Finite Group Databasebeta

← C3×#83413 #11878405

Subgroups — C3×#83413 #11878405

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#536C211yesmaximal, characteristic
2C3×#5825C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4C3×#5228C212yesmaximal, complemented
5C3×#5052C212yesmaximal, complemented
6C3×#5051C212yesmaximal, complemented
7C3×#5050C212yesmaximal, complemented
8C3×#5045C212yesmaximal, complemented
9C3×#4996C212yesmaximal, complemented
10C3×#3202—31nomaximal
11#83413C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×C4⋊Q8—21no—
16C32×#124—21no—
17C32×#123—21no—
18C32×#123—21no—
19C32×C22⋊Q8C2212yes—
20C32×C22⋊Q8C2212yes—
21C32×#117C2211yescharacteristic
22C3×#944—21no—
23C2×C3×#216C2212yes—
24C2×C3×#216C2212yes—
25C3×#936—21no—
26C3×#935—21no—
27C3×#935—21no—
28C3×#926C2211yescharacteristic
29C3×#924C2212yes—
30C3×#924C2212yes—
31C2×C3×#208C2211yescharacteristic
32C22×C3×C3⋊C8C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×#830C2212yes—
36C3×#830C2212yes—
37C3×#810C2212yes—
38C3×#810C2212yes—
39C3×#808C2212yes—
40C3×#807C2212yes—
41C3×#536—21no—
42C3×#536—31no—
43C3×#536D311yescharacteristic
44C3×#536C2×C311yescharacteristic
45#5825C2×C311yescharacteristic
46C3×#485—32no—
47C3×#485—32no—
48C3×#470—32no—
49C3×#467—32no—
50C3×#451—32no—
51C3×#451—32no—
52C3×#408—31no—
53#5234C2×C311yescharacteristic
54#5228C2×C312yescomplemented
55#5052C2×C312yescomplemented
56#5051C2×C312yescomplemented
57#5050C2×C312yescomplemented
58#5045C2×C312yescomplemented
59#4996C2×C312yescomplemented
60C32×#41—41no—
61C32×#41—41no—
62C2×C32×Q8—21no—
63C2×C32×Q8—41no—
64C2×C32×Q8—41no—
65C2×C32×Q8D411yescharacteristic
66C2×C32×Q8C2312yes—
67C2×C32×D4D411yescharacteristic
68C2×C32×D4D411yescharacteristic
69C2×C32×D4D411yescharacteristic
70C22×C32×C4—21no—
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C3×Dic3—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—41no—
77C2×C3×Dic6—41no—
78C2×C3×Dic6C2312yes—
79C32×C4⋊C4—22no—
80C32×C4⋊C4—22no—
81C32×C4⋊C4C2312yes—
82C32×C22⋊C4—21no—
83C32×C22⋊C4—22no—
84C32×C22⋊C4—22no—
85C32×C42—21no—
86C3×#217—22no—
87C3×#217—22no—
88C3×#217—21no—
89C3×#216—42no—
90C3×#216—42no—
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×#208—41no—
96C2×C3×C3⋊C8—41no—
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3202—31noSylow
100C2×C3×#41—21no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C22×C311yescharacteristic
103C22×C3×Q8—21no—
104C22×C3×Q8—31no—
105C22×C3×Q8C2×D311yescharacteristic
106C22×C3×Q8C22×C311yescharacteristic
107C22×Dic6C22×C311yescharacteristic
108C2×C3×Q16—32no—
109C2×C3×Q16—32no—
110C2×C3×M16—31no—
111C22×C3×C8—31no—
112C3×C4⋊Q8—22no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8—61no—
116C3×#124—22no—
117C3×#124—21no—
118C3×#124—21no—
119C3×#124—61no—
120C3×#123—22no—
121C3×#123—22no—
122C3×#123—21no—
123C3×#123—21no—
124C3×#123—21no—
125C3×#123—21no—
126C3×#123—61no—
127C3×#123—61no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—32no—
131C3×C22⋊Q8—32no—
132C3×C22⋊Q8C2×D312yes—
133C3×C22⋊Q8C2×D312yes—
134C3×C22⋊Q8C22×C312yes—
135C3×C22⋊Q8C22×C312yes—
136C3×#117—21no—
137C3×#117—31no—
138C3×#117C2×D311yescharacteristic
139C3×#117C22×C311yescharacteristic
140#944—21no—
141C2×#216C22×C312yes—
142C2×#216C22×C312yes—
143#936—21no—
144#935—21no—
145#935—21no—
146#926C22×C311yescharacteristic
147#924C22×C312yes—
148#924C22×C312yes—
149C2×#208C22×C311yescharacteristic
150C22×C3⋊C8C22×C311yescharacteristic
151C3×#107—32no—
152C3×#106—32no—
153C3×#103—32no—
154C3×#103—32no—
155C3×#103—32no—
156C3×#103—32no—
157C3×C22⋊C8—32no—
158C3×C22⋊C8—32no—
159#835C22×C312yes—
160#835C22×C312yes—
161#830C22×C312yes—
162#830C22×C312yes—
163#810C22×C312yes—
164#810C22×C312yes—
165#808C22×C312yes—
166#807C22×C312yes—
