Finite Group Databasebeta

← C3×#71590 #11785842

Subgroups — C3×#71590 #11785842

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#117C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#4532C214yesmaximal, complemented
5C3×#1826—31nomaximal
6#71590C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C32×#117—21no—
9C32×#117—21no—
10C32×#117C412yescomplemented
11C32×#117C2212yes—
12C2×C32×C4⋊C4C411yescharacteristic, complemented
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C32×C22⋊C4—21no—
15C2×C32×C42—21no—
16C2×C3×#217—21no—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×#208C2212yes—
19C3×C3⋊#95—21no—
20C3×#830—21no—
21C3×#830—21no—
22C2×C3×#117—21no—
23C2×C3×#117D311yescharacteristic
24C2×C3×#117C2×C311yescharacteristic
25C3×#407—31no—
26C3×C4×C22⋊C4—31no—
27C4×#217C2×C311yescharacteristic
28#5207C2×C311yescharacteristic
29C3×#339—34no—
30#4532C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—24no—
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3×Dic3—22no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45C32×C4⋊C4C2×C412yes—
46C32×C22⋊C4—22no—
47C32×C22⋊C4—22no—
48C32×C42—22no—
49C32×C42—22no—
50C3×#217—24no—
51C3×C4×Dic3—24no—
52C3×#208—24no—
53C2×C3×C3⋊C8—22no—
54#1826—31noSylow
55C23×C3×C4—21no—
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C22×C311yescharacteristic
58C2×C3×M16—32no—
59C3×#117—22no—
60C3×#117—22no—
61C3×#117—21no—
62C3×#117—21no—
63C3×#117—21no—
64C3×#117—21no—
65C3×#117—22no—
66C3×#117—22no—
67C3×#117Dic312yescomplemented
68C3×#117C3×C412yescomplemented
69C3×#117C2×D312yes—
70C3×#117C22×C312yes—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4Dic311yescharacteristic, complemented
74C2×C3×C4⋊C4Dic311yescharacteristic, complemented
75C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
76C2×C3×C4⋊C4C3×C411yescharacteristic, complemented
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—61no—
81C2×C3×C42—22no—
82C2×C3×C42—21no—
83C2×C3×C42—21no—
84C2×C3×C42—32no—
85C2×#217—21no—
86C2×C4×Dic3C22×C312yes—
87C2×#208C22×C312yes—
88C3×C22⋊C8—61no—
89C3×C22⋊C8—61no—
90C3×#95—61no—
91C3⋊#95—21no—
92#830—21no—
93#830—21no—
94C23×C32—22no—
95C23×C32—22no—
96C23×C32—41no—
97C23×C32C22⋊C411yescharacteristic
98C23×C32C22⋊C411yescharacteristic
99C23×C32C2×D411yescharacteristic
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4#4114yes—
114C2×C3×Dic3—24no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C3×C3⋊C8—42no—
118C2×#117C3×D311yescharacteristic
119#407—31no—
120C4×C22⋊C4—31no—
121#339—34no—
122C24×C3—21no—
123C24×C3#6711yescharacteristic
124C24×C3C3×D411yescharacteristic
125C22×C3×C4—28no—
126C22×C3×C4—24no—
127C22×C3×C4—24no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—62no—
141C22×C3×C4C2×Dic311yescharacteristic
142C22×C3×C4C2×Dic311yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C2×C3×C411yescharacteristic
147C22×C3×C4C2×C3×C411yescharacteristic
148C22×C3×C4C3×D411yescharacteristic
149C22×C3×C4C3×D411yescharacteristic
150C22×C3×C4C3×D411yescharacteristic
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C23×C311yescharacteristic
153C22×Dic3—22no—
154C3×M16—64no—
155C2×C3×C8—62no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—21no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4C2×Dic312yes—
165C3×C4⋊C4C2×Dic312yes—
166C3×C4⋊C4C2×C3×C412yes—
167C3×C4⋊C4C2×C3×C412yes—
168C3×C22⋊C4—24no—
169C3×C22⋊C4—24no—
170C3×C22⋊C4—22no—
171C3×C22⋊C4—22no—
172C3×C22⋊C4—22no—
173C3×C22⋊C4—22no—
174C3×C22⋊C4—64no—
175C3×C42—24no—
176C3×C42—24no—
177C3×C42—22no—
178C3×C42—22no—
179C3×C42—22no—
180C3×C42—22no—
181C3×C42—64no—
182#217—24no—
183C4×Dic3—24no—
184#208—24no—
185C2×C3⋊C8—22no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32—44no—
194C22×C32#10412yes—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32#12312yes—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—42no—
200C32×C4—42no—
201C32×C4#11712yes—
202C32×C4#12312yes—
203C3×Dic3—44no—
204C23×C4C2×C3×D311yescharacteristic
205C2×M16—32no—
206#117—21no—
207#117—21no—
208#117C3×Dic312yescomplemented
209#117C2×C3×D312yes—
210C2×C4⋊C4C3×Dic311yescharacteristic, complemented
211C2×C4⋊C4C3×Dic311yescharacteristic, complemented
212C2×C22⋊C4—21no—
213C2×C22⋊C4—61no—
214C2×C42—21no—
215C2×C42—32no—
216C22⋊C8—61no—
217C22⋊C8—61no—
218#95—61no—
219C23×C3—24no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—22no—
224C23×C3—21no—
225C23×C3—21no—
226C23×C3—21no—
227C23×C3—42no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3—42no—
