Finite Group Databasebeta

← C3×#83510 #11888018

Subgroups — C3×#83510 #11888018

Order 1152.

918 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic
2C3×#5542C211yesmaximal, characteristic, complemented
3C3×#5239C212yesmaximal, complemented
4C3×#5233C212yesmaximal, complemented
5C3×#5090C211yesmaximal, characteristic, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×#5051C212yesmaximal, complemented
8C3×#5045C212yesmaximal, complemented
9C3×C4×#214C211yesmaximal, characteristic, complemented
10C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
11C3×#5007C211yesmaximal, characteristic, complemented
12C3×#3302—31nomaximal
13#83510C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#123—22no—
17C32×C22⋊Q8C2212yes—
18C32×#121—21no—
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×C32×C4⋊C4—21no—
22C2×C3×#216C2212yes—
23C3×#936—21no—
24C2×C3×#214C2211yescharacteristic
25C3×#926C2212yes—
26C3×#924C2212yes—
27C22×C3×C3⋊C8C2212yes—
28C3×#887—21no—
29C3×#879—22no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×#835C2212yes—
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×#832C2211yescharacteristic
36C3×#832C2212yes—
37C3×#830C2212yes—
38C3×#810C2211yescharacteristic
39C3×#808C2211yescharacteristic
40C3×#807C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#556—31no—
44C3×#547—21no—
45C3×#547D311yescharacteristic
46C3×#547C2×C311yescharacteristic
47#5542C2×C311yescharacteristic, complemented
48C3×#487—31no—
49C3×#485—32no—
50C3×#474—31no—
51C3×#467—32no—
52C3×#462—31no—
53C3×#452—32no—
54C3×C4×SD16—31no—
55C3×C8×D4—31no—
56C3×#416—32no—
57#5239C2×C312yescomplemented
58#5233C2×C312yescomplemented
59#5090C2×C311yescharacteristic, complemented
60#5079C2×C311yescharacteristic, complemented
61#5051C2×C312yescomplemented
62#5045C2×C312yescomplemented
63C4×#214C2×C311yescharacteristic, complemented
64D4×C3⋊C8C2×C311yescharacteristic, complemented
65#5007C2×C311yescharacteristic, complemented
66C32×#41—24no—
67C32×#41—42no—
68C2×C32×Q8C2312yes—
69C2×C32×D4—22no—
70C2×C32×D4D411yescharacteristic
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—22no—
73C22×C32×C4—21no—
74C22×C32×C4C2312yes—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4—21no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4C2311yescharacteristic
82C32×C22⋊C4—22no—
83C32×C22⋊C4—21no—
84C32×C22⋊C4D412yes—
85C32×C42C2311yescharacteristic
86C3×#217—22no—
87C3×#217—22no—
88C3×#216—42no—
89C3×#214—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—21no—
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3302—31noSylow
102C2×C3×#41—22no—
103C2×C3×#41C2×D312yes—
104C2×C3×#41C22×C312yes—
105C2×C3×Q16—32no—
106C2×C3×SD16—31no—
107C22×C3×C8—32no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8C2×D311yescharacteristic
111C3×C4⋊Q8C22×C311yescharacteristic
112C3×#126—62no—
113C3×#124—61no—
114C3×#123—24no—
115C3×#123—22no—
116C3×#123—22no—
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8—32no—
119C3×C22⋊Q8C2×D312yes—
120C3×C22⋊Q8C22×C312yes—
121C3×#121—22no—
122C3×#121—21no—
123C3×#121—21no—
124C3×C4×Q8—31no—
125C3×C4×Q8—61no—
126C3×C4×D4—21no—
127C3×C4×D4—21no—
128C3×C4×D4C2×D311yescharacteristic
129C3×C4×D4C2×D311yescharacteristic
130C3×C4×D4C22×C311yescharacteristic
131C3×C4×D4C22×C311yescharacteristic
132C3×#117—32no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×#216C22×C312yes—
137#936—21no—
138C2×#214C22×C311yescharacteristic
139#926C22×C312yes—
140#924C22×C312yes—
141C22×C3⋊C8C22×C312yes—
142#887—21no—
143#879—22no—
144#869C22×C311yescharacteristic
145C4×Dic6C22×C311yescharacteristic
146C3×#107—32no—
147C3×#106—31no—
148C3×C4⋊C8—31no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—32no—
152C3×#103—31no—
153C3×#102—31no—
154C3×#102—32no—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#835C22×C312yes—
158#835C22×C312yes—
159#835C22×C312yes—
160#832C22×C311yescharacteristic
161#832C22×C312yes—
162#830C22×C312yes—
