Finite Group Databasebeta

← C3×#70175 #11793152

Subgroups — C3×#70175 #11793152

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
5C2×C3×#818C211yesmaximal, characteristic, complemented
6C3×#4987C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2033—31nomaximal
9#70175C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#938—22no—
17C3×#938—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#102—22no—
23C3×#832—22no—
24C3×C3⋊#95—21no—
25C3×(C2×D3)⋊C8—22no—
26C3×#818—22no—
27C2×C3×#121—31no—
28C2×#938C2×C311yescharacteristic
29C2×C3×#107—31no—
30C2×C3×#102—21no—
31C2×C3×#102—31no—
32C2×C3×#102D311yescharacteristic, complemented
33C2×C3×#102C2×C311yescharacteristic, complemented
34C2×C3×C22⋊C8—31no—
35C3×#380—31no—
36C2×#832C2×C311yescharacteristic, complemented
37C2×(C2×D3)⋊C8C2×C311yescharacteristic, complemented
38C2×#818C2×C311yescharacteristic, complemented
39#4987C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C23×C3×D3D411yescharacteristic
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—24no—
53C2×C3×#67—42no—
54C2×C3×#67—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
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×C8D412yescomplemented
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C3×#217—24no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3D412yes—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78#2033—31noSylow
79C22×C3×D4—21no—
80C22×C3×D4—61no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C22×C311yescharacteristic
83C23×C3×C4—31no—
84C22×#67—21no—
85C22×C4×D3C22×C311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8—31no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C22×C311yescharacteristic
90C3×#121—62no—
91C3×#121—62no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C22×C311yescharacteristic
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×#217—21no—
100#938—22no—
101#938—22no—
102C2×(C2×D3)⋊C4—21no—
103C2×C4⋊Dic3C22×C311yescharacteristic
104C2×C4⋊Dic3C22×C311yescharacteristic
105C22×C3⋊C8C22×C311yescharacteristic
106C3×#107—62no—
107C3×#102—24no—
108C3×#102—22no—
109C3×#102—22no—
110C3×#102—62no—
111C3×C22⋊C8—62no—
112C3×#95—61no—
113#832—22no—
114C3⋊#95—21no—
115(C2×D3)⋊C8—22no—
116#818—22no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3D812yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C3×#67—48no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C32×C8—22no—
160C3×C3⋊C8—41no—
161C2×#121—31no—
162C2×#107—31no—
163C2×#102—31no—
164C2×#102C3×D311yescharacteristic, complemented
165C2×C22⋊C8—31no—
166#380—31no—
167#340—31no—
168C24×C3—21no—
169C24×C3—21no—
170C24×C3—31no—
171C24×C3—41no—
172C23×D3C3×D411yescharacteristic
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—64no—
190C2×C3×D4—122no—
191C2×C3×D4—122no—
192C2×C3×D4D1212yes—
193C2×C3×D4C3×D412yes—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—41no—
199C22×C3×C4—61no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C2×#67—24no—
210C2×#67—42no—
211C2×#67—42no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3C3×D411yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8#6712yescomplemented
232C2×C3×C8C3×D412yescomplemented
233C3×C4⋊C4—22no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4—122no—
245#217—24no—
246(C2×D3)⋊C4—42no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—21no—
250C4⋊Dic3C3×D412yes—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32—81no—
260C22×C32—81no—
261C22×C32#12011yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32#12311yescharacteristic
264C22×C32C2×D811yescharacteristic
265C22×C32#13511yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C22×C32#13711yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—81no—
276C32×C4#12111yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4#12311yescharacteristic
279C32×C4#12411yescharacteristic
280C3×Dic3—41no—
281C3×Dic3—42no—
282C3×Dic3—81no—
283C22×D4—61no—
284C22×D4C2×C3×D311yescharacteristic
285C23×C4—31no—
286C22×C8—31no—
287C22×C8C2×C3×D311yescharacteristic
288#121—62no—
289#121—62no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4C2×C3×D311yescharacteristic
293C2×C22⋊C4—61no—
294C2×C22⋊C4—61no—
295#107—62no—
296#102—22no—
297#102—62no—
298C22⋊C8—62no—
299#95—61no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—61no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—81no—
326C23×C3—81no—
327C23×C3—81no—
328C23×C3—81no—
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×D812yes—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—42no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—41no—
350C3×D4—128no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—42no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—81no—
369C2×C3×C4—81no—
370C2×C3×C4—121no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4C2×D1211yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C3×#4111yescharacteristic
389C2×C3×C4C3×#4111yescharacteristic
390C2×C3×C4C3×#4111yescharacteristic
391#67—48no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C4×D3—41no—
402C4×D3—41no—
403C4×D3—41no—
