Finite Group Databasebeta

← C3×#70273 #11792005

Subgroups — C3×#70273 #11792005

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×C3×#897C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2001—31nomaximal
9#70273C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C3×#946—22no—
16C3×#946—22no—
17C2×C3×#216—22no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×C4⋊Dic3—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#897—22no—
27C3×#897—22no—
28C32×#103—22no—
29C3×(C2×D3)⋊C8—22no—
30C3×#816—22no—
31C22×C3×Q16—31no—
32C2×C3×C22⋊Q8—31no—
33C2×C3×C22⋊Q8—31no—
34C2×#946C2×C311yescharacteristic
35C22×#216C2×C311yescharacteristic, complemented
36C2×#897C2×C311yescharacteristic
37C2×C3×#103—21no—
38C2×C3×#103—31no—
39C2×C3×#103D311yescharacteristic, complemented
40C2×C3×#103C2×C311yescharacteristic, complemented
41C2×C3×C22⋊C8—31no—
42C2×(C2×D3)⋊C8C2×C311yescharacteristic
43C2×#816C2×C311yescharacteristic, complemented
44C3×#340—31no—
45#4529C2×C311yescharacteristic, complemented
46C23×C3×D3D411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8D412yes—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8—21no—
74C32×C4⋊C4—21no—
75C32×C4⋊C4D412yes—
76C3×#216—28no—
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—24no—
79C3×C4⋊Dic3—24no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3D412yes—
82C3×Dic3⋊C4—24no—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8—21no—
85C2×C3×C3⋊C8D412yes—
86#2001—31noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8—31no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C22×C311yescharacteristic
91C23×C3×C4—31no—
92C22×C4×D3C22×C311yescharacteristic
93C22×Dic6C22×C311yescharacteristic
94C2×C3×Q16—62no—
95C2×C3×Q16—62no—
96C2×C3×Q16—62no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C22×C311yescharacteristic
101C3×C22⋊Q8—62no—
102C3×C22⋊Q8—62no—
103C3×C22⋊Q8—62no—
104C3×C22⋊Q8—62no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—61no—
108C2×C3×C4⋊C4—61no—
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C4⋊C4C22×C311yescharacteristic
111C2×C3×C22⋊C4—61no—
112C2×C3×C22⋊C4—61no—
113#946—22no—
114#946—22no—
115C2×#216—22no—
116C2×#216—22no—
117C2×#216—22no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C22×C311yescharacteristic
122C2×Dic3⋊C4—21no—
123C22×C3⋊C8C22×C311yescharacteristic
124#897—22no—
125#897—22no—
126C3×#103—24no—
127C3×#103—22no—
128C3×#103—22no—
129C3×#103—62no—
130C3×C22⋊C8—62no—
131(C2×D3)⋊C8—22no—
132#816—22no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—21no—
135C22×C3×D3—21no—
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3Q1612yescomplemented
141C32×Q8—22no—
142C32×Q8—22no—
143C32×Q8—41no—
144C32×Q8—41no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—41no—
148C2×C32×C4—41no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4111yescharacteristic
157C2×C3×Dic3—21no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—41no—
165C2×C3×Dic3—41no—
166C3×C4×D3—41no—
167C3×C4×D3—41no—
168C3×C4×D3—41no—
169C3×C4×D3—41no—
170C3×Dic6—22no—
171C3×Dic6—22no—
172C3×Dic6—41no—
173C3×Dic6—41no—
174C32×C8—41no—
175C3×C3⋊C8—22no—
176C22×Q16—31no—
177C2×C22⋊Q8—31no—
178C2×C22⋊Q8—31no—
179C2×#103—31no—
180C2×#103C3×D311yescharacteristic, complemented
181C2×C22⋊C8—31no—
182#340—31no—
183C24×C3—31no—
184C23×D3C3×D411yescharacteristic
185C2×C3×Q8—21no—
186C2×C3×Q8—21no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—21no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—22no—
198C2×C3×Q8—32no—
199C2×C3×Q8—41no—
200C2×C3×Q8—41no—
201C2×C3×Q8—41no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204C2×C3×Q8—61no—
205C2×C3×Q8—61no—
206C2×C3×Q8—61no—
207C2×C3×Q8D1212yes—
208C2×C3×Q8C3×D412yes—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—31no—
215C22×C3×C4—41no—