231C23×C3#21711yescharacteristic
232C23×C3#21711yescharacteristic
233C23×C3C3×C22⋊C411yescharacteristic
234C23×C3C3×C22⋊C411yescharacteristic
235C23×C3C2×#6711yescharacteristic
236C23×C3C2×C3×D411yescharacteristic
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—24no—
253C2×C3×C4—24no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—24no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—44no—
264C2×C3×C4—42no—
265C2×C3×C4—42no—
266C2×C3×C4—44no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—64no—
270C2×C3×C4—122no—
271C2×C3×C4—122no—
272C2×C3×C4#21711yescharacteristic
273C2×C3×C4#21711yescharacteristic
274C2×C3×C4C3×C22⋊C411yescharacteristic
275C2×C3×C4C3×C22⋊C411yescharacteristic
276C2×C3×C4#23514yes—
277C2×C3×C4C22×Dic311yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C22×C3×C411yescharacteristic
280C2×C3×C4C2×C3×D411yescharacteristic
281C2×C3×C4C3×#4114yes—
282C2×Dic3—24no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C3×C8—122no—
286C3⋊C8—42no—
287C2×C32—22no—
288C2×C32—22no—
289C2×C32—41no—
290C2×C32#38111yescharacteristic
291C2×C32C2×#10411yescharacteristic
292C2×C32#42111yescharacteristic
293C24C3×#6711yescharacteristic
294C22×C4—24no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—62no—
298C22×C4C2×C3×Dic311yescharacteristic
299C22×C4C2×C3×Dic311yescharacteristic
300C22×C4C3×#6711yescharacteristic
301C22×C4C3×#6711yescharacteristic
302C22×C4C3×#6711yescharacteristic
303C22×C4C22×C3×D311yescharacteristic
304M16—64no—
305C2×C8—62no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4C2×C3×Dic312yes—
309C4⋊C4C2×C3×Dic312yes—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—64no—
313C42—22no—
314C42—22no—
315C42—64no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—22no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—22no—
334C22×C3—21no—
335C22×C3—22no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—44no—
341C22×C3—44no—
342C22×C3—48no—
343C22×C3#83712yes—
344C22×C3C3×#10412yes—
345C22×C3#92912yes—
346C22×C3C2×#21711yescharacteristic
347C22×C3C2×C3×C22⋊C411yescharacteristic
348C22×C3C3×#12312yes—
349C3×C4—22no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—44no—
358C3×C4—44no—
359C3×C4—42no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—42no—
363C3×C4—124no—
364C3×C4#92612yes—
365C3×C4#92912yes—
366C3×C4C3×#11712yes—
367C3×C4C3×#12312yes—
368Dic3—44no—
369C32#182611yescharacteristic, complemented, Sylow
370C23—22no—
371C23—22no—
372C23—41no—
373C23C3×#21711yescharacteristic
374C23C3×#21711yescharacteristic
375C23C2×C3×#6711yescharacteristic
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—64no—
386C2×C4—122no—
387C2×C4—122no—
388C2×C4C3×#21711yescharacteristic
389C2×C4C3×#21711yescharacteristic
390C2×C4C3×#23514yes—
391C2×C4C22×C3×Dic311yescharacteristic
392C2×C4C2×C3×#6711yescharacteristic
393C8—122no—
394C2×C3—24no—
395C2×C3—22no—
396C2×C3—22no—
397C2×C3—22no—
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—42no—
403C2×C3—42no—
404C2×C3—41no—
405C2×C3—41no—
406C2×C3#521111yescharacteristic
407C2×C3C2×#83711yescharacteristic
408C2×C3#523611yescharacteristic
409C2×C3C3×#38111yescharacteristic
410C2×C3C2×C3×#10411yescharacteristic
411C2×C3C3×#42111yescharacteristic
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—44no—
420C22C3×#83712yes—
421C22C3×#92912yes—
422C22C2×C3×#21711yescharacteristic
423C4—21no—
424C4—21no—
425C4—42no—
426C4—42no—
427C4—124no—
428C4C3×#92612yes—
429C4C3×#92912yes—
430C3—21no—
431C3#7159011yescharacteristic, direct product factor
432C3C3×#182611yescharacteristic, complemented
433C2—22no—
434C2—22no—
435C2—41no—
436C2C3×#521111yescharacteristic
437C2C2×C3×#83711yescharacteristic
438C2C3×#523611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#117C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#117D3
hypocenterC3C3×#1826
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
4. C3×#4532C2semidirect
6. #71590C3direct (N × H)
10. C32×#117C4semidirect
12. C2×C32×C4⋊C4C4semidirect
13. C2×C32×C4⋊C4C4semidirect
30. #4532C2×C3semidirect
67. C3×#117Dic3semidirect
68. C3×#117C3×C4semidirect
73. C2×C3×C4⋊C4Dic3semidirect
74. C2×C3×C4⋊C4Dic3semidirect
75. C2×C3×C4⋊C4C3×C4semidirect
76. C2×C3×C4⋊C4C3×C4semidirect
208. #117C3×Dic3semidirect
210. C2×C4⋊C4C3×Dic3semidirect
211. C2×C4⋊C4C3×Dic3semidirect
369. C32#1826semidirect
431. C3#71590direct (N × H)
432. C3C3×#1826semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1172
C3×C4×#2172
C3×#52072
C3×#45322
C3×#18263
#715903