Finite Group Databasebeta

← C3×#67637 #11772552

Subgroups — C3×#67637 #11772552

Order 1152.

611 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#386C211yesmaximal, characteristic
2C2×C3×#834C211yesmaximal, characteristic
3C2×C3×#833C211yesmaximal, characteristic
4C3×#1390—31nomaximal
5#67637C311yesmaximal, characteristic, direct product factor
6C22×C32×D4C2211yescharacteristic
7C23×C32×C4C411yescharacteristic, complemented
8C2×C32×C22⋊C4—21no—
9C2×C32×C22⋊C4C411yescharacteristic, complemented
10C2×C3×#217—21no—
11C2×C3×#208—21no—
12C32×#95—21no—
13C3×#834—21no—
14C3×#834C412yescomplemented
15C3×#833—21no—
16C3×#833C412yescomplemented
17C2×C3×#100—31no—
18C2×C3×#99—31no—
19C3×#386—21no—
20C3×#386D311yescharacteristic
21C3×#386C2×C311yescharacteristic
22C2×#834C2×C311yescharacteristic
23C2×#833C2×C311yescharacteristic
24C24×C32C2×C411yescharacteristic
25C24×C32D411yescharacteristic
26C2×C32×D4—41no—
27C2×C32×D4—41no—
28C2×C32×D4C2×C411yescharacteristic
29C2×C32×D4C2×C411yescharacteristic
30C2×C32×D4D411yescharacteristic
31C2×C32×D4Q811yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4—21no—
34C22×C32×C4—42no—
35C22×C32×C4—41no—
36C22×C32×C4D411yescharacteristic
37C22×C3×Dic3—41no—
38C32×C22⋊C4—42no—
39C32×C22⋊C4—41no—
40C3×#217—22no—
41C3×#217—41no—
42C3×#208—22no—
43C3×#208—41no—
44C2×C3×C3⋊C8—41no—
45#1390—31noSylow
46C22×C3×D4—21no—
47C22×C3×D4C2×D311yescharacteristic
48C22×C3×D4C22×C311yescharacteristic
49C23×C3×C4—21no—
50C23×C3×C4Dic311yescharacteristic, complemented
51C23×C3×C4C3×C411yescharacteristic, complemented
52C2×C3×M16—61no—
53C2×C3×C22⋊C4—22no—
54C2×C3×C22⋊C4—21no—
55C2×C3×C22⋊C4—21no—
56C2×C3×C22⋊C4—21no—
57C2×C3×C22⋊C4—61no—
58C2×C3×C22⋊C4Dic311yescharacteristic, complemented
59C2×C3×C22⋊C4C3×C411yescharacteristic, complemented
60C2×#217—21no—
61C2×#208—21no—
62C3×#100—32no—
63C3×#100—61no—
64C3×#99—32no—
65C3×#99—61no—
66C3×#95—22no—
67C3×#95—21no—
68C3×#95—21no—
69#834—21no—
70#834C3×C412yescomplemented
71#833—21no—
72#833C3×C412yescomplemented
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32—21no—
77C23×C32—41no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32—41no—
81C23×C32C4211yescharacteristic
82C23×C32C22⋊C411yescharacteristic
83C23×C32C22⋊C411yescharacteristic
84C23×C32C4⋊C411yescharacteristic
85C23×C32C4⋊C411yescharacteristic
86C32×D4—41no—
87C32×D4—41no—
88C32×D4—41no—
89C32×D4—41no—
90C2×C32×C4—22no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4—42no—
95C2×C32×C4—41no—
96C2×C32×C4—42no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C4⋊C411yescharacteristic
102C2×C3×Dic3—42no—
103C2×C3×Dic3—81no—
104C2×C3×Dic3—81no—
105C3×C3⋊C8—42no—
106C2×#100—31no—
107C2×#99—31no—
108#386C3×D311yescharacteristic
109C24×C3—21no—
110C24×C3—21no—
111C24×C3C2×Dic311yescharacteristic
112C24×C3#6711yescharacteristic
113C24×C3C2×C3×C411yescharacteristic
114C24×C3C3×D411yescharacteristic
115C2×C3×D4—21no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—21no—
119C2×C3×D4—41no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—41no—
123C2×C3×D4—42no—
124C2×C3×D4—42no—
125C2×C3×D4Dic611yescharacteristic
