Finite Group Databasebeta

← C3×#81108 #11868725

Subgroups — C3×#81108 #11868725

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic
2C3×C4×D3×Q8C211yesmaximal, characteristic
3C32×#477C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5C3×#5020C211yesmaximal, characteristic, complemented
6C3×#4881C212yesmaximal
7C3×#4877C212yesmaximal, complemented
8C3×#4851C211yesmaximal, characteristic, complemented
9C3×#4837C211yesmaximal, characteristic
10C3×#4802C212yesmaximal
11C3×#4799C212yesmaximal, complemented
12C3×#3078—31nomaximal
13#81108C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×Q8×Dic3C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2212yes—
21C3×#897—21no—
22C3×#892C2212yes—
23C3×D3×C4⋊C4—21no—
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#890C2212yes—
26C3×#887—21no—
27C3×#887—21no—
28C3×#887C2211yescharacteristic
29C3×C42×D3—21no—
30C3×C42×D3C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C3×C4×Dic6—21no—
33C3×C4×Dic6C2211yescharacteristic
34C32×#107C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36C32×#103C2212yes—
37C3×#835C2212yes—
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#808C2212yes—
43C3×#807C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C2×C3×C4×Q8—31no—
47#5728C2×C311yescharacteristic
48C4×D3×Q8C2×C311yescharacteristic
49C3×#479—32no—
50C3×#479—32no—
51C3×#477—21no—
52C3×#477—31no—
53C3×#477D311yescharacteristic, complemented
54C3×#477C2×C311yescharacteristic, complemented
55C3×#475—31no—
56C3×#475—31no—
57C3×#428—32no—
58C3×#423—31no—
59C3×#419—32no—
60#5091C2×C311yescharacteristic, complemented
61#5020C2×C311yescharacteristic, complemented
62#4881C2×C312yes—
63#4877C2×C312yescomplemented
64#4851C2×C311yescharacteristic, complemented
65#4837C2×C311yescharacteristic
66#4802C2×C312yes—
67#4799C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×Q8C2311yescharacteristic
70C3×D3×Q8—22no—
71C3×D3×Q8Q814yescomplemented
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2311yescharacteristic
80C2×C32×C8C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C4⋊C4C2312yes—
85C32×C42—21no—
86C32×C42C2311yescharacteristic
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×ΓL(1,𝔽25)—24no—
106#3078—31noSylow
107C22×C3×Q8—31no—
108C2×D3×Q8C22×C311yescharacteristic
109C2×C3×M16—32no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4⋊Q8C22×C311yescharacteristic
114C3×#125—32no—
115C3×C22⋊Q8—61no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—21no—
118C3×C4×Q8—31no—
119C3×C4×Q8—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—61no—
122C3×C4×Q8—61no—
123C3×C4×Q8—61no—
124C3×C4×Q8—61no—
125C3×C4×Q8C2×D311yescharacteristic
126C3×C4×Q8C22×C311yescharacteristic
127C3×#117—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#946—21no—
133Q8×Dic3—21no—
134Q8×Dic3C22×C311yescharacteristic
135C2×ΓL(1,𝔽25)C22×C312yes—
136#897—21no—
137#892C22×C312yes—
138D3×C4⋊C4—21no—
139D3×C4⋊C4C22×C311yescharacteristic
140#890C22×C312yes—
141#887—21no—
142#887—21no—
143#887C22×C311yescharacteristic
144C42×D3—21no—
145C42×D3C22×C311yescharacteristic
146#869C22×C311yescharacteristic
147C4×Dic6—21no—
148C4×Dic6C22×C311yescharacteristic
149C3×#107—22no—
150C3×#107—32no—
151C3×#107C2×D312yes—
152C3×#107C22×C312yes—
153C3×#106—32no—
154C3×#106—32no—
155C3×C4⋊C8—21no—
156C3×C4⋊C8—32no—
157C3×C4⋊C8—31no—
158C3×C4⋊C8C2×D311yescharacteristic
159C3×C4⋊C8C22×C311yescharacteristic
160C3×#103—22no—
161C3×#103—32no—
162C3×#103—32no—
163C3×#103—32no—
164C3×#103C2×D312yes—
165C3×#103C22×C312yes—
166#835C22×C312yes—
167#817C22×C312yes—
168#816C22×C312yes—
169Dic3⋊C8C22×C312yes—
170#810C22×C312yes—
171#808C22×C312yes—
172#807C22×C312yes—
173C4⋊(C3⋊C8)C22×C311yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8—42no—
177C32×Q8C2×Q812yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—22no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C3×C4×D3—24no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—42no—
