Finite Group Databasebeta

← C3×#25832 #10644439

Subgroups — C3×#25832 #10644439

Order 768.

954 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic
2C3×#3166C211yesmaximal, characteristic, complemented
3C3×#3080C211yesmaximal, characteristic
4C3×#2660C211yesmaximal, characteristic, complemented
5C3×#2061C212yesmaximal, complemented
6C3×#2060C212yesmaximal, complemented
7C3×#1997C211yesmaximal, characteristic, complemented
8C3×#1995C211yesmaximal, characteristic, complemented
9C3×#1860C212yesmaximal
10C3×#1859C212yesmaximal
11C3×#1759C211yesmaximal, characteristic
12#25832C311yesmaximal, characteristic, direct product factor, Sylow
13C3×Q82—21no—
14C3×#557—21no—
15C3×#554—21no—
16C3×#554—22no—
17C3×D4×Q8—22no—
18C3×D4×Q8—21no—
19C3×#544—22no—
20C3×#544C2212yes—
21C3×#533—21no—
22C3×#533C2211yescharacteristic
23C2×C3×C4⋊Q8—21no—
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×#125C2211yescharacteristic
26C3×#520C2212yes—
27C3×C4×#41C2211yescharacteristic
28C3×#501—21no—
29C3×#501—21no—
30C3×#499—22no—
31C3×#479—21no—
32C3×#479—21no—
33C3×#478—21no—
34C3×#478—21no—
35C3×#428C2212yes—
36C3×#428C2212yes—
37C3×#428C2211yescharacteristic
38C3×#428C2211yescharacteristic
39C3×#423C2211yescharacteristic
40C2×C3×#104C2212yes—
41C3×#417C2211yescharacteristic
42C3×#417C2211yescharacteristic
43C3×C4×M16C2211yescharacteristic
44C3×#398—22no—
45C3×#395—22no—
46C3×#384C2212yes—
47C3×#382C2212yes—
48C3×#376C2211yescharacteristic
49C3×#343C2212yes—
50C3×#343C2212yes—
51C3×#339C2212yes—
52C3×#339C2212yes—
53C3×#339C2212yes—
54#3503C2×C311yescharacteristic
55#3166C2×C311yescharacteristic, complemented
56#3080C2×C311yescharacteristic
57#2660C2×C311yescharacteristic, complemented
58#2061C2×C312yescomplemented
59#2060C2×C312yescomplemented
60#1997C2×C311yescharacteristic, complemented
61#1995C2×C311yescharacteristic, complemented
62#1860C2×C312yes—
63#1859C2×C312yes—
64#1759C2×C311yescharacteristic
65C2×C3×#41C2311yescharacteristic
66C22×C3×Q8—22no—
67C22×C3×Q8D412yes—
68C2×C3×M16C2311yescharacteristic
69C2×C3×M16C2311yescharacteristic
70C2×C3×M16C2312yes—
71C3×C4⋊Q8—22no—
72C3×C4⋊Q8—24no—
73C3×C4⋊Q8—22no—
74C3×C4⋊Q8—22no—
75C3×C4⋊Q8—22no—
76C3×C4⋊Q8—21no—
77C3×C4⋊Q8—21no—
78C3×C4⋊Q8—21no—
79C3×C4⋊Q8—21no—
80C3×C4⋊Q8D411yescharacteristic
81C3×C4⋊Q8D411yescharacteristic
82C3×#125—24no—
83C3×#125—22no—
84C3×#125—22no—
85C3×#125—21no—
86C3×#125—21no—
87C3×#125—21no—
88C3×#125—21no—
89C3×#125D412yes—
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—24no—
93C3×C22⋊Q8—24no—
94C3×C22⋊Q8—21no—
95C3×C22⋊Q8—21no—
96C3×C22⋊Q8—24no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8—21no—
101C3×C4×Q8—21no—
102C3×C4×Q8D411yescharacteristic
103C3×C4×Q8D411yescharacteristic
104C3×C4×D4—22no—
105C3×C4×D4—21no—
106C3×C4×D4—21no—
107C3×C4×D4—24no—
108C3×C4×D4D411yescharacteristic
109C3×C4×D4D411yescharacteristic
110C3×#117—22no—
111C3×#117—21no—
112C3×#117C2311yescharacteristic
113C3×#117C2312yes—
114C2×C3×C4⋊C4—22no—
115C2×C3×C4⋊C4—22no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4D412yes—
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C42—21no—
124C2×C3×C42C2312yes—
125C2×C3×C42C2311yescharacteristic
126C3×#107—21no—
127C3×#107—21no—
128C3×#107—22no—
129C3×#107—22no—
130C3×#106—21no—
131C3×#106—21no—
132C3×#106—22no—
133C3×#106—22no—
134C3×C4⋊C8—21no—
135C3×C4⋊C8—21no—
136C3×#104Q818yescomplemented
137C3×#103—21no—
138C3×#103—21no—
139C3×#102—21no—
140C3×#102—21no—
141C3×#97—21no—
142C3×C4×C8—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—24no—
146Q82—21no—
147#557—21no—
148#554—21no—
149#554—22no—
150D4×Q8—22no—
151D4×Q8—21no—
152#544—22no—
153#544C22×C312yes—
154#533—21no—
155#533C22×C311yescharacteristic
156C2×C4⋊Q8—21no—
157C2×C4⋊Q8C22×C311yescharacteristic
