Finite Group Databasebeta

← C3×#68822 #11793164

Subgroups — C3×#68822 #11793164

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic
2C2×C3×#821C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C32×#340C211yesmaximal, characteristic, complemented
8C3×#2033—31nomaximal
9#68822C311yesmaximal, characteristic, direct product factor
10C22×C3×D12—21no—
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#895—22no—
21C3×#895—22no—
22C3×C3⋊#95—21no—
23C3×#821—22no—
24C3×(C2×D3)⋊C8—22no—
25C3×#809—22no—
26C3×#807—22no—
27C2×C3×#121—31no—
28C2×#895C2×C311yescharacteristic
29C2×C3×#107—31no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C2×C3×C22⋊C8—31no—
33C3×#380—31no—
34C2×#821C2×C311yescharacteristic, complemented
35C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
36#4987C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic, complemented
38C2×#807C2×C311yescharacteristic, complemented
39C3×#340—21no—
40C3×#340D311yescharacteristic, complemented
41C3×#340C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—24no—
54C2×C3×D12—21no—
55C2×C3×D12—42no—
56C2×C3×D12—42no—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—21no—
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×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4D412yes—
71C3×(C2×D3)⋊C4—24no—
72C3×(C2×D3)⋊C4—42no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yescomplemented
78#2033—31noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—31no—
82C22×D12—21no—
83C22×D12C22×C311yescharacteristic
84C22×C4×D3C22×C311yescharacteristic
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C3×#121—62no—
90C3×#121—62no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C4⋊C4C22×C311yescharacteristic
98C2×C3×C22⋊C4—61no—
99C2×C3×C22⋊C4—61no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×C4⋊Dic3C22×C311yescharacteristic
103C22×C3⋊C8C22×C311yescharacteristic
104#895—22no—
105#895—22no—
106C3×#107—62no—
107C3×#102—62no—
108C3×#102—62no—
109C3×C22⋊C8—62no—
110C3×#95—61no—
111C3⋊#95—21no—
112#821—22no—
113(C2×D3)⋊C8—22no—
114#809—22no—
115#807—22no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—22no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3D812yes—
131C2×C32×C4—22no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—48no—
152C3×D12—41no—
153C3×D12—41no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C32×C8—41no—
159C3×C3⋊C8—22no—
160C2×#121—31no—
161C2×#107—31no—
162C2×#102—31no—
163C2×#102—31no—
164C2×C22⋊C8—31no—
165#380—31no—
166#340C3×D311yescharacteristic, complemented
167C24×C3—31no—
168C24×C3—61no—
169C23×D3—21no—
170C23×D3C3×D411yescharacteristic
171C2×C3×D4—32no—
172C2×C3×D4—64no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—122no—
179C2×C3×D4—122no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4—61no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C23×C311yescharacteristic
197C22×Dic3—21no—
198C22×Dic3C3×D411yescharacteristic
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—24no—
204C2×D12—21no—
205C2×D12—42no—
206C2×D12—42no—
207C2×D12C3×D412yes—
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×C4×D3—21no—
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×C4×D3—21no—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4D1212yes—
239C3×C4⋊C4C3×D412yes—
240C3×C22⋊C4—64no—
241C3×C22⋊C4—122no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—42no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8C3×D412yescomplemented
249C22×C32#12011yescharacteristic
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C22×C32C2×D811yescharacteristic
253C22×C32#13511yescharacteristic
