Finite Group Databasebeta

← C3×#71690 #11775599

Subgroups — C3×#71690 #11775599

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#4538C214yesmaximal, complemented
5C3×#1520—31nomaximal
6#71690C311yesmaximal, characteristic, direct product factor
7C22×C32×Q8C411yescharacteristic, complemented
8C23×C32×C4C2211yescharacteristic
9C32×C22⋊Q8—21no—
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8C412yescomplemented
12C32×C22⋊Q8C2212yes—
13C2×C32×C4⋊C4—21no—
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⋊#95C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C2×C3×C22⋊Q8—21no—
23C2×C3×C22⋊Q8D311yescharacteristic
24C2×C3×C22⋊Q8C2×C311yescharacteristic
25C2×C3×C22⋊C8—31no—
26C3×#380—31no—
27#5212C2×C311yescharacteristic
28C2×#830C2×C311yescharacteristic
29C3×#328—34no—
30#4538C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C2×C32×Q8—21no—
33C2×C32×Q8—42no—
34C2×C32×Q8C2×C412yes—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4—42no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—22no—
45C32×C4⋊C4—22no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—22no—
48C32×C4⋊C4C2×C412yes—
49C32×C22⋊C4—22no—
50C32×C22⋊C4—22no—
51C3×#217—42no—
52C3×C4⋊Dic3—42no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—42no—
55#1520—31noSylow
56C22×C3×Q8—21no—
57C22×C3×Q8Dic311yescharacteristic, complemented
58C22×C3×Q8C3×C411yescharacteristic, complemented
59C23×C3×C4—21no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C22×C311yescharacteristic
62C22×C3×C8—61no—
63C3×C22⋊Q8—22no—
64C3×C22⋊Q8—22no—
65C3×C22⋊Q8—21no—
66C3×C22⋊Q8—21no—
67C3×C22⋊Q8—21no—
68C3×C22⋊Q8—21no—
69C3×C22⋊Q8—22no—
70C3×C22⋊Q8—22no—
71C3×C22⋊Q8Dic312yescomplemented
72C3×C22⋊Q8C3×C412yescomplemented
73C3×C22⋊Q8C2×D312yes—
74C3×C22⋊Q8C22×C312yes—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—21no—
79C2×C3×C4⋊C4—61no—
80C2×C3×C4⋊C4Dic311yescharacteristic, complemented
81C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—21no—
84C2×C3×C22⋊C4—21no—
85C2×C3×C22⋊C4—61no—
86C2×#217—21no—
87C2×C4⋊Dic3—21no—
88C22×C3⋊C8—21no—
89C3×C22⋊C8—32no—
90C3×C22⋊C8—61no—
91C3×#95—32no—
92C3⋊#95C22×C312yes—
93#830—21no—
94#830C22×C312yes—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32C22⋊C411yescharacteristic
98C23×C32C22⋊C411yescharacteristic
99C23×C32SD1612yes—
100C23×C32Q1612yes—
101C23×C32C2×D411yescharacteristic
102C32×Q8—42no—
103C32×Q8—42no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—42no—
113C2×C32×C4—42no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×C3⋊C8—42no—
122C2×C22⋊Q8C3×D311yescharacteristic
123C2×C22⋊C8—31no—
124#380—31no—
125#328—34no—
126C24×C3—21no—
127C24×C3#6711yescharacteristic
128C24×C3C3×D411yescharacteristic
129C2×C3×Q8—22no—
130C2×C3×Q8—21no—
131C2×C3×Q8—21no—
132C2×C3×Q8—22no—
133C2×C3×Q8—42no—
134C2×C3×Q8—42no—
135C2×C3×Q8—44no—
136C2×C3×Q8C2×Dic312yes—
137C2×C3×Q8C2×C3×C412yes—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—42no—
151C22×C3×C4—42no—
152C22×C3×C4—44no—
153C22×C3×C4—62no—
154C22×C3×C4C2×Dic311yescharacteristic
155C22×C3×C4C2×Dic311yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4C2×C3×C411yescharacteristic
160C22×C3×C4C2×C3×C411yescharacteristic
161C22×C3×C4C3×D411yescharacteristic
162C22×C3×C4C3×D411yescharacteristic
163C22×C3×C4C3×D411yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C311yescharacteristic
166C22×Dic3—22no—
167C2×C3×C8—62no—
168C2×C3×C8—122no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—122no—
180C3×C4⋊C4C2×Dic312yes—
181C3×C4⋊C4C2×C3×C412yes—
182C3×C22⋊C4—24no—
183C3×C22⋊C4—24no—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—122no—
189#217—42no—
190C4⋊Dic3—42no—
191C2×C3⋊C8—22no—
192C2×C3⋊C8—42no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—21no—
199C22×C32—42no—
200C22×C32—42no—
201C22×C32#10312yes—
202C22×C32#10312yes—
203C22×C32C2×C22⋊C411yescharacteristic
204C22×C32C2×SD1611yescharacteristic
205C22×C32C2×Q1611yescharacteristic
206C32×C4—21no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4—42no—
210C32×C4—42no—
211C32×C4#9912yes—
212C3×Dic3—82no—
213C22×Q8C3×Dic311yescharacteristic, complemented
214C23×C4C2×C3×D311yescharacteristic
215C22×C8—61no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8C3×Dic312yescomplemented
219C22⋊Q8C2×C3×D312yes—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—61no—
222C2×C4⋊C4C3×Dic311yescharacteristic, complemented
223C2×C22⋊C4—21no—
224C2×C22⋊C4—61no—
225C22⋊C8—32no—
226C22⋊C8—61no—