158C2×#125C22×C311yescharacteristic
159#520C22×C312yes—
160C4×#41C22×C311yescharacteristic
161#501—21no—
162#501—21no—
163#499—22no—
164#479—21no—
165#479—21no—
166#478—21no—
167#478—21no—
168#428C22×C311yescharacteristic
169#428C22×C311yescharacteristic
170#428C22×C312yes—
171#428C22×C312yes—
172#423C22×C311yescharacteristic
173C2×#104C22×C312yes—
174#417C22×C311yescharacteristic
175#417C22×C311yescharacteristic
176C4×M16C22×C311yescharacteristic
177#398—22no—
178#395—22no—
179#384C22×C312yes—
180#382C22×C312yes—
181#376C22×C311yescharacteristic
182#343C22×C312yes—
183#343C22×C312yes—
184#339C22×C312yes—
185#339C22×C312yes—
186#339C22×C312yes—
187C3×#41—22no—
188C3×#41C2×Q814yes—
189C2×C3×Q8—24no—
190C2×C3×Q8—21no—
191C2×C3×Q8—22no—
192C2×C3×Q8—21no—
193C2×C3×Q8—22no—
194C2×C3×Q8—82no—
195C2×C3×Q8—84no—
196C2×C3×Q8C2×D411yescharacteristic
197C2×C3×D4—21no—
198C2×C3×D4C2×D411yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—24no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C2×D414yes—
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2411yescharacteristic
210C3×M16—22no—
211C3×M16—22no—
212C3×M16—22no—
213C3×M16C2×Q814yescomplemented
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C3×C4⋊C4—24no—
218C3×C4⋊C4—24no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—24no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—41no—
237C3×C4⋊C4—41no—
238C3×C4⋊C4—41no—
239C3×C4⋊C4—84no—
240C3×C4⋊C4C2×D412yes—
241C3×C4⋊C4C2×D412yes—
242C3×C4⋊C4C2×D411yescharacteristic
243C3×C4⋊C4C2×D411yescharacteristic
244C3×C22⋊C4—24no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C42—24no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—22no—
254C3×C42—22no—
255C3×C42C2×D411yescharacteristic
256C3×C42C2×D411yescharacteristic
257C3×C42C2×D411yescharacteristic
258C3×C42C2×D411yescharacteristic
259C3×C42C2×Q814yescomplemented
260C2×#41C23×C311yescharacteristic
261C22×Q8—22no—
262C22×Q8C3×D412yes—
263C2×M16C23×C311yescharacteristic
264C2×M16C23×C311yescharacteristic
265C2×M16C23×C312yes—
266C4⋊Q8—22no—
267C4⋊Q8—22no—
268C4⋊Q8—24no—
269C4⋊Q8—22no—
270C4⋊Q8—22no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—21no—
274C4⋊Q8—21no—
275C4⋊Q8C3×D411yescharacteristic
276C4⋊Q8C3×D411yescharacteristic
277#125—24no—
278#125—22no—
279#125—22no—
280#125—21no—
281#125—21no—
282#125—21no—
283#125—21no—
284#125C3×D412yes—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—24no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8C3×D411yescharacteristic
298C4×Q8C3×D411yescharacteristic
299C4×D4—22no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—24no—
303C4×D4C3×D411yescharacteristic
304C4×D4C3×D411yescharacteristic
305#117—22no—
306#117—21no—
307#117C23×C311yescharacteristic
308#117C23×C312yes—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4C3×D412yes—
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C4⋊C4C23×C311yescharacteristic
317C2×C4⋊C4C23×C312yes—
318C2×C42—21no—
319C2×C42C23×C312yes—
320C2×C42C23×C311yescharacteristic
321#107—21no—
322#107—21no—
323#107—22no—
324#107—22no—
325#106—21no—
326#106—21no—
327#106—22no—
328#106—22no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331#104C3×Q818yescomplemented
332#103—21no—
333#103—21no—
334#102—21no—
335#102—21no—
336#97—21no—
337C4×C8—21no—
338#95—21no—
339#95—21no—
340#95—24no—
341C23×C3—21no—
342C23×C3C22×D411yescharacteristic
343C3×Q8—21no—
344C3×Q8—42no—
345C3×Q8—44no—
346C3×Q8—42no—
347C3×Q8—82no—
348C3×Q8—84no—
349C3×Q8C4⋊Q812yes—
350C3×D4—24no—
351C3×D4—21no—
352C3×D4C4⋊Q812yes—
353C2×C3×C4—21no—
354C2×C3×C4—24no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—24no—
359C2×C3×C4—22no—
360C2×C3×C4—24no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—44no—
368C2×C3×C4—42no—