194C3×C4×D3C2×Q812yes—
195C3×C4×D3#4112yes—
196C3×Dic6—21no—
197C3×Dic6—24no—
198C3×Dic6—42no—
199C3×Dic6C2×Q812yes—
200C32×C8—22no—
201C3×C3⋊C8—22no—
202#533—31no—
203C2×C4×Q8—31no—
204#479—32no—
205#479—32no—
206#477—31no—
207#477C3×D311yescharacteristic, complemented
208#475—31no—
209#475—31no—
210#428—32no—
211#423—31no—
212#419—32no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—34no—
217C2×C3×Q8—31no—
218C2×C3×Q8—41no—
219C2×C3×Q8—61no—
220C2×C3×Q8—62no—
221C2×C3×Q8—61no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C23×C311yescharacteristic
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229D3×Q8—22no—
230D3×Q8C3×Q814yescomplemented
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3C3×D411yescharacteristic
234C2×C4×D3C3×D411yescharacteristic
235C2×C4×D3C23×C311yescharacteristic
236C2×Dic6—21no—
237C2×Dic6—21no—
238C2×Dic6C23×C311yescharacteristic
239C3×M16—64no—
240C2×C3×C8—22no—
241C2×C3×C8—32no—
242C2×C3×C8C22×D312yes—
243C2×C3×C8C23×C312yes—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—32no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—41no—
253C3×C4⋊C4—41no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4C22×D312yes—
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C4⋊C4C23×C312yes—
264C3×C4⋊C4C23×C311yescharacteristic
265C3×C22⋊C4—62no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—41no—
273C3×C42—61no—
274C3×C42—61no—
275C3×C42—62no—
276C3×C42—61no—
277C3×C42C22×D311yescharacteristic
278C3×C42C23×C311yescharacteristic
279(C2×D3)⋊C4—22no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—22no—
283C4⋊Dic3C23×C311yescharacteristic
284C4⋊Dic3C23×C312yes—
285Dic3⋊C4—21no—
286Dic3⋊C4—21no—
287Dic3⋊C4—21no—
288Dic3⋊C4—22no—
289C4×Dic3—21no—
290C4×Dic3—21no—
291C4×Dic3—21no—
292C4×Dic3—22no—
293C4×Dic3C3×D411yescharacteristic
294C4×Dic3C3×D411yescharacteristic
295C4×Dic3C23×C311yescharacteristic
296C2×C3⋊C8C23×C312yes—
297ΓL(1,𝔽25)—24no—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—21no—
300C2×C3×D3—21no—
301C2×C3×D3C22⋊Q812yes—
302C32×C4—22no—
303C32×C4—21no—
304C32×C4—41no—
305C32×C4—42no—
306C32×C4#13712yes—
307C32×C4C22×Q811yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3×Dic3—22no—
310C3×Dic3—21no—
311C3×Dic3—21no—
312C3×Dic3—42no—
313C3×Dic3—41no—
314C3×Dic3C22⋊Q812yes—
315C22×Q8—31no—
316C2×M16—32no—
317C4⋊Q8—31no—
318C4⋊Q8C2×C3×D311yescharacteristic
319#125—32no—
320C22⋊Q8—61no—
321C22⋊Q8—61no—
322C4×Q8—31no—
323C4×Q8—31no—
324C4×Q8—31no—
325C4×Q8—61no—
326C4×Q8—61no—
327C4×Q8—61no—
328C4×Q8—61no—
329C4×Q8C2×C3×D311yescharacteristic
330#117—32no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—61no—
333C2×C42—31no—
334C2×C42—61no—
335#107—32no—
336#107C2×C3×D312yes—
337#106—32no—
338#106—32no—
339C4⋊C8—32no—
340C4⋊C8—31no—
341C4⋊C8C2×C3×D311yescharacteristic
342#103—32no—
343#103—32no—
344#103—32no—
345#103C2×C3×D312yes—
346C23×C3—31no—
347C22×D3C2×C3×D411yescharacteristic
348C3×Q8—21no—
349C3×Q8—21no—
350C3×Q8—22no—
351C3×Q8—32no—
352C3×Q8—41no—
353C3×Q8—42no—
354C3×Q8—42no—
355C3×Q8—64no—
356C3×Q8—61no—
357C3×Q8—82no—
358C3×Q8—122no—
359C3×Q8D3×Q812yes—
360C3×Q8C2×C3×Q812yes—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—31no—
371C2×C3×C4—32no—
372C2×C3×C4—32no—
373C2×C3×C4—31no—
374C2×C3×C4—31no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—42no—
378C2×C3×C4—64no—
379C2×C3×C4—61no—
380C2×C3×C4—62no—
381C2×C3×C4—61no—
382C2×C3×C4—62no—
383C2×C3×C4—121no—
384C2×C3×C4—122no—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C2×C3×D411yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C24×C311yescharacteristic
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3C2×C3×D411yescharacteristic
395C2×Dic3C2×C3×D411yescharacteristic
396C2×Dic3C2×C3×D411yescharacteristic
397C4×D3—24no—
398C4×D3—22no—
399C4×D3—41no—
400C4×D3—42no—
401C4×D3C2×C3×Q812yes—
402C4×D3C3×#4112yes—