163#810C22×C311yescharacteristic
164#808C22×C311yescharacteristic
165#807C22×C312yes—
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C4×C3⋊C8C22×C311yescharacteristic
168C23×C32—21no—
169C23×C32C2×D412yes—
170C32×Q8—22no—
171C32×Q8—22no—
172C32×D4—21no—
173C32×D4—22no—
174C32×D4—44no—
175C32×D4#4112yes—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—44no—
181C2×C32×C4—42no—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6—42no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195#556—31no—
196#547C3×D311yescharacteristic
197#487—31no—
198#485—32no—
199#474—31no—
200#467—32no—
201#462—31no—
202#452—32no—
203C4×SD16—31no—
204C8×D4—31no—
205#416—32no—
206C3×#41—24no—
207C3×#41—24no—
208C3×#41—44no—
209C3×#41—42no—
210C3×#41—42no—
211C3×#41—44no—
212C2×C3×Q8—22no—
213C2×C3×Q8—31no—
214C2×C3×Q8—61no—
215C2×C3×Q8C22×D312yes—
216C2×C3×Q8C23×C312yes—
217C2×C3×D4—24no—
218C2×C3×D4—22no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4#6711yescharacteristic
223C2×C3×D4C3×D411yescharacteristic
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C23×C311yescharacteristic
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—21no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C23×C312yes—
235C2×Dic6—21no—
236C2×Dic6C23×C311yescharacteristic
237C3×Q16—122no—
238C3×SD16—62no—
239C2×C3×C8—31no—
240C2×C3×C8—31no—
241C2×C3×C8—32no—
242C2×C3×C8—122no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—22no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4#6711yescharacteristic
260C3×C4⋊C4C3×D411yescharacteristic
261C3×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C23×C311yescharacteristic
263C3×C22⋊C4—22no—
264C3×C22⋊C4—24no—
265C3×C22⋊C4—22no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—62no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4#6712yes—
273C3×C22⋊C4C3×D412yes—
274C3×C42—21no—
275C3×C42—62no—
276C3×C42—61no—
277C3×C42C22×D311yescharacteristic
278C3×C42C23×C311yescharacteristic
279#217—22no—
280#217—22no—
281#216—42no—
282#214—22no—
283C4⋊Dic3—21no—
284C4⋊Dic3C23×C312yes—
285C4⋊Dic3C23×C311yescharacteristic
286Dic3⋊C4—21no—
287Dic3⋊C4—22no—
288C4×Dic3—21no—
289C4×Dic3—22no—
290C2×C3⋊C8—42no—
291C2×C3⋊C8C23×C311yescharacteristic
292C2×C3⋊C8C23×C311yescharacteristic
293C2×C3⋊C8C23×C312yes—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—41no—
299C22×C32—41no—
300C22×C32C22×D411yescharacteristic
301C32×C4—22no—
302C32×C4—21no—
303C32×C4—42no—
304C32×C4—41no—
305C32×C4#13512yes—
306C32×C4C2×#4111yescharacteristic
307C32×C4H(5,𝔽2)11yescharacteristic
308C3×Dic3—41no—
309C3×Dic3—42no—
310C3×Dic3—41no—
311C2×#41C2×C3×D312yes—
312C2×Q16—32no—
313C2×SD16—31no—
314C22×C8—32no—
315C4⋊Q8—31no—
316C4⋊Q8C2×C3×D311yescharacteristic
317#126—62no—
318#124—61no—
319#123—22no—
320C22⋊Q8—32no—
321C22⋊Q8C2×C3×D312yes—
322#121—21no—
323C4×Q8—31no—
324C4×Q8—61no—
325C4×D4C2×C3×D311yescharacteristic
326C4×D4C2×C3×D311yescharacteristic
327#117—32no—
328C2×C4⋊C4—21no—
329#107—32no—
330#106—31no—
331C4⋊C8—31no—
332#103—32no—
333#103—32no—
334#103—32no—
335#103—31no—
336#102—31no—
337#102—32no—
338C22⋊C8—32no—
339C4×C8—31no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—22no—
344C23×C3C2×#6712yes—
345C23×C3C2×C3×D412yes—
346C3×Q8—22no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—22no—
350C3×Q8—42no—
351C3×Q8—42no—
352C3×Q8—61no—
353C3×Q8—61no—
354C3×Q8—122no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—21no—
359C3×D4—21no—
360C3×D4—22no—
361C3×D4—42no—
362C3×D4—44no—
363C3×D4—44no—
364C3×D4—48no—
365C3×D4#23712yes—
366C3×D4C3×#4112yes—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—44no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—48no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4—61no—
392C2×C3×C4C2×#6712yes—
393C2×C3×C4C2×#6711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×C3×D412yes—
396C2×C3×C4C2×C3×D411yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C24×C311yescharacteristic