216C22×C3×C4—41no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4—61no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C23×C311yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3C3×D411yescharacteristic
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6—21no—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6C3×D412yes—
242C3×Q16—68no—
243C2×C3×C8—22no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—32no—
251C2×C3×C8—41no—
252C2×C3×C8—41no—
253C2×C3×C8—61no—
254C2×C3×C8—61no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—41no—
260C3×C4⋊C4—64no—
261C3×C4⋊C4—64no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4#6712yes—
264C3×C4⋊C4C3×D412yes—
265C3×C22⋊C4—64no—
266C3×C22⋊C4—64no—
267#216—28no—
268(C2×D3)⋊C4—24no—
269(C2×D3)⋊C4—24no—
270C4⋊Dic3—24no—
271C4⋊Dic3—21no—
272C4⋊Dic3C3×D412yes—
273Dic3⋊C4—24no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8C3×D412yes—
277C22×C32#12011yescharacteristic
278C22×C32#12011yescharacteristic
279C22×C32#12111yescharacteristic
280C22×C32C2×Q1611yescharacteristic
281C22×C32#13511yescharacteristic
282C22×C32#13711yescharacteristic
283C22×C32#13711yescharacteristic
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—22no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C32×C4—42no—
292C32×C4—42no—
293C32×C4#12011yescharacteristic
294C32×C4#12111yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12711yescharacteristic
297C3×Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—31no—
301C22×Q8C2×C3×D311yescharacteristic
302C23×C4—31no—
303C2×Q16—62no—
304C2×Q16—62no—
305C2×Q16—62no—
306C22×C8—31no—
307C22×C8C2×C3×D311yescharacteristic
308C22⋊Q8—62no—
309C22⋊Q8—62no—
310C22⋊Q8—62no—
311C22⋊Q8—62no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—61no—
314C2×C4⋊C4—61no—
315C2×C4⋊C4C2×C3×D311yescharacteristic
316C2×C22⋊C4—61no—
317C2×C22⋊C4—61no—
318#103—22no—
319#103—62no—
320C22⋊C8—62no—
321C23×C3—21no—
322C23×C3—32no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×C3×D411yescharacteristic
331C22×D3—21no—
332C22×D3—21no—
333C22×D3—21no—
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3C3×Q1612yescomplemented
338C3×Q8—24no—
339C3×Q8—22no—
340C3×Q8—22no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—42no—
344C3×Q8—42no—
345C3×Q8—42no—
346C3×Q8—41no—
347C3×Q8—41no—
348C3×Q8—41no—
349C3×Q8—41no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—121no—
353C3×Q8—121no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—81no—
382C2×C3×C4—81no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—121no—
387C2×C3×C4—121no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4C2×D1211yescharacteristic
392C2×C3×C4#23511yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C2×C3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C3×#4111yescharacteristic
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3—21no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C4×D3—41no—
413C4×D3—41no—
414C4×D3—41no—
415C4×D3—41no—
416Dic6—22no—
417Dic6—22no—
418Dic6—41no—
419Dic6—41no—
420C3×C8—42no—
421C3×C8—41no—
422C3×C8—41no—
423C3×C8—62no—
424C3⋊C8—22no—
425C2×C32#39211yescharacteristic
426C2×C32#45111yescharacteristic
427C2×C32#45111yescharacteristic
428C2×C32#45211yescharacteristic
429C2×C32#45211yescharacteristic
430C2×C32#46711yescharacteristic
431C2×C32#47011yescharacteristic
432C3×D3—42no—
433C24—31no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—32no—
440C2×Q8—61no—
441C2×Q8—61no—
442C2×Q8—61no—
443C2×Q8—61no—
444C2×Q8—61no—
445C2×Q8C3×D1212yes—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—31no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4C22×C3×D311yescharacteristic
458Q16—68no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—32no—
463C2×C8—61no—
464C2×C8—61no—
465C4⋊C4—21no—
466C4⋊C4—32no—
467C4⋊C4—64no—
468C4⋊C4—64no—
469C4⋊C4—61no—
470C4⋊C4C3×#6712yes—
471C22⋊C4—64no—
472C22⋊C4—64no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3#88211yescharacteristic