404C4×D3—41no—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—42no—
408C3×C8—121no—
409C3⋊C8—41no—
410C2×C32—82no—
411C2×C32#39411yescharacteristic
412C2×C32#44711yescharacteristic
413C2×C32#45211yescharacteristic
414C2×C32#46611yescharacteristic
415C2×C32#46811yescharacteristic
416C2×C32#48011yescharacteristic
417C2×C32#48211yescharacteristic
418C3×D3—42no—
419C24—21no—
420C24—31no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—64no—
427C2×D4—122no—
428C2×D4—122no—
429C2×D4C3×D1212yes—
430C22×C4—21no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—61no—
435C22×C4—61no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4C22×C3×D311yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8C3×#6712yescomplemented
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—32no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C22⋊C4—64no—
454C22⋊C4—122no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—44no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—82no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3—81no—
485C22×C3—81no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#88211yescharacteristic
491C22×C3#88311yescharacteristic
492C22×C3D3×D811yescharacteristic
493C22×C3#91211yescharacteristic
494C22×C3#91411yescharacteristic
495C22×C3#91511yescharacteristic
496C22×C3#93811yescharacteristic
497C22×C3C3×#12011yescharacteristic
498C22×C3C3×#12111yescharacteristic
499C22×C3C3×#12311yescharacteristic
500C22×C3C2×C3×D811yescharacteristic
501C22×C3C3×#13511yescharacteristic
502C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
503C22×C3C3×#13711yescharacteristic
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—22no—
507C2×D3—41no—
508C2×D3—41no—
509C2×D3—41no—
510C2×D3—41no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—82no—
516C3×C4—81no—
517C3×C4—81no—
518C3×C4—121no—
519C3×C4—122no—
520C3×C4—241no—
521C3×C4#88511yescharacteristic
522C3×C4#88611yescharacteristic
523C3×C4#93011yescharacteristic
524C3×C4#93911yescharacteristic
525C3×C4C3×#12111yescharacteristic
526C3×C4C3×#12111yescharacteristic
527C3×C4C3×#12311yescharacteristic
528C3×C4C3×#12411yescharacteristic
529Dic3—41no—
530Dic3—42no—
531Dic3—81no—
532C32#203311yescharacteristic, complemented, Sylow
533C23—22no—
534C23—32no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—61no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23—61no—
546C23—61no—
547C23C3×D3×D411yescharacteristic
548D4—22no—
549D4—22no—
550D4—41no—
551D4—41no—
552D4—128no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
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×C4—121no—
569C2×C4C2×C3×D1211yescharacteristic
570C2×C4C3×#23511yescharacteristic
571C2×C4C3×D3×D411yescharacteristic
572C2×C4C3×#23711yescharacteristic
573C2×C4C3×#23711yescharacteristic
574C2×C4C2×C3×#6711yescharacteristic
575C8—22no—
576C8—121no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—84no—
585C2×C3—82no—
586C2×C3—82no—
587C2×C3—122no—
588C2×C3#477311yescharacteristic
589C2×C3#477411yescharacteristic
590C2×C3#478311yescharacteristic
591C2×C3#478411yescharacteristic
592C2×C3#496111yescharacteristic
593C2×C3#515711yescharacteristic
594C2×C3#517411yescharacteristic
595C2×C3C3×#39411yescharacteristic
596C2×C3C3×#44711yescharacteristic
597C2×C3C3×#45211yescharacteristic
598C2×C3C3×#46611yescharacteristic
599C2×C3C3×#46811yescharacteristic
600C2×C3C3×#48011yescharacteristic
601C2×C3C3×#48211yescharacteristic
602D3—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22C3×#88211yescharacteristic
618C22C3×#88311yescharacteristic
619C22C3×D3×D811yescharacteristic
620C22C3×#91211yescharacteristic
621C22C3×#91411yescharacteristic
622C22C3×#91511yescharacteristic
623C22C3×#93811yescharacteristic
624C4—81no—
625C4—121no—
626C4—122no—
627C4—241no—
628C4C3×#88511yescharacteristic
629C4C3×#88611yescharacteristic
630C4C3×#93011yescharacteristic
631C4C3×#93911yescharacteristic
632C3—21no—
633C3#7017511yescharacteristic, direct product factor
634C3C3×#203311yescharacteristic, complemented
635C2—82no—
636C2—122no—
637C2C3×#477311yescharacteristic
638C2C3×#477411yescharacteristic
639C2C3×#478311yescharacteristic
640C2C3×#478411yescharacteristic
641C2C3×#496111yescharacteristic
642C2C3×#515711yescharacteristic
643C2C3×#517411yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC2×C3×#102D3
hypocenterC3C3×#2033
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C2×C3×#832C2semidirect
4. C2×C3×(C2×D3)⋊C8C2semidirect
5. C2×C3×#818C2semidirect
6. C3×#4987C2semidirect
7. C3×#4529C2semidirect
9. #70175C3direct (N × H)
32. C2×C3×#102D3semidirect
33. C2×C3×#102C2×C3semidirect
36. C2×#832C2×C3semidirect
37. C2×(C2×D3)⋊C8C2×C3semidirect
38. C2×#818C2×C3semidirect
39. #4987C2×C3semidirect
41. #4529C2×C3semidirect
66. C2×C32×C8D4semidirect
164. C2×#102C3×D3semidirect
231. C2×C3×C8#67semidirect
232. C2×C3×C8C3×D4semidirect
446. C2×C8C3×#67semidirect
532. C32#2033semidirect
633. C3#70175direct (N × H)
634. C3C3×#2033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×C32×#1022
C2×C3×#8322
C2×C3×(C2×D3)⋊C82
C2×C3×#8182
C3×#49872
C3×#45292
C3×#20333
#701753