Finite Group Databasebeta

← C3×#71675 #11775570

Subgroups — C3×#71675 #11775570

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C3×#4537C214yesmaximal, complemented
5C3×#1519—31nomaximal
6#71675C311yesmaximal, characteristic, direct product factor
7C22×C32×D4—21no—
8C22×C32×D4C411yescharacteristic, complemented
9C23×C32×C4C2211yescharacteristic
10C32×#121—21no—
11C32×#121—21no—
12C32×#121C412yescomplemented
13C32×#121C2212yes—
14C2×C32×C4⋊C4C411yescharacteristic, complemented
15C2×C32×C22⋊C4—21no—
16C2×C3×#217—21no—
17C2×C3×C4⋊Dic3—21no—
18C22×C3×C3⋊C8—21no—
19C3×C3⋊#95C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×C3×#121—21no—
23C2×C3×#121D311yescharacteristic
24C2×C3×#121C2×C311yescharacteristic
25C2×C3×C22⋊C8—31no—
26C3×#380—31no—
27#5212C2×C311yescharacteristic, complemented
28C2×#830C2×C311yescharacteristic, complemented
29C3×#327—34no—
30#4537C2×C314yescomplemented
31C24×C32—21no—
32C24×C32D411yescharacteristic
33C2×C32×D4—22no—
34C2×C32×D4—22no—
35C2×C32×D4—21no—
36C2×C32×D4—42no—
37C2×C32×D4—42no—
38C2×C32×D4—42no—
39C2×C32×D4C2×C412yes—
40C22×C32×C4—21no—
41C22×C32×C4—42no—
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D411yescharacteristic
46C22×C32×C4D411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—22no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4C2×C412yes—
51C32×C22⋊C4—22no—
52C32×C22⋊C4—22no—
53C3×#217—42no—
54C3×C4⋊Dic3—42no—
55C2×C3×C3⋊C8—22no—
56C2×C3×C3⋊C8—42no—
57#1519—31noSylow
58C22×C3×D4—22no—
59C22×C3×D4—21no—
60C22×C3×D4—21no—
61C22×C3×D4—21no—
62C22×C3×D4Dic311yescharacteristic, complemented
63C22×C3×D4C3×C411yescharacteristic, complemented
64C23×C3×C4—21no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C22×C311yescharacteristic
67C22×C3×C8—61no—
68C3×#121—22no—
69C3×#121—22no—
70C3×#121—21no—
71C3×#121—21no—
72C3×#121—21no—
73C3×#121—21no—
74C3×#121—22no—
75C3×#121—22no—
76C3×#121Dic312yescomplemented
77C3×#121C3×C412yescomplemented
78C3×#121C2×D312yes—
79C3×#121C22×C312yes—
80C2×C3×C4⋊C4—21no—
81C2×C3×C4⋊C4—61no—
82C2×C3×C4⋊C4Dic311yescharacteristic, complemented
83C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—21no—
86C2×C3×C22⋊C4—21no—
87C2×C3×C22⋊C4—61no—
88C2×#217—21no—
89C2×C4⋊Dic3—21no—
90C22×C3⋊C8—21no—
91C3×C22⋊C8—32no—
92C3×C22⋊C8—61no—
93C3×#95—32no—
94C3⋊#95C22×C312yescomplemented
95#830—21no—
96#830C22×C312yescomplemented
97C23×C32—22no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—42no—
101C23×C32—42no—
102C23×C32—42no—
103C23×C32C22⋊C411yescharacteristic
104C23×C32C22⋊C411yescharacteristic
105C23×C32D812yes—
106C23×C32SD1612yes—
107C23×C32C2×D411yescharacteristic
108C32×D4—42no—
109C32×D4—44no—
110C32×D4—42no—
111C32×D4—42no—
112C32×D4—42no—
113C2×C32×C4—22no—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—22no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—41no—
120C2×C32×C4—42no—
121C2×C32×C4C22⋊C411yescharacteristic
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C3×Dic3—42no—
126C2×C3×Dic3—42no—
127C2×C3×Dic3—42no—
128C3×C3⋊C8—42no—
129C2×#121C3×D311yescharacteristic
130C2×C22⋊C8—31no—
131#380—31no—
132#327—34no—
133C24×C3—22no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3—21no—
137C24×C3#6711yescharacteristic
138C24×C3C3×D411yescharacteristic
139C2×C3×D4—24no—
140C2×C3×D4—24no—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—21no—
147C2×C3×D4—21no—
148C2×C3×D4—22no—
149C2×C3×D4—44no—
150C2×C3×D4—42no—
151C2×C3×D4—42no—
152C2×C3×D4—44no—
153C2×C3×D4—44no—
154C2×C3×D4—42no—
155C2×C3×D4—42no—
156C2×C3×D4—42no—
157C2×C3×D4—42no—
