Finite Group Databasebeta

← C3×#80438 #11882225

Subgroups — C3×#80438 #11882225

Order 1152.

844 conjugacy classes of subgroups.

The subgroup lattice has 615 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5548C211yesmaximal, characteristic
3C32×#461C211yesmaximal, characteristic, complemented
4C3×#5171C212yesmaximal, complemented
5C3×#5163C212yesmaximal, complemented
6C3×#5083C211yesmaximal, characteristic, complemented
7C3×#5008C211yesmaximal, characteristic, complemented
8C3×#4842C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4807C212yesmaximal, complemented
11C3×#4791C212yesmaximal, complemented
12C3×#3246—31nomaximal
13#80438C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C2×C32×SD16C2212yes—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#946C2212yes—
19C3×Q8×Dic3C2212yes—
20C2×C3×#215C2212yes—
21C3×#940C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C3×C4×#67—21no—
24C2×C3×D3×C8C2212yes—
25C3×#897—21no—
26C3×#895C2211yescharacteristic
27C3×#892—21no—
28C3×#890—21no—
29C3×#888C2211yescharacteristic
30C3×#887—21no—
31C3×#885—21no—
32C3×#884—21no—
33C3×C4×D12C2211yescharacteristic
34C3×C42×D3C2211yescharacteristic
35C3×#869C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×#103C2212yes—
38C3×#835C2212yes—
39C3×#832C2212yes—
40C3×#821C2212yes—
41C3×#817C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C3×#532—31no—
47#5728C2×C311yescharacteristic, complemented
48#5548C2×C311yescharacteristic
49C3×#476—31no—
50C3×#476—31no—
51C3×#475—32no—
52C3×#465—32no—
53C3×#465—32no—
54C3×#461—21no—
55C3×#461—31no—
56C3×#461D311yescharacteristic, complemented
57C3×#461C2×C311yescharacteristic, complemented
58C3×#460—32no—
59C2×C3×C4⋊C8—31no—
60#5171C2×C312yescomplemented
61#5163C2×C312yescomplemented
62#5083C2×C311yescharacteristic, complemented
63#5008C2×C311yescharacteristic, complemented
64#4842C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4807C2×C312yescomplemented
67#4791C2×C312yescomplemented
68C2×C32×Q8C2312yes—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C3×#235—44no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6—21no—
83C32×SD16—42no—
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2311yescharacteristic
88C32×C22⋊C4—21no—
89C32×C42C2311yescharacteristic
90C3×#217—21no—
91C3×#215—42no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—22no—
101C3×C4×Dic3—22no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D3×C8—42no—
107#3246—31noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C2×C3×SD16—22no—
111C2×C3×SD16—32no—
112C2×C3×SD16C2×D312yes—
113C2×C3×SD16C22×C312yes—
114C22×C3×C8—32no—
115C3×C4⋊Q8—21no—
116C3×C4⋊Q8—31no—
117C3×C4⋊Q8—31no—
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4⋊Q8C22×C311yescharacteristic
120C3×#127—31no—
121C3×#125—61no—
122C3×#124—61no—
123C3×C22⋊Q8—32no—
124C3×C22⋊Q8—61no—
125C3×#121—31no—
126C3×#121—31no—
127C3×#121—61no—
128C3×C4×Q8—32no—
129C3×C4×Q8—61no—
130C3×C4×D4—21no—
131C3×C4×D4—31no—
132C3×C4×D4—61no—
133C3×C4×D4C2×D311yescharacteristic
134C3×C4×D4C22×C311yescharacteristic
135C3×#117—61no—
136C2×C3×C42—31no—
137#946C22×C312yes—
138Q8×Dic3C22×C312yes—
139C2×#215C22×C312yes—
140#940C22×C311yescharacteristic
141#938C22×C311yescharacteristic
142C4×#67—21no—
143C2×D3×C8C22×C312yes—
144#897—21no—
145#895C22×C311yescharacteristic
146#892—21no—
147#890—21no—
148#888C22×C311yescharacteristic
149#887—21no—
150#885—21no—
151#884—21no—
152C4×D12C22×C311yescharacteristic
153C42×D3C22×C311yescharacteristic
154#869C22×C311yescharacteristic
155C3×#106—32no—
156C3×#106—32no—
157C3×C4⋊C8—21no—
158C3×C4⋊C8—32no—
159C3×C4⋊C8—31no—
160C3×C4⋊C8C2×D311yescharacteristic
161C3×C4⋊C8C22×C311yescharacteristic
162C3×#103—22no—
163C3×#103—32no—
164C3×#103C2×D312yes—
165C3×#103C22×C312yes—
166C3×#102—32no—
167C3×#102—32no—
168#835C22×C312yes—
169#832C22×C312yes—
170#821C22×C312yes—
171#817C22×C312yes—
172Dic3⋊C8C22×C312yes—
173#808C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C23×C32—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—22no—
179C32×Q8—22no—
180C32×D4—21no—
181C32×D4—21no—
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—42no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C3×#67—42no—
189C3×#67—42no—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C3×D12—21no—