167C23×C32C2×D411yescharacteristic
168C23×C32C2×D411yescharacteristic
169C23×C32C2×D411yescharacteristic
170C32×Q8—22no—
171C32×Q8—22no—
172C32×Q8—41no—
173C32×Q8—42no—
174C32×D4—41no—
175C32×D4—41no—
176C32×D4—41no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—42no—
193C3×Dic6—22no—
194C3×Dic6—22no—
195C3×Dic6—42no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8—22no—
198#536—31no—
199#536C3×D311yescharacteristic
200#485—32no—
201#485—32no—
202#470—32no—
203#467—32no—
204#451—32no—
205#451—32no—
206#408—31no—
207C3×#41—41no—
208C3×#41—41no—
209C3×#41—41no—
210C3×#41—41no—
211C3×#41—42no—
212C3×#41—42no—
213C2×C3×Q8—22no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—22no—
218C2×C3×Q8—32no—
219C2×C3×Q8—41no—
220C2×C3×Q8—41no—
221C2×C3×Q8—41no—
222C2×C3×Q8—41no—
223C2×C3×Q8—42no—
224C2×C3×Q8—42no—
225C2×C3×Q8—61no—
226C2×C3×Q8—121no—
227C2×C3×Q8—121no—
228C2×C3×Q8#6711yescharacteristic
229C2×C3×Q8C3×D411yescharacteristic
230C2×C3×Q8C22×D312yes—
231C2×C3×Q8C23×C312yes—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4#6711yescharacteristic
236C2×C3×D4#6711yescharacteristic
237C2×C3×D4#6711yescharacteristic
238C2×C3×D4C3×D411yescharacteristic
239C2×C3×D4C3×D411yescharacteristic
240C2×C3×D4C3×D411yescharacteristic
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—61no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C23×C311yescharacteristic
252C22×C3×C4C23×C311yescharacteristic
253C22×C3×C4C23×C311yescharacteristic
254C22×Dic3—21no—
255C2×Dic6—21no—
256C2×Dic6—41no—
257C2×Dic6—41no—
258C2×Dic6C23×C312yes—
259C3×Q16—122no—
260C3×Q16—122no—
261C3×M16—121no—
262C2×C3×C8—32no—
263C2×C3×C8—32no—
264C2×C3×C8—121no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—32no—
273C3×C4⋊C4—62no—
274C3×C4⋊C4—62no—
275C3×C4⋊C4C22×D312yes—
276C3×C4⋊C4C23×C312yes—
277C3×C22⋊C4—22no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—21no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—22no—
285C3×C22⋊C4—22no—
286C3×C22⋊C4—61no—
287C3×C22⋊C4—62no—
288C3×C22⋊C4—62no—
289C3×C42—22no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—61no—
293#217—22no—
294#217—22no—
295#217—21no—
296#216—42no—
297#216—42no—
298C4⋊Dic3C23×C312yes—
299Dic3⋊C4—22no—
300Dic3⋊C4—22no—
301C4×Dic3—21no—
302#208—41no—
303C2×C3⋊C8—41no—
304C2×C3⋊C8C23×C312yes—
305C2×C3⋊C8C23×C312yes—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32C22×D411yescharacteristic
313C32×C4—21no—
314C32×C4—21no—
315C32×C4—21no—
316C32×C4—42no—
317C32×C4—42no—
318C32×C4H(5,𝔽2)11yescharacteristic
319C32×C4H(5,𝔽2)11yescharacteristic
320C3×Dic3—42no—
321C3×Dic3—42no—
322C2×#41C2×C3×D311yescharacteristic
323C22×Q8—31no—
324C22×Q8C2×C3×D311yescharacteristic
325C2×Q16—32no—
326C2×Q16—32no—
327C2×M16—31no—
328C22×C8—31no—
329C4⋊Q8—21no—
330C4⋊Q8—61no—
331#124—21no—
332#124—61no—
333#123—21no—
334#123—21no—
335#123—61no—
336#123—61no—
337C22⋊Q8—32no—
338C22⋊Q8—32no—
339C22⋊Q8C2×C3×D312yes—
340C22⋊Q8C2×C3×D312yes—
341#117—31no—
342#117C2×C3×D311yescharacteristic
343#107—32no—
344#106—32no—
345#103—32no—
346#103—32no—
347#103—32no—
348#103—32no—
349C22⋊C8—32no—
350C22⋊C8—32no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3C2×#6711yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C23×C3C2×#6711yescharacteristic
357C23×C3C2×C3×D411yescharacteristic
358C23×C3C2×C3×D411yescharacteristic
359C23×C3C2×C3×D411yescharacteristic
360C3×Q8—22no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—42no—
365C3×Q8—42no—
366C3×Q8—41no—
367C3×Q8—41no—
368C3×Q8—44no—
369C3×Q8—42no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—62no—
373C3×Q8—62no—
374C3×Q8—122no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—42no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—44no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—122no—