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—22no—
403Dic6—21no—
404Dic6—21no—
405Dic6—42no—
406C3×C8—61no—
407C3×C8—61no—
408C3×C8—62no—
409C3⋊C8—21no—
410C3⋊C8—21no—
411C3⋊C8—22no—
412C2×C32—42no—
413C2×C32—42no—
414C2×C32#54611yescharacteristic
415C2×C32C2×#13511yescharacteristic
416C2×C32#57811yescharacteristic
417#41—24no—
418#41—42no—
419C2×Q8—31no—
420C2×Q8—61no—
421C2×Q8C22×C3×D312yes—
422C2×D4—22no—
423C2×D4C3×#6711yescharacteristic
424C2×D4C22×C3×D311yescharacteristic
425C22×C4—21no—
426C22×C4—22no—
427C22×C4C22×C3×D312yes—
428Q16—122no—
429SD16—62no—
430C2×C8—31no—
431C2×C8—31no—
432C2×C8—32no—
433C2×C8—122no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—31no—
438C4⋊C4—32no—
439C4⋊C4—61no—
440C4⋊C4—62no—
441C4⋊C4—61no—
442C4⋊C4C3×#6711yescharacteristic
443C4⋊C4C22×C3×D311yescharacteristic
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—62no—
447C22⋊C4—62no—
448C22⋊C4C3×#6712yes—
449C42—62no—
450C42—61no—
451C42C22×C3×D311yescharacteristic
452C22×C3—24no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—41no—
471C22×C3C22×#6711yescharacteristic
472C22×C3C22×C3×D411yescharacteristic
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—21no—
479C3×C4—21no—
480C3×C4—42no—
481C3×C4—41no—
482C3×C4—44no—
483C3×C4—42no—
484C3×C4—41no—
485C3×C4—42no—
486C3×C4—41no—
487C3×C4—42no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4—121no—
491C3×C4#95012yes—
492C3×C4C3×#13512yes—
493C3×C4C2×#23711yescharacteristic
494C3×C4#100411yescharacteristic
495C3×C4C2×C3×#4111yescharacteristic
496C3×C4C3×H(5,𝔽2)11yescharacteristic
497Dic3—42no—
498Dic3—41no—
499Dic3—41no—
500C32#330211yescharacteristic, complemented, Sylow
501C23—21no—
502C23C2×C3×#6712yes—
503Q8—22no—
504Q8—22no—
505Q8—61no—
506Q8—61no—
507Q8—122no—
508D4—22no—
509D4—21no—
510D4—44no—
511D4C3×#23712yes—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—61no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4C2×C3×#6712yes—
522C2×C4C2×C3×#6711yescharacteristic
523C2×C4C2×C3×#6711yescharacteristic
524C2×C4C23×C3×D311yescharacteristic
525C8—61no—
526C8—61no—
527C8—62no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—44no—
532C2×C3—42no—
533C2×C3—42no—
534C2×C3—42no—
535C2×C3—42no—
536C2×C3—82no—
537C2×C3#580611yescharacteristic
538C2×C3C2×#95011yescharacteristic
539C2×C3#583811yescharacteristic
540C2×C3C3×#54611yescharacteristic
541C2×C3C2×C3×#13511yescharacteristic
542C2×C3C3×#57811yescharacteristic
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22C22×C3×#6711yescharacteristic
550C4—22no—
551C4—21no—
552C4—42no—
553C4—41no—
554C4—121no—
555C4—122no—
556C4—121no—
557C4C3×#95012yes—
558C4C2×C3×#23711yescharacteristic
559C4C3×#100411yescharacteristic
560C3—21no—
561C3#8351011yescharacteristic, direct product factor
562C3C3×#330211yescharacteristic, complemented
563C2—42no—
564C2—42no—
565C2C3×#580611yescharacteristic
566C2C2×C3×#95011yescharacteristic
567C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#547C2
socleC22×C32C22×D4
hypercenterC3×#547D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#547

Complements

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

NH ≅ G/Ntype
2. C3×#5542C2semidirect
3. C3×#5239C2semidirect
4. C3×#5233C2semidirect
5. C3×#5090C2semidirect
6. C3×#5079C2semidirect
7. C3×#5051C2semidirect
8. C3×#5045C2semidirect
9. C3×C4×#214C2semidirect
10. C3×D4×C3⋊C8C2semidirect
11. C3×#5007C2semidirect
13. #83510C3direct (N × H)
47. #5542C2×C3semidirect
57. #5239C2×C3semidirect
58. #5233C2×C3semidirect
59. #5090C2×C3semidirect
60. #5079C2×C3semidirect
61. #5051C2×C3semidirect
62. #5045C2×C3semidirect
63. C4×#214C2×C3semidirect
64. D4×C3⋊C8C2×C3semidirect
65. #5007C2×C3semidirect
500. C32#3302semidirect
561. C3#83510direct (N × H)
562. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
C3×#55422
C3×#52392
C3×#52332
C3×#50902
C3×#50792
C3×#50512
C3×#50452
C3×C4×#2142
C3×D4×C3⋊C82
C3×#50072
C3×#33023
#835103