197C3×D12—21no—
198C3×D12—42no—
199C3×C4×D3—21no—
200C3×C4×D3—21no—
201C3×C4×D3—41no—
202C3×C4×D3—42no—
203C3×C4×D3SD1614yescomplemented
204C3×Dic6—42no—
205C3×Dic6—42no—
206C32×C8—22no—
207C3×C3⋊C8—22no—
208#533—31no—
209#532—31no—
210#476—31no—
211#476—31no—
212#475—32no—
213#465—32no—
214#465—32no—
215#461—31no—
216#461C3×D311yescharacteristic, complemented
217#460—32no—
218C2×C4⋊C8—31no—
219C3×#41—124no—
220C2×C3×Q8—22no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8C22×D312yes—
224C2×C3×Q8C23×C312yes—
225C2×C3×D4—21no—
226C2×C3×D4—31no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C23×C311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—41no—
239C22×C3×C4—61no—
240C2×#67—21no—
241C2×#67—21no—
242C2×#67—21no—
243#235—44no—
244C2×D12—21no—
245C2×D12C23×C311yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C3×D411yescharacteristic
249C2×C4×D3C23×C311yescharacteristic
250C2×Dic6—21no—
251C2×Dic6—21no—
252C3×SD16—42no—
253C3×SD16—42no—
254C3×SD16—44no—
255C3×SD16—122no—
256C2×C3×C8—22no—
257C2×C3×C8—32no—
258C2×C3×C8—122no—
259C2×C3×C8C22×D312yes—
260C2×C3×C8C23×C312yes—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—41no—
269C3×C4⋊C4—41no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—62no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C4⋊C4C23×C311yescharacteristic
276C3×C22⋊C4—21no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—41no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—62no—
281C3×C22⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C42—21no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—62no—
288C3×C42C22×D311yescharacteristic
289C3×C42C23×C311yescharacteristic
290#217—21no—
291#215—42no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—22no—
297C4⋊Dic3C23×C312yes—
298C4⋊Dic3C23×C311yescharacteristic
299Dic3⋊C4—21no—
300Dic3⋊C4—22no—
301C4×Dic3—22no—
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C3×D411yescharacteristic
304C4×Dic3C23×C311yescharacteristic
305C2×C3⋊C8C23×C312yes—
306D3×C8—42no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—21no—
312C2×C3×D3—21no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3C2×SD1612yes—
317C32×C4—21no—
318C32×C4—42no—
319C32×C4—41no—
320C32×C4C2×SD1612yes—
321C32×C4H(5,𝔽2)11yescharacteristic
322C32×C42−1+411yescharacteristic
323C3×Dic3—21no—
324C3×Dic3—21no—
325C3×Dic3—41no—
326C3×Dic3—42no—
327C3×Dic3C2×SD1612yes—
328C2×#41—61no—
329C2×SD16—32no—
330C2×SD16C2×C3×D312yes—
331C22×C8—32no—
332C4⋊Q8—31no—
333C4⋊Q8—31no—
334C4⋊Q8C2×C3×D311yescharacteristic
335#127—31no—
336#125—61no—
337#124—61no—
338C22⋊Q8—32no—
339C22⋊Q8—61no—
340#121—31no—
341#121—31no—
342#121—61no—
343C4×Q8—32no—
344C4×Q8—61no—
345C4×D4—31no—
346C4×D4—61no—
347C4×D4C2×C3×D311yescharacteristic
348#117—61no—
349C2×C42—31no—
350#106—32no—
351#106—32no—
352C4⋊C8—32no—
353C4⋊C8—31no—
354C4⋊C8C2×C3×D311yescharacteristic
355#103—32no—
356#103C2×C3×D312yes—
357#102—32no—
358#102—32no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—31no—
362C23×C3—41no—
363C23×C3—61no—
364C22×D3—21no—
365C22×D3C2×C3×D411yescharacteristic
366C3×Q8—22no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—22no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—122no—
373C3×Q8—122no—
374C3×D4—22no—
375C3×D4—21no—
376C3×D4—21no—
377C3×D4—21no—
378C3×D4—21no—
379C3×D4—41no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—122no—
383C3×D4—122no—
384C3×D4—122no—
385C3×D4—122no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—31no—
394C2×C3×C4—34no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—61no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—61no—
405C2×C3×C4—82no—
406C2×C3×C4—121no—
407C2×C3×C4—122no—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4C2×C3×D411yescharacteristic
411C2×C3×C4C2×C3×D411yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C24×C311yescharacteristic
414#67—42no—
415#67—42no—
416#67—42no—
417C2×Dic3—22no—
418C2×Dic3—21no—
419C2×Dic3C2×C3×D411yescharacteristic
420C2×Dic3C2×C3×D411yescharacteristic
421C2×Dic3C2×C3×D411yescharacteristic
422D12—21no—
423D12—21no—
424D12—42no—
425C4×D3—21no—
426C4×D3—21no—
427C4×D3—41no—
428C4×D3—42no—
429C4×D3C3×SD1614yescomplemented
430Dic6—42no—
431Dic6—42no—
432C3×C8—22no—
433C3×C8—22no—
434C3×C8—42no—