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×C3×D411yescharacteristic
422C2×C3×C4C2×C3×D411yescharacteristic
423C2×C3×C4C2×C3×D411yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C24×C311yescharacteristic
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—42no—
429Dic6—22no—
430Dic6—22no—
431Dic6—42no—
432C3×C8—62no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—22no—
436C2×C32—41no—
437C2×C32—41no—
438C2×C32—41no—
439C2×C32#53411yescharacteristic
440C2×C32#57812yes—
441#41—41no—
442#41—41no—
443C2×Q8—21no—
444C2×Q8—32no—
445C2×Q8—41no—
446C2×Q8—41no—
447C2×Q8—61no—
448C2×Q8—121no—
449C2×Q8—121no—
450C2×Q8C3×#6711yescharacteristic
451C2×Q8C22×C3×D312yes—
452C2×D4C3×#6711yescharacteristic
453C2×D4C3×#6711yescharacteristic
454C2×D4C3×#6711yescharacteristic
455C22×C4—21no—
456C22×C4—61no—
457C22×C4C22×C3×D311yescharacteristic
458C22×C4C22×C3×D311yescharacteristic
459C22×C4C22×C3×D311yescharacteristic
460Q16—122no—
461Q16—122no—
462M16—121no—
463C2×C8—32no—
464C2×C8—32no—
465C2×C8—121no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—32no—
469C4⋊C4—62no—
470C4⋊C4—62no—
471C4⋊C4C22×C3×D312yes—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—61no—
476C22⋊C4—62no—
477C22⋊C4—62no—
478C42—21no—
479C42—61no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3C22×#6711yescharacteristic
500C22×C3C22×C3×D411yescharacteristic
501C3×C4—22no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—44no—
513C3×C4—44no—
514C3×C4—42no—
515C3×C4—42no—
516C3×C4—42no—
517C3×C4—42no—
518C3×C4—122no—
519C3×C4—122no—
520C3×C4#100411yescharacteristic
521C3×C4#100411yescharacteristic
522C3×C4C3×H(5,𝔽2)11yescharacteristic
523C3×C4C3×H(5,𝔽2)11yescharacteristic
524Dic3—42no—
525Dic3—42no—
526C32#320211yescharacteristic, complemented, Sylow
527C23C2×C3×#6711yescharacteristic
528C23C2×C3×#6711yescharacteristic
529C23C2×C3×#6711yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—42no—
534Q8—62no—
535Q8—62no—
536Q8—122no—
537D4—41no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—42no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—122no—
552C2×C4C2×C3×#6711yescharacteristic
553C2×C4C2×C3×#6711yescharacteristic
554C2×C4C2×C3×#6711yescharacteristic
555C2×C4C23×C3×D311yescharacteristic
556C8—62no—
557C8—62no—
558C2×C3—21no—
559C2×C3—22no—
560C2×C3—42no—
561C2×C3—41no—
562C2×C3—41no—
563C2×C3—41no—
564C2×C3—41no—
565C2×C3—41no—
566C2×C3—41no—
567C2×C3—81no—
568C2×C3—81no—
569C2×C3#580411yescharacteristic
570C2×C3#583812yes—
571C2×C3C3×#53411yescharacteristic
572C2×C3C3×#57812yes—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22C22×C3×#6711yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—42no—
584C4—42no—
585C4—122no—
586C4—122no—
587C4C3×#100411yescharacteristic
588C4C3×#100411yescharacteristic
589C3—21no—
590C3#8341311yescharacteristic, direct product factor
591C3C3×#320211yescharacteristic, complemented
592C2—41no—
593C2—41no—
594C2—41no—
595C2C3×#580411yescharacteristic
596C2C3×#583812yes—
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#536C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
hypercenterC3×#536D3
hypocenterC3C3×#3202
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×#41 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
4. C3×#5228C2semidirect
5. C3×#5052C2semidirect
6. C3×#5051C2semidirect
7. C3×#5050C2semidirect
8. C3×#5045C2semidirect
9. C3×#4996C2semidirect
11. #83413C3direct (N × H)
54. #5228C2×C3semidirect
55. #5052C2×C3semidirect
56. #5051C2×C3semidirect
57. #5050C2×C3semidirect
58. #5045C2×C3semidirect
59. #4996C2×C3semidirect
526. C32#3202semidirect
590. C3#83413direct (N × H)
591. C3C3×#3202semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
C3×#58252
C3×#52342
C3×#52282
C3×#50522
C3×#50512
C3×#50502
C3×#50452
C3×#49962
C3×#32023
#834133