Finite Group Databasebeta

← C3×#70280 #11794040

Subgroups — C3×#70280 #11794040

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#215C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3C3×#5229C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#70280C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
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
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#103—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#821—22no—
26C3×Dic3⋊C8—22no—
27C22×C3×SD16—31no—
28C22×#215C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#103—21no—
31C2×C3×#103D311yescharacteristic, complemented
32C2×C3×#103C2×C311yescharacteristic, complemented
33C2×C3×#102—31no—
34C3×#391—31no—
35C3×#390—31no—
36#5229C2×C311yescharacteristic, complemented
37C2×#821C2×C311yescharacteristic
38C2×Dic3⋊C8C2×C311yescharacteristic, complemented
39#4988C2×C311yescharacteristic
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×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C3×#215—28no—
67C3×(C2×D3)⋊C4—42no—
68C3×(C2×D3)⋊C4—42no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—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—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C22×C311yescharacteristic
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#215—22no—
97C2×#215—22no—
98C2×#215—22no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4×Dic3C22×C311yescharacteristic
103C22×C3⋊C8C22×C311yescharacteristic
104C3×C4⋊C8—62no—
105C3×#103—24no—
106C3×#103—22no—
107C3×#103—22no—
108C3×#102—62no—
109C3×#95—61no—
110C3×#95—61no—
111C3⋊#95—21no—
112C3⋊#95—21no—
113#821—22no—
114Dic3⋊C8—22no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C32×Q8—22no—
124C32×Q8—22no—
125C32×Q8—41no—
126C32×Q8—41no—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C32×C8—41no—
153C3×C3⋊C8—22no—
154C22×SD16—31no—
155C2×C4⋊C8—31no—
156C2×#103C3×D311yescharacteristic, complemented
157C2×#102—31no—
158#391—31no—
159#390—31no—
160#340—31no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×Q8—21no—
164C2×C3×Q8—21no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
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#6712yes—
180C2×C3×Q8C3×D412yes—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C23×C311yescharacteristic
199C22×Dic3—21no—
200C22×Dic3C3×D411yescharacteristic
201C22×Dic3C3×D411yescharacteristic
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12C3×D412yes—
208C3×SD16—68no—
209C2×C3×C8—22no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8—41no—
218C2×C3×C8—41no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—122no—
230C3×C22⋊C4—122no—
231C3×C42—61no—
232C3×C42—61no—
233#215—28no—
234(C2×D3)⋊C4—42no—
235(C2×D3)⋊C4—42no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4×Dic3—21no—
239C4×Dic3—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8C3×D412yes—
243C22×C32#12111yescharacteristic
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32C2×SD1611yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C22×C32#13711yescharacteristic
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C32×C4—42no—
258C32×C4—81no—
259C32×C4#12011yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12311yescharacteristic
262C32×C4#12411yescharacteristic
263C3×Dic3—22no—
264C3×Dic3—41no—
265C3×Dic3—81no—
266C22×Q8C2×C3×D311yescharacteristic
267C22×D4—31no—
268C2×SD16—62no—
269C2×SD16—62no—
270C2×SD16—62no—
271C22×C8—31no—
272C22×C8C2×C3×D311yescharacteristic
273C2×C4⋊C4—31no—
274C2×C4⋊C4C2×C3×D311yescharacteristic
275C2×C22⋊C4—61no—
276C2×C22⋊C4—61no—
277C2×C42—31no—
278C4⋊C8—62no—
279#103—22no—
280#102—62no—
281#95—61no—
282#95—61no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×C3×D411yescharacteristic
293C22×D3—22no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C3×Q8—24no—
301C3×Q8—22no—
302C3×Q8—22no—
303C3×Q8—22no—
304C3×Q8—22no—
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—42no—
308C3×Q8—41no—
309C3×Q8—41no—
310C3×Q8—41no—
311C3×Q8—41no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—121no—
315C3×D4—121no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—42no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—81no—
345C2×C3×C4—81no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×C3×D411yescharacteristic
356C2×C3×C4C2×C3×D411yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C3×#4111yescharacteristic
359C2×C3×C4C3×#4111yescharacteristic
360C2×C3×C4C3×#4111yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3C3×SD1612yescomplemented
