Finite Group Databasebeta

← C3×#68754 #11785839

Subgroups — C3×#68754 #11785839

Order 1152.

667 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic
2C3×#5126C211yesmaximal, characteristic
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C32×#339C211yesmaximal, characteristic, complemented
5C3×#4555C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1826—31nomaximal
9#68754C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#892C411yescharacteristic, complemented
19C3×#892C411yescharacteristic, complemented
20C3×D3×C4⋊C4C411yescharacteristic, complemented
21C3×D3×C4⋊C4C411yescharacteristic, complemented
22C3×D3×C22⋊C4—21no—
23C3×#877—21no—
24C3×#872—21no—
25C3×C42×D3—21no—
26C3×C3⋊#95—21no—
27C3×(C2×D3)⋊C8—21no—
28C3×(C2×D3)⋊C8—21no—
29C2×C3×#117—31no—
30D3×#117C2×C311yescharacteristic
31C3×#407—31no—
32C3×C4×C22⋊C4—31no—
33#5126C2×C311yescharacteristic
34C4×(C2×D3)⋊C4C2×C311yescharacteristic
35C3×#339—21no—
36C3×#339—31no—
37C3×#339—31no—
38C3×#339—31no—
39C3×#339D311yescharacteristic, complemented
40C3×#339C2×C311yescharacteristic, complemented
41#4555C2×C311yescharacteristic, complemented
42#4532C2×C311yescharacteristic, complemented
43#4523C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3C2×C411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C4⋊C4C2×C411yescharacteristic
64C32×C22⋊C4—21no—
65C32×C42—21no—
66C32×C42—21no—
67C32×C42—21no—
68C3×#217—21no—
69C3×(C2×D3)⋊C4—24no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×C4⋊Dic3C2×C411yescharacteristic
74C3×Dic3⋊C4—21no—
75C3×Dic3⋊C4—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81C3×#208—21no—
82C3×#208—21no—
83C2×C3×C3⋊C8—21no—
84#1826—31noSylow
85C23×C3×C4—31no—
86C22×C4×D3C22×C311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C3×#117—21no—
92C3×#117—31no—
93C3×#117—31no—
94C3×#117—31no—
95C3×#117—61no—
96C3×#117—61no—
97C3×#117C2×D311yescharacteristic
98C3×#117C22×C311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C22⋊C4—61no—
103C2×C3×C42—21no—
104C2×C3×C42—31no—
105C2×C3×C42—61no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C311yescharacteristic
108C2×(C2×D3)⋊C4—21no—
109#926C22×C311yescharacteristic
110C2×C4×Dic3C22×C311yescharacteristic
111C2×#208C22×C311yescharacteristic
112#892C3×C411yescharacteristic, complemented
113#892C3×C411yescharacteristic, complemented
114D3×C4⋊C4C3×C411yescharacteristic, complemented
115D3×C4⋊C4C3×C411yescharacteristic, complemented
116D3×C22⋊C4—21no—
117#877—21no—
118#872—21no—
119C42×D3—21no—
120C3×C22⋊C8—61no—
121C3×C22⋊C8—61no—
122C3×#95—61no—
123C3⋊#95—21no—
124(C2×D3)⋊C8—21no—
125(C2×D3)⋊C8—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—22no—
130C22×C3×D3—41no—
131C22×C3×D3C22⋊C411yescharacteristic
132C22×C3×D3C22⋊C411yescharacteristic
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3C22⋊C411yescharacteristic
152C2×C3×Dic3C22⋊C411yescharacteristic
153C3×C4×D3—21no—
154C3×C4×D3—21no—
155C3×C4×D3—21no—
156C3×C4×D3—21no—
157C3×C4×D3—21no—
158C3×C4×D3—21no—
159C3×C4×D3—21no—
160C3×C4×D3—21no—
161C3×C4×D3—42no—
162C3×C4×D3—42no—
163C32×C8—41no—
164C3×C3⋊C8—41no—
165C2×#117—31no—
166#407—31no—
167C4×C22⋊C4—31no—
168#339—31no—
169#339—31no—
170#339—31no—
171#339C3×D311yescharacteristic, complemented
172C24×C3—31no—
173C23×D3C3×D411yescharacteristic
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C311yescharacteristic
192C22×Dic3—21no—
193C22×Dic3C3×D411yescharacteristic
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×C4×D3—21no—
197C2×C4×D3—21no—
198C2×C4×D3—21no—
199C2×C4×D3—21no—
200C2×C4×D3C2×C3×C411yescharacteristic
201C2×C4×D3C2×C3×C411yescharacteristic
202C2×C4×D3C3×D411yescharacteristic
203C2×C4×D3C3×D411yescharacteristic
204C3×M16—22no—
205C3×M16—21no—
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—41no—
210C3×M16—61no—