158C2×C3×D4C2×Dic312yes—
159C2×C3×D4C2×C3×C412yes—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—42no—
170C22×C3×C4—42no—
171C22×C3×C4—44no—
172C22×C3×C4—62no—
173C22×C3×C4C2×Dic311yescharacteristic
174C22×C3×C4C2×Dic311yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4C2×C3×C411yescharacteristic
179C22×C3×C4C2×C3×C411yescharacteristic
180C22×C3×C4C3×D411yescharacteristic
181C22×C3×C4C3×D411yescharacteristic
182C22×C3×C4C3×D411yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C23×C311yescharacteristic
185C22×Dic3—22no—
186C2×C3×C8—62no—
187C2×C3×C8—122no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—122no—
193C3×C4⋊C4C2×Dic312yes—
194C3×C4⋊C4C2×C3×C412yes—
195C3×C22⋊C4—24no—
196C3×C22⋊C4—24no—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—22no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C22⋊C4—122no—
202#217—42no—
203C4⋊Dic3—42no—
204C2×C3⋊C8—22no—
205C2×C3⋊C8—42no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—42no—
213C22×C32—42no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—42no—
217C22×C32—84no—
218C22×C32#10212yes—
219C22×C32#10212yes—
220C22×C32C2×C22⋊C411yescharacteristic
221C22×C32C2×D811yescharacteristic
222C22×C32C2×SD1611yescharacteristic
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C32×C4—42no—
227C32×C4#9912yes—
228C3×Dic3—82no—
229C22×D4—21no—
230C22×D4C3×Dic311yescharacteristic, complemented
231C23×C4C2×C3×D311yescharacteristic
232C22×C8—61no—
233#121—21no—
234#121—21no—
235#121C3×Dic312yescomplemented
236#121C2×C3×D312yes—
237C2×C4⋊C4—61no—
238C2×C4⋊C4C3×Dic311yescharacteristic, complemented
239C2×C22⋊C4—21no—
240C2×C22⋊C4—61no—
241C22⋊C8—32no—
242C22⋊C8—61no—
243#95—32no—
244C23×C3—24no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—22no—
248C23×C3—22no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—41no—
253C23×C3—41no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—42no—
257C23×C3—42no—
258C23×C3—44no—
259C23×C3—42no—
260C23×C3—42no—
261C23×C3—44no—
262C23×C3—44no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3#21312yes—
268C23×C3#21412yes—
269C23×C3#21711yescharacteristic
270C23×C3#21711yescharacteristic
271C23×C3C3×C22⋊C411yescharacteristic
272C23×C3C3×C22⋊C411yescharacteristic
273C23×C3C3×D812yes—
274C23×C3C3×SD1612yes—
275C23×C3C2×#6711yescharacteristic
276C23×C3C2×C3×D411yescharacteristic
277C3×D4—42no—
278C3×D4—42no—
279C3×D4—44no—
280C3×D4—44no—
281C3×D4—44no—
282C3×D4—44no—
283C3×D4—48no—
284C3×D4—44no—
285C3×D4—44no—
286C3×D4—42no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—42no—
292C2×C3×C4—24no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—44no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—122no—
321C2×C3×C4—122no—
322C2×C3×C4—122no—
323C2×C3×C4#21711yescharacteristic
324C2×C3×C4#21711yescharacteristic
325C2×C3×C4C3×C22⋊C411yescharacteristic
326C2×C3×C4C3×C22⋊C411yescharacteristic
327C2×C3×C4C22×Dic311yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C22×C3×C411yescharacteristic
330C2×C3×C4C2×C3×D411yescharacteristic
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3—42no—
334C3×C8—122no—
335C3⋊C8—42no—
336C2×C32—22no—
337C2×C32—21no—
338C2×C32—22no—
339C2×C32—21no—
340C2×C32—82no—
341C2×C32C2×#9911yescharacteristic
342C2×C32C2×#10211yescharacteristic
343C2×C32#42111yescharacteristic
344C24—21no—
345C24C3×#6711yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4C2×C3×Dic312yes—
353C22×C4—21no—
354C22×C4—42no—
355C22×C4—62no—
356C22×C4C2×C3×Dic311yescharacteristic
357C22×C4C2×C3×Dic311yescharacteristic
358C22×C4C3×#6711yescharacteristic