126C2×C3×D4C4×D311yescharacteristic
127C2×C3×D4C4×D311yescharacteristic
128C2×C3×D4D1211yescharacteristic
129C2×C3×D4C2×C3×C411yescharacteristic
130C2×C3×D4C2×C3×C411yescharacteristic
131C2×C3×D4C3×D411yescharacteristic
132C2×C3×D4C3×Q811yescharacteristic
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—44no—
141C22×C3×C4—42no—
142C22×C3×C4—42no—
143C22×C3×C4—42no—
144C22×C3×C4—41no—
145C22×C3×C4—41no—
146C22×C3×C4—121no—
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×Dic3—41no—
150C3×M16—62no—
151C3×M16—121no—
152C2×C3×C8—121no—
153C3×C22⋊C4—42no—
154C3×C22⋊C4—42no—
155C3×C22⋊C4—44no—
156C3×C22⋊C4—42no—
157C3×C22⋊C4—41no—
158C3×C22⋊C4—41no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—121no—
161#217—22no—
162#217—41no—
163#208—22no—
164#208—41no—
165C2×C3⋊C8—41no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32—42no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32—41no—
180C22×C32—41no—
181C22×C32—81no—
182C22×C32#9511yescharacteristic
183C22×C32#9911yescharacteristic
184C22×C32#9911yescharacteristic
185C32×C4—21no—
186C32×C4—21no—
187C32×C4—42no—
188C32×C4—81no—
189C3×Dic3—82no—
190C22×D4C2×C3×D311yescharacteristic
191C23×C4C3×Dic311yescharacteristic, complemented
192C2×M16—61no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—61no—
195C2×C22⋊C4C3×Dic311yescharacteristic, complemented
196#100—32no—
197#100—61no—
198#99—32no—
199#99—61no—
200#95—21no—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—21no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—42no—
223C23×C3—42no—
224C23×C3—41no—
225C23×C3—41no—
226C23×C3—41no—
227C23×C3—41no—
228C23×C3—42no—
229C23×C3—42no—
230C23×C3C4×Dic311yescharacteristic
231C23×C3Dic3⋊C411yescharacteristic
232C23×C3C4⋊Dic311yescharacteristic
233C23×C3(C2×D3)⋊C411yescharacteristic
234C23×C3#21711yescharacteristic
235C23×C3C3×C4211yescharacteristic
236C23×C3C3×C22⋊C411yescharacteristic
237C23×C3C3×C22⋊C411yescharacteristic
238C23×C3C3×C4⋊C411yescharacteristic
239C23×C3C3×C4⋊C411yescharacteristic
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—42no—
249C3×D4—42no—
250C3×D4—42no—
251C3×D4—42no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—24no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—42no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—42no—
267C2×C3×C4—44no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—44no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—122no—
285C2×C3×C4—241no—
286C2×C3×C4—241no—
287C2×C3×C4Dic3⋊C411yescharacteristic
288C2×C3×C4(C2×D3)⋊C411yescharacteristic
289C2×C3×C4C3×C22⋊C411yescharacteristic
290C2×C3×C4C3×C4⋊C411yescharacteristic
291C2×Dic3—42no—
292C2×Dic3—81no—
293C2×Dic3—81no—
294C3×C8—122no—
295C3⋊C8—42no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—41no—
299C2×C32—41no—
300C2×C32—41no—
301C2×C32—41no—
302C2×C32#34211yescharacteristic
303C2×C32AΣL(1,𝔽16)11yescharacteristic
304C2×C32#35211yescharacteristic
305C24C2×C3×Dic311yescharacteristic
306C24C3×#6711yescharacteristic
307C2×D4—41no—
308C2×D4—41no—
309C2×D4C3×Dic611yescharacteristic
310C2×D4C3×C4×D311yescharacteristic
311C2×D4C3×C4×D311yescharacteristic