488C22×C3#88411yescharacteristic
489C22×C3#91511yescharacteristic
490C22×C3#91611yescharacteristic
491C22×C3D3×Q1611yescharacteristic
492C22×C3#91811yescharacteristic
493C22×C3#93711yescharacteristic
494C22×C3C3×#12011yescharacteristic
495C22×C3C3×#12011yescharacteristic
496C22×C3C3×#12111yescharacteristic
497C22×C3C2×C3×Q1611yescharacteristic
498C22×C3C3×#13511yescharacteristic
499C22×C3C3×#13711yescharacteristic
500C22×C3C3×#13711yescharacteristic
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—41no—
505C2×D3—41no—
506C2×D3—41no—
507C2×D3—41no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—44no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—82no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4—122no—
521C3×C4#88211yescharacteristic
522C3×C4#88411yescharacteristic
523C3×C4#93011yescharacteristic
524C3×C4#94011yescharacteristic
525C3×C4C3×#12011yescharacteristic
526C3×C4C3×#12111yescharacteristic
527C3×C4C3×#12111yescharacteristic
528C3×C4C3×#12711yescharacteristic
529Dic3—42no—
530Dic3—41no—
531Dic3—42no—
532C32#200111yescharacteristic, complemented, Sylow
533C23—32no—
534C23—61no—
535C23—61no—
536C23—61no—
537C23—61no—
538C23—61no—
539C23—61no—
540C23C3×D3×D411yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—62no—
546Q8—62no—
547Q8—121no—
548Q8—121no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—62no—
559C2×C4—61no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4C2×C3×D1211yescharacteristic
569C2×C4C3×#23511yescharacteristic
570C2×C4C3×D3×D411yescharacteristic
571C2×C4C3×D3×D411yescharacteristic
572C2×C4C3×D3×D411yescharacteristic
573C2×C4C2×C3×#6711yescharacteristic
574C8—41no—
575C8—62no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—122no—
584C2×C3#480811yescharacteristic
585C2×C3#480911yescharacteristic
586C2×C3#481311yescharacteristic
587C2×C3#481611yescharacteristic
588C2×C3#496011yescharacteristic
589C2×C3#517311yescharacteristic
590C2×C3#518611yescharacteristic
591C2×C3C3×#39211yescharacteristic
592C2×C3C3×#45111yescharacteristic
593C2×C3C3×#45111yescharacteristic
594C2×C3C3×#45211yescharacteristic
595C2×C3C3×#45211yescharacteristic
596C2×C3C3×#46711yescharacteristic
597C2×C3C3×#47011yescharacteristic
598D3—42no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22—121no—
603C22—121no—
604C22—121no—
605C22—121no—
606C22C3×#88211yescharacteristic
607C22C3×#88411yescharacteristic
608C22C3×#91511yescharacteristic
609C22C3×#91611yescharacteristic
610C22C3×D3×Q1611yescharacteristic
611C22C3×#91811yescharacteristic
612C22C3×#93711yescharacteristic
613C4—42no—
614C4—42no—
615C4—121no—
616C4—122no—
617C4—122no—
618C4C3×#88211yescharacteristic
619C4C3×#88411yescharacteristic
620C4C3×#93011yescharacteristic
621C4C3×#94011yescharacteristic
622C3—21no—
623C3#7027311yescharacteristic, direct product factor
624C3C3×#200111yescharacteristic, complemented
625C2—122no—
626C2C3×#480811yescharacteristic
627C2C3×#480911yescharacteristic
628C2C3×#481311yescharacteristic
629C2C3×#481611yescharacteristic
630C2C3×#496011yescharacteristic
631C2C3×#517311yescharacteristic
632C2C3×#518611yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C3×#103D3
hypocenterC3C3×#2001
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
2. C22×C3×#216C2semidirect
4. C2×C32×#103C2semidirect
6. C2×C3×#816C2semidirect
7. C3×#4529C2semidirect
9. #70273C3direct (N × H)
35. C22×#216C2×C3semidirect
39. C2×C3×#103D3semidirect
40. C2×C3×#103C2×C3semidirect
43. C2×#816C2×C3semidirect
45. #4529C2×C3semidirect
140. C22×C3×D3Q16semidirect
180. C2×#103C3×D3semidirect
337. C22×D3C3×Q16semidirect
532. C32#2001semidirect
623. C3#70273direct (N × H)
624. C3C3×#2001semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C22×C3×#2162
C2×C3×#8972
C2×C32×#1032
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C3×#45292
C3×#20013
#702733