Finite Group Databasebeta

← C3×#70318 #11789663

Subgroups — C3×#70318 #11789663

Order 1152.

559 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#418C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#1931—31nomaximal
9#70318C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C32×#102—21no—
18C32×#102—21no—
19C3×#833C414yescomplemented
20C3×#832—21no—
21C3×#832—21no—
22C3×#808—21no—
23C3×#807—21no—
24C3×#803—21no—
25C3×C4×C3⋊C8—21no—
26C3×#428—31no—
27C3×#418—21no—
28C3×#418D311yescharacteristic
29C3×#418C2×C311yescharacteristic
30C2×C3×#102—31no—
31C2×C3×#100—31no—
32C3×#405—31no—
33C2×#833C2×C311yescharacteristic
34C2×#832C2×C311yescharacteristic
35#4997C2×C311yescharacteristic, complemented
36#4995C2×C311yescharacteristic, complemented
37C3×#343—31no—
38C3×#341—31no—
39#4558C2×C311yescharacteristic, complemented
40#4554C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3×Dic3—21no—
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4D411yescharacteristic
54C32×C4⋊C4D411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69#1931—31noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C22×C311yescharacteristic
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C22×C311yescharacteristic
78C22×C3×C8—31no—
79C3×#117—21no—
80C3×#117C2×D311yescharacteristic
81C3×#117C22×C311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C4⋊Dic3C22×C311yescharacteristic
84C2×#208C22×C311yescharacteristic
85C2×#208C22×C311yescharacteristic
86C22×C3⋊C8C22×C311yescharacteristic
87C3×#107—61no—
88C3×#106—61no—
89C3×#102—22no—
90C3×#102—22no—
91C3×#102—21no—
92C3×#102—21no—
93C3×#102—21no—
94C3×#102—21no—
95C3×#102—61no—
96C3×#102—61no—
97C3×#100—34no—
98C3×#97—61no—
99C3×C4×C8—61no—
100#833C3×C414yescomplemented
101#832—21no—
102#832—21no—
103#808—21no—
104#807—21no—
105#803—21no—
106C4×C3⋊C8—21no—
107C23×C32—22no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32—81no—
111C23×C32—81no—
112C23×C32#4111yescharacteristic
113C32×D4—22no—
114C32×D4—22no—
115C32×D4—41no—
116C32×D4—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C32×C8—41no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—21no—
132#428—31no—
133#418C3×D311yescharacteristic
134C2×#102—31no—
135C2×#100—31no—
136#405—31no—
137#343—31no—
138#341—31no—
139C24×C3—21no—
140C24×C3—21no—
141C24×C3—41no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—21no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—22no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4—41no—
158C2×C3×D4C4×D312yes—
159C2×C3×D4C2×C3×C412yes—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C22×Dic3—21no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—21no—
168C3×M16—21no—
169C3×M16—32no—
170C3×M16—32no—
171C3×M16—41no—
172C3×M16—41no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—22no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—31no—
179C2×C3×C8—31no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4#6711yescharacteristic
190C3×C4⋊C4C3×D411yescharacteristic
191C3×C4⋊C4C3×D411yescharacteristic
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—41no—
195C3×C42—21no—
196C3×C42—21no—
197C3×C42—41no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200#208—21no—
201#208—21no—
202#208C2×C3×C412yes—
203#208C2×C3×C412yes—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8C3×D411yescharacteristic
209C2×C3⋊C8C3×D411yescharacteristic
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—42no—
213C22×C32—82no—
214C22×C32—82no—
215C22×C32—81no—
216C22×C32—81no—
217C22×C32#11711yescharacteristic
218C22×C32#12111yescharacteristic
219C22×C32#12611yescharacteristic
220C32×C4—41no—
221C32×C4—41no—
222C32×C4C4×D411yescharacteristic
223C32×C4C4×D411yescharacteristic
224C32×C4#12311yescharacteristic
225C32×C4#12411yescharacteristic
226C3×Dic3—81no—
227C22×D4C2×C3×D311yescharacteristic
228C2×M16—31no—
229C2×M16—31no—
230C2×M16C2×C3×D311yescharacteristic
231C22×C8—31no—
232#117C2×C3×D311yescharacteristic
233C2×C4⋊C4—31no—
234#107—61no—
235#106—61no—
236#102—21no—
237#102—21no—
238#102—61no—
239#102—61no—
240#100—34no—
241#97—61no—
242C4×C8—61no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—21no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3—42no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—81no—
254C23×C3—81no—
255C23×C3—81no—
256C23×C3—81no—
257C23×C3—82no—
258C23×C3—82no—
259C23×C3#23711yescharacteristic
260C23×C3C3×#4111yescharacteristic