254C22×C32AGL(1,ℤ/8)11yescharacteristic
255C22×C32#13711yescharacteristic
256C2×C3×D3—22no—
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—41no—
260C2×C3×D3—41no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C2×C3×D3—81no—
267C2×C3×D3—81no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C32×C4—42no—
271C32×C4—81no—
272C32×C4#12111yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12311yescharacteristic
275C32×C4#12411yescharacteristic
276C3×Dic3—41no—
277C3×Dic3—81no—
278C22×D4—31no—
279C22×D4—61no—
280C23×C4—31no—
281C22×C8—31no—
282C22×C8C2×C3×D311yescharacteristic
283#121—62no—
284#121—62no—
285C2×C4⋊C4—31no—
286C2×C4⋊C4C2×C3×D311yescharacteristic
287C2×C4⋊C4C2×C3×D311yescharacteristic
288C2×C22⋊C4—61no—
289C2×C22⋊C4—61no—
290#107—62no—
291#102—62no—
292#102—62no—
293C22⋊C8—62no—
294#95—61no—
295C23×C3—21no—
296C23×C3—32no—
297C23×C3—61no—
298C23×C3—61no—
299C23×C3—61no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—62no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3—121no—
310C23×C3D3×D411yescharacteristic
311C23×C3C2×C3×D411yescharacteristic
312C22×D3—21no—
313C22×D3—21no—
314C22×D3—21no—
315C22×D3—21no—
316C22×D3—21no—
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—41no—
320C22×D3—41no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3C3×D812yes—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—128no—
329C3×D4—121no—
330C3×D4—121no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—81no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4—81no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4—121no—
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4#23511yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23911yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C3×#4111yescharacteristic
375C2×C3×C4C3×#4111yescharacteristic
376C2×C3×C4C3×#4111yescharacteristic
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383D12—22no—
384D12—22no—
385D12—48no—
386D12—41no—
387D12—41no—
388C4×D3—41no—
389C4×D3—41no—
390C4×D3—41no—
391C4×D3—41no—
392C3×C8—42no—
393C3×C8—41no—
394C3×C8—41no—
395C3×C8—62no—
396C3⋊C8—22no—
397C2×C32#39411yescharacteristic
398C2×C32#44711yescharacteristic
399C2×C32#45211yescharacteristic
400C2×C32#46611yescharacteristic
401C2×C32#46811yescharacteristic
402C2×C32#48011yescharacteristic
403C2×C32#48211yescharacteristic
404C3×D3—42no—
405C3×D3—82no—
406C24—31no—
407C24—61no—
408C2×D4—32no—
409C2×D4—64no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—61no—
415C2×D4—122no—
416C2×D4—122no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—31no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4C22×C3×D311yescharacteristic
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—32no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4C3×D1212yes—
440C22⋊C4—64no—
441C22⋊C4—122no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—122no—
459C22×C3—241no—
460C22×C3—241no—
461C22×C3—241no—
462C22×C3—241no—
463C22×C3#88211yescharacteristic
464C22×C3#88411yescharacteristic
465C22×C3#89411yescharacteristic
466C22×C3D3×D811yescharacteristic
467C22×C3#91411yescharacteristic
468C22×C3#91611yescharacteristic
469C22×C3#91811yescharacteristic
470C22×C3C3×#12011yescharacteristic
471C22×C3C3×#12111yescharacteristic
472C22×C3C3×#12311yescharacteristic
473C22×C3C2×C3×D811yescharacteristic
474C22×C3C3×#13511yescharacteristic
475C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
476C22×C3C3×#13711yescharacteristic
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—41no—
481C2×D3—41no—
482C2×D3—41no—
483C2×D3—41no—