211C3×M16—61no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—41no—
215C2×C3×C8—61no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4C4×D311yescharacteristic
223C3×C4⋊C4C4×D311yescharacteristic
224C3×C4⋊C4C2×C3×C411yescharacteristic
225C3×C4⋊C4C2×C3×C411yescharacteristic
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—41no—
229C3×C22⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—64no—
232C3×C22⋊C4—61no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—22no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—41no—
241C3×C42—41no—
242C3×C42—61no—
243C3×C42—61no—
244C3×C42—61no—
245C3×C42—61no—
246C3×C42—61no—
247#217—21no—
248(C2×D3)⋊C4—24no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—21no—
251C4⋊Dic3C2×C3×C411yescharacteristic
252C4⋊Dic3C2×C3×C411yescharacteristic
253Dic3⋊C4—21no—
254Dic3⋊C4—21no—
255C4×Dic3—21no—
256C4×Dic3—21no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260#208—21no—
261#208—21no—
262C2×C3⋊C8—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32C2×C22⋊C411yescharacteristic
266C22×C32#12311yescharacteristic
267C22×C32#12311yescharacteristic
268C2×C3×D3—21no—
269C2×C3×D3—21no—
270C2×C3×D3—21no—
271C2×C3×D3—21no—
272C2×C3×D3—21no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3#10412yes—
276C32×C4—42no—
277C32×C4—41no—
278C32×C4—41no—
279C32×C4#11711yescharacteristic
280C32×C4#11711yescharacteristic
281C32×C4#12311yescharacteristic
282C32×C4#12311yescharacteristic
283C3×Dic3—21no—
284C3×Dic3—21no—
285C3×Dic3—42no—
286C3×Dic3—41no—
287C3×Dic3—41no—
288C23×C4—31no—
289C2×M16—31no—
290C2×M16C2×C3×D311yescharacteristic
291#117—31no—
292#117—31no—
293#117—31no—
294#117—61no—
295#117—61no—
296#117C2×C3×D311yescharacteristic
297C2×C4⋊C4—31no—
298C2×C4⋊C4—31no—
299C2×C22⋊C4—61no—
300C2×C22⋊C4—61no—
301C2×C42—31no—
302C2×C42—61no—
303C2×C42C2×C3×D311yescharacteristic
304C22⋊C8—61no—
305C22⋊C8—61no—
306#95—61no—
307C23×C3—21no—
308C23×C3—31no—
309C23×C3—31no—
310C23×C3—62no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—121no—
314C23×C3D3×D411yescharacteristic
315C23×C3C2×C3×D411yescharacteristic
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—41no—
320C22×D3C3×C22⋊C411yescharacteristic
321C22×D3C3×C22⋊C411yescharacteristic
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—31no—
335C2×C3×C4—31no—
336C2×C3×C4—42no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—122no—
359C2×C3×C4—122no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4C2×C4×D311yescharacteristic
363C2×C3×C4#23511yescharacteristic
364C2×C3×C4#23511yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4#23911yescharacteristic
368C2×C3×C4C22×C3×C411yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371C2×C3×C4C3×#4111yescharacteristic
372C2×C3×C4C3×#4111yescharacteristic
373C2×C3×C4C3×#4111yescharacteristic
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3C3×C22⋊C411yescharacteristic
382C2×Dic3C3×C22⋊C411yescharacteristic
383C4×D3—21no—
384C4×D3—21no—
385C4×D3—21no—
386C4×D3—21no—
387C4×D3—21no—
388C4×D3—21no—
389C4×D3—21no—
390C4×D3—21no—
391C4×D3—42no—
392C4×D3—42no—
393C3×C8—42no—
394C3×C8—41no—
395C3×C8—41no—
396C3×C8—121no—
397C3⋊C8—41no—
398C2×C32—21no—
399C2×C32—21no—
400C2×C32#38111yescharacteristic
401C2×C32C2×#10411yescharacteristic
402C2×C32#42111yescharacteristic
403C3×D3—22no—
404C3×D3—41no—
405C24—31no—
406C22×C4—21no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—31no—
410C22×C4—31no—
411C22×C4—31no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4C22×C3×D311yescharacteristic
420M16—21no—
421M16—21no—
422M16—61no—
423M16—61no—
424C2×C8—21no—
425C2×C8—61no—
426C4⋊C4—31no—
427C4⋊C4—31no—
428C4⋊C4—61no—
429C4⋊C4—61no—
430C4⋊C4C3×C4×D311yescharacteristic
431C4⋊C4C3×C4×D311yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—61no—
434C22⋊C4—61no—
435C22⋊C4—64no—