359C22×C4C3×#6711yescharacteristic
360C22×C4C3×#6711yescharacteristic
361C22×C4C22×C3×D311yescharacteristic
362C2×C8—62no—
363C2×C8—122no—
364C4⋊C4—21no—
365C4⋊C4—122no—
366C4⋊C4C2×C3×Dic312yes—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—122no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—22no—
388C22×C3—22no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—44no—
400C22×C3—44no—
401C22×C3—44no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—88no—
409C22×C3—84no—
410C22×C3—84no—
411C22×C3#83212yes—
412C22×C3#83212yes—
413C22×C3C3×#10212yes—
414C22×C3C3×#10212yes—
415C22×C3C2×#21311yescharacteristic
416C22×C3C2×#21411yescharacteristic
417C22×C3C2×#21711yescharacteristic
418C22×C3C2×C3×C22⋊C411yescharacteristic
419C22×C3C2×C3×D811yescharacteristic
420C22×C3C2×C3×SD1611yescharacteristic
421C3×C4—22no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—44no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—242no—
435C3×C4#83412yes—
436C3×C4C3×#9912yes—
437Dic3—82no—
438C32#151911yescharacteristic, complemented, Sylow
439C23—22no—
440C23—41no—
441C23—41no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23C3×#21312yes—
446C23C3×#21412yes—
447C23C3×#21711yescharacteristic
448C23C3×#21711yescharacteristic
449C23C2×C3×#6711yescharacteristic
450D4—42no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—42no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4—122no—
466C2×C4C3×#21711yescharacteristic
467C2×C4C3×#21711yescharacteristic
468C2×C4C22×C3×Dic311yescharacteristic
469C2×C4C2×C3×#6711yescharacteristic
470C8—122no—
471C2×C3—24no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—22no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—42no—
486C2×C3—84no—
487C2×C3—82no—
488C2×C3—82no—
489C2×C3C2×#83211yescharacteristic
490C2×C3C2×#83411yescharacteristic
491C2×C3#523611yescharacteristic
492C2×C3C2×C3×#9911yescharacteristic
493C2×C3C2×C3×#10211yescharacteristic
494C2×C3C3×#42111yescharacteristic
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—84no—
507C22C3×#83212yes—
508C22C3×#83212yes—
509C22C2×C3×#21311yescharacteristic
510C22C2×C3×#21411yescharacteristic
511C22C2×C3×#21711yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—42no—
516C4—242no—
517C4C3×#83412yes—
518C3—21no—
519C3#7167511yescharacteristic, direct product factor
520C3C3×#151911yescharacteristic, complemented
521C2—21no—
522C2—22no—
523C2—21no—
524C2—22no—
525C2—82no—
526C2C2×C3×#83211yescharacteristic
527C2C2×C3×#83411yescharacteristic
528C2C3×#523611yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
Fitting, prime radicalC2×C32×#121C2
socleC22×C32C2×C22⋊C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#121D3
hypocenterC3C3×#1519
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C2×C3×#830C2semidirect
4. C3×#4537C2semidirect
6. #71675C3direct (N × H)
8. C22×C32×D4C4semidirect
12. C32×#121C4semidirect
14. C2×C32×C4⋊C4C4semidirect
19. C3×C3⋊#95C22semidirect
21. C3×#830C22semidirect
27. #5212C2×C3semidirect
28. C2×#830C2×C3semidirect
30. #4537C2×C3semidirect
62. C22×C3×D4Dic3semidirect
63. C22×C3×D4C3×C4semidirect
76. C3×#121Dic3semidirect
77. C3×#121C3×C4semidirect
82. C2×C3×C4⋊C4Dic3semidirect
83. C2×C3×C4⋊C4C3×C4semidirect
94. C3⋊#95C22×C3semidirect
96. #830C22×C3semidirect
230. C22×D4C3×Dic3semidirect
235. #121C3×Dic3semidirect
238. C2×C4⋊C4C3×Dic3semidirect
438. C32#1519semidirect
519. C3#71675direct (N × H)
520. C3C3×#1519semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C3×#52122
C2×C3×#8302
C3×#45372
C3×#15193
#716753