Finite Group Databasebeta

← C3×#69929 #11786498

Subgroups — C3×#69929 #11786498

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic
3C3×#5212C211yesmaximal, characteristic
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×C3×#817C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8C3×#1854—31nomaximal
9#69929C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C3×#926—22no—
16C3×#926—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C32×C22⋊C8C414yescomplemented
23C3×C3⋊#95—21no—
24C3×#818—22no—
25C3×#817—22no—
26C2×C3×#117—31no—
27C2×#926C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#106—31no—
30C2×C3×C22⋊C8—21no—
31C2×C3×C22⋊C8D311yescharacteristic
32C2×C3×C22⋊C8C2×C311yescharacteristic
33C3×#380—31no—
34#5212C2×C311yescharacteristic
35C2×#818C2×C311yescharacteristic, complemented
36C2×#817C2×C311yescharacteristic, complemented
37C3×#340—31no—
38C3×#340—31no—
39#4551C2×C311yescharacteristic, complemented
40#4551C2×C311yescharacteristic, complemented
41C24×C32D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2×C412yes—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4Q812yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8C2×C412yes—
59C2×C32×C8C2×C412yes—
60C3×#217—24no—
61C3×#217—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×C4⋊Dic3D412yes—
70C3×C4×Dic3—24no—
71#1854—31noSylow
72C23×C3×C4—21no—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C22×C311yescharacteristic
75C22×C3×C8—21no—
76C22×C3×C8—21no—
77C22×C3×C8C2×D311yescharacteristic
78C22×C3×C8C2×D311yescharacteristic
79C22×C3×C8C22×C311yescharacteristic
80C22×C3×C8C22×C311yescharacteristic
81C3×#117—62no—
82C3×#117—62no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—61no—
90C2×#217—21no—
91C2×#217—21no—
92#926—22no—
93#926—22no—
94C2×C4⋊Dic3C22×C311yescharacteristic
95C2×C4⋊Dic3C22×C311yescharacteristic
96C2×C4⋊Dic3C22×C311yescharacteristic
97C2×C4⋊Dic3C22×C311yescharacteristic
98C2×C4×Dic3—21no—
99C3×#107—62no—
100C3×#106—62no—
101C3×C22⋊C8—24no—
102C3×C22⋊C8Dic314yescomplemented
103C3×C22⋊C8C3×C414yescomplemented
104C3×#95—61no—
105C3⋊#95—21no—
106#818—22no—
107#817—22no—
108C23×C32—21no—
109C23×C32—21no—
110C23×C32—21no—
111C23×C32—21no—
112C23×C32—21no—
113C23×C32—21no—
114C23×C32C4⋊C412yes—
115C23×C32C2×D411yescharacteristic
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—22no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4C4⋊C412yes—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C32×C8—22no—
142C32×C8—22no—
143C2×#117—31no—
144C2×#107—31no—
145C2×#106—31no—
146C2×C22⋊C8C3×D311yescharacteristic
147#380—31no—
148#340—31no—
149#340—31no—
150C24×C3—21no—
151C24×C3D1211yescharacteristic
152C24×C3C3×D411yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—41no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4Dic612yes—
174C22×C3×C4D1211yescharacteristic
175C22×C3×C4C2×Dic312yes—
176C22×C3×C4C2×C3×C412yes—
177C22×C3×C4C3×D411yescharacteristic
178C22×C3×C4C3×Q812yes—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—22no—
194C2×C3×C8—22no—
195C2×C3×C8—41no—
196C2×C3×C8—41no—
197C2×C3×C8—41no—
198C2×C3×C8—41no—
199C2×C3×C8C2×Dic312yes—
200C2×C3×C8C2×Dic312yes—
201C2×C3×C8C2×C3×C412yes—
202C2×C3×C8C2×C3×C412yes—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—64no—
212C3×C22⋊C4—122no—
213C3×C42—64no—
214#217—24no—
215#217—42no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3C3×D412yes—
223C4⋊Dic3C3×D412yes—
224C4×Dic3—24no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—22no—
228C22×C32—41no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C22×C32#13511yescharacteristic
236C22×C32#13511yescharacteristic
237C22×C32AGL(1,ℤ/8)11yescharacteristic
238C22×C32#13711yescharacteristic
239C32×C4—22no—
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C3×Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C3×Dic3—81no—
248C23×C4C2×C3×D311yescharacteristic
249C22×C8C2×C3×D311yescharacteristic
250C22×C8C2×C3×D311yescharacteristic
251#117—62no—
252#117—62no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C22⋊C4—61no—
258C2×C22⋊C4—61no—
259C2×C42—61no—
260#107—62no—
261#106—62no—
262C22⋊C8C3×Dic314yescomplemented
263#95—61no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3C4⋊Dic312yes—
285C23×C3C3×C4⋊C412yes—
286C23×C3C2×D1211yescharacteristic
287C23×C3C2×C3×D411yescharacteristic
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C4⋊Dic312yes—
326C2×C3×C4C3×C4⋊C412yes—
327C2×C3×C4C2×Dic611yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4#23711yescharacteristic
