Finite Group Databasebeta

← C3×#69680 #11794043

Subgroups — C3×#69680 #11794043

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C3×#4939C211yesmaximal, characteristic
6C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#69680C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C3×#215—22no—
15C2×C3×#215—22no—
16C2×C3×#215—22no—
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#95—21no—
23C32×#95—21no—
24C3×#835—22no—
25C3×#809—22no—
26C3×C4⋊(C3⋊C8)—22no—
27C22×C3×SD16—31no—
28C22×#215C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#103—31no—
31C2×C3×#102—31no—
32C3×#391—21no—
33C3×#391D311yescharacteristic, complemented
34C3×#391C2×C311yescharacteristic, complemented
35C3×#390—31no—
36C2×#835C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic
38#4939C2×C311yescharacteristic
39C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—21no—
48C2×C32×Q8D412yes—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C32×C42—21no—
64C32×C42—21no—
65C3×#215—28no—
66C3×(C2×D3)⋊C4—42no—
67C3×(C2×D3)⋊C4—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76#2055—31noSylow
77C22×C3×Q8—21no—
78C22×C3×Q8C2×D311yescharacteristic
79C22×C3×Q8C22×C311yescharacteristic
80C22×C3×D4—31no—
81C22×D12C22×C311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C22×C311yescharacteristic
91C2×C3×C22⋊C4—61no—
92C2×C3×C22⋊C4—61no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C22×C311yescharacteristic
96C2×#215—22no—
97C2×#215—22no—
98C2×#215—22no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C22×C3⋊C8C22×C311yescharacteristic
103C22×C3⋊C8C22×C311yescharacteristic
104C3×C4⋊C8—62no—
105C3×#103—62no—
106C3×#102—62no—
107C3×#95—22no—
108C3×#95—22no—
109C3×#95—21no—
110C3×#95—21no—
111C3×#95—21no—
112C3×#95—21no—
113#835—22no—
114#809—22no—
115C4⋊(C3⋊C8)—22no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C32×Q8—22no—
125C32×Q8—22no—
126C32×Q8—41no—
127C32×Q8—41no—
128C2×C32×C4—22no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—41no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4SD1612yescomplemented
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—41no—
152C3×D12—41no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—41no—
155C22×SD16—31no—
156C2×C4⋊C8—31no—
157C2×#103—31no—
158C2×#102—31no—
159#391C3×D311yescharacteristic, complemented
160#390—31no—
161#340—31no—
162C24×C3—61no—
163C23×D3—21no—
164C2×C3×Q8—22no—
165C2×C3×Q8—21no—
166C2×C3×Q8—21no—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—22no—
176C2×C3×Q8—41no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8—41no—
180C2×C3×Q8D1212yes—
181C2×C3×Q8C3×D412yes—
182C2×C3×D4—32no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—22no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—61no—
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4C3×D411yescharacteristic
201C22×C3×C4C3×D411yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C23×C311yescharacteristic
204C22×Dic3—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12C3×D412yes—
211C3×SD16—68no—
212C2×C3×C8—32no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—122no—
227C3×C22⋊C4—122no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—41no—
233C3×C42—41no—
234#215—28no—
235(C2×D3)⋊C4—42no—
236(C2×D3)⋊C4—42no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8C3×D412yes—
245C22×C32#12111yescharacteristic
246C22×C32#12111yescharacteristic
247C22×C32#12111yescharacteristic
248C22×C32C2×SD1611yescharacteristic
249C22×C32#13511yescharacteristic
250C22×C32AGL(1,ℤ/8)11yescharacteristic
251C22×C32#13711yescharacteristic
252C2×C3×D3—42no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C32×C4—22no—
260C32×C4—42no—
261C32×C4—41no—
262C32×C4—81no—
263C32×C4#12011yescharacteristic
264C32×C4#12311yescharacteristic
265C32×C4#12311yescharacteristic
266C32×C4#12411yescharacteristic
267C3×Dic3—81no—
268C22×Q8C2×C3×D311yescharacteristic
269C22×D4—31no—
270C2×SD16—62no—
271C2×SD16—62no—
272C2×SD16—62no—
273C22×C8—31no—
274C22×C8—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4C2×C3×D311yescharacteristic
277C2×C22⋊C4—61no—
278C2×C22⋊C4—61no—
279C2×C42C2×C3×D311yescharacteristic
280C4⋊C8—62no—
281#103—62no—
282#102—62no—
283#95—21no—
284#95—21no—
285C23×C3—21no—
286C23×C3—62no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3C2×#6711yescharacteristic
294C23×C3C2×C3×D411yescharacteristic
295C22×D3—22no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—22no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—42no—
309C3×Q8—42no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×Q8—41no—
313C3×Q8—41no—
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—121no—
317C3×D4—121no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
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—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—41no—
357C2×C3×C4—41no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4#21512yescomplemented
362C2×C3×C4C3×SD1612yescomplemented
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4#23511yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4#23711yescharacteristic