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—81no—
488C2×D3—81no—
489C2×D3—81no—
490C2×D3—81no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—82no—
498C3×C4—82no—
499C3×C4—81no—
500C3×C4—81no—
501C3×C4—121no—
502C3×C4—241no—
503C3×C4#87511yescharacteristic
504C3×C4#88411yescharacteristic
505C3×C4#89411yescharacteristic
506C3×C4#89511yescharacteristic
507C3×C4C3×#12111yescharacteristic
508C3×C4C3×#12111yescharacteristic
509C3×C4C3×#12311yescharacteristic
510C3×C4C3×#12411yescharacteristic
511Dic3—41no—
512Dic3—81no—
513C32#203311yescharacteristic, complemented, Sylow
514C23—32no—
515C23—61no—
516C23—61no—
517C23—61no—
518C23—61no—
519C23—61no—
520C23—61no—
521C23—62no—
522C23—121no—
523C23—121no—
524C23—121no—
525C23—121no—
526C23—121no—
527C23—121no—
528C23C3×D3×D411yescharacteristic
529D4—62no—
530D4—62no—
531D4—128no—
532D4—121no—
533D4—121no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—121no—
548C2×C4—121no—
549C2×C4—121no—
550C2×C4C2×C3×D1211yescharacteristic
551C2×C4C3×#23511yescharacteristic
552C2×C4C3×#23511yescharacteristic
553C2×C4C3×D3×D411yescharacteristic
554C2×C4C3×D3×D411yescharacteristic
555C2×C4C3×#23911yescharacteristic
556C8—41no—
557C8—62no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—122no—
566C2×C3—242no—
567C2×C3#467211yescharacteristic
568C2×C3#477311yescharacteristic
569C2×C3#477511yescharacteristic
570C2×C3#480811yescharacteristic
571C2×C3#481211yescharacteristic
572C2×C3#486611yescharacteristic
573C2×C3#488211yescharacteristic
574C2×C3C3×#39411yescharacteristic
575C2×C3C3×#44711yescharacteristic
576C2×C3C3×#45211yescharacteristic
577C2×C3C3×#46611yescharacteristic
578C2×C3C3×#46811yescharacteristic
579C2×C3C3×#48011yescharacteristic
580C2×C3C3×#48211yescharacteristic
581D3—42no—
582D3—82no—
583C22—62no—
584C22—62no—
585C22—62no—
586C22—121no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—122no—
591C22—122no—
592C22—122no—
593C22—241no—
594C22—241no—
595C22—241no—
596C22—241no—
597C22C3×#88211yescharacteristic
598C22C3×#88411yescharacteristic
599C22C3×#89411yescharacteristic
600C22C3×D3×D811yescharacteristic
601C22C3×#91411yescharacteristic
602C22C3×#91611yescharacteristic
603C22C3×#91811yescharacteristic
604C4—42no—
605C4—81no—
606C4—121no—
607C4—241no—
608C4C3×#87511yescharacteristic
609C4C3×#88411yescharacteristic
610C4C3×#89411yescharacteristic
611C4C3×#89511yescharacteristic
612C3—21no—
613C3#6882211yescharacteristic, direct product factor
614C3C3×#203311yescharacteristic, complemented
615C2—122no—
616C2—242no—
617C2C3×#467211yescharacteristic
618C2C3×#477311yescharacteristic
619C2C3×#477511yescharacteristic
620C2C3×#480811yescharacteristic
621C2C3×#481211yescharacteristic
622C2C3×#486611yescharacteristic
623C2C3×#488211yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
hypercenterC3×#340D3
hypocenterC3C3×#2033
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C3×#340

Complements

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

NH ≅ G/Ntype
2. C2×C3×#821C2semidirect
3. C2×C3×(C2×D3)⋊C8C2semidirect
4. C3×#4987C2semidirect
5. C2×C3×#809C2semidirect
6. C2×C3×#807C2semidirect
7. C32×#340C2semidirect
9. #68822C3direct (N × H)
34. C2×#821C2×C3semidirect
35. C2×(C2×D3)⋊C8C2×C3semidirect
36. #4987C2×C3semidirect
37. C2×#809C2×C3semidirect
38. C2×#807C2×C3semidirect
40. C3×#340D3semidirect
41. C3×#340C2×C3semidirect
77. C2×C3×C3⋊C8D4semidirect
166. #340C3×D3semidirect
248. C2×C3⋊C8C3×D4semidirect
513. C32#2033semidirect
613. C3#68822direct (N × H)
614. C3C3×#2033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
C3×#49872
C2×C3×#8092
C2×C3×#8072
C32×#3402
C3×#20333
#688223