Finite Group Databasebeta

← C3×#69030 #11788512

Subgroups — C3×#69030 #11788512

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C3×#5139C211yesmaximal, characteristic
4C3×#5120C211yesmaximal, characteristic, complemented
5C3×#5006C211yesmaximal, characteristic
6C32×#344C211yesmaximal, characteristic, complemented
7C3×#4557C211yesmaximal, characteristic, complemented
8C3×#1905—31nomaximal
9#69030C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C3×#926C2211yescharacteristic
17C3×#909—22no—
18C3×#909—22no—
19C2×C3×Dic12C412yescomplemented
20C2×C3×#204C412yescomplemented
21C3×#887—22no—
22C3×#877—22no—
23C3×C4×Dic6—22no—
24C3×#825—22no—
25C3×#816—22no—
26C3×#806—22no—
27C2×C3×#137—31no—
28C3×#519—31no—
29C2×#909C2×C311yescharacteristic
30#5516C2×C311yescharacteristic, complemented
31C3×#421—31no—
32C3×#419—31no—
33C3×#410—31no—
34#5139C2×C311yescharacteristic
35#5120C2×C311yescharacteristic, complemented
36#5006C2×C311yescharacteristic
37C3×#344—21no—
38C3×#344D311yescharacteristic, complemented
39C3×#344C2×C311yescharacteristic, complemented
40C3×H(3,ℤ/4)—31no—
41#4557C2×C311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—21no—
44C22×C3×Dic3—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6C2×C411yescharacteristic
55C2×C3×Dic6C2×C412yes—
56C2×C3×Dic6D412yes—
57C2×C3×Dic6D412yes—
58C32×M16—21no—
59C32×M16—21no—
60C32×M16—21no—
61C32×M16—21no—
62C2×C32×C8—21no—
63C2×C32×C8C2×C412yes—
64C32×C4⋊C4—21no—
65C32×C22⋊C4D412yes—
66C32×C42—21no—
67C3×#217—21no—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×Dic3⋊C4—24no—
72C3×C4×Dic3—24no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3D412yes—
75C3×Dic12—24no—
76C3×#204—24no—
77#1905—31noSylow
78C2×C3×#41—31no—
79C22×C3×Q8—31no—
80C2×#235C22×C311yescharacteristic
81C22×Dic6C22×C311yescharacteristic
82C3×#137—62no—
83C3×#137—62no—
84C2×C3×Q16—32no—
85C2×C3×SD16—32no—
86C2×C3×M16—21no—
87C2×C3×M16—21no—
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C2×C3×M16C22×C311yescharacteristic
92C3×C4×Q8—62no—
93C3×C4×Q8—62no—
94C3×#117—21no—
95C3×#117—31no—
96C3×#117—31no—
97C3×#117—62no—
98C3×#117C2×D311yescharacteristic
99C3×#117C22×C311yescharacteristic
100#926C22×C311yescharacteristic
101#926C22×C311yescharacteristic
102#909—22no—
103#909—22no—
104C2×Dic12C3×C412yescomplemented
105C2×#204C3×C412yescomplemented
106#887—22no—
107#877—22no—
108C4×Dic6—22no—
109C3×#104—62no—
110C3×#103—62no—
111C3×#99—62no—
112#825—22no—
113#816—22no—
114#806—22no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—22no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—22no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C3×D12—21no—
133C3×D12—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—21no—
140C3×Dic6—21no—
141C3×Dic6C22⋊C414yes—
142C32×C8—22no—
143C32×C8—41no—
144C2×#137—31no—
145#519—31no—
146#421—31no—
147#419—31no—
148#410—31no—
149#344C3×D311yescharacteristic, complemented
150H(3,ℤ/4)—31no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—32no—
156C2×C3×Q8—31no—
157C2×C3×Q8—32no—
158C2×C3×Q8—32no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C23×C311yescharacteristic
169C2×#67—21no—
170C22×Dic3—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174#235—21no—
175C2×D12C2×C3×C411yescharacteristic
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6C2×C3×C411yescharacteristic
181C2×Dic6C2×C3×C412yes—
182C2×Dic6C3×D412yes—
183C2×Dic6C3×D412yes—
184C3×Q16—64no—
185C3×SD16—64no—
186C3×M16—21no—
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—22no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—41no—
196C3×M16—41no—
197C3×M16—41no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—22no—
201C2×C3×C8—41no—
202C2×C3×C8C4×D312yes—
203C2×C3×C8C2×C3×C412yes—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—64no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4D1212yes—
214C3×C22⋊C4C3×D412yes—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—32no—
218C3×C42—41no—
219C3×C42—64no—
220C3×C42—61no—
221#217—21no—
222#217—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225Dic3⋊C4—24no—
226C4×Dic3—24no—
227C4×Dic3—21no—
228C4×Dic3C3×D412yes—
229Dic12—24no—
230#204—24no—
231C22×C32—41no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12111yescharacteristic
235C2×C3×D3—41no—
236C2×C3×D3—81no—
237C32×C4—42no—
238C32×C4C2×C22⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12311yescharacteristic
242C3×Dic3—24no—
243C3×Dic3—42no—
244C3×Dic3—41no—
245C3×Dic3—81no—
246C2×#41—31no—
