescharacteristic
403C3×C4D3×C4⋊C411yescharacteristic
404C3×C4#89611yescharacteristic
405C3×C4C2×C3×C4⋊C411yescharacteristic
406C3×C4C3×C4×D411yescharacteristic
407C3×C4C3×C22⋊Q811yescharacteristic
408C3×C4C3×#12311yescharacteristic
409Dic3—22no—
410Dic3—42no—
411Dic3—41no—
412Dic3—41no—
413Dic3—81no—
414C32#186011yescharacteristic, complemented, Sylow
415C23—61no—
416C23C2×C3×D1211yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—61no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—62no—
431C2×C4—121no—
432C2×C4—121no—
433C2×C4—122no—
434C2×C4—121no—
435C2×C4—242no—
436C2×C4C2×C3×C4×D311yescharacteristic
437C2×C4C3×#23511yescharacteristic
438C2×C4C3×D3×D411yescharacteristic
439C2×C4C3×D3×D411yescharacteristic
440C2×C4C3×#23711yescharacteristic
441C2×C4C3×D3×Q811yescharacteristic
442C8—22no—
443C8—41no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—122no—
454C2×C3#466811yescharacteristic
455C2×C3#474611yescharacteristic
456C2×C3#475311yescharacteristic
457C2×C3C3×#38511yescharacteristic
458C2×C3C3×#45411yescharacteristic
459C2×C3C3×#45511yescharacteristic
460D3—42no—
461C22—21no—
462C22—21no—
463C22—62no—
464C22—121no—
465C22—121no—
466C22C3×C4×D1211yescharacteristic
467C22C3×#88211yescharacteristic
468C22C3×#89711yescharacteristic
469C4—42no—
470C4—62no—
471C4—122no—
472C4—121no—
473C4—121no—
474C4—241no—
475C4C3×#67⋊C411yescharacteristic
476C4C3×#88311yescharacteristic
477C4C3×D3×C4⋊C411yescharacteristic
478C4C3×#89611yescharacteristic
479C3—21no—
480C3#6900311yescharacteristic, direct product factor
481C3C3×#186011yescharacteristic, complemented
482C2—21no—
483C2—21no—
484C2—122no—
485C2C3×#466811yescharacteristic
486C2C3×#474611yescharacteristic
487C2C3×#475311yescharacteristic
subgroupG/H
centerC22×C3#882
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#343D3
hypocenterC3C3×#1860
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
4. C3×#5121C2semidirect
5. C3×#4977C2semidirect
6. C32×#343C2semidirect
7. C3×#4555C2semidirect
9. #69003C3direct (N × H)
23. C3×#825C4semidirect
36. #5121C2×C3semidirect
37. #4977C2×C3semidirect
39. C3×#343D3semidirect
40. C3×#343C2×C3semidirect
42. #4555C2×C3semidirect
59. C32×M16C2×C4semidirect
74. C3×C4×Dic3C2×C4semidirect
110. #825C3×C4semidirect
149. #343C3×D3semidirect
189. C3×M16C4×D3semidirect
190. C3×M16C2×C3×C4semidirect
224. C4×Dic3C2×C3×C4semidirect
352. M16C3×C4×D3semidirect
414. C32#1860semidirect
480. C3#69003direct (N × H)
481. C3C3×#1860semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C2×C3×#8252
C3×#51332
C3×#51212
C3×#49772
C32×#3432
C3×#45552
C3×#18603
#690033