370D12—22no—
371D12—22no—
372D12—41no—
373D12—41no—
374C3×C8—42no—
375C3×C8—41no—
376C3×C8—41no—
377C3×C8—62no—
378C3⋊C8—22no—
379C2×C32#39411yescharacteristic
380C2×C32#46011yescharacteristic
381C2×C32#46111yescharacteristic
382C2×C32#46311yescharacteristic
383C2×C32#46411yescharacteristic
384C2×C32#46511yescharacteristic
385C2×C32#46811yescharacteristic
386C3×D3—82no—
387C24—61no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8C3×#6712yes—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—61no—
405C22×C4C22×C3×D311yescharacteristic
406SD16—68no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—32no—
411C2×C8—61no—
412C2×C8—61no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C22⋊C4—122no—
418C22⋊C4—122no—
419C42—61no—
420C42—61no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3—241no—
434C22×C3—241no—
435C22×C3#88411yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3D3×SD1611yescharacteristic
438C22×C3#91411yescharacteristic
439C22×C3#91811yescharacteristic
440C22×C3#91911yescharacteristic
441C22×C3#93911yescharacteristic
442C22×C3C3×#12111yescharacteristic
443C22×C3C3×#12111yescharacteristic
444C22×C3C3×#12111yescharacteristic
445C22×C3C2×C3×SD1611yescharacteristic
446C22×C3C3×#13511yescharacteristic
447C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
448C22×C3C3×#13711yescharacteristic
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—81no—
455C2×D3—81no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—44no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—62no—
464C3×C4—82no—
465C3×C4—81no—
466C3×C4—81no—
467C3×C4—121no—
468C3×C4—241no—
469C3×C4#88311yescharacteristic
470C3×C4#88511yescharacteristic
471C3×C4#92911yescharacteristic
472C3×C4#93711yescharacteristic
473C3×C4C3×#12011yescharacteristic
474C3×C4C3×#12311yescharacteristic
475C3×C4C3×#12311yescharacteristic
476C3×C4C3×#12411yescharacteristic
477Dic3—22no—
478Dic3—41no—
479Dic3—81no—
480C32#205511yescharacteristic, complemented, Sylow
481C23—62no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23C3×D3×D411yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493D4—62no—
494D4—62no—
495D4—121no—
496D4—121no—
497C2×C4—22no—
498C2×C4—32no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4C3×#23511yescharacteristic
513C2×C4C3×#23511yescharacteristic
514C2×C4C3×D3×D411yescharacteristic
515C2×C4C3×D3×D411yescharacteristic
516C2×C4C3×#23711yescharacteristic
517C2×C4C2×C3×#6711yescharacteristic
518C8—41no—
519C8—62no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—242no—
528C2×C3#480711yescharacteristic
529C2×C3#481211yescharacteristic
530C2×C3#481811yescharacteristic
531C2×C3#481911yescharacteristic
532C2×C3#495911yescharacteristic
533C2×C3#516311yescharacteristic
534C2×C3#518511yescharacteristic
535C2×C3C3×#39411yescharacteristic
536C2×C3C3×#46011yescharacteristic
537C2×C3C3×#46111yescharacteristic
538C2×C3C3×#46311yescharacteristic
539C2×C3C3×#46411yescharacteristic
540C2×C3C3×#46511yescharacteristic
541C2×C3C3×#46811yescharacteristic
542D3—82no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—241no—
547C22—241no—
548C22—241no—
549C22—241no—
550C22C3×#88411yescharacteristic
551C22C3×#88411yescharacteristic
552C22C3×D3×SD1611yescharacteristic
553C22C3×#91411yescharacteristic
554C22C3×#91811yescharacteristic
555C22C3×#91911yescharacteristic
556C22C3×#93911yescharacteristic
557C4—42no—
558C4—62no—
559C4—81no—
560C4—121no—
561C4—241no—
562C4C3×#88311yescharacteristic
563C4C3×#88511yescharacteristic
564C4C3×#92911yescharacteristic
565C4C3×#93711yescharacteristic
566C3—21no—
567C3#7028011yescharacteristic, direct product factor
568C3C3×#205511yescharacteristic, complemented
569C2—242no—
570C2C3×#480711yescharacteristic
571C2C3×#481211yescharacteristic
572C2C3×#481811yescharacteristic
573C2C3×#481911yescharacteristic
574C2C3×#495911yescharacteristic
575C2C3×#516311yescharacteristic
576C2C3×#518511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×#103D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. C3×#5229C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
7. C3×#4529C2semidirect
9. #70280C3direct (N × H)
31. C2×C3×#103D3semidirect
32. C2×C3×#103C2×C3semidirect
36. #5229C2×C3semidirect
38. C2×Dic3⋊C8C2×C3semidirect
41. #4529C2×C3semidirect
147. C2×C3×Dic3SD16semidirect
156. C2×#103C3×D3semidirect
369. C2×Dic3C3×SD16semidirect
480. C32#2055semidirect
567. C3#70280direct (N × H)
568. 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
C2×C32×#1032
C3×#52292
C2×C3×#8212
C2×C3×Dic3⋊C82
C3×#49882
C3×#45292
C3×#20553
#702803