312C2×D4C3×D1211yescharacteristic
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—121no—
318C22×C4C3×#6711yescharacteristic
319M16—62no—
320M16—121no—
321C2×C8—121no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—62no—
325C22⋊C4—121no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—42no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—44no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—81no—
373C22×C3—81no—
374C22×C3—81no—
375C22×C3—81no—
376C22×C3—82no—
377C22×C3C3⋊#9511yescharacteristic
378C22×C3#83411yescharacteristic
379C22×C3#83411yescharacteristic
380C22×C3C3×#9511yescharacteristic
381C22×C3C3×#9911yescharacteristic
382C22×C3C3×#9911yescharacteristic
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—44no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—82no—
393C3×C4—81no—
394C3×C4—81no—
395C3×C4—242no—
396Dic3—82no—
397C32#139011yescharacteristic, complemented, Sylow
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23C3×C4×Dic311yescharacteristic
407C23C3×Dic3⋊C411yescharacteristic
408C23C3×C4⋊Dic311yescharacteristic
409C23C3×(C2×D3)⋊C411yescharacteristic
410C23C3×#21711yescharacteristic
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—122no—
426C2×C4—241no—
427C2×C4—241no—
428C2×C4C3×Dic3⋊C411yescharacteristic
429C2×C4C3×(C2×D3)⋊C411yescharacteristic
430C8—122no—
431C2×C3—22no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—42no—
441C2×C3—42no—
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—81no—
451C2×C3—81no—
452C2×C3#452611yescharacteristic
453C2×C3#453611yescharacteristic
454C2×C3#453911yescharacteristic
455C2×C3C3×#34211yescharacteristic
456C2×C3C3×AΣL(1,𝔽16)11yescharacteristic
457C2×C3C3×#35211yescharacteristic
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22C3×C3⋊#9511yescharacteristic
475C22C3×#83411yescharacteristic
476C22C3×#83411yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—81no—
481C4—242no—
482C3—21no—
483C3#6763711yescharacteristic, direct product factor
484C3C3×#139011yescharacteristic, complemented
485C2—21no—
486C2—21no—
487C2—41no—
488C2—41no—
489C2—41no—
490C2—41no—
491C2C3×#452611yescharacteristic
492C2C3×#453611yescharacteristic
493C2C3×#453911yescharacteristic
subgroupG/H
centerC22×C3#834
commutatorC23×C3C3×C42
FrattiniC22×D4C2×C3×D3
FittingC32×#386C2
socleC22×C32#99
prime radicalC22×C32×D4C22
cosocleC22×C3×D4C22×C3
hypercenterC3×#386D3
hypocenterC3C3×#1390
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×D4 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
5. #67637C3direct (N × H)
7. C23×C32×C4C4semidirect
9. C2×C32×C22⋊C4C4semidirect
14. C3×#834C4semidirect
16. C3×#833C4semidirect
50. C23×C3×C4Dic3semidirect
51. C23×C3×C4C3×C4semidirect
58. C2×C3×C22⋊C4Dic3semidirect
59. C2×C3×C22⋊C4C3×C4semidirect
70. #834C3×C4semidirect
72. #833C3×C4semidirect
191. C23×C4C3×Dic3semidirect
195. C2×C22⋊C4C3×Dic3semidirect
397. C32#1390semidirect
483. C3#67637direct (N × H)
484. C3C3×#1390semidirect

Maximal subgroups

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

subgroupindex
C32×#3862
C2×C3×#8342
C2×C3×#8332
C3×#13903
#676373