247C22×Q8—31no—
248#137—62no—
249#137—62no—
250C2×Q16—32no—
251C2×SD16—32no—
252C2×M16C2×C3×D311yescharacteristic
253C2×M16C2×C3×D311yescharacteristic
254C4×Q8—62no—
255C4×Q8—62no—
256#117—31no—
257#117—31no—
258#117—62no—
259#117C2×C3×D311yescharacteristic
260#104—62no—
261#103—62no—
262#99—62no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3C2×D1211yescharacteristic
266C23×C3C2×C3×D411yescharacteristic
267C22×D3—21no—
268C3×Q8—34no—
269C3×Q8—62no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—61no—
273C3×Q8—61no—
274C3×D4—61no—
275C3×D4—61no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23911yescharacteristic
301C2×C3×C4C22×C3×C411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C3×#4111yescharacteristic
306C2×C3×C4C3×#4111yescharacteristic
307#67—41no—
308#67—41no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—21no—
313C2×Dic3—22no—
314C2×Dic3—41no—
315D12—21no—
316D12—21no—
317C4×D3—41no—
318C4×D3—41no—
319Dic6—22no—
320Dic6—22no—
321Dic6—22no—
322Dic6—21no—
323Dic6—21no—
324Dic6C3×C22⋊C414yes—
325C3×C8—22no—
326C3×C8—22no—
327C3×C8—42no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#38611yescharacteristic
335C3×D3—81no—
336#41—61no—
337#41—61no—
338#41—61no—
339#41—61no—
340C2×Q8—32no—
341C2×Q8—31no—
342C2×Q8—32no—
343C2×Q8—32no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×Q8—61no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4C22×C3×D311yescharacteristic
352Q16—64no—
353SD16—64no—
354M16—21no—
355M16—21no—
356M16—21no—
357M16—21no—
358C2×C8—21no—
359C2×C8C3×C4×D312yes—
360C4⋊C4—21no—
361C4⋊C4—64no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4C3×D1212yes—
367C42—21no—
368C42—32no—
369C42—64no—
370C42—61no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—81no—
377C22×C3—121no—
378C22×C3—241no—
379C22×C3C4×D1211yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3#89511yescharacteristic
382C22×C3C3×C4×D411yescharacteristic
383C22×C3C3×#12011yescharacteristic
384C22×C3C3×#12111yescharacteristic
385C2×D3—41no—
386C2×D3—81no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—64no—
394C3×C4—82no—
395C3×C4—122no—
396C3×C4—121no—
397C3×C4—241no—
398C3×C4D3×C22⋊C411yescharacteristic
399C3×C4#88411yescharacteristic
400C3×C4#89311yescharacteristic
401C3×C4#89411yescharacteristic
402C3×C4C2×C3×C22⋊C411yescharacteristic
403C3×C4C3×C4×D411yescharacteristic
404C3×C4C3×#12111yescharacteristic
405C3×C4C3×#12311yescharacteristic
406Dic3—24no—
407Dic3—42no—
408Dic3—41no—
409Dic3—81no—
410C32#190511yescharacteristic, complemented, Sylow
411C23—61no—
412C23C2×C3×D1211yescharacteristic
413Q8—34no—
414Q8—62no—
415Q8—62no—
416Q8—62no—
417Q8—61no—
418Q8—61no—
419D4—61no—
420D4—61no—
421D4—121no—
422D4—121no—
423C2×C4—22no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—61no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4C2×C3×C4×D311yescharacteristic
433C2×C4C3×#23511yescharacteristic
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C3×D3×D411yescharacteristic
436C2×C4C3×D3×D411yescharacteristic
437C2×C4C3×#23911yescharacteristic
438C8—22no—
439C8—41no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—241no—
451C2×C3#466511yescharacteristic
452C2×C3C3×#38611yescharacteristic
453D3—81no—
454C22—41no—
455C22—121no—
456C22—241no—
457C22C3×C4×D1211yescharacteristic
458C22C3×#88211yescharacteristic
459C22C3×#89511yescharacteristic
460C4—42no—
461C4—64no—
462C4—122no—
463C4—121no—
464C4—241no—
465C4C3×D3×C22⋊C411yescharacteristic
466C4C3×#88411yescharacteristic
467C4C3×#89311yescharacteristic
468C4C3×#89411yescharacteristic
469C3—21no—
470C3#6903011yescharacteristic, direct product factor
471C3C3×#190511yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—21no—
475C2—241no—
476C2C3×#466511yescharacteristic
subgroupG/H
centerC2×C3#4665
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#344D3
hypocenterC3C3×#1905
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. C3×#5120C2semidirect
6. C32×#344C2semidirect
7. C3×#4557C2semidirect
9. #69030C3direct (N × H)
19. C2×C3×Dic12C4semidirect
20. C2×C3×#204C4semidirect
30. #5516C2×C3semidirect
35. #5120C2×C3semidirect
38. C3×#344D3semidirect
39. C3×#344C2×C3semidirect
41. #4557C2×C3semidirect
104. C2×Dic12C3×C4semidirect
105. C2×#204C3×C4semidirect
149. #344C3×D3semidirect
410. C32#1905semidirect
470. C3#69030direct (N × H)
471. C3C3×#1905semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C3×#55162
C3×#51392
C3×#51202
C3×#50062
C32×#3442
C3×#45572
C3×#19053
#690303