435C3×C8—62no—
436C3⋊C8—22no—
437C2×C32—81no—
438C2×C32#53711yescharacteristic
439C2×C32C22×SD1611yescharacteristic
440C2×C32#57511yescharacteristic
441C3×D3—22no—
442C3×D3—81no—
443#41—124no—
444C2×Q8—61no—
445C2×Q8—61no—
446C2×Q8C22×C3×D312yes—
447C2×D4—31no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4C22×C3×D311yescharacteristic
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—61no—
458SD16—42no—
459SD16—122no—
460C2×C8—32no—
461C2×C8—122no—
462C2×C8C22×C3×D312yes—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—32no—
466C4⋊C4—31no—
467C4⋊C4—61no—
468C4⋊C4—62no—
469C4⋊C4—62no—
470C4⋊C4—61no—
471C4⋊C4C22×C3×D311yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—61no—
474C22⋊C4—62no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—62no—
481C42C22×C3×D311yescharacteristic
482C22×C3—21no—
483C22×C3—32no—
484C22×C3—42no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—81no—
494C22×C3—81no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C22×C3×D411yescharacteristic
500C2×D3—21no—
501C2×D3—21no—
502C2×D3—41no—
503C2×D3—41no—
504C2×D3—41no—
505C2×D3C2×C3×SD1612yes—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—22no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—32no—
512C3×C4—41no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—61no—
518C3×C4—61no—
519C3×C4—81no—
520C3×C4—82no—
521C3×C4—121no—
522C3×C4—122no—
523C3×C4D3×SD1612yes—
524C3×C4C2×C3×SD1612yes—
525C3×C4#100411yescharacteristic
526C3×C4#101011yescharacteristic
527C3×C4C3×H(5,𝔽2)11yescharacteristic
528C3×C4C3×2−1+411yescharacteristic
529Dic3—21no—
530Dic3—21no—
531Dic3—41no—
532Dic3—42no—
533Dic3C2×C3×SD1612yes—
534C32#324611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—31no—
537C23—61no—
538Q8—22no—
539Q8—22no—
540Q8—122no—
541Q8—122no—
542D4—21no—
543D4—21no—
544D4—61no—
545D4—61no—
546D4—122no—
547D4—122no—
548D4—122no—
549D4—122no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—31no—
553C2×C4—34no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—42no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—61no—
561C2×C4—121no—
562C2×C4—122no—
563C2×C4C3×D3×D411yescharacteristic
564C2×C4C3×D3×D411yescharacteristic
565C2×C4C23×C3×D311yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—62no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—81no—
575C2×C3—241no—
576C2×C3#560811yescharacteristic
577C2×C3C2×D3×SD1611yescharacteristic
578C2×C3#577711yescharacteristic
579C2×C3C3×#53711yescharacteristic
580C2×C3C22×C3×SD1611yescharacteristic
581C2×C3C3×#57511yescharacteristic
582D3—22no—
583D3—81no—
584C22—32no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—61no—
589C22—61no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22C2×C3×D3×D411yescharacteristic
594C4—21no—
595C4—32no—
596C4—41no—
597C4—42no—
598C4—61no—
599C4—61no—
600C4—121no—
601C4—122no—
602C4C3×D3×SD1612yes—
603C4C3×#100411yescharacteristic
604C4C3×#101011yescharacteristic
605C3—21no—
606C3#8043811yescharacteristic, direct product factor
607C3C3×#324611yescharacteristic, complemented
608C2—62no—
609C2—81no—
610C2—241no—
611C2C3×#560811yescharacteristic
612C2C2×C3×D3×SD1611yescharacteristic
613C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#461C2
socleC22×C32C22×D4
prime radicalC3×#5548C2
hypercenterC3×#461D3
hypocenterC3C3×#3246
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#461

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#461C2semidirect
4. C3×#5171C2semidirect
5. C3×#5163C2semidirect
6. C3×#5083C2semidirect
7. C3×#5008C2semidirect
8. C3×#4842C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4807C2semidirect
11. C3×#4791C2semidirect
13. #80438C3direct (N × H)
47. #5728C2×C3semidirect
56. C3×#461D3semidirect
57. C3×#461C2×C3semidirect
60. #5171C2×C3semidirect
61. #5163C2×C3semidirect
62. #5083C2×C3semidirect
63. #5008C2×C3semidirect
64. #4842C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
66. #4807C2×C3semidirect
67. #4791C2×C3semidirect
203. C3×C4×D3SD16semidirect
216. #461C3×D3semidirect
429. C4×D3C3×SD16semidirect
534. C32#3246semidirect
606. C3#80438direct (N × H)
607. C3C3×#3246semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#55482
C32×#4612
C3×#51712
C3×#51632
C3×#50832
C3×#50082
C3×#48422
C3×D3×C4⋊C82
C3×#48072
C3×#47912
C3×#32463
#804383