261C3×D4—24no—
262C3×D4—22no—
263C3×D4—22no—
264C3×D4—22no—
265C3×D4—22no—
266C3×D4—42no—
267C3×D4—42no—
268C3×D4—42no—
269C3×D4—41no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C2×C3×C4—21no—
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—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—121no—
286C2×C3×C4—241no—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C22×C3×C411yescharacteristic
294C2×C3×C4C2×C3×D411yescharacteristic
295C2×C3×C4C2×C3×D411yescharacteristic
296C2×C3×C4C3×#4111yescharacteristic
297C2×C3×C4C3×#4111yescharacteristic
298C2×C3×C4C3×#4111yescharacteristic
299C2×Dic3—41no—
300C2×Dic3—81no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—62no—
305C3×C8—61no—
306C3×C8—61no—
307C3×C8—62no—
308C3⋊C8—22no—
309C3⋊C8—22no—
310C3⋊C8—21no—
311C3⋊C8—21no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32—82no—
315C2×C32#38811yescharacteristic
316C2×C32#47111yescharacteristic
317C2×C32#47211yescharacteristic
318C24—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4C3×C4×D312yes—
325C22×C4—61no—
326C22×C4C22×C3×D311yescharacteristic
327M16—21no—
328M16—21no—
329M16—32no—
330M16—32no—
331M16—61no—
332M16—61no—
333C2×C8—21no—
334C2×C8—31no—
335C2×C8—31no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4C3×#6711yescharacteristic
343C4⋊C4C3×#6711yescharacteristic
344C22⋊C4—21no—
345C42—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—44no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—82no—
359C22×C3—82no—
360C22×C3—82no—
361C22×C3—82no—
362C22×C3—82no—
363C22×C3—82no—
364C22×C3—84no—
365C22×C3—84no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3#87711yescharacteristic
371C22×C3#87911yescharacteristic
372C22×C3#93911yescharacteristic
373C22×C3C3×#11711yescharacteristic
374C22×C3C3×#12111yescharacteristic
375C22×C3C3×#12611yescharacteristic
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—81no—
385C3×C4—81no—
386C3×C4—241no—
387C3×C4#67⋊C411yescharacteristic
388C3×C4#88311yescharacteristic
389C3×C4C4×#6711yescharacteristic
390C3×C4#93611yescharacteristic
391C3×C4C3×C4×D411yescharacteristic
392C3×C4C3×C4×D411yescharacteristic
393C3×C4C3×#12311yescharacteristic
394C3×C4C3×#12411yescharacteristic
395Dic3—81no—
396C32#193111yescharacteristic, complemented, Sylow
397C23—22no—
398C23—41no—
399C23—41no—
400C23—81no—
401C23—81no—
402C23C3×#23711yescharacteristic
403D4—22no—
404D4—22no—
405D4—41no—
406D4—41no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—121no—
410C2×C4—241no—
411C2×C4C2×C3×C4×D311yescharacteristic
412C2×C4C3×#23511yescharacteristic
413C2×C4C3×D3×D411yescharacteristic
414C2×C4C3×#23711yescharacteristic
415C2×C4C3×#23711yescharacteristic
416C2×C4C2×C3×#6711yescharacteristic
417C8—41no—
418C8—62no—
419C8—61no—
420C8—61no—
421C8—62no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3—84no—
432C2×C3—82no—
433C2×C3—82no—
434C2×C3#494511yescharacteristic
435C2×C3#519911yescharacteristic
436C2×C3#520011yescharacteristic
437C2×C3C3×#38811yescharacteristic
438C2×C3C3×#47111yescharacteristic
439C2×C3C3×#47211yescharacteristic
440C22—21no—
441C22—21no—
442C22—42no—
443C22—82no—
444C22—82no—
445C22—81no—
446C22—81no—
447C22C3×#87711yescharacteristic
448C22C3×#87911yescharacteristic
449C22C3×#93911yescharacteristic
450C4—41no—
451C4—41no—
452C4—241no—
453C4C3×#67⋊C411yescharacteristic
454C4C3×#88311yescharacteristic
455C4C3×C4×#6711yescharacteristic
456C4C3×#93611yescharacteristic
457C3—21no—
458C3#7031811yescharacteristic, direct product factor
459C3C3×#193111yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—82no—
463C2C3×#494511yescharacteristic
464C2C3×#519911yescharacteristic
465C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#418C2
socleC22×C32#121
prime radicalC22×C32×D4C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#418D3
hypocenterC3C3×#1931
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
4. C3×#4997C2semidirect
5. C3×#4995C2semidirect
6. C3×#4558C2semidirect
7. C3×#4554C2semidirect
9. #70318C3direct (N × H)
19. C3×#833C4semidirect
35. #4997C2×C3semidirect
36. #4995C2×C3semidirect
39. #4558C2×C3semidirect
40. #4554C2×C3semidirect
100. #833C3×C4semidirect
396. C32#1931semidirect
458. C3#70318direct (N × H)
459. C3C3×#1931semidirect

Maximal subgroups

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

subgroupindex
C32×#4182
C2×C3×#8332
C2×C3×#8322
C3×#49972
C3×#49952
C3×#45582
C3×#45542
C3×#19313
#703183