Finite Group Databasebeta

← C3×#70283 #11792631

Subgroups — C3×#70283 #11792631

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic
3C22×C3×Dic12C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic
5C3×#4973C211yesmaximal, characteristic
6C2×C3×#810C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic
8C3×#2016—31nomaximal
9#70283C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C3×#944—22no—
16C3×#944—22no—
17C2×C3×#216—22no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×C3×Dic12—22no—
24C2×C3×Dic12—22no—
25C2×C3×Dic12—22no—
26C32×#103—22no—
27C3×C3⋊#95—22no—
28C3×#810—22no—
29C22×C3×Q16—31no—
30C22×C3×Q16—31no—
31C2×C3×C4⋊Q8—31no—
32C2×#944C2×C311yescharacteristic
33C22×#216C2×C311yescharacteristic
34C22×Dic12C2×C311yescharacteristic
35C2×C3×#103—21no—
36C2×C3×#103—31no—
37C2×C3×#103D311yescharacteristic
38C2×C3×#103C2×C311yescharacteristic
39C3×#391—31no—
40#4973C2×C311yescharacteristic
41C2×#810C2×C311yescharacteristic
42C3×#336—31no—
43#4550C2×C311yescharacteristic
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8D412yes—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6D412yes—
67C2×C3×Dic6D412yes—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8D412yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C3×#216—28no—
74C3×Dic3⋊C4—28no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80C3×Dic12—28no—
81#2016—31noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8—31no—
85C22×C3×Q8C2×D311yescharacteristic
86C22×C3×Q8C22×C311yescharacteristic
87C22×Dic6C22×C311yescharacteristic
88C22×Dic6C22×C311yescharacteristic
89C2×C3×Q16—62no—
90C2×C3×Q16—62no—
91C2×C3×Q16—62no—
92C2×C3×Q16—62no—
93C2×C3×Q16—62no—
94C2×C3×Q16—62no—
95C22×C3×C8—21no—
96C22×C3×C8—31no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C22×C311yescharacteristic
99C3×C4⋊Q8—62no—
100C3×C4⋊Q8—62no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—62no—
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C4⋊C4C22×C311yescharacteristic
105C2×C3×C42—31no—
106#944—22no—
107#944—22no—
108C2×#216—22no—
109C2×#216—22no—
110C2×#216—22no—
111C2×Dic3⋊C4—22no—
112C2×C4×Dic3C22×C311yescharacteristic
113C22×C3⋊C8C22×C311yescharacteristic
114C2×Dic12—22no—
115C2×Dic12—22no—
116C2×Dic12—22no—
117C3×#103—24no—
118C3×#103—22no—
119C3×#103—22no—
120C3×#103—62no—
121C3×#95—62no—
122C3⋊#95—22no—
123#810—22no—
124C23×C32C2×D411yescharacteristic
125C32×Q8—22no—
126C32×Q8—22no—
127C32×Q8—41no—
128C32×Q8—41no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4—42no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3Q1614yescomplemented
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C32×C8—22no—
158C3×C3⋊C8—22no—
159C22×Q16—31no—
160C22×Q16—31no—
161C2×C4⋊Q8—31no—
162C2×#103—31no—
163C2×#103C3×D311yescharacteristic
164#391—31no—
165#336—31no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—22no—
179C2×C3×Q8—32no—
180C2×C3×Q8—32no—
181C2×C3×Q8—41no—
182C2×C3×Q8—41no—
183C2×C3×Q8—41no—
184C2×C3×Q8—61no—
185C2×C3×Q8—61no—
186C2×C3×Q8—61no—
187C2×C3×Q8—61no—
188C2×C3×Q8—61no—
189C2×C3×Q8—61no—
190C2×C3×Q8—61no—
191C2×C3×Q8—61no—
192C2×C3×Q8—61no—
193C2×C3×Q8—61no—
194C2×C3×Q8D1212yes—
195C2×C3×Q8C3×D412yes—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—32no—
202C22×C3×C4—41no—
203C22×C3×C4—41no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3C3×D412yes—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—21no—
220C2×Dic6—21no—
221C2×Dic6C3×D412yes—
222C2×Dic6C3×D412yes—
223C3×Q16—68no—
224C3×Q16—68no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—22no—
230C2×C3×C8—32no—
231C2×C3×C8—41no—
232C2×C3×C8—41no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8#6712yes—
236C2×C3×C8C3×D412yes—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4—68no—
244C3×C42—61no—
245C3×C42—61no—
246#216—28no—
247Dic3⋊C4—28no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8C3×D412yes—
253Dic12—28no—
254C22×C32#12011yescharacteristic
255C22×C32#12111yescharacteristic
256C22×C32#12711yescharacteristic
257C22×C32C2×Q1612yes—
258C22×C32#13712yes—
259C32×C4—42no—
260C32×C4—81no—
261C32×C4#12011yescharacteristic
262C32×C4#12011yescharacteristic
263C32×C4#12111yescharacteristic
264C32×C4#12111yescharacteristic
265C3×Dic3—24no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C22×Q8—31no—
269C22×Q8—31no—
270C22×Q8C2×C3×D311yescharacteristic
271C2×Q16—62no—
272C2×Q16—62no—
273C2×Q16—62no—
274C2×Q16—62no—
275C2×Q16—62no—
276C2×Q16—62no—
277C22×C8—31no—
278C22×C8C2×C3×D311yescharacteristic
279C4⋊Q8—62no—
280C4⋊Q8—62no—
281C2×C4⋊C4—62no—