332C2×C3×C4C22×Dic311yescharacteristic
333C2×C3×C4C22×C3×C411yescharacteristic
334C2×C3×C4C2×C3×D411yescharacteristic
335C2×C3×C4C2×C3×D411yescharacteristic
336C2×C3×C4C2×C3×Q811yescharacteristic
337C2×C3×C4C3×#4111yescharacteristic
338C2×C3×C4C3×#4111yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—42no—
357C2×C32—42no—
358C2×C32#38511yescharacteristic
359C2×C32#42711yescharacteristic
360C2×C32#42811yescharacteristic
361C2×C32#44911yescharacteristic
362C2×C32#45211yescharacteristic
363C2×C32#48211yescharacteristic
364C2×C32#48511yescharacteristic
365C24C3×D1211yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4C3×Dic612yes—
375C22×C4C3×D1211yescharacteristic
376C22×C4C2×C3×Dic312yes—
377C22×C4C22×C3×D311yescharacteristic
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C3×Dic312yes—
383C2×C8C2×C3×Dic312yes—
384C4⋊C4—32no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C22⋊C4—64no—
393C22⋊C4—122no—
394C42—64no—
395C22×C3—24no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—42no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3#88211yescharacteristic
424C22×C3#88611yescharacteristic
425C22×C3#90411yescharacteristic
426C22×C3#90411yescharacteristic
427C22×C3#90811yescharacteristic
428C22×C3#90911yescharacteristic
429C22×C3C2×C4⋊Dic311yescharacteristic
430C22×C3C2×C3×C4⋊C411yescharacteristic
431C22×C3C3×#12011yescharacteristic
432C22×C3C3×#12311yescharacteristic
433C22×C3C3×#13511yescharacteristic
434C22×C3C3×#13511yescharacteristic
435C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
436C22×C3C3×#13711yescharacteristic
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4—241no—
447C3×C4—241no—
448C3×C4#87811yescharacteristic
449C3×C4#87811yescharacteristic
450C3×C4D4×Dic311yescharacteristic
451C3×C4D4×Dic311yescharacteristic
452C3×C4C3×C4×D411yescharacteristic
453C3×C4C3×C4×D411yescharacteristic
454C3×C4C3×C22⋊Q811yescharacteristic
455C3×C4C3×C22⋊Q811yescharacteristic
456Dic3—42no—
457Dic3—42no—
458Dic3—81no—
459Dic3—81no—
460C32#185411yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23C3×C4⋊Dic312yes—
468C23C2×C3×D1211yescharacteristic
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—121no—
487C2×C4C3×C4⋊Dic312yes—
488C2×C4C2×C3×Dic611yescharacteristic
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D411yescharacteristic
491C2×C4C3×#23711yescharacteristic
492C2×C4C3×#23711yescharacteristic
493C2×C4C22×C3×Dic311yescharacteristic
494C8—22no—
495C8—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—44no—
504C2×C3—42no—
505C2×C3—42no—
506C2×C3#472311yescharacteristic
507C2×C3#473311yescharacteristic
508C2×C3#473411yescharacteristic
509C2×C3#473711yescharacteristic
510C2×C3#495011yescharacteristic
511C2×C3#510611yescharacteristic
512C2×C3#512111yescharacteristic
513C2×C3C3×#38511yescharacteristic
514C2×C3C3×#42711yescharacteristic
515C2×C3C3×#42811yescharacteristic
516C2×C3C3×#44911yescharacteristic
517C2×C3C3×#45211yescharacteristic
518C2×C3C3×#48211yescharacteristic
519C2×C3C3×#48511yescharacteristic
520C22—22no—
521C22—22no—
522C22—22no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22C3×#88211yescharacteristic
528C22C3×#88611yescharacteristic
529C22C3×#90411yescharacteristic
530C22C3×#90411yescharacteristic
531C22C3×#90811yescharacteristic
532C22C3×#90911yescharacteristic
533C22C2×C3×C4⋊Dic311yescharacteristic
534C4—22no—
535C4—122no—
536C4—122no—
537C4—241no—
538C4—241no—
539C4C3×#87811yescharacteristic
540C4C3×#87811yescharacteristic
541C4C3×D4×Dic311yescharacteristic
542C4C3×D4×Dic311yescharacteristic
543C3—21no—
544C3#6992911yescharacteristic, direct product factor
545C3C3×#185411yescharacteristic, complemented
546C2—42no—
547C2C3×#472311yescharacteristic
548C2C3×#473311yescharacteristic
549C2C3×#473411yescharacteristic
550C2C3×#473711yescharacteristic
551C2C3×#495011yescharacteristic
552C2C3×#510611yescharacteristic
553C2C3×#512111yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#1854
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#818C2semidirect
5. C2×C3×#817C2semidirect
6. C3×#4551C2semidirect
7. C3×#4551C2semidirect
9. #69929C3direct (N × H)
22. C32×C22⋊C8C4semidirect
35. C2×#818C2×C3semidirect
36. C2×#817C2×C3semidirect
39. #4551C2×C3semidirect
40. #4551C2×C3semidirect
102. C3×C22⋊C8Dic3semidirect
103. C3×C22⋊C8C3×C4semidirect
262. C22⋊C8C3×Dic3semidirect
460. C32#1854semidirect
544. C3#69929direct (N × H)
545. C3C3×#1854semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×C32×C22⋊C82
C3×#52122
C2×C3×#8182
C2×C3×#8172
C3×#45512
C3×#18543
#699293