369C2×C3×C4—42no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—84no—
373C2×C3×C4#12011yescharacteristic
374C2×C3×C4#12011yescharacteristic
375C2×C3×C4#12011yescharacteristic
376C2×C3×C4#12011yescharacteristic
377C2×C3×C4C22×D411yescharacteristic
378C2×C3×C4C22×D411yescharacteristic
379C2×C3×C4C22×Q812yes—
380C2×C3×C42−1+412yes—
381C3×C8—24no—
382C3×C8—41no—
383C3×C8—41no—
384#41—22no—
385#41C2×C3×Q814yes—
386C2×Q8—24no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8—84no—
393C2×Q8C2×C3×D411yescharacteristic
394C2×D4—21no—
395C2×D4C2×C3×D411yescharacteristic
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4C2×C3×D414yes—
404C22×C4C2×C3×D411yescharacteristic
405C22×C4C2×C3×D411yescharacteristic
406C22×C4C24×C311yescharacteristic
407M16—22no—
408M16—22no—
409M16—22no—
410M16C2×C3×Q814yescomplemented
411C2×C8—22no—
412C2×C8—21no—
413C2×C8—21no—
414C4⋊C4—24no—
415C4⋊C4—24no—
416C4⋊C4—24no—
417C4⋊C4—24no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—84no—
437C4⋊C4C2×C3×D412yes—
438C4⋊C4C2×C3×D412yes—
439C4⋊C4C2×C3×D411yescharacteristic
440C4⋊C4C2×C3×D411yescharacteristic
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C42—24no—
447C42—21no—
448C42—21no—
449C42—21no—
450C42—22no—
451C42—22no—
452C42C2×C3×D411yescharacteristic
453C42C2×C3×D411yescharacteristic
454C42C2×C3×D411yescharacteristic
455C42C2×C3×D411yescharacteristic
456C42C2×C3×Q814yescomplemented
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3C2×#12011yescharacteristic
463C22×C3D4×Q812yes—
464C3×C4—22no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—44no—
470C3×C4—41no—
471C3×C4—44no—
472C3×C4—42no—
473C3×C4—41no—
474C3×C4—42no—
475C3×C4—81no—
476C3×C4—81no—
477C3×C4C2×C4⋊Q811yescharacteristic
478C3×C4#53611yescharacteristic
479C3×C4D4×Q812yes—
480C23—21no—
481C23C22×C3×D411yescharacteristic
482Q8—21no—
483Q8—44no—
484Q8—42no—
485Q8—42no—
486Q8—82no—
487Q8—84no—
488Q8C3×C4⋊Q812yes—
489D4—24no—
490D4—21no—
491D4C3×C4⋊Q812yes—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—84no—
512C2×C4C3×#12011yescharacteristic
513C2×C4C3×#12011yescharacteristic
514C2×C4C3×#12011yescharacteristic
515C2×C4C3×#12011yescharacteristic
516C2×C4C22×C3×D411yescharacteristic
517C2×C4C22×C3×D411yescharacteristic
518C2×C4C22×C3×Q812yes—
519C2×C4C3×2−1+412yes—
520C8—24no—
521C8—41no—
522C8—41no—
523C2×C3—22no—
524C2×C3—42no—
525C2×C3#243411yescharacteristic
526C2×C3#301911yescharacteristic
527C2×C3#302011yescharacteristic
528C22—21no—
529C22—21no—
530C22—22no—
531C22—41no—
532C22—41no—
533C22C2×C3×#12011yescharacteristic
534C22C3×D4×Q812yes—
535C4—22no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—44no—
541C4—41no—
542C4—44no—
543C4—42no—
544C4—41no—
545C4—42no—
546C4—81no—
547C4—81no—
548C4C2×C3×C4⋊Q811yescharacteristic
549C4C3×#53611yescharacteristic
550C4C3×D4×Q812yes—
551C3#2583211yescharacteristic, direct product factor, Sylow
552C2—22no—
553C2—42no—
554C2C3×#243411yescharacteristic
555C2C3×#301911yescharacteristic
556C2C3×#302011yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3166C2semidirect
4. C3×#2660C2semidirect
5. C3×#2061C2semidirect
6. C3×#2060C2semidirect
7. C3×#1997C2semidirect
8. C3×#1995C2semidirect
12. #25832C3direct (N × H)
55. #3166C2×C3semidirect
57. #2660C2×C3semidirect
58. #2061C2×C3semidirect
59. #2060C2×C3semidirect
60. #1997C2×C3semidirect
61. #1995C2×C3semidirect
136. C3×#104Q8semidirect
213. C3×M16C2×Q8semidirect
259. C3×C42C2×Q8semidirect
331. #104C3×Q8semidirect
410. M16C2×C3×Q8semidirect
456. C42C2×C3×Q8semidirect
551. C3#25832direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35032
C3×#31662
C3×#30802
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C3×#20602
C3×#19972
C3×#19952
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