282C2×C4⋊C4C2×C3×D311yescharacteristic
283C2×C42—31no—
284#103—22no—
285#103—62no—
286#95—62no—
287C23×C3—21no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×C3×D411yescharacteristic
290C3×Q8—24no—
291C3×Q8—22no—
292C3×Q8—22no—
293C3×Q8—22no—
294C3×Q8—22no—
295C3×Q8—42no—
296C3×Q8—42no—
297C3×Q8—42no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—41no—
301C3×Q8—41no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—62no—
306C3×Q8—121no—
307C3×Q8—121no—
308C3×Q8—121no—
309C3×Q8—121no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—34no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—42no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—82no—
336C2×C3×C4—121no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C2×C3×D411yescharacteristic
349C2×C3×C4C2×C3×D411yescharacteristic
350C2×C3×C4C2×C3×D411yescharacteristic
351C2×C3×C4C3×#4111yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3C3×Q1614yescomplemented
361Dic6—22no—
362Dic6—22no—
363Dic6—22no—
364Dic6—22no—
365Dic6—41no—
366Dic6—41no—
367Dic6—41no—
368Dic6—41no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—42no—
372C3×C8—62no—
373C3⋊C8—22no—
374C2×C32#39211yescharacteristic
375C2×C32#45112yes—
376C2×C32#46212yes—
377C2×C32#49411yescharacteristic
378C2×C32#49711yescharacteristic
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—32no—
385C2×Q8—32no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8C3×D1212yes—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—32no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4C22×C3×D311yescharacteristic
403Q16—68no—
404Q16—68no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—32no—
408C2×C8—61no—
409C2×C8—61no—
410C2×C8C3×#6712yes—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—68no—
414C42—61no—
415C42—61no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3#88211yescharacteristic
422C22×C3#88411yescharacteristic
423C22×C3#91512yes—
424C22×C3D3×Q1612yes—
425C22×C3#94011yescharacteristic
426C22×C3C3×#12011yescharacteristic
427C22×C3C3×#12111yescharacteristic
428C22×C3C3×#12711yescharacteristic
429C22×C3C2×C3×Q1612yes—
430C22×C3C3×#13712yes—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—44no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—64no—
439C3×C4—82no—
440C3×C4—81no—
441C3×C4—81no—
442C3×C4—122no—
443C3×C4—122no—
444C3×C4#88211yescharacteristic
445C3×C4#88411yescharacteristic
446C3×C4#93011yescharacteristic
447C3×C4#93711yescharacteristic
448C3×C4C3×#12011yescharacteristic
449C3×C4C3×#12011yescharacteristic
450C3×C4C3×#12111yescharacteristic
451C3×C4C3×#12111yescharacteristic
452Dic3—24no—
453Dic3—42no—
454Dic3—42no—
455C32#201611yescharacteristic, complemented, Sylow
456C23C3×D3×D411yescharacteristic
457Q8—22no—
458Q8—22no—
459Q8—41no—
460Q8—41no—
461Q8—62no—
462Q8—62no—
463Q8—62no—
464Q8—62no—
465Q8—121no—
466Q8—121no—
467Q8—121no—
468Q8—121no—
469C2×C4—22no—
470C2×C4—34no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4C2×C3×D1211yescharacteristic
484C2×C4C3×#23511yescharacteristic
485C2×C4C3×D3×D411yescharacteristic
486C2×C4C3×D3×D411yescharacteristic
487C2×C4C3×D3×D411yescharacteristic
488C2×C4C2×C3×#6711yescharacteristic
489C8—22no—
490C8—62no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3#479512yes—
497C2×C3#480912yes—
498C2×C3#496011yescharacteristic
499C2×C3#516711yescharacteristic
500C2×C3#518311yescharacteristic
501C2×C3C3×#39211yescharacteristic
502C2×C3C3×#45112yes—
503C2×C3C3×#46212yes—
504C2×C3C3×#49411yescharacteristic
505C2×C3C3×#49711yescharacteristic
506C22C3×#88211yescharacteristic
507C22C3×#88411yescharacteristic
508C22C3×#91512yes—
509C22C3×D3×Q1612yes—
510C22C3×#94011yescharacteristic
511C4—42no—
512C4—64no—
513C4—81no—
514C4—122no—
515C4—122no—
516C4C3×#88211yescharacteristic
517C4C3×#88411yescharacteristic
518C4C3×#93011yescharacteristic
519C4C3×#93711yescharacteristic
520C3—21no—
521C3#7028311yescharacteristic, direct product factor
522C3C3×#201611yescharacteristic, complemented
523C2C3×#479512yes—
524C2C3×#480912yes—
525C2C3×#496011yescharacteristic
526C2C3×#516711yescharacteristic
527C2C3×#518311yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×C3×#103D3
hypocenterC3C3×#2016
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
9. #70283C3direct (N × H)
148. C2×C3×Dic3Q16semidirect
360. C2×Dic3C3×Q16semidirect
455. C32#2016semidirect
521. C3#70283direct (N × H)
522. C3C3×#2016semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
C22×C3×#2162
C22×C3×Dic122
C2×C32×#1032
C3×#49732
C2×C3×#8102
C3×#45502
C3×#20163
#702833