436C22⋊C4—61no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42—61no—
441C42—61no—
442C42—61no—
443C42—61no—
444C42—61no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—32no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3—61no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3—61no—
459C22×C3—61no—
460C22×C3—122no—
461C22×C3—122no—
462C22×C3D3×C22⋊C411yescharacteristic
463C22×C3#88311yescharacteristic
464C22×C3#89411yescharacteristic
465C22×C3C2×C3×C22⋊C411yescharacteristic
466C22×C3C3×#12311yescharacteristic
467C22×C3C3×#12311yescharacteristic
468C2×D3—21no—
469C2×D3—21no—
470C2×D3—21no—
471C2×D3—21no—
472C2×D3—21no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3C3×#10412yes—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—44no—
483C3×C4—41no—
484C3×C4—41no—
485C3×C4—41no—
486C3×C4—41no—
487C3×C4—61no—
488C3×C4—61no—
489C3×C4—81no—
490C3×C4—81no—
491C3×C4—122no—
492C3×C4—121no—
493C3×C4—121no—
494C3×C4#87211yescharacteristic
495C3×C4#88311yescharacteristic
496C3×C4#89211yescharacteristic
497C3×C4#89411yescharacteristic
498C3×C4C3×#11711yescharacteristic
499C3×C4C3×#11711yescharacteristic
500C3×C4C3×#12311yescharacteristic
501C3×C4C3×#12311yescharacteristic
502Dic3—21no—
503Dic3—21no—
504Dic3—42no—
505Dic3—41no—
506Dic3—41no—
507C32#182611yescharacteristic, complemented, Sylow
508C23—31no—
509C23—31no—
510C23—62no—
511C23—61no—
512C23—61no—
513C23—121no—
514C23C3×D3×D411yescharacteristic
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—62no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—122no—
536C2×C4—122no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4C2×C3×C4×D311yescharacteristic
540C2×C4C3×#23511yescharacteristic
541C2×C4C3×#23511yescharacteristic
542C2×C4C3×D3×D411yescharacteristic
543C2×C4C3×#23711yescharacteristic
544C2×C4C3×#23911yescharacteristic
545C8—41no—
546C8—121no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—41no—
555C2×C3—41no—
556C2×C3—62no—
557C2×C3—121no—
558C2×C3#466411yescharacteristic
559C2×C3D3×#10411yescharacteristic
560C2×C3#482111yescharacteristic
561C2×C3C3×#38111yescharacteristic
562C2×C3C2×C3×#10411yescharacteristic
563C2×C3C3×#42111yescharacteristic
564D3—22no—
565D3—41no—
566C22—21no—
567C22—21no—
568C22—32no—
569C22—61no—
570C22—61no—
571C22—61no—
572C22—61no—
573C22—61no—
574C22—122no—
575C22—122no—
576C22C3×D3×C22⋊C411yescharacteristic
577C22C3×#88311yescharacteristic
578C22C3×#89411yescharacteristic
579C4—42no—
580C4—41no—
581C4—41no—
582C4—61no—
583C4—61no—
584C4—122no—
585C4—121no—
586C4—121no—
587C4C3×#87211yescharacteristic
588C4C3×#88311yescharacteristic
589C4C3×#89211yescharacteristic
590C4C3×#89411yescharacteristic
591C3—21no—
592C3#6875411yescharacteristic, direct product factor
593C3C3×#182611yescharacteristic, complemented
594C2—21no—
595C2—21no—
596C2—62no—
597C2—121no—
598C2C3×#466411yescharacteristic
599C2C3×D3×#10411yescharacteristic
600C2C3×#482111yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#339D3
hypocenterC3C3×#1826
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C3×#339

Complements

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

NH ≅ G/Ntype
4. C32×#339C2semidirect
5. C3×#4555C2semidirect
6. C3×#4532C2semidirect
7. C3×#4523C2semidirect
9. #68754C3direct (N × H)
18. C3×#892C4semidirect
19. C3×#892C4semidirect
20. C3×D3×C4⋊C4C4semidirect
21. C3×D3×C4⋊C4C4semidirect
39. C3×#339D3semidirect
40. C3×#339C2×C3semidirect
41. #4555C2×C3semidirect
42. #4532C2×C3semidirect
43. #4523C2×C3semidirect
112. #892C3×C4semidirect
113. #892C3×C4semidirect
114. D3×C4⋊C4C3×C4semidirect
115. D3×C4⋊C4C3×C4semidirect
171. #339C3×D3semidirect
507. C32#1826semidirect
592. C3#68754direct (N × H)
593. C3C3×#1826semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
C3×#51262
C3×C4×(C2×D3)⋊C42
C32×#3392
C3×#45552
C3×#45322
C3×#45232
C3×#18263
#687543