368C2×C3×C4#23711yescharacteristic
369C2×C3×C4C2×C3×D411yescharacteristic
370C2×C3×C4C2×C3×D411yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C3×#4111yescharacteristic
373C2×C3×C4C3×#4111yescharacteristic
374C2×C3×C4C3×#4111yescharacteristic
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—41no—
378D12—22no—
379D12—22no—
380D12—41no—
381D12—41no—
382C3×C8—62no—
383C3×C8—121no—
384C3⋊C8—22no—
385C3⋊C8—41no—
386C2×C32#39411yescharacteristic
387C2×C32#46011yescharacteristic
388C2×C32#46111yescharacteristic
389C2×C32#46311yescharacteristic
390C2×C32#46411yescharacteristic
391C2×C32#46511yescharacteristic
392C2×C32#46811yescharacteristic
393C3×D3—82no—
394C24—61no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8C3×D1212yes—
401C2×D4—32no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—61no—
410C22×C4C3×#6711yescharacteristic
411C22×C4C3×#6711yescharacteristic
412C22×C4C22×C3×D311yescharacteristic
413SD16—68no—
414C2×C8—32no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C22⋊C4—122no—
425C22⋊C4—122no—
426C42—21no—
427C42—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—241no—
439C22×C3—241no—
440C22×C3—241no—
441C22×C3—241no—
442C22×C3#93011yescharacteristic
443C22×C3#93811yescharacteristic
444C22×C3#93911yescharacteristic
445C22×C3C2×#21511yescharacteristic
446C22×C3#94211yescharacteristic
447C22×C3#94911yescharacteristic
448C22×C3#95011yescharacteristic
449C22×C3C3×#12111yescharacteristic
450C22×C3C3×#12111yescharacteristic
451C22×C3C3×#12111yescharacteristic
452C22×C3C2×C3×SD1611yescharacteristic
453C22×C3C3×#13511yescharacteristic
454C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
455C22×C3C3×#13711yescharacteristic
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—42no—
459C2×D3—81no—
460C2×D3—81no—
461C2×D3—81no—
462C2×D3—81no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—42no—
470C3×C4—44no—
471C3×C4—42no—
472C3×C4—42no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—82no—
477C3×C4—81no—
478C3×C4—81no—
479C3×C4—241no—
480C3×C4#88211yescharacteristic
481C3×C4#88311yescharacteristic
482C3×C4#88511yescharacteristic
483C3×C4#88611yescharacteristic
484C3×C4C3×#12011yescharacteristic
485C3×C4C3×#12311yescharacteristic
486C3×C4C3×#12311yescharacteristic
487C3×C4C3×#12411yescharacteristic
488Dic3—81no—
489C32#205511yescharacteristic, complemented, Sylow
490C23—62no—
491C23—121no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23C2×C3×#6711yescharacteristic
498Q8—22no—
499Q8—22no—
500Q8—41no—
501Q8—41no—
502D4—62no—
503D4—62no—
504D4—121no—
505D4—121no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4C3×#21512yescomplemented
521C2×C4C2×C3×D1211yescharacteristic
522C2×C4C3×#23511yescharacteristic
523C2×C4C3×D3×D411yescharacteristic
524C2×C4C3×D3×D411yescharacteristic
525C2×C4C3×#23711yescharacteristic
526C2×C4C3×#23711yescharacteristic
527C8—62no—
528C8—121no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—242no—
537C2×C3#496111yescharacteristic
538C2×C3#502711yescharacteristic
539C2×C3#502811yescharacteristic
540C2×C3#504811yescharacteristic
541C2×C3#504911yescharacteristic
542C2×C3#505711yescharacteristic
543C2×C3#508311yescharacteristic
544C2×C3C3×#39411yescharacteristic
545C2×C3C3×#46011yescharacteristic
546C2×C3C3×#46111yescharacteristic
547C2×C3C3×#46311yescharacteristic
548C2×C3C3×#46411yescharacteristic
549C2×C3C3×#46511yescharacteristic
550C2×C3C3×#46811yescharacteristic
551D3—82no—
552C22—122no—
553C22—122no—
554C22—122no—
555C22—241no—
556C22—241no—
557C22—241no—
558C22—241no—
559C22C3×#93011yescharacteristic
560C22C3×#93811yescharacteristic
561C22C3×#93911yescharacteristic
562C22C2×C3×#21511yescharacteristic
563C22C3×#94211yescharacteristic
564C22C3×#94911yescharacteristic
565C22C3×#95011yescharacteristic
566C4—22no—
567C4—42no—
568C4—41no—
569C4—81no—
570C4—241no—
571C4C3×#88211yescharacteristic
572C4C3×#88311yescharacteristic
573C4C3×#88511yescharacteristic
574C4C3×#88611yescharacteristic
575C3—21no—
576C3#6968011yescharacteristic, direct product factor
577C3C3×#205511yescharacteristic, complemented
578C2—242no—
579C2C3×#496111yescharacteristic
580C2C3×#502711yescharacteristic
581C2C3×#502811yescharacteristic
582C2C3×#504811yescharacteristic
583C2C3×#504911yescharacteristic
584C2C3×#505711yescharacteristic
585C2C3×#508311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#391C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC3×#391D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
2. C32×#391C2semidirect
3. C2×C3×#835C2semidirect
6. C2×C3×C4⋊(C3⋊C8)C2semidirect
7. C3×#4529C2semidirect
9. #69680C3direct (N × H)
33. C3×#391D3semidirect
34. C3×#391C2×C3semidirect
36. C2×#835C2×C3semidirect
39. C2×C4⋊(C3⋊C8)C2×C3semidirect
41. #4529C2×C3semidirect
139. C2×C32×C4SD16semidirect
159. #391C3×D3semidirect
361. C2×C3×C4#215semidirect
362. C2×C3×C4C3×SD16semidirect
489. C32#2055semidirect
520. C2×C4C3×#215semidirect
576. C3#69680direct (N × H)
577. C3C3×#2055semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2152
C32×#3912
C2×C3×#8352
C2×C3×#8092
C3×#49392
C2×C3×C4⋊(C3⋊C8)2
C3×#45292
C3×#20553
#696803