227#95—32no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3#21512yes—
240C23×C3#21612yes—
241C23×C3#21711yescharacteristic
242C23×C3#21711yescharacteristic
243C23×C3C3×C22⋊C411yescharacteristic
244C23×C3C3×C22⋊C411yescharacteristic
245C23×C3C3×SD1612yes—
246C23×C3C3×Q1612yes—
247C23×C3C2×#6711yescharacteristic
248C23×C3C2×C3×D411yescharacteristic
249C3×Q8—42no—
250C3×Q8—42no—
251C3×Q8—44no—
252C3×Q8—44no—
253C3×Q8—42no—
254C3×Q8—42no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—44no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—44no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4#21711yescharacteristic
293C2×C3×C4#21711yescharacteristic
294C2×C3×C4C3×C22⋊C411yescharacteristic
295C2×C3×C4C3×C22⋊C411yescharacteristic
296C2×C3×C4C22×Dic311yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C22×C3×C411yescharacteristic
299C2×C3×C4C2×C3×D411yescharacteristic
300C2×Dic3—42no—
301C2×Dic3—42no—
302C2×Dic3—42no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—22no—
306C2×C32—21no—
307C2×C32—22no—
308C2×C32—21no—
309C2×C32C2×#9911yescharacteristic
310C2×C32C2×#10311yescharacteristic
311C2×C32#42111yescharacteristic
312C24C3×#6711yescharacteristic
313C2×Q8—21no—
314C2×Q8—42no—
315C2×Q8C2×C3×Dic312yes—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—62no—
320C22×C4C2×C3×Dic311yescharacteristic
321C22×C4C2×C3×Dic311yescharacteristic
322C22×C4C3×#6711yescharacteristic
323C22×C4C3×#6711yescharacteristic
324C22×C4C3×#6711yescharacteristic
325C22×C4C22×C3×D311yescharacteristic
326C2×C8—62no—
327C2×C8—122no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—22no—
331C4⋊C4—122no—
332C4⋊C4C2×C3×Dic312yes—
333C22⋊C4—22no—
334C22⋊C4—22no—
335C22⋊C4—122no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3#83512yes—
366C22×C3#83512yes—
367C22×C3C3×#10312yes—
368C22×C3C3×#10312yes—
369C22×C3C2×#21511yescharacteristic
370C22×C3C2×#21611yescharacteristic
371C22×C3C2×#21711yescharacteristic
372C22×C3C2×C3×C22⋊C411yescharacteristic
373C22×C3C2×C3×SD1611yescharacteristic
374C22×C3C2×C3×Q1611yescharacteristic
375C3×C4—22no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—22no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—44no—
386C3×C4—44no—
387C3×C4—42no—
388C3×C4—42no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—242no—
392C3×C4#83412yes—
393C3×C4C3×#9912yes—
394Dic3—82no—
395C32#152011yescharacteristic, complemented, Sylow
396C23—41no—
397C23—41no—
398C23C3×#21512yes—
399C23C3×#21612yes—
400C23C3×#21711yescharacteristic
401C23C3×#21711yescharacteristic
402C23C2×C3×#6711yescharacteristic
403Q8—42no—
404Q8—42no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—122no—
418C2×C4C3×#21711yescharacteristic
419C2×C4C3×#21711yescharacteristic
420C2×C4C22×C3×Dic311yescharacteristic
421C2×C4C2×C3×#6711yescharacteristic
422C8—122no—
423C2×C3—24no—
424C2×C3—21no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—22no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—42no—
438C2×C3C2×#83411yescharacteristic
439C2×C3C2×#83511yescharacteristic
440C2×C3#523611yescharacteristic
441C2×C3C2×C3×#9911yescharacteristic
442C2×C3C2×C3×#10311yescharacteristic
443C2×C3C3×#42111yescharacteristic
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—42no—
451C22—42no—
452C22C3×#83512yes—
453C22C3×#83512yes—
454C22C2×C3×#21511yescharacteristic
455C22C2×C3×#21611yescharacteristic
456C22C2×C3×#21711yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—42no—
461C4—42no—
462C4—242no—
463C4C3×#83412yes—
464C3—21no—
465C3#7169011yescharacteristic, direct product factor
466C3C3×#152011yescharacteristic, complemented
467C2—21no—
468C2—21no—
469C2—22no—
470C2—22no—
471C2C2×C3×#83411yescharacteristic
472C2C2×C3×#83511yescharacteristic
473C2C3×#523611yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#1520
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. C3×#4538C2semidirect
6. #71690C3direct (N × H)
7. C22×C32×Q8C4semidirect
11. C32×C22⋊Q8C4semidirect
14. C2×C32×C4⋊C4C4semidirect
30. #4538C2×C3semidirect
57. C22×C3×Q8Dic3semidirect
58. C22×C3×Q8C3×C4semidirect
71. C3×C22⋊Q8Dic3semidirect
72. C3×C22⋊Q8C3×C4semidirect
80. C2×C3×C4⋊C4Dic3semidirect
81. C2×C3×C4⋊C4C3×C4semidirect
213. C22×Q8C3×Dic3semidirect
218. C22⋊Q8C3×Dic3semidirect
222. C2×C4⋊C4C3×Dic3semidirect
395. C32#1520semidirect
465. C3#71690direct (N × H)
466. C3C3×#1520semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C3×#52122
C2×C3×#8302
C3×#45382
C3×#15203
#716903