403Dic6—21no—
404Dic6—24no—
405Dic6—42no—
406Dic6C2×C3×Q812yes—
407C3×C8—22no—
408C3×C8—22no—
409C3×C8—42no—
410C3×C8—62no—
411C3⋊C8—22no—
412C2×C32C2×C22⋊Q811yescharacteristic
413C2×C32C2×#13711yescharacteristic
414C2×C32#57511yescharacteristic
415C3×D3—22no—
416C2×Q8—21no—
417C2×Q8—34no—
418C2×Q8—31no—
419C2×Q8—61no—
420C2×Q8—62no—
421C2×Q8—61no—
422C2×Q8C22×C3×D311yescharacteristic
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—61no—
427C22×C4—61no—
428M16—64no—
429C2×C8—32no—
430C2×C8C22×C3×D312yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—32no—
434C4⋊C4—31no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—61no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4C22×C3×D312yes—
443C4⋊C4C22×C3×D311yescharacteristic
444C22⋊C4—62no—
445C42—21no—
446C42—31no—
447C42—31no—
448C42—31no—
449C42—61no—
450C42—61no—
451C42—62no—
452C42—61no—
453C42C22×C3×D311yescharacteristic
454C22×C3—21no—
455C22×C3—32no—
456C22×C3—61no—
457C22×C3—61no—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C22×C3×D411yescharacteristic
460C2×D3—21no—
461C2×D3—21no—
462C2×D3C3×C22⋊Q812yes—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—32no—
471C3×C4—41no—
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—42no—
475C3×C4—41no—
476C3×C4—42no—
477C3×C4—61no—
478C3×C4—61no—
479C3×C4—62no—
480C3×C4—82no—
481C3×C4—81no—
482C3×C4—122no—
483C3×C4—121no—
484C3×C4#91812yes—
485C3×C4C3×#13712yes—
486C3×C4C2×D3×Q811yescharacteristic
487C3×C4D3×#4111yescharacteristic
488C3×C4C22×C3×Q811yescharacteristic
489C3×C4C2×C3×#4111yescharacteristic
490Dic3—21no—
491Dic3—21no—
492Dic3—22no—
493Dic3—42no—
494Dic3—41no—
495Dic3C3×C22⋊Q812yes—
496C32#307811yescharacteristic, complemented, Sylow
497C23—31no—
498Q8—21no—
499Q8—32no—
500Q8—42no—
501Q8—64no—
502Q8—61no—
503Q8—122no—
504Q8C3×D3×Q812yes—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—31no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—31no—
512C2×C4—31no—
513C2×C4—64no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—121no—
519C2×C4—122no—
520C2×C4C3×D3×D411yescharacteristic
521C2×C4C3×D3×D411yescharacteristic
522C2×C4C23×C3×D311yescharacteristic
523C8—22no—
524C8—62no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—62no—
529C2×C3D3×C22⋊Q811yescharacteristic
530C2×C3C2×#91811yescharacteristic
531C2×C3#577311yescharacteristic
532C2×C3C2×C3×C22⋊Q811yescharacteristic
533C2×C3C2×C3×#13711yescharacteristic
534C2×C3C3×#57511yescharacteristic
535D3—22no—
536C22—32no—
537C22—61no—
538C22—61no—
539C22C2×C3×D3×D411yescharacteristic
540C4—21no—
541C4—22no—
542C4—32no—
543C4—41no—
544C4—42no—
545C4—61no—
546C4—61no—
547C4—62no—
548C4—122no—
549C4—121no—
550C4C3×#91812yes—
551C4C2×C3×D3×Q811yescharacteristic
552C4C3×D3×#4111yescharacteristic
553C3—21no—
554C3#8110811yescharacteristic, direct product factor
555C3C3×#307811yescharacteristic, complemented
556C2—62no—
557C2C3×D3×C22⋊Q811yescharacteristic
558C2C2×C3×#91811yescharacteristic
559C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#477C2
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC3×#477D3
hypocenterC3C3×#3078
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#477

Complements

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

NH ≅ G/Ntype
3. C32×#477C2semidirect
4. C3×#5091C2semidirect
5. C3×#5020C2semidirect
7. C3×#4877C2semidirect
8. C3×#4851C2semidirect
11. C3×#4799C2semidirect
13. #81108C3direct (N × H)
53. C3×#477D3semidirect
54. C3×#477C2×C3semidirect
60. #5091C2×C3semidirect
61. #5020C2×C3semidirect
63. #4877C2×C3semidirect
64. #4851C2×C3semidirect
67. #4799C2×C3semidirect
71. C3×D3×Q8Q8semidirect
207. #477C3×D3semidirect
230. D3×Q8C3×Q8semidirect
496. C32#3078semidirect
554. C3#81108direct (N × H)
555. C3C3×#3078semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×C4×D3×Q82
C32×#4772
C3×#50912
C3×#50202
C3×#48812
C3×#48772
C3×#48512
C3×#48372
C3×#48022
C3×#47